user manual fine turbo v6.2-9

N U M E R I C A L M E C H A N I C S A P P L I C A T I O N S

FINE™

Flow Integrated Environment

User Manual

contains:

FINETM GUI v6.2

Euranus v5.1

N U M E R I C A L M E C H A N I C S A P P L I C A T I O N S

FINE™

User Manual

Version 6.2-d (May 2005)

NUMECA International

5, Avenue Franklin Roosevelt

1050 Brussels

Belgium

Tel: +32 2 647.83.11

Fax: +32 2 647.93.98

Web: http://www.numeca.com

Contents

FINE™ iii

CHAPTER 1: Getting Started 1-1

1-1 Overview 1-11-2 Introduction 1-1

What is CFD? 1-1Components 1-3Multi-tasking 1-3Project Management 1-3

1-3 How To Use This Manual 1-5Outline 1-5Conventions 1-5

1-4 First Time Use 1-6Basic Installation 1-6Expert Graphics Options 1-6

1-5 How to start FINE™ Interface 1-71-6 Required Licenses 1-8

Standard FINE™ License 1-8Additional Licenses 1-8

CHAPTER 2: User Interface 2-1

2-1 Overview 2-12-2 Project Selection 2-2

Creating a New Project 2-2Opening of an Existing Project 2-3Grid Units and Project Configuration 2-4

2-3 Main Menu Bar 2-4File Menu 2-4Mesh Menu 2-8Solver Menu 2-9Modules Menu 2-10

2-4 Icon Bar 2-10File Buttons 2-10Grid Selection Bar 2-11Solver Buttons 2-12Module Buttons 2-12User Mode 2-12

2-5 Computations Button 2-122-6 Parameters Button 2-132-7 View Area 2-132-8 Mesh Information 2-152-9 Parameters Area 2-152-10 Graphics Area 2-16

Viewing Buttons 2-162-11 File Chooser 2-192-12 Profile Manager 2-19

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Contents

CHAPTER 3: Fluid Model 3-1

3-1 Overview 3-13-2 The Fluid Model in the FINE™ Interface 3-2

Properties of Fluid Used in the Project 3-2List of Fluids 3-2Add Fluid 3-3Delete Fluid from List 3-7Edit Fluid in List 3-7Showing Fluid Properties 3-8Filters 3-8Import Fluids Database 3-8Expert Parameters 3-8

3-3 Theory 3-9Transport Properties 3-9Fluid Models 3-10

CHAPTER 4: Flow Model 4-1

4-1 Overview 4-14-2 Time Configuration 4-2

The Interface for an Unsteady Computation 4-2Expert Parameters for Unsteady Computations 4-5Best Practice on Time Accurate Computations 4-6Theoretical Aspects for Unsteady Computations 4-9

4-3 Mathematical Model 4-15Euler 4-15Laminar Navier-Stokes 4-15Turbulent Navier-Stokes 4-16Expert Parameters for Turbulence Modelling 4-16Best Practice for Turbulence Modelling 4-19Theoretical Aspect of Turbulence Modelling 4-27Gravity Forces 4-41Low Speed Flow (Preconditioning) 4-42

4-4 Characteristic and Reference Values 4-47Reynolds Number Related Information 4-47Reference Values 4-47

CHAPTER 5: Rotating Machinery 5-1

5-1 Overview 5-15-2 Rotating Blocks 5-25-3 Rotor/Stator Interaction in the FINE™ Interface 5-35-4 How to Set-up a Simulation with Rotor/Stator Interfaces? 5-5

Mixing Plane Approach 5-5Frozen Rotor 5-9Domain Scaling Method 5-11Phase Lagged Method 5-13

5-5 Theoretical Background on Rotor/Stator Interfaces 5-15

Contents

FINE™ v

Introduction 5-15Default Mixing Plane Approach 5-16Full Non-matching Technique for Mixing Planes 5-19Domain Scaling Method 5-21

CHAPTER 6: Throughflow Model 6-1

6-1 Overview 6-16-2 Throughflow Blocks in the FINE™ Interface 6-2

Global Parameters 6-2Block Dependent Parameters 6-2Mesh for Throughflow Blocks 6-6Boundary Conditions for Throughflow Blocks 6-7Initial Solution for Throughflow Blocks 6-8Output for Throughflow Blocks 6-8

6-3 File Formats for Throughflow Blocks 6-9One-dimensional Throughflow Input File 6-9Two-dimensional Throughflow Input File 6-11Output File 6-11

6-4 Expert Parameters Related to Throughflow Blocks 6-12Under-relaxation Process 6-12Others. 6-12

6-5 Theoretical Background on Throughflow Method 6-13The Time Dependent Approach 6-13Basic Equations and Assumptions 6-13The Tangential Blockage Factor 6-13The Blade Force 6-14

CHAPTER 7: Optional Models 7-1

7-1 Overview 7-17-2 Fluid-Particle Interaction 7-1

Introduction 7-1Fluid-Particle Interaction in the FINE™ Interface 7-3Outputs 7-6Specific Output of the Fluid-Particle Interaction Model 7-7Expert Parameters for Fluid-Particle Interaction 7-8Theory 7-9References 7-11

7-3 Conjugate Heat Transfer 7-11Introduction 7-11Conjugate Heat Transfer in the FINE™ Interface 7-11Theory 7-13

7-4 Cooling/Bleed 7-15Introduction 7-15Cooling/Bleed Model in the FINE™ Interface 7-16Expert Parameters 7-31Theory 7-32Cooling/Bleed Data File: ’.cooling-holes’ 7-33

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Contents

7-5 Transition Model 7-37Introduction 7-37Transition Model in the FINE™ Interface 7-38Expert Parameters 7-39Theory 7-40

CHAPTER 8: Boundary Conditions 8-1

8-1 Overview 8-18-2 Boundary Conditions in the FINE™ Interface 8-1

Inlet Condition 8-4Outlet Condition 8-6Periodic Condition 8-9Solid Wall Boundary Condition 8-10External Condition (Far-field) 8-13

8-3 Expert Parameters for Boundary Conditions 8-13Imposing Velocity Angles of Relative Flow 8-13Extrapolation of Mass Flow at Inlet 8-14Outlet Mass Flow Boundary Condition 8-14Torque and Force Calculation 8-14Euler or Navier-Stokes Wall for Viscous Flow 8-15Pressure Condition at Solid Wall 8-15

8-4 Best Practice for Imposing Boundary Conditions 8-15Compressible Flows 8-15Incompressible or Low Speed Flow 8-16Special Parameters (for Turbomachinery) 8-16

8-5 Theory on Boundary Conditions 8-16Inlet Boundary Conditions 8-17Outlet Boundary Conditions 8-22Solid Wall Boundary Conditions 8-26Far-field Boundary Condition 8-29

CHAPTER 9: Numerical Model 9-1

9-1 Overview 9-19-2 Numerical Model in FINE™ 9-2

CFL Number 9-2Multigrid parameters 9-2Preconditioning Parameters 9-3

9-3 Expert Parameters for the Numerical Model 9-3Interfaced Expert Parameters 9-3Non-interfaced Expert Parameters 9-5

9-4 Theory 9-7Spatial Discretization 9-7Multigrid Strategy 9-13Full Multigrid Strategy 9-16Time Discretization: Multistage Runge-Kutta 9-17Implicit residual smoothing 9-20

Contents

FINE™ vii

CHAPTER 10:Initial Solution 10-1

10-1 Overview 10-110-2 Block Dependent Initial Solution 10-1

How to Define a Block Dependent Initial Solution 10-2Examples for the use of Block Dependent Initial Solution 10-2

10-3 Initial Solution Defined by Constant Values 10-310-4 Initial Solution from File 10-4

General Restart Procedure 10-4Restart in Unsteady Computations 10-5Expert Parameters for an Initial Solution from File 10-5

10-5 Initial Solution for Turbomachinery 10-610-6 Throughflow-oriented Initial Solution 10-7

CHAPTER 11:Output 11-1

11-1 Overview 11-111-2 Output in FINE™ 11-2

Computed Variables 11-2Surface Averaged Variables 11-7Azimuthal Averaged Variables 11-9ANSYS 11-10Global Performance Output 11-15Plot3D Formatted Output 11-17

11-3 Expert Parameters for Output Selection 11-18Azimuthal Averaged Variables 11-18Global Performance Output 11-18

11-4 Theory 11-20Computed Variables 11-20Surface Averaged Variables 11-21Azimuthal Averaged Variables 11-21Global Performance Output 11-24

CHAPTER 12:Blade to Blade Module 12-1

12-1 Overview 12-112-2 Blade-to-Blade in the FINE™ Interface 12-2

Start New or Open existing Blade-to-Blade Computation 12-2Blade-to-Blade Data 12-3Boundary Conditions 12-8Numerical Model 12-10Initial Solution Menu 12-10Output Parameters 12-10Control Variables Page 12-10Launch Blade-to-Blade Flow Analysis 12-11

12-3 Expert Parameters 12-1112-4 Theory 12-11

Mesh Generator 12-11Flow Solver 12-12

viii FINE™

Contents

12-5 File Formats used by Blade-to-Blade Module 12-13Input Files 12-13Output Files 12-15

CHAPTER 13:Design 2D Module 13-1

13-1 Overview 13-113-2 Inverse Design in the FINE™ Interface 13-2

Start New or Open Existing Design 2D Project 13-2Creation of Inverse Design Input Files 13-3Initial Solution Menu 13-5Launch or Restart Inverse Design Calculation 13-6Expert Parameters 13-6

13-3 Theory 13-713-4 File Formats used for 2D Inverse Design 13-8

Input Files 13-8Output Files 13-9

CHAPTER 14:The Task Manager 14-1

14-1 Overview 14-114-2 Getting Started 14-1

The PVM Daemons 14-1Multiple FINE™ Sessions 14-2Machine Connection from UNIX/LINUX Platforms 14-2Machine Connection from Windows Platforms 14-4Remote Copy Features on UNIX/LINUX 14-4Remote Copy Features on Windows 14-4

14-3 The Task Manager Interface 14-5Hosts Definition 14-5Tasks Definition 14-6

14-4 Parallel Computations 14-11Introduction 14-11Modules Implemented in the Parallel Version 14-12Management of Inter-block Communication 14-12How to Run a Parallel Computation 14-13Troubleshooting 14-14Limitations 14-14

14-5 Task Management Using Scripts 14-14 Launch IGG™ Using Scripts 14-15Launch AutoGrid using Scripts 14-15Launch EURANUS in Sequential using Scripts 14-16Launch EURANUS in Parallel using Scripts 14-17Launch CFView™ Using Scripts 14-21

14-6 Limitations 14-22

CHAPTER 15:Computation Steering and Monitoring 15-1

15-1 Overview 15-1

Contents

FINE™ ix

15-2 Control Variables 15-115-3 Convergence History 15-2

Steering Files Selection and Curves Export 15-3Available Quantities Selection 15-3New Quantity Parameters Definition 15-4Quantity Selection Area 15-5Definition of Global Residual 15-5The Graphics View 15-6

15-4 MonitorTurbo 15-7Introduction 15-7The Residual File Box 15-9Quantities to Display 15-9

15-5 Best Practice for Computation Monitoring 15-10Introduction 15-10Convergence History 15-11MonitorTurbo 15-11Analysis of Residuals 15-12

APPENDIX A:Governing Equations A-1

A-1 Overview A-1A-2 Reynolds-Averaged Navier-Stokes Equations A-1

General Navier-Stokes Equations A-1Time Averaging of Quantities A-2Treatment of Turbulence in the Equations A-2Formulation in Rotating Frame for the Relative Velocity A-3

A-3 Formulation in Rotating Frame for the Absolute Velocity A-3

APPENDIX B:File Formats B-1

B-1 Overview B-1B-2 Files Produced by IGG™ B-1

The Identification File: project.igg B-2The Binary File: project.cgns B-2The Geometry File: project.geom B-2The Boundary Condition File: project.bcs B-2

B-3 Files Produced by FINE™ B-2The Project File: project.iec B-2The Computation File: project_computationName.run B-3

B-4 Files Produced by the Flow Solver EURANUS B-3The cgns file: project_computationName.cgns B-3The mf file: project_computationName.mf B-4The res file: project_computationName.res B-4The log file: project_computationName.log B-5The std file: project_computationName.std B-5The wall file: project_computationName.wall B-5The aqsi file: project_computationName.aqsi B-6The Plot3D files B-6The me.cfv file: project_computationName.me.cfv B-7

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Contents

B-5 Files Used as Data Profile B-7Boundary Conditions Data B-7Fluid Properties B-9

B-6 Resource Files B-10Boundary Conditions Resource File euranus_bc.def B-10Fluids Database File euranus.flb B-10Units Systems Resource File euranus.uni B-10

APPENDIX C:List of Expert Parameters C-1

C-1 Overview C-1C-2 List of Integer Expert Parameters C-1C-3 List of Float Expert Parameters C-2

APPENDIX D: Characteristics of Water (steam) Tables D-1

D-1 Overview D-1D-2 Main Characteristics D-1

FINE™ 1-1

CHAPTER 1: Getting Started

1-1 OverviewWelcome to the FINE™ User’s Guide, a presentation of NUMECA’s Flow INtegrated Environ-ment for computations on structured meshes. This chapter presents the basic concepts of FINE™and shows how to get started with the program by describing:

•what is CFD,

•what FINE™ does and how it operates,

• how to use this guide,

• how to start the FINE™ interface.

1-2 Introduction

1-2.1 What is CFD?

All the mathematical sciences are founded on relations between physical laws and laws of numbers,so that the aim of exact science is to reduce the problems of nature to the determination of quanti-ties by operations with numbers.

James Clerk Maxwell, 1856

In the late 1970’s, the use of supercomputers to solve aerodynamic problems began to pay off. Oneearly success was the experimental NASA aircraft called HiMAT, designed to test concepts of highmanoeuvrability for the next generation of fighter planes. Wind tunnel tests of a preliminary designfor HiMAT showed that it would have unacceptable drag at speeds near the speed of sound; if builtthat way the plane would be unable to provide any useful data. The cost of redesigning it in furtherwind tunnel tests would have been around $150,000 and would have unacceptably delayed theproject. Instead, the wing was redesigned by a computer at a cost of $60,000.

Paul E. Ceruzzi, 1989

Computational Fluid Dynamics (CFD) is commonly accepted as referring to the broad topic encom-passing the numerical solution, by computational methods, of the governing equations that describe

Getting Started Introduction

1-2 FINE™

fluid flow related conservative equations (for instance involving energy or species concentration). Ithas grown from a mathematical curiosity few decades ago, to become an essential tool in almostevery branch of fluid dynamics, from aerospace propulsion to weather prediction.

Key elements of CFD are briefly described below. Please notice these informations have mostlybeen extracted from the web at http://www.crankfield.ac.uk/sme/cfd/whatiscfd.htm and http://ltp.larc.nasa.gov/aero/login.htm. The reader is invited to consult the web at www.cfd-online.comfor more insight in CFD theory.

By 1900, theoretical and mathematical developments in fluid dynamics had not achieved signifi-cant progress as quickly as experimental efforts. Although the Navier-Stokes equations describingfluid behaviour had existed for over 75 years before the Wright brothers' first flight, they were sim-ply too complex to solve in their complete form for anything but simplified problems under specificconditions. Even today, theoretical solutions to the Navier-Stokes equations are rare and only suitedto specific classes of problems.

As a developing science, CFD has received extensive attention throughout the international com-munity since the advent of the digital computer. CFD interests are mainly driven by the desire tomodel complex physical fluid phenomena, that couldn't be easily or cost effectively simulated witha physical experiment.

Computational techniques differ from analytical or theoretical solutions in the sense that they onlysolve equations at a finite number of points rather than for the entire flow field. Choosing thesepoints may become quite difficult - especially for a complex geometry and may require hundreds ofthousands or even million of points. In general, a dense grid with many points will give a solutionof great detail, but require more computer memory and time to reach a solution. Since this trade-offin computer resources and solution quality is required, the current trend is often to use a dense gridin areas where the solution may change rapidly such as in the boundary layer or near a shock wave,but use of a coarser grid with fewer computational points in areas where the solution is expected tochange more gradually.

The selection of grid nodes is the science of grid generation. It is a complex field on its own and hasmany applications outside CFD, such as in constructing solid models for stress, vibration and heattransfer analysis. There are several different techniques that are commonly used to develop compu-tational grids for CFD.

Grid nodes can be arranged either in a regular or irregular pattern. Depending on the patternselected, the method of generation is referred to as structured or unstructured. Both techniques havetheir own advantages and disadvantages.

Basically, structured methods enable the generation of regular grids, with high quality standardsand good control in the distribution of grid nodes in shear and boundary layers. However, they maysometimes be hard to generate for very complex geometries. On the contrary, unstructured methodsallow a limited control in the grid quality (and thus in the grid solution) but the grid generationprocess does usually require limited user resources, even for complex geometries.

It is thus important that the user recognizes these so that the best grid can be created for a particulargeometry. The quality of the grid is definitely important, since it strongly influences the solution -including whether or not a solution can be found at all.

FINE™/Turbo and FINE™/Design3D environments developed by NUMECA rely on structuredgrid methods, based on AutoGrid and IGG™ software tools. NUMECA offer also includes unstruc-tured capabilities, through HEXPRESS™ hexahedral grid generator and FINE™/HEXA environ-ment. More details can be provided upon request.

Introduction Getting Started

FINE™ 1-3

Usually, about 4 to 5 unknowns are computed at each grid node. This makes methods of presentingCFD results a difficult matter, mainly due to the large number of data to manage. Adequate post-processing is then required to easily and quickly outline the major characteristics of the flow. Thisis usually done through surface color techniques and particle paths/ribbons. The latter method ismostly used to depict vortices and complex flow-wall interactions. The user is invited to refer toCFView™ manual for a detailed information on NUMECA offer in that area.

1-2.2 Components

The resolution of Computational Fluid Dynamics (CFD) problems involves three main steps:

• spatial discretization of the flow domain,

• flow computation,

• visualization of the results.

To perform these steps NUMECA has developed three software systems. The first one, IGG™, isan Interactive Geometry modeller and Grid generation system for multiblock structured grids. Thesecond software system, the flow solver EURANUS, is a state of the art 3D multiblock flow solverable to simulate Euler or Navier-Stokes (laminar or turbulent) flows. The third one, CFView™, is ahighly interactive Computational Field Visualization system.

These three software systems have been integrated in a unique and user friendly Graphical UserInterface (GUI), called FINE™, allowing the achievement of complete simulations of 3D internaland external flows from the grid generation to the visualization, without any file manipulation,through the concept of project. Moreover, multi-tasking capabilities are incorporated, allowing thesimultaneous treatment of multiple projects.

1-2.3 Multi-tasking

FINE™ has the particularity of integrating the concept of multi-tasking. This means that the usercan manage a complete project in FINE™ interface; making the grid using IGG™, running thecomputation with EURANUS and visualizing the results with CFView™. Furthermore, the user hasthe possibility to start, stop and control multiple computations. Please note that the flow simulationcan be time consuming, therefore the possibility of running computations in background has beenimplemented. See chapter 13 for more detail on how to manage multiple tasks through the interfaceor in background.

1-2.4 Project Management

To manage complete flow analyses, FINE™ integrates the concept of project. A project involvesgrid generation, flow computation and visualization tasks. The results of each of these tasks arestored in different files that are automatically created, managed and modified within FINE™:

•The grid files: The grid generation process, IGG™, creates files containing the representationof the geometry and the grid related to the project. The definition of the types of boundary con-ditions is also done during this process. The four files that contain the information about themesh have the extensions .igg, .geom, .bcs and .cgns.

•The project file: The project file is created by FINE™. It has the extension .iec and containsthe input parameters needed for the flow computations.

•The result files: FINE™ creates a new subdirectory for each computation where it stores thefollowing files:

— a file with extension .run containing all computation input parameters used by the solver andby CFView™,

Getting Started Introduction

1-4 FINE™

— a .cgns file that contains the solution and is used for restarting the solver,

— a .res file used by the Monitor to visualize the residual history (see Chapter 15),

— two files used to visualize the convergence history in the Steering with extensions .steeringand .steering.binary (see Chapter 15).

— two files with extensions .mf and .wall that contain global solution parameters.

— two files with extensions .std and .log that contain information on the flow computationprocess.

— a .batch file used to launch the computation in batch (see Chapter 15).

•The CFView™ visualization files: In addition to the .run file, the flow solver creates a seriesof files, which can be read by CFView™. These files have different extensions. For example incase of turbomachinery flow problem, the solver will create a file for the azimuthal averagedresults with extension .me.cfv.

Through the interface, the user can modify all the information stored in the files associated to theproject.

When creating a new project a new directory is made, e.g.; \project. In this directory the project fileis stored: \project\project.iec and a directory is created called \project\_mesh. In this directory thegrid files used for the computations can be stored. It is however also possible to select a grid that islocated in another directory.

Only one mesh file should be used for all computations in a project. If computations

need to be done on another mesh file it is advised to duplicate the project (see section 2-3.1.4) or to create a new project (see section 2-3.1.1) for those computations.

FIGURE 1.2.4-1 Example of file management for a FINE™ project

batchbatch

How To Use This Manual Getting Started

FINE™ 1-5

1-3 How To Use This Manual

1-3.1 Outline

This manual consists of five distinct parts:

• Chapters 1and 2: introduction and description of the interface,

• Chapters 3 to 13: computation definition,

• Chapter 14: task management,

• Chapter 15: monitoring capabilities,

• Annex A: the Navier-Stokes equations,

• Annex B: used file formats,

• Annex C: list of supported non-interfaced expert parameters.

At first time use of FINE™ it is recommended to read this first chapter carefully and certainly sec-tion 1-4 to section 1-6. Chapter 2 gives a general overview of the FINE™ interface and the way tomanage a project. For every computation the input parameters can be defined as described in thechapters 3 to 13. Chapter 14 gives an overview of how to run computations using the Task Manageror using a script. Chapter 15 finally describes the available tools to monitor the progress on a com-putation.

The expert user finds in chapter 3 to 13 a section describing advanced options that are available inexpert user mode. Additionally Annex C provides a list with all supported expert parameters on thepage Computation Steering/Control Variables in expert user mode. For each parameter a refer-ence is given to the section in the manual where it is described.

The use of non-supported parameters is at own risk and will not guarantee correct

results.

1-3.2 Conventions

Some conventions are used to ease information access throughout this guide:

• Commands to type in are in italics.

• Keys to press are in italics and surrounded by <> (e.g.: press <Ctrl>).

• Names of menu or sub-menu items are in bold.

• Names of buttons that appear in dialog boxes are in italics.

• Numbered sentences are steps to follow to complete a task. Sentences that follow a step and arepreceded with a dot (•) are substeps; they describe in detail how to accomplish the step.

The hand indicates an important note

The pair of scissors indicates a keyboard short cut.

A light bulb in the margin indicates a section with a description of expert parameters.

Getting Started First Time Use

1-6 FINE™

1-4 First Time Use

1-4.1 Basic Installation

When using FINE™ for the first time it is important to verify that FINE™ is properly installedaccording to the installation note. The installation note provided with the installation softwareshould be read carefully and the following points are specifically important:

• Hardware and operating system requirements should be verified to see whether the chosenmachine is supported.

• Installation of FINE™ according to the described procedure in a directory chosen by the userand referenced in the installation note as ‘NUMECA_INSTALLATION_DIRECTORY’.

• A license should be requested that allows for the use of FINE™ and the desired component andmodules (see section 1-6 for all available licenses). The license should be installed according tothe described procedure in the installation note.

• Each user willing to use FINE™ or any other NUMECA software must perform a user configu-ration as described in the installation note.

When these points are checked the software can be started as described in the installation note orsection 1-5 of this users guide.

1-4.2 Expert Graphics Options

a) Graphics Driver

The Graphics area of FINE™ interface uses by default an OPENGL driver that takes advantage ofthe available graphics card. When the activation of OPENGL is causing problems, FINE™ uses anX11 driver (on UNIX) or MSW driver (for Windows) instead.

It is possible to explicitly change the driver used by FINE™ in the following ways:

On UNIX:

in csh, tcsh or bash shell:setenv NI_DRIVER X11

in korn shell:NI_DRIVER=X11export NI_DRIVER

The selection will take effect at the next session.

On Windows:

• Log in as Administrator.

• Launch regedit from the Start/Run menu.

•Go to the HKEY_LOCAL_MACHINE/SOFTWARE/NUMECA International/Fine# register.

•Modify the DRIVER entry to either OPENGL or MSW.


How to start FINE™ Interface Getting Started

FINE™ 1-7

b) Background Color

The background color of the Graphics area can be changed by setting the environment variableNI_IGG_REVERSEVIDEO on UNIX/LINUX platforms or IGG_REVERSEVIDEO on Windowsplatforms. Set the variable to ’ON’ to have a black background and set it to ’OFF’ to have a whitebackground. The variable can be manually specified through the following commands:

On UNIX:

in csh, tcsh or bash shell:

setenv NI_IGG_REVERSEVIDEO ON

in korn shell:

NI_IGG_REVERSEVIDEO=ONexport NI_IGG_REVERSEVIDEO


On Windows:

• Log in as Administrator.

• Launch System Properties from the Start/Settings/Control Panel/System menu.

•Go in the Environment Variables.

•Modify or add the IGG_REVERSEVIDEO entry to either ON or OFF.


1-5 How to start FINE™ InterfaceIn order to run FINE™, the following command should be executed:

On UNIX and LINUX platforms type: fine -print <Enter>

When multiple versions of FINE™ are installed the installation note should be con-

sulted for advice on how to start FINE™ in a multi-version environment.

On Windows click on the FINE™ icon in Start/Programs/NUMECA software/fine#. Alterna-tively FINE™ can be launched from a dos shell by typing:

<NUMECA_INSTALLATION_DIRECTORY>\fine#\bin\fine <Enter>

where NUMECA_INSTALLATION_DIRECTORY is the directory indicated in section 1-4.1 and #is the number corresponding to the version to be used.

Getting Started Required Licenses

1-8 FINE™

1-6 Required Licenses

1-6.1 Standard FINE™ License

The standard license for FINE™ allows for the use of all basic features of FINE™ including:

• IGG™ (see separate IGG™ manual),

•AutoGrid (see separate AutoGrid manual),

•CFView™ (see separate CFView™ manual),

• Task Manager (see Chapter 14),

•Monitor (see Chapter 15).

1-6.2 Additional Licenses

Within FINE™ the following features are available that require a separate license:

• parallel computations (see Chapter 14),

• treatment of unsteady rotor-stator interfaces (see Chapter 5),

• transition (see Chapter 7),

• fluid-particle interaction (see Chapter 7),

• conjugate heat transfer (see Chapter 7),

• steam tables (see Chapter 3),

• cooling/bleed flow (see Chapter 7),

• throughflow (see Chapter 6),

• blade to blade and 2D inverse design (Chapter 12 and Chapter 13).

Next to FINE™ other products are available that require a separate license:

• FINE™/Design 3D (3D inverse design, see separate user manual).

FINE™ 2-1

CHAPTER 2: User Interface

2-1 OverviewWhen launching FINE™ as described in Chapter 1 the interface appears in its default layout asshown in Figure 2.1.0-1. An overview of the complete layout of the FINE™ interface is shown onthe next page in Figure 2.1.0-2. In the next sections the items in this interface are described in moredetail.

Together with the FINE™ interface a Project Selection window is opened, which allows to create anew project or to open an existing project. See section 2-2 for a description of this window.

A File Chooser window is available for browsing through the file system and to select a file. Moredetail on the File Chooser window is given in section 2-11.

To define a profile through the FINE™ interface a Profile Manager is included. The Profile Man-ager is described in more detail in section 2-12.

FIGURE 2.1.0-1 Default FINE™ Interface

User Interface Project Selection

2-2 FINE™

FIGURE 2.1.0-2 Complete overview of the FINE™ interface

2-2 Project SelectionWhen the FINE™ interface is started the Project Selection window is appearing together with theinterface. This window allows to create a new project or to open an existing one as described in thenext sections. After use of this window it is closed. To open a project or to create a new one withoutthe Project Selection window is also possible using the File menu.

2-2.1 Creating a New Project

To create a new project when launching the FINE™ interface:

1. click on the Create a New Project... icon. A File Chooser will appear, which allows to select aname and location for the new project (for more detailed information on the File Chooser win-dow see section 2-11).

2. In the Directories text box on UNIX a name can be typed or the browser under the text box maybe used to browse to an appropriate location. On Windows, the browser under the Save in textbox is used to browse to an appropriate location.

3. Once the location is defined type on UNIX and on Windows a new name in the text box underrespectively Files and File name, for example project.iec (it is not strictly necessary to add theextension .iec, FINE™ will automatically create a project file with this extension).

4. Click on OK (on UNIX) or Save (on Windows) to accept the selected name and location of thenew project.

Main menu bar Icon bar (Section 2-3) (Section 2-4)

(Section 2-6)

Computations button

Parameters

(Section 2-5)

View button(Section 2-7)

button

Graphics area(Section 2-10)

Parameters area(Section 2-9)

Mesh information(Section 2-8)

Project Selection User Interface

FINE™ 2-3

5. A new directory is automatically created with the chosen name as illustrated in Figure 2.3.1-5indicated by point (1). All the files related to the project are stored in this new directory. Themost important of them is the project file with the extension .iec, which contains all the projectsettings (Figure 2.3.1-5, no. 2). Inside the project directory FINE™ creates automatically a sub-directory "_mesh" (Figure 2.3.1-5, no. 3).

6. A Grid File Selection window (Figure 2.2.1-3) appears to assign a grid to the new project. Thereare three possibilities:

• to open an existing grid click on Open Grid File. A File Chooser allows to browse to the gridfile with extension .igg. Select the grid file and press OK to accept the selected mesh. A win-dow appears to define the Grid Units and Project Configuration. Set the parameters in thiswindow as described in section 2-2.3 and click OK to accept.

• if the grid to use in the project was not yet created use Create Grid File to start IGG™. Createa mesh in IGG™ or AutoGrid (Modules/AutoGrid) and save the mesh in the directory"_mesh" of the new project. Click on Modules/Fine Turbo to return to the FINE™ project.Select the created mesh with the pull down menu in the icon bar. A window will appear todefine the Grid Units and Project Configuration. Set the parameters in this window asdescribed in section 2-2.3 and click OK to accept.

•When using the AutoBlade™ or Design 3D Module it is not necessary to select a grid. In thatcase close the Grid File Selection window and select Modules/AutoBlade or Modules/Design 3D menu to use these modules.

FIGURE 2.2.1-3 Grid File Selection window.

2-2.2 Opening of an Existing Project

To open an existing project the two following possibilities are available in the Project Selectionwindow:

•Click on the icon Open an Existing Project... A File Chooser will appear that allows to browseto the location of the existing project. Automatically the filter in the File Chooser is set to dis-play only the files with extension .iec, the default extension for a project file.

• Select the project to open in the list of Recent Projects, which contains the five most recentlyused project files. If a project no longer exists it will be removed from the list when selected.To view the full path of the selected project click on Path... To open the selected project clickon Open Selected Project.

1.1

1.22.1

2.2 3

User Interface Main Menu Bar

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2-2.3 Grid Units and Project Configuration

The Grid Units and Project Configuration window shows some properties of the selected meshwhen linking the mesh to the project:

•Grid Units: the user specifies the grid units when importing a mesh. The user may define a dif-ferent scale factor to convert the units of the mesh to meters. The scale factor is for instance0.01 when the grid is in centimetres.

• Space Configuration: allows the user to specify whether the mesh is cylindrical or Cartesianand the dimensionality of the mesh. In case the mesh is axisymmetric the axis of symmetryshould be defined.

FIGURE 2.2.3-4 Grid Units and Project Configuration window.

The mesh properties are always accessible after linking the mesh to the

project through the menu Mesh/Properties...

2-3 Main Menu Bar

2-3.1 File Menu

2-3.1.1 New Project

The menu item File/New allows to create a new FINE™ project. When clicking on File/New a FileChooser window appears as described in section 2-11. Browse in the Directory list to the directoryin which to create a new project directory (in the example of Figure 2.3.1-5 the directory /fermatwas selected). Give a new name for the project in the File list, for example project.iec and click onOK to create the new project.

When starting a new project a new directory is automatically created with the chosen name (1). Allthe files related to the project are stored in this new directory. The most important of them is theproject file with the extension .iec, which contains all the project settings (2). Inside the projectdirectory FINE™ creates automatically a subdirectory "_mesh" (3). As all the computations of theproject must have the same mesh it is advised to store the mesh in this specially dedicated directory.

Main Menu Bar User Interface

FINE™ 2-5

Each time the user creates a new computation, a subdirectory is added (4). The output files gener-ated by the flow solver will be written in the subdirectory of the running computation.

FIGURE 2.3.1-5 Directories managed through FINE™

After the new project is created a Grid File Selection window (Figure 2.2.1-3) appears to assign agrid to the new project. There are two possibilities:

• to open an existing grid click on Open Grid File. A File Chooser allows to browse to the gridfile with extension .igg. Select the grid file and press OK to accept the selected mesh. A win-dow appears to define the Grid Units and Project Configuration. Set the parameters in thiswindow as described in section 2-2.3 and click OK to accept.

• if the grid to use in the project was not yet created use Create Grid File to start IGG™. Createa mesh in IGG™ or AutoGrid (Modules/AutoGrid) and save the mesh in the directory"_mesh" of the new project. Click on Modules/Fine Turbo to return to the FINE™ project.Select the created mesh with the pull down menu in the icon bar. A window will appear todefine Grid Units and Project Configuration. Set the parameters in this window as describedin section 2-2.3 and click OK to accept.

2-3.1.2 Open Project

There are two ways to open an existing project file:

a) Using the File/Open Menu Item:

1. Click on File/Open.

2. A File Chooser window appears.

3. Browse through the directory structure to find the project file to open. This file has normally the.iec extension. If this is not the case, the file filter in the input box named `List Files of Type', hasto be modified.

4. Select the project file.

5. Click on the file name and press the OK button.The opened project becomes the active project. All subsequent actions will be applied to thisproject.

b) Selecting the File From the List of Files in the File Menu.

The File menu lists the names of the five most recent projects that have already been opened. Clickon a project name from this menu to open this project.

(1) project directory

(2)

(3)

automatically created _mesh directory

(4) computation directory


2-6 FINE™

FINE™ will check the write permission of the project directory and the project file and will issue awarning if the project or directory is read only. In both cases the project can be modified, but thechanges will not be saved.

Only one project can be active. Opening a second project will save and close the first

one.

An attempt to open a no longer existing project will remove its name from the list in the

File menu.

2-3.1.3 Save Project

The File/Save menu item stores the project file (with extension .iec) on disk. The project file isautomatically saved when the flow solver is started, when FINE™ is closed, or when anotherproject is opened.

2-3.1.4 Save As Project

File/Save As is used to store the active project on disk under different name. A File Chooser opensto specify the new directory and name of the project. When this is done a dialog box asks whetherto save all the results files associated with the project. If deactivated, only the project file (with theextension .iec) will be saved in the new location.

2-3.1.5 Save Run Files

File/Save Run Files is used to store all the information needed for the flow solver in the .run file ofthe active computation. This menu is mainly useful when the Task Manager is used (see chapter 14for a detailed description of the Task Manager).

If more than one computation is selected in the Computations list, then all parameters in

the Parameters area will be assigned to all selected (active) computations. This may bedangerous if the parameters for the currently opened information page are not the samefor all the selected computations. To avoid this it is recommended to select only onecomputation at a time.

The run file is automatically updated (or created if not existing) when starting a computationthrough the main menu (Solver/Start...).

2-3.1.6 Preferences

When clicking on File/Preferences... the Preferences window appears that gives access to someproject specific and global settings:

a) Project Units

In this section the user can change the units system of the project. The units can be changed inde-pendently for a selected physical quantity or for all of them at the same time. To change the unitsfor one specific quantity select the quantity in the list (see (1) in Figure 2.3.1-6). Then select theunit under Select New Units (2). To change the units for all physical quantities at the same time usethe box Reset Units System To (3).

The default system proposed by NUMECA is the standard SI system except for the unit for therotational speed, which is [RPM].

When the user changes the units, all the numerical values corresponding to the selected physicalquantity are multiplied automatically by the appropriate conversion factor. The numerical values


FINE™ 2-7

are stored into the project file in the same units as they appear in the interface, but in the .run file,which is used by the flow solver, the numerical values are always stored in SI units. The results canbe visualized with the flow visualization system CFView™ in the units specified in FINE™.Thechange of the units can be done at any stage of the creation of the project.

User-defined units can be defined through a text file euranus.uni. Please contact NUMECA supportteam at [email protected] for more information.

FIGURE 2.3.1-6 Project Units in the Preferences Window

b) Global Layout

Under the Global Layout thumbnail the user may specify project independent preferences for thelayout of the interface. More specifically the user may activate or deactivate the balloon help, whichgives short explanation of the buttons when the mouse pointer is positioned over them. By defaultballoon help is activated. Deactivation of the balloon help will only be effective for the current ses-sion of FINE™. When FINE™ is closed and launched again the balloon help will always be activeby default.

2-3.1.7 Quit

Select the File/Quit menu item to quit the FINE™ integrated environment. The active project willbe saved automatically. Note that this action will not stop the running calculations. A TaskManagerwindow will remain open for each running computation. Closing the TaskManager window(s) willkill the running calculation(s) after confirmation from the user.

2-3.1.8 Limitations in File Names

If the name of an already existing project is specified, this project file will be overridden. All otherfiles and subdirectories will remain the same as before.

By default, no IGG™ file is associated with the new project and it is indicated "usr/unknown" in theplace of the grid file name. The procedure to link a mesh file to the project is explained in section 2-4.2.

(1) (2) (3)


2-8 FINE™

2-3.2 Mesh Menu

2-3.2.1 View On/Off

This toggle menu is used to visualize the grid in FINE™. It may take few seconds to load the meshfile for the first time. The parameters area will be overlapped by the graphic window, and the smallcontrol button on the upper - left corner of the graphic window can be used to resize the graphicsarea in order to visualize simultaneously the parameters and the mesh (see section 2-10). Once themesh is opened, the same menu item Mesh/View On/Off will hide it. Note that the mesh will stayin the memory and the following use of the menu will visualize it much faster than the first time.

When the mesh is loaded the following items appear in the FINE™ interface:

• the View sub-pad (see section 2-7 for more details),

• the Mesh Information Area (see section 2-8 for more details),

• the Graphics Area will appear in the FINE™ interface (see section 2-10 for more details),

• The Viewing buttons will appear on the bottom of the Graphics Area. Their function isdescribed in section 2-10.1).

The Graphics Area and the Viewing buttons will disappear when the mesh is hidden (Mesh/ViewOn/Off). All the three tools will disappear when the mesh is unloaded (Mesh/Unload).

2-3.2.2 Tearoff graphics

This menu transfers the graphics area and its control buttons into a separate window. Closing thiswindow will display the graphics area back in the main FINE™ window.

Currently this feature is only available on UNIX systems.

2-3.2.3 Unload

Mesh/Unload clears the mesh from the memory of the computer.

2-3.2.4 Properties

Clicking on Mesh/Properties... opens a dialog box that displays global information about themesh:

•Grid Units: the user specifies the grid units when importing a mesh. When importing a meshthe Grid Units and Project Configuration window appears, which allows the user to check themesh units (see section 2-2.3). The chosen units can be verified and, if necessary, changed.

• Space Configuration: allows the user to verify whether the mesh is cylindrical or Cartesian andthe dimensionality of the mesh. When importing a mesh the Grid Units and Project Configu-ration window allow the user to check these properties. Those chosen properties can be veri-fied and, if necessary, changed.

• The total number of blocks and the total number of points are automatically detected from themesh.

• For each block: the current (depending on the current grid level) and maximum number ofpoints in each I,J and K directions, and the total number of points are automatically detectedfrom the mesh.


FINE™ 2-9

FIGURE 2.3.2-7 Mesh Properties dialog box

2-3.3 Solver Menu

This menu gives access to the NUMECA flow solver EURANUS, which is a powerful 3D codededicated to Navier-Stokes or Euler computations. EURANUS uses the computational parametersand boundary conditions set through FINE™ and can be fully controlled both from FINE™ SolverMenu and from the Task Manager (see chapter 13).

In this section, the information is given on how to start, suspend, interrupt and restart the flowsolver. All these actions may be simply performed by using the pull down menu appearing when thebutton Solver of the Menu bar is clicked.

2-3.3.1 Start the Flow Solver

To start the flow solver, select the menu item Solver/Start....

It is not recommended to start the flow solver before setting the physical boundary conditions andthe computational parameters.

Using the Start item to run the flow solver on active computation implies that the result file pro-duced by a previous calculations on that computation will be overwritten with the new result val-ues. It also implies that the initial solution will be created from the values set in the Initial Solutionpage.

2-3.3.2 Save

To save an intermediate solution while the flow solver is running click on Solver/Save....

2-3.3.3 Stop the Flow Solver

There are two different ways to stop the flow solver:

• Solver/Suspend... interrupts the flow computation after the next iteration. This means that theflow solver stops the computation at the end of the next finest grid iteration and outputs thecurrent state of the solution (solution file + CFView™ files) exactly as if the computation wasfinished. This operation may take from few seconds to few minutes depending on the numberof grid points in the mesh. Indeed, if the finest grid is not yet reached, the flow solver contin-ues the full multigrid stage and stops only after completion of the first iteration on the finestgrid.

User Interface Icon Bar

2-10 FINE™

• Solver/Kill... allows to stop immediately the computation for the active project.In this case nooutput is created and the only solution left is the last one that was output during the run. Thismay become a dangerous choice if asked during the output of the solution. The output is thenruined and all the computation time is lost. To avoid this, it is better to use Solver/Suspend...or to kill the computation some iterations after the writing operations.

2-3.3.4 Restart the Flow Solver

To restart a computation from an existing solution the solver should be started using the Solver/Start... menu. On the Initial Solution page the initial solution has to be specified from an existingfile (’.run’). See Chapter 10 that describes the several available ways to define an initial solution.

2-3.4 Modules Menu

Clicking on the menu item Modules shows a pull down menu with the available modules. The firstthree items are related to geometry and mesh definition:

•AutoBlade™ is the parametric blade modeller,

• IGG™ is the interactive geometry modeller and grid generator,

•AutoGrid is the automated grid generator for turbomachinery.

Furthermore two design modules are available:

•Design2D is a tool for two-dimensional blade analysis and design.

•Design3D is a product for three-dimensional blade analysis and optimization.

The Task Manager is accessible with Modules/Task Manager. For more detailed information onthe Task Manager consult Chapter 14.

To start the flow visualization from FINE™, click on the Modules/CFView button and confirm tostart a CFView™ session. Wait until the layout of CFView™ appears on the screen. CFView™automatically loads the visualization file associated with the active computation. To visualize inter-mediate results of a computation, wait until the flow solver has written output. For more informa-tion about the flow visualization system, please refer to the CFView™ User’s Guide.

2-4 Icon Bar

The icon bar contains several buttons that provide a short cut for menu items in the main menu bar.Also the icon bar contains a File Chooser to indicate the mesh linked to the project and a pull downmenu to choose between Standard Mode and Expert Mode.

2-4.1 File Buttons

The four buttons on the left of the icon bar are short cuts for items of the File menu:

The New Project icon is a short cut for the menu item File/New.

Icon Bar User Interface

FINE™ 2-11

The Open Project icon is a short cut for the menu item File/Open.

The Save Project icon is a short cut for the menu item File/Save.

The Save RUN Files icon is a short cut for the menu item File/Save Run Files.

2-4.2 Grid Selection Bar

By clicking on the open envelope on the right of the bar aFile Chooser is opened, which allows to select the grid file(with extension .igg) of the mesh to use for the project.

To select a grid not only the grid file with extension .igg needs to be present but all four

files (with extensions .igg, .geom, .bcs and .cgns) need to be available in the same direc-tory with the same name for the chosen mesh.

If a mesh has already been linked to the current project and another mesh is opened, FINE™ willcheck the topological data into the project against the data into the mesh file and will open a newdialog box (Figure 2.4.2-8) The dialog box will inform the user that a merge of the topologies hasbeen performed and will also show at which item the first difference was detected.

FIGURE 2.4.2-8 Merge Topology Dialog Box

The three following possibilities are available:

•Merge Mesh Definition will merge the two if needed. For example, if a new block has beenadded to the mesh, linked with the current project. The existing project parameters have beenkept for the old blocks, and the default parameters have been set for the new block.

•Open Another Grid File will open a File Chooser allows to browse to the a new grid file withextension .igg. Select the grid file and press OK to accept the selected mesh. Then the dialogbox Mesh Merge Information will appear.

• Start IGG will load automatically the new mesh into IGG™.

User Interface Computations Button

2-12 FINE™

The merge may also occur when opening an existing project, or when switching between IGG™and FINE™, because the check of the topology is performed each time when a project is read.

In case the mesh file is no longer existing, or not accessible, an appropriate warning will pop-upwhen opening the project. In this case it will not be possible to start the flow solver, so the userneeds to locate the mesh by means of the File Chooser button on the right of the Grid Selection bar.

Once the grid file selected and its topology checked the Grid Units and Project Configuration win-dow appears. This window allows to check the properties of the mesh and to modify them if neces-sary. See section 2-2.3 for more detail on this window.

2-4.3 Solver Buttons

Three buttons allow to start, suspend and kill the active computation:

The Start Flow Solver icon is a short cut for the menu item Solver/Start....

The Suspend Flow Solver icon is a short cut for the menu item Solver/Suspend....

The Kill Flow Solver icon is a short cut for the menu item Solver/Kill....

2-4.4 Module Buttons

Two buttons allow to start the pre- and post processor:

The Start IGG icon is a short cut for the menu item Modules/IGG.

The Start CFView icon is a short cut for the menu item Modules/CFView.

2-4.5 User Mode

By clicking on the arrow at the right the user may select the usermode. For most projects the available parameters in StandardMode are sufficient. When selecting Expert Mode parameters

area included additional parameters. These expert parameters may be useful in some more complexprojects. The next chapters contain sections in which the expert parameters are described for theadvanced user.

2-5 Computations ButtonWhen clicking on the Computations button at the top left of the interface a list of all the computa-tions of the project is shown. The active computation is highlighted and the corresponding parame-ters are shown in the Parameters area. All the project parameters of the computation can becontrolled separately by selecting (from this list) the computation on which all the user modifica-tions are applied.

Parameters Button User Interface

FINE™ 2-13

When selecting multiple computations, the parameters of the active page in the Parame-

ters area are copied from the first selected computation to all other computations.

With the buttons New and Remove computations can be created or removed. When clicking on Newthe active computation is copied and the new computation has the same name as the original withthe prefix new_ as shown in the example below. In this example computation_2 was the activecomputation at the moment of pressing the button New. A new computation is created callednew_computation_2 that has the same project parameters as computation_2.

To rename the active computation click on Rename, type the new name and press <Enter>.

2-6 Parameters ButtonThe Parameters button is the second button on the left, below the Computations button. Whenclicking on this button a directory structure appears allowing the user to go through the availablepages of the project definition. The Parameters area shows the parameters corresponding to theselected page in the Parameters list.

To see the pages in a directory double click on the name or click on the + sign in front of the name.

2-7 View AreaWhen the mesh is loaded with Mesh/View On/Off, a third button is shown in the list on the left: theView button. This button is used in order to show or hide the View sub-pad. By default the View sub-pad is opened. It consists of three pages and controls the viewing operations on the geometry andthe grid. The two first pages show the created geometry and/or block groups of the mesh and allowto create new groups. This possibility is only useful in FINE™ for visualization purposes (forexample, to show only some blocks of the mesh to get a clearer picture in the case of a complexconfiguration).

User Interface View Area

2-14 FINE™

FIGURE 2.7.0-1 The View sub-pad

The third page provides visualization commands on the grid. It consists of two rows: a row of but-tons and a row of icons.

The row of buttons is used to determine the viewing scope, that is the grid scope on which the view-ing commands provided by the icons of the second row will apply. There are five modes determin-ing the scope, each one being represented by a button: Segment, Edge, Face, Block, Grid. Onlyone mode is active at a time and the current mode is highlighted. Simply left-click on a button toselect the desired mode.

• : in Segment mode, a viewing operation applies to the active segment only.

• : in Edge mode, a viewing operation applies to the active edge only.

• : in Face mode, a viewing operation applies to the active face only.

• : in Block mode, a viewing operation applies to the active block only.

• : in Grid mode, a viewing operation applies to all the blocks of the grid.

The icons of the second row and their related commands are listed in the following table:

Icon Command

Toggles vertices.

Toggles fixed points.

Toggles segment grid points.

Toggles edges.

Toggles face grid.

Toggles shading.

Mesh Information User Interface

FINE™ 2-15

The display of vertices should be avoided since it allows to modify interactively in the

Graphics area the location of the vertices and therefore alter the mesh. The Graphicsarea is for display purposes only and any modification on the mesh in the Graphics areawill not be saved in the mesh files and therefore not used by the flow solver.

2-8 Mesh InformationWhen the mesh is loaded also the Mesh Information Area is shown containing the following infor-mation for the selected section of the mesh:

FIGURE 2.8.0-1 Mesh Information Area

• Active Block, Face, Edge and Segment indices.

• Number of grid blocks, active block faces, active face edges, active edge segments.

• Block:

— Number of active block points.

— Number of grid points.

— Name of the block.

— Number of points in each block direction.

• Face: constant direction and the corresponding index.

• Edge: constant direction according to the active face and the corresponding index.

• Segment: number of points on the segment.

2-9 Parameters AreaThe Parameters area displays a page containing the parameters related to the selected item of theParameters list. Depending on the selected User Mode the available expert parameters will be dis-played.

Active block, face, edge and segment indices

Number of blocks, faces, edges and segmentsfor the active topology

User Interface Graphics Area

2-16 FINE™

2-10 Graphics AreaThe Graphics area shows the mesh of the open project. The Graphics area appears and disappearswhen clicking on Mesh/View On/Off. When the Graphics area appears it is covering the Parame-ters area. Use the button on the left boundary of the Graphics area to reduce its size and to displaythe Parameters area. The View items on the left and the grid icons in the Graphics area can be usedto influence the visualization of the mesh. The View items are described in section 2-7 and the iconsin the Graphics area are described below.

FIGURE 2.10.0-2 Resizing of Graphics Area

2-10.1 Viewing Buttons

The Viewing buttons are used to perform viewing manipulations on the active view, such as scroll-ing, zooming and rotating. The manipulations use the left, middle and right buttons of the mouse indifferent ways. The sub-sections below describe the function associated with each mouse button foreach viewing button.

For systems that only accept a mouse with two buttons, the middle mouse button can be

emulated for viewing options by holding the <Ctrl> key with the left mouse button.

2-10.1.1 X, Y, and Z Projection Buttons

These buttons allow to view the graphics objects on X, Y or Z projection plane. Press the left mousebutton to project the view on an X, Y or Z constant plane. If the same button is pressed more thanone time, the horizontal axis sense changes at each press.

button to resizeGraphics area

Graphics Area User Interface

FINE™ 2-17

2-10.1.2 Coordinate Axes

The coordinate axes button acts as a toggle to display different types of coordinate axes on theactive view using the following mouse buttons:

• Left: press to turn on/off the display of symbolic coordinate axis at the lower right corner of theview.

•Middle: press to turn on/off the display of scaled coordinate axis for the active view. The axissurrounds all objects in the view and may not be visible when the view is zoomed in.

• Right: press to turn on/off the display of IJK axis at the origin of the active block (in BlockViewing Scope) or of all the blocks (in Grid Viewing Scope). For more informations about theviewing scope, see section 2-7.

2-10.1.3 Scrolling

This button is used to translate the contents of active view within the plane of graphics window inthe direction specified by the user. Following functions can be performed with the mouse buttons:

• Left: press and drag the left mouse button to indicate the translation direction. The translationis proportional to the mouse displacement. Release the button when finished. The translationmagnitude is automatically calculated by measuring the distance between the initial clickedpoint and the current position of the cursor.

•Middle: press and drag the middle mouse button to indicate the translation direction. Thetranslation is continuous in the indicated direction. Release the button when finished. Thetranslation speed is automatically calculated by measuring the distance between the initialclicked point and the current position of the cursor.

2-10.1.4 3D Viewing Button

This button allows to perform viewing operations directly in the graphics area. Allowed operationsare 3D rotation, scrolling and zooming.

After having selected the option, move the mouse to the active view, then:

• Press and drag the left mouse button to perform a 3D rotation

• Press and drag the middle mouse button to perform a translation

• Press and drag the middle mouse button, while holding the <Shift> key, to perform a zoom

• To select the centre of rotation, hold the <Shift> key and press the left mouse button on ageometry curve, a vertex or a surface (even if this one is visualized with a wireframe model).The centre of rotation is always located in the centre of the screen. So, when changing it, themodel is moved according to its new value.

This 3D viewing tool is also accessible with the <F1> key.

2-10.1.5 Rotate About X, Y or Z Axis

The rotation buttons are used to rotate graphical objects on the active view around the X, Y or Zaxis. The rotations are always performed around the centre of the active view. Following functionscan be performed with the mouse buttons:

• Left: press and drag the left mouse button to the left or to the right. A clockwise or counter-clockwise rotation will be performed, proportional to the mouse displacement. Release thebutton when finished.

•Middle: press and drag the middle mouse button to the left or to the right. A continuous rota-tion will be performed, clockwise or counter-clockwise. Release the button when finished.

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2-10.1.6 Zoom In/Out

This button is used for zooming operations on the active view. Zooming is always performedaround the centre of the view. Following functions can be performed with the mouse buttons:

• Left: press and drag the left mouse button to the left or to the right. A zoom in - zoom out willbe performed, proportional to the mouse displacement. Release the button when finished.

•Middle: press and drag the middle mouse button to the left or to the right. A continuous zoomin - zoom out will be performed. Release the button when finished.

2-10.1.7 Region Zoom

This button allows to specify a rectangular area of the active view that will be fitted to the viewdimensions. After having selected the button:

1. Move the mouse to the active view.

2. Press and drag the left mouse button to select the rectangular region.

3. Release the button to perform the zoom operation.These operations can be repeated several times to perform more zooming.

Press <q> or the right mouse button to quit the option.

This tool is also accessible with the <F2> key.

2-10.1.8 Fit Button

The fit button is used to fit the content of the view to the view limits without changing the currentorientation of the camera (which can be interpreted as the user's eyes).

2-10.1.9 Original Button

The original button is used to fit the content of the view and to give a default orientation to the cam-era.

2-10.1.10Cutting Plane

This option displays a movable plane that cuts the geometry and the blocks of the mesh. The planeis symbolically represented by four boundaries and its normal, and is by default semi-transparent.After having selected the button:

• Press and drag the left mouse button to rotate the plane

• Press and drag the middle mouse button to translate the plane

• Press < x >, < y > or < z > to align the plane normal along the X, Y or Z axis

• Press <n> to revert the plane normal

• Press < t > to toggle the transparency of the plane (to make it semi-transparent or fully trans-parent). It is highly advised to deactivate the plane transparency when using X11 driver toincrease the execution speed.

File Chooser User Interface

FINE™ 2-19

2-11 File ChooserFor file management (opening and saving of files) FINE™ uses the standard File Chooser window.The layout of the File Chooser depends on the used operating system but a typical layout is shownin Figure 2.11.0-3. The Directories list allows to browse through the available directory structure tothe project directory.

Then the Files list can be used to select the file name. In the case a file needs to be opened an exist-ing file should be selected in the list of available files. In the case a new file needs to be created theuser can type a new file name with the appropriate extension.

In the List Files of Type bar the default file type is set by default to list only the files of the requiredtype. For a description of all available file types in FINE™ see section 1-2.4.

FIGURE 2.11.0-3 Typical layout of a File Chooser window

2-12 Profile ManagerWhen a law is defined by a profile clicking on the button right next to the pull down menu willinvoke a Profile Manager.

FIGURE 2.12.0-4 Profile Manager for fluid parameters

User Interface Profile Manager

2-20 FINE™

The Profile Manager is used to interactively define and edit profiles for both fluids and boundaryconditions parameters. The user simply enters the corresponding coordinates in the two columns onthe left. The graph is updated after each coordinate (after each pressing of <Enter> key).

The button Import may be used if the profile exists already as a file on the disk. The Export buttonis used to store the current data in the profile manager as a file (for example to share profilesbetween different projects and users). The formats of the profile files are explained in Appendix Bwhere all file formats used by FINE™ and EURANUS are detailed.

If the mouse cursor is placed over a point in the graph window, this point is highlighted and the cor-responding coordinates on the left will be also highlighted, giving the user the possibility to verifythe profile.

The button OK will store the profile values and return back to the main FINE™ window.

FINE™ 3-1

CHAPTER 3: Fluid Model

3-1 OverviewEvery FINE™ project contains a fluid with the corresponding properties. In FINE™ the fluid to usefor a computation can be defined by:

1. Using the fluid defined in the project file of which the properties are shown on the fluid selec-tion page (see section 3-2.1), or

2. selecting a fluid from the fluid database included in the release that contains a set of pre-definedfluids (see section 3-2.2), or

3. creating a new fluid (see section 3-2.3).

In the next section the interface is described in detail including advice for use of the fluid defini-tion. The theoretical background for the different fluid models is described in section 3-3.

Fluid Model The Fluid Model in the FINE™ Interface

3-2 FINE™

3-2 The Fluid Model in the FINE™ Interface

FIGURE 3.2.0-1 Fluid Selection page

3-2.1 Properties of Fluid Used in the Project

Every FINE™ project contains a fluid with the corresponding properties that are displayed in theinterface (see Figure 3.2.0-1). When a new project is created the used fluid is a default fluid. Whenan existing project is opened the used fluid is defined by the properties as defined in the project file’.iec’.

The first listed fluid property is the fluid type. Four fluid types are available:

• perfect gas,

• real gas,

• incompressible gas or liquid,

• condensable fluid.

For more detail on each of these types see section 3-3. For the first three fluid types the propertiescan be defined through the interface as described in section 3-2.3. For the use of the condensablefluid contact NUMECA to obtain the appropriate tables to add a condensable fluid to the list of flu-ids.

To modify the properties of the used fluid a fluid may be selected from the list of pre-defined fluids(section 3-2.2) or a new fluid may be defined (where the new fluid is based on the current one, seesection 3-2.3 for more detail).

3-2.2 List of Fluids

The list of fluids (see Figure 3.2.0-1) contains pre-defined fluids in a database with for each fluidthe fluid type and the permissions.

list of properties

list of pre-defined fluids

filters

The Fluid Model in the FINE™ Interface Fluid Model

FINE™ 3-3

Every fluid is associated with the user who created it and can be modified or removed only by itsowner (the owner has Read Write Delete permissions). All other users will have Read Only permis-sions only.

The user may select a fluid from the list. The selection will be highlighted and the properties of theselected fluid are displayed in the information box below the fluid list. Those fluid properties willbe saved in the project file ’.iec’ as soon as the project is saved.

3-2.3 Add Fluid

To add a fluid to the database click on the Add New Fluid... button. A new fluid is then created withthe current properties as shown in the list of properties. A wizard will appear allowing the user tomodify those properties.

On the first page of this wizard the user can enter the name and the type of the new fluid. The nameshould be entered by moving the mouse to the text box for the Fluid Name and to type the name onthe keyboard. By default a name is proposed like new_fluid_1. The fluid type can be entered byselecting the appropriate check boxes. First make a choice for a compressible or incompressiblefluid. For a compressible fluid select a perfect gas or a real gas. The fluid type corresponding to theselected checkboxes is shown in the text box for the Fluid Type. To cancel the modifications to thefluid definition and close the wizard click on the Cancel button.

Once the fluid name and type are correctly set, click on Next>> to go to the next page of the wiz-ard. On this page the following properties have to be defined:

• Specific Heat Law,

•Heat Conduction Law,

•Viscosity Law,

•Density Law (for an incompressible fluid only).

The possible values to enter for these laws depend on the selected fluid type as described in the nextparagraphs. In the case a law is defined by a constant value, type the value in the corresponding dia-log box. In the case a law is defined by a profile, the Profile Manager can be opened by clicking on

the button ( ) right next to the pull down menu (see section 3-2.3.6 for more detail). In the case a

law is defined by a formula, the Formula Editor can be opened by clicking on the button ( ) rightnext to the pull down menu (see section 3-2.3.5).

Information linked to fluid creation is stored in the fluid database only when closing the

FINE™ interface. As a consequence, this information will not be available to other usersas long as this operation is not completed.

3-2.3.1 Definition of a Perfect Gas

For the definition of a perfect gas the user has to specify:

• The specific heat at constant pressure. For a perfect gas only a constant Cp is allowed.

• The specific heat ratio (Cp/Cv) characteristic of the fluid.

• The heat conductivity which may be constant, defined by a polynome in temperature or speci-fied through a constant Prandtl number.


3-4 FINE™

• The viscosity law which may be constant, temperature dependent or specified by the Sutherlandlaw. In case the viscosity depends on the temperature the user can specify the law through a pol-ynome or as a profile through the Profile Manager. Furthermore, when the viscosity law isdefined by the Sutherland law, the Sutherland parameters are accessible by clicking on the but-

ton ( ) right next to the pull down menu.

The user can select a law for the dependence of the laminar viscosity in function of the static tem-perature. The default is the Sutherland’s law that imposes a temperature dependence of the dynamicviscosity. The viscosity may also be maintained constant.

3-2.3.2 Definition of a Real Gas

A real gas is defined by laws for the dependence of Cp and/or γ with the temperature.

The user can either define a profile, using the Profile Manager, or impose a polynomial approxima-tion using the Formula Editor. In this last case, the polynomes take the following form:

, (3-1)

, (3-2)

where the coefficients are chosen by the user

and set in the dialog box for Cp and γ respectively. In the definition of real gas properties, lower andupper bounds of temperature variations [Tmin-Tmax] allowed in the domain must be provided.Depending on the local temperature during the iterative process, the physical properties will then beable to vary according to the laws defined in the fluid database. Note that it is necessary to cover thewhole temperature range occurring in the system otherwise some inaccuracy in the results might beintroduced. In addition, the local temperature may not fit at some occasion in the prescribed range;this is especially true during the transient. If so, as indicated by the formula editor (section 3-2.3.5),the physical properties are kept constant, at a value that corresponds to the lower/upper boundallowed by the range.

For the default definition of a real gas, involving a compressibility factor, the user has to specify:

• The specific heat at constant pressure characteristic and the specific heat ratio (γ=Cp/Cv) of thefluid, that can be dependent on the temperature through a polynome or a profile. In both cases,the user has to specify the temperature range over which the specific heat is defined. For alterna-tive modelling methods for a real gas see section 3-2.9 and section 3-3.2.2.

• The heat conductivity which is constant, defined by a polynome or profile in temperature orspecified through a constant Prandtl number.

• The viscosity law which may be constant, dependent on temperature or specified by the Suther-land law. In case the viscosity depends on the temperature the user can specify the law through apolynome or as profile. Furthermore, when the viscosity law is defined by the Sutherland law,

the Sutherland parameters are accessible by clicking on the button ( ) right next to the pulldown menu.

Compared to a perfect gas computation (Cp and γ constant), the real gas option results in anincrease of about 25% of the CPU time. Real gas calculations are usually robust enough to avoidany use of preliminary run with average physical properties. However, convergence difficultiesmay arise in the transient (say the first 100-200 iterations) if either the temperature range allowed istoo large or if the properties are expected to vary very significantly in the temperature rangeallowed. At these occasions, it is often useful to run an equivalent perfect gas, with average proper-

Cp T( ) A0T3–

A1T2–

A2T1–

A3 A+4T

1A5T

2A6T

3+ + + + +=

γ T( ) B0T3–

B1T2–

B2T1–

B3 B+4T

1B5T

2B6T

3+ + + + +=

A0 A1 A2 A3 A4 A5 A6 B0 B1 B2 B3 B4 B5and B6, , , , , , , , , , , ,


FINE™ 3-5

ties, in order to remove any temperature dependency and ease the convergence process in the tran-sient.

3-2.3.3 Definition of a Liquid

For the definition of a liquid two models are available:

• a ’pure’ liquid with constant density,

• a barotropic liquid for which the density varies with pressure.

Depending on the type of liquid the user has to specify:

• The specific heat at constant pressure. For liquids only a constant Cp is allowed.

• The heat conductivity which may be constant, defined by a polynome in temperature or speci-fied through a constant Prandtl number.

• The viscosity law which may be constant or depend on temperature. In case the viscositydepends on the temperature the user can specify the law through a polynome or as a profilethrough the Profile Manager.

• The density law can be pressure dependent (using a polynomial law or as a profile through theProfile Manager) or follow Boussinesq law. In this latter case the density is constant and theBoussinesq coefficients are taken into account only if the button Gravity Forces (Flow Modelpage) is activated. These coefficients are used in source terms of the density equation in order tomodelize the gravitational effect (i.e. natural convection) although the density is assumed to bestrictly constant.

For liquids, the reference temperature and pressure must lie in the expected range of the

static temperature and pressure of the flow field. The reference pressure and temperatureare defined on the Flow Model page (Eq. 4-85).

3-2.3.4 Definition of a Condensable Gas

The aim of the Condensable Fluid module is the modelling of the real thermodynamic properties ofthe fluid by means of interpolation of the variables from dedicated tables.

The module can be used for a single-phase fluid whose properties are too complex to be treatedwith a perfect or real gas model. It can also be used in order to treat thermodynamic conditions thatare close to the saturation line. Note that the model can be used on the liquid or on the vapour sideof the saturation curve. In case the thermodynamic state lies inside the two-phase region a homoge-neous equilibrium two-phase mixture of vapour and liquid is considered. The hypothesis of an equi-librium mixture is however not valid if the dryness (wetness) fraction exceeds 20%. The modulecan not be used above these fractions, as it completely ignores evaporation-condensation phenom-ena.

The approach that has been adopted in EURANUS consists of using a series of thermodynamictables, one table being required each time a thermodynamic variable must be deduced from twoother ones. This implies the creation of many tables as input, but presents the advantage that no iter-ative inversion of the tables is done in the solver, with as a consequence a very small additionalCPU time.

The thermodynamic tables are provided by NUMECA, upon request. The tables corresponding towater steam have been generated on basis of literature. NUMECA has also developed a tool for thegeneration of the thermodynamic tables on basis of equations presented in the literature.

In order to use a condensable gas as fluid model, the user has to copy the provided tables in a user-defined subdirectory called /tables_username/ in /NUMECA_INSTALLATION_DIRECTORY/COMMON/steam_tables on UNIX or in /NUMECA_INSTALLATION_DIRECTORY/bin/


3-6 FINE™

steam_tables/ on Windows before launching FINE™. When the subdirectory is created, the con-densable gas is recognized by FINE™ and the fluid will appear in the list with respectively FluidName and Fluid Type as "_name" and Condensable Fluid.

3-2.3.5 Formula Editor

When a law is defined by a formula clicking on the button right next to the pull down menu willinvoke a formula editor. When a law is defined by a formula clicking on the button right next to thepull down menu will invoke the Formula Editor.

FIGURE 3.2.3-2 The Formula Editor for polynomials in the fluid properties

The Formula Editor is used to define polynomial values for the fluid properties. The user has todefine the seven coefficients of the polynomial according to the displayed formula on the top, andalso the lower and upper limits of the range, in which the polynomial function is defined. Press<Enter> after each entry. The constant values equal to the minimal and maximal values will be con-sidered outside of this range (as shown in the graph).

If a fluid with "Read Only" permissions contains formulas they may be visualized by

means of the Show Fluid Properties... button that opens the Formula Editor window, butthey can not be modified - a message will warn the user that the selected fluid can not bemodified.

3-2.3.6 Profile Manager

When a law is defined by a profile clicking on the button right next to the pull down menu willinvoke a Profile Manager.

The Profile Manager is used to interactively define and edit profiles for both fluids and boundaryconditions parameters. The user simply enters the corresponding coordinates in the two columns onthe left. The graph is updated after each coordinate (after each pressing of <Enter> key).

The button Import may be used if the profile exists already as file on the disk. The Export button isused to store the current data in the profile manager as a file (for example to share profiles betweendifferent projects and users). The formats of the profile files are explained in detail in Appendix B.


FINE™ 3-7

FIGURE 3.2.3-3 Profile Manager for fluid parameters

If the mouse cursor is placed over a point in the graph window, this point is highlighted and the cor-responding coordinates on the left will be also highlighted, giving the user the possibility to verifythe profile.

The button OK will store the profile values into the fluid definition.

If a fluid with "Read Only" permissions contains profiles they may be visualized by

means of the Show Fluid Properties... button that opens the Profile Manager window,but they can not be modified - a message will warn the user that the selected fluid can notbe modified.

3-2.4 Delete Fluid from List

When the user has the permission to delete a fluid the button Delete Fluid... allows to remove theselected fluid from the list of fluids.

Information linked to fluid removal is stored in the fluid database only when closing the

FINE™ interface. As a consequence, this information will not be available to other usersas far as this operation is not completed. A message will however warn users that thefluid properties have been modified (up to removal in the present situation) by the owner.

3-2.5 Edit Fluid in List

When the user has the permission to write for a fluid, the properties of the selected fluid can bemodified by clicking on Edit Fluid.... A wizard will appear allowing to modify the name, the typeand the laws defining the selected fluid. The two pages of this wizard and the laws to define aredescribed in detail in section 3-2.3.

Information linked to fluid edition is stored in the fluid database only when closing the

FINE™ interface. As a consequence, this information will not be available to other usersas far as this operation is not completed. A message will however warn users that thefluid properties have been modified by the owner.


3-8 FINE™

3-2.6 Showing Fluid Properties

When the user does not have the write permission (Read Only) for a fluid the Show Fluid Proper-ties... button opens the wizard with the properties of the fluid. In this case it is not possible to mod-ify any of the properties in the wizard but the user has access to visualize the fluid propertiesincluding the defined profiles and formulae.

3-2.7 Filters

On the Fluid Model page two filters are available to display only a limited amount of fluids in thelist of fluids. Select the owner(s) and fluid type(s) to display from the pull down menus to limit thelist of fluids.

Please notice that under Windows™ the fluid database is not owner-oriented. The data-

base is stored locally and user defined fluids is accessible with full permissions to allWindows™ users.

3-2.8 Import Fluids Database

When the user has is own fluid database, the Import Fluids Database... enables to load a userdefined database through a File Chooser window to select the ’.flb’ file containing the properties ofall the fluids.

When loading an existing project and opening the Fluid Model page, please notice that

FINE™ is automatically checking if the fluid is existing or not in the fluid database. Ifthe fluid name is existing but the properties are different, a comparison window willinvite the user to select the fluid to use (the default fluid in the database or the fluiddefined in the project).

3-2.9 Expert Parameters

A list of the expert parameters which can be used in the definition of the fluid type follows hereaf-ter. It is only a summary to know directly the expert parameters related to the definition of a fluid.More details about these expert parameters are given in section 3-3.

All expert parameters related to fluid definition are available in Expert Mode on the Control Varia-bles page. For these expert parameters the default values are appropriate ones that only have to bechanged in case the user has specific wishes concerning the fluid modelling.

PRT: Allows to define the turbulent Prandtl number.

For the real gas (thermally perfect gas):

IRGCON: defines how the real gas is modelled (default IRGCON = 0)

= 0: a compressibility factor is used: two laws have to be entered to define the depend-ence of Cp and γ with the temperature.

= 1: constant r model, γ is calculated from r and Cp. The dependence of Cp with tem-perature needs to be entered.

RGCST: value of the gas constant r used with IRGCON equal to 1 (default RGCST = 287)

Theory Fluid Model

FINE™ 3-9

For condensable fluid:

IHXINL = 0 (default),

= 1: activation of special inlet boundary condition.

3-3 Theory

3-3.1 Transport Properties

3-3.1.1 The Laminar Viscosity

In general the kinematic viscosity (in m2/s) is defined in FINE™. The laminar kinematic viscositymay be

• constant,

• given in terms of a polynomial function of the temperature,

• given by a profile for a certain temperature range,

• varying according to Sutherland’s law.

The dynamic viscosity is then computed within the code by multiplying the kinematic viscosity bythe reference density.

The Sutherland law is given by:

For

(3-3)

For

(3-4)

The viscosity in Eq. 3-3 and Eq. 3-4 is the dynamic viscosity specified in the Fluid Model page

or is obtained from the kinematic viscosity and the density both specified in the Fluid Model page,

while and TSUTHE are respectively the reference temperature and the Sutherland temperature

specified also in the Fluid Model page.

T∞ 120K≥

µ T( ) µ 120( ) T120---------= T 1200

K≤

µ T( ) µ∞T

T∞------

⎝ ⎠⎛ ⎞

1.5 T∞ TSUTHE+

T TSUTHE+------------------------------------

⎝ ⎠⎛ ⎞= T 1200K≥

T∞ 120K≤

µ T( ) µ∞T

T∞------= T 1200K≤

µ T( ) µ 120( ) T120---------

⎝ ⎠⎛ ⎞

1.5 120 TSUTHE+T TSUTHE+

---------------------------------------⎝ ⎠⎛ ⎞= T 1200K≥

µ∞

T∞

Fluid Model Theory

3-10 FINE™

3-3.1.2 The Heat Conductivity

The laminar heat conductivity may be

• constant,

• given in terms of a polynomial function of the temperature,

• given by a profile for a certain temperature range,

• specified through the Prandtl number.

In case the Prandtl number Pr is specified, the laminar thermal conductivity is obtained as:

(3-5)

The turbulent viscosity is calculated iteratively using one of the turbulence models discussed in sec-tion 4-3.3. The turbulent conductivity is obtained from the turbulent viscosity and a turbulentPrandtl number whose value can be controlled through the expert parameter PRT (default: 1.0):

. (3-6)

3-3.2 Fluid Models

In this section, details are provided about the different fluid types available in FINE™:

• perfect gas,

• real gas,

• liquid,

• condensable fluid.

3-3.2.1 Calorically Perfect Gas

The perfect gas law is used as constitutive equation:

(3-7)

with the gas constant for the perfect gas under consideration:

, (3-8)

with the universal gas constant and the molecular weight of the perfect gas.

is the specific heat ratio, the specific heat at constant pressure, and the specific heat at

constant volume with:

. (3-9)

When the gas temperature is so low that the vibrational and electronic modes are frozen, the inter-nal energy of the gas will be proportional to the temperature and the specific heats as well as areconstant. The gas is "calorically perfect". This is the usual assumption of moderate speed aerody-namics.

κµCp

Pr----------=

κt

µtCp

Prt

-----------=

p ρrT=

r

rRM----- cp cv–= =

R M

γ CpCv

γCp

Cv

------=

γ

Theory Fluid Model

FINE™ 3-11

The relation between and is given by

. (3-10)

The values of and are user input. The static pressure is obtained from the conservative varia-

bles through the following relation:

. (3-11)

3-3.2.2 Real Gas

For real gases or more precisely thermally perfect gases, and depend on the temperature T.

The corresponding values can be entered either through a polynomial approximation or through aprofile.

The thermally perfect gas model is based on two equations:

• the perfect gas relation, still valid:

, (3-12)

• the enthalpy equation:

, (3-13)

where T0 is a reference temperature. In practice T0 is set equal to the minimum temperature of thetemperature range specified in the Fluid Model page.

These two equations lead to:

. (3-14)

In the case of a real gas with varying specific heats one can notice that it is not possible to respectthe 2 above equations with a constant value of r, unless the difference (Cp-Cv) does not vary withtemperature.

Two solutions are proposed in EURANUS in order to model real gases:

• Perfect gas with compressibility factor (expert parameter IRGCON=0)

— the equation of state is modified to include a compressibility factor Z:

(3-15)

(3-16)

•Constant r model

r Cp

rγ 1–

γ-----------Cp=

γ Cp

p γ 1–( ) ρEρw( )2

2ρ--------------–=

Cp γ

p ρrT ρ RM-----T= =

h Cp TdT0

T

∫⎝ ⎠⎜ ⎟⎛ ⎞

epρ---+ Cv Td

T0

T

∫⎩ ⎭⎨ ⎬⎧ ⎫

rT+= = =

rT Cp Cv–( ) TdT0

T

∫⎝ ⎠⎜ ⎟⎛ ⎞

=

p ZρrT Zρ RM-----T= =

Z

Cp Cv–( ) TdT0

T

∫⎝ ⎠⎜ ⎟⎛ ⎞

rT--------------------------------------------=

Fluid Model Theory

3-12 FINE™

— the user specifies the gas constant r (expert parameter RGCST). Then Cp is provided and γ

calculated as (expert parameter IRGCON=1).

3-3.2.3 Incompressible Fluid

a) Liquid

The density is user input:

. (3-17)

This implies a decoupling of the mass and momentum conservation equations from the energy con-servation equation, since no term in the mass and momentum equations depends on the tempera-ture.

b) Barotropic Liquid

The density is a user defined function of the pressure:

. (3-18)

The corresponding values can be entered either through a polynomial approximation or through aprofile (see section 3-2.3.5 and section 3-2.3.6).

The particularity of the barotropic liquid formulation is that although the density is not constant, adecoupling of the energy equation is still adopted, exactly as in the full incompressible formulation.

Modification of the treatment of the energy equation

A modification of the treatment of the energy is required in order to account for the density varia-tions. The temperature equation for any type of fluid can be written as:

, (3-19)

where εv is the viscous dissipation term and V is the specific volume (inverse of density). Since for

a barotropic fluid there is a unique relation between the pressure and the density the first term onthe right hand side of the above equation vanishes and the temperature for a barotropic fluidbecomes:

. (3-20)

In addition, since we have from classical thermodynamics that

, (3-21)

the specific heat at constant volume depends only on the temperature cv=cv(T). Note that we also

have as for an incompressible fluid that the specific heats at constant pressure and at constant vol-ume are equal (cv=cp).

The modification of the formulation of the energy for a barotropic fluid can be derived from theabove relations. Since we have for a barotropic fluid:

γCp

Cp r–--------------=

ρ Cst=

ρ f p( )=

ρcvdTdt------ T

∂p∂T------

⎝ ⎠⎛ ⎞

V∇V

⎝ ⎠⎛ ⎞– ∇ k∇T

⎝ ⎠⎛ ⎞ εv+ +=

ρcvdTdt------ ∇ k∇T

⎝ ⎠⎛ ⎞ εv+=

∂cv

∂V-------- T

∂2p

∂T2

--------⎝ ⎠⎜ ⎟⎛ ⎞

V

=

Theory Fluid Model

FINE™ 3-13

. (3-22)

The barotropic relation can be integrated from a reference state to obtain finally

. (3-23)

Compared to an incompressible formulation the energy depends on both pressure and temperature.

3-3.2.4 Condensable Fluid

a) Introduction

The aim of the Condensable Fluid module is the modelling of the real thermodynamic properties ofthe fluid by means of interpolation of the variables from dedicated tables.

The module can be used for a single-phase fluid whose properties are too complex to be treatedwith a perfect or real gas model. It can also be used in order to treat thermodynamic conditions thatare close to the saturation line. Note that the model can be used on the liquid or on the vapour sideof the saturation curve. In case the thermodynamic state lies inside the two-phase region a homoge-neous equilibrium two-phase mixture of vapour and liquid is considered. The hypothesis of an equi-librium mixture is however not valid if the dryness (wetness) fraction exceeds 20%. The modulecan not be used above these fractions, as it completely ignores evaporation-condensation phenom-ena.

For a real fluid the equation of state may be a complicated and usually implicit expression, generat-ing unacceptable computational overhead if the corresponding equations are explicitly introducedin the solver. Similarly when an equilibrium mixture of vapour and droplets (wet steam forinstance) is considered as a single fluid, the calculation from the saturation properties of thermody-namic variables must be done iteratively.

The approach that has been adopted in EURANUS consists of using a series of thermodynamictables, one table being required each time a thermodynamic variable must be deduced from twoother ones. This implies the creation of many tables as input, but presents the advantage that no iter-ative inversion of the tables is done in the solver, with as a consequence a very small additionalCPU time. This additional time corresponds to the one that is needed by the bilinear (or bicubic)interpolation procedures through the tables. In order to optimize the efficiency of these interpola-tions the input tables are always built on basis of a Cartesian mesh in the plane of the input varia-bles (V1,V2) (N1 and N2 values for the variables V1 and V2 respectively).

b) Thermodynamic Tables

Tables are generated based on NUMECA internal tools, based on various sets of well-known equa-tions as described below:

• Benedict-Webb-Rubin equation (usually used with refrigerants),

• Modified Benedict-Webb-Rubin model (selected equation for hydrogen),

• Vander Waals equation.

Single tables are generally used, which means that the tables cover both single-phase and two-phaseregions, as for instance depicted in the figure 3.3.2-4, showing one of the tables used to modelhydrogen. A bilinear interpolation approach is well adapted to these tables, providing an adequatesmoothing of the saturation region. Bicubic interpolation techniques have also been implementedand tested. They provide a higher accuracy for a given number of data points but tend to create spu-

de cvdT T∂p∂T------

⎝ ⎠⎛ ⎞

Vp–

⎝ ⎠⎛ ⎞ dV+ cvdT pdV–= =

e p T,( ) e0 cv Td

T0

T

∫⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

p

ρ2-----∂ρ

∂p------ pd

p0

p

∫+ +=

Fluid Model Theory

3-14 FINE™

rious oscillations in the saturation region. These oscillations can be avoided by adopting separatedtables covering respectively the single and the two-phase regions, these two tables intersectingalong the saturation line.

Five categories of tables are used by the solver

1. Basic tables: p(e,ρ) and T(e,ρ)

The numerical scheme being based on a formulation of the equations on basis of the energy and thedensity, the basic tables are used in order to update the pressure and the temperature after eachupdate of the formulation variables.

2. Entropy tables: p(h,s), ρ(h,s), s(h,p), h(s,p)

The entropy tables are used at the inlet/outlet boundary conditions, and are required in order to cal-culate the total (static) thermodynamic conditions from the static (total) ones.

3. The (p,T) tables: e(p,T) and ρ(p,T)

These tables are required in order to allow the use of the inlet boundary conditions based on totalpressure and temperature. They are also required by the turbomachinery initial solution procedure.

FIGURE 3.3.2-4 Thermodynamic Table: ρ(p,Τ)

4. The viscosity and conductivity tables: µ(e,ρ) and κ(e,ρ)

ρ [kg/m3]

Theory Fluid Model

FINE™ 3-15

The viscosity and conductivity can also be interpolated from tables. If these tables are not presentthe other laws available within the user interface can be used.

5. The saturation table

This table contains the liquid and vapour values of all thermodynamic variables along the saturationline. It is only required if the user activates the dryness fraction output and/or if the inlet boundarycondition based on total enthalpy and dryness fraction is selected.

c) Integration of Thermodynamic Tables in the Solver

Provided that all the input tables are present, the full functionality of the basic solver is accessible.All boundary conditions are available, as well as the initial solution procedures. The numericalschemes are not different, making use of the same acceleration techniques (multigrid, local timestepping, residual smoothing) providing robust and fast convergence to steady state.

The evaluation of the advective, viscous and artificial dissipation fluxes involves the pressure in themomentum and energy equations and the temperature in the energy equation. For a perfect gas bothare easily deduced from the equation of state, the conversion being so rapid that only the pressureand the density are stored and the other variables recalculated from these whenever they are needed.In the condensable fluid module the density, the pressure, the temperature and the energy are storedin order to limit the number of interpolations. Only one interpolation is made in order to deduce thenew values of pressure and temperature after the update of the density and the energy.

The speed of sound which enters the numerical solution process through the spectral radius in thetime step and in the residual smoothing and artificial dissipation coefficients is also required. It caneither be interpolated from a table or computed from the partial derivatives of the p(e,ρ) table:

(3-24)

The Baldwin-Lomax, Spalart-Allmaras and (k,e) turbulence models can be used. The turbulent con-ductivity calculation is based on the usual relation:

(3-25)

The specific heat at constant pressure can either be constant (the value being provided in the userinterface) or deduced from the specific table.

Condensable fluid option is not compatible with the use of cooling/bleed module and/or

upwind schemes for space discretization.

By default, a set of thermodynamic tables for water (steam) is proposed starting FINE™/

Turbo v6.2-9. More details can be found in Appendix D. The installation of the thermo-dynamic tables must be performed as described in section 3-2.3.4

d) Specific Output

Specific outputs can be created by the condensable fluid module:

• enthalpy: static, total absolute and total relative

• dryness fraction (0<x<1), and generalised dryness fraction

c2 ∂p

∂ρ------

⎝ ⎠⎛ ⎞

e

p

ρ2----- ∂p

∂e------

⎝ ⎠⎛ ⎞

ρ+=

κt

µt

Prt--------cp=

Fluid Model Theory

3-16 FINE™

Below is a list of the buttons appearing in the Outputs/Computed Variables page under the thumb-nail Thermodynamics when the condensable gas is selected as fluid model.

FIGURE 3.3.2-5 Condensable Gas Outputs

e) Selection of the Viscosity, Conductivity, and Specific Heat

As mentioned above the viscosity and conductivity can be specified in two-dimensional tables. If itis not the case the other laws can be used (constant, polynomial expression or user profiles).

Unfortunately because of the incomplete integration of the condensable fluid module in the userinterface the selection of these laws is no longer available as soon as a condensable fluid is chosen.

The way to select these laws is the following:

1. create a perfect gas,

2. enter the desired properties for the viscosity and conductivity,

3. save the corresponding computation,

4. change the fluid type by selecting the condensable fluid.

The same procedure applies to the specific heat at constant pressure, that is used in order to derivethe turbulent conductivity from the turbulent viscosity.

n

FINE™ 4-1

CHAPTER 4: Flow Model

4-1 OverviewThe Flow Model page, as displayed in Figure 4.1.0-1, can be used in order to specify several char-acteristics of the flow:

• the time configuration to define time dependence of the equations to solve,

• the mathematical model to:

— choose between viscous and non-viscous flow,

— choose between laminar and turbulent flow,

— activate gravity,

— activate pre-conditioning for low speed flow,

• characteristic scales defining the Reynolds number of the flow,

• reference values of the temperature and pressure in the flow.

This chapter is organised in the following way:

• section 4-2 describes the interface, best practice and theoretical background for unsteady com-putations,

• section 4-3 describes the interface, best practice and theoretical background for the definitionof the mathematical model and especially the available turbulence models,

• section 4-4 provides details on the Reynolds number related information and reference values.

Flow Model Time Configuration

4-2 FINE™

FIGURE 4.1.0-1Flow Model page.

4-2 Time ConfigurationTo perform time independent computations it is sufficient to select Steady. In case time dependenceneeds to be included in the simulation Unsteady should be selected which gives access to additionalparameters for unsteady flow simulation. All parameters in the FINE™ interface related tounsteady computations are described in the following section. For more theoretical information onunsteady flow simulation section 4-2.4 should be consulted.

4-2.1 The Interface for an Unsteady Computation

When selecting Unsteady time configuration in the Flow Model page the following additionalparameters become accessible in the FINE™ interface:

a) Rotating Machinery

On the Rotating Machinery page, under the Rotor-Stator thumbnail, the domain scaling rotor/statorinteraction is activated. Furthermore, the Phase Lagged capability can be activated on the top ofthe page. When activated, the phase-lagged rotor/stator interaction will be applied.

Finally in both cases, the Number of Angular Positions (in one periodicity) is requested in the Com-putation Steering/Control Variables page instead of the time step.

b) Time Dependent Boundary Conditions

On the Boundary Conditions page the boundary conditions at inlet and outlet may be defined as afunction of time. To define a time dependent boundary condition go to the Boundary Conditionspage and change the default (Constant Value) with the pull down menu to:

Time Configuration Flow Model

FINE™ 4-3

• fct(time) to define a constant value in space but varying in time. Click on the profile data but-

ton ( ) to activate the Profile Manager.

• fct(space-time) to define a space and time dependent variation of the boundary conditionvalue. In this case a one-dimensional space profile has to be defined. The time profile toimpose is a scaling factor that is applied to the space profile. This means that the profile inspace is only varying in time with a certain scaling factor.

Another way to define an inlet/outlet unsteady boundary condition is to set an absolute rotationalspeed to the boundary condition by activating Rotating Boundary Condition and specifying therotational speed in Rotational Speed Unsteady respectively under the INLET and OUTLET thumb-nails, and to set the periodicity of the signal entered in FINE™ through the expert parameterNPERBC.

It is important to notice that EURANUS allows only one rotation speed (combined

with a zero rotation speed).

It is important that the inlet/outlet unsteady boundary condition circumferential profile

is imposed on a range covering the initial blade passage location and the blade passagelocation after one period of the signal.

Example

The blade channel is initially (t0) located at θ1,θ2 and will after one period of the signal (T) belocated at θ3,θ4. Τhe circumferential signal has thus to be imposed from at least θ1 to θ4.

When Rotating Boundary Condition is activated, the time step is no longer specified by the physicaltime step in the FINE™ interface in the Computation Steering/Control Variables page. Instead thetime step is imposed by defining the Number Of Angular Positions.

c) Phase Lagged

When activating Rotating Boundary Condition in the Boundary Conditions page to rotate the refer-ence system of the boundary condition at the inlet and/or outlet, the period of the boundary condi-tion should be compared to the blade passing period. In the case of a single blade row calculationwith the period of the varying inlet or outlet boundary conditions different from the blade passingperiod, the Phase Lagged option should be activated in the Configuration/Rotating Machinery page

v2.2

θ0 2ππ

t0

T

t0+T

v2.2

θ0 2ππ

t0

T

t0+T

θ1 θ2 θ3 θ4


4-4 FINE™

and the periodicity of the signal entered in FINE™ has to be specified through the expert parameterNPERBC. See section 4-2.3.2 and section 4-2.4.5 for more detailed information on the phaselagged boundary condition.

In the case of phase lagged approach, the Number Of Angular Positions is the number

of time iterations per full machine rotation.

It is important to notice that EURANUS allows only one rotation speed (combined

with a zero rotation speed).


is imposed on a range covering the initial blade passage location and the blade passagelocation after one period of the signal (see example on page 4-3).

d) Control Variables

On the Computation Steering/Control Variables page the following parameters appear when select-ing an unsteady time configuration non-turbomachine:

• Physical Time Step: in general cases the user specifies the magnitude of the physical time stepin seconds. This time step is constant through the whole calculation. In cases of turbomachin-ery applications where Rotor/Stator interfaces are detected or Rotating Boundary Conditionactivated, the Number Of Angular Positions is requested instead of the time step as describedin section 4-2.2.

•Number Of Physical Time Steps: to define the number of time steps to perform. In cases of tur-bomachinery applications where Rotor/Stator interfaces are detected or Rotating BoundaryCondition activated, the Number of Periods can also be specified.

• Save Solution Every: allows to save the solution after a constant number of time steps. Bydefault the solution is overwritten in the same output files. In order to keep the successiveunsteady solutions, the multiple output (Multiple Files) option has to be activated.

•Outputs For Visualization:

— Output For Visualization/At end only and Multiple Files: multiple set of output files savedfor restart of the unsteady computation and visualization in CFView™ only available at theend of the computation.

— Output For Visualization/At end only and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ only available at the endof the computation.

— Output For Visualization/Intermediate and Multiple Files: multiple set of output files savedfor restart of the unsteady computation and visualization in CFView™ during the computa-tion.

— Output For Visualization/Intermediate and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ during the computation.

•Number Of Steady Iterations: the number of iterations to initialize the unsteady computation.Such initialization is performed with the steady state algorithm, using fixed geometry andmesh as well as constant inlet/outlet boundary conditions. In case this initialization procedureis used the steady state iterations can even be preceeded by a full multigrid process allowing arapid initialization of the flow (see section 9-4.3).

• Save Steady Solution Every: the number of iterations at which the solution of steady initializa-tion is saved

By default only one output file is created. For the generation of multiple output files,


FINE™ 4-5

Multiple Files option has to be selected.

e) Second Order Accurate in Time

EURANUS performs second order accurate simulations in time. In order to allow to do a secondorder restart it is necessary to select Multiple Files in the Computation Steering/Control Variablespage. When Multiple Files option is selected, in unsteady calculations the ’.cfv’ and ’.cgns’ aresaved at the requested time steps and only a part of the ’.cgns’ file is saved for the previous timestep. When requesting a restart of an unsteady computation EURANUS will automatically find thissecond solution file to use. If this file is not found, a first order scheme is used for the first time step.

Note that only limited output is saved when selecting Multiple Files with Output For

Visualization/At end only and a solution is requested every x time steps, only solutionfiles with extension ’.cgns’ are written every x time steps instead of the full set of solu-tion files. This limited output still allows to restart from this solution (see section 15-2).

4-2.2 Expert Parameters for Unsteady Computations

4-2.2.1 Numerical Model in Expert User Mode

On the Numerical Model page, two new parameters appear in the user expert mode when selectingthe Dual time stepping technique. They are the control variables for the inner iterations of this lasttechnique. For each physical time step a certain amount of iterations is performed in pseudo timeleading to a converged solution independent of the pseudo time (see section 4-2.4 for detailedinformation).

•Convergence criteria of the inner iterations (orders of magnitude of reduction). The inner iter-ations are stopped if the reduction of the residuals reaches the specified value.

•Maximum number of inner iterations: it allows to define the maximum number of iterations toperform for each time step. In general the default of 100 iterations per time step is sufficient.The inner iterations is automatically stopped after this maximum number of iterations if theconvergence criteria has not been satisfied.

4-2.2.2 List of Non-interfaced Expert Parameters

The following expert parameter related to unsteady computations are accessible on the ControlVariables page by selecting the Expert Mode. Please consult section 4-2.4 for more theoreticaldetail on this parameter.

ICYOUT can be equal to 0 or 1 (the default):

• ICYOUT=0: name of output changes with suffix _t#iter,

• ICYOUT=1(default): each solution is overwritten every cycle (every NOFROT time steps).

IFNMB can be equal to 0 (the default) or 1:

• IFNMB=0 (default): to keep all PERNM boundaries,

• IFNMB=1(default): to transform all PERNM boundaries into periodic full non matching ones.

NPERBC can be equal to 1 (the default) or integer value:

•NPERBC=1 (default): when the inlet/outlet unsteady boundary condition is a rotating circum-ferential profile (activating Rotating Boundary Condition and specifying the rotational speedin Rotational Speed Unsteady respectively under the INLET and OUTLET thumbnails) and theboundary condition is entered in the FINE™ interface for the full range [0,2π].


4-6 FINE™

•NPERBC= N: when the inlet/outlet unsteady boundary condition is a rotating circumferentialprofile (activating Rotating Boundary Condition and specifying the rotational speed in Rota-tional Speed Unsteady respectively under the INLET and OUTLET thumbnails) and the bound-ary condition is entered in the FINE™ interface for part of the range [0,2π/N] covering one ormultiple periods of the signal.

RELPHL =0.5 0.5 if necessary, under-relaxation factor can be applied on Periodic and R/S bound-ary conditions by reducing the two values of the expert parameter for respectively the periodic andthe R/S boundary conditions.

NPLOUT =0 (by default) enables to visualize multiple non periodic passage output in CFView™by loading the corresponding ’.cfv’ file.

4-2.3 Best Practice on Time Accurate Computations

To perform time accurate computations, general advice is provided in this section. For advice onhow to perform a time accurate turbomachinery calculation including rotor/stator interactions seesection 5-4.3.

4-2.3.1 General Project Set-up for Time Accurate Computations

1. Create a new project,

2. Select the fluid to use in the Fluid Model page,

3. Select Unsteady time configuration in the FINE™ Flow Model page and set all the other param-eters on this page in the same way as for a steady computations as detailed in section 4-3 andsection 4-4.

4. On the Rotating Machinery page set all the parameters (Phase-Lagged option) in the same wayas for a steady computation as described in Chapter 5.

5. Set the steady or unsteady boundary conditions. For more detail on time dependent boundaryconditions and phase lagged approach see section 4-2.3.2.

6. Concerning the initial solution for unsteady computations there are three possibilities:

— to start from a steady solution,

— to start from an unsteady solution,

— to use constant values, initial solution for turbomachinery or throughflow as an initial guesswith or without steady state initialisation.

For more detail on these initalisation procedures see section 4-2.3.3.

7. All outputs available in steady mode are also available in unsteady mode (see Chapter 11).

8. On the Control Variables page set:

— the physical time step or number of angular position (see section 4-2.3.4) and the number oftime steps or periods,

— the amount of output files (see section 4-2.3.5),

— amount of iterations in steady state initialisation (see section 4-2.3.3).

4-2.3.2 Time Dependent Boundary Conditions

Unsteadiness can be generated by means of time varying inlet/outlet boundary conditions. Two dif-ferent situations can be encountered:

1. The time variation is imposed as an amplitude factor of the space variation,

2. The time variation is imposed by rotating the inlet and/or outlet boundary condition. The abso-lute rotation speed of the boundary condition(s) is imposed in the Boundary Conditions page.


FINE™ 4-7

Depending on the periodicity of the boundary condition the phase lagged approach needs to beused:

1. The circumferential distribution of the imposed inlet/outlet conditions has the same period asthe blade row. The calculation of such time-dependent flow does not require to activate phaselagged approach.

2. The period of the time varying inlet/outlet boundary condition is different from the blade pass-ing period. The calculation of such time-dependent flow requires to activate the Phase Laggedapproach at the top of the Rotating Machinery page.

A circumferential profile must be entered in the FINE™ interface for the full range

[0,2π] and NPERBC = 1 or for part of the range [0,2π/N] covering one or multiple peri-ods of the signal and NPERBC = N. The profile should be based either on θ, z-θ or r-θ.The profile is automatically rotating at the speed of rotation that is specified through therotation speed specified in the Boundary Conditions page.


is imposed on a range covering the initial blade passage location and the blade passagelocation after one period of the signal (see example on page 4-3).

A profile as a function of r-θ must be structured. The profiles must be given at stations

of constant θ for increasing r. Also θ must be increasing going from one station to thenext in the file.

4-2.3.3 Initialisation Procedure

a) Start From a Steady Solution

In most cases it is first required to perform a preliminary steady state computation. The objectivemight be to ensure that the problem naturally depicts the unsteady behaviour and/or to get an ade-quate guess solution before going towards time accurate calculations depicting periodic behaviours.The steady state initialisation may be done in a separate computation, performed in steady modeusing a time-marching approach based on local time stepping by default. The time accurate calcula-tion is then started using this solution as an initial solution. To set up the time accurate calculationin this case follow the steps 1 to 8 as detailed in section 4-2.3.1. In step 6 select in the Initial Solu-tion page from file and select the solution of the steady computation. In step 8 (section 4-2.3.1) it ispossible to select additional steady state initialisation in the Control Variables page (see paragraphc).

b) Start From Time Accurate Solution

It is possible to start from a previously performed time accurate solution. For general informationabout starting from an initial solution see section 10-4.

In order to allow to do a second order accurate restart it is necessary that Multiple Files option isselected in the Control Variables page in the Output Files parameters. When the option is activatedin unsteady calculations the ’.cfv’ and ’.cgns’ are saved at the requested time steps and only a partof the ’.cgns’ file is saved for the previous time step. When requesting a restart of an unsteady com-putation EURANUS will automatically find this second solution file to use. If this file is not found,a first order scheme is used for the first time step.


4-8 FINE™

c) Steady State Initialisation in Unsteady Computation

The steady state initialisation is automatically performed before starting the time accurate computa-tion (that means within the same computation). To perform a steady state initialisation in anunsteady computation, the number of iterations has to be entered in Steady Initialization parameterson the Control Variables page.

4-2.3.4 Physical Time Step

The physical time step should be entered on the Control Variables page. The time step to choosedepends on the expected frequency of the flow phenomena to capture. In general it is recommendedto compute at least 10 to 20 time steps per period.

When working with turbomachines, using a Number Of Angular Positions of 10 points per bladepassage is giving a coarse but reasonable result. To have a more accurate (but more CPU consum-ing) result choose 20 to 30 points per passage (see chapter 5 for more details).

Under the phase lagged option, the Number Of Angular Positions is the amount of stations per 2πand therefore it should be 10 to 20 times the number of blades (see chapter 5 for more details).

Example 1: single blade row calculation involving phase-lagged boundary conditions

When working with N1 blades turbomachine and a periodic signal at inlet presenting a periodicityof N2 and plotted on [0,2π/N2] range.

•Number Of Angular Positions = i x N1 where i is an integer imposed so that (i x N1) is around30.

•Number Of Time Steps = j x (Number Of Angular Positions) where j is the number of full rev-olution. Usually j is set to 20.

•NPERBC = period of the signal (N2)

(Number Of Angular Positions)x(NPERBC) corresponds to the number of time steps per full revo-lution (2π)

Example 2: complete row calculation involving sliding boundary conditions

When working with N1 blades turbomachine and a periodic signal at inlet presenting a period of N2and plotted on [0,2π] range.

•Number Of Angular Positions = i x N1 x N2 where i is an integer so that (i x N1) and (i x N2)are around 30.

•Number Of Time Steps = j x (Number Of Angular Positions) where j is the number of full rev-olution. Usually j is set to 20.

•NPERBC = 1

(Number Of Angular Positions)x(NPERBC) corresponds to the number of time steps per full revo-lution (2π)

4-2.3.5 Amount of Output

By default only one set of output files is created that is periodically overwritten. Activate MultipleFiles in the Control Variables page to create a set of output files for each time step that an outputwill occur (that depends on the Save solution Every entry available in the Control Variables page).

’.cgns’ files will be generated. The files are automatically renamed accordingly to the

time step computed using the suffix ’_t#.’ that is thus determining the #th physical timestep. The corresponding ’.cfv’ files can be read in CFView™ only if in addition of theMultiple Files the Intermediate has been selected in the Output For Visualization option.


FINE™ 4-9

Note that the ’.run’ and ’.cgns’ files (without ’_t#.’ suffix) are linked to the initial state of calcula-tion.

4-2.4 Theoretical Aspects for Unsteady Computations

Unsteady flow phenomena may arise intrinsically as for example in separated flows, wake flows or may becaused by an external time dependent driving force as for example an oscillating structure. In any case an effi-cient time-accurate solver has to be employed to obtain time dependent solutions within a reasonable compu-tational time.

At present, the most effective approach is called the dual time stepping approach proposed by Jameson,(1991) and it consist in adding to the time dependent Navier-Stokes equations pseudo-time derivative terms.At each physical time step, a steady state problem is solved in a pseudo time and all available accelerationtechniques such as multigrid, local time stepping and implicit residual smoothing can be applied. Thisapproach has been used for compressible flow simulations by several authors, Arnone, (1995), Melson et al.,(1993), Pierce et al., (1997), Eliasson et al., (1995) and has shown to be an important improvement over theclassical global time stepping approach.

4-2.4.1 Standard Time Accurate Solver (Non-preconditioned Formulation)

For unsteady flow simulations the Reynolds-Averaged Navier-Stokes equations are expressed as:

, (4-1)

where t is the physical time and τ is pseudo time, U is the solution vector of the conservative variables, V is

the volume, are the conservative fluxes and ST are the source terms. The time discretization of the deriva-tive of the conservative variables with respect to the physical time t is made to meet the desired accuracy intime. Two formulations are available:

First order upwind in time:

. (4-2)

This first order scheme is used only for the first time step of the unsteady computation except for a restartwhen the two previous solutions are available (see section 4-2.2).

Second order upwind in time:

. (4-3)

All other terms in Eq. 4-1 are computed at time n+1. The equation is then treated as a modified steady stateproblem in the pseudo time τ:

. (4-4)

Denoting by R the residual corresponding to the steady state problem, the new residual used for time accuratecomputations RTA is given by:

. (4-5)

∂∂t---- U Vd∫

V

∫∫∂U∂τ------- Vd∫

V

∫∫ F Sd⋅S

∫∫+ + ST Vd∫V

∫∫=

F

∂∂t---- U Vd∫

V

∫∫⎝ ⎠⎜ ⎟⎛ ⎞ n 1+

Un 1+ Vn 1+ UnVn–∆t

---------------------------------------------=

∂∂t---- U Vd∫

V

∫∫⎝ ⎠⎜ ⎟⎛ ⎞ n 1+

1.5Un 1+

Vn 1+ 2U

nV

n– 0.5Un 1–

Vn 1–+

∆t------------------------------------------------------------------------------------------------=

∂U∂τ-------V

n 1+RTA U( )+ 0=

RTA U( ) R U( )β1UV

n 1+ β0UnV

n β 1– Un 1–

Vn 1–+ +

∆t----------------------------------------------------------------------------------------+=


4-10 FINE™

For the second order upwind scheme we have β1=1.5, β0=-2, β-1=0.5 while for the first order

scheme we have β1=1, β0=-1, β-1=0. The new residual contains terms that depend only on the solu-tion of previous time steps, all other terms depend on the current solution vector U.

When steady state is reached at each physical time step, the left hand side of Eq. 4-5 tends to zeroand the time accurate solution is obtained.

a) The Time Stepping

When integrating equation Eq. 4-4 in the pseudo time τ, it is recommended, Arnone et al. (1995),

Pierce and Alonso (1997) to treat the term implicitly. This is obtained by

developing the solution vector U in a Taylor expansion:

. (4-6)

Putting Eq. 4-6 into Eq. 4-5, a modified pseudo time step is introduced:

. (4-7)

The pseudo time step is modified by an additional term containing the physical time step. This termbecomes dominant if the physical time step is significantly smaller than the pseudo time step. Thissituation does not often happen since the physical time step is taken as large as possible. However,in the far field where mesh dimensions are increased the pseudo time step might reach high valuesand the contribution of the physical time step will have a stabilizing effect there.

The physical time step ∆t is limited by the level of desired accuracy. For periodic flows the timestep is usually taken a fraction lying between 1/20-1/40 of the expected period.

b) Initial Solution at Each Physical Time Step

The simplest way to obtain an initial solution on the next time level is to choose the latest availablesolution:

(4-8)

Vn+1 being the cell volume evaluated at the next time step. The volume evaluation at each physicaltime step is only performed for moving meshes.

In Jameson (1991) it is suggested to take as initial solution an extrapolated solution from the previ-ous time steps. This is obtained by a Taylor expansion:

(4-9)

This expression leads to the following initial solution:

. (4-10)

In practice however, using this expression does not show any convergence enhancement for thenext time step compared to the convergence obtained with Eq. 4-8. Eq. 4-8 is therefore imple-mented.

β1Un 1+

Vn 1+( ) ∆t( )⁄

Ul 1+ Ul ∂U∂τ-------∆τ+=

∆τmod∆τ

1 β1∆τ∆t------+

----------------------=

Uinitialn 1+ Vn 1+ UnVn=

U V⋅( )n 1+U V⋅( )n ∂ U V⋅( )n

∂t-----------------------∆t O ∆t

2( )+ +=

Uinitialn 1+

Vn 1+

U V⋅( )n β1 U V⋅( )n β0 U V⋅( )n 1– β 1– U V⋅( )n 2–+ + +=


FINE™ 4-11

In the particular case of turbomachinery applications a discretization in time of the blade passingperiod is performed by the unsteady algorithm, and once one full period has been accomplished bythe algorithm, the solution may be initialised using the solution obtained at the same position at theprevious rotation. This requires the storage of all the intermediate solutions and the experience hasshown that it did not bring significant convergence improvements. The approach has however beenimplemented in EURANUS, and can be activated by setting the expert parameter PREROT to 1.

4-2.4.2 Density Based Time Accurate Solver and Preconditioning

Application of the dual time stepping approach along with low speed preconditioning to variableand constant density flows is presented in Hakimi, (1997). For unsteady flow simulations the pre-conditioned Reynolds-Averaged Navier-Stokes equations are expressed as:

, (4-11)

where t is the physical time and τ is pseudo time, U is the solution vector of the conservative varia-bles, Q is the solution vector of chosen dependent variables, Γ is the preconditioning matrix, V is

the volume, are the conservative fluxes and ST are the source terms. For all fluids we have:

. (4-12)

The time discretization of the derivative of the conservative variables with respect to the physicaltime t is made to meet the desired accuracy in time. The equation is then treated as a modifiedsteady state problem in the pseudo time τ:

, (4-13)

with

. (4-14)

The residual RTA in Eq. 4-14 being the preconditioned residual. The new residual contains terms

that depend only on the solution of previous time steps, all other terms depend on the current solu-tion vector Q. When steady state is reached at each physical time step, the left hand side tends tozero and the time accurate solution is obtained

a) The Time Stepping

When integrating Eq. 4-14 in the pseudo time τ, we treat the term implicitly.

This is obtained by developing the solution vector U in a Taylor expansion:

(4-15)

Putting this relation into equations Eq. 4-13 we obtain the following updating procedure:

(4-16)

where I is the identity matrix. The updating procedure has been modified and includes now the timesteps ratios, leading to a stabilizing effect.

∂∂t---- U Vd∫

V

∫∫ Γ 1– ∂Q∂τ------- Vd∫

V

∫∫ F Sd⋅S

∫∫+ + ST Vd∫V

∫∫=

F

Q pg u v w E, g ρk ρε Yi, , , , , ,( )=

∂Q∂τ-------V

n 1+RTA Q( )+ 0=

RTA Q( ) R Q( )Γ β1U Q( )V

n 1+ β0UnV

n β 1– Un 1–

Vn 1–+ +( )

∆t-----------------------------------------------------------------------------------------------------------+=

Γβ1UVn 1+( ) ∆t( )⁄

Ul 1+

Ul ∂U

∂Q-------∂Q

∂τ-------∆τ+=

∆Q∆τ--------V

n 1+I Γβ1

∂U∂Q-------∆τ

∆t------+

⎝ ⎠⎛ ⎞–

1–

RTA

U( )=


4-12 FINE™

b) Initial Solution at Each Physical Time Step

The initial solution on the next time level is the latest available solution:

(4-17)

Since the dependent variables are Q, these variables have to be computed at the beginning of eachphysical time step from the conservative variables U.

4-2.4.3 Unsteady Inlet and Outlet Boundary Conditions

For a steady state flow problem, to any quantity imposed at the inlet section or at the outlet sectioncorresponds a space distribution on the surface that is uniform, one dimensional (x,y,z,r,θ,z) or twodimensional (xy,xz,yz,rθ,rz,θz). These distributions are written in a file and the code performs a lin-ear interpolation to obtain the desired quantity on the cell face centre of the section.

For an unsteady flow problem, the inlet and outlet imposed quantities may vary in time. Two possi-bilities are available within EURANUS:

1) user specified time function

For a fixed system of reference with time dependent boundary conditions, the boundary conditionsfor a quantity q is given by:

q(t)=qo f(t),

where qo is a space distribution (uniform, 1D or 2D) and f(t) is a scaling function read from a file:(tn, f(tn)).

2) rotation of the reference system

In turbomachinery the relative motion between stator and rotor blades induces an unsteadiness, dueto the fact that for instance in a turbine stage the flow conditions that a rotor sees at the inlet aretime dependent, whereas these conditions would be fixed for a fixed reference system.

If one of the imposed variable along the inlet or the outlet is not uniformly distributed in the tangen-tial direction in the fixed space the inlet/outlet section sees a boundary condition that changes intime. In this case, the space distribution of the imposed quantity being defined by qo (1D or 2D),

each cell face centre coordinate is rotated by an angle at each time step, before

performing a new space interpolation.

The activation of this procedure along the inlet and/or the outlet is obtained by activating RotatingBoundary Condition in the Boundary Conditions page and specifying the rotational speed in Rota-tional Speed Unsteady respectively under the INLET and OUTLET thumbnails.

The use of a Rotating Boundary Condition imposes a limitation for the specified pro-

files at the inlet and outlet. Only θ profiles (f(θ), f(r-θ) or f(θ-z)) are allowed and the 2Dspace profile f(r-θ) must be structured (profile f(r) with the same number of points fordifferent θ)

4-2.4.4 Unsteady Turbomachinery Calculations

The relative motion between successive blade rows together with boundary layers, wakes, shocksand tip leakage jets are the major sources of unsteadiness that may affect a turbomachinery flowlocally or as it travels through the next rows. All these interactions are strongly coupled, increasing

Uinitialn 1+

Vn 1+

UnV

n=

Qinitialn 1+ Q Uinitial

n 1+( )=

∆θ Ωrelative ∆t•=


FINE™ 4-13

in magnitude as the gap between successive blade rows is decreased, and affecting consequently theperformance of the machine.

Three types of unsteady simulations are available within EURANUS:

• single blade row calculation, periodic boundary conditions: the unsteadiness is created by atime varying inlet or outlet conditions. The circumferential distribution of the imposed inlet/outlet conditions has the same periodicity as the blade row, which permits to avoid the intro-duction of any time periodicity in the periodic boundary conditions. The activation of thisunsteady mode requires to activate Rotating Boundary Condition in the Boundary Conditionspage and specifying the rotational speed in Rotational Speed Unsteady respectively under theINLET and OUTLET thumbnails.

• single blade row calculation, phase-lagged periodic boundary conditions: contrary to the previ-ous case, the period of the varying inlet or outlet boundary conditions is different from theblade passing period, and phase-lagged periodic boundary conditions have to be used. To acti-vate this mode, on the Rotating Machinery page, the Phase Lagged capability has to be acti-vated on the top of the page.

•multi-stage calculations with unsteady rotor/stator interactions: the domain scaling or phaselagged approach are used within EURANUS. The theoretical background and implementationof this approach are presented in the chapter 5.

4-2.4.5 Phase Lagged Periodicity Boundary Conditions

If the inlet and/or outlet boundary conditions present a pitchwise variation with a period differentfrom the blade passing period, a time periodicity has to be introduced along the periodic boundaryconditions upstream and downstream of the blade passage, leading to the so-called "phase-lagged"boundary conditions (Fatsis, Pierret and Van den Braembussche, 1995).

n=

FIGURE 4.2.4-2Illustration of a typical pump with periodicity conditions

Y

Z X

AB

C

D

E

FG

H

n ∆ t

Ω

NumberOfAngularPositionsNumberOfBlades

--------------------------------------------------------------------------- NOFROTNBLADES---------------------------=


4-14 FINE™

Let us consider that the computational domain is the one defined by ABCDHGFE as shown inFigure 4.2.4-2, where the solid blade walls correspond to the segments BC and FG. Under the con-text of phase-lagged boundary conditions, the scalar variables (density, pressure, turbulent viscos-ity,...)on AB, EF and CD, GH are not equal and the velocity vectors are not related by a simplerotation operator, since the flow is not periodic.

Boundary conditions for segments EF and GH:

Since, in the absolute system of reference, the actual positions of segments EF and GH correspondrespectively to the positions of segments AB and CD n time steps earlier, the variables at time t onsegments EF, GH are obtained from those on segments AB, CD at time t- n ∆t:

, (4-18)

Therefore, the flow variables of segments AB and CD need to be stored for the n preceding timesteps.

Boundary conditions for segments AB and CD:

In the absolute system of reference, the actual positions of segments AB and CD correspond respec-

tively to the positions of segments EF and GH, time steps earlier, with ϕ the angle

between D and H. The variables at time t on segments AB, CD are obtained from those on segmentsEF, GH using:

.. (4-19)

Therefore, the flow variables of segments EF and GH need to be stored for the pre-

ceding time steps.

Since at the beginning of the computation no solution is available at the previous time steps, stand-ard periodic boundary conditions are applied at the first iteration and then frozen during n timesteps for segments EF, GH and (NOFROT-n) time steps for segments AB and CD. Although thisprocedure is the simplest, it might contribute to slow down the convergence to a periodic state.

The current implementation of the phase-lagged boundary conditions only allows

matching and full non matching periodic boundary conditions. This option can be usedwith non matching periodic boundary conditions (PERNMB) if they are automaticallytransformed into full non matching boundary by setting the expert parameter IFNMB to1.

4-2.4.6 Choice of the Physical Time Step

For a general case the user specifies the amplitude of the physical time step. This time step is con-stant through the whole calculation.

In the case of turbomachinery applications the user defines the time step in another manner, byimposing the Number Of Angular Positions that the unsteady algorithm should solve within oneperiod. The time to accomplish one full rotation being equal to 2π /Ω (Ω the rotation speed of thedomain as defined in the Rotating Machinery page), the time step is computed using the relations:

, (4-20)

UGH t( ) UCD t n ∆t⋅( )–( )=

2π ϕ–NOFROT n–( )

--------------------------------------

UCD t( ) UGH t2π ϕ–

NOFROT n–( )--------------------------------------∆t–

⎝ ⎠⎛ ⎞=

2π ϕ–NOFROT n–( )

--------------------------------------

∆t2π

Ω Nperiods NOFROT⋅ ⋅---------------------------------------------------------------=

Mathematical Model Flow Model

FINE™ 4-15

where Nperiods is the number of blades, or in case of phase lagged option:

. (4-21)

4-2.4.7 References

Arnone, A., Liou, M. and Povinelli, L., 1995, " Integration of Navier-Stokes Equations using dualtime stepping and multigrid method:, AIAA-Journal, Vol. 33, No. 6, 1995, pp. 985-990.

Eliasson, P., and Nordstrom, J., 1995, " The development of an unsteady solver for moving meshes", FFA/TN 1995-39.

Fatsis, A., Pierret, S., Van den Braembussche, R., 1995, " 3D unsteady flow and forces in centrifu-gal impellers with circumferential distortion of the outlet static pressure ", ASME, 95-GT-33.

Hakimi N. (1997) ’Preconditioning methods for time dependent Navier-Stokes equations’, PhDThesis, Dept of Fluid Mechanics, Vrije Universiteit Brussel.

Hirsch Ch. (1990) 'Numerical Computation of Internal and External Flows. Volume 2', John Wiley& Sons.

Jameson, A., 1991, "Time dependent calculations using multigrid, with applications to unsteadyflows past airfoils and wings", AIAA-Paper 91-1596.

Melson, N.D., Sanetrik, M.D., Atkins, H.L., 1993, "Time accurate Navier-Stokes calculations withmultigrid acceleration", AIAA paper, pp. 1041-1042.

Pierce, N.A., Alonso, J.J., 1997,"A preconditioned implicit multigrid algorithm for parallel compu-tation of unsteady aeroelastic compressible flows:, AIAA-Paper 97-0444.

4-3 Mathematical Model

4-3.1 Euler

When selecting Euler on the Flow Model page an inviscid calculation will be performed. In such acase all solid walls are considered as Euler walls and the (non-zero) velocity is tangential to thewall. Euler walls do not require any boundary conditions (in contrast to viscous walls).

Since the Reynolds number has no meaning for Euler calculations this number is not displayedwhen Euler flow is selected.

See section 8-5.3 for more detailed information on the boundary conditions.

4-3.2 Laminar Navier-Stokes

When selecting Laminar Navier-Stokes equations the only effect is on the thermodynamic propertyof the flow. The viscosity will be the laminar kinematic viscosity and thus does not contain any tur-bulent component.

∆t2πΩ------ 1

NOFROT-------------------------=

Flow Model Mathematical Model

4-16 FINE™

4-3.3 Turbulent Navier-Stokes

When selecting Turbulent Navier-Stokes equations, turbulence is taken into account depending on thechosen turbulence model. In FINE™ several turbulence models are available:

•Baldwin-Lomax,

• Spalart-Allmaras,

•Chien (low Reynolds number k-ε),

• Extended wall function k-ε,

• Launder-Sharma (low Reynolds number k-ε),

•Yang-Shih (low Reynolds number k-ε),

•Non Linear k-ε (high Reynolds number),

•Non Linear k-ε (low Reynolds number).

In this section the parameters in the interface related to the turbulence models are described. In section4-3.6 more theoretical information is provided on those models.

For the Baldwin-Lomax model, algebraic formula are used to compute the turbulent data and conse-quently no additional input are needed in the interface.

For the Spalart-Allmaras model and the k-e models, additional equations are solved and consequentlysuitable initial and boundaries conditions must be defined in the interface.

a) Boundary Condition

Inlet

• Spalart-Allmaras: the value of the turbulent viscosity must be defined. It might be constant orvarying in space and time. The user can specify the time or spatial variation through the profilemanager.

• k-ε models: the values of the turbulent quantities (k and ε) must be defined. They might be con-stant or vary in space and time. The user can specify the time or spatial variations through theprofile manager.

b) Initial Condition

• Spalart-Allmaras: a constant initial value of the turbulent viscosity is defined through the expertparameter NUTFRE on the Control Variables page under the Expert Mode.

• k-ε models: the initial values of the turbulent quantities (k and ε) are specified by the user if con-stant or turbomachinery initial solutions are chosen.

4-3.4 Expert Parameters for Turbulence Modelling

4-3.4.1 Interfaced Expert Parameters

In expert mode additional parameters related to turbulence modelling are available when using the k-εmodels with wall functions (extended wall function k-ε and high Reynolds non linear k-ε models). Forthese turbulence models the wall type can be defined as smooth or rough:

• For a smooth solid wall (default) only the von Karman constant and Bo have to be specified (κand B on page 35 of this chapter).

•When selecting a rough solid wall two additional parameters have to be specified: the equivalentroughness height and the zero-displacement plane (k0 and d0, see page 35 of this chapter).


FINE™ 4-17

4-3.4.2 Non-interfaced Expert Parameters

All non-interfaced expert parameters related to the turbulence models are accessible on the ControlVariables page by selecting the Expert Mode. Please consult section 4-3.6 for more theoreticaldetail on those parameters.

Calculation of the wall distances

NREPET: repetition of the computed domain to find the closest wall (default value =1).

NSUBM: maximum number of subdomains a domain is split into (default value = 1000).

NTUPTC: number of patches whose sub-patches will be searched (default value = 20).

RTOL: maximum angle allowed between two normals of a patch (default value = 1.8).

When problems occur during the wall distance calculation (wall distance not equal to

0 on the wall), we recommend to rise the value of NTUPTC to 40. Furthermore, RTOLhas to be decreased to 0.9 if the wall distance gradient is not smooth.

Baldwin-Lomax

IATFRZ: multigrid parameter

= 0: apply the turbulence model on all grid levels,

= 1: freeze turbulence on coarser grids (default),

= 2: freeze turbulence on all grids (see ITFRZ and RESFRZ).

ITFRZ: freeze the turbulent viscosity field if the fine grid iteration exceeds ITFRZ (default value =1000000).

RESFRZ: freeze the turbulent viscosity field if the fine grid residual is lower than RESFRZ (defaultvalue = -12).

Spalart-Allmaras

MUCLIP: controls the maximum allowable value for the ratio MUT/MU (default value = 5000).

NUTFRE: constant to initialize the turbulent viscosity field (default value = 0.0003).

k-ε models

CMU: constant for the k-ε model in Eq. 4-59 (default value = 0.09).

CE1: constant for the k-ε model in Eq. 4-57 (default value = 1.44 automatically set to 1.35 for theChien k-ε model).

CE2: constant for the k-ε model in Eq. 4-57 (default value = 1.92 automatically set to 1.8 for theChien k-ε model).

SIGK: constant for the k-ε model in Eq. 4-56 (default value = 1.).

SIGE: constant for the k-ε model in Eq. 4-57 (default value = 1.3).

PRT: constant for the k-ε model - the turbulent Prandtl Number (default value = 1.).

INEWKE: defines the high Reynolds k-ε model when k-epsilon (Extended Wall Function) isselected:

= 0: standard formulation of the wall functions,

= 10 (default): mesh independent formulation of the wall functions (extended wall functions).

ICOPKE: (= 1) applies the pressure gradient-velocity model to take into account a compressibilitycorrection. It is useful only for high Mach number flows (M>3). The default value is 0.


4-18 FINE™

SIGRO: constant in the k-ε model when ICOPKE =1 in Eq. 4-70 and Eq. 4-72 (default value = 0.5).

C3: constant for the k-ε model when ICOPKE = 1 in Eq. 4-72 (default value = 2.).

ICODKE: parameter to active the compressible dissipation,

= 0 (default): no compressible dissipation,

= 1: Sarkar model for compressible dissipation (Eq. 4-75),

= 2: Nichols model for compressible dissipation (Eq. 4-77).

ALF: constant of Sarkar model for compressible dissipation when ICODKE=1 (default = 0.5).

CP1: constant of Nichols model for compressible dissipation when ICODKE=2 (default value = 4.).

MAVRES: allows to control the update of k and ε (default = 0.95),

> 0: according to the restrictions defined by Eq. 4-78 and Eq. 4-79,

= 0: according to the restriction defined by Eq. 4-78,

< 0: according to the restriction defined by Eq. 4-80.

MAVREM: allows to control the multigrid corrections for k and ε (default = 0.95),

> 0: according to the restrictions defined by Eq. 4-78 and Eq. 4-79,

= 0: according to the restriction defined by Eq. 4-78,

< 0: according to the restriction defined by Eq. 4-80.

MUCLIP: controls the maximum allowable value for the ratio MUT/MU (default value = 5000).

LTMAX: maximum turbulent length scale (default = 1.E+6),

= -1: control of turbulent length scale with automatic clipping.

IYAP: (= 1) applies the Yap’s modification to control the turbulent length scale (default value = 0).The value of the expert parameter LTMAX must be the default value.

TEDAMP: parameter to improve the robustness of the k-ε models (default value = -1),

> 0: a minimum of TEDAMP multiplication factor of the clipping value (EKCLIP) is usedfor in the factor in Eq. 4-57,

a minimum of TEDAMP multiplication factor of the clipping value (EPCLIP) is usedfor to compute the turbulent viscosity (Eq. 4-59),

<= 0 : the minimum values used for and correspond to the expert parameter EPS,

GAMMAT: introduces the turbulence time scale in the computation of the local time step to controlstability (default value = 10).

PRCLIP: sets an upper bound for the ratio between production and dissipation (default value = 50).

LIPROD: (= 1) corresponds to a linearization of the production term (default value = 0) when strainrate is large (i.e. impinging flow) and PRCLIP has no more effect on the flow field.

EKCLIP: clipping value for the turbulent kinetic energy k (default value = 1.E-5).

EPCLIP: clipping value for the turbulent dissipation rate ε (default value = 1E-5).

KEGRID: Full multigrid parameter corresponding to the finest grid level on which the Baldwin-Lomax model is used (default = 2). On the lower grid levels, the k-ε model is used.

IUPWTE: (= 1) uses an upwind scheme for the convection of k-ε instead of a centre scheme(default = 1).

k 1 T⁄

ε

k ε


FINE™ 4-19

IKENC: (= 1) solves the k-ε equations with a non-conservative approach (default = 1).

IKELED: (= 1) actives the LED scalar scheme for k-ε instead of the standard central scheme(default = 0).

IOPTKE: (= 1) optimized implementation for k-ε (Yang-Shi, Wall function, Lauder Sharma)(default = 1).

4-3.5 Best Practice for Turbulence Modelling

4-3.5.1 Introduction to Turbulence

Turbulence can be defined as the appearance of non-deterministic fluctuations of all variables(velocity u", pressure p", etc ...) around mean values. Turbulence is generated above a critical Rey-nolds number that may range in values from 400 to 2000 depending on the specific case. In 95% ofindustrial applications the critical Reynolds number falls above that range. That is why it is in gen-eral necessary to predict adequately the turbulence effects on the flow-field behaviour.

Τo model turbulent flow in a satisfactory way, four steps should be performed:

• choosing a turbulence model,

• generating an appropriate grid,

• defining initial and boundary conditions,

• setting expert parameters to procure convergence.

4-3.5.2 First Step: Choosing a Turbulence Model.

A turbulence model is chosen based on the specific application. Table 4-1 states the most appropri-ate turbulence models to use for different types of flows. Although these are the "most appropriate"this does not mean that certain turbulence models cannot be used for the flow types listed, but justthat they are "less appropriate".

TABLE 4-1 Recommended turbulence models for different flow types

Three main kinds of turbulence models exist:

• algebraic models (e.g. Baldwin-Lomax),

• one-equation models (e.g. Spalart-Allmaras),

• two-equation(s) models (k-ε).

When quick turbulence calculations are required, for example, in design-cycle analysis, it is recom-mended that the Baldwin-Lomax model is used due to its high numerical stability and low compu-tational expense. To simulate more precisely the turbulent quantities with also a good rate ofconvergence the Spalart-Allmaras model should be preferred.


4-20 FINE™

Another model often used in design is "standard" k-ε. This model employs an empirically basedlogarithmic function to represent the near-wall physics and requires a lower grid resolution in thisregion as a result. One drawback of this treatment is that the logarithmic function does not apply forseparated flows, although the NUMECA extended wall function will still work. If it is expected thata significant amount of separation will have to be predicted, one of the low-Reynolds number tur-bulence models would be more appropriate. All of the listed turbulence models employ constantturbulent Prandtl numbers which is somewhat of a restriction when performing heat transfer calcu-lations. However, experience has shown quite successful prediction of heat transfer coefficientswhen using Baldwin-Lomax and Launder-Sharma k-ε.

4-3.5.3 Second Step: Generating an Appropriate Grid.

a) Cell Size

Note that the sublayer extends up to y+=5 but 10 is an acceptable approximation for design calculations.Note: The variable v* displayed in the figure is uτ.Picture from White, F.M., Viscous Fluid Flow, McGraw Hill, 1991.

FIGURE 4.3.5-3Boundary layer profiles

When calculating turbulence quantities it is important to place the first grid node off the wall withina certain range (ywall). This can be done for the blade and the endwalls (hub and shroud) independ-ently. When doing computations including viscosity (Navier-Stokes equations) the boundary layernear a solid wall presents high gradients. To properly capture those high gradients in a numericalsimulation it is important to have a sufficient amount of grid points inside the boundary layer. WhenEuler computations are performed no boundary layer exists and therefore the cell size near solidwalls is of less importance.

logarithmic law

Data of Lindgren (1965)

viscous sub-layer buffer layer log layer

Separating flow


FINE™ 4-21

To estimate an appropriate cell size ywall for Navier-Stokes simulations including turbulence, the

local Reynolds number based on the wall variable y+is computed. The value of y+ associated with

the first node off the wall will be referred to here as y1+:

y1+ (4-22)

where uτ is the friction velocity:

(4-23)

Note that the value of ywall depends on the value of y1+.

In Figure 4.3.5-3 is represented the evolution of u+ against y+ from the measurements of Lind-gren(1965) with:

u+= /

Low-Re models resolve the viscous sublayer and are well suited for y1+ values between 1 and 10

whereas high-Re models apply analytical functions to the log-layer and are appropriate to y1+ val-

ues ranging from 20 to 50 (it depends on the extension of the buffer layer for the considered flow).

Moreover one can notice that the logarithmic function does not apply for separated flow. Sowhether it is expected that a significant amount of separation will have to be predicted, one of thelow-Reynolds number turbulence models would be more appropriate.

Recommendations are given in the table below for ranges of y1+ specific to the different types of

models.

One way to estimate ywall as a function of a desired y+ value is to use a truncated series solution of

the Blasius equation:

y+... (4-24)

Note that the reference velocity, Vref, can be taken from an average at the inlet. For instance, if themass flow is known the value can be calculated using density and the cross-sectional area of theinlet. If the mass flow is not known the reference velocity may be calculated from the inlet totalpressure and an estimated static pressure using isentropic relations. The reference length, Lref,should be based on streamwise distance since an estimation of boundary layer thickness is implied

TurbulenceModels

High-Re:Standard k-ε, Extended wall-function k-ε (will accept lower values)

Low-Re:Baldwin-Lomax, Spalart-Allmaras, Launder-Sharma k-ε, Yang-Shih k-ε, Chien k-ε, Extended wall-function k-ε.

Non-linear k-e(Suited for research, not design-cycle analysis)

High-Re Low-Re

Y1+ 20-50 1-10 20-50 1-10

TABLE 4-2 Appropriate y1+ values for available turbulence models

ρuτywall

µ---------------------=

uττwall

ρ-----------

12--- Vref( )2Cf= =

u uτ

ywall 6Vref

ν---------

⎝ ⎠⎛ ⎞

7 8/– Lref

2---------

⎝ ⎠⎛ ⎞

1 8/=


4-22 FINE™

in this calculation. For instance, in the case of a turbomachinery simulation one could use the dis-tance of hub and shroud curves that exist upstream of the first row of blades. This is approximate,of course, as the thickness of boundary layers will vary widely within the computational domain.

Fortunately it is only necessary to place y+ within a range and not at a specific value.

Another method of estimating ywall is to apply the 1/7th velocity profile. In this case the skin fric-tion coefficient Cf is related to the Reynolds number:

(4-25)

where Rex should be based on average streamwise values of Vref and Lref as discussed above. Sinceuτ is based on Cf it may be calculated based on Eq. 4-23, and ywall may then be calculated from

Eq. 4-22. Note that either method is not exact but they will yield results that are quite close to eachother. In fact, it can be instructive to calculate ywall using both methods as a check. Since only onewall distance is being calculated, the particular flow being studied should be kept in mind. For

instance if it is a diffusing flow Cf, and hence y+, can be expected to drop. Since a certain range is

desired (e.g., 20< y+<50 for high-Re Standard k- ε) the user may choose to base the calculation ofwall distance on an average of that range (e.g., 40).

b) Things to Look Out For

These instructions should provide reasonable estimates but it is always wise to plot y+ once a solu-

tion has finished. Spot checks should be made to ensure that most y+ values fall within the desired

range. For instance it is useful to plot y+ contours over the first layer of nodes from a given wall.There are some special cases where such checks do not strictly apply. For instance, skin friction

approaches zero at points of separation so it is expected that y+ will be low in such regions. It isgenerally recommended that turbomachinery blade tip clearances are meshed with uniform span-

wise node distributions. In such cases, the y+ values will tend to be higher within the gap than else-where in the computational domain near-wall regions. This should not raise concern as the tipclearance flow consists of thoroughly sheared vortical fluid that undergoes significant accelerationand is therefore quite different than a standard boundary layer. It is expected that the skin frictionwill be high in this region due to the acceleration.

c) General Advice

•What grid resolution is adequate?

The resolution method employed in the EURANUS flow solver requires approximately 9 nodesacross a free shear-layer and approximately 15 across a boundary layer to provide grid-independentresults for turbulent flows. If wall functions are used the boundary layer only requires approxi-mately 9 nodes.

Of course the flow field under study will realistically consist of shear layers of which the width var-ies substantially throughout the flow field. The user must therefore decide what is important to cap-ture and what is not. For instance, in the design-cycle analysis of a compressor with a volute itwould probably be acceptable to choose a fully-developed boundary layer. The number of nodesacross the diameter would therefore be approximately 29. However, it would be wise to select anumber like 33 to maintain a a large number of multi-grid levels. The selection of nodes in thestreamwise direction should be governed by what resolution adequately represents the studiedgeometry. Regions of concentrated high gradients, such as airfoil leading or trailing edges or anygeometrical corners should contain a relatively high clustering of nodes.

Cf0.027Rex

1 7/--------------=


FINE™ 4-23

•What determines the grid quality?

After the various grid resolution concerns are addressed, the level of skewness must be analysed.

Providing clustering in a curved geometry can often lead to internal angles of grids cells of 10o. It isimportant to minimize the number of cells containing such low angles as the calculation of fluxescan become significantly erroneous under such conditions. More information concerning how tocheck the quality of a grid can be found in the IGG™ or AutoGrid manual. If the adjustment ofnode numbers and clustering does not reduce the level of skewness, local smoothing should beapplied. The expansion ratio, or the ratio of adjacent cell sizes, should also be checked. It is partic-ularly important to keep this value within an absolute range of about 0-1.6 in regions of high gradi-ents, such as boundary layers, free shear-layers and shocks. If it is evident that adjacent cells aredifferent in size by factors significantly greater than two, the clustering in this region should bereduced or the number of nodes should be increased.

d) Verification of y1+

By following this instructions it should be possible to generate a grid of reasonable quality for tur-

bulent flows. It is recommended however, that the user checks values of y1+ after approximately

one hundred iterations on the fine grid to ensure the proper range has been specified. At the sametime, it can be useful to plot contours of residuals (continuity, momentum, energy and turbulence)over selective planes. If the level of skewness is too high, this will be indicated by local peaks inresiduals that are orders of magnitude greater than the rest of the flow field. If a multi-block grid isused, the residual levels in each block can be compared in the monitor.

4-3.5.4 Defining Initial and Boundary Conditions

Turbulence is commonly modelled by emulating molecular diffusion with a so-called "eddy-viscos-ity" (µT). A standard method for determining µT is based on turbulent-eddy length and time scales

that are modelled through turbulence kinetic energy (k) and dissipation (e.g. ε) equations. It isimportant to note that the level of turbulence quantities (i.e. turbulence intensity, µT, k, ε) specifiedat the inlet boundary can have a strong effect on the flow-field prediction for quantities like the totalpressure, velocity profiles, flow angles, total temperature etc. Since the measurement of turbulenceis rarely conducted in a design and test environment, the designer faces the problem of setting thesequantities without knowing the correct values.

a) Spalart-Allmaras Model

When the Spalart-Allmaras model is selected the user should specify in the inlet boundary condi-

tion the kinematic turbulent viscosity νΤ (m2/s). If no information is available on the turbulenceproperties of the flow, estimates can be made based on the following assumptions that:

• For internal flows (e.g. turbomachinery): = 1 to 5.

• For external flows (e.g. vehicle aerodynamics): .

b) K-ε Models

•Estimation of k

The value of the turbulent kinetic energy can be derived from the turbulence intensity Tu or fromthe wall shear stress.

νT

ν-----

νT

ν----- 1=


4-24 FINE™

— From the turbulence intensity. The turbulence intensity Tu can be expressed against thestreamwise fluctuating velocity u" and the streamwise velocity Uref:

. (4-26)

For internal flows the value of Tu is about 5% and for external flows it is reduced to 1%. Withthese considerations k can be calculated in considering an isotropic turbulence:

(4-27)

— From the wall shear stress. If the wall shear stress is known, the user can use the wall func-tions defined for the fully turbulent flow:

(4-28)

This value of k could be used as an initial value and also for the inlet boundary condition.

•Estimation of ε

The value of the turbulent dissipation can be specified through one of the following rules:

— Specify the ratio of the turbulent viscosity to the laminar viscosity

(4-29)

For internal flows (such as turbomachinery flow), typical values are .

For external flows (in aerodynamics computations), typical values are .

— Specify the turbulent length scale (only for internal flows).

A typical values is . where DH is the hydraulic diameter of the inlet section

. (4-30)

— Derive ε from the asymptotic turbulent kinetic equation:In a free uniform flow the turbulent kinetic energy equation reduces to

. (4-31)

This relation can be used to specify the value of the turbulent dissipation in the following way:

, (4-32)

where u is the inlet velocity, ∆k the decay of the turbulent kinetic energy over a length L. Forexample, in a turbomachine, L is the maximum geometric length and ∆k could be set to 10% ofthe inlet value of k.

Tuu

″2

Uref------------=

k32--- u

″2( )2

=

kτwall

ρCµ-----------=

ε Cµµµi t

------ρrefk

2

µ--------------=

µi t µ⁄ 50=

µit µ⁄ 1=

l 0.1DH=

εcµ

34---

k

32---

l----------=

uk∂x∂

----- ε–=

ε u–∆kL

------=


FINE™ 4-25

Using this method, the user must make sure that the value of the turbulent viscosity obtained

from these values of k and ε is not too big or too small. i.e. . If this condition is not

satisfied, it is advised to scale down or up the value of k inlet or the ∆k and compute again theturbulent dissipation

— Specify the wall shear stress.If the wall shear stress is known, the user can use the wall functions defined for the fully turbu-lent flow.

(4-33)

If there is an initial solution file containing and , the and values of this file are used toinitialize the fields.

The initial values mentioned above can also be used to set the inlet boundary conditions for the

and fields. However, to reduce the possibility of oscillations in skin friction due to non-physical

relaminarisation during convergence, it is recommended to insure ε ≈ 0.1 .

Either of the above methods can be applied for setting the boundary conditions in tur-

bomachine applications. However, if the given values of k and ε lead to the killing of theturbulence shortly after the inlet section, we suggest to apply Eq. 4-32 and select an inletvalues of k such that the ratio of the turbulent viscosity to the laminar viscosity equals50.

In some cases a cross-check between Eq. 4-29 and Eq. 4-31 may result in very differ-

ent values for ε. In such a case it is recommended to re-evaluate k and ε in the followingmanner:

1. Use relation Eq. 4-32:

. (4-34)

This relation expresses that k0 (k at the inlet) is expected to be decreased by about 10% over a

length ∆L that is characteristic to the size of the domain.

2. Use relation Eq. 4-29. In this relation Cµ=0.09 and ν represents the laminar viscosity of thefluid.

3. Combine the relations of the two previous steps to remove ε0, leading to:

. (4-35)

4. Using either relation Eq. 4-29 or Eq. 4-32 then easily leads to an estimation of ε0.

4-3.5.5 Setting Expert Parameters to Procure Convergence

Several expert parameters may be set to procure convergence.

1µt

µ---- 1000< <

ετwall ρ⁄( )

32---

l-------------------------=

k ε k ε

k

εεinlet

ε u–∆k∆L------- u

0.1k∆L

----------= =

k00.1U∆L

------------µT

µ------ ν

Cµ------

⎝ ⎠⎛ ⎞=


4-26 FINE™

a) Cut-off (Clipping) of Minimum k Value

The float parameter EKCLIP controls the minimum allowable value of k. This is done to preventnon-physical laminarisation and remove the possibility of negative values being calculated duringnumerical transients. Setting this value to a reasonable level has been shown to significantlyincrease convergence rate.

EKCLIP: clipping k to about 1% of inlet value maintains minimum residual turbulence in thedomain.

b) Minimizing Artificial Dissipation in the Boundary Layer

An alternative treatment of the dissipation terms in the k and ε equations has been introduced toovercome difficulties related to turbulence decay in boundary layers observed in some specific testcases. Currently, the dissipation terms are scaled with the spectral radius of the equations and arefurther damped in an exponential manner across the boundary layer. The major drawback of thisformulation is that it introduces an excessive amount of artificial dissipation into the boundarylayer, leading to non-physical relaminarisation problems. A different implementation, based on theL.E.D. (Local Extrema Diminishing) version of the Jameson-Schmidt-Turkel treatment introducesbetter monotonicity properties of the k and ε equations.

IKELED = 0 (default): Dissipation scaled with spectral radius.

= 1: Less diffusive L.E.D. scheme activated.

c) Wall Function for the k-ε Turbulence Model

INEWKE = 0: Wall function applies for first node off the wall at Y+ =20-50, Launder & Spalding.

= 10 (default): Mesh-independent formulation of the wall function.

d) Full Multigrid k-ε / Baldwin-Lomax Model Switch

KEGRID = 2(default) Grid 222 - Baldwin Lomax,

Grid 111 - Baldwin Lomax,

Grid 000 - k-e Model.

KEGRID = 3: Grid 222 - Baldwin Lomax,

Grid 111 - k-e Model,

Grid 000 - k-e Model.

Example: k-ε run on the finest grid level (000) with 3 levels of grid (222, 111 & 000) in the multi-grid procedure. The Baldwin-Lomax model remains active on levels 222 and 111 before k-e is auto-matically switched on when the finest grid is reached. This is controlled through the expert parame-ter KEGRID whose value is set to 2 by default, meaning that the Baldwin Lomax model is used upto the second level of grid. The µt / µ field computed using the Baldwin-Lomax model is then trans-ferred to the finest mesh and used to calculate initial k and ε values. The use of a KEGRID valuehigher than the number of grid levels available enables the k and ε equations to be solved on all gridlevels.

A similar procedure can be followed when a calculation on 111 mesh is first desired. ProvidingKEGRID is set to 2 (default value), the Baldwin-Lomax is then active on level 222 before the k-εmodel is automatically switched on when the finest grid level (111 in this case) is reached. How-ever, the question then arises when a restart procedure on the 000 level is required. How to restarton 000 while transferring strictly the k and ε fields already computed on 111? By default, sinceKEGRID=2, the solution computed on 111 is seen as a Baldwin-Lomax solution. The k and ε fields


FINE™ 4-27

are then reset using the classical procedure while the other variable fields (density, velocity andenergy) are transferred adequately. To overcome this difficulty, KEGRID must again be set to avalue higher than the number of grids. This procedure results in a much better initialization of k andε, thus preventing some relaminarisation while enhancing convergence.

e) Cut-off (clipping) of Maximum Turbulence Production/Destruction Value

The float parameter PRCLIP controls the maximum allowable value of turbulence production/destruction (=production/density*dissipation in k-e model). Limiting this to a finite value enhancesconvergence rate by removing the possibility of unbounded turbulence spikes occurring during thenumerical transient. However, care must be taken to apply a reasonable limit. Recommended valuesare:

PRCLIP (Float):

For most flows: 50 (default),

In turbulent diffusion dominated flows (e.g., seals): 200.

f) Linearization of Turbulence Production/Destruction Value

The integer parameter LIPROD activates the linear production (PRCLIP is no more used ifLIPROD set at 1). This linearization of the turbulence production is relevant for impingement flowsfor which the standard model is well known to overestimate the production of kinetic energy atstagnation point.

LIPROD = 1: activate the linear production (PRCLIP no more used in that case).

4-3.6 Theoretical Aspect of Turbulence Modelling

An algebraic (Baldwin-Lomax), an one-equation (Spalart-Allmaras) and several two-equation tur-

bulence models ( ) are available.

Wall distance

All turbulence models need to compute the wall distances everywhere in the computed domain. It isa rather time consuming process so that they are saved in the *.cgns mesh file at the beginning ofthe first computation. These values will be read and used for the next computations. If the mesh fileis modified or saved again, they are erased and will be computed again.

Different important expert parameter are used in the calculation of the wall distance. The defaultvalues are generally sufficient and they have to be changed only if a problem arises. The expertparameter NREPET allows to take into account the periodicity of the computed domain. Indeed, ateach point of the domain, the closest wall is not always in the computed domain if periodic bound-ary conditions are used. Consequently the domain is repeated beyond the periodic boundaries tocompute correctly the wall distance. The default value is 1 and can be increased to 2 in very partic-ular cases. The expert parameter NSUBM is the maximum number of subdomains a domain is splitinto. Its value is sufficiently high and it must be changed only if an error message tells you toincrease it. The expert parameter NTUPTC is the number of patches whose sub-patches will besearched. In a very complex geometry, the value of this parameter can be increased if the calcula-tion of the wall distances fails. Another expert parameter can be decreased in parallel with theincrease of NTUPTC. This parameter is the real RTOL. It is the maximum angle allowed betweentwo normals of a patch. If a larger value is found, the patch is subdivided.

k ε–


4-28 FINE™

4-3.6.1 Baldwin-Lomax

The Baldwin-Lomax algebraic turbulence model, Baldwin & Lomax (1978) is a two layer modelwhere the turbulent viscosity in the inner layer is determined using Prandtl’s mixing length model,and the turbulent viscosity in the outer layer is determined from the mean flow and a length scale.The strain-rate parameter in Prandtl’s mixing length model is taken to be the magnitude of the vor-ticity.

The influence on the mean flow equations through the turbulent kinetic energy is neglected.

The turbulent viscosity is given by

(4-36)

where is the normal distance to the wall, and is the smallest value of at which the inner and

outer viscosity is equal.

The inner viscosity is

(4-37)

where

(4-38)

(4-39)

and

(4-40)

with the Kronecker symbol.

The outer viscosity is

(4-41)

where is the smaller of

(4-42)

The term is the value of n corresponding to the maximum value of , , where

(4-43)

and

µt

µt( )i n nc≤,

µt( )0 n nc>,⎩⎨⎧

=

n nc n

µt( )i ρl2 ω=

l kn 1 ey– +

A+⁄–( )=

y+ ρwτw

µw

----------------⎝ ⎠⎜ ⎟⎛ ⎞

n=

ωi εijk xk∂∂uj=

εijk

µt( )0 KCcpρFwakeFKleb n( )=

Fwake

nmaxFmax

and Cwknmax u2

v2

w2+ +( )max u

2v

2w

2+ +( )min–

2/Fmax

nmax F Fmax

F n( ) n ω 1 e n+/A+––( )=


FINE™ 4-29

(4-44)

The constants used are hard coded and equal: , , , ,

, .The turbulent Prandtl number, needed to calculate the turbulent con-

ductivity, is accessible through the expert parameter PRT (see section 3-3.1.2).

The expert parameter IATFRZ allows to control the interaction of the model with the multigrid sys-tem. When IATFRZ is set to 0, the model is applied separately on all grid levels. When it is set to 1,the model is only applied on the finest grid and the turbulent viscosity is restricted (through therestriction operator) to the coarser grids where the turbulent viscosity is frozen. It is possible tofreeze the turbulent viscosity field on all grid level by setting IATFRZ to 2. The value can be auto-matically changed by using a criteria based on a maximum iteration number or on a minimum con-vergence. The maximum iteration number is specified by the expert parameter ITFRZ. Theminimum reduction of order of magnitude is set in the expert parameter RESFRZ.

4-3.6.2 Spalart-Allmaras

The Spalart-Allmaras turbulence model is a one equation turbulence model which can be consid-ered as a bridge between the algebraic model of Baldwin-Lomax and the two equation models. TheSpalart-Allmaras model has become quite popular in the last years because of its robustness and itsability to treat complex flows. The main advantage of the Spalart-Allmaras model when comparedto the one of Baldwin-Lomax is that the turbulent eddy viscosity field is always continuous. Itsadvantage over the k-ε model is mainly its robustness and the lower additional CPU and Memoryusage.

The principle of this turbulence model is based on the resolution of an additional transport equationfor the eddy viscosity. The equation contains an advective, a diffusive and a source term and isimplemented in a non conservative manner. The implementation is based on the papers of Spalartand Allmaras (1992) with the improvements described in Ashford and Powell (1996) in order to

avoid negative values for the production term ( in Eq. 4-50).

The turbulent viscosity is given by

(4-45)

where is the turbulent working variable and a function defined by

(4-46)

with is the ratio between the working variable and the molecular viscosity ,

(4-47)

The turbulent working variable obeys the transport equation

(4-48)

where is the velocity vector, Q the source term and , constants.

FKleb 1 5.5 nCKleb/nmax( )6+1–

=

A+ 26= Cwk 1.= Ccp 1.6= k 0.41=

Ckleb 0.3= K 0.0168=

S

νt νfv1=

ν fv1

fv1χ3

χ3 cv1+-------------------=

χ ν ν

χ νν---=

ν∂t∂

------ V ν∇⋅+1σ--- ∇ ν 1 cb2+( )ν+( ) ν∇[ ] cb2ν ν∆–⋅ Q+=

V σ cb2


4-30 FINE™

The source term includes a production term and a destruction term:

(4-49)

where

(4-50)

(4-51)

The production term P is constructed with the following functions:

; (4-52)

; (4-53)

where d is the distance to the closest wall and S the magnitude of vorticity.

In the destruction term (Eq. 4-51), the function is

(4-54)

with

; (4-55)

The constants arising in the model are

, , , ,

, , ,

The equation Eq. 4-48 is solved with the appropriate boundary conditions:

on solid wall , along the inflow boundaries the value of is specified ( is obtained byusing a Newton-Raphson procedure to solve Eq. 4-45) and along the outflow boundaries it isextrapolated from the interior values.

Q νP ν( ) νD ν( )–=

νP ν( ) cb1Sν˜

=

νD ν( ) cw1fwνd---

⎝ ⎠⎛ ⎞

2

=

S Sfv3ν

κ2d2-----------fv2+=

fv21

1 χ cv2⁄+( )3-------------------------------= fv3

1 χfv1+( ) 1 fv2–( )χ

--------------------------------------------=

fw

fw g1 cw3

6+

g6 cw36+

-------------------⎝ ⎠⎜ ⎟⎛ ⎞

16---

=

g r cw2 r6

r–( )+= rν

Sκ2d

2--------------=

cw1 cb1 κ2⁄ 1 cb2+( ) σ⁄+= cw2 0.3= cw3 2.= cv1 7.1= cv2 5.=

cb1 0.1355= cb2 0.622= κ 0.41= σ 2 3⁄=

ν 0= νt ν


FINE™ 4-31

4-3.6.3 k-ε Turbulence Models

a) General Formulation

In the turbulence model two additional transport equations for the turbulent kinetic energy, ,

and the turbulent dissipation rate, , are solved. In EURANUS, 4 linear and 2 non-linear modelsare currently used.

In the following, the trace of the tensor X will be written X

In the turbulence model two additional differential equations need to be solved respectively

for and . These additional equations can be put in the following general form:

(4-56)

(4-57)

where is the mean strain tensor and the turbulent Reynolds stress tensor.

The variable is the modified dissipation rate

(4-58)

and the turbulent viscosity is given by the following relation

(4-59)

b) Linear Models

In the linear models, the turbulent Reynolds stress tensor is related to the mean strain tensor in a lin-ear way.

(4-60)

The implemented linear models are:

- Chien, low Reynolds number k-ε model (Chien, 1982).

- Extended wall functions (Hakimi, 1997) = Standard high Reynolds (Launder & Spalding,1974) if the expert parameter INEWKE is set to 0.

- Launder-Sharma, low Reynolds number k-ε model (Launder & Sharma, 1974).

- Yang-Shih, low Reynolds number k-ε model (Yang & Shih, 1993).

k ε– k

ε

k ε–

k ε

ρk∂t∂

--------- ρwk µµt

σk

-----+ k∇–⎝ ⎠⎛ ⎞∇•+ ρw″ w″⊗ S

⎩ ⎭⎨ ⎬⎧ ⎫

– ρε–=

ρε∂t∂

--------- ρw ε µµt

σε-----+ ε∇–

⎝ ⎠⎛ ⎞∇•+

1T--- Cε1f1 ρw″ w″⊗ S

⎩ ⎭⎨ ⎬⎧ ⎫

Cε2f2ρε+⎝ ⎠⎜ ⎟⎛ ⎞

–= E+

S ρw″ w″⊗–

ε

ε ε D–=

µt

µt ρCµfµkT=

ρ– w″ w″⊗( )i j 2µt Sij23--- ∇w( )δi j–

23---ρkδi j–=

Sij12---

xj∂∂wi

xi∂∂wj+

⎝ ⎠⎜ ⎟⎛ ⎞

=


4-32 FINE™

The constants or functions Cµ, Cε1, Cε2, σk, σε, fµ,f1, f2, D, E and T are model dependent and they

are defined in the Table 4-3 where and

The constants Cµ, Cε1, Cε2, σk, σε can however be changed by the user (respectively the expert param-eters CMU, CE1, CE2, SIGK, SIGE in the Computation Steering/Control variables page. The tur-bulent Prandtl number, needed to calculate the turbulent conductivity, is also an expert parameter(PRT).

TABLE 4-3 Coefficients of the k-ε models

k-ε Model

Chien Standard high-Re

Launder & Sharma Yang & Shih

Cµ 0.09 0.09 0.09 0.09

Cε1 1.35 1.44 1.44 1.44

Cε2 1.80 1.92 1.92 1.92

σk 1.0 1.0 1.0 1.0

σε 1.3 1.3 1.3 1.3

fµ 1.0

x Rey

A 1.5 10-4

a 1

B 5 10-7

b 3

C 10-10

c 5

d 0.5

f1 1.0 1.0 1.0 1.0

f2 1.0 1.0

T

D 0. 0.

E 0.

kw 0. /

DNS0. 0.

εw 0. /

DNS0.

Retk

2

νε------= Rey

k0.5

yν

-----------=

1 e0.0115y

+–

–e

3.4–

1 Ret( ) 50⁄+( )2---------------------------------------

1 eAx

aBx

bCx

c+ +( )–

–[ ]d

1 0.22eRet

2 36⁄–– 1 0.3e

Ret2–

–

k ε⁄ k ε⁄ k ε⁄ k ε⁄ ν ε⁄( )0.5+

2νk y2⁄ 2ν k∇( )

2

2µεe0.5y

+––

y2

----------------------------- 2νµt S∇•( )2 νµt S∇•( )2

uτ2

Cµ0.5⁄

uτ3 κy( )⁄

2ν k∇( )2


FINE™ 4-33

Two variants of the high Reynolds k-ε with wall functions (section d) Solid Boundary

and Wall Functions) exist:

• If the expert parameter INEWKE=10 (Default), the wall functions are derived from DNS(Direct Numerical Simulation) curve fitting. The k-ε model is in that case derived from theYang-Shih model. This new model, named extended wall functions, allows to obtain accurateresults on fine mesh contrary to the standard high Reynolds k-ε model.

• if the expert parameter INEWKE=0, standard wall function are applied and the y+ value of thenear wall cell should be greater than 20.

The Chien and the Launder-Sharma models belong to the same family (zero value of εat the wall) while the standard model and Yang-Shih model belong to a second family(non zero value of ε at the wall). Launching the restart is allowed as long as the usersticks to the same family.

c) Non Linear Models

The non-linear models are based on two linear models: the Yang and Shih model for low Reynoldsvariant and the Standard k-ε model for high Reynolds variant.

c.1) The low Reynolds model

The production term is modified through:

(4-61)

where T is defined in Table 4-3 and:

and Cτ2 = 46; Cτ3 = -7; A1 = 4; A2 = 1000 and γ = 0.2

c.2) The high Reynolds model

The model is modified in the following way:

• is set to unity

ρw″ w″⊗–43---

fµ

A1 fµs+----------------------- 1

γRiti

1 γRiti+

----------------------–⎝ ⎠⎜ ⎟⎛ ⎞

kTS23---ρkI–=

Cτ2

A2 s3 ω3+ +

-----------------------------kT'2 2S2

SΩ– ΩS23--- S

2 –+⎝ ⎠⎛ ⎞–

Cτ3

A2 s3 ω3+ +

-----------------------------kT'2 2S2 SΩ Ω– S23--- S2 –+

⎝ ⎠⎛ ⎞–

T' 1 ft1 Tw ft2 T⁄+⁄( ) ; Tw

A21 3⁄

2 S2

------------------- =⁄=

ft1 11

1 2 S2 ν ε⁄+( )

2---------------------------------------------- ft2 1

ft1

1 Ret 70⁄+---------------------------–=;–=

Sij12---

xj∂∂wi

xi∂∂wj+

⎝ ⎠⎜ ⎟⎛ ⎞

; Ωij12---

xj∂∂wi

xi∂∂wj–

⎝ ⎠⎜ ⎟⎛ ⎞

==

s T' 2 S2 ; ω T' 2– Ω2 = ; Rit2 ωs ω––==

fµ


4-34 FINE™

• T’ is replaced by T

The production term becomes:

(4-62)

where s and are modified according to:

(4-63)

The coefficients Cτ2, Cτ3, A1, A2 and γ remain unchanged.

Note that the High Reynolds non-linear model uses the wall functions as it is based on the standardk-ε model.

Before launching the non-linear model, it is recommended to apply first the linear

model and restart from this solution. This procedure will provide a good initial solutionfor the non-linear model and prevent the non-linear terms to cause divergence of thecode at the early stage.

Since the non-linear model is from Yang-Shih, the restart can be done only from the

Yang-Shih model (linear or not) and the Standard model with wall functions.

d) Solid Boundary and Wall Functions

The values of kw and εw are imposed at the boundary for the Chien, Launder & Sharma and Low

Reynolds non-linear models, while for the Standard and non-linear High Reynolds number models,it is imposed in the first inner cell. The wall friction velocity uτ is calculated through a wall function(Eq. 4-64 or Eq. 4-65) from the velocity at the cell center and the normal distance to the wall.

For the models that do not use wall functions (Chien, Launder Sharma, Yang & Shih

and Low Reynolds non linear model), the profile of the boundary layer is directlyinferred from the input values at the wall. Consequently, particular attention must be paidto the grid refinement in this region in order to capture the viscous sublayer. A typical

value is given by at the first node from the wall.

The wall functions are used to mimic the presence of the walls by reflecting the effect of the steep,non-linear variations of the flow properties through the turbulent boundary layer. They define theshear stress and the heat flux on the cell faces lying on solid boundaries as well as the values of kand ε in the vicinity of the wall.

The wall functions are applied in the Standard (see kw and εw in Table 4-3 ) and in the High Rey-nolds non linear k-ε models. For the extended wall functions model, the wall functions for k and εare fitted with polynomials to the DNS data.

ρw″ w″⊗–43--- 1

A1 s+-------------- 1

γRiti

1 γRiti+

----------------------–⎝ ⎠⎜ ⎟⎛ ⎞

kTS23---ρkI–=

Cτ2

A2 s3 ω3+ +

-----------------------------kT2 2S2 SΩ– ΩS23--- S2 –+

⎝ ⎠⎛ ⎞–

Cτ3

A2 s3 ω3+ +

-----------------------------kT2 2S2 SΩ Ω– S23--- S2 –+

⎝ ⎠⎛ ⎞–

ω

s T 2 S2 =

ω T 2– Ω2 =

1 y+

10< <


FINE™ 4-35

d.1) Velocity

For smooth walls:

The wall function in the viscous sublayer is given by:

(4-64)

with , the dimensionless normal distance from the walls and , the wall

friction velocity directly related to the wall shear stress.

While in the turbulent layer, the wall function becomes:

(4-65)

where κ is the von Karman constant (default value 0.41) and B another constant (default value5.36). They can be modified by the user in the Boundary Condition page.

For rough walls:

The wall function is given by (no viscous sublayer considered):

(4-66)

where κ and B are defined just above and k0 and d0 are constants asked for each rough wall. Theconstant k0 is the equivalent roughness height while d0 is known as the height of the zero displace-

ment plane, defined by (if B=0). For small roughness elements, . For high

roughness elements, the flow behaves as if the wall was located at a distance d0 from the real wall

position.

where ks is the average roughness height

For rough walls, the constant B is usually zero (when ks+ > 70 with ). Otherwise the

value of B is evolving as presented in below graph.

uuτ----- y

+=

y+ yuτ

ν--------= uτ τwall ρ⁄=

uuτ----- 1

κ--- y

+ln B+=

uuτ----- 1

κ---

y d0–

k0--------------ln B+=

u k0 d0+( ) 0.= d0 0=

k0

ks

30------=

ks+ ks y

+

y------------=

s+s+


4-36 FINE™

When a rough wall is specified, the distance from the wall to the cell-centre of the first

inner cell should be bigger than k0 + d0. In general, the first inner cell should be locatedwithin the fully turbulent layer.

d.2) Temperature

Similarly, for isothermal walls, the following laws are considered in the code:

in the viscous sublayer (4-67)

where Pr is the laminar Prandtl number and:

in the turbulent layer (4-68)

where .

The heat flux at the wall is defined as:

(4-69)

A complete description of the available thermal boundary conditions at walls is provided in section8-5.3.

The "law of the wall" distributions of velocity, temperature and other variables are

assumed to prevail across the boundary layer. They are imposed at the node of a single

grid cell for which the user is advised to check that . As a result, if the first

cell node from the wall is placed too close, calculation is conducted in the viscous sub-layer and the law is no longer valid. Similarly, if the first node is placed too far away,then a discrepancy may exist between the profiles and their assumed shape.

e) Numerical Concerns

This paragraph provides a description of the numerical method used to deal with the k and ε equa-tions.

e.1) Choice of the initial and boundary conditions

Initial values for and must be specified by the user, as well as the inlet boundary condition.The specified values at the inlet boundary can have a strong effect on the flow-field prediction. Sev-eral methods are proposed in section 4-3.5.4 to help the user in the choice of suitable values.

e.2) Compressibility correction

The compressibility correction is present only in the k-ε model of Chien and is useful only for highMach number flows (M>3). Two kinds of compressibility effects are implemented:

1) the contributions from the modelled pressure gradient-velocity term and

2) the compressible dissipation.

They can be activated by using respectively the expert parameters ICOPKE or ICODKE.

The first compressibility correction is associated with the modelling of pressure gradient-velocityterm in the equation of the turbulent kinetic energy, and, according to Zhang et al. (1991), leads tothe source term Rk:

T+

Pr y+

=

T+ Prt

κ-------

y+

13.2----------

⎝ ⎠⎛ ⎞ 13.2Pr+ln=

T+ Tw T–

Tτ----------------=

qw ρCpuτTτ=

20 y+

100< <

k ε


FINE™ 4-37

, (4-70)

which modifies the term D of Eq. 4-58:

. (4-71)

Similarly a term can be added to the equation. After Vandromme (1991) one has:

, (4-72)

which modifies the term E of Eq. 4-57:

. (4-73)

The above terms are included in the equations if the expert parameter ICOPKE is set to 1; ifICOPKE=0 (Default) they are set to zero.

The empirical constants in these equations are two expert parameters (SIGRO and C3), with defaultvalues:

. (4-74)

The second correction concerns the modelling of compressible dissipation. The physical foundationfor this correction is the observation of decreased turbulent viscosity with increased Mach number(Nichols, 1990). The type of compressible dissipation is controlled by the expert parameterICODKE.

For ICODKE=0 no correction for compressible dissipation is done.

In the correction of Sarkar (1989) (ICODKE=1), the dissipation of is expressed as the sum of

solenoidal ( ) and dilatational ( ) components. The dissipation in the source term of the -equa-

tion (Eq. 4-56) is then corrected according to:

(4-75)

with a turbulent Mach number defined as

(4-76)

where is the speed of sound.The constant is an expert parameter (ALF), with default value=0.5.

Nichols (1990) developed a model that corrects the production term in the turbulent kinetic energyequation (ICODKE=2):

(4-77)

Rk

µt

ρ2σp

-----------xi∂

∂ρxi∂

∂p–=

D' Dµt

ρ3σp

-----------xi∂

∂ρxi∂

∂p+=

Rε ε

Rε C3

µt

ρ2σp

-----------εk--

xi∂∂ρ

xi∂∂p

–=

E' E C3

µt

ρ2σp

-----------εk--

xi∂∂ρ

xi∂∂p

–=

k ε–

σp 0.5= C3 2.0=

k

ε εd k

εcorr ε 1 αMt2+( )=

Mt

M2

tk

a2

-----=

a α

ρw″ w″⊗ S–⎝ ⎠⎛ ⎞

corr( )ρw″ w″⊗ S– 1 Cp1 γ 1–( )M

k

a2

-----–⎝ ⎠⎛ ⎞=


4-38 FINE™

where a is the local speed of sound, is the specific heat ratio and an empirical constant (CP1

in the list of expert parameters available on the Control Variables page, with default value =4.).This correction improves the prediction of the turbulent production level by directly taking theeffect of the Mach number (M) into account.

e.3) Limiters for the turbulence variables

Successive limitations are set for the turbulence variables to ensure physical values and the stabilityof the calculation. Indeed, the term sources in the k-ε equations can vary strongly especially at thebeginning of the computation and lead to unphysical values and divergence.

1. To control the stability of the calculation, the expert parameter MAVRES, denoted here , isused This parameter limits the variation of the turbulence variables for each Runge-Kutta stage.

Denoting the new value of or as , the following restrictions are imposed when MAVRES> 0:

(4-78)

(4-79)

where EPS is an expert parameter with a small value, default 1E-28, also used to avoid possibledivisions by zero.

The restriction defined in Eq. 4-79 is not applied to the turbulent dissipation rate (ε) when this tendsto increase, in order to avoid excessive values of the turbulent viscosity.

If MAVRES = 0, only the restriction defined in Eq. 4-78 is applied (avoiding negative values)

If MAVRES < 0, the restriction is:

(4-80)

2. A similar system is applied to the multigrid corrections with the expert parameter MAVREM,denoted below as :

If MAVREM > 0:

If MAVREM = 0: restriction to positive values

If MAVREM < 0:

3. The expert parameter LTMAX is used to limit the turbulence length scale to a

value compatible with the domain scale.

If Lturb>LTMAX and MAVRES > 0, the value of ε is set to respect the maximum length scale.

If Lturb>LTMAX and MAVRES <= 0, the values of k and ε are set to a small value EPS.

The default value for LTMAX is 1E+6.

γ Cp1

ζ

k ε qn+1

qn+1 max qn+1 EPS,ζqn,( )=

qn+1

min qn+1 2 ζ–( )q

n,( )=

qn 1+ qn–1 ζ+( ) q

n 1+q

n–( )

1q

n 1+q

n–

qn

--------------------------+⎝ ⎠⎜ ⎟⎛ ⎞

---------------------------------------------=

ζ

qn 1+ qn– 1 ζ–( )qn<

qn 1+

qn–

1 ζ+( ) qn 1+ qn–( )

1qn 1+ qn–

qn--------------------------+

⎝ ⎠⎜ ⎟⎛ ⎞

---------------------------------------------=

Lturbk

3 2⁄

ε---------=


FINE™ 4-39

4. An automatic control of the turbulent length scale is possible by setting the expert parameterLTMAX to a negative value (LTMAX = -1). In this case, the following length scale control is pro-posed:

(4-81)

with the maximum equilibrium length scale in the computation, defined by

(4-82)

where is the maximum distance to the wall among all grid points of all blocks. The factor 5 in

Eq. 4-81 is set to avoid to clip the length scale too early.

The turbulent viscosity is then written as

For the update of turbulent variables (previous paragraph), LTMAX is replaced by

5. Another way to control the turbulent length scale is the Yap’s modification. It is applied by set-ting the expert parameter IYAP to 1. In this case, the expert parameter LTMAX should be set to itsdefault value (1.E+6) to avoid conflicts.

Yap’s modification consists of adding to the epsilon equation a source term that control the turbu-lent length scale. It can be applied to all k-ε models. The source term to be added writes:

(4-83)

where and are respectively the turbulent length scale ( ) and the equilibrium

length scale ( ).

A weakness of Yap’s correction is that it might conflict with Inlet boundary conditions if these areset without respecting a turbulent length scale criteria.

6. The expert parameter TEDAMP is another parameter to control stability. This parameter prevents

the factor in the equation from being singular as tends to zero (see Eq. 4-57 and the rela-

tionship between k and T in Table 4-3 ). A minimum of TEDAMP multiplication factor of the clip-

ping value (expert parameter EKCLIP) is used for .

The same parameter is used to damp coming from T in the calculation of the turbulent viscos-ity, Eq. 4-59: a minimum of TEDAMP multiplication factor of the clipping value (expert parameterEPCLIP) is used for .

If TEDAMP<=0, the minimum values used for and correspond to the expert parameter EPS.

The default value of TEDAMP is -1.

Irrespective of the value of TEDAMP, this strategy always avoids the use of possible negative val-ues of in the source term and of in the turbulent viscosity.

L min kT 5lemax,( )=

lemax

lemax κdmaxCµ3 4⁄–=

dmax

νt Cµfµ kL=

5lemax

SYAP 0.83maxlle

--- 1– 0,⎝ ⎠⎛ ⎞ l

le

---⎝ ⎠⎛ ⎞

2 εT---=

l le l kT=

le κdCµ3 4⁄–=

1 T⁄ ε k

k

1/ε

ε

k ε

k ε


4-40 FINE™

7. Another control on the stability is available through the parameter GAMMAT which introducesthe turbulence time scale Tturb in the computation of the local time step:

(4-84)

The default value of GAMMAT is set to 10.

8. Another important consideration is the amount of turbulence production compared to its dissipa-tion, . This quantity should stay within physically admissible ranges so that the turbu-lence production remains limited. The parameter PRCLIP allows the control of this ratio. As an

example, for homogeneous core flows and thin shear layers, whereas for separated shear layers and wakes. Flows of high shear, such as jets in cross

flow, can exhibit much higher values of . An upper bound of PRCLIP=50 is recom-mended to the user. However, this control is removed by the use of a linearised turbulent productionmodel introduced in all linear k-ε models. This simple modification is relevant for impinging flows,for which the turbulence models are well known to overestimate the turbulent production of kineticenergy. It corresponds to a linearisation of the production term when the strain rate is large when theexpert parameter LIPROD is set at 1.

9. The expert parameters EKCLIP and EPCLIP are respectively the minimum allowable values ofthe turbulent kinetic energy (k) and the turbulent dissipation rate (ε). They avoid non-physical neg-ative values. Moreover the minimum value of k (EKCLIP) allows to maintain a minimum residualturbulence in the domain. The default value is 1.E-5.

The minimum value of ε is chosen so that the computed value of the turbulent viscosity is reasona-ble. With a default value set to 1.E-5, the turbulent viscosity has a value of the order 1.E-6.

10. The input parameter KEGRID allows the use of a particular full multigrid strategy for k-ε com-putations. The Baldwin-Lomax model is used on the coarse grids during the full multigrid stage andthe k and ε initial solution is obtained from the Baldwin-Lomax model solution.

KEGRID corresponds to the last grid level on which the algebraic model is used. For example, ifthe computation is done with 4 levels of multigrid and KEGRID is equal to 2, the Baldwin-Lomaxmodel is used on the 333 (or level 4), 222 (or level 3) and 111 (or level 2) and the k-ε computationis initiated when transferring to the finest grid. If KEGRID is set to 3, the k-ε computation will beinitiated when transferring to 222. If KEGRID is greater than the number of multigrid levels, thecomputation will be started on the coarsest level with k-ε.

11. The expert parameter IKENC allows solving k-ε equations with a non-conservative approach.This settings avoids the appearance of an artificial source term in the k-ε equations during the con-vergence process. This artificial term comes from the residuals of the equation of the mass conser-vation that can be non-negligible at the beginning of the convergence process. This approach is newand not sufficiently tested to ensure that the loss of conservation is not excessive in all cases.

12. The expert parameter IKELED allows to avoid an excessive artificial dissipation of the standardcentral scheme into the boundary layer. Indeed this scheme can lead to a non-physical relaminarisa-tion in some specific test cases. An alternative computation of the artificial dissipation, based on theLocal Extrema Diminishing (LED) version of the Jameson-Schmidt-Turkel treatment has beenimplemented. It is active when the expert parameter IKELED is set to 1.

All the above mentioned limiters are very important for the robustness of k-ε compu-

tations. With the exception of the length scale LTMAX all limiters are given appropriatedefaults and we do not recommend to modify them. For LTMAX we recommend to set itto ten times the geometrical length scale.

1∆tkε--------- 1

∆t----- GAMMAT

Tturb

--------------------------+=

Prod ρε( )⁄ ·

Prod ρε( )⁄ 1≈Prod ρε( )⁄ 1<

Prod ρε( )⁄ ·


FINE™ 4-41

4-3.6.4 References

Ashford G.A. , and Powell K.G. 1996, "An unstructured grid generation and adaptative solutiontechnique for high-Reynolds number compressible flow", VKI (Von Karman Institute) LectureSeries 1996-06.

Baldwin B., Lomax H. (1978) 'Thin Layer Approximation and Algebraic Model for Separated Tur-bulent Flows', AIAA-78-257.

Chien K.Y. (1982) 'Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model', AIAA J., Vol. 20, No. 1.


Jameson A., Schmidt W., Turkel E. (1981) 'Numerical Solutions of the Euler Equations by FiniteVolume Methods using Runge-Kutta Time-Stepping Schemes', AIAA-81-1259.

Jameson A., 1995, "Positive schemes and shocks modelling for compressible flows", InternationalJournal for Numerical Methods in Fluids, Vol 20, pp 773-776.

Launder B.E. and Sharma B.I., 1974,"Application of the Energy-Dissipation Model of turbulence tothe Calculation of Flow Near a Spinning Disc", Letters in Heat and Mass Transfer, Vol. 1, pp. 131-138.

Launder B.E. and Spalding D.B., 1974, "The numerical computation of turbulent flow", Comput.Methods App. Mech. Eng., vol. 3, pp. 269-289.

Nichols R.H. (1990) 'A Two-Equation Model for Compressible Flows', AIAA paper 90-0494.

Sarkar S., Erlebacher G., Hussaini M.Y., Kreiss H.O. (1991) 'The analysis and modelling of dilata-tional terms in compressible turbulence', J Fluid Mech, Vol.227, pp.473-493.

Spalart P.R. and Allmaras S.R. (1992),"A one equation turbulence model for aerodynamic flows",,AIAA 92-0439

Vandromme D. (1991) 'Turbulence Modelling for Compressible Flows and Implementation inNavier-Stokes Solvers', VKI Lecture Series 1991-02.

Yang Z. and Shih T.H., 1993, "A k-e model for turbulence and transitional boundary layer", Near-Wall Turbulent Flows, R.M.C. So., C.G. Speziale and B.E. Launder(Editors), Elsevier-Science Pub-lishers B. V., pp. 165-175.

Zhang H.S., So R.M.C., Speziale C.G., Lai Y.G. (1991) 'A Near-Wall Model for Compressible Tur-bulent Flow', ICASE Report 91-82.

4-3.7 Gravity Forces

When gravity should be taken into account the box marked Gravity Forces should be checked. Ifgravity is activated by checking this box three input dialog boxes appear to define the Gravity Vec-

tor. The default gravity vector is defined as: (gx,gy,gz)=(0,-9.81,0) [m/s2], representing the gravityon Earth where the y-axis is oriented normal to the ground.

When the gravity is taken into account in the Navier-Stokes equations, the source terms

and are respectively introduced in the momentum and energy conservation equations

where ρ is the density, the gravity vector and the velocity vector.

ρg

ρ g V⋅( )

g V


4-42 FINE™

If the fluid is a liquid, the density is constant and you do not have any influence of the pressure ortemperature on the flow by interaction with the gravity. To simulate these interactions, one can usethe Boussinesq approximation in the gravity source terms. With this approximation, the density isdeveloped in the first order of the MacLaurin series. It becomes:

(4-85)

with α the compressibility and β the dilatation coefficients specified in the fluid properties.

This variation of the density is only applied to the gravity source term (Boussinesq approximation).Otherwise, the density is kept constant in the conservation equations. The value of is the

characteristic density specified in the Flow Model page. and are the reference values in

the Flow Model page.

When the gravity is taken into account, a reference pressure must be specified at a ref-

erence altitude to add the hydrostatic pressure in the initial pressure field. The referencepressure is the reference value in the Flow Model page. The reference altitude is speci-fied in the expert parameter IREFPT.

4-3.8 Low Speed Flow (Preconditioning)

This option appears in the Flow Model page only if the fluid type is compressible.

Indeed, the preconditioning is automatically used for an incompressible fluid.

This option is only implemented for central schemes. Consequently, the upwind spa-

tial scheme (Numerical Model page) is not available if the preconditioning option is cho-sen.

4-3.8.1 General Description

In the low subsonic Mach number regime, time-marching algorithms designed for compressibleflows show a pronounced lack of efficiency. When the magnitude of the flow velocity becomessmall in comparison with the acoustic speeds, time marching compressible codes converge veryslowly.

The problems faced by compressible codes at low Mach number are:

•High disparity between the convective eigenvalues u and the acoustic eigenvalues u+c, u-cleading to a much too restrictive time step for the convective waves causing thus poor conver-gence characteristics.

•Round off errors mostly due to the use of absolute pressure in the momentum equations.

• Impossibility to treat strictly incompressible flows.

Therefore the development of a low speed preconditioner was motivated in order to provide fastconvergence characteristics and accurate solutions as the Mach number approaches zero. Over thepast years and up to now, many attempts have been made to solve nearly incompressible flow prob-lems within available compressible codes and with minor programming efforts. The correctiveaction brought to the discretization of the conservation equations is called preconditioning and isderived from the artificial compressibility method introduced for incompressible flows by Chorin,(1967).

ρ ρref α p pref–( ) β T Tref–( )–+=

ρref

pref Tref


FINE™ 4-43

For steady state applications solved by time marching algorithms the time derivatives of theunknowns arising in the flow equations are of no physical meaning and can thus be modified with-out altering the final steady state solution. The idea of preconditioning precisely uses this propertyand consists of multiplying the time derivatives of the dependent variables with a matrix called pre-conditioning matrix. The main property of this matrix is to remove the stiffness of the eigenvalues.In addition, reduced flow variables such as the dynamic pressure and the dynamic enthalpy areintroduced, reducing drastically the round off errors at low Mach numbers. The acoustic wavespeed c is replaced by a pseudo-wave speed c’ of the same order of magnitude as the fluid speed. Tobe efficient the selected preconditioning matrix should be valid for inviscid computations as well asfor viscous computations with heat transfer.

The preconditioning methodology developed (Hakimi, 1997) is of sufficient generality and cantreat any type of fluids including perfect gases and incompressible Newtonian and non Newtonianfluids. On the numerical level, the solution procedure including space discretization, time integra-tion and boundary conditions have been adapted to the new transient behaviour of the conservationequations.

The low speed preconditioner has been validated for inviscid flows, viscous flows, turbulent flowsand unsteady flows. Efficient convergence rates and accurate solution have been obtained for Mach

numbers from M=0.1 to M=10-6, Reynolds numbers from Re=106 to 10-6 and aspect ratios from 1to 2000.

4-3.8.2 Basic Equations

The preconditioned equations considered for a compressible fluid are:

(4-86)

Compared to the unpreconditioned Navier-Stokes equations a pressure time derivative is added tothe continuity equation and also to the momentum equations. The internal energy equation is con-

sidered to build the system and is a dissipation term defined as: ;

is the velocity vector. At this stage the eigenvalues as well as the eigenvectors associ-ated with the preconditioned method defined by Eq. 4-86 are already completely defined.

4-3.8.3 General Form of the Preconditioning Matrix

The Preconditioned Reynolds-Averaged Navier-Stokes equations including turbulence and speciestransport equations written in a Cartesian frame of reference and integrated over a control volume

are expressed as:

1

β2-----∂p

∂t------ ∂ρu

∂x--------- ∂ρv

∂y--------- ∂ρw

∂z----------+ + + 0=

αu

β2-------∂p

∂t------ ρdu

dt------ ∂p

∂x------+ +

∂τxx

∂x----------

∂τyx

∂y----------

∂τzx

∂z----------+ +=

αv

β2------∂p

∂t------ ρdv

dt------ ∂p

∂y------+ +

∂τxy

∂x----------

∂τyy

∂y----------

∂τzy

∂z---------- ρg–+ +=

αw

β2--------∂p

∂t------ ρdw

dt------- ∂p

∂z------+ +

∂τxz

∂x----------

∂τyz

∂y----------

∂τzz

∂z---------+ +=

ρdedt------ p ∇ V⋅

⎝ ⎠⎛ ⎞+ ∇ k∇T

⎝ ⎠⎛ ⎞ εv+⋅=

εv εv τ ∇⋅⎝ ⎠⎛ ⎞ V⋅ τi j

∂vi

∂xj

-------= =

V u v w, ,( )=

Ω


4-44 FINE™

(4-87)

with

. (4-88)

The variable is the gauge pressure and the variables is the total gauge energy.

For a perfect gas with constant , is given by:

(4-89)

For an incompressible fluid with constant , is given by:

. (4-90)

The extension of the preconditioning matrix to the turbulence transport equations is then given in itsgeneral form both for compressible and incompressible fluids by:

(4-91)

* the term -1 should be added in compressible cases only.

We notice from Eq. 4-91 that the preconditioning matrix does not apply to the transport equations ofk and ε. This choice is the simplest and did not cause any particular instability for turbulent test casesrun so far.

4-3.8.4 Eigenvalues of the System

The eigenvalues of the preconditioned system defined by Eq. 4-86 are determined from the Eulerpart and can be obtained easily if the equations are written in terms of the primitive variables(p,u,v,w,p or e ).

Γ 1– ∂Q∂t------- Ωd∫

Ω∫∫ F Sd⋅

S

∫∫+ ST Ωd∫Ω∫∫=

Q pg u v w Eg ρk ρε, , , , , ,( )T=

pg p pref–= Eg

Cv Eg

Eg Cv T Tref–( ) V2

2-----+=

Cp Eg

Eg Cp T Tref–( ) V2

2-----+=

Γ 1–

1

β2----- 0 0 0 0 0 0 0 . . 0

1 α+( )u

β2--------------------- ρ 0 0 0 0 0 0 . . 0

1 α+( )v

β2--------------------- 0 ρ 0 0 0 0 0 . . 0

1 α+( )w

β2---------------------- 0 0 ρ 0 0 0 0 . . 0

αv2

Eg+

β2---------------------- 1–( )∗ 0 0 0 ρ 0 0 0 . . 0

0 0 0 0 0 1 0 0 . . 0

0 0 0 0 0 0 1 0 . . 0⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

=


FINE™ 4-45

Their expression is given in 3D for compressible fluids by:

(4-92)

The two parameters α and β are chosen so that the stiffness of the eigenvalues is minimised at lowspeed.

The corresponding eigenvalues for incompressible fluids are:

(4-93)

Compared to preconditioned system of compressible fluids, the first three eigenvalues are unchangedand the eigenvalues of the acoustic waves can be obtained by setting in Eq. 4-92 the speed of sound toinfinity. We note in particular that the acoustic eigenvalues are always of opposite sign showing thatthe flow remains subsonic with respect to the pseudo-sonic speed. As for the compressible precondi-tioner the two parameters α and β are chosen so that the stiffness of the eigenvalues is minimised atlow speed.

Note that if a k-ε model is considered, the corresponding eigenvalues will be:

(4-94)

4-3.8.5 Choice of the Parameters α, β and the Reference Velocity

The user control variables are .

are accessible through the Flow Model page and are referred to as reference pressure and

reference temperature.

A value of Tref of the order of magnitude of the expected temperature field will reduce

the machine round-off errors influence on the temperature field.

The value of Pref fixes the absolute level of the pressure in the field. This value is used in

the equation of state for a compressible fluid and in the second order artificial dissipationterm. A value of Pref close to the real pressure level is therefore recommended.

The parameter α is accessible in the ‘Expert parameters’ list of the Control variables page as ALP-HAP. According to several computations accomplished with the central scheme, good convergencerates were obtained for values of α lying in the range [-1,1]. So far the best value is found to be α=-1.This optimal value is not surprising since it increases the spectral radius and therefore adds an addi-tional amount of artificial dissipation.

Τhe preconditioning parameter β is imposed by the user in the Numerical Model page through a coef-

ficient β∗ and a characteristic velocity such that

λ1 2, 3, V n⋅=

λ4 5 ,12--- V n 1 α–

β2

c2-----+

⎝ ⎠⎜ ⎟⎛ ⎞

⋅ V n 1 α–β2

c2-----+

⎝ ⎠⎜ ⎟⎛ ⎞

⋅⎝ ⎠⎜ ⎟⎛ ⎞

2

4 n2 V n⋅( )

2

c2------------------–

⎝ ⎠⎜ ⎟⎛ ⎞

β2+±=

λ1 2, 3, V n⋅=

λ4 5 ,12--- V n 1 α–( )⋅ V n 1 α–( )⋅( )

24n

2β2+±=

λi k-ε V n⋅=

Pref Tref α β,,,

Pref Tref,

Uref


4-46 FINE™

(4-95)

is representative of the maximum velocity in the flow field. For example, in external flows,

Uref could be taken as the free stream velocity whereas in internal flows it could be taken as the

maximum inlet velocity. For the user’s convenience, the constant Uref is however always set equalto the reference velocity specified in the Flow Model page and used in the calculation of the Rey-nolds Number.

The choice of Uref has an influence on the convergence.

The default value of β∗ is 3. Based on our experience with the presented low speed preconditionerthe parameter β∗ can be taken of order unity for inviscid flow computations. For viscous computa-tions associated with Reynolds numbers greater than about Re=1000, a constant value β∗ of orderunity is also adequate. If convergence difficulties are encountered at the very beginning of a compu-tation, it is recommended to increase the value of the parameter β∗. Remember however that a toolarge value of β∗ will introduce excessive artificial dissipation into the solution.For lower Reynolds number the parameter β∗ has to vary in order to preserve numerical stability anda good convergence rate. The parameter β∗ should increase as the Reynolds number decreases andmay vary over several orders of magnitude (see Figure 4.3.8-4).

If the local velocity scaling option is activated in the Numerical Model page, another definition of βis used:

(4-96)

where is the local velocity.

FIGURE 4.3.8-4 Typical variation of the preconditioning parameter β* with Reynolds number

For high Reynolds flows it is suggested to choose β among the following values:

• β=3

• β=30

• β=300

Too small or too big values of β may lead to divergence and to a too dissipative solution (if β is toohigh)

β2 β∗Uref2

=

Uref

β2 β∗max Uref2

Uloc2,( )=

Uloc

101 100 1000 100001

10

100

10000

1000

β*

Re

Characteristic and Reference Values Flow Model

FINE™ 4-47

4-3.8.6 References

Chorin, A. J. (1967) ’A numerical method for solving incompressible viscous flow problems’, J. ofComput. Phys., Vol 2, pp. 12-26.


4-4 Characteristic and Reference Values

4-4.1 Reynolds Number Related Information

The user has to specify some characteristic values (length, velocity and density). These values areused to calculate the Reynolds Number (only plotted when the kinematic viscosity is constant) thatprovides an useful information to choose the suitable model (section 4-3.5). These characteristicvalues can be used for other purposes as well.

The characteristic length is used:

— in the outlet boundary condition for which the mass flow is imposed with pressure adapta-tion,

— in the computation of CP1 and CP3 for cylindrical cases.

The characteristic velocity is used:

— in the preconditioning method to compute the parameter β (see section 4-3.8.5),

— in the computation of the solid data Cf (normalized by ).

The characteristic density is used:

— in the Boussinesq approximation for incompressible fluid (Eq. 4-85),

— in the computation of the solid data Cf (normalized by ),

— in the evaluation of the Reynolds number only when the dynamic viscosity of the fluid isspecified in the Sutherland law on the Fluid Model page.

4-4.2 Reference Values

The reference values have been introduced for the precoditioning to define a gauge pressure and agauge total energy. Now these reference values have some additional uses which are describedhereafter:

— in the Boussinesq approximation for incompressible fluid (Eq. 4-85),

— in the outlet boundary condition for which the mass flow is imposed with pressure adapta-tion.

ρrefUref2

2⁄( )

ρrefUref2

2⁄( )

Flow Model Characteristic and Reference Values

4-48 FINE™

FINE™ 5-1

CHAPTER 5: Rotating Machinery

5-1 OverviewThe Rotating Machinery page contains the following thumbnails:

• Rotating Blocks defining for each block typical information concerning cylindrical cases. Thisthumbnail is only available when the mesh is cylindrical (see Mesh/Properties... to seewhether the mesh is cylindrical or Cartesian). See section 5-2 for more detail on this thumb-nail.

• Rotor/Stator defining the properties of each rotor/stator interface. This thumbnail is only avail-able when the mesh contains Rotor/Stator interfaces. Rotor/Stator interfaces are defined inIGG™ as ROT boundary condition. For more detail on this thumbnail see section 5-3.

• Throughflow Blocks giving access to two-dimensional throughflow Euler simulation and thisis only accessible for non-viscous flow (Euler selected as mathematical model on the FlowModel page). See Chapter 6 for more detail on the options available under this thumbnail.

Rotating Machinery Rotating Blocks

5-2 FINE™

5-2 Rotating Blocks

FIGURE 5.2.0-1 Rotating Blocks on Rotating Machinery Page

When selecting the Rotating Blocks thumbnail the page appears as shown in Figure 5.2.0-1. On theleft a list of all blocks is displayed. It is possible to group the blocks that have the same propertieson this page:

1. Select several blocks in the list of blocks by simply clicking on them. Clicking on a block dese-lects the currently selected block(s). It is possible to select several blocks situated one afteranother in the list by clicking on the first one and holding the left mouse button while selectingthe next. To select a group of blocks which are not situated one after another in the list, click oneach of them while keeping the <Ctrl> key pressed.

2. Click on the Group button. A text box will appear just below the Group button. Place the cursorin the text box and type the name of the group and press <Enter>. The name of the group willappear on the list of blocks in red with a plus sign on the left of the name. To see the blocks thatare included in a certain group double click on the name of the group or click on the + symbol infront of the name.

3. To remove a group of blocks select the group and click on the Ungroup button. The group willbe removed and the blocks that were in this group will be listed again in the list as separateblocks.

On the right of the list with blocks the information is given for the selected block or group ofblocks. If multiple blocks are selected the information is only displayed for the first selected block.For each block the current and maximum number of nodes in the three grid directions is given. Fouritems need to be defined by the user: the streamwise direction, the spanwise direction, the azimuthaldirection and the rotational speed:

— The streamwise, spanwise and azimuthal directions allow to determine the block orientation.Remark that if the AutoGrid module is used for the grid generation, the streamwise directionis automatically taken as being the k-direction, the spanwise direction as the j-direction andthe azimuthal direction as the i-direction.

— EURANUS flow solver solves the equations in a relative frame of reference. This impliesthat the mesh blocks surrounding rotating blades rotate with the blades and should thereforebeen set as "rotating" in this page. The rotational speed of the block has to be given in RPM(Revolutions Per Minute). A positive value for the rotation speed indicates a rotation in pos-

Rotor/Stator Interaction in the FINE™ Interface Rotating Machinery

FINE™ 5-3

itive θ-direction with θ positive according to a right handed coordinate system. InFigure 5.2.0-2 this is illustrated for the case where the z-axis is the axis of rotation which isautomatically the case in a mesh created with AutoGrid.

FIGURE 5.2.0-2 Positive rotation speed

The different computations in a project can not have different configuration settings. If

any of the settings in this area is changed, the modifications will be taken for all (activeand not active) computations.

The rotation axis should be the z-axis in order to be compatible with the EURANUS

flow solver.

5-3 Rotor/Stator Interaction in the FINE™ InterfaceThe Rotor-Stator thumbnail gives access to the definition of the rotor/stator interfaces as shown inFigure 5.3.0-3. This thumbnail is only accessible when the mesh contains rotor/stator interfaces.Rotor/stator interfaces are defined in IGG™ as ROT boundary condition. Consult the IGG™ man-ual for more detailed information on how to define this boundary condition. For more theoreticalinformation on rotor/stator interfaces see section 5-5.

The rotor/stator patches should not include R=0 regions.

On the left the list of patches is displayed which are defined as part of a rotor/stator interface inIGG™ (boundary condition type: "ROT"). It is possible to display only a limited amount of patchesby using the Filter. Type in the text box the part of the name that is common to all patches to displayand press <Enter>. All patches containing in the name the entered text will be displayed. Note thatthe filter is case insensitive.

It is possible to group patches that have the same definition by selecting them in the list and click-ing on the Group button. A text box will appear below this button which allows to enter a name forthe group. The group will be displayed in red in the list of patches. Double click on the group nameto see which patches are in the group. To select multiple patches select them while keeping the<Ctrl> key pressed. To remove the group simply select the group from the list and click onUngroup. The patches in the selected group will be put back into the list of patches and the groupname will be removed from the list.

Rotating Machinery Rotor/Stator Interaction in the FINE™ Interface

5-4 FINE™

Multiple rotor/stator interfaces can be treated in one single project. Each rotor/stator interface isindicated by an ID number and each of them may contain an arbitrary number of upstream anddownstream patches. For each patch in the list the ID number of the corresponding rotor/statorinterface has to be provided by the user. Also it should be specified whether the patch is located inthe upstream or downstream side of the interface. It should be mentioned that no hypothesis is madeon the direction of the flow through the interface. The purpose of the upstream and downstreamdenominations is only to establish the two groups of patches belonging to respectively the rotor andthe stator side.

.The ID number of the rotor/stator interface cannot be higher than the total number of

rotor/stator interfaces.

FIGURE 5.3.0-3 Rotor/stator Interface Definition

In addition to the ID number and the upstream/downstream side specifications the user has to selectalso:

• the order of extrapolation (zero or first order). Zero order extrapolation (default) is used inmost cases and usually provides satisfactory results. First order extrapolation may be useful incase of important flow gradients in the direction normal to the interface together with a rela-tively coarse mesh.

• one of the four available steady state techniques (for steady state applications only), i.e. theLocal Conservative Coupling, Conservative Coupling by Pitchwise Rows, Full Non MatchingMixing plane and Full Non Matching Frozen Rotor approaches.

1. The first approach is only recommended for the rotor/stator interface between an impeller and avolute. Experience has shown that in cases where significant flow variations are observed in the cir-cumferential direction (as for instance in the case of rotor-volute interactions) it is more stable tobase the flux decomposition on the local flow direction as it is done in the Local Conservative Cou-pling. Small conservation errors can be observed with this technique, which is therefore only usedfor special configurations.

How to Set-up a Simulation with Rotor/Stator Interfaces? Rotating Machinery

FINE™ 5-5

2. The second approach is recommended due to its capability to provide an exact conservation ofmass flow, momentum and energy through the interface. This approach adopts the same couplingprocedure for all the nodes along the circumferential direction, even if the local flow direction isdifferent from the averaged one. This technique offers the advantage of being able to guarantee astrict conservation of mass, momentum and energy through the interface. Moreover it shows to bevery robust and is therefore used by default.

3. The third approach is respecting an exact conservation of mass flow, momentum and energythrough the interface as the second approach but has less constraint on the interface geometry.

4. The fourth approach is considering the rotor/stator interface as a perfect connection and isneglecting the rotor movement in the connecting algorithm. In this approach, the periodicities mustbe equal between the rotor and the stator.

5-4 How to Set-up a Simulation with Rotor/Stator Interfaces?Three different approaches are available in FINE™ to simulate the interaction between rotating andnon-rotating blocks:

Steady state:

•Mixing plane approach: a pitchwise averaging of the flow solution is performed at the rotor/stator interface and the exchange of information at the interface depends on the local directionof the flow. See section 5-4.1 for more detail on how to use this approach and section 5-5.3 andsection 5-5.3 for the theoretical background.

• Frozen rotor: a steady simulation of one specific position of the rotor with respect to the stator.For more information on how to set up a project according to this method see section 5-4.2.For its theoretical background see section 5-5.4.4.

Unsteady:

•Domain scaling method: unsteady simulation in which the mesh periodicities are constrainedto be identical on both sides of the interface. See section 5-4.3 for more detail on how to usethis approach and section 5-5.4 for the theoretical background.

• Phase lagged method: unsteady simulation in which the mesh periodicities are not constrainedto be identical on both sides of the interface. See section 5-4.4 for more detail on how to usethis approach and section 5-5.3 for the theoretical background.

5-4.1 Mixing Plane Approach

In the mixing plane approach the flow solution at the rotor/stator interface is azimuthally averagedand the exchange of information at the interface depends on the local direction of the flow. In thissection it is described how to use this approach in FINE™. For more theoretical detail on the mix-ing plane approach itself consult section section 5-5.2 and section 5-5.3.

5-4.1.1 Geometrical Constraints

The default mixing plane method (Local Conservative Coupling and Conservative Coupling byPitchwise Rows) used in FINE™ imposes the following geometrical constraints:

Rotating Machinery How to Set-up a Simulation with Rotor/Stator Interfaces?

5-6 FINE™

• The patches on both sides of the rotor/stator interface must cover the same range in spanwisedirection,

• The meshes need not to match in the spanwise direction, but the azimuthal mesh lines on theboundary must be circular arcs.

An illustration of these constraints is given in Figure 5.4.1-4. Consisting of two stripes, the depictedconfiguration provides a complete description of the capabilities. The upstream side of the quasi-steady interface consists of three blocks, represented by the bold frames and the surface meshes,while a single block is assumed for the downstream side. A gap may exist between two blocks, e.g.,if the mixing plane coincides with the exit plane of a blade row having a blunt trailing edge. Thegrid points distribution are different for each of the boundary patches involved, but the pitchwisegrid lines have constant radius and the pitchwise line along which two patches of the same side join(e.g., BC 1 and BC 3) exists as an inner grid line on all other boundaries. In the example, the inter-face is thus decomposed into two stripes, stripe 1, consisting of BC 1 and BC 2 on the upstream sideand BC 5 on the downstream side, and stripe 2, consisting of BC 3 and BC 4 on the upstream sideand BC 6 on the downstream side.

.

FIGURE 5.4.1-4 Example of stripe configuration

A new interpolation technique (Full Non Matching Mixing plane) has been implemented to avoidthose geometrical constraints. This new technique is based on the full non-matching algorithm andhas clear advantages:

• The geometrical constraints have been removed, the only remaining constraint being that therotor/stator patches belonging to a given interface should lie on the same common axisymmet-ric surface.


FINE™ 5-7

•An exact conservation of the mass flow, momentum and energy is guaranteed.

In special configurations such as rotor-volute interaction it is preferable to use Local

Conservative Coupling and thus it may be required to use the previous approach(IRSNEW=0).

When setting the expert parameter IRSNEW=1 only Full Non Matching Mixing plane

approach will be applied on all rotor/stator interfaces even if another mixing planeapproach has been selected in the Rotating Machinery page under Rotor-Stator thumb-nail.

5-4.1.2 Constraints on the Mesh

Only one blade passage needs to be meshed for both the rotor and the stator, regardless of theirrespective periodicity. The boundary condition type must be set to "ROT" in IGG™ for all gridpatches belonging to a rotor/stator interface.

5-4.1.3 Settings in FINE™

1. The mixing plane approach is a steady simulation technique which requires to set on the FlowModel page the Time Configuration to Steady.

2. The patches that have boundary condition type "ROT" in the mesh are listed in FINE™ on theRotating Machinery page under the Rotor-Stator thumbnail. The user has to specify for each ofthese patches:

• an ID number that will identify the rotor/stator interface (useful when multistage),

• a switch to indicate if the patch is belonging to the "upstream" or "downstream" part of therotor/stator interface.

FIGURE 5.4.1-5 Aachen Turbine: Upstream/Downstream and ID number identification

• the boundary condition: Local Conservative Coupling, Conservative Coupling by PitchwiseRows or Full Non Matching Mixing plane as described in section 5-3.

When setting IRSNEW=1 only conservative coupling by pitchwise rows is available.

Selecting local conservative coupling in the FINE™ interface will have no effect whenIRSNEW=1.

Flow Direction

ID = 1

ID = 2

Downstream

DownstreamUpstream

Upstream

Flow Direction

ID = 1

ID = 2

Downstream

DownstreamUpstream

Upstream


5-8 FINE™

5-4.1.4 Illustrative Example

To illustrate the mixing plane approach the flow around a cube is considered as shown inFigure 5.4.1-6. The flow is entering the domain at the bottom of the figure. The upstream portion ofthe domain is the 'rotor' with a cube fixed on it. The second part is a 'stator'. Due to the pitch wiseaveraging process one can see that the vortex occurring slightly downstream the 'trailing edge' ofthe cube is spread when entering in the 'stator' component. If the rotational speed of the cube ishigh, this approximation is acceptable since one can consider that the stator "sees" a more statisti-cally average flow. If the rotational speed is low, this approximation is essentially invalid and thusanother method should be considered.

FIGURE 5.4.1-6 Flow around a cube: Mixing Plane approach

5-4.1.5 Expert Parameters

This section provides a summary of the expert parameters related to mixing plane approach.

a) Selection of Technique

IRSNEW = 0: default mixing plane interpolation technique imposing geometrical constraints aslisted in section 5-4.1.1.

= 1: new full non-matching algorithm for rotor/stator interfaces removing the geometrical con-straints of the default mixing plane technique. More detail on this interpolation technique can befound in section 5-5.3.

When setting IRSNEW=1 only conservative coupling by pitchwise rows is available.

Selecting local conservative coupling in the FINE™ interface will have no effect whenIRSNEW=1.


FINE™ 5-9

b) Under-relaxation with Default Mixing Plane Approach

NQSTDY gives the possibility to the user to update the rotor-stator boundary conditions everyNQSTDY iterations. If the parameter NQSTDY is set to zero (default), the update is done at everyRunge-Kutta step. This is an under-relaxation technique that is rarely used.

Before the mixing process, the averaged variables can be under-relaxed to stabilize the calculation:

RQSTDY= 1 (default): no relaxation

= 0 to 1: under-relaxation

This is another under-relaxation technique that allows to limit the changes in the variables from oneiteration to the next. This technique is used in special cases where stability problems are encoun-tered.

5-4.2 Frozen Rotor

The basic idea at the origin of the frozen rotor technique consists of neglecting the rotor movementin the connecting algorithm.

The governing equations are solved for the rotor in a rotating frame of reference, including Coriolisand centrifugal forces; whereas, the equations for the stator are solved in a absolute referenceframe. The two components are literally connected, and hence a rotor-stator approximation is notrequired, rather the continuity of velocity components and pressure is imposed. As a result, the finalsteady solution will be depending on the relative position of the rotor and the stator. Unsteady 'his-tory effect' (such as shedding separated zones) are neglected.

It is usually well accepted that the frozen rotor approach is an appropriate solution for the treatmentof rotor-volute interactions, where pitchwise variations of the flow are too important to beneglected. However, it requires the meshing of the complete impeller (all passages). Another draw-back is that the flow solution depends on the rotor position.


Exactly as for the domain scaling approach a constraint must be satisfied on the mesh periodicity.The pitchwise distance must be the same for both side of the rotor/stator and coincident (no gapallowed between rotor and stator components in the pitchwise direction). For each different positionof the rotor with respect to the stator a new mesh will have to be created in IGG™ and a new steadycalculation has to be performed.


There are three ways to run a frozen rotor calculation:

1. To mesh all blade rows completely and to use matching connections (CON) in IGG™ for thepatches at the interface of the rotor and the stator. The blocks of the rotor should be made rotat-ing, as well as the boundary conditions. A steady calculation can be run for this configuration. Anon matching (NMB) connection or periodic non matching (PERNM) connection can not beused in this case: even though the computation might run the result would not be correct. Thiswas previously the only way to perform frozen rotor calculations in FINE™. This approach isno longer used as the constraint on matching connections is too restrictive.

Only CON matching connections are allowed in this first method.

2. To create a mesh covering the same pitchwise distance on both sides of the interface and toimpose Full Non Matching Frozen Rotor in the Rotating Machinery page under the Rotor-Statorthumbnail. Furthermore the user has to specify for each of these patches the ID and the


5-10 FINE™

upstream/downstream location as described in section 5.4.1.3 at step 2. Therefore, the boundarycondition type must be set to "ROT" in IGG™ for all grid patches belonging to a rotor/statorinterface.

3. To start an unsteady computation by imposing iterations as a steady initialization in the ControlVariables page.

Note that for example for an impeller-volute computation the complete impeller

would need to be meshed in all three cases since the periodicity of the volute is 1.


Results obtained from frozen rotor calculations usually look similar to unsteady ones. Moredetailed analysis shows that the approximation introduced in the connection algorithm induces adeviation of the wake when passing through the interface.

FIGURE 5.4.2-7 Aachen Turbine: Frozen Rotor approach

As an illustration the frozen rotor method is compared to the sliding mesh approach for the AachenTurbine in Figure 5.4.2-7 and Figure 5.4.2-8.

FIGURE 5.4.2-8 Aachen Turbine: Domain Scaling (Sliding Mesh) approach


FINE™ 5-11


The only expert parameter in case of a frozen rotor simulation is IRSNEW. This parameter shouldalways be set to 2 when performing a frozen rotor simulation.

5-4.3 Domain Scaling Method

The Domain Scaling Method is an unsteady simulation technique for rotor/stator interfaces. Theeffect of displacement due to rotation is taken into account. At each time step, the rotor is set at itscorrect position and equations are solved for that particular time step for the whole computationdomain. The final solution is therefore a succession of instantaneous solutions for each incrementof the rotor position.


The boundary condition type must be set to "ROT" in IGG™ for all grid patches belonging to arotor/stator interface. The blade passages of each blade row to include in the mesh should cover thesame pitch distance (have the same periodicity). If the periodicity of the rotor and the stator is notthe same this can be solved in three different ways:

•modelling a higher number of blade passages on each side to find a common periodicity,

• scaling the geometry (with the scaling being as close to 1 as possible). The common way toscale the geometry is to modify the number of blades during the mesh generation process. Thetime frequencies are resolved with an error that is proportional to the scaling coefficient.

• using the phase lagged approach explained in section 5-4.4.

Apart from this constraint on the periodicity, there is no constraint on the patches and mesh nodesconfigurations.


1. Domain Scaling Method is an unsteady simulation technique so the Time Configuration in theFlow Model page should be set to Unsteady.

2. By default, in the Rotating Machinery page under Rotor-Stator thumbnail, the Domain Scalingapproach is selected. However the user has to specify for each of these patches the ID and theupstream/downstream location as described in section 5.4.1.3 at step 2. Therefore, the boundarycondition type must be set to "ROT" in IGG™ for all grid patches belonging to a rotor/statorinterface.

3. The initialization process can be performed in two ways:

•A steady state initialization is performed in a separate computation with steady Time Configu-ration. It is suggested to model all rotor/stator interfaces in this case using frozen rotorapproach. The unsteady domain scaling computation is using the result of this steady computa-tion as initial solution. See Chapter 10 for more information on how to start a computationfrom an initial solution file.

• The steady state initialization is automatically performed before starting the time accuratecomputation (that means within the same computation), switching to unsteady Time Configu-ration in the Flow Model page and selecting in the interface an appropriate Number of SteadyIterations in the Steady Initialization parameters on the Control Variables page.

4. The Number Of Angular Positions is defined in the Control Variables page.

5. The Number Of Time Steps is defined in the Control Variables page.

6. The Outputs Files available in the Control Variables page are:


5-12 FINE™

•Output For Visualization/At end only and Multiple Files: multiple set of output files saved forrestart of the unsteady computation and visualization in CFView™ only available at the end ofthe computation.

•Output For Visualization/At end only and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ only available at the end ofthe computation.

•Output For Visualization/Intermediate and Multiple Files: multiple set of output files saved forrestart of the unsteady computation and visualization in CFView™ during the computation.

•Output For Visualization/Intermediate and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ during the computation.

IRSNEW =1 to activate the full non-matching interpolation algorithm at the rotor/sta-

tor interface. This is in general recommended since it requires less memory and signifi-cantly reduces the pre-processing time. It also offers the advantage that conservation ofmass, momentum and energy is guaranteed.

Note: When a sliding mesh simulation with IRSNEW=1 is started from a mixing

plane simulation with IRSNEW=0 it is not possible to use the *.fnmb file of the mixingplane simulation to read in the initialization of the sliding mesh simulation. It is neces-sary to compute the full non-matching connections again.


For the example case of the flow around a cube where the flow is entering the domain at the bottomof Figure 5.4.3-9. The upstream portion of the domain is the 'rotor' with a cube fixed on it. The sec-ond part is a 'stator'. With domain scaling approach, one can observe a strong vortex shed into thestator passage, leading to a correct physical simulation of the unsteady phenomenon (at the expenseof much higher CPU time compared to mixing plane approach).

FIGURE 5.4.3-9 Flow around a cube: Domain Scaling method


FINE™ 5-13


The following expert parameters can be used with an unsteady computation using domain scaling method:

IRSNEW = 0 (default): old interpolation method at the rotor/stator interface

IRSNEW = 1: full non-matching interpolation at the rotor/stator interface. This is in general recommendedsince less memory is required.

Parameters for Saving/Reading of Pre-Processing Data:

When IRSNEW = 0 (default approach):

ISIDAT = 1 (default): pre-processing performed and results saved in the file with extension ".burs".

ISIDAT = 2: pre-processing not performed, results read in the file with extension ".burs".

When IRSNEW = 1 (new approach):

IFNMFI =1 (default): pre-processing performed and results saved in .fnmb file.

IFNMFI =2: pre-processing not performed and results read from .fnmb file.

In both cases the pre-processing needs to be restarted if either the Number Of Angular Positions or the numberof grid levels is changed.

ICYOUT =1 is used in combination with Multiple Files option to avoid overwritting of the output files at eachblade passage.

5-4.4 Phase Lagged Method

The Phase Lagged Method is an unsteady simulation technique for rotor/stator interfaces. The effect of dis-placement due to rotation is taken into account. At each time step, the rotor is set at its correct position andequations are solved for that particular time step for the whole computation domain. The final solution is there-fore a succession of instantanious solutions for each increment of the rotor position.

This method is allowing the user to reduce the CPU time needed for computing an unsteady simulation of a tur-bomachinery stage (rotor-stator interaction). This capability has been implemented as an additional functional-ity into the release FINE™/Turbo.


The only constraints is that the boundary condition type must be set to "ROT" in IGG™ for all grid patchesbelonging to a rotor/stator interface.

It is recommended to have an overlapping in the circumferential direction between the channel(s)

of the rotor and the channel(s) of the stator.


1. Phase Lagged Method is an unsteady simulation technique so the Time Configuration in the Flow Modelpage should be set to Unsteady.

2. At the top of the Rotating Machinery page, the Phase Lagged option has to be activated and under Rotor-Stator thumbnail, the Phase Lagged approach is selected automatically. However the user has to specify foreach of these patches the ID and the upstream/downstream location as described in section 5.4.1.3 at step 2.Therefore, the boundary condition type must be set to "ROT" in IGG™ for all grid patches belonging to arotor/stator interface.

3. The initialization process can be performed in two ways:


5-14 FINE™

•A steady state initialization is performed in a separate computation with steady Time Configu-ration. It is suggested to model all rotor/stator interfaces in this case using frozen rotorapproach. The unsteady domain scaling computation is using the result of this steady computa-tion as initial solution. See Chapter 10 for more information on how to start a computationfrom an initial solution file.

• The steady state initialization is automatically performed before starting the time accuratecomputation (that means within the same computation), switching to unsteady Time Configu-ration in the Flow Model page and selecting in the interface an appropriate Number of SteadyIterations in the Steady Initialization parameters on the Control Variables page.

4. The Number Of Angular Positions defined in the Control Variables page is the number of timestep per full revolution (2π) of the rotor. In theory, the number of time step per full rotation hasto be a multiple of the number of blades in the rotor (Nbrotor) and number of blades in the stator(Nbstator).

Number Of Angular Positions = i x Nbrotor x Nbstator

The two periods of blade passing frequencies are respectively (ixNbrotorx∆t) and

(ixNbstatorx∆t). Since the number of time step per passage is usually imposed around 40,the value of i should be adjusted so that (ixNbrotor) and (ixNbstator) are both close to this

number. By experience, if the number of time step per passage is lower than 30 the solu-tion starts to be deteriorated.

5. The Number Of Time Steps in the Control Variable page is defined as:

Number Of Time Steps = j x (Number Of Angular Positions)/min(Nbrotor,Nbstator)

During the calculation, it is recommended to repeat the longer period at least 15 to 20

times (j evolves from 15 to 20). By experience, usually after 20 times (j=20), the flowbecomes periodic. There are thus no need to make many full rotation and sometimeseven one full rotation.

6. The Outputs Files available in the Control Variables page are:

•Output For Visualization/At end only and Multiple Files: multiple set of output files saved forrestart of the unsteady computation and visualization in CFView™ only available at the end ofthe computation.

•Output For Visualization/At end only and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ only available at the end ofthe computation.

•Output For Visualization/Intermediate and Multiple Files: multiple set of output files saved forrestart of the unsteady computation and visualization in CFView™ during the computation.

•Output For Visualization/Intermediate and One Output File: one set of output files saved forrestart of the unsteady computation and visualization in CFView™ during the computation.

By default, the Phase Lagged method used to compute the viscous fluxes at the rotor/

stator interface from dummy cells values set from other side inner cells instead fromsame side inner cells by extrapolation (more detail in section 5-5.4.3).

Theoretical Background on Rotor/Stator Interfaces Rotating Machinery

FINE™ 5-15


Results obtained from Phase Lagged calculations usually look similar to unsteady ones when the expertparameter IRSVFL=1.

FIGURE 5.4.4-10 Aachen Turbine: Domain Scaling method: IRSVFL=0 vs IRSVFL=1


The following expert parameters can be used with an unsteady computation using phase lagged method:

ICYOUT =1 is used in combination with Multiple Files option to avoid overwritting of the output files ateach blade passage.

RELPHL =0.5 0.5 if necessary, under-relaxation factor can be applied on Periodic and R/S boundaryconditions by reducing the two values of the expert parameter for respectively the periodic and the R/Sboundary conditions.

NPLOUT =0 (by default) enables to visualize multiple non periodic passage output in CFView™ byloading the corresponding ’.cfv’ file.

5-5 Theoretical Background on Rotor/Stator Interfaces

5-5.1 Introduction

The relative motion between successive blade rows together with boundary layers, wakes, shocks and tipleakage jets are the major sources of unsteadiness that may affect a turbomachinery flow locally or as ittravels through the next rows. All these interactions are strongly coupled, increasing in magnitude as thegap between successive blade rows is decreased, and affecting consequently the performance of themachine.

Old Viscous Fluxes Detection at R/S interface

IRSVFL = 0

New Viscous Fluxes Detection at R/S interface

IRSVFL = 1

Rotating Machinery Theoretical Background on Rotor/Stator Interfaces

5-16 FINE™

Solving for such flows requires an unsteady and viscous flow solver with the capability to manageenormous data storage. One way to optimize the computer memory requirement is to resolve thesteady flowfield on a truncated computational domain. This requires a pitchwise averaging processto be performed at the so-called rotor/stator interfaces. This particular boundary condition is availa-ble under the FINE™/Turbo environment as the mixing plane approach. The rotor-stator interactionis done by exchanging circumferentially averaged flow quantities. Physically, this means that theblade wake or separation occurring in the blade passage are mixed circumferentially before enteringthe downstream component. As a result, the velocity components and pressure is uniform in the cir-cumferential direction at the rotor/stator interface. This physical approximation tends to becomemore acceptable as rotational speed is increased. This mixing plane technique is by far the mostused rotor/stator modeling in industry approach. See section 5-5.2 and section 5-5.3 for more detailon the mixing plane approach.

The second step allowing for a higher level of accuracy consists of considering an unsteady rotor/stator interaction. Various techniques allowing to treat configurations with an arbitrary number ofblades in the rotor and the stator have been proposed by many authors (Giles, 1990, Lemeur, 1992,Erdos et al, 1977, He, 1997), each of them having their own advantages and disadvantages, each ofthem affecting differently the memory requirement, solution time and the most important parame-ter, the accuracy of the computed flow solution. But none of these techniques allows to resolve on atruncated computational domain all time frequencies present in the turbomachinery configuration,except if the pitch distance is the same in the successive rotors and stators. In fact, each of them areaffecting the computed time frequencies and Fourier modes that are propagating the flow informa-tion inside the gap region.

The Domain Scaling Method is another type of unsteady rotor/stator interface treatment (Rai,1989), that has been selected and implemented in the EURANUS flow solver. This technique isbased on the constraint that the pitch distance must be identical on both sides of the interface. If thenumbers of blades in the rotor and the stator are different, this implies either to increase the numberof passages modelled or to scale the geometry. The Domain Scaling Method presents the advantagethat it allows to resolve all time frequencies with an error that is proportional to the scaling coeffi-cient. The accuracy of the computed unsteady flow solution may then be improved at the expenseof more data storage and larger solution time if more blade passages are considered.

Finally, the Phase Lagged Method is the last type of unsteady rotor/stator interface treatment thathas been selected and implemented in the EURANUS flow solver. This technique is removing theDomain Scaling constraint that the pitch distance must be identical on both sides of the interface.The Phase Lagged Method presents the advantage that it allows to resolve all time frequencies withan error that is proportional to the scaling coefficient. The accuracy of the computed unsteady flowsolution may then be improved at the expense of more data storage and larger solution time if moreblade passages are considered.

5-5.2 Default Mixing Plane Approach

5-5.2.1 Geometrical and Topological Constraints

The rotor-stator interfaces are defined by stripes. A stripe is the element along which the requiredaveraging in tangential direction is carried out. It is composed of a number of boundary patcheswhich must cover the same range in the spanwise direction. The upstream and the downstreamsides are distinguished. Each boundary condition must belong either to the upstream or to thedownstream side. These two sides communicate through the exchange of pitch-averaged variables.The meshes do not need to match in the spanwise direction, but the azimuthal mesh lines on theboundaries must be circular arcs.


FINE™ 5-17

5-5.2.2 Communication Process

On both sides, the flow state is extrapolated from the inner cells onto the interface. It is then inter-polated onto meshes that share the same spanwise grid point distribution on both sides. The pitch-wise averaging is carried out on those meshes and the mixing process, depending on the boundarycondition type, is applied. This mixing process combines the variable on one side of the interfacewith the pitchwise averaged variables of the other side. Once the mixing process is completed, theflow state is interpolated back onto the initial mesh interface and the dummy cells are set to imposethe calculated variables on the interface.

The extrapolation of the flow state from the inner cells onto the interface can be done using differ-ent techniques. These are the same as those used by the outlet boundary conditions exposed in sec-tion 8-5.

Before the mixing process, the averaged variables can be underrelaxed to stabilize the calculation.The relaxation factor is user input (RQSTDY), the default value being 1, which means that nounder-relaxation is performed in the default configuration of the solver. The possibility is given tothe user to update the rotor-stator boundary conditions every NQSTDY iterations. If the parameterNQSTDY is set to zero (default), the update is done at every Runge-Kutta step.

5-5.2.3 Different Available Boundary Conditions

The rotor/stator interface included in the EURANUS flow solver exchange the mass, momentum,and energy fluxes instead of the classical primitive variables. The advantage of a flux-basedapproach is that a more strict global conservation through the interface is ensured. Two kinds ofboundary conditions are currently available and are described in this paragraph:

• The local conservative coupling (with flux decoding),

• The conservative coupling by pitchwise rows (no flux decoding).

a) Local Conservative Coupling (With Flux Decoding):

On each mesh point of both sides of the interface, a test is done to detect whether the interface canbe considered as a sub- or supersonic in- or outlet. Then a transfer of the fluxes and pressure fromthe other side is performed depending on the result of the test.

• If the side is considered as a supersonic inlet, all the averaged fluxes from the other side aretaken with the averaged pressure.

• If the side is considered as a subsonic inlet, the averaged fluxes are taken from the other side.The local pressure is kept.

• If the side is considered as a subsonic outlet, only the pressure is transferred from the otherside. The local fluxes are kept.

• If the side is considered as a supersonic outlet, nothing is taken from the other side.

Once the transfer is completed, a decoding of the fluxes with pressure is carried out on each sidewith the formulas which depend on the type of fluid.

Compressible flows

For compressible flows, the density, velocity vector and pressure are derived from ,

respectively the flux of mass, the flux of momentum plus the pressure force and the flux of energy.The other variables such as k or ε are also derived from their fluxes. They are referred to, in the fol-lowing as X an QX. The fluxes are constructed from the primitive variables using:

Qρ Qv QE, ,


5-18 FINE™

. (5-1)

where ρ is the density, the absolute velocity vector, T the temperature, Cp the heat capacity and

the surface vector of the cell face. After application of the mixing process the primitive variablesare calculated from the fluxes using:

(5-2)

where γ is the specific heat ratio.

Incompressible flows

For incompressible flows, the velocity vector and pressure are derived from , respectively

the flux of mass and the flux of momentum plus the pressure force (See Eq. 5-1). The other varia-bles like k or ε are also derived from their fluxes. They are referred to, in the following, as X andQX. As far as the energy equation is concerned, the temperature is also derived from its flux like theother X variables.

(5-3)

b) Conservative Coupling by Pitchwise Rows (No Flux Decoding):

The local conservative coupling approach presents two weaknesses:

• The decoding of the fluxes might in some case lead to a blow up of the process, especially attransonic flow conditions, because of the presence of a square root in Eq. 5-2, whose positivityis not always guaranteed.

• The local approach may lead to opposite decisions on the flow direction for the correspondingmesh points of both sides of the interface, which as a consequence decreases the accuracy onthe global conservation.

Qρ ρ V S⋅( )=

Qv ρV V S⋅( )=

QE ρ CpT V2 2⁄+( ) V S⋅( )=

QX ρX V S⋅( )=

V

S

ps

Qv S⋅

S2 γ 1+( )----------------------

Qv S⋅

S2 γ 1+( )----------------------

⎝ ⎠⎜ ⎟⎛ ⎞

2γ 1–( )·

Qv2 2QρQE( )–( )

S2 γ 1+( )----------------------------------------------------------+±=

vQv psS–

Qρ--------------------=

ρQρ

v S⋅----------=

XQX

Qρ-------=

Qρ Qv,

ps

Qv S Qρ2 ρ⁄–⋅( )

S2--------------------------------------=

VQv psS–( )

Qρ-------------------------=

XQX

Qρ-------=


FINE™ 5-19

Therefore a new boundary conditions has been developed, in which the decision on the direction ofthe flow is taken only once per pitchwise row, and which avoids the fluxes decoding. This newboundary condition has shown to be more robust in most cases and guarantees a strict global con-servation. As mentioned in section 5-3 the only type of application for which a local approachwould better suit is the impeller-volute interaction.

5-5.3 Full Non-matching Technique for Mixing Planes

5-5.3.1 Concept

The major purpose of the development of the new mixing plane module was the elimination of thegeometrical constraints imposed by the previous module.

The new module uses the concept of image. An image of the real mesh patches is built on bothsides of the interface, the left and right images respecting the above constraints and being in addi-tion matching in the spanwise direction. The only remaining constraints are the followings:

• the hub and the shroud lines are assumed to be located on a circular arc, and each extremity ofthe hub and shroud lines should coincide with one corner of one of the patches.

• all patches constituting a rotor/stator interface should form a filled closed surface with no gap

• the rotor/stator patches should be fully included in the rotor/stator interface: contrary to the fullnon matching algorithm, which includes an automatic detection of the connection zone, and inwhich the patches can then be partially connected, the rotor/stator module assumes that thepatches are fully connected.

FIGURE 5.5.3-11 Creation of the image mesh

One image mesh is constructed on both sides of the interface. It respects the following constraints:


5-20 FINE™

• The image is a "concatenation" of all the patches constituting the left or right side of the inter-face.

• The pitchwise mesh lines lie on circular arcs.

• The left and right images have the same spanwise distribution of the nodes.

• The mesh density of the image is similar to the one of the initial patch.

The creation of the image mesh is illustrated by Figure 5.5.3-11, showing the creation of the imageof a butterfly configuration. With the previous version of the mixing plane module such a configu-ration would have required the creation of an intermediate block with one face connected to the but-terfly and the opposite face respecting the constraints of rotor/stator patches.

5-5.3.2 Implementation of Mixing Plane Approach with Full Non-matching Technique

The communication algorithm between rotors and stators is organised in several steps:

1. Extrapolation of the flow solution from the inner cells to the boundary: the cylindrical velocitycomponents are extrapolated.

2. Sending of the flow solution from the initial mesh to the image (on both sides): an interpolationtree is built between the image and the initial mesh, by applying the full non matching connect-ing algorithm.

3. Application of the mixing plane algorithm between the left and right images, with constructionof flux variables to be imposed on the left and right side.

4. Sending of the fluxes from the image to the initial meshes: this is again performed with the aidof the full non matching algorithm, which allows for an exactly conservative distribution of thecalculated fluxes throughout the cells. The transformation of the flux variables to the primitiveones is not required, as the fluxes are directly added to the residuals of the finite volumescheme, without the use of the dummy cells.

The mixing plane algorithm implementation is similar to the one of the previous module. Only theconservative coupling by pitchwise rows has been implemented. The algorithm is organised underthe following steps:

1. Calculation of the flux variables on both sides

2. For all spanwise positions perform a pitchwise averaging of the flux and of the primitive varia-bles.

3. For all spanwise positions determine the upstream and downstream side according to the flowdirection, and build the mixing plane fluxes.

F1 ρVn∆S=

F2 ρVrVn∆S=

F3 ρVθVn∆S=

F4 ρVzVn∆S=

F5 ρHVn∆S=


FINE™ 5-21

The local fluxes on the upstream side are taken from the upstream, with a contribution of the aver-aged downstream static pressure.:

On the downstream side the local fluxes are taken as the averaged fluxes on the upstream side witha contribution of the local static pressure:

5-5.4 Domain Scaling Method

The Domain Scaling Method considers in the computational domain respectively K1 and K2 bladepassages with the following condition to be satisfied:

. (5-4)

where the indices 1 & 2 refer to the upstream and downstream sides of the interface, and P1 & P2

are the pitches of the two connected blade rows.

If the numbers of blades in respectively the rotor and the stator are not equal, the user should makethe choice between:

•modelling a higher number of blade passages (or even the entire machine if a common multi-ple can not be found). If for instance the numbers of blades are 16 & 24, the numbers of pas-sages to model are respectively 3 & 2. This permits to avoid the introduction of an error due tothe geometry scaling, at the cost of an increased memory requirement.

• scaling the geometry. The easiest way to proceed in order to obtain the required scaling is togenerate a mesh with a blade number different from the real one. The ratio between the modi-fied and the real blade numbers should be as close as possible to 1.0.

In some cases the most appropriate treatment may be a combination of the 2 above approaches. Iffor instance the numbers of blades are 18 & 24, one could scale the stator by changing the numberof blades from 18 to 16, and then choose to model 2 & 3 passages. The scaling factor is then 1.125,instead of 1.33 in case only one blade passage is modelled.

The major advantage of having the same pitch distance on both sides of the interface is that it per-mits to avoid considering any time periodicity in the boundary condition treatment. The boundaryconditions to be imposed along the periodic boundaries inside the gap region are given by

F1ups

F1ups=

F2ups

F2ups

pdown

nr∆S+=

F3ups

F3ups=

F4ups

F4ups

pdown

nz∆S+=

F5ups

F5ups=

F1down

F1ups

=

F2down

F2ups

pdown

nr∆S+=

F3down

F3ups

=

F4down

F4ups

pdown

nz∆S+=

F5down

F5ups

=

K1P1 K2P2=


5-22 FINE™

, (5-5)

where is the pitch distance on both sides of the interface. The “+” sign is to be used

when imposing boundary conditions on the lower periodic segment (minimum azimuthal coordi-nates) and the “-” sign is to be used for the higher periodic segment (maximum azimuthal coordi-nates). Along the rotor/stator interface, the boundary condition is defined as

, (5-6)

where the parameter m is selected such that the point is part of the computational

domain of row 3-i to allow for the interpolation across the interface. Since only the spatial periodic-ity is accounted for in the connecting boundary condition, the periodic surfaces become simple non-matching rotating boundaries, while the interface is a non-matching connecting boundary. The solu-tion procedure is then as follows, for each physical time t:

•Rotate the grid in function of the physical time step and of the rotation speed of each row.

•Resolve the flowfield at the given physical time t. The boundary conditions to be imposedalong the periodic segments are defined by equation Eq. 5-5. The boundary condition to beimposed along the interface boundary is defined by equation Eq. 5-6.

• Save the flow solution for future post-processing.

This method does not impose any time periodicity in the boundary condition treatment and thus,allows to capture all time frequencies of the various unsteady interactions, but occurring on a mod-ified geometry due to the grid scaling. The effect of the grid scaling on the accuracy of the com-puted flow solution is of great importance when comparing computational results with theexperimental data, as another one-stage configuration has been truly resolved. These effects may besummarized as:

• a shift in the spectrum of time frequencies for the blade row that has not been scaled.

• the modification in both blade rows of the Fourier modes that are propagating the flow infor-mation.

The unsteady governing flow equations are resolved in the relative system of each row. Thus, nogrid rotation needs to be performed at each physical time step and only the interpolation data struc-ture needs to be modified in function of the relative position of each component. For example, adownstream rotor will see an upstream stator moving in the opposite direction of its own rotationvelocity, while the upstream stator will see the rotor moving in the direction of the rotor rotationvelocity.

Finally, the previous implementation lets the rotor do the full rotation. The problem in this methodis that the rotor and the stator are in front of each other for a little fraction of time. During this time,no time shift is necessary at the R/S interface which acts then as a pure connection. The modifica-tion proposed aims at increasing the time during which the R/S interface acts as a connection. Toperform this, only the periods during which the rotor and the stator are in front of each other, arerepeated. But, since the length of the periods are different in the 2 blades rows, the solution has tobe stored and reset in the row with the smallest period.

Example: if row 1 has the highest number of blades and therefore is submitted to the larger period,this last period T1 is repeated over and over, while a fractional number of periods will be simulatedin row 2. The solution is thus stored at the end of the last completed period in row 2, to be reused atthe beginning of each T1. This method increases a lot the speed of exchange between the two bladerows. It increases also the robustness of the computation.

UiR

r θiR

z, t, ,( ) UiR

r θiR

p± z, t, ,( )= i 1 2,=

p K1P1=

UiR i( )

r θiR i( )

z, t, ,( ) U3 i–R i( )

r θiR i( )

mp– z, t, ,( )=m Z∈

i 1 2,=

θiR i( ) mp–


FINE™ 5-23

5-5.4.1 Full Non-matching Approach (IRSNEW=1)

It is highly recommended to activate the FNMB approach when using the domain scaling method as itpresents several advantages:

• smaller pre-processing CPU time,

• smaller memory requirement,

• strict conservation of mass, momentum and energy.

The implementation is practically identical to the one that is adopted in the steady state frozen rotorapproach. The FNMB connecting algorithm is used in order to exchange the flow variables and fluxesbetween the left and right image. The difference in the case of unsteady calculations is that the bound-ary condition patches linked to the rotor side need to be positioned according to the current time step.

This implementation is organised in nearly the same way as the mixing plane approach, except fromthe fact that the mixing plane technique applied between the two image must be replaced by an addi-tional full non-matching connection. The global organisation is the following:

1. Extrapolate the inner flow solution to boundary condition patches (on both sides),

2. Interpolate the flow solution from initial patches to the image (on both sides),

3. Full non-matching connection between the two images (with appropriate rotation of the rotor-linked image),

4. Transfer of the calculated fluxes to the initial boundary condition patches.

5-5.4.2 Sliding Grid Interpolation Approach (IRSNEW=0)

The sliding grid interpolation approach is still available (IRSNEW=0), mainly for backward compati-bility reasons. This connection algorithm is based on a high order interpolation of the flow variables.Although well validated the approach does not strictly guarantee conservation. Another drawback isthat different interpolation data structures are built for all relative stator/rotor positions, with as a con-sequence a very long pre-processing time.

5-5.4.3 Improved Rotor/Stator Viscous Fluxes (IRSVFL=1)

The previous implementation of the R/S interface only ensured the continuity of the inviscid fluxes.The viscous fluxes were computed at the interface from the value in the dummy cells which wereextrapolated from the inner cells.

This new implementation simply interpolates the value from the other side inner cells to the dummycells, reproducing the correct behaviour of a connection (Figure 5.5.4-12).

FIGURE 5.5.4-12 Rotor/stator interface improvement: viscous fluxes continuity


5-24 FINE™

X’ and X” are respectively extrapolated on R/S interface from X3 and X4. Then X2’ is interpolatedfrom X’ and X”. Finally, X2” is defined in the dummy cell by extrapolating X2 (result coming fromthe stator) and X2’ (result coming from the rotor). This last method, automatically activated whendealing with phase-lagged simulation, can be activated for non phase-lagged simulation through theexpert parameter IRSVFL (by default set at 0) that has to be set at 1.

5-5.4.4 Frozen Rotor

The frozen rotor technique consists of a simple connecting boundary condition, ignoring the rota-tion of the rotor. The implementation is identical to the one adopted in the full non-matchingdomain scaling approach (section 5-5.4.1), except from the fact that no rotation of the rotor-linkedimage is performed, allowing the creation of a steady-state solution.

5-5.4.5 References

Erdos J.I., Alzner E. & McNally W. (1977), Numerical Solution of Periodic Transonic FlowThrough a Fan Stage, AIAA Journal, Vol. 15, No. 11, pp. 1559-1568

Giles M.B. (1990), Stator/Rotor Interaction in a Transonic Turbine, Journal of Propulsion, pp. 621-627

He L. (1997), Computational Study of Rotating-Stall Inception in Axial Compressors, Journal ofPropulsion & Power, Vol. 13, No. 1, pp. 31-38

Lemeur A. (1992), Calculs 3D stationnaire et instationnaire dans un étage de turbine transonique,AGARD Report CP-510

Rai M.M. (1989), Three-Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interac-tion; Part I - Methodology and Part II - Results, Journal of Propulsion, Vol. 5, No. 3, pp. 305-319

Van Leer B. (1985), Upwind-Difference Methods for Aerodynamic Flows Governed by the EulerEquation, Lectures in Applied Mathematics, Vol. 23, Part 2, AMS, Providence, pp. 327-336

FINE™ 6-1

CHAPTER 6: Throughflow Model

6-1 OverviewThe Throughflow module is intended for the design and the analysis of turbomachinery flows. Thiskind of simulation is based on the two-dimensional steady state axisymmetric Euler equations witha specific model for blade rows. It is fully integrated in EURANUS, the three-dimensional Euler-Navier-Stokes flow solver. As a consequence:

•Options that apply to comparable 3D calculations also apply to throughflow calculations: thephysical fluid model, the boundary conditions, the spatial and time discretization, the conver-gence acceleration techniques and the output, including data for visualization.

• The code accepts any number of blade rows.

• Throughflow blocks can be combined with 3D blocks in a single computation.

•Any improvement introduced in the 3D solver also applies to the througflow blocks.

The throughflow simulation should be used only with the perfect gas model currently

available through the FINE™ interface.

The throughflow simulation can be activated directly from the FINE™ interface by clicking on theThroughflow Blocks thumbnail in the Configuration/Rotating Machinery page. This thumbnail isonly accessible when the Mathematical Model is set to Euler on the Flow Model page. In the nextsection the Throughflow Blocks option in the FINE™ interface is described including all relatedparameters. Finally, section 6-5 provides its theoretical background.

Throughflow Model Throughflow Blocks in the FINE™ Interface

6-2 FINE™

6-2 Throughflow Blocks in the FINE™ InterfaceWhen selecting this thumbnail the page as displayed in Figure 6.2.0-1 is appearing. Two sectionsare displayed: Global parameters and Block dependent parameters. The global parameters affectall throughflow blocks, while the block dependent parameters can be tuned independently for eachthroughflow block.

FIGURE 6.2.0-1Throughflow Blocks in Rotating Machinery page

6-2.1 Global Parameters

The Global parameter for the throughflow method only concern the time discretization of the bladeforce equation (see section 6-5.1). The relaxation factor determines the amplitude of the blade forceupdates and can be interpreted as a CFL number whose value can be different from the one that isadopted for the other equations. The default value is 1. The optimal value usually varies between0.5 and 5. Higher values result in faster convergence, but can lead to divergence if the stability limitis exceeded.

6-2.2 Block Dependent Parameters

The Block dependent parameters section is subdivided into two areas. The left area is dedicated tothe block selection. The right area allows to specify the throughflow parameters for the selectedblock(s). The Apply to Selection button assigns to the selected block(s) the values of the parametersspecified in the right area.

One or several blocks may be selected in the left area by simply clicking on them. Clicking on ablock unselects the currently selected block(s). Clicking on several blocks while simultaneouslypressing the <Ctrl> key allows to select a group of blocks.

6-2.2.1 Block Type: Throughflow or 3D

Two toggle buttons are provided to specify the block type: 3D or Throughflow. The 3D choice disa-bles the throughflow method for the selected block(s). This is the default. It is also the required set-ting for 3D blocks coupled with throughflow blocks in a single computation. Each throughflowblock contains exactly one blade row, with a mesh configuration that corresponds to the one pre-scribed in section 6-2.3.

Throughflow Blocks in the FINE™ Interface Throughflow Model

FINE™ 6-3

Two different types of throughflow blocks are available. The throughflow module is fully active byselecting either the Compressor or Turbine options. The difference between the two lies in the defi-nition of the loss coefficient: for a turbine the pressure used as reference is taken at the trailing edgeand for a compressor at the leading edge.

6-2.2.2 Analysis or Design Mode

Two main working modes are available:

•Classical Analysis: the blade geometry is known, and the user specifies the relative flow angledistribution along the trailing edge. The leading edge flow angle distribution results from thecalculation and the user specifies the type of streamwise distribution to be used between theleading and trailing edges.

•Design: the user specifies the relative tangential velocity distribution along the trailing edge,and the throughflow module is used to compute the flow angles and hence to define the bladegeometry. The leading edge tangential velocity distribution results from the calculation and theuser specifies the type of streamwise distribution to be used between the leading and trailingedges.

Two additional analysis modes are provided to the user, more appropriate than the classical one insome cases:

•Hybrid Analysis mode: similar to the classical analysis mode, but the user specifies the stream-wise distribution of the tangential velocity instead of the flow angle, which has shown to pro-vide more accurate results especially at transonic conditions.

• analysis mode with Throat Control: this mode permits to impose the throat section instead ofthe tangential thickness, which is more appropriate in case of high relative flow angles withrespect to the axial direction (high turning turbine blades for instance). In this working modethe user has to specify the flow angle distributions along both leading and trailing edges.

In all working modes the user has to specify:

• the blockage distribution (tangential thickness of the blades) or the throat section.

• the relative flow angle (analysis) or relative tangential velocity (design) at the trailing edge

• the value of the loss coefficient along the trailing edge.

Depending on the chosen analysis or design mode the appropriate parameters are available underthe three thumbnails described in the next paragraphs.

6-2.2.3 Number of Blades

When the block type throughflow is selected, the number of blades needs to be specified for each

throughflow block presenting a grid recommended periodicity of 360 (α = 1o), with a mesh config-uration that corresponds to the one prescribed in section 6-2.3.

6-2.2.4 Blade Geometry

When clicking on the Blade geometry thumbnail the parameters as shown in Figure 6.2.2-2 appear.In the case the analysis mode with Throat Control is selected different parameters will appear asshown in Figure 6.2.2-3 and described at the end of this paragraph.


6-4 FINE™

FIGURE 6.2.2-2Blade Geometry Parameters in Design, Classical or Hybrid Analysis mode

In all modes except the analysis mode with Throat Control the geometry can be defined by:

• 2D input file: the file defining the blade geometry should contain the (Z,R,θcl,θss,θps) coordi-nates of the blade camber line, suction and pressure sides throughout the meridional domaincovered by the blade. For each (Z,R) meridional position the circumferential coordinate θ isgiven at the camber line, the suction and pressure sides. For the format of a 2D input file seesection 6-3.

• 1D input parameters where the user specifies:

— the streamwise location of the maximum thickness at hub and shroud (a linear evolution isassumed from hub to shroud),

— a file containing the spanwise distribution of maximum tangential thickness,

— the normalised streamwise distribution of blade thickness: This distribution can be com-puted using a power function whose exponent has also to be specified or loaded from a 1Dinput file with the format as specified in section 6-3. For most configurations a power func-tion with an exponent of 2 leads to a correct modelling of the blade generating a quadraticthickness evolution. The thickness function is set to zero at the leading and trailing edgesand presents a maximum at the prescribed position of maximum thickness.

An additional blockage can be introduced to take the endwall boundary layers (Endwall boundarylayer and wake blockage factors) into account. The two real parameters refer to the inlet and outletvalues of the endwalls blockage. A linear variation is assumed between the inlet and the outlet.


FINE™ 6-5

FIGURE 6.2.2-3Blade geometry parameters in Throat control Analysis mode

In case the analysis mode with Throat Control is selected the user specifies the streamwise evolu-tion of the effective blockage, which results from the tangential blockage and the flow angle beff= bcosβ, with b the tangential blockage and β the relative flow angle at the trailing edge.

The user specifies:

— the streamwise location of the throat at hub and shroud. If a negative value is entered, it isassumed that there is no throat and a linear evolution of the effective blockage from the lead-ing to the trailing edge will be adopted.

— a file containing the spanwise distribution of the throat section. The throat is by definitionthe section in which the effective blockage is minimum. In transonic turbines it determinesthe mass flow.

— the normalised streamwised distribution of effective blockage: This distribution can be com-puted using a power function whose exponent has also to be specified, or loaded from aninput file. The streamwise distribution of effective blockage results from the values specifiedby the user at the leading and trailing edges and at the throat (if a throat is given).

6-2.2.5 Flow Angle/Tangential Velocity

When clicking on the Flow angle/Tangential velocity thumbnail the parameters related to the direc-tion of the velocity at the trailing edge become available:

In Analysis mode the user should always provide the spanwise distribution of the flow angle β at thetrailing edge. In Design mode the tangential velocity Wθ (design) at the trailing edge is requiredinstead of the flow angle.

A normalized streamwise distribution is also required. It is either read from a file or specifiedthrough a power function whose exponent is given by the user. A zero value at the shroud impliesthat the shroud value is equal to the hub one. The leading edge value being a result of the calcula-


6-6 FINE™

tion, the streamwise distribution of the flow angle or of the tangential velocity is iteratively com-puted according to the calculated value at the leading edge and the value defined at the trailingedge. The default value of the exponent is 1, which generates linear evolutions from leading to trail-ing edge.

Two definitions of the flow angle are available, respectively based on the axial and

meridional directions. The choice between these definitions is made through the expertparameter ITHVZM:

Wθ=Wz.tan β(ITHVZM=0, default)

Wθ=Vm.tan β(ITHVZM=1).

In case of radial configurations the parameter ITHVZM should be set to 1.

In the case of the analysis mode with throat control one additional input is required: the spanwisedistribution of the leading edge flow angle has to be provided in a file. This is required in order todefine the value of the effective blockage at the leading edge.

6-2.2.6 Loss Coefficient

When clicking on the Loss coefficient thumbnail the distribution of the loss coefficient can bedefined through:

• The spanwise distribution along the trailing edge as specified in a file.

• The normalized streamwise distribution as imposed through an external file or by using apower function. The value 1 (recommended value) for the exponent of the power functionmeans that a linear function with a shift towards front is used. The leading edge value of theloss coefficient is assumed to be 0.

6-2.3 Mesh for Throughflow Blocks

Figure 6.2.3-4 shows a configuration with two blade rows. Each throughflow block contains a sin-gle blade row. The mesh has only one cell in the pitchwise direction. The cell opening angle, α in

Figure 6.2.3-4, has no influence theoretically but excessive values should be avoided (α > 10o or α< 0.01o). A value of 1o is recommended. All blocks, must have the same cell opening angle. Themesh indices I, J, and K are oriented as shown in Figure 6.2.3-4. The hub and shroud surfaces cor-respond to the I=1 and I=Imax grid surfaces respectively, whereas the I=Cst grid surfaces corre-

spond to the successive streamwise positions. Rotors are computed in the relative frame ofreference.

The leading trailing edges positions are described by spanwise mesh lines (I=Cst). The blade regionis identified through the patch-decomposition of the periodic faces (See section 6-2.4.1). If multi-grid is to be used, the inlet region, blade row, and outlet region must each have a suitable number ofcells in the I-J-directions.

Please note that according to Figure 6.2.3-4 the K=1 surface must be defined along the (Y=0) plane.


FINE™ 6-7

FIGURE 6.2.3-4 The throughflow mesh

6-2.4 Boundary Conditions for Throughflow Blocks

Compared with 3D turbomachine cases, throughflow calculations require the same boundary condi-tions. All the necessary boundary conditions can be set through the general dialog box Patch Selec-tor through the menu Grid/Boundary Conditions... in IGG™. Table 6-1 lists the four types ofboundaries and the pertaining boundary conditions.

6-2.4.1 Periodic Boundaries

The axisymmetric periodic boundaries require a rotational periodicity condition. Except for thepatch decomposition, they are set exactly as periodic boundaries of a 3D or axisymmetric non-throughflow block.

As described in section 6-2.3 the block is composed of an inlet region, a blade passage, and an out-let region. Instead of specifying one boundary condition for the entire K-face, the latter must beartificially divided in three boundary patches, labelled P1, P2, and P3 in Figure 6.2.3-4 and desig-nating respectively the inlet, the blade, and the outlet region. Both patches P1 and P3 must have atleast one cell in the J-direction. The decomposition needs to be performed in IGG™.

• The block is composed by the blade passage only. One boundary patch covers the entire K-face, leading and trailing edge coincide with respectively inlet and exit of the domain.

TABLE 6-1 Boundary Conditions

Type of Boundary Boundary condition number

Periodic Boundaries (K-faces) BC 2

Hub and Shroud Walls (I-faces) BC 16, BC 17

Inlets and Exits (J-faces) BC 124, BC 125, BC 27, BC 23, BC 22

Connecting Boundaries (J-faces) BC 1, BC 44


6-8 FINE™

6-2.4.2 Hub and Shroud Walls

The present throughflow model assumes an inviscid fluid. Euler wall boundary conditions have tobe applied to the hub and to the shroud walls (I-faces).

6-2.4.3 Inlet and Exit

All rotor inlet and outlet boundary conditions as described in Chapter 8 can be applied at inlet andoutlet (J-faces).

6-2.4.4 Connecting Boundaries

Under the framework of throughflow calculations, rotor/stator interfaces are replaced by simpleconnections between the throughflow blocks.

Connection between throughflow blocks must be matching.

Throughflow blocks can also be connected to 3D blocks. This implies the use of a quasi-steadyinterface (rotor-stator interface).

6-2.5 Initial Solution for Throughflow Blocks

Especially for the throughflow module the initial flow solution has an important influence on thespeed and robustness of the resolution algorithm.

Exactly as in FINE™/Turbo for 3D applications, a turbomachinery-oriented initial solution algo-rithm has been implemented, generating automatically an initial solution based on the inlet/outletboundary conditions and on a user-specified value for the inlet static pressure. The initial solutionconstructed with this algorithm respects the basic laws of rothalpy and mass conservations.

In order to activate this algorithm, the user should select on the Initial Solution page the for tur-bomachinery option. The user then has to enter a value for the inlet static pressure and a radius ifradial equilibrium is selected.

The rotor/stator interfaces do not appear in the Initial Solution page because they are identified assimple connections. The static pressure level at the successive rotor/stator interfaces can howeverbe specified through the expert parameter PRSCON. The values to be entered are p1, R1, p2,R2,...,pi,Ri, where i is the index of the rotor/stator interface, p the static pressure in Pascal [Pa] andR the radius in meters [m]. If the expert parameter is not modified by the user, a linear pressure evo-lution is assumed from inlet to outlet.

In order to impose a constant pressure at the rotor/stator interface, the corresponding

radius has to be set at zero.

6-2.6 Output for Throughflow Blocks

The output for throughflow simulations can be selected on the Output/Computed Variables pageunder the Throughflow thumbnail. The following quantities can be stored:

•Blockage: tangential blockage factor ,

•Grad(B)/B-1st component: radial component of the vector,

b 1ds---–

⎝ ⎠⎛ ⎞=

∇bb

-------

File Formats for Throughflow Blocks Throughflow Model

FINE™ 6-9

•Grad(B)/B-3rd component: axial component of the vector,

• Lean vector (tangential vector along the blade in the spanwise direction),

• Shape function for or ,

• Loss coefficient ,

•Blade force vector ,

• Friction force vector ,

•Unit stream vector (USV),

• Flow angle ,

• Effective streamtube thickness,

•Blade force magnitude: magnitude of blade force ,

• Friction force magnitude: magnitude of friction force ,

•W_theta target: target relative tangential velocity ,

•Beta target: target relative flow angle .

6-3 File Formats for Throughflow BlocksThe names of all throughflow input files are specified by the user in the above described interactivewindows (Figure 6.2.2-2). The aim of this section is to present the structure of these files. A shortdescription of a specific throughflow output file generated by the interface is also provided.

One can distinguish two types of files: the two-dimensional and the one-dimensional files. The fileformat for each is described in the next paragraphs.

6-3.1 One-dimensional Throughflow Input File

The one-dimensional files consist of two parts:

1. A header line containing four integer (the number of data points and 3 integer switches).2. The data, organised in 2 columns.

The 4 integers contained in the header line define:

— the number of data points.

— the type of coordinate along which the data is given. The available coordinates are the X-coordinate (1), the Z-coordinate (3), the radius (4) and the meridional coordinate (6).

— if the coordinate should be normalized (1) or not (0). The normalized data describes a distri-bution between the leading and the trailing edge, or between the hub and the shroud.

∇bb

-------

β Wθ Wm⁄( )atan= Wθ

ψ

fB

fF

Wθ Wm·

USV⋅( )⁄( )atan

fB

fF

Wθt etarg

βt etargWθ

t etargWm⁄( )atan=

Throughflow Model File Formats for Throughflow Blocks

6-10 FINE™

— if for a streamwise distribution, the leading and/or trailing edge values should be extended tothe upstream/downstream ends of the block. Values of 1 and 3 extend the upstream region,whereas values of 2 and 4 extend the downstream regions. This switch is used to achieve ablockage factor below 1. upstream and/or downstream of the blade passages.

The angles are in degrees, the length in meters, except for the blade thickness, which is in millime-tres.

Some examples of the geometrical files are given hereafter:

• Spanwise distribution of the maximum blade thickness:14 4 1 0.1181262 8.20958.1282913 8.22191.138422 8.16546.1484767 8.03777.1583352 7.85892.1680261 7.58743.1778827 7.26814.1877939 6.86779.197697 6.45259.2076666 6.11613.217709 5.78311.2277728 5.65696.2378241 5.84635.2477884 6.27821

• Spanwise distribution of the trailing edge flow angle:11 4 1 0.0 10.10562.1060092 -5.70642.2095564 -16.2939.3126917 -27.0153.4146 -35.7384.5148696 -41.7166.6134925 -46.4628.7112999 -50.3735.8084939 -54.3548.9048644 -57.93921.0 -59.542

• Spanwise distribution of trailing edge loss coefficient:11 4 1 01.0 3.78416E-02.9048644 3.78416E-02.8084939 3.28353E-02.7112999 3.74248E-02.6134925 1.96157E-02.5148696 3.18909E-02.4146 3.61507E-02.3126917 3.23982E-02.2095564 5.45700E-02.1060092 9.97951E-02.0 9.97951E-02

File Formats for Throughflow Blocks Throughflow Model

FINE™ 6-11

6-3.2 Two-dimensional Throughflow Input File

The two-dimensional input file, only available for the blade geometry definition, consists of twoparts:

1. A header line containing the number of points in the two dimensions of the structured datasurface and three switches.2. The data organised in 5 columns (the coordinates should be R,Z,θcl,θss,θps where θcl,θss,θps

are respectively the angle at the camber line, suction side and pressure side of the blade) andevolves from hub to shroud and from the leading to the trailing edge.

The three additional switches define:

— the type of coordinates: should be 4.

— the type of structure: should be 3.

— the number of variables: should be 5.

All lengths in the data files should be in meters, and the angles in radians.

Following is an example of the two-dimensional input file:

5 7 4 3 5 **(5*7 points: 5 points in spanwise and 7 points in streamwise)** 9.37745E-02 -8.87817E-03 6.47041E-02 7.40556E-02 5.53526E-02.1934945 8.93166E-03 5.71797E-02 5.99261E-02 5.44332E-02...

6-3.3 Output File

FIGURE 6.3.3-5 Throughflow Output File ".gtf"

Absolute (V) and Relative (W) velocities components along R,T,M

ALPHA = arctg(VT/VZ)BETA = arctg(WT/VZ)GAMMA = arctg(VR/VZ)

Static Pressure, Static Temperature,

Density

Absolute Total PressureRothalpy Total PressureRelative Total Pressure

Absolute Total TemperatureRothalpy Total TemperatureRelative Total Temperature

Isentropic EfficiencyPolytropic Efficiency

Mass FlowTotal Area

Mach NumberMeridional Mach Number

Throughflow Model Expert Parameters Related to Throughflow Blocks

6-12 FINE™

In addition of files which can be read by CFView™, a summary file is created when the through-flow module is activated. It has the extension ".gtf" and gives the average inlet and outlet results foreach block in SI units.

6-4 Expert Parameters Related to Throughflow Blocks

6-4.1 Under-relaxation Process

Two types of under-relaxations have been introduced, allowing for an increased robustness of thealgorithm during the initiation of the resolution procedure.

This under-relaxation process is controlled through 2 sets of expert parameters (accessed on theComputation steering/Control variables page in expert mode), THNINI (2 integer parameters) andTHFREL (2 real - float parameters).

• the first THNINI and THFREL parameters permit to impose that during the first THNINI(1)iterations, the blade force update factor is not the one specified in the "Throughflow blocks"menu (section 6-2.1), but a (lower) value given by THFREL(1). This under-relaxation processcan be important for transonic cases especially. The default values for THNINI and THFRELare respectively 10 and 0.1

• the second THNINI and THFREL parameters permit to under-relax the imposed value of trail-ing edge velocity or flow angle during the first THNINI(2) iterations. The under-relaxationfactor multiplying by the imposed value varies linearly between THFREL(1) and 1.0 duringthe first THNINI(2) iterations. The default values for THNINI and THFREL are respectively10 and 0.85.

6-4.2 Others.

• ITHVZM = 0 (default): Wθ=Wz.tan β = 1: Wθ=Vm.tan β

Definition of the flow angle. The selection of ITHVZM to 1 is crucial for a correct treatment of

radial machines.

• PRCON to define the pressure for the initial solution at rotor/stator interfaces. If this parameteris not modified a linear pressure distribution from inlet to outlet is assumed.

Theoretical Background on Throughflow Method Throughflow Model

FINE™ 6-13

6-5 Theoretical Background on Throughflow Method

6-5.1 The Time Dependent Approach

The dominant aspect of an Euler throughflow method is the modelling of the turning and the associ-ated distributed blade force. Most authors so far have adopted a spatial discretization approach, inwhich the blade force is determined from the tangential projection of the momentum equation inconjunction with the imposed flow direction (analysis) or swirl (design), leaving four differentialequations to be solved.

In the present approach the blade force is treated as an additional time dependent unknown. The full5-equations Euler system is then solved, with an additional equation for the blade force. This is theso-called time dependent approach, which has proven to be more robust than the space discretiza-tion, especially at transonic and supersonic flow conditions. The other advantage is that the fact thatthe throughflow solver is based on the same time marching algorithm as the 3D one makes hybrid3D-throughflow calculations possible.

6-5.2 Basic Equations and Assumptions

The basic equations describing axisymmetric throughflow are obtained through averaging in the θ-direction of the three-dimensional Euler conservation laws for mass, momentum, and energy, yield-ing, in concise notation and after introduction of the distributed loss model,

(6-1)

This is a system of 5 PDE for 5 unknowns (the dependent variables, e.g., the primitive variables incylindrical coordinates, ρ, Wr, Wθ, Wz, p) in two spatial dimensions (r and z). Apart from theabsence in the differential operators of derivatives with respect to the tangential direction, the sys-tem differs from the three-dimensional Euler equations in three ways:

• The presence of the blockage factor b in the fluxes.

• Source terms and representing the inviscid action of the blades.

•A source term grouping all the effects of viscosity and heat conduction.

The system is solved in Cartesian coordinates using explicit Runge-Kutta integration in time andeither central or upwind spatial discretization.

6-5.3 The Tangential Blockage Factor

The tangential blockage factor, b, also called the stream tube thickness parameter, represents thecontraction of the flow path that arises from the tangential thickness of the blades, d. With the pitch,s, depending on the radius, r, and the number of blades, z, the tangential blockage factor is definedas:

∂∂t----

ρ

ρW

ρE

1b---∇

bρW

b ρW W pI+⊗( )

bρWH

⋅+

0

ρQ p∇bb

------- ρ fB fF+( )+ +

ρQ

=

p∇bb

------- fB

fF

Throughflow Model Theoretical Background on Throughflow Method

6-14 FINE™

where (6-2)

Thus, outside blade rows and inside blade rows (including the hypothetical case ofblades with zero thickness). The blockage factor is an external input to the computation.

6-5.4 The Blade Force

By definition, the inviscid action of the blades consists in a distributed force normal to the bladesurfaces, i.e., suction and pressure surface. In our implementation the blade force is split into twocomponents:

• the first main component is proportional to the suction-to-pressure side difference, and is ori-ented in the direction normal to the mean camber surface. The tangential component of thisforce is the additional unknown considered in the time dependent approach, for which an addi-tional equation will be solved together with the 5 Euler equations.

• the second component is due to the deviation of the suction and pressure side normals from the

normal to the mean camber surface. It is computed according to , and is therefore deter-

mined entirely by the tangential blockage factor, b, which is external input as seen in the pre-ceding section, and by the static pressure, which is a result of the computation.

As mentioned in section 6-5.2, the blade force is treated as an additional unknown with the presentapproach. Starting from some initial value in each cell, the blade force is modified locally, until thecurrent converged solution exactly matches the externally imposed target, for instance the flowangle β (analysis) or the tangential velocity Wθ (design). The correction is proportional to the dif-ference between the actual and a required tangential velocity:

(6-3)

where the constant κ is user input. The target tangential velocity Wθt is either direct external input

(design mode) or locally calculated from the prescribed relative flow angle β and the current merid-

ional velocity (analysis mode: Wθ=Vmtanβ). The vector of the blade force, , is perpendicular to

the mean camber surface, which is internally defined by the flow angle and the lean angle. Cur-rently, a zero lean angle is assumed.

Robust analysis mode

In the case of the analysis mode another formulation of the above equation is adopted, based on themagnitude of the blade force instead of its tangential component:

(6-4)

where FB is the magnitude of the blade force and is the normal vector whose direction results

from the imposed relative flow angle distribution. In case the angle is measured with respect to theaxial direction (ITHVZM=0):

(6-5)

b 1ds---–= s

2πrz

---------=

b 1= 0 b 1≤<

p∇bb

-------

ρFBθ( )k 1+ ρFBθ( )k κ Wθt

Wθ–( )+=

fB

ρFB( )k 1+ ρFB( )k κ W·

n⎝ ⎠⎛ ⎞

·F

W-----–=

n

nr 0.0= nθ βsin–= nz βcos=

Theoretical Background on Throughflow Method Throughflow Model

FINE™ 6-15

6-5.4.1 The Friction Force

The distributed loss model retains, from all the effects of heat conduction and viscous stresses, thecontribution to the entropy production. The dissipative action of the viscous stresses is expressed

through a distributed friction force, . It acts in the direction opposite to the velocity vector and

for a perfect gas its amplitude is proportional to the loss coefficient derivative in the streamwisedirection:

(6-6)

This formulation ensures that a loss coefficient of zero will give exactly a zero friction force. Theimposed loss coefficient is defined as:

(6-7)

where ptrot is the total pressure associated with rothalpy defined as:

where (6-8)

where W is the relative velocity magnitude and pref is a reference dynamic pressure taken at theleading edge (for compressors) or trailing edge (for turbines) on each streamwise mesh line.

fF

ρfFp

ptrot------------pref∂mψ W

W---------–=

ψptrot

LEptrot–

pref-------------------------------=

ptrot pTtrot

T-------------

⎝ ⎠⎛ ⎞

γγ 1–-----------

= Ttrot TW

2 ωr( )2–2cp

-----------------------------+=

Throughflow Model Theoretical Background on Throughflow Method

6-16 FINE™

FINE™ 7-1

CHAPTER 7: Optional Models

7-1 OverviewFINE™ contains the following three optional models:

• Fluid-Particle Interaction to model solid particles in the flow.

•Conjugate Heat Transfer to model the heat transfer between the fluid and solid walls.

•Cooling/Bleed to model cooling holes or bleed.

• Transition Model to model the flow transition.

Each of these models requires a special license feature. If the model is not accessible due to a miss-ing license it is displayed in gray under Optional Models. Contact NUMECA sales or support teamfor more information about the possibility to obtain a license.

7-2 Fluid-Particle Interaction

7-2.1 Introduction

Particle-laden flows cover a large class of two-phase flows, such as droplets or solid particles in agas or liquid flow, or bubbles in liquids. One phase is assumed to be continuous and occupies themajority of the flow. It is called the "carrier" phase. Another phase, whose volume fraction is rela-

tively small (usually less than 10-2), exists as a number of separate elements or particles. It is calledthe "dispersed" phase.

7-2.1.1 Lagrangian Approach

A Lagrangian approach is used here, whereby the trajectories of individual groups of particles arecalculated as transported by the velocity field of the carrier phase, including the effect of drag andother forces. The calculations of the carrier flow and of the particles can be fully coupled, the fullycoupling approach implying that the calculation of the particles trajectories is followed by a secondflow calculation, taking into account the presence of the particles in the flow (the interphase forcesare introduced as source terms in the flow calculation). The sequence consisting of a flow calcula-

Optional Models Fluid-Particle Interaction

7-2 FINE™

tion and of the particle traces tracking can be repeated several times until no changes are observedin the results (usually 3 to 10 times).

In the present Lagrangian model, the motion of the particles is only influenced by their own inertiaand by the flow, i.e. the local aerodynamic or hydrodynamic forces. Interactions between the parti-cles are currently not considered. This implies the hypothesis of a dilute flow. On the contrary in adense flow, particle motion is governed by their direct interaction, which implies more complexmodels, such as the Eulerian ones, in which both phases are modelled as continuous phases.

Particle-laden flows are found in many industrial applications such as cyclone separators, pneu-matic transport of powder, droplet and coal combustion system, spray drying and cooling or sand-blasting. In all cases, the flow consists of a continuous phase - also named carrier flow - and adispersed phase in the form of solid particles, liquid droplets or gas bubbles. In general, the motionsof the carrier flow and of the dispersed phase are interdependent.

In the lagrangian approach, the physical particle cloud is represented by a finite number of compu-tational particles. The continuous phase (fluid) is treated as a continuum using a boundary-control-led method whereas the dispersed phase (particles) is treated as a number of separate particles. Theparticles are successively tracked as a single probe particle through the flow field using a Lagrang-ian formulation.

In the case of laminar flows, each particle will follow a unique deterministic trajectory. In the caseof turbulent flows however, particles will have their own random path due to interactions with thefluctuating turbulent velocity field. This feature is taken into account in EURANUS through a sto-chastic treatment. This approach consists of employing a sampling technique based on a Gaussianprobability density function to introduce the random nature of the turbulent velocity field. The par-ticle diffusion due to turbulence can therefore be modelled without introducing artificial diffusionproperties of the cloud.

According to the distribution and contents of the particles, an averaging procedure provides phasecoupling source terms to be added into the Eulerian carrier phase conservation equations. The two-way coupling can be achieved through global iterations.

7-2.1.2 The Algorithm

The hypothesis of a dilute mixture permits to have a very simple sequential calculation of the trajec-tories of the different particles injected through the inlet sections.

The algorithm considers successively the different inlet patches. The user specifies the number oftrajectories per cell. The origins can be located at a given point chosen by the user, or equally dis-tributed throughout the cell.

The algorithm proceeds cell by cell, the time step being calculated so that several time steps are per-formed in each mesh cell. The procedure starts at a cell of an inlet boundary and stops when aboundary is reached.

Each time step consists of:

• the calculation of the force on the particle.

• the integration to find the new velocity and position.

• the determination of the cell in which the particle is located.

7-2.1.3 Overview

In this chapter an overview is given of the fluid particle interaction module incorporated inNUMECA’s FINE™ environment:

Fluid-Particle Interaction Optional Models

FINE™ 7-3

• section 7-2.2 describes the main functionalities of the module and the way to proceed in theFINE™ interface.

• section 7-2.3 gives the format of the files associated with the module.

• section 7-2.6 summarizes the main theoretical features of the Lagrangian model.

7-2.2 Fluid-Particle Interaction in the FINE™ Interface

To access the parameters related to Fluid-Particle Interaction select the corresponding page underthe Optional Models. In the parameters section click on Fluid-particle calculation to activate thismodel (see Figure 7.2.2-1). The user enters not only the main features of the numerical simulationsbut also the characteristics (i.e. processes to be taken into account) of the interphase force betweenthe fluid and the particles.

The top window allows to choose the degree of influence of the particles on the flow. The calcula-tion of the carrier flow and of the particles can be fully (2-way) or weakly (1-way) coupled:

• in the 1-way coupling approach the flow calculation (ignoring the influence of the particles onthe flow field) is followed by a calculation of the trajectories of particles. In this case, there isno influence of the particles on the flow.

• in the 2-way coupling approach the calculation of the trajectories of particles is followed by asecond flow calculation, taking into account the presence of the particles in the flow (the inter-phase forces are introduced as source terms in the flow calculation). The sequence can berepeated several times (by entering the Number of global iterations) until no changes areobserved in the results (usually 3 to 10 times).

Concerning the simulation itself, the user can choose the Global Strategy:

• Start from scratch: to start the flow calculations and then pursue with the particle tracking sim-ulation. In this particular case, the criterion for the carrier flow calculations convergence is theone set on the Control variables page (-6 by default).

• Start from converged flow solution: to proceed directly with the Lagrangian coupling from aprevious converged flow calculation.

FIGURE 7.2.2-1 Parameters page of the lagrangian fluid-particle interaction model.

The usual way to proceed is:

1. perform a pure flow study without activating the Fluid-Particle Interaction model in a computa-tion.

2. while this computation is active in the list of Computations on the top left of the interface createa new project by clicking on the New button.


7-4 FINE™

3. in this new computation activate the Lagrangian Fluid-particle calculation and perform a com-putation with Lagrangian coupling.The particles encounter several forces: the friction force, i.e.the resultant of the pressure and viscous stress in the carrier phase over the particle surface, aswell as potential inertia and gravity forces. The user is free to introduce the gravity forcethrough the vectorial components of the acceleration of gravity on the Flow Model page. Aninertial force due to the rotation of the system of reference can also be included. If some of theblocks are rotating this button should systematically be activated. In this case the reference rota-tion velocity is the one specified on the Rotating Machinery page.

7-2.2.1 The Boundary Conditions

All boundary conditions available for the carrier flow solver are also accepted by the particle track-ing algorithm. The only boundary conditions requiring user’s input are:

• inlet boundary

• solid boundary

The boundary conditions are imposed by selecting a patch on which to fix the condition. The userhas to confirm the entered values by clicking on the Apply to selection button (Figure 7.2.2-2). Inthe list of patches it is not possible to group patches but multiple patches can be selected at the sametime to apply the same boundary conditions to all of them. To select multiple patches hold the<Ctrl> key while selecting them.

a) Inlet Boundary

The user can enter a number of classes of particles, each class representing a different type of parti-cles. For each class the inlet boundary conditions have to be specified. The displayed boundary con-ditions are the one for the class specified in the bar as indicated (a) in Figure 7.2.2-2. To selectanother class use the scroll buttons on both sides of this bar. The purpose of this is to be able to sim-ulate the presence of different types of particles in the same patch.

FIGURE 7.2.2-2 Inlet boundary conditions for the fluid-particle interaction model

(a)


FINE™ 7-5

Note however that multiple classes are of interest for fully couples calculations only, by allowingthe flow calculation to account for the presence of different particle types. In the case of a weakcoupling strategy it is recommended to create one computation per particle class, because only oneparticle class can be visualized in CFView™. The Expert parameter (in Expert Mode on the ControlVariables page) CLASID permits to specify which particle class must be included in the CFView™output.

The inlet boundary conditions are the following:

• spatial distribution of the injection points: uniform over the chosen patch or located at a chosenpoint of coordinates (x,y,z).

• inlet velocity of the particles (absolute or relative frame of reference). The velocity is alwaysconsidered in the same relative frame of reference as the one of the block in which the inletparticle is located. The relative velocities here defined as the difference between the particleand the flow velocity (a zero relative velocity is therefore very commonly used) whereas theabsolute velocity boundary conditions is used when the velocity of the particle is well knownand different from the velocity of the flow. Note that only the Cartesian coordinate system isavailable.

• density and mean diameter of the particles.

• particle concentration (number of particles/m3).

• number of particles per cell should be seen as the number of trajectories per cell.

The use of multiple trajectories per cell permits to ensure a more uniform covering of the inlet (andhence of the computational domain) by the particles. This is only of interest in the case of fully cou-pled calculations where it is important to ensure that the source terms are correctly evaluated in allmesh cells. The use of multiple trajectories does not modify the number of particles entering thedomain. Each trajectory must be seen as an ensemble of particles. It is also very often referred to asa computational particle.

In the case of full coupling, the number of particles per cell should be statistically large enough toprovide accurate averaging of the dispersed phase parameters. Therefore it is recommended in thiscase to have a high number of particles per cell. This increases the computational time required forthe particle tracking process, but gives rise to a smoother distribution of the particles in the domain.In the case of a weak (1-way) coupling, only one particle per cell is usually enough to provide a suf-ficiently detailed description of the particles distribution in the field.

b) Solid Wall Boundary Condition

The solid wall boundary condition requires an additional input data, which is the reflection ratio. Ifthe ratio is zero, all the particles remain stuck on the wall, whereas if it is 1.0, all particles arereflected, without any loss of mass or energy. The user can choose the reflection ratio by clicking onthe corresponding button while moving the mouse (Figure 7.2.2-3).

Two reflection modes are available and can be selected by the expert parameter IBOUND:

• In the default mode (IBOUND = 1) the particle loses a fraction of its mass and hence of itskinetic energy at each wall hit. After several wall hits, the size of the particles becomes verysmall, and the tracking stops (once the diameter has reached a given ratio of the initial one,specified by the expert parameter DIAMR).

• In the other mode (IBOUND = 2) the velocity of the particle is reduced, with an unchangedmass. The particle is stopped as soon as the velocity becomes too small (also specified by theparameter DIAMR).


7-6 FINE™

FIGURE 7.2.2-3 Solid boundary conditions for the fluid-particle interaction model

7-2.3 Outputs

The following quantities are calculated by the solver (see Figure 7.2.3-4):

• the number concentration where Ni is the number of particles of class i in the cell

of volume Ω,

• the mass concentration (mass of particles per cell volume) where

is the density of the particle of class i and volume ,

• the volumetric concentration (volume of particles per cell volume),

• the components of the mass weighted absolute velocity vector

,

• the weighted mass and weighted absolute or relative velocity vectors number,

• the components of the interphase force .

The solver automatically writes an output file containing the particle traces that is read by theCFView™ post processing software.

Ni

i∑

⎝ ⎠⎜ ⎟⎛ ⎞

Ω⁄

ρipartNiΩipart

i∑

⎝ ⎠⎜ ⎟⎛ ⎞

Ω⁄

ρipart Ωipart

NiΩipart

i∑

⎝ ⎠⎜ ⎟⎛ ⎞

Ω⁄

Vx VxiρipartΩipartNii∑

⎝ ⎠⎜ ⎟⎛ ⎞

= ρipartΩipartNi

i∑⁄

F FiNi

i∑

⎝ ⎠⎜ ⎟⎛ ⎞

Ω⁄=


FINE™ 7-7

FIGURE 7.2.3-4 Outputs of the fluid-particle interaction model

7-2.4 Specific Output of the Fluid-Particle Interaction Model

This section describes the specific outputs generated by the Lagrangian module.

7-2.4.1 Field Quantities

The solver automatically includes in the CFView™ output (’.cgns’) of the project the field quanti-ties that have been specified by the user under the Outputs thumbnail in the Fluid-Particle Interac-tion page. These quantities can be scalars or vectors, and are the following:

•VectorsMass-weighted relative velocity (1)Number-weighted relative velocity (2)Mass-weighted absolute velocity (3)Number-weighted absolute velocity (4)Interphase force vector (5)

• ScalarsNumber concentration (51)Mass of particles per cell volume (52)Volume of particles per cell volume (53)Presence (1) or absence (0) of particles in cells (54)Vx: x-component of mass-weighted velocity vector (55)Vy: y-component of mass-weighted velocity vector (56)Vz: z-component of mass-weighted velocity vector (57)Fx: x-component of interphase force (58)Fy: y-component of interphase force (59)Fz: z-component of interphase force (60)

7-2.4.2 Particles Traces (’.tr’)

The solver also creates an specific lagrangian output file (’.tr’), containing the trajectories of the allthe particles. This file is automatically transmitted to CFView™, which allows for the visualizationof the trajectories.


7-8 FINE™

7-2.4.3 Summary File (’.tr.sum’)

In addition to the previous outputs, a summary file ’.tr.sum’ is automatically written by the solver(in the same directory as the CFView™ project), giving for each injection patch the particles num-bers and mass flows through the inlet/outlet boundaries, and the number of particles that remainstuck on the walls.

7-2.5 Expert Parameters for Fluid-Particle Interaction

Other parameters appear in the Expert Mode of the Fluid-Particle Interaction page under theParameters thumbnail:

• The maximum residence time (TMAX in corresponding ’.run’ file), which is the time limita-tion for particle residence in the flow. It may be used either to prevent particle stopping or toavoid an infinite loop, having for instance a particle captured in a separation bubble. After thetime has expired, the particle disappears.

• The governing equations for particles in a carrier flow consist of a set of non-linear ordinaryequations. Two methods are provided to integrate this equations with respect to time (that canbe selected in expert mode):

— The Runge-Kutta scheme, in which the transfer to the next time level is fulfilled through afinite number of intermediate steps. A two-stage and a four-stage option (NRKS in corre-sponding ’.run’ file) are available. This scheme is limited to big particles.

— The exponential scheme that lies on a semi-analytical method. This scheme is particularlysuitable for small particles.

• The Drag force is in general the only considered part of the interphase force. It corresponds tothe force on a particle moving in a still fluid at constant velocity (or using the particle refer-ence system, a fixed particle in a uniform laminar flow). At extremely low Reynolds numbers(Rep << 1 i.e. at low relative velocities), it is expressed through the Stokes formula. For higherReynolds numbers, an optional standard curve fit may be chosen (section 7-2.6.1). The choicebetween the two types of forces can be made in expert mode.

Other parameters have a standard value, which may be modified only on rare occasions. They areaccessible in the Expert Mode of the Computation Steering/Control Variables page:

CLASID: selection of class for CFView™ outputLMAX: the maximum number of segments along a trajectory may be used to avoid an infiniteloop in the case of an oscillatory movement for instance.DDIMAX: tolerance factor to establish that a particle has left a cell (default=1.E-4).I2DLAG: simplification for 2D problems (0 if 3D, 1 if 2D).DIAMR: diameter ratio under which the particle tracking process stops (default value: 0.1).CELT: coefficient for eddy life time (for turbulent flows only): 0.28.KOUTPT: enables to write the ASCII ’.tr.out’ file containing the output of the trajectories(default value: 0). Contact support at [email protected] to have more details on this file.


FINE™ 7-9

7-2.6 Theory

In a Lagrangian approach the particle cloud is modelled by a finite number of computational parti-cles, representing a group of real physical particles with similar properties. The particles are trackedseparately, each as a single probe particle, through the flow field.

7-2.6.1 Calculation of the Trajectories - Integration Method

The calculation of the trajectories is based on the Newton law:

(7-1)

where is the acceleration vector of the particle of velocity V and F is the sum of the friction forcebetween the fluid and the particle and the eventual inertia and gravity forces:

(7-2)

The gravity force is defined by the user on the Flow Model page:

It is assumed that the mesh blocks for which a rotation of the reference system is introduced in thecarrier flow equations (when rotation of the reference system is selected under the Parametersthumbnail of the Fluid-Particle interaction page) are also considered as rotating ones for the parti-cles calculation. The inertia force due to the rotation of the reference system contains the two termsrelated to the inertia and Coriolis effects:

(7-3)

Fd is the drag force between the flow and the particles, calculated according to the Stokes law:

(7-4)

where D is the diameter of the particles, U is the velocity of the fluid and Fs depends on the viscos-ity of the fluid and on the Reynolds number based on D:

(7-5)

where:

(simple Stokes law for )

or (standard curve approximation).

Up to now, no model is incorporated in which the mass and the volume of the particle would change(for instance by combustion or evaporation).

F ma m∆V∆t-------= =

a

F Fd Finertia Fgravity+ +=

Fgravity mg=

Finertia m ω ω r×( )× 2ω V×+[ ]–=

FdDFs----- V U–( )–=

Rep

Fs 1 3πµC( )⁄=

C 1= Repρ V U–( )D

µ--------------------------- 1«≡

C 1 0.179Rep0.5

0.013Rep+ +=


7-10 FINE™

7-2.6.2 Integration Time Step - Relaxation Time

The calculation of the trajectories is obtained by integrating the Newton law in time, using either a2- or 4-steps Runge-Kutta or an exponential scheme. At each time step the force vector is re-calcu-lated to obtain a new value for the velocity vector, whereas the velocity vector is used to calculatethe new position of the particle. This sequence is repeated until a boundary is reached. In order tohave an appropriate integration method to calculate the trajectories, the integration time step mustbe properly chosen.

The time step used by the algorithm is the minimum between the time required to traverse the meshcell (which depends on the particle velocity and on the cell size) and the relaxation time, which isthe time required by the particle to lose its initial slip velocity:

(7-6)

For a stationary reference system (no inertia force) and in the case of no gravity, the relaxation timeis the time required by the particle to reach the flow velocity U, whereas in the presence of an iner-tia and/or a gravity force, the velocity reached by the particle after the relaxation time is not U, butU + g . τdrag.

In some cases (for instance with very small particles) the relaxation time is very small, which leadsto a large number of time steps per mesh cell, and hence to a larger CPU time for the particle track-ing algorithm. A faster convergence may then be reached by using the so-called exponential schemefor the time integration step.

7-2.6.3 Full Coupling Between the Carrier and Particle Flows

In case of a full coupling between the carrier and particles flows, the particles traces calculation isfollowed by a coupled carrier flow calculation including the effect of the presence of the particles.This is achieved by the introduction of source terms in the momentum equations, these source termsbeing calculated according to the interphase force vector:

(7-7)

7-2.6.4 Interaction with Turbulence

While moving through a turbulent flow, each particle faces a sequence of random turbulent eddiesthat result in a lack of accuracy in particle velocity and position. This process is taken into accountusing a stochastic treatment. The k-ε turbulence model is assumed for the carrier flow simulation.

The instantaneous fluid velocity is represented as the sum of the local mean velocity (availablefrom the computed carrier flow field) and a random fluctuation:

(7-8)

The fluctuation is randomly sampled from the normal Gaussian distribution with the probabil-ity-density-function f:

and (7-9)

The individual components of the velocity fluctuation are assumed to be non-correlated. The meansquare deviation is evaluated from the turbulent kinetic energy:

τdrag ρD2( ) 18µC( )⁄=

Finterphase m∆V∆t------- Finertia– Fgravity–=

U U U'+=

U'

f u'( ) 1

2πu'2

----------------- u'2

2u'2

----------–⎝ ⎠⎜ ⎟⎛ ⎞

exp= U' f u'( ) u'd

∞–

u'

∫=

Conjugate Heat Transfer Optional Models

FINE™ 7-11

(7-10)

It is accepted that this sample velocity fluctuation remains unchanged within the turbulent eddyduring its life time. The eddy life time Te and size Le are calculated according to:

and (7-11)

Where is an empirical coefficient with a default value of 0.28.

The calculated fluctuation gives the instantaneous flow velocity, which is used while tracking theparticle. As soon as the life time has expired or the particle has left the eddy, a new fluctuation ischosen as described before, assuming no correlation with the previous sample.

Note that turbulence is therefore taken into account only for the different linear and

non linear k-ε models. In the particular case of the Baldwin-Lomax model, turbulencedoes not have a direct influence on the particles trajectories.

7-2.7 References

Chang, K. C., Wang, M. R., Wu, W. J., Liu, Y. C., Theoretical and Experimental Study on Two-Phase Structure of Planar Mixing Layer, AIAA Journal, Vol. 31, No 1, pp 68-74, 1993.

7-3 Conjugate Heat Transfer

7-3.1 Introduction

The conjugate heat transfer model allows the simulation of the thermal coupling between a fluidflow and the surrounding solid bodies, i.e. the simultaneous calculation of the flow and of thetemperature distribution within the solid bodies.

The current version of the model has been validated for steady state applications. It assumes thatsome of the blocks of the multiblock mesh are "solid", whereas the other ones are "fluid". Theconnections between the solid and fluid blocks become "thermal connections" along which the fluid-solid coupling is performed.

First section 7-3.2 explains how to set up a project involving the Conjugate Heat Transfer modelunder the FINE™ user environment. In section 7-3.3 a theoretical description is provided, present-ing the approach used to solve the conduction problem and describing the adopted solid-fluid cou-pling strategy.

7-3.2 Conjugate Heat Transfer in the FINE™ Interface

The Conjugate Heat Transfer model can be directly activated from the FINE™ interface underOptional Models. When opening the Conjugate Heat Transfer page it looks like Figure 7.3.2-5. Allblocks in the mesh are listed on the left of the page and all of them are by default set as "fluid".

u'2 2

3---k=

Te Cltkε--= Le Te

23---k

⎝ ⎠⎛ ⎞

1 2⁄=

Clt

Optional Models Conjugate Heat Transfer

7-12 FINE™

FIGURE 7.3.2-5 Conjugate Heat Transfer page

The only action required from the user to set up a computation involving the Conjugate Heat Trans-fer model can be decomposed in three steps:

1. Determine the Solid and Fluid Blocks.

2. Set the Global Parameters.

3. Define the thermal connections.

Those steps are described in the following paragraphs in more detail.

7-3.2.1 Step 1: Determine the Solid and Fluid Blocks

The use of the Conjugate Heat Transfer model requires the generation of a multi-block mesh, the"solid" and "fluid" parts of the domain being discretised with separate blocks.

Once the mesh is generated, the first step consists in pointing the "fluid" and the "solid" blocks viathe FINE™ user interface. In the default configuration of the solver all blocks are of "fluid" type, sothat the Conjugate Heat Transfer page does not need to be entered for a classical flow calculation.The transfer of some of the blocks from "fluid" to "solid" is performed by selecting those blocks onthe left part of the window and by pressing the button Solid.

For each solid block the thermal conductivity has to be specified (in W/m/K).

7-3.2.2 Step 2: Setting the Global Parameters

The only global parameter is the CFL number used for the time integration of the conduction equa-tion. It can be different from the one used for the fluid. The default value is 1.0.

7-3.2.3 Step 3: Setting the Thermal Connections

Once some blocks of the multi-block mesh are pointed as "solid" blocks, the connections betweensolid and fluid blocks become "thermal connections". These connections are solid wall boundaryconditions with a particular thermal condition, along which the imposed temperature profile is iter-atively recalculated in order to ensure a correct coupling.

These patches appear in the list of patches under the thumbnail Solid on the Boundary Conditionspage. Although the thermal aspect is fully controlled by the coupling procedure, the kinematicboundary condition must be specified by the user (rotation speed).

7-3.2.4 Type of Connections Between Solid and Fluid Blocks

Two types of thermal connections are allowed:

•matching connections (one patch on each side),

Conjugate Heat Transfer Optional Models

FINE™ 7-13

• full non-matching connections (one patch or one group of patches on each side). The connec-tion algorithm is implemented in a general way, allowing on both sides a grouping of solid andfluid patches. This is useful for instance in order to facilitate the coupling of a turbine blockwith holes with the external flow. One single connection can be built, with on the inner side agroup of patches including the blade surface and the outer face of the holes.

7-3.3 Theory

This section describes the Conjugated Heat Transfer model implemented within EURANUS:

• the technique used to solve the conduction in the solid bodies,

• the thermal coupling strategy.

7-3.3.1 Simulation of Conduction in EURANUS

It has been shown in the previous chapters that the EURANUS flow solver is based on a cell centredfinite volume approach, associated with a entered or upwind space discretization scheme togetherwith an explicit Runge-Kutta time integration method. The same type of approach can be used tosimulate the conduction in solid bodies. The only term remaining in the finite volume equilibriumresults from the heat conduction. The discretised form of the remaining part of the energy equationapplied to the control volumes can be written as:

(7-12)

where Vol is the volume of the control volume, n∆S is the normal vector to the faces of the controlvolume and k,ρ and Cp are respectively the conductivity, density and specific heat of the solid body.This equation is applied to calculate the change of temperature T at a given time step resulting fromthe equilibrium of the conduction fluxes through the faces of the control volume.

One can notice that the absence of any advective contribution in the equilibrium permits to avoid theuse of artificial dissipation (case of a centred scheme). It also imposes to adopt a pure diffusiveapproach for the calculation of the time step. For a 2D problem the time step is calculated accordingto:

(7-13)

One can notice that once the 2 above equations are put together the heat capacity Cp is eliminatedfrom the equation, and is hence not required as input data.

Exactly as for the flow solver the adopted time integration approach is a 4- or 5-step Runge-Kuttascheme whose efficiency is largely enhanced by the use of an implicit residual technique and of amultigrid strategy.

This finite volume approach can be used for both steady and unsteady conduction problems. Itsefficiency has been compared for steady state applications to the classical Gauss-Seidel and PSORschemes often employed for the resolution of pure elliptic equations. The results have shown that theuse of a time marching approach together with multigrid is much more efficient.

7-3.3.2 Thermal Coupling Between the Solid and Fluid Blocks

The fluid-solid interfaces constitute a new type of boundary condition, referred to as "thermal

ρCp∆T∆τ-------Vol Σ k∇T

⎝ ⎠⎛ ⎞ n∆S=

∆τVol---------

ρCp

k--------- Vol

Si2

Sj2 2Si·Sj+ +

-----------------------------------------=

Optional Models Conjugate Heat Transfer

7-14 FINE™

connections", along which the heatflux and temperature are imposed to be equal.

The calculation is performed simultaneously on the fluid and solid blocks. The thermal coupling isapplied each time the boundary conditions are applied. Note that no particular procedure is requiredin order to initiate the calculation. The full multigrid strategy is very efficient in order to rapidlyestablish an overall temperature distribution in the domain.

On both solid and fluid sides, the thermal boundary condition imposes a temperature profile. Thisprofile is iteratively recalculated in order to ensure equality of the heatfluxes calculated on bothsides:

hf(Tw-Tf)=-hs(Tw-Ts), (7-14)

where hf and hs are the heat transfer coefficients and Tf and Ts are the inner temperatures. The heat

transfer coefficients are calculated in a simple way, assuming a sufficient orthogonality of the mesh:

, (7-15)

where k is the local conductivity and ∆y is the distance between the inner cell centre (where thetemperature of Tf and Ts is taken) and the wall.

7-3.3.3 Full Non-matching Thermal Connections

The Full Non-matching algorithm already used for the fluid-fluid connections can be used in theConjugate Heat Transfer (CHT) module. It is based on the same coupling procedure, including thecalculation of the interface temperature and heatflux. In case the patches are not fully connected, asfor instance in Figure 7.3.3-6, the remaining patch is assumed to be adiabatic.

The thermal coupling equation is applied successively to all elements resulting from the FNMBdecomposition algorithm. This procedure gives as a result a separate value of the interface tempera-ture and of the heatflux for all elements.

The interface temperature on the left and right patch cells is then calculated as a weighted averagingof the temperatures of the elements concerned by the cell. If the cell is not fully connected an addi-tional contribution is added, the non connected part of the cell being assumed to be adiabatic:

with . (7-16)

In the generic case of Figure 7.3.2-5:

• the cell 1 is not connected and the above equation is applied with Wi=1,

• the cell 2 is partially connected and 0<Wi<1,

• the cell 3 is fully connected and Wi=0.

The heatflux density is calculated as the summation of the contribution of the elements:

(7-17)

Note that the heatflux density is saved instead of the heatflux so that the thermal connection bound-ary condition is compatible with the boundary condition imposing the heatflux density. In the rou-tine imposing the heatflux into the residual the heatflux density is re-multiplied by the cell surface.

It should be mentioned that hybrid connections are allowed, this means that each side of the inter-face can be composed of fluid and solid patches.

hk

∆y------=

Twi

Tnwni

TinnerWi+

elmts∑= wn

iWi+

elmts∑ 1=

ϕwi ϕn

iSn

elmts∑

⎝ ⎠⎜ ⎟⎛ ⎞

Si⁄=

Cooling/Bleed Optional Models

FINE™ 7-15

FIGURE 7.3.3-6 Generic example of FNMB/CHT connection

7-4 Cooling/Bleed

7-4.1 Introduction

The Cooling/Bleed model allows both the simulation of cooling flows injected through solid wallsinto the flow or bleed flows where mass flow leaves the main flow through solid wall.

The adopted technique makes use of additional sources of mass, momentum and energy located atgiven points or along given lines of the solid walls and does not require the meshing of the cooling

flow injection channels. The objective of this model is not to describe the details of the cooling flowitself but rather to consider its effect on the main flow.

In the next sections the following information is given on the Cooling/Bleed model:

• section 7-4.4 provides a theoretical description of the approach used to solve the cooling flowproblem.

• section 7-4.3 gives a summary of the available expert parameters related to cooling or bleedflow.

• section 7-4.2 describes how to set up a project involving the Cooling/Bleed model under theFINE™ user environment.

Optional Models Cooling/Bleed

7-16 FINE™

7-4.2 Cooling/Bleed Model in the FINE™ Interface

The Cooling/Bleed model can be directly activated from the FINE™ interface by opening the Cool-ing/Bleed page under Optional Models. The layout of the page is shown in Figure 7.4.2-7.

FIGURE 7.4.2-7 Cooling/Bleed page in FINE™

The list box on the top of the page (a) displays all the injectors (Cooling or Bleed) imported oradded by the user. The buttons below the list enable to add, edit, remove or import (more details ondata file in section 7-4.5) injectors (b). Clicking with the left mouse button over a selected injectorwill display its corresponding parameters in the lower part of the page (c). Clicking with the rightmouse button over a selected injector will display a popup menu enabling to add/edit/remove theinjector.

7-4.2.1 Injector Sector Wizard

When adding an injector (Add Injector), for each injection the following parameters need to bespecified through a wizard:

• injector name,

• injector role: Cooling or Bleed,

• injector solid patches location,

• definition of the geometry,

• position of the injector,

• flow parameters.

On the first page of this wizard the user can enter the name, the role, the solid patches, the geometrydefinition and the type of positioning of the injector.

a)

c)

b)


FINE™ 7-17

FIGURE 7.4.2-8 Injection Sector Wizard

a) Injection Sector Name

The name should be entered by moving the mouse to the text box for the Injector Name and to typethe name on the keyboard. By default a name is proposed like injector_1.

It is strongly recommended to use only standard english letters, arabic numerals and

underscore "_" symbol when naming an injection sector. Non-standard characters maynot be recognized or may be misinterpreted when using the project on other computers.

b) Injection Sector Role

The role of the injector should be entered: Cooling if the flow is injected through solid walls into themain flow or Bleed if part of the mass flow leaves the main flow through solid walls.

c) Injection Sector Geometry

Three types of injection sectors can be defined through the interface: point, line or slot.

• the point type corresponds to a single cooling hole.

• the line type stands for a series of cooling holes regularly distributed along a line with thesame geometrical and flow properties.

• a hub or shroud slot is a continuous line of holes placed at constant radius and axial position(typically used on the hub or shroud surface of a turbomachine). Slots are only defined alongaxisymmetric surfaces.

In case a slot (or a line) should traverse several patches (as for instance in a HOH

mesh configuration) all the patches should be selected and one single slot should be cre-ated.

d) Injection Sector Positioning

Four modes are available to place the holes:


7-18 FINE™

•Relative mode: this mode is used for blade walls and is valid for AutoGrid meshes only. Inthis case, the spanwise and streamwise positions of the hole (or of the 2 extremities in the caseof a line of holes) are specified.

• Space Cartesian mode: the user specifies the (X,Y,Z) Cartesian coordinates of the hole or ofthe 2 extremities for a line. For a slot the user enters the radius and the Z-coordinate of onepoint of the slot.

• Space Cylindrical mode: the user specifies the (R,θ,Z) cylindrical coordinates of the hole orof the 2 extremities for a line. For a slot the user enters the radius and the Z-coordinate of onepoint of the slot.

•Grid mode: the user specifies the (I,J,K) indices of the hole or of the 2 extremities of a line ofholes.

The injection sectors of type "Slot" can not be presented in relative coordinates.

The combination of injector geometry and positioning can be summarized as follow:

TABLE 7-1 Injector sector geometry/positioning combination and restriction

To cancel the modifications to the injector definition and close the wizard click on the Cancel but-ton.

Once the injector sector role, type and mode are correctly set, click on Next>> to go to the nextpage of the wizard. On this page, depending of the role, type and mode of injector, the flow param-eters and geometry/positioning parameters have to be defined in the second page of the wizard.

When defining a cooling or bleed using the Cartesian or cylindrical coordinates no

procedure are implemented to check if the specified direction is correct.

e) Injection Sector Geometry/Positioning Parameters

As presented in Table 7-1, 11 combinations are available. As the transformation from cylindrical toCartesian coordinates is obvious, only 8 combinations will be described in more details.

e.1) Relative positioning for a single hole

The user specifies the diameter of the hole in case of a single hole.

Each hole is circular. The diameter of the hole is specified by the user but a hole is

included in one cell only even when the diameter exceeds the cell width.


FINE™ 7-19

As for the old algorithm, the holes are located by means of a spanwise and a streamwise relativeposition. The algorithm can be applied to H, I or O-meshes generated by AutoGrid. For O-mesh theblade surface is divided in two different sub-patches (one for the pressure side and one for the suc-tion side). Therefore, the user has to select on which side of the blade (Side1/Side2) the injectionwill be located. A button has been added in the interface in order to select the side. This button isactive only for O-meshes.

FIGURE 7.4.2-9 Geometry Parameters for relative positioning of a hole

Only the version of AutoGrid provided with FINE™ 6.1-1 (and latter versions) can be

used to generate the mesh and this relative positioning is only available for blade sur-faces.

The location is defined as a fraction of the arc length from hub to shroud and from the leading edgeto the trailing edge. Spanwise and streamwise coordinates are computed for each cell vertex. Theclosest point found in this relative coordinate frame is the one that is concerned by the injection.

An option has been set-up in order to use the axial chord (Axial Coordinates button) instead of thearc length (only available for axial machines).

The relative positioning does not accept meshes with a blunt at the leading edge

FIGURE 7.4.2-10 . Relative positioning of a hole at 70% spanwise and 50% streamwise.

Finally, when a cooling injection sector has been selected, three ways to impose the injection direc-tion are proposed through the interface: Cartesian, cylindrical or grid indices.


7-20 FINE™

When Grid Indices is selected, the injection direction is provided by the user through 2 anglesexpressed in degrees (depending of the units selected in the menu File/Preferences). Each angle ismeasured with respect to the local normal and one of the 2 grid line directions tangent to the wall.

In case of an = ct surface, the angles are measured with respect to the grid lines

respectively. Figure 7.4.2-11 illustrates the definition of angle βk for an I = cst surface.

FIGURE 7.4.2-11 Angle definition in the cooling flow page of the FINE™ interface

Each angle is defined as:

(7-18)

For example, in order to make the velocity direction oriented along the normal, the two anglesshould be set equal to 0. A 90 degrees angle is not allowed as it will induce a velocity vector tan-gent to the corresponding grid line direction, with null mass flow.

For holes located on the blade walls and when the mesh is generated with Numeca’s AutoGrid soft-ware, the K- and J- lines are the two tangent directions along the blade wall, respectively oriented inthe streamwise and spanwise directions.

e.2) Relative positioning for a line of holes

The user specifies the diameter of the hole in case of a line of holes. Furthermore, the number ofholes has to be specified and will be uniformly distributed on the line.



As for the old algorithm, the line of holes is defined by two points (holes) that are located by meansof a spanwise and a streamwise relative position. The algorithm can be applied to H, I or O-meshesgenerated by AutoGrid. For O-mesh the blade surface is divided in two different sub-patches (onefor the pressure side and one for the suction side). Therefore, the user has to select on which side ofthe blade (Side1/Side2) the injection will be located. A button has been added in the interface inorder to select the side. This button is active only for O-meshes.

I

J

K

J K,( )K I,( )I J,( )

J

n

V

βk

I=constant surface

K

βk is the angle of the velocity projection in the (K,n) plane with respect to the normaln to the surface.

βi j k, ,Vi j k, ,

Vn-------------

⎝ ⎠⎛ ⎞atan=


FINE™ 7-21

For each point of the line the algorithm works as for the single hole positioning.

FIGURE 7.4.2-12 Geometry Parameters for relative positioning of a line of holes

Only the version of AutoGrid provided with FINE™ 6.1-1 (and latter versions) can be

used to generate the mesh and this relative positioning is only available for blade sur-faces.

The location is defined as a fraction of the arc length from hub to shroud and from the leading edgeto the trailing edge. Spanwise and streamwise coordinates are computed for each cell vertex. Theclosest point found in this relative coordinate frame is the one that is concerned by the injection.

An option has been set-up in order to use the axial chord (Axial Coordinates button) instead of thearc length (only available for axial machines).

The relative positioning does not accept meshes with a blunt at the leading edge

Finally, three ways to impose the injection direction are proposed through the interface: Cartesian,cylindrical or grid indices. When Grid Indices is selected, refer to the end of section e.1) for moredetails.

e.3) Cartesian positioning for a single hole




As for the old algorithm, the holes are located by means of the (X,Y,Z) Cartesian coordinates.

For a single hole, the cell that is concerned by the injection is the closest cell face cen-

tre to the defined point. In case of repetition, the point is automatically transferred to themeshed patch


7-22 FINE™

Furthermore, in order to ease the capture of the right coordinates, the button Get Coordinates ena-bles the user to interactively select the point in the mesh view after opening the mesh through themenu Mesh/View On/Off or Mesh/Tearoff graphics (only available on UNIX).

FIGURE 7.4.2-13 Geometry Parameters for space Cartesian positioning of a hole


e.4) Cartesian positioning for a line of holes

The user specifies the diameter of the hole in case of a line of holes. Furthermore, the number ofholes has to be specified.



As for the old algorithm, the line of holes is defined by two points (holes) that are located by meansof the (X,Y,Z) Cartesian coordinates.

For the two points defining the line, the cells that are concerned by the injection are

the closest cell face centre to the defined point. In case of repetition, the point is automat-ically transferred to the meshed patch

FIGURE 7.4.2-14 Geometry Parameters for space Cartesian positioning of a line of holes


FINE™ 7-23


A line is drawn from those two points (this line do not necessarily follow the surface of the patch,see Figure 7.4.2-15). The segment is then uniformly divided into N-1 sub-segments (where N is thenumber of holes on this line). Each N-2 limits of the sub-segment is then projected on the patch (theclosest cell face centre is found). Those are the cells where the injection will be applied. They arenot necessarily uniformly distributed on the patch.

FIGURE 7.4.2-15 Construction of a line of holes on a turbine hub

For a mesh with an important clustering, or for an important number of points in the

line, several projected points could end on the same cell. This is taken into account in thealgorithm. The mass flow injected is then multiplied by the relevant factor. Therefore,one should be aware that the number of cells that are highlighted in the interface shouldnot strictly match the number of hole in the line.

FIGURE 7.4.2-16 Definition of a line of holes without or within the parametric space

points defined by userpoints at cell face centre where injection will be applied

View from the top View at Constant Radius

without Parametric Space

within Parametric Space


7-24 FINE™

On the contrary for a mesh with a relatively poor spatial discretisation, the location of the cell facecentres where the injection will be applied will not be strictly on a line. A limitation of this algo-rithm is that the line does not necessarily follow the patch surface. Therefore, defining a line ofholes at the hub of a gap (upper surface of a rotor blade) could produce the problem presented onthe left side of Figure 7.4.2-16. The same problem can arise generally on a convex surface. In orderto solve this problem, it has been decided to allow the user to define a line of holes following a par-ametric surface defined by the grid lines by activating Parametric Space. Therefore, a line of holeon a convex surface could be more easily defined (right side of Figure 7.4.2-16).

One limitation of this option is that a line of hole cannot cross a connection. For

instance defining a line of holes (in the parametric space) close to the trailing edge of a Omesh will produce the result sketched bellow.

FIGURE 7.4.2-17 Definition of a line of holes in the parametric space.

For turbomachinery configuration with periodic conditions, points could be located either on themeshed passage or on one of its repetitions. Therefore, the injections should automatically be trans-ferred to the meshed patch. Two methods are available.

FIGURE 7.4.2-18 Two methods to respect repetition for a line of 3 holes.

POSSIBLE

Meshed Repetition Patches

Meshed Repetition Patches

FINE™ 6.1 FINE™ 6.2


FINE™ 7-25

• In FINE™ 6.1, the method was transferring only the extremities of the line of holes to themeshed patch.

• In FINE™ 6.2, the method is rotating only the final position of the injections in order to belocated on the meshed patch. As illustrated in Figure 7.4.2-18, those two options could lead torather different results.

In case of multi-patch selection the algorithm described above is applied independently for eachpatch. Therefore, a direct definition of a line of hole crossing several patches is not possible. In thiscase it is recommended to define as many line as necessary (see figure bellow). In order to over-come this problem the multi-patch selection has been restricted to the slots defined by Cartesian orcylindrical coordinates.

FIGURE 7.4.2-19 Example of definition of a line of 5 holes with multi-patch selection.


e.5) Cartesian positioning for a slot

The user specifies the width of the slot. has to be specified.

The multi-patch selection has been restricted to the slots defined by Cartesian or cylin-

drical coordinates.

FIGURE 7.4.2-20 Geometry Parameters for space Cartesian positioning of a slot

FINE™ 6.2FINE™ 6.1


7-26 FINE™

For the positioning of the slot, the radius and z values are asked to the user. The closest cell face ofthe patch to this point is found. The radius and axial position of this cell face centre become the slotposition in the (r,z) plane. It should be noted that this slot position is not identical to the initial userinput. For most axial machines the radius can be easily identify by calculating the closest point onthe patch. In this case only the axial position of the slot is required in the interface. For radialmachines, or for axial machines with complex vein geometry, the two components of the originalpoint are required (Figure 7.4.2-21).

FIGURE 7.4.2-21 Examples of slot positioning

The algorithm that defines the cell faces that are concerned by this slot is the following one. Foreach cell face of the patch, the two extremities in the (r,z) plane of this polygon (A,B and A’,B’) areidentified (i.e., the two vertices with the maximum distance in this plane). They define the limits ofthe cell face in the (r,z) plane. If those two points are called A,B for cell 1 and A’,B’ for cell 2, andS is the slot location specified by the user in the (r,z) plane through FINE™, as presented onFigure 7.4.2-22, S is only included in the domain of cell 1 limited by A,B in the (r,z) plane, there-fore, the cell 1 is the only cell concerned by the slot S.

FIGURE 7.4.2-22 Identification of the cells concerned by the slot S in the (r,z) plane. δ is the distance between A and B.

Axial Machine

Radial Machine


FINE™ 7-27

On the contrary, S is not inside the domain defined by A',B'. Thus, the cell 2 will not be concernedby the slot.

For O-meshes with small cells close to leading or trailing edges, this algorithm could

leads to missing cells. This problem is due to a (r,z) position specified by the user inFINE™ for the slot that is not precise enough.

FIGURE 7.4.2-23 Definition of a slot for a O-mesh



e.6) Grid positioning for a single hole




The grid positioning used in EURANUS depends on the grid indices of the centre of the cell faces.It is different from the grid indices used in IGG™ and in CFView™. The grid indices are directlyused by the flow solver in order to introduce the flow of mass, momentum and energy at this cellface.

points are missing points are represented

not precise enough value

exact value

points are missing points are represented

not precise enough value

exact value


7-28 FINE™

FIGURE 7.4.2-24 Geometry Parameters for Grid positioning of a hole


e.7) Grid positioning for a line of holes

The user specifies the diameter of the hole in case of a line of holes. Furthermore, the number ofholes has to be specified.



From the two cell face centres defined in the interface, two geometrical points are defined by their(x,y,z) coordinates. Then, a line is constructed in the same way as for the Cartesian positioning(section e.4). In this case there is no problem of repetition because the two extremities of the lineare located on the meshed patch. Furthermore, concerning the Parametric Space option, refer tosection e.4) on page 7-24 for more details.

FIGURE 7.4.2-25 Geometry Parameters for Grid positioning of a line of holes



FINE™ 7-29

e.8) Grid positioning for a slot

The user specifies the width of the slot. has to be specified.

From the grid indices a geometrical point is defined. Then the slot is defined in the same way as forthe Cartesian positioning (section e.5).

FIGURE 7.4.2-26 Geometry Parameters for Grid positioning of a slot


f) Flow Parameters

The user has to specify the Mass flow: the specified mass flow is actually the total mass flowthrough all the blades and through all the holes in the case of a line of holes. Thus the mass flowthrough one hole is the specified mass flow divided by the number of blades and the number ofholes. The mass flow is often responsible for initialization troubles as it might be too high. TheFINE™ interface allows a tuning of the specified mass flow through an expert parameter. This isdescribed in section 7-4.3.

For cooling flow the mass flow specified in FINE™ will be considered as positive and

as negative for bleed flow.

FIGURE 7.4.2-27 Flow Parameters for Bleed

FIGURE 7.4.2-28 Flow Parameters for Cooling


7-30 FINE™

Furthermore, the Arrows scaling factor parameter enables the user to control the shape of thearrows representing the injection direction after opening the mesh through the menu Mesh/ViewOn/Off or Mesh/Tearoff graphics (only available on UNIX).

For cooling additional parameters have to be defined:

• static or total temperature.

• turbulent kinetic energy and dissipation or turbulent intensity when the k-ε model is used.

• kinematic turbulent viscosity when the Spalart-Allmaras model is used.

7-4.2.2 Injector Sector Visualization

When adding an injection sector into FINE™, the location (cell face are highlighted) and the direc-tion of the injection can be visualized. In order to be able to visualize, the user has to load the meshthrough the menu Mesh/View On/Off.

FIGURE 7.4.2-29 Injection Sector Visualization within FINE™

The parameters area will then be overlapped by the graphic window, and the small control buttonon the upper - left corner of the graphic window can be used to resize the graphics area in order tovisualize simultaneously the parameters and the mesh (see section 2-10).

Mesh/Tearoff graphics is only available on UNIX and enables to open the mesh in a

new window.


FINE™ 7-31

Furthermore, new outputs have been added into FINE™ on the Outputs/Computed Variables pageunder the thumbnail Solid data in order to enable the visualisation in CFView™ of the injected flowand the injection direction.

FIGURE 7.4.2-30 Injector Sector Outputs for CFView™


a) COOLRT

In the old algorithm (COOLFL=0), in case some difficulties appear at the beginning of the simula-tion, the mass flow can be reduced with the expert parameter COOLRT. The value of COOLRT(less than 1) corresponds to a constant factor applied to the imposed mass flow. This parameter hasan influence on the initialization as the specified mass flow is sometimes too large. The user shoulddefinitely tune this parameter in case of problems.

b) ZMNMX

In the old algorithm (COOLFL=0) for the relative mode, the injector position in streamwise direc-tion can be provided with 0 and 1 defined in two different ways:

ZMNMX = 0 (default): the leading and trailing edges are the grid edges, i.e the points where theperiodic lines of the mesh meet the blade walls

= 1: the points located at respectively the minimum and maximum axial positions.

c) COOLFL

There is a possibility to specify the cooling/bleed flow data through an external input file with theextension ’.cooling-holes’. This file can be useful in case the flow calculation is integrated into anautomatic procedure. For more details on the format of the file, refer to section 7-4.5.

COOLFL = 0: the old algorithm of the cooling/bleed model will be used (model used in FINE™6.1 and previous releases). The backward is ensured through this parameter set at 0.

= 1: the old algorithm of the cooling/bleed model will be used (model used in FINE™6.1 and previous releases) based on an external file with the extension ’.cooling-holes’ located inthe corresponding computation subfolder will be read and the data specified through the FINE™interface will be ignored.

= 2 (default): the new algorithm of the cooling/bleed model will be used.


7-32 FINE™

d) MAXNBS

The maximum allowed number of injection sectors is controlled through the expert parameterMAXNBS (the default value is 50). If the input file contains a higher number of sectors the param-eter should be modified.

7-4.4 Theory

If COOLFL=0, the model consists in the addition of local source terms to all the flow equations(mass, momentum, energy and k-e equations when a 2-equations turbulence model is used). Theseterms are added as fluxes through the solid boundary cells where a cooling hole has been placed bythe user. Fluxes are computed as:

•Mass:

•Momentum

• Energy

• k,ε-equations:

where ρ is the density, Vn is the velocity component normal to the solid wall and S is the cooling

hole surface.The increased static pressure is computed as:

(7-19)

and the total energy E* is:

(7-20)

The density required to calculate the velocity components is obtained from the computed pressurefield along the walls and from the imposed static or total temperature.

Note that for the momentum equations only the velocity term is added as a source

term. The pressure term already exists even in the absence of holes.

If COOLFL=2, the cooling injection/bleed are treated as additionnal inlet or outlet boundary condi-tion.

Finally, the turbulent kinetic energy and dissipation can either be directly imposed by the user or becalculated from the turbulent intensity. In that case, the turbulent kinetic energy is obtained as:

(7-21)

where V is the velocity magnitude and Tu is the turbulent intensity. The turbulent dissipation isobtained from the relation:

(7-22)

where D is the diameter of the hole and Cµ = 0.09.

It should be noted that the velocity remains equal to zero at the walls even in the cool-

ing flow region. Thus the boundary condition on the velocity is left unchanged and the

Fmass ρVnS=

Fmomentum

x y z, , ρVx y z, , VnS p∗nx y z, , S+=

Fenergy

Vn ρE p∗+( )S=

Fk ε, ρVn k ε,( )S=

p∗ p23---ρk+=

E∗ eV2---

2k+ +=

k 1.5 Tu V⋅( )2=

εCµ

0.75k1.5

0.1D--------------------=


FINE™ 7-33

effect of the cooling flow will be observed in the surrounding cells. However, the tem-perature field will be affected on the wall itself.

7-4.5 Cooling/Bleed Data File: ’.cooling-holes’

A parser is used to find the data in this file, using keywords to locate the position of the data in thefile. The advantage of this technique is that the data do not have to be positioned at a given line inthe file, but only have to be followed by the appropriate keyword (the keywords can be written withcapitals or not).

The user specifies in the file a series of 'injection sectors'. An injection sector is either

— a single cooling hole

— a series of distributed cooling holes along a line (all holes having the same geometrical andflow properties)

— a hub or shroud slot (continuous line of holes along a constant radius and axial position line)Each injection sector should respectively start and end with the keywords

INJECTION SECTOR

END DATA

Each injection sector should contain all the appropriate data. If one data is missing, the

flow solver will stop and a message will appear on the screen.

7-4.5.1 Specification of an injection sector

a) Type of injection sector

The user should start by defining if the sector is a single injection hole (1), a line of holes (2) or aslot (3):

b) Boundary patch

The user should specify the block and face number, as well as the boundary patch on which theholes are located. The face number can be 1 (I=1), 2 (J=1), 3 (K=1), 4 (K=KM), 5 (J=JM), 6 (I=IM)

The patch number is only required if several solid patches are present on the face (for instance on ahub or shroud wall).

c) Position of the holes and slot

Three modes are available to locate the holes:

c.1) Relative Positioning - for blade walls (can not be used for slots)

• spanwise position(s) of the hole or of the 2 extremities of the line of holes (between 0 at thehub and 1 at the shroud)

• streamwise position(s) of the hole or of the 2 extremities of the line of holes (between 0 at theleading edge and 1 at the trailing edge). The leading and trailing edges can either be the gridedges, i.e. the points where the periodic lines of the mesh meet the blade walls (parameterZMNMX=0), or the points located at respectively the minimum and maximum axial positions(parameter ZMNMX=1, valid for axial flow machines). The choice between the two possibili-ties is made through the expert parameter ZMNMX, whose default value is 0.

Note that this "blade wall" positioning option is only valid for H- or I-type meshes, the


7-34 FINE™

pressure and suction surfaces being assumed to be located on two opposite faces of themesh.

c.2) space Cartesian (X,Y,Z) positioning data

• in case of a hole or of a line of holes the user specifies the Cartesian coordinates of the hole orof the 2 extremities.

• in case of slot the user specifies the radius and the Z-coordinate of one point of the slot.A searching procedure is applied to find the closest solid wall cell to the specified point(s). Thepoint is periodically repeated around the machine axis so that the specified point does not need tobe located in the blade passage used for the computation.

c.3) Grid positioning data

The user specifies the grid indices of the hole, of one point of the slot or of the 2 extremities of theline of holes. Depending on the face number, only 2 indices have to be provided (for instance, alongthe I=1 face, only the J and K indices are required).

d) Size of the holes or Width of the slot

The user specifies in addition either the diameter of the holes in case of a single hole or a line ofholes, or the width of the slot (in meters).

e) Flow properties

• the mass flow through the hole(s): the specified mass flow is the total mass flow through allthe blades. In case of a line of holes, the specified mass flow is the overall mass flow throughall the holes. Therefore the mass flow through one hole is the specified mass flow divided bythe number of blades and by the number of holes. Mass flow has to be negative for Bleed flow.

• the static or total temperature (if both are present only the static temperature will be read).

• he turbulent kinetic energy and dissipation, or the turbulent intensity (if the k-ε model is used).

The kinematic turbulent viscosity (if Spalart-Allmaras model is used) cannot be speci-

fied through an external file ’cooling-holes’.

f) Velocity direction

Finally, when a cooling injection sector has been selected, three ways to impose the injection direc-tion are proposed through the interface: Cartesian, cylindrical or grid indices. When the injectiondirection is provided by the user through grid indices, 2 angles have to be expressed in degrees.Each angle is measured with respect to the local normal and one of the 2 grid line directions tangentto the wall. The user specifies 2 of the following 3 angles (in degrees), depending on the face onwhich the hole is located:

•Angle with respect to I-grid line

•Angle with respect to J-grid line

•Angle with respect to K-grid lineNote that the two angles should be equal to 0 degree to make the velocity direction oriented in thenormal direction to the blade wall, whereas a 90 degrees angle induces the velocity vector to be tan-gent to the corresponding grid line direction.

In the case of holes located on the blade walls, and if the mesh has been generated with the AutoG-rid software, the K- and J-lines are the two tangent directions along the blade wall, respectively ori-ented in the streamwise and spanwise directions. The K-angle is the streamwise angle, whereas theJ-angle is the spanwise angle.

n

kjikji V

Varctg ,,

,, (=β )


FINE™ 7-35

7-4.5.2 Summary of all required input data

a) Global Data

b) Positioning

KeywordSingle hole (1), line(2) or slot(3) type

Number of holes (if line) number of holes

Diameter (single hole or line) diameter

Width (slot) width

Block Number block

Face Number face

Patch Number (only if several patches) patch

Input Mode (1-relative, 2-Cartesian(X,Y,Z), 3-Grid(I,J,K)) mode

Positioning - Single Injection Hole if mode 1 KeywordStreamwise position of the hole Streamwise position

Spanwise position of the hole Spanwise position

Positioning - Single Injection Hole if mode 2X-coordinate of the hole X-coordinate

Y-coordinate of the hole Y-coordinate

Z-coordinate of the hole Z-coordinate

Positioning - Single Injection Hole if mode 3I-index of the hole I-index

J-index of the hole J-index

K-index of the hole K-index

Positioning - Line of Injection Holes if mode 1Streamwise position of first point streamwise position of first point

Spanwise position of first point spanwise position of first point

Streamwise position of second point streamwise position of second point

Spanwise position of second point spanwise position of second point

Positioning - Line of Injection Holes if mode 2X-coordinate of first point X-coordinate of first point

Y-coordinate of first point Y-coordinate of first point

Z-coordinate of first point Z-coordinate of first point

X-coordinate of second point X-coordinate of second point

Y-coordinate of second point Y-coordinate of second point

Z-coordinate of second point Z-coordinate of second point

Positioning - Line of Injection Holes if mode 3I-index of first point I-index of first point

J-index of first point J-index of first point

K-index of first point K-index of first point

I-index of second point I-index of second point

J-index of second point J-index of second point

K-index of second point K-index of second point


7-36 FINE™

c) Flow Properties

d) Flow Direction (only for cooling flow)

7-4.5.3 Examples

Example 1 - Bleed Flow through a Slot define in Grid (I,J,K) mode

Positioning - Slot - mode 2Radius of one point of slot radius

Z-coordinate of one point of slot Z-coordinate

Positioning - Slot - mode 3I-index of one point of slot I-index

J-index of one point of slot J-index

K-index of one point of slot K-index

KeywordMass Flow (negative if bleed flow) mass flow

Static Temperature (only for cooling flow) static temperature

Total Temperature (only for cooling flow) total temperature

Turbulent Kinetic Energy (only for cooling flow and k-ε model) width

Turbulent Dissipation (only for cooling flow and k-ε model) turbulent dissipation

Turbulent Intensity (only for cooling flow and k-ε model) turbulent intensity

Flow Direction - Cartesian mode KeywordAngle with respect to x-direction(degrees) x-angle

Angle with respect to y-direction(degrees) y-angle

Angle with respect to z-direction(degrees) z-angle

Flow Direction - Cylindrical modeAngle with respect to r-direction(degrees) r-angle

Angle with respect to theta-direction(degrees) theta-angle

Angle with respect to z-direction(degrees) z-angle

Flow Direction - Grid modeAngle with respect to K-grid line(degrees) K-angle

Angle with respect to J-grid line(degrees) J-angle

Angle with respect to I-grid line(degrees) I-angle

Transition Model Optional Models

FINE™ 7-37

Example 2 - Bleed Flow through a Slot define in Cartesian (X,Y,Z) mode

Example 3 - Cooling Flow through a Hole define in Cartesian (X,Y,Z) mode

7-5 Transition Model

7-5.1 Introduction

The boundary layer which develops on the surface of a solid body starts as a laminar layer butbecomes turbulent over a relatively short distance known as the transition region. This Laminar-Turbulent transition is a complex and not yet fully understood phenomenon. Among the numerousparameters that affect the transition one can list: the free stream turbulence intensity, the pressuregradient, the Reynolds number, and the surface curvature.

Furthermore, predicting the onset of turbulence is a critical component of many engineering flows.It can have a tremendous impact on the overall drag, heat transfer, and performances especially forlow-Reynolds number applications. However, most of the turbulent models fail to predict thetransition location.

Therefore, it is proposed to include a transition model in the original Spalart-Allmaras turbulencemodel in order to take into account the transition onset at a certain chord distance on a blade pressureand suction sides. The transition location (transition line in 3D) should be imposed either through a

Transition ModelTransition Model

Optional Models Transition Model

7-38 FINE™

user input or via a separate guess. It should be pointed out that these transition terms should only beactive when the transition module is used. When it is not used, the fully turbulent version of theSpalart-Allmaras turbulence model remains unchanged.

In the next sections the following information is given on the Transition Model:

• section 7-4.4 provides a theoretical description of the approach used to solve the transitionregion.

• section 7-4.3 gives a summary of the available expert parameters related to the Transitionmodel.

• section 7-4.2 describes how to set up a project involving the Transition Model under theFINE™ user environment.

7-5.2 Transition Model in the FINE™ Interface

The transition model can be directly activated from the FINE™ interface by opening the TransitionModel page under Optional Models. The layout of the page is shown in Figure 7.4.2-7.

FIGURE 7.5.2-31 Transition Model page in FINE™

A list of all the blades appears in the left box and the remaining area is divided into two boxes forsuction and pressure side, respectively. Four choices are possible:

— Fully Turbulent

— Fully Laminar

— Forced Transition

— Abu-Ghannam and Shaw (AGS) Model

Furthermore, for Forced Transition, the user has to specify the position of the transition lines on eachside of each blade. It is based on the relative stream-wise position and it is defined as a line on theblade pressure and/or suction sides from hub to shroud. The user specifies two anchor points throughwhich a straight line will be built by the solver. It should be noted that only blades are transitionalwhile end walls are fully turbulent.

The transition model is only available for the one-equation Spalart-Allmaras model

using AutoGrid mesh and is applied to blade boundaries and work in both steady and


FINE™ 7-39

unsteady modes.

The transition model is not adapted to external cases.

R/S interfaces should be correctly oriented (from upstream to downstream) and solid

wall of the blades should be adiabatic.

For the Abu-Ghannam and Shaw model: only one "downstream" R/S upstream of

each blade is allowed. Furthermore, there are no restrictions on the number of inlets.

Finally, a new output has been added into FINE™ on the Outputs/Computed Variables page underthe thumbnail Solid data in order to enable the visualisation in CFView™ of Intermittency (moredetails on this quantity in section 7-5.4).


INITRA (integer): control the number of multigrid iterations (default = 100) performed in fully tur-bulent after the coarse grid initialization process. Thereafter, the blade pressure side and suctionside are identified and the transition line is defined. The computation pursue for the remaining iter-ations in transitional mode. The transition line derived from the Abu-Ghannam and Shaw model iscomputed at each iteration.

.

For starting or restarting a computation in transitional mode from a previous solution

(fully turbulent or in transitional mode) the expert parameter INITRA should be set to 0(otherwise iterations will be performed in fully turbulent mode).

INTERI (integer): control the type of intermittency distribution (0:binary or 1: from Dhawan andNarasimah) (default = 0).

INTERL (integer): control the type of location used for forced transition (0: base on arc length or 1:based on axial chord) (default = 0).

FTURBT (real): control the proportion close to the trailing edge that is fully turbulent (default =0.95).

Full MultiGrid

Coarse Grid Initialization

Transition Model

MultiGrid

Fully Turbulent

MultiGrid

Initialization

INITRAFull MultiGrid

Coarse Grid Initialization

Transition Model

MultiGrid

Fully Turbulent

MultiGrid

Initialization

INITRA


7-40 FINE™

FTRAST (real): prevents the transition to start in an area defined from the leading edge of the mesh.The value set is a percentage of the chord upstream of which the transition is not allowed (bydefault 0.05: 5%).

ITRWKI (integer): switches on the wake induced transition model. When activated (ITRWKI setto 1), the free stream turbulence intensity (defined at the inlet or at the rotor/stator interface) and theturbulence intensity from the boundary layer edge are used to define the transition region. Whenthis parameter is not checked, only the free stream turbulence intensity is used.

7-5.4 Theory

The Transition Model consists of introducing a so-called intermittency, Γ, defined as the fraction oftime during which the flow over any point on a surface is turbulent. It should be zero in the laminarboundary layer and one in fully developed turbulent boundary layer.

The intermittency function is defined on each point of the blade surface and at each iteration. It isextended to the computational domain by a simple orthogonal extension (i.e., each point of thecomputational domain has the same intermittency than the closest point on the blade surface).

The intermittency is used to multiply the turbulence production term. For the Spalart-Allmaras tur-bulence model this gives:

(7-23)

where is the production term in the Spalart-Allmaras in Eq. 4-52. Free-stream wakes (with onlya weak production term) will not be affected by the intermittency. A laminar boundary layer will bepreserved upstream of the transition location and turbulence could freely develop thereafter.

The transition location imposed by the user through the Forced Transition option and

by the AGS Model is only appearing if it has been defined in a turbulent boundary layer.

7-5.4.1 Fully Turbulent

When the Fully Turbulent model is selected, the intermittency, Γ is set at 1 on the whole blade suc-tion and/or pressure sides (fully developed turbulent boundary layer).

7-5.4.2 Fully Laminar

When the Fully Laminar model is selected, the intermittency, Γ is set at 0 on the whole blade suc-tion and/or pressure sides (laminar boundary layer).

7-5.4.3 Forced Transition

The first step is to have a description of the blades in EURANUS to be able to position the transi-tion line. Therefore AutoGrid has been adapted to output the position of the leading and trailingedges and the topological patches composing the blade surfaces.

This last information is read by FINE™ and transmitted to the solver EURANUS. A dialog box hasbeen created to allow the positioning the transition line on the blade surfaces (Figure 7.5.4-32).

SS~~ Γ=

S


FINE™ 7-41

In Forced Transition mode, each transition line is positioned through a point on the hub and a pointon the shroud. By default, these points are defined by a percentage of the arc length(Appendix 7.5.4-32). However, a special treatment is also available where the transition points aredefined by a percentage of the axial chord (only available for axial machines). This option can beactivated via the expert parameter INTERL that should be set to 1 (default value = 0).

The intermittency, Γ, is then computed on each point of the blade surface (it is set to 0 upstream ofthe transition line and tends towards 1 downstream). Each point of the computational domain hasthe same intermittency as the one of the closest point on the blade surface. However a special treat-ment is required close to the trailing edge and in tip gaps.

FIGURE 7.5.4-32 Example of the calculation of a transition point on a blade suction side as a percentage of the chord length.

A last aspect of the implementation is the post-processing. Spalart & Allmaras propose in their arti-cle a turbulent index to be able to distinguish turbulent zone from laminar zone. This index isimplemented in EURANUS as a solid data. It is defined as:

(7-24)

where n is the direction normal to the solid wall. It is near 0 in the laminar zone and near 1 in theturbulent zone.

7-5.4.4 Abu-Ghannam & Shaw Model (AGS)

The location of transition could be computed from the flow solution by using empirical relationsrelated to external parameters. It is here proposed to use the correlations obtained by Abu-Ghannam

nit ∂

∂= νωνκ

~1


7-42 FINE™

and Shaw [1980] and derived from experimental data from transition on a flat plate with pressuregradients. According to these authors transition starts at a momentum thickness Reynolds number:

. (7-25)

λθ is a dimensionless pressure gradient defined as:

(7-26)

where Ue is the velocity at the edge of the boundary layer, s is the streamwise distance from the

leading edge, and θ denotes the momentum thickness in the laminar region. τ is the free stream tur-bulence level (in %). The function F(λθ ) depends on the sign of the pressure gradient:

for adverse pressure gradient (λθ < 0), (7-27)

for a favourable pressure gradient (λθ > 0). (7-28)

Therefore, according to these relations, transition is promoted in adverse pressure gradient whereasit is retarded in favourable pressure gradient.

The range of application of the AGS correlation is 0.1 > λθ > -0.1, and for a free stream turbulentlevel ranging from 0.3 to 10%.


Either using the Forced Transition option or the Abu-Ghannam and Shaw (AGS) Model, the stream-wise evolution of intermittency should be defined. It could be either a binary field or a smootherfield. In the current implementation those two options are available. It is controlled by the expertparameter INTERI. With its default value (INTERI = 0) the intermittency is 0 before transition and1 after the transition onset. If INTERI = 1, intermittency is defined following the relation of Dha-wan and Narasimha [1958]:

(7-29)

(7-30)

where st is the position of the transition onset and s is the current position on the arc from leadingedge to trailing edge. λ is the characteristic extent of the transition region and is determined fromthe correlation:

(7-31)

Close to the trailing edge the intermittency is set to 1. This is necessary in order to allow a turbulentwake to be generated downstream of the blade. This special treatment is controlled by the expertparameter FTURBT that is set to 0.95 by default (i.e., only the last 5% of a blade side will have an

⎟⎠

⎞⎜⎝

⎛ −+= τλλ θθθ 91.6

)()(exp163

FFR s

ds

dUe

νθλθ

2

=

2)(64.6375.1291.6)( θθθ λλλ ++=F

2)(27.1248.291.6)( θθθ λλλ −+=F

)412.0exp(1 2ξ−−=Γ

)0,(1

tssMax −=λ

ξ

75.0Re9Re st=λ


FINE™ 7-43

intermittency of 1). In order to get a tri-dimensional distribution of the intermittency, the intermit-tency of a cell is the one of the closest cell on a solid surface (hub, shroud, and tip gap are fully tur-bulent and have an intermittency equal to unity).


7-44 FINE™

FINE™ 8-1

CHAPTER 8: Boundary Conditions

8-1 OverviewDuring the IGG™ grid generation process, the user has to define the type of boundary condition tobe imposed along all boundaries. The parameters associated with these boundary condition typescan be fully defined using the Boundary Conditions page.

This chapter gives a description of the boundary conditions available on the Boundary Conditionspage. In section 8-2 the Boundary Conditions page is described. For expert use section 8-3 gives anoverview of the available expert parameters. In section 8-4 some advice is provided on the combi-nations of boundary conditions to use. For more detailed information section 8-5 provides a theoret-ical description of each available boundary condition

8-2 Boundary Conditions in the FINE™ InterfaceWhen selecting the Boundary Conditions page the Parameters area appears as shown inFigure 8.2.0-1. Five thumbnails are available, depending on the boundary condition types defined

in the mesh. There are currently five types of boundary conditions available in the NUMECA flowsolver:

• inlet,

• outlet,

• periodic (connection with or without rotational or translational periodicity),

• solid walls,

• external (far-field).

Each of those is described in the next sections.

Note that the connecting (matching (CON) and non-matching (NMB)) boundary con-

ditions (without periodicity) do not appear in this menu, because they do not require anyinput from the user. Only the "periodic" conditions appear under the Periodic menu.

Boundary Conditions Boundary Conditions in the FINE™ Interface

8-2 FINE™

A common particularity of the five Boundary Conditions pages is their subdivision into two areas.The left area contains always a list of the different patches that are of the boundary condition typeof the selected thumbnail. A patch can be identified either by the name of the block face to which itbelongs and by its number, or by the numbers of the block and face and by its local index on theface (if no name is provided in IGG™). The right area is the area where the boundary conditionparameters are specified for the selected patch(es).

FIGURE 8.2.0-1 Boundary Conditions page

One or several patches may be selected in the left area by simply clicking on them. Clicking on apatch unselects the currently selected patch(es). It is possible to select several patches situated oneafter another in the list by clicking on the first one and holding the left mouse button while selectingthe next. To select a group of patches that are not situated one after another in the list, the usershould click on each of them while simultaneously holding the <Ctrl> key pressed.

Several patches can be grouped by selecting them and clicking on the Group button. A dialog boxwill appear asking for a group name. The name of the group will appear in red color in the list ofpatches to indicate that this is a group of patches. Every change in the parameters when a group isselected applies to all patches in the group. The Ungroup button removes the group and its patchesare displayed individually in the list.

The Ungroup button is active only when at least one group is selected.

Clicking with the left mouse button on the plus sign + left of a group name in the list will displaythe patches included in this group.

If some of the patches have been given names in IGG™, these names will appear in

Boundary Conditions in the FINE™ Interface Boundary Conditions

FINE™ 8-3

FINE™. If the patches have been grouped in IGG™, by giving the same name to manypatches, they will appear ungrouped in FINE™ (with block, face and patch numbershown after the name) to avoid contradiction between grouping in IGG™ and FINE™.Ungroup button will toggle the IGG™ name of the selected patch(es) with the defaultFINE™ name (block, face and patch number).

If the Graphics Area window with the mesh topology of the project is opened (Mesh/View On/Offmenu), all the selected patches and/or groups will be highlighted. A click with the right mouse but-ton over a selected patch will select all the patches and groups in the list that have the same param-eters.

If the user selects several patches that have different parameters, a warning dialog box will appear.When clicking on OK all parameters will be set equal to the ones of the first patch. Selecting Cancelinstead will cancel the selection.

FIGURE 8.2.0-2 Two patches have been grouped into a group called HUB.

The right area of all the notebook boundary condition pages is created in a generic way by means ofa resource file, where all the boundary condition parameters are described altogether with theirdefault values.

Some boundary conditions are only available for an incompressible, compressible or

condensable gas flow. FINE™ will automatically disable the boundary conditions thatare not available, depending on the type of fluid selected on the Fluid Model page. Alsothe type of boundary conditions are adjusted according to the selection for Cartesian orcylindrical boundary conditions.

The five pages associated to each of the five types of boundary conditions are described in detail inthe following sections.

(1)

(2)

(3)


8-4 FINE™

8-2.1 Inlet Condition

8-2.1.1 Available Inlet Boundary Condition Types

The inlet boundary condition page is customized according to the configuration of the project (Car-tesian or cylindrical) as shown in the following two figures. The user has the freedom to access bothtypes of configurations in the boundary conditions page independently of the mesh properties.

FIGURE 8.2.1-3 Subsonic inlet boundary conditions page for cylindrical problems.

FIGURE 8.2.1-4 Subsonic inlet boundary conditions page for Cartesian problems.


FINE™ 8-5

The upper part of the inlet boundary condition page allows the user to select the type of inlet condi-tion to apply to the selected patches through a series of toggle buttons. There are two categories ofinlet conditions: conditions applicable to subsonic inlets and conditions applicable to supersonicinlets.

Note that to determine whether an inlet (or an outlet) boundary is subsonic or super-

sonic, the velocity component normal to the boundary should be considered.

For each inlet condition type, the lower part of the page is adapted in order to provide input boxesonly for the physical variables that are required to fully determine the boundary condition. Thesevariables are for instance: the pressure and temperature (static or total), the velocity components,the velocity magnitude, the velocity angles (specified in radians), or the mass flow. In case of a sim-ulation involving the k-ε turbulence model, the inlet values of the parameters k and ε are alsorequired. A turbulent viscosity entry appears in case the Spalart-Allmaras turbulence model is used.

For the inlet boundary conditions:

• The velocity components are defined in the Cartesian or cylindrical coordinate system,depending on the selected type.

• The pressure and the temperature values to specify can be the static or the total values.

• For rotating configurations, the specified values are always the absolute quantities.

Three major types of inlet boundary conditions can be identified:

• velocity components and the static temperature,

• total pressure, total temperature and the flow angles,

• total enthalpy, dryness fraction and the flow angles (only for condensable fluid),

•mass flow and the static temperature (see the next paragraph for detail on coupling with theoutlet).

See section 8-5.1 for more theoretical detail on those boundary conditions.

8-2.1.2 Coupling Temperature with Outlet

FIGURE 8.2.1-5 Meridional view of the "Coupling with Outlet ID" functionality

When mass flow is imposed at an inlet patch, the temperature may be chosen to be coupled to anoutlet patch. The coupling is performed through the static temperature. Only in that case, the aver-age temperature Taverage is computed at the specified outlet and imposed at the inlet as Tinlet = Taver-

age + ∆T (see Figure 8.2.1-5). The quantity ∆T is a constant temperature difference (>=0 or <0)

Taverage + ∆T

TaverageOutlet

Inlet


8-6 FINE™

specified by the user. This is done in FINE™ by choosing Mass Flow Imposed as boundary condi-tion type for the inlet and clicking on the Coupling Temperature With Outlet button. A pull-downmenu allows to select which patch of the outlet must be involved in the coupling. The value to beentered in the static temperature box is ∆T.

8-2.1.3 Imposing Variables as an Interpolation Profile

Each variable can be defined as constant or as an interpolation profile of the variable. The imposedboundary condition may be variable in space (one or two dimensions) and/or in time (in case of anunsteady calculation).

To visualize and/or edit the profile data press the small button ( ) on the right side of the label"profile data". This button opens the Profile Manager with the existing profile. See section 2-12 fora detailed description of the Profile Manager. It offers the possibility to modify or to create a dataprofile interactively. Click on the OK button to set the new profile to the selected patch(es).

FIGURE 8.2.1-6 The Profile Manager

The button Surface data toggles 1D and 2D editing modes. It can be used to change the dimensionof an existing profile. 2D profiles are displayed as a "cloud of points". Selecting a point will displaythe f(x,y) value in blue in the corresponding column of the Profile Manager.

If a quantity is defined as a function without the definition of a valid profile a warning

message will appear when saving the project or opening a new page or thumbnail. Insuch a case a default constant value is used in the computation.

8-2.2 Outlet Condition

For a supersonic outlet all variables are extrapolated. An outlet is considered as supersonic on thebasis of the normal velocity direction to the boundary.


FINE™ 8-7

Three types of subsonic outlet boundary condition are available, as shown in Figure 8.2.2-7. Thesethree different boundary conditions are described in the following paragraphs.

An option for treatment of Backflow Control can be activated in the case of radial dif-

fusers outlet. The purpose of this option is to control the total temperature distributionalong the exit section. In case the flow partially re-enters the domain through the bound-ary, the total temperature of the entering flow is controlled so that the entering and outgo-ing flows globally have the same total temperature.

.

FIGURE 8.2.2-7 Outlet boundary conditions page.

8-2.2.1 Pressure Imposed

There are three different methods to impose the pressure at the outlet:

• Static Pressure Imposed: the static pressure is imposed on the boundary, the static temperatureand the absolute velocity components are extrapolated. As described for the inlet conditions,the static pressure can be constant or defined as a data profile.

• Averaged Static Pressure: if imposing an uniform static pressure at the outlet is not an appro-priate approximation of the physical pressure distribution at the outlet this boundary conditionmay be used. In this case only an averaged value for the static pressure is imposed while thepressure profile (around this average) is extrapolated from the interior field (see section 8-5.2.1).

• Radial Equilibrium: This boundary condition is applicable only to cylindrical problems. It isadapted for a patch in which the mesh lines in the circumferential direction have a constantradius. The outlet static pressure is then imposed on the given radius and the integration of theradial equilibrium law along the spanwise direction permits to calculate the hub-to-shroud pro-file of the static pressure. A constant static pressure is imposed along the circumferential direc-tion. See section 8-5.2.1 for further details.


8-8 FINE™

The pressure imposed at the outlet can be constant or as a function of space and/or time. To define a

profile as a function of space and/or time click on the profile button ( ) right next to the input textbox. The Profile Manager will appear as described in section 8-2.1.3.

8-2.2.2 Mass Flow Imposed

When imposing the mass flow at the outlet the related patches must be grouped. This permits tohave several groups of patches, each of the groups constituting an outlet through which the massflow can be controlled.

Two different techniques are available to impose the mass flow:

• Velocity Scaling: the pressure is extrapolated and the velocity vector is scaled to respect themass flow. This technique is only valid for subsonic flows, and is not recommended in case ofsignificant back flows along the exit boundary.

• Pressure Adaptation: this boundary condition is identical to the ’Uniform outlet pressure’ or’Radial equilibrium’ boundary conditions, except from the fact that the exit pressure is auto-matically modified during the resolution process so that after convergence, the prescribedmass flow is obtained.

The pressure asked in addition to the imposed mass flow with both options is only used to create theinitial solution and for the full-multigrid process, during which a uniform static pressure outlet con-dition is used.

8-2.2.3 Characteristic Imposed

This boundary condition has been implemented to increase the robustness in the frame of a designprocess and is only available when using a perfect and real gas in the Fluid Model page.

Figure 8.2.2-8 shows as an illustration performance curves for a centrifugal compressor. Near chok-ing conditions the mass flow stays almost constant with a variation of the pressure. Therefore it isrecommended in this region to impose the static pressure at the outlet. Near stall however, the pres-sure varies only slightly with varying mass flow. Therefore it is recommended in this region of theperformance curve to impose the mass flow at the outlet instead of the static pressure.

FIGURE 8.2.2-8 Example of performance curves for centrifugal compressor

(static pressure)

(mass flow)


FINE™ 8-9

In a design process, with a variation of the geometry, it is not always known in advance where in theperformance curve the computations are performed. Therefore it is not always possible to choosethe appropriate boundary condition at the outlet for the complete design process.

To overcome this problem this boundary condition allows to impose a relation between the massflow and the pressure at the outlet. It is no longer needed to choose between imposing pressurewhen working around the chocking part and imposing mass flow when working close to the stalllimit.

The user has to impose a very simple characteristic line defined through 3 parameters: a target out-let mass flow and a target outlet pressure (at point 2 in Figure 8.2.2-8) and the pressure at zero massflow (point 1 in Figure 8.2.2-8). For more detail on this boundary condition see section 8-5.2.

8-2.3 Periodic Condition

One important feature of the IGG™ mesh generator concerns the automatic establishment of allconnecting and periodic boundary conditions. The corresponding information is transmitted to theFINE™ interface, with the advantage that the user does not need to specify any input concerningthese boundary conditions.

In the present version, periodic connection is not allowed for blocks with different

rotation speed on each side of an interface. Thus no frozen rotor calculation should beperformed with periodic connections.

Normally no user input is required on this page. The only periodic boundary condition cases forwhich a user input is required are those in which some of the boundary conditions have to beapplied with a periodicity angle that differs from the global periodicity angle of the block.

FIGURE 8.2.3-9 Periodic boundary condition page.

In case some input is required this section explains how to define the periodic conditions using thePERIODIC thumbnail.

The type of periodicity connection between the patches (Matching or Non Matching) can beentered. A connection is Matching if the numbers of mesh points along the connected patches are


8-10 FINE™

identical, and if all the corresponding points along these patches coincide. The Non Matching con-nection requires the use of an interpolation process to establish the connection, whereas a matchingone consists of a single communication of the flow variables.

Some additional characteristics need to be given to fully determine the periodic boundary condi-tion:

• For rectangular (Cartesian) problems, the user has to specify the translation vector defining theperiodicity. The positive translation vector goes from the current patch to the periodicitypatches.

• For cylindrical problems, the user has to specify the rotation angle in degrees. The rotationangle is calculated from the connected patch to the current patch, according to the rule of theright handed system.

8-2.4 Solid Wall Boundary Condition

The solid wall boundary condition page is customized essentially according to the type of calcula-tion (inviscid or viscous).

For Euler cases (i.e. inviscid), no parameter is requested for the wall boundary conditions. ForNavier-Stokes cases, the box at the top of the page allows to set both velocity and thermal condi-tions. The type of boundary conditions determines the way the velocity and thermal conditions aredefined for the solid boundary.

8-2.4.1 Cylindrical Boundary Condition

a) Area Defined Rotation Speed

The wall rotation velocity can be constant or area defined (see Figure 8.2.4-10). The area definedoption allows to attribute a specific rotation velocity to a rectangular zone in the meridional planeindependently of the grid structure.

FIGURE 8.2.4-10 Solid boundary conditions page in case of a cylindrical boundary condition


FINE™ 8-11

When the area defined option is selected, a small picture defining the parameters is displayed (the zaxis is the rotation axis, the r axis is the radial axis). The rotation velocity is set to outside the

domain and to inside the domain.

The specified range must be a valid range for the used geometry. For example, for an

axial machine the limits for rotation of the hub can be defined by setting the lower andhigher axial limit to appropriate values. In such a case it is important to set the radial lim-its such that they include the full solid (hub) patch.

b) Thermal Condition

Three options are available for the thermal condition: constant heat flux (in W/m2), adiabatic or iso-thermal. The imposed heat flux or temperature can be constant on the patch or defined as a profile.Use the pull down menu to change Constant Value to for example Fct(space). Click on the profilebutton to launch the Profile Manager as described insection 8-2.1.3.

8-2.4.2 Cartesian Boundary Conditions

The user can define a translation or a rotation velocity vector. In the latter case, the coordinates ofthe rotation centre are requested. The thermal conditions are similar to those for cylindrical flows.

8-2.4.3 Force and Torque

Below the box, a "Compute force and torque" button is provided that permits to include the selectedpatches in the calculation of the global solid boundary characteristics.

For a cylindrical project (as defined in Mesh/Properties) in an internal flow (the expert parameterIINT set to 1 as by default):

— the axial thrust, i.e. the projection of the global force on the rotation axis,

— the torque, i.e. the couple exerted by the global force, calculated at (0,0,0).

These quantities are often calculated on the rotating walls. They are calculated from the pressureand the velocity fields on the walls. The axial thrust is computed as:

. (8-1)

The projection of the torque along a given direction , i.e. the couple exerted by the global forcealong the rotation axis:

(8-2)

In all other cases the force and torque are computed as:

— the lift,

— the drag,

— the moment calculated at (0,0,0) by default.

The direction of the forces and torque as well as the location of the point for the moment can bedetermined with the expert parameters IDCLP, IDCDP, IDCMP and IXMP (see section 8-3).

Within EURANUS v5.1-6 it is possible to calculate and to store the partial torque in the corre-sponding ".wall" file of the computation through the use of the expert parameter IFRCTO withinFINE™ GUI.

ω1

ω2

F nz⋅S∑

z

r F×S∑

⎝ ⎠⎜ ⎟⎛ ⎞

z⋅


8-12 FINE™

The partial torque is the torque computed for each layer on the whole blade. When IFRCTO is set to2 (1 or 3), the torque is defined on each J-direction (I-direction or K-direction) layer (i.e. whenusing AutoGrid meshes, J-direction corresponds to the spanwise direction).

FIGURE 8.2.4-11 File ".wall" when computing partial torque along the blade

Finally, the resulting ".wall" will contain, in addition of the global torque and force on the selectedblade, the partial torque for each layer along the J-direction of the blade as presented inFigure 8.2.4-11.

8-2.4.4 Properties of Solid for Turbulence

In addition, if the standard k-ε model or the non-linear high-Reynolds k-ε model is used, the userhas to specify the type of wall ("Smooth" or "Rough") and the following constants: the von Karmanconstant κ and the B constant. If the wall type is rough, the equivalent roughness height k0 and theheight of the zero displacement plane d0 are also required. A description of these constants is pro-vided in section 4-3.6.3. The application field of the ’law of the wall’ imposes restrictions on thegrid. The user is strongly advised to check the conformity of this grid with these conditions (section4-3).

IFRCTO = 0

IFRCTO = 2

Total Torque and Force on Suction Side

Partial Torque and Force on Suction Side

• 56 = 56 sublayers in J-direction (spanwise)• column 1: %span corresponding to the layer• column 2: Fx on the sublayer• column 3: Fy on the sublayer• column 4: Fz on the sublayer

Total Torque and Force on Suction Side

Expert Parameters for Boundary Conditions Boundary Conditions

FINE™ 8-13

8-2.5 External Condition (Far-field)

The external boundary condition is provided to treat the far-field boundaries when dealing withexternal flow computations (the expert parameter IINT=0). An example is given in Figure 8.2.5-12.This type of boundary condition determines whether the flow is locally entering or leaving the flowdomain and uses the theory of the Riemann invariants to act consequently on the appropriate varia-bles (see section 8-5.4). Depending on the chosen turbulence model, five or seven input boxes areprovided to specify the free-stream values of the variables to be used in the boundary condition for-mulation.

FIGURE 8.2.5-12 External (far-field) boundary conditions page.

Use an external condition rather than an inlet condition for cases for which it is not

known if the flow enters or leaves the domain.

Condensable gas is not compatible with external boundary condition.

8-3 Expert Parameters for Boundary Conditions

8-3.1 Imposing Velocity Angles of Relative Flow

In case of a stator calculation it may be convenient to impose the velocity angles of the relative flowat the exit of the upstream rotor. In case of rotors the user may also prefer to impose relative bound-ary conditions. This procedure is only available in case total conditions and flow angles are

Boundary Conditions Expert Parameters for Boundary Conditions

8-14 FINE™

imposed. In addition to that the extrapolation of Vz must be selected. Note also that both flowangles and total conditions are then treated in the relative mode.

The following parameters have to be defined:

INLREL: allows to specify relative angles for the cylindrical inlet boundary conditions with

total quantities imposed (default value = 0)

= 1: inlet for a stator (extrapolation of the axial velocity only). The expert parameterOMGINL has also to be specified,

= 2: inlet for a rotor.

ANGREL (for stator only): data use with the expert parameter INLREL (default = 1 0.05 0.05):

1st real: relaxation angle (in degrees),

2nd real: distance (%) from hub where the absolute flow angle is extrapolated,

3rd real: distance (%) from shroud where the absolute flow angle is extrapolated.

8-3.2 Extrapolation of Mass Flow at Inlet

IMASFL: expert parameter specially dedicated to radial inlets. The mass flow is extrapolated

instead of the velocity for the cylindrical inlet boundary conditions with imposed

total quantities:

= 0 (default): treatment inactive, the velocity is extrapolated,

= 1: option activated, extrapolation of the mass-flow.

8-3.3 Outlet Mass Flow Boundary Condition

RELAXP: is the under-relaxation for the outlet boundary condition where the mass flow is

imposed with the exit pressure adaptation (default value = 1.).

VELSCA: is the maximum value allowed for the velocity scaling (outlet boundary condition

with mass flow imposed by scaling velocity) (default value = 2.)

8-3.4 Torque and Force Calculation

IDCDP: if cylindrical project (as defined in Mesh/Properties) and IINT=1: direction (x,y,z)of axial thrust,

in all other cases: direction (x,y,z) of drag.

IDCLP: direction (x,y,z) for lift (not used if cylindrical project and IINT=1),

IDCMP: direction (x,y,z) for moment,

IFRCTO: calculate and to store the partial torque in the corresponding ".wall" file. More

details in section 8-2.4.3, on page 11,

IXMP: coordinate (x,y,z) of the point around which the moment has to be calculated.

Best Practice for Imposing Boundary Conditions Boundary Conditions

FINE™ 8-15

8-3.5 Euler or Navier-Stokes Wall for Viscous Flow

If the flow type selected is laminar or turbulent Navier-Stokes, it is possible in Expert Mode tochoose between an Euler wall (zero normal velocity) and a Navier-Stokes wall (no-slip condition).Further details on the numerical treatment of the walls are provided in section 8-5.3. Note that thedefault (’normal mode’) is a Navier-Stokes wall.

8-3.6 Pressure Condition at Solid Wall

When the interface is in Expert Mode, two toggle buttons are provided to select the type of pressurecondition at the wall: extrapolated or computed from the normal momentum equation. The default(active in Standard Mode) is the extrapolation of the pressure.

8-4 Best Practice for Imposing Boundary ConditionsThe quality of the flow simulation rests primarily on the quality of the grid and the imposed bound-ary conditions. In this section the most adapted boundary conditions are proposed according to thetype of studied flow.

In case of divergence in calculations it is strongly recommended to check by post

processing of the solution (in CFView™) that appropriate boundary conditions havebeen imposed.

8-4.1 Compressible Flows

For compressible flows it is recommended that the inlet boundary condition fixes the absolute totalquantities (pressure, temperature) and the flow angles and that the outlet boundary condition fixesthe static pressure (exit pressure). This exit pressure can be imposed as:

• a constant value along the exit,

• an average value at the exit,

• the pressure at mid-span for radial equilibrium (only for an axial outlet).

The static pressure at the exit of the domain is rarely constant. It is thus advised to impose the pres-sure as an average value or as a initialization data for radial equilibrium.

Even if this value of pressure is known, for numerical reasons it is possible that the computed mass-flow differs from the expected one. It is thus necessary to modify the exit pressure repeatedly untilobtaining the accurate mass-flow. This procedure can be numerically expensive especially if thecalculations are carried out on fine grid.

A solution to overcome this drawback is to impose the mass-flow at the outlet. This can be made bythe way of two options:

• Velocity Scaling: for low subsonic outlet (Mach number lower than 0.4) this condition fixes themass-flow at a given control surface by scaling the vectors on this surface. This is not as robustas to impose the exit pressure and is not recommended in case significant backflow aredetected along the exit. In this condition the next option is better suited.

Boundary Conditions Theory on Boundary Conditions

8-16 FINE™

• Pressure Adaptation: in this case, an automatic procedure introduces a variation of theimposed exit pressure at each iteration of the calculation. The pressure is then iterativelyupdated in order to reach at convergence the imposed mass-flow. This is not as robust as toimpose the exit pressure but is more robust than the velocity scaling option.

8-4.2 Incompressible or Low Speed Flow

For compressible or low speed flows it is recommended to impose the mass-flow and the static tem-perature at the inlet and a static pressure at the exit. This couple of conditions inlet-outlet has a sta-bilizing effect on calculations and is also well adapted to provide initial solutions for multi-stagecalculations.

8-4.3 Special Parameters (for Turbomachinery)

In case of flow separation at the outlet of radial diffusers it is recommended to use the backflowtreatment option. This option can be activated by pressing the corresponding button (Backflow Con-trol) in the FINE™ interface on the Boundary Conditions page under the OUTLET thumbnail.

When end-walls in the inlet regions are strongly varying in radius (e.g. centripetal turbines as inFigure 8.4.3-13) or in case of highly tangential inlet flow angles it is advised to use the IMASFLexpert parameter (in the list of expert parameters on the Computation Steering/Control Variablespage in Expert Mode). This option is adapted when the inlet boundary conditions fixes the absolutetotal quantities (pressure, temperature) and is only valid for non-preconditioned computations.When it is activated, the mass-flow is extrapolated instead of the velocity.

FIGURE 8.4.3-13 Example of case with strongly varying radius in the inlet1

8-5 Theory on Boundary ConditionsThe boundary conditions are identified in EURANUS by a number (ITYPE) indicating the type ofboundary condition and an index (OPSEL) indicating the variant of the type of boundary condition.In this section the type number and variant index of each described boundary condition is given.

1. Picture from D. Japikse, N.C. Balines, Introduction to Turbomachinery, Concept ETI Inc. and Oxford Uni-versity Press, 1994.

Radial turbine

Theory on Boundary Conditions Boundary Conditions

FINE™ 8-17

8-5.1 Inlet Boundary Conditions

8-5.1.1 Cylindrical Inlet Boundary Conditions

This boundary condition is activated for the values of the parameter ITYPE = 124 (subsonic) andITYPE=23 (supersonic).

a) Static Quantities Imposed (Subsonic)

The complete absolute velocity vector followed by the static temperature on the boundary are spec-ified. Several possibilities exist:

• the magnitude of the velocity and the flow angles α and γ are specified (OPSEL = 1):

(8-3)

• the magnitude of the velocity and other flow angles δ and ε are specified (OPSEL = 5):

(8-4)

with the meridional velocity ( ). This option has been designed to allow

radial inlet with zero axial velocities,

• the cylindrical velocity components are specified (OPSEL = 7).

The static pressure is extrapolated from the interior by Eq. 8-13, which allows to calculate all theprimitive variables on the boundary.

For a turbulent calculation with the Spalart-Allmaras model, the turbulent viscosity has also to bespecified on the inlet boundary. When the two-equation turbulent model is selected, the boundaryvalues of k and ε have to be specified.

These conditions can also be used for incompressible flows.

b) Total Quantities Imposed (Subsonic)

Several variants are available based on the specification of flow angles or velocity components.

b.1) Absolute flow angles from axial direction:

The user specifies two flow angles (of the absolute flow) at the boundary, α and γ, which aredefined by Eq. 8-3 and given in radians.

The absolute total pressure and the absolute total temperature on the inlet boundary are also speci-fied and imposed.

For turbulent models with additional equations, the corresponding quantities are also specified andimposed.

Three variants are available depending on the value that is extrapolated.

αVθ

Vz

------atan=

γVr

Vz

-----atan=

δVr

Vm

------acos=

εVt

Vm

------atan=

Vm Vm Vr2 Vz

2+=


8-18 FINE™

• the module of the absolute velocity vector is obtained by extrapolation from the interior field,cf. Eq. 8-15. (OPSEL=2)

• the axial velocity component is extrapolated (OPSEL = 3):

(8-5)

Note that it is assumed that the angular velocity vector is in the z-direction,

, (8-6)

which makes this direction the axial one. Also note that, as a result of Eq. 8-6 the absolute andrelative axial velocity component are equal.

• the mass flow is extrapolated, assuming that the meridional component of the velocity is theone contributing to the mass flow.

, (8-7)

with . (8-8)

This boundary condition is specially dedicated to radial turbomachinery for which problem ofmass flow conservation can arise. It is not interfaced but it can be used by selecting the previousboundary condition (absolute flow angles with extrapolation of velocity) and setting the expertparameter IMASFL to 1.

the inlet patches have to be grouped in one group to use this last boundary condition

(extrapolation of mass flow).

b.2) Relative flow angles from axial direction

For a stator calculation it may be convenient to impose the velocity angles of the relative flow at theexit of the upstream rotor. In case of rotors the user may also prefer to impose relative boundaryconditions. This procedure is only available in case total conditions and flow angles are imposed. Inaddition to that the extrapolation of Vz must be selected. Note also that both flow angles and totalconditions are then treated in the relative mode. This boundary condition is not directly available inthe Boundary Conditions page of the interface. It can be used by selecting the previous boundarycondition (absolute flow angles with extrapolation of the axial velocity component) and using theexpert parameter INLREL. In this case, relative flow angles, relative total pressure and relative totaltemperature are specified in the interface instead of the absolute values. Set INLREL to 1 in thecase of stators. In the case of rotors (INLREL=2) the approach is exactly the same as the one usedwhen absolute conditions are imposed.

The adopted approach consists of imposing boundary conditions, which are still defined in theabsolute frame of reference, but which vary from one iteration to the other in order to respect theimposed relative value. This technique provides a robust algorithm with an under-relaxation of theevolution of absolute conditions and a special treatment of the hub and shroud boundary layers.Indeed as the hub and shroud walls are usually not rotating, the relative flow angle tends to 90degrees in the boundary layer, which complicates the boundary condition treatment if the relativeconditions are imposed. The above approach (switch to the absolute frame of reference) allowscomputing the absolute flow angles distribution through an extrapolation in the boundary layers.The under-relaxation factor as well as the percentage of the distance from the hub and the shroudwhere the angle is extrapolated are specified in the expert parameter ANGREL.

The relation between the relative (β) and absolute (α) angles is the following:

Vz( )0 Vz( )1=

ω ω 1z⋅=

Qm( )0 Qm( )1=

Qm ρVmS=


FINE™ 8-19

(8-9)

where is the speed of rotation of the upstream rotor specified in the expert parameter OMGINLand r the radial position.

The update of the flow angle is followed by the update of the absolute total conditions according to:

. (8-10)

The initial values of the absolute flow angle and total conditions are set to the value of

the relative ones except with the initial solution for turbomachinery. In the initial solutionfor turbomachinery, Eq. 8-9 and Eq. 8-10 are used to compute the initial absolute flowangle and total conditions from the specified relative values.

b.3) Velocity direction

The user first specifies a direction (given under the form of a vector) that corresponds to the direc-tion of the absolute velocity vector. Note that this vector does not have to be a unitary vector. Ther,θ,z components of the direction vector are given. E.g. if the user enters the direction (0,1,1) theuser imposes that the θ- and z-components of the absolute velocity vector at inlet are equal and thatthe radial velocity is zero.

The absolute total pressure and the absolute total temperature on the inlet boundary are also speci-fied. These values will be imposed.

The module of the absolute velocity vector is extrapolated from the interior field. Using subscript 0for the boundary, and subscript 1 for the first internal cell:

(8-11)

where V represents the absolute velocity. (OPSEL = 4).

The velocity vector on the boundary is found by scaling the velocity vector specified in the bound-ary condition file such that the correct module is obtained.

For a turbulent calculation with the Spalart-Allmaras model, the turbulent viscosity has also to bespecified on the inlet boundary. When the two-equations turbulent model is chosen, the boundaryvalues of k and ε have to be specified.

c) Mass Flow Imposed (Subsonic)

This boundary condition permits to impose the value of the mass flow through a specified controlsurface. The control surface is defined by grouping several patches into the same group. In additionto the mass flow the direction of the velocity vector and the static temperature are imposed(ITYPE=28).

Two variants are available:

• the swirl can be imposed, as well as the direction of the velocity vector in the meridional plane(Vr/Vm,Vθ,Vz/Vm) (OPSEL 1).

• the direction of the absolute velocity vector can be imposed (Vr /|V|, Vθ/|V|, Vz/|V|) (OPSEL

2).

αtan βtanωrVz

------+=

ω

T0a

T0r ωr( )2

2cp

-------------–ωrVθ

cp

-------------+=

p0a p0

r T0a

T0r

-----⎝ ⎠⎜ ⎟⎛ ⎞

γ γ 1–( )⁄

=

V0 V1=


8-20 FINE™

Two possibilities exist for the treatment of the static temperature:

• it can be imposed at a given fixed value,

• a relation can be imposed between the inlet static temperature and the averaged temperaturealong a specified outlet. In this case the user specifies the patch name (or group name) of theconnected outlet and the difference of temperature between the inlet and outlet temperatures.The difference of temperature is specified instead of the static temperature. If the specifiedvalue is zero, the temperature at the inlet will be equal to the average outlet temperature,whereas if the specified values is for instance 20, the temperature will be equal to the outlettemperature + 20.

For turbulent models with additional equations, the corresponding quantities are also specified andimposed on the inlet boundary.

d) Imposing the Complete Flow Conditions (Compressible, Supersonic)

d.1) Total quantities

Instead of specifying static pressure, static temperature and the three absolute velocity components,one can also specify absolute total pressure, absolute total temperature, absolute Mach number andtwo flow angles α, β defined as (ITYPE = 23, OPSEL = 1):

, (8-12)

with the angles given in radians.

For a turbulent calculation with two-equation model the boundary values of k and ε also have to bespecified. With the Spalart-Allmaras model, the turbulent viscosity has to be specified along theboundary.

d.2) Static quantities

The flow at inlet is completely specified, by giving the static pressure, static temperature and thethree absolute cylindrical velocity components (ITYPE = 23, OPSEL = 2).


e) Total Enthalpy & Dryness Fraction Imposed (Subsonic - Condensable Gas)

In cases where the inlet thermodynamic state is located on the saturation curve or inside the bipha-sic zone, traditional boundary conditions based on total temperature and total pressure are not suffi-cient, as pressure and temperature become interdependent. An additional information is required,which is the dryness fraction.

The boundary condition proposed under FINE™ GUI is based on the absolute total enthalpy andthe dryness fraction. The velocity direction is also specified, either by means of two flow angles(from axial direction) or of velocity direction vectors.

It should be mentioned that the use of this boundary condition requires the presence of

the saturation table (’PSA.atab’) of the fluid in the corresponding subfolder.

The boundary condition is based on the dryness fraction (X), whose value is bounded

between 0 and 1. The inlet thermodynamic must be either saturated or be located inside

αVθ

Vr

------atan=

βVz

V------acos=


FINE™ 8-21

the biphasic zone.

The validity of the condensable fluid model is limited to gases with small fraction of

liquid (X > 0.9) or reversely to liquids with small fraction of gas (X < 0.1).

The implementation of the boundary condition is based on extrapolation of the static pressure,which permits to evaluate the saturated liquid and gas values of the density and enthalpy. The dry-ness fraction permits to deduce the values of the local static enthalpy and density. The other bound-ary conditions are then used to calculate the velocity vector.

8-5.1.2 Cartesian Inlet Boundary Conditions

This boundary condition is activated for the values of the parameter ITYPE = 24 (subsonic) orITYPE=23 (supersonic).

a) Static Quantities Imposed with Extrapolation of the Static Pressure (Subsonic)

The complete absolute velocity vector followed by the static temperature on the boundary are spec-ified (OPSEL = 1). For turbulent models with additional equations, the corresponding quantities arespecified also.

The static pressure is extrapolated from the interior. Using subscript 0 for the boundary, and sub-script 1 for the first internal cell one has:

, (8-13)

which allows to calculate all the primitive variables on the boundary.

These conditions can also be used for incompressible flows.

b) Total Quantities Imposed (Subsonic)

The user first specifies a direction (given under the form of a vector) that corresponds to the direc-tion of the absolute velocity vector. Note that this vector does not have to be a unitary vector. Thex,y,z components of the direction vector are given. E.g., entering the direction (0,1,1) imposes thatthe y- and z-component of the absolute velocity vector at inlet should be equal. In other words, theflow comes in at an angle of 45 degrees between z- and y-direction, whereas the angle between z-and x-direction is 0 degrees.

The absolute total pressure and the absolute total temperature on the inlet boundary are also speci-fied. These values will be imposed.Two variants are available depending on the value that is extrap-olated:

• the absolute Mach number is extrapolated from the interior field (OPSEL = 2, only availablefor compressible fluid):

, (8-14)

• the module of the absolute velocity vector is extrapolated from the interior field.

(8-15)

where V represents the absolute velocity. (OPSEL = 3).

For both variants, the velocity vector on the boundary is found by scaling the velocity vector speci-fied in the boundary condition file such that the correct module is obtained.

p0 p1=

M0 M1=

V0 V1=


8-22 FINE™

For a turbulent calculation with the Spalart-Allmaras model, the turbulent viscosity has also to bespecified on the inlet boundary. For a turbulent calculation with a two-equation model, the bound-ary values of k and ε have to be specified.

c) Mass flow, Direction of Absolute Velocity Vector and Static Temperature Imposed (Subsonic)

This boundary condition permits to impose the value of the mass flow through a specified controlsurface. The control surface is defined by grouping several patches into the same group. In additionto the mass flow, the direction of the velocity vector and the static temperature are imposed(ITYPE=28).

• the direction of the absolute velocity vector is imposed in the Cartesian coordinate system (Vx/|V|,Vy/|V|,Vz/|V|) (OPSEL 3).

Two possibilities exist for the treatment of the static temperature:

• it can be imposed at a given fixed value,

• a relation can be imposed between the inlet static temperature and the averaged temperaturealong a specified outlet. In this case the user specifies the patch name (or group name) of theconnected outlet and the difference of temperature between the inlet and outlet temperatures.The difference of temperature is specified instead of the static temperature. If the specifiedvalue is zero, the temperature at the inlet will be equal to the average outlet temperature,whereas if the specified values is for instance 20, the temperature will be equal to the outlettemperature + 20.


d) Imposing the Complete Flow Conditions (Supersonic)

The flow at inlet is completely specified, by giving the static pressure, static temperature and thethree absolute Cartesian velocity components (ITYPE = 23, OPSEL = 0). This boundary conditionis only available for a compressible fluid.

For a turbulent calculation with the Spalart-Allmaras model, the turbulent viscosity has also to bespecified on the inlet boundary. When the two-equation turbulent model is selected, the boundaryvalues of k and ε have to be specified.

8-5.2 Outlet Boundary Conditions

8-5.2.1 Outlet Boundary Conditions for Subsonic Flow

a) Static Pressure Imposed

ITYPE = 25; OPSEL = 10.

The static pressure at the outlet boundary is specified. The remaining dependent variables on theoutlet boundary are obtained from the interior field through extrapolation.

The default extrapolation is a zero order extrapolation of the static temperature and the absolutevelocity.

Several options are available:

• order of extrapolation: zero or first order (in expert user mode),

• backflow treatment (see section 8-5.2.3): active or not.


FINE™ 8-23

The purpose of the treatment of backflow is to control the total temperature distribution along theexit boundary. In case the flow partially re-enters the domain through the exit boundary, the totaltemperature of the entering flow is controlled so that the entering and outgoing flow globally havethe same total temperature.

b) Averaged Static Pressure Imposed

ITYPE = 27; OPSEL = 40

In some cases, an uniform pressure can not be imposed on the whole outlet area. This boundarycondition allows imposing an averaged static pressure. The remaining dependent variables on theoutlet boundary are obtained from the interior field through extrapolation.

The pressure profile is obtained by extrapolation from the interior field and it is translated to ensurethat the computed averaged pressure on the outlet area is the target averaged pressure specified bythe user. This translated profile is then the imposed pressure profile.

The options described in the previous paragraph (section a) are still available.

The outlet patches have to be grouped in one group to use this boundary condition.

c) Static Pressure Imposed with Radial Equilibrium

ITYPE = 125

This boundary condition is only valid on surfaces with mesh lines at constant radius.

The static pressure in the outlet section is assumed to be uniform in the tangential direction and tovary in radial direction according to:

. (8-16)

The user specifies the static pressure at a specific radius, followed by that radius and the radialdirection. The radial direction is specified by using the block orientation (I-direction, J-direction orK-direction).

The pressure distribution in the outlet section is then found by integrating Eq. 8-16 with pitchwiseaveraged values of Vθ and r.

The other variables are extrapolated following the system of options exposed above. See “StaticPressure Imposed” on page 22. The treatment of backflow is not implemented for this boundarycondition.

d) Mass Flow Imposed

ITYPE = 27

The outlet patches have to be grouped in one group to use this boundary condition.

d.1) Velocity Scaling

OPSEL = 20

This condition can be used for low speed subsonic outlet (Mach Number < 0.3). It fixes the massflow at a given control surface by scaling the velocity vectors on this surface. The other variablesare extrapolated following the system of options exposed above.

r∂∂p ρ v2

θ

r-------⋅=


8-24 FINE™

The scaling of the velocity vector is not totally free. The value of the scaling factor is constrainedbetween VELSCA and 1/VELSCA, where VELSCA is an expert parameter available in the Controlvariables page in the expert mode.

Given that the pressure is also extrapolated with this condition, it is imperative that the inlet bound-ary condition fixes the pressure through the total pressure.

Fixing the mass flow is not as robust as to impose the pressure and this is particularly sensitive withfull-multigrid. A pressure is thus requested as input and is imposed during the full-multigrid proc-ess. Consequently, the mass flow computed at outlet is not exactly the target mass flow during thecomputation on the coarse grids.

This option is not recommended in case significant backflow is detected along the exit. The nextoption (exit pressure adaptation) is then better recommended.

d.2) Pressure Adaptation

OPSEL = 30

This boundary conditions is an adaptation of the "uniform static pressure imposed" and "static pres-sure imposed with radial equilibrium" boundary conditions.

The only difference is that an automatic procedure is included that introduces a variation of theimposed exit pressure at each iteration of the calculation. The pressure is iteratively updatet in orderto reach at convergence the imposed mass flow. The successive pressure modifications are calcu-lated according to:

, (8-17)

where Lref and Tref are the characteristic length and reference temperature specified in the Flow

Model page. rgas (RGAS) and RELAXP are expert parameters defined in the Control Variables

page. The expert parameter RELAXP introduces an under-relaxation of the successive modifica-tions of the exit pressure. The default value is 1.

The value of the exit pressure provided by the user is the initial one. In case the radial equilibrium isused, the initial value of the exit pressure is imposed at midspan.

Contrary to the previous option fixing the mass flow through velocity scaling, it is only after con-vergence of the procedure that the mass flow reaches the imposed value.

e) Characteristic Imposed

ITYPE = 29

This boundary condition has been implemented to increase the robustness in the frame of a designprocess. Indeed it is not always suitable to impose the pressure at the exit because it can drive themachine to stall when the geometry change affects its characteristic line.

The proposed solution is to impose a relation between the mass flow and the pressure at the outlet.It is no longer needed to choose between imposing pressure when working around the chocking partand imposing mass flow when working close to the stall limit.

The user has to impose a line defined through 3 parameters: a target outlet mass flow ( ), a target

outlet pressure ( ) and the pressure at zero mass flow ( ). See section 8-2.2 for a schematic

representation of this boundary condition.

The implementation follows three principles:

pnew pold RELAXPrgas

·Tref

L2

ref

---------------------- Qactual Qimposed–( )+=

Qt

pQt pQ0


FINE™ 8-25

• The relation between mass flow and pressure is imposed from a function of the type:

, (8-18)

with

. (8-19)

(8-20)

A linearisation of the relation is applied to obtain:

, (8-21)

where the δ are the variations of the mass flow and averaged exit pressure and where F and itsderivatives are computed from the old values of p and Q.

• The local outgoing characteristic variables are extrapolated.

• the relation between and is imposed as follows:

, (8-22)

with ∆p is constant over the whole outlet and with the subscripts 0 and 1 corresponding respec-tively to the value in the first outer cell and in the first inner cell.

Combining these three principles and expressing Q and p in function of ∆p at the outlet, Eq. 8-21can be written as a polynome of second order in ∆p. The suitable root is chosen so that the imposedpressure always respects the relation defined between the mass flow and the pressure during thecomputation.

8-5.2.2 Outlet Boundary Conditions for Supersonic Flow

ITYPE = 22

This condition is to be used in case of supersonic outflow and is only valid for compressible fluids.

The dependent variables at the outlet are extrapolated from the interior through first-order extrapo-lation.

If no preconditioning is used, there is some checking on negative or small pressures: if the staticpressure is less than 1E-15 after extrapolation, it is put to 1E-15.

8-5.2.3 Treatment of Backflow at Outlet (Radial Diffuser)

The option for the treatment of backflow can be activated by pressing the corresponding button inthe FINE™ interface. This option has been initially implemented in order to ensure a proper treat-ment of radial diffusers outlets in case of flow separations.

The treatment is based on the hypothesis that the absolute total temperature should be constantthroughout the outlet section. If the flow is re-entering the numerical domain through a part of theoutlet section, a hybrid boundary condition is applied in that region:

• the static pressure is imposed,

• the velocity vector is extrapolated,

F Q p,( ) 0=

F p pQ0–pQt pQ0–( )

Qt2---------------------------Q

2–=

FF∂Q∂

------- QF∂p∂

------ pδ+δ+ 0=

p1 p0

p0 p1 p∆+=


8-26 FINE™

• the absolute total temperature is imposed at a value equal to the averaged total temperaturealong the outlet (the averaging is performed throughout the region where the flow leaves thedomain.

This treatment permits to avoid the introduction of an uncontrolled total temperature level in theregions where the flow re-enters the domain, and in this way to better respect the physics of theflow.

Limitations:

• only for compressible fluid,

• it is applied separately on each outlet patch when an uniform static pressure is imposed (it isapplied to a group of patches if ITYPE=27, i.e. averaged static pressure and mass flowimposed).

• not available for the outlet boundary conditions where static pressure is imposed with radialequilibrium.

8-5.3 Solid Wall Boundary Conditions

8-5.3.1 Euler Walls

ITYPE = 15, ITYPE = 16 (default).

For Euler walls the velocity has to be tangential to the wall.

To obtain the velocity vector on the wall, the velocity vector is first extrapolated from the interior

with zero or first order extrapolation according to the selected option in the FINE™ interface:

(8-23)

with subscripts w,1,2 denoting respectively the wall, the first and the second inner cell.

The tangential part of the extrapolated velocity vector is:

, (8-24)

with the normal to the wall. The velocity vector on the wall is finally found by a scaling processsuch that its module equals:

. (8-25)

The wall density and pressure are obtained through extrapolation from the interior with zero order:

w∗w w1=

w∗w32---w1

12---w2–=

w**

w w∗w w∗w n⋅( )n–=

n

ww w1=

ww32--- w1⋅ 1

2--- w2⋅–=

ρw ρ1=

pw p1=


FINE™ 8-27

or first order:

. (8-26)

Alternatively the pressure can be solved from the normal momentum equation (ITYPE=15):

, (8-27)

which is written in a local curvilinear system as:

, (8-28)

where represent the coordinate directions, and where it is assumed that the j-direction and ηis the direction away from the wall (which is not necessarily perpendicular to the wall).

Eq. 8-28 is then solved for , whereas zero-order extrapolation is used for the density.

8-5.3.2 Navier-Stokes Walls

a) Adiabatic Walls

The velocity vector on the wall vanishes. ITYPE = 11 or 13 are used for Cartesian boundary condi-tion, 111 or 113 for cylindrical.

If condition 111 or 113 is used, the angular velocity of the wall (in the absolute frame of reference)has to be specified.

The velocity relative to the wall should be zero, leading to:

, (8-29)

with subscripts s, w referring to respectively the system and the wall.

A relation for the pressure is obtained by projection of the momentum equation onto the wall nor-

mal direction . Written in the absolute frame of reference:

. (8-30)

The normal pressure gradient can be written as a function of pressure derivatives along the coordi-nate lines:

, (8-31)

where represent the coordinate in the i, j and k directions, and where it is assumed that the j-

direction is directed away from the wall (not necessarily perpendicular to the wall). are thesurface vectors of the corresponding cell faces.

Combining Eq. 8-30 and Eq. 8-31 and considering that the velocity vanishes on the wall, yields:

ρw32---ρ1

12---ρ2–=

pw32---p1

12---p2–=

n ∇p⋅ ρv v ∇⋅⎝ ⎠⎛ ⎞ n⋅=

ρvwall vwall Si⋅( )∂n∂ξ------ vwall Sk⋅( )∂n

∂ζ------+ Si n

∂p∂ξ------⋅ Sj n

∂p∂η------⋅ Sk n

∂p∂ζ------⋅+ +=

ξ η ζ, ,

∂p∂η------

w us uw–( )–=

n

n p∇⋅ ρ– n V ∇⋅⎝ ⎠⎛ ⎞V n ∇ τ⋅

⎝ ⎠⎛ ⎞⋅+=

n ∇p⋅ 1

Sj Ω------------ Sj Si ζ∂

∂p⋅ Sj Sj η∂∂p⋅ Sj Sk ζ∂

∂p⋅+ +=

ξ η ζ, ,

Si j k, ,


8-28 FINE™

(8-32)

= COR 1 COR2 COR3

Two implementations of the adiabatic Navier-Stokes wall are available.

In the simplest one (ITYPE=13 or 113), only the terms COR1 and COR2 of the equation above aretaken into account in the evaluation of the pressure derivative. This corresponds to assume that thenormal pressure gradient equals zero. Taking into account that the velocity, appearing in the termCOR2, is the velocity on the wall, this term can be simplified to:

(8-33)

Note that COR2 vanishes for a stator wall.

In the more complicated implementation (ITYPE=11 or 111) the complete normal momentumequation is considered in the evaluation of the pressure derivative, i.e. the term COR3 is alsoaccounted for. Applying Gauss' theorem this term can be rewritten as:

. (8-34)

Once is determined, the pressure on the wall is obtained as (assuming the direction points

inside the interior field, and with indices w,1 representing the wall and the first inner cell):

. (8-35)

The temperature on the wall is obtained by expressing that the normal temperature gradient van-ishes, or in terms of the derivatives along the coordinate lines, cf. Eq. 8-31:

. (8-36)

The wall temperature is then found using a similar equation as Eq. 8-35.

The density follows from pressure and temperature through the appropriate relation, depending onthe type of gas.

b) Isothermal Walls

The implementation of this boundary condition is very similar to the adiabatic Navier-Stokes wall.The only difference is in the determination of the wall temperature, which is fixed to the specifiedtemperature in the current boundary condition. Again two versions are available, depending onwhether all the terms in the normal momentum equation are taken into account when determining

the wall pressure (ITYPE 12 11; 14 13; 112 111; 114 113).

For the cylindrical isothermal walls, #112 and #114, the angular velocity of the wall has to be spec-ified. For all versions (#12,#112,#14,#114) the wall temperature is specified.

The pressure is determined as in the adiabatic condition and the density follows from pressure andtemperature through the appropriate relation, depending on the type of gas.

η∂∂p 1

Sj2

---------– Sj Si ξ∂∂p⋅ Sj Sk ξ∂

∂p⋅+Ωρ

Sj

--------– n V ∇⋅⎝ ⎠⎛ ⎞V⋅ Ω

Sj

-------+ n ∇ τ⋅⎝ ⎠⎛ ⎞=

COR2Ωρ

Sj2

--------- Sjr ω2w⋅⋅=

COR3n

S-----Ω ∇ τ⋅

⎝ ⎠⎛ ⎞ n

S----- ∇ τ⋅

⎝ ⎠⎛ ⎞ Ωd∫

n

S----- τdS∫°

Sj

S2

-------- τi Si⋅faces

∑≈= = =

∂p/∂η

pw p112--- ∂p

∂η------–=

η∂∂T 1

Sj2

---------– Sj Si ξ∂∂T⋅ Sj Sk ξ∂

∂T⋅+=

≡ ≡ ≡ ≡


FINE™ 8-29

c) Wall with Imposed Heat Flux

The implementation of this boundary condition is very similar to the previous ones. For this condi-

tion (ITYPE = 10 or 110) the temperature is determined from the imposed heat flux (W/m2).

The pressure is determined as in the adiabatic condition and the density follows from pressure andtemperature through the appropriate relation, depending on the type of gas.

8-5.4 Far-field Boundary Condition

ITYPE = 21 uses Riemann invariants that are defined as:

, (8-37)

where are the Riemann variables associated with the direction and c is the local speed of

sound.

For subsonic inflow, corresponds to a positive, incoming characteristic. is then obtained

from the free stream values:

, (8-38)

where is the free stream velocity, the free stream speed of sound.

, on the other hand, corresponds to an outgoing characteristic and has to be estimated frominside the computational domain by an appropriate extrapolation:

, (8-39)

where subscript i refers to values from the interior. Linear extrapolation of the variables to theexternal boundary will be used to obtain a sufficiently accurate solution:

, (8-40)

where subscript 1 and 2 refer to the first two inner points.

The normal velocity and the local speed of sound can now be obtained on the boundary by adding

and subtracting both Riemann variables and :

. (8-41)

The entropy on the wall is set to the free stream entropy. All the flow variables can then beobtained.

Corresponding formulas hold for a subsonic outflow with the difference that and the wall

entropy are obtained from interior values.

Rn ± Vn

2cγ 1–-----------±=

Rn

+n

Rn+

Rn+

Rn+

V∞ n⋅2c∞

γ 1–-----------+=

V∞ c∞

R-n

Rn-

Vi n⋅2ci

γ 1–-----------–=

qi32---q1

12---q2–=

Rn+ R-

n

Vw n⋅Rn

+Rn

-+

2------------------ cwall Rn

+ Rn-–( )γ 1–

4-----------=,=

Rn+


8-30 FINE™

For supersonic flows, both Riemann variables and the entropy are obtained from free stream valuesfor inflow, interior values for outflow.

For preconditioning computation, the same principle is used with modified invariants defined as:

, (8-42)

where

. (8-43)

The free stream variables of static pressure, static temperature and the three velocity componentsare specified by the user in the boundary condition file.

For a turbulent calculation with a two-equation model, the k and ε values on the boundary are set totheir free stream values (inflow) or extrapolated from the interior (outflow).

Rn ±

vn

pg

2ρβ2------------ vn 1

β2

c2

-----– α–⎝ ⎠⎜ ⎟⎛ ⎞

vn2 1

β2

c2

-----– α–⎝ ⎠⎜ ⎟⎛ ⎞

2

4 1vn

2

c2

-------–⎝ ⎠⎜ ⎟⎛ ⎞

β2++−–=

pg p pref–=

β2 β∗Uref2=

FINE™ 9-1

CHAPTER 9: Numerical Model

9-1 OverviewTo define numerical parameters of the computation, the Numerical Model page allows to defineseveral aspects of the computation:

• the CFL number,

• the multigrid parameters,

• preconditioning parameters (if applicable).

These parameters are described in the next section.

FIGURE 9.1.0-1 Numerical model interface

In expert user mode (Expert Mode) additional parameters are available as shown in Figure 9.1.0-2:additional multigrid parameters and unsteady parameters. These interfaced expert parameters aredescribed in section 9-3. Also the non-interfaced expert parameters are described in this section.

More theoretical information on the available parameters related to the numerical model (spatialand temporal discretizations) is provided in section 9-4.

Numerical Model Numerical Model in FINE™

9-2 FINE™

FIGURE 9.1.0-2 Numerical Model page in expert mode

9-2 Numerical Model in FINE™

9-2.1 CFL Number

This box allows to tune the CFL (Courant-Friedrich-Levy) number to be employed in the computa-tion. This number globally scales the time-step sizes used for the time-marching scheme of the flowsolver. A higher value of the CFL number results in a faster convergence, but will lead to diver-gence if the stability limit is exceeded.

9-2.2 Multigrid parameters

In the left part of the Numerical Model page, three boxes are visible. The first one is an informationbox, named ’Grid levels: current/coarsest’. It indicates for each of the i, j and k directions the cur-rently selected grid level and the number of the coarsest grid level available in the correspondingdirection. The second box of the Numerical Model page is an input box that allows to define foreach of the i, j and k directions the ’Current grid level’.

• The coarsest grid level depends on the number of times the grid can be coarsened, along each ofthe (i,j,k) directions. For example, if the grid has 17*33*33 points in the i, j, k directions, it hasrespectively 16*32*32 cells. The i direction (16 cells) can thus be divided 4 times by 2, whilethe others can be divided 5 times by 2. The following grid levels are then available:

0 0 0 17*33*33 (18,513 points)1 1 1 9*17*17 (2,601 points)2 2 2 5*9*9 (405 points)3 3 3 3*5*5 (75 points)4 4 4 2*3*3 (18 points)4 5 5 2*2*2 (8 points)

Expert Parameters for the Numerical Model Numerical Model

FINE™ 9-3

The coarsest grid level available is then 4 along i and 5 along j and k.

• The current grid level is the finest grid level (for each of the i, j and k directions) on which thecomputation will take place. The selected levels should be in the range between 0 and the coars-est grid level available for each of the i, j and k directions. Referring to the example given justabove, the user can do a first run on level 3 3 3 to validate the computational parameters andthen switch to level 1 1 1 or 0 0 0 for a finer solution. It gives a high flexibility to the systemsince with one grid, the user can run simulations on several sub-meshes.

All combinations between the i, j and k grid levels, in the specified range, are possible

such as 2 3 1 or 0 3 2...etc.

Press <Enter> after each modification to validate the new specified levels.

The use of multigrid is highly recommended in order to ensure fast convergence of the flow solver.The mesh used to discretise the space can have multiple grid levels in each direction of the compu-tational domain i, j and k. These levels are numbered from 0 (finest grid) to N (coarsest grid).

The grid level (N) available in one direction (I, J, or K) is the smallest grid among all

patches on that particular direction (I, J, or K).

The third box, named ’Number of Grid(s)’, permits to significantly accelerate the convergence tosteady state if several grid levels are available: the flow calculation is performed simultaneously onall the grid levels. This technique is referred to as the multigrid strategy. This number should bechosen as high as possible, and deduced from the information displayed on the available grid leveland the grid level on which the computation will be performed (’Current Grid Level’).

Finally, the toggle button ’Coarse Grid Initialization’ enables, before calculating the flow on themesh contained in the IGG™ files, to perform a preliminary flow calculations on a coarser meshautomatically created by the flow solver by coarsening the initial one. This provides a rapid estima-tion of the flow. This technique is referred to Full Multigrid.

9-2.3 Preconditioning Parameters

This box allows to define the preconditioning numerical parameters. These parameters are onlyavailable when an incompressible fluid is selected on the Fluid Model page or when the Low SpeedFlow (M<0.3) option is selected on the Flow Model page. Preconditioning is described in detail insection 4-3.8. Especially section 4-3.8.5 provides more information on the value to choose for β*,the reference velocity and the option to use Local velocity scaling.

9-3 Expert Parameters for the Numerical Model

9-3.1 Interfaced Expert Parameters

9-3.1.1 Multigrid Strategy

If the button ’Coarse Grid Initialization’ is activated, the computation starts on the coarsest gridlevel and includes a finer grid level each time one of the two following criteria is satisfied:

Numerical Model Expert Parameters for the Numerical Model

9-4 FINE™

• The maximum number of cycles to be performed on each grid level is reached. This parameteris specified through the input box in the Full MultiGrid Parameters area as the Maximumnumber of cycles per grid level.

• The residual on the current grid level has dropped a certain order of magnitude as indicated bythe Convergence criteria on each grid level in the Full MultiGrid Parameters area.

• An additional input box permits to select the number of sweeps to be performed on the coarsegrid levels through the input box ’Number of sweeps on successive grid levels’. The amount ofsweeps is the amount of times the Runge-Kutta operator respectively the chosen relaxationoperator is applied (see section 9-4.4 for more detail). In the default configuration of the solvercalled ’Linear progression’, the number of sweeps on each level equals the level number (2sweeps on second level,...). It has been observed in many cases that the convergence rate may besignificantly improved by performing a higher number of sweeps on the coarsest levels. Recom-mended sets of values are proposed in the Sweeps area through the parameter Scheme definition:for instance (1,2,16) in case of 3 grid levels. However, it is should be noted that more sweepshave as a consequence more time required for an iteration.

9-3.1.2 Spatial Discretization

Two types of spatial discretization are available:

• central scheme (default) and

• upwind scheme.

Furthermore, if an upwind discretization is chosen, an input box appears in a ‘Spatial discretizationparameters’ area to specify the order of accuracy of the desired upwind scheme: first or secondorder. See section 9-4 for more detail on those different schemes.

Condensable fluid option is not compatible with the use of upwind schemes for space

discretization.

9-3.1.3 Temporal Discretization

The temporal discretization scheme used for the computation is an explicit multi-stage Runge-Kuttascheme. In the interface, the time stepping technique should be selected between Local time step-ping (default) and Global time stepping. See section 9-4 for more detailed information on the tem-poral discretization. In general the default scheme is recommended.

If the computation is an unsteady computation, unsteady parameters box appears. Please refer tochapter section 4-2.1 for a description of those unsteady parameters.

Expert Parameters for the Numerical Model Numerical Model

FINE™ 9-5

9-3.2 Non-interfaced Expert Parameters

Additional parameters related to the numerical model are available in the list on the Control Varia-bles page in Expert Mode.

9-3.2.1 Multigrid

IPROLO: Indicates the order of the prolongation within the multigrid approach:

= 0: is piecewise constant prolongation,= 1 (default): is linear prolongation (no damping if -1),= 2 linear prolongation except at boundaries(-2).

When used with a preconditioned formulation, this damping option is somewhat use-

less and can be damaging. FINETM sets it therefore to off when the preconditioning isinvolved.

IRESTR: Gives the order of the restriction operator of the multigrid.

= 0 (default): corresponds to linear restriction,

= 1: to quadratic restriction.

MGRSTR: Applies only for multigrid and fixes the type of multigrid cycle. MGRSTR=1: V-cycle; MGRSTR=2: W-cycle; MGRSTR=3: F-cycle; MGRSTR=4: V-cycle in sawtooth; MGRSTR=5: W-cycle in sawtooth; MGRSTR=6: F-cycle in sawtooth. Default MGRSTR=1.

MGSIMP: Applies only for multigrid. If MGSIMP>1 a simplification will be used on coarser lev-els. If MGSIMP=1 a more dissipative scheme is used on coarser meshes, i.e. first-orderupwind (if IUPWIN=1) or central scheme with increased 4th order dissipation on solidwalls (if IUPWIN=0). If MGSIMP=2, in addition to the simplification for MGSIMP=1,viscous and source terms (of turbulence) are neglected on coarser levels. No simplifica-tion for MGSIMP=0. Default MGSIMP=1

RSMPAR: Residual smoothing parameter σ*/σ. A value less or equal to zero means no residualsmoothing.

SMCOR: Only used in case of multigrid. SMCOR has the same meaning as RSMPAR but appliesto the interpolated multigrid corrections instead of the residuals. SMCOR indicateswhether interpolated corrections should be smoothed or not. The default value forSMCOR is 0.

9-3.2.2 Spatial Discretization

IFACE: = 1(default): Cell face gradients are used for the viscous fluxes,

= 0: cell corner gradients.

IWAVVI: Only used if IFACE=0. If IWAVVI=0 the cell face gradients are obtained by arithmeticaveraging of the cell corner gradients. If IWAVVI=1 a weighted averaging is usedinstead, taking the cell volumes into account.

a) Central Discretization

CDIDTE: Constant used in the exponential damping factor that is used in the numerical dissi-pation for k and ε, both if central or upwind schemes are used. The default value for CDIDTE is 100

Numerical Model Expert Parameters for the Numerical Model

9-6 FINE™

EXPMAR: Exponent in the multi-dimensional scaling model of Martinelli of the dissipationused in central schemes (see section 9-4.1.3). Default EXPMAR=0.5 i.e. multi-dimensional scaling not used.

IARTV2: Define whether the second order artificial dissipation switch should be based on bothpressure and temperature gradients (parameter IARTV2=1) or on pressure gradientsonly (IARTV2=0). In the default configuration, only pressure gradients are takeninto account. Both pressure and temperature gradients (IARTV2=1) can only betaken into account for compressible cases.

VIS2: Coefficient κ(2) for 2nd order dissipation in the central scheme (default VIS2=1.0).

VIS2KE: Used only for k-ε turbulence model. Coefficient κ(2) for 2nd order dissipation in thecentral scheme, as applied to the k and ε equations. Default VIS2KE=1.0

VIS2SW: This parameter switches off all second order dissipation for incompressible fluids (when set to the default: VIS2SW=1). Second order dissipation is intended for stabi-lization of the shocks but there are no shocks in incompressible flows. Therefore the default is to switch off all second order dissipation for incompressible fluids. Some-times it may be stabilizing to use some second order dissipation. In that case set this parameter to zero.

VIS4: Coefficient κ(4) for 4th order dissipation in the central scheme. Default VIS4=0.1

VIS4KE: Used only for k-ε turbulence model. Coefficient κ(4) for 4th order dissipation in the central scheme, as applied to the k and ε equations. Default VIS4KE=0.1

VISNUL: Eliminates 2nd order dissipation fluxes along the physical boundaries (centralscheme). Default VISNUL=1. If VISNUL=0, the procedure is not applied.

b) Upwind Discretization

ENTRFX: Entropy coefficients, see Eq. 9-2, on page 9-8 and Eq. 9-3, on page 9-8. The first value is the entropy coefficient applied to the linear field, the second value is applied to the non-linear field. ENTRFX<1. means a constant value, ENTRFX>1. means scaled with the spectral radius through a factor ENTRFX-1.

IRATIO: Vector of two values, that indicate which effective ratio is to be used, see Eq. 9-27, on page 9-13. The first value applies to the linear field, the second to the non-lin-ear field.

IRATIO is only active for second-order upwind schemes.

IROEAV:1 indicates that Roe averages are to be used to calculate cell face data. See Eq. 9-14, onpage 9-10. If IROEAV=0, arithmetic averaging will be used.

9-3.2.3 Time Discretization

IBOTH: used in combination with ISWV. The latter parameter indicates whether the dissipationterms are recalculated or not in the different Runge-Kutta stages. IBOTH=0 means that thedissipation term only contains the physical, viscous dissipation; IBOTH=1 means that italso contains the artificial/upwind dissipation. The default value = 2 means that the dissipa-tion term contains only the artificial dissipation. The physical dissipation is computed onceper time step.

IRKCO: Runge-Kutta coefficients. One for each stage, the first one for the first stage, the secondone for the 2nd stage and so on.

The default values that are used when nothing is set in IRKCO are:

Theory Numerical Model

FINE™ 9-7

1st order upwind - Van Leer:4stage .0833 .2069 .4265 1.5stage .0533 .1263 .2375 .4414 1.2nd order upwind - Van Leer:4stage .1084 .2602 .5052 1.5stage .0695 .1602 .2898 .5060 1.central scheme - Jameson:4stage .25 .3333 .5 1.5 stage .25 .1666 .375 .5 1.both central and upwind - Eliasson:4stage .125 .306 .587 1.5stage .0814 .191 .342 .574 1.

NSTAGE: number of stages for the explicit Runge-Kutta scheme. In practice, 4 or 5 stage schemes are mostly used.

IRSMCH: specifies the type of residual/correction smoothing.

= 1: standard version, Eq. 9-58,= 2 (default in incompressible cases): Radespiel & Rossow, Eq. 9-59, = 3 (default in compressible cases): Zhu, time step dependent coefficients, see

Eq. 9-61,= 4: Swanson & Turkel viscous,= 5: Vatsa, Eq. 9-63. On meshes without high aspect ratio.

ISWV: governs the recalculation of the dissipative residual in the different Runge-Kutta stages.A value α between 0 and 1 is allowed. Zero means no recalculation of dissipative resid-ual (latest available value will be used); 1 means recalculation. For intermediate values,a weighted averaging of the latest dissipation residual and of the preceding one isapplied with the weight α and (1-α) respectively. E.g. for a 5-stage scheme: ISWV = 1 01 0 1, means that the dissipative residual is calculated in 1st,3rd and 5th stage only.ISWV is used in combination with IBOTH.

RSMPAR: residual smoothing parameter σ*/σ. A value less or equal to zero means no residualsmoothing. Default value 2.

9-4 Theory

9-4.1 Spatial Discretization

The discretization in space is based on a cell entered control volume approach. The general Navier Stokes equation Eq. 9-1 is discretised as:

, (9-1)

where , are respectively the inviscid and viscous fluxes.

t∂∂U

ΩΩd∫ FI∆S

faces

∑ FV S∆faces

∑+ + Q Ωd

Ω∫=

FI∆S FV∆S

Numerical Model Theory

9-8 FINE™

9-4.1.1 Viscous Fluxes

The viscous fluxes are determined in a purely central way. As they contain gradients, gradients must be evaluated on the cell faces. This is done by applying Gauss' theorem:

. (9-2)

Two options exist:

If the expert parameter IFACE=0, the gradients are first calculated in cell corners. This is done byapplying Eq. 9-2 using as control volume, the volume that has the cell centres that surround the cellcorner of interest as corner points, as depicted in Figure 9.4.1-3 (a) below for two dimensions. Thecell face gradient is then obtained by averaging the gradients in the 4 corners of the cell face. Arith-metic averaging (input variable IWAVVI=0) or a more accurate weighted averaging may be chosen(IWAVVI=1).

FIGURE 9.4.1-3 : Different control volumes used to calculate gradients in cell corners or cell faces.

If IFACE=1 (Default), gradients are calculated directly on cell faces. Figure 9.4.1-3 (b) and (c)illustrate the control volumes used to find the gradient on respectively the cell face i+1/2 and j+1/2.

The option IFACE=1 is more robust and therefore preferred (default), although it is more expensiveas the total number of cell faces is approximately 3 times the number of cell corners.

9-4.1.2 Inviscid Fluxes

The inviscid fluxes appearing in Eq. 9-1 are upwind based numerical fluxes, and therefore noted with a * superscript.

The inviscid numerical flux is expressed as, Hirsch (1990):

. (9-3)

The first term in the right-hand-side of Eq. 9-3 corresponds to a purely central evaluation of theflux. The term represents a numerical dissipation term, that may be an artificial dissipation,

used in combination with central schemes, or the dissipation associated with upwind schemes.

In Eq. 9-3 an arithmetic averaging technique is used. Alternatively, instead of averaging the fluxesin Eq. 9-3, a flux can be used, based on the averaged unknowns, i.e.

∇Φ 1Ω---- ∇Φ Ωd∫

1Ω---- ΦdS∫°= =

cell centre cell corner cell face i+1/2 cell face j+1/2

(a) (b) (c)

Fn( )*

i 1 2⁄+12--- Fn( )i Fn( )i 1++ di 1 2⁄+–=

di 1 2⁄+


FINE™ 9-9

. (9-4)

Theoretically, the formulation Eq. 9-3 is to be preferred, but, in combination with the centralscheme, the formulation of Eq. 9-4 (default) is sometimes more robust, especially for high speedflows.

Both central schemes and upwind schemes are available within EURANUS.

Currently, the arithmetic averaging given by Eq. 9-4 is the only available option.

9-4.1.3 Central Scheme

In the former case, a Jameson type dissipation is used with 2nd and 4th order derivatives of the con-servative variables, Jameson (1981):

. (9-5)

The scalar coefficients ε are given by:

. (9-6)

The coefficients are user input, respectively VIS2,VIS4 in the non-interfaced parame-ters.

The cell entered values of in Eq. 9-5 are obtained by arithmetic averaging of the cell face val-

ues of Eq. 9-6. The variables are sensors to activate the second-difference dissipation in regions

of strong gradients, such as shocks, and to deactivate it elsewhere. They are based on pressure andtemperature variations (depending on the value for the expert parameter IARTVZ) and are definedas:

(9-7)

for all equations except the k and ε equations. For liquids, only a pressure switch is used. For the k

and ε equations, is based on the pressure, on the turbulent kinetic energy and on the dissipation

rate:

. (9-8)

in Eq. 9-6 is a measure of the inviscid fluxes and is commonly chosen as the spectral radiusmultiplied with the cell face area:

. (9-9)

On high aspect ratio meshes, the resulting dissipation in the streamwise direction may become verylow. Increasing it may improve the robustness and the convergence rate. According to Martinelli(1987), the spectral radii in the other directions are also accounted for. Instead of Eq. 9-9 one uses:

Fn( )*

i+1/2 FnUi Ui 1++

2------------------------

⎝ ⎠⎛ ⎞ di 1 2⁄+–=

di 1 2⁄+ ε 2( )i 1 2⁄+ δUi 1 2⁄+ εi

4( )δ3Ui 1++=

ε 2( )i 1 2⁄+

12---κ 2( )λ*max νi 1– νi νi 1+ νi 2+, , ,( )=

ε 4( )i 1 2⁄+ max 0

12---κ 4( )λ*-ε 2( )

i 1 2⁄+,⎝ ⎠⎛ ⎞=

κ 2( ) κ 4( ),

ε 4( )

vi

vi maxpi 1+ 2pi– pi 1–+

pi 1+ 2pi pi 1–+ +------------------------------------------

Ti 1+ 2Ti– Ti 1–+

Ti 1+ 2Ti Ti 1–+ +-------------------------------------------,

⎩ ⎭⎨ ⎬⎧ ⎫

=

vi

vi maxpi 1+ 2pi– pi 1–+

pi 1+ 2pi pi 1–+ +------------------------------------------

ki 1+ 2ki– ki 1–+

ki 1+ 2ki ki 1–+ +-----------------------------------------

εi 1+ 2εi– εi 1–+

εi 1+ 2εi εi 1–+ +-----------------------------------------, ,

⎩ ⎭⎨ ⎬⎧ ⎫

=

λ*

λ* λ*i 1 2⁄+ v∆S c∆S+( )i 1 2⁄+= =


9-10 FINE™

(9-10)

The spectral radii in the other directions are defined similar as in Eq. 9-9, e.g. for the j-direction:

(9-11)

The cell face normal is obtained by averaging the normals on the 4 cell faces in the j-direction, belonging to the 2 cells that share the i+1/2 cell face.

The parameter is user input (EXPMAR). The default value is 0.5, i.e. Eq. 9-9 is used. In the cur-rent version of EURANUS, the Martinelli approach is not yet implemented for the turbulence equa-tions.

Note that if the turbulence model is chosen, the resulting equations for and are solved

with the central scheme. Separate coefficients for the artificial dissipation can be cho-sen, respectively VIS2KE and VIS4KE in the non-interfaced expert parameters. Both the 2nd and4th order dissipation are damped by multiplying them with the following exponential function:

. (9-12)

The constant corresponds to the input variable CDIDTE. The above expression means that the

damping is applied in the region where y+<CDIDTE, the default is CDIDTE=100; is the cell vol-

ume and the cell face area.

9-4.1.4 Upwind Schemes

In the upwind case, the dissipation term is:

, (9-13)

where represents the variation of the characteristic variables which is related to the conserva-

tive variables or the primitive variables through

. (9-14)

The matrices and contain respectively the right and left eigenvectors of the Jacobian matrix.

in Eq. 9-13 represents a diagonal matrix with the element in row and col-umn l.

They are to be evaluated on the cell faces, and therefore require the knowledge of the primitive var-iables on the cell face. These can be obtained either by arithmetic averaging of the primitive varia-bles in the cell centres left and right of the cell face (input variable IROEAV=0) or by a Roe-type ofaveraging (IROEAV=1). In the latter case the following formulas are used:

λ*max λ*

i 1 2⁄+ λ*i 1 2⁄+( )

1 σ–λ*

j 1 2⁄+( )σ, λ*

i 1 2⁄+( )1 σ–

λ*k 1 2⁄+( )

σ, =

λ*j 1 2⁄+ vi 1 2⁄+ ∆Sj 1 2⁄+ ci 1 2⁄+ ∆Sj 1 2⁄++( )=

∆Sj 1 2⁄+

σ

k ε– k ε

κ 2( ) κ 4( ),

1y

+

C-----

⎝ ⎠⎛ ⎞

2

–⎝ ⎠⎛ ⎞exp–

V2

S3

-----–⎝ ⎠⎜ ⎟⎛ ⎞

exp

C

V

S

di 1 2⁄+12---Ri 1 2⁄+ diag αl

i 1 2⁄+( )δi 1 2⁄+ W=

δW

U V

δW R1– δU L

1– δV= =

R R1–

diag αli 1 2⁄+( ) αl

i 1 2⁄+


FINE™ 9-11

(9-15)

Theoretically the Roe averages have to be used. However, in practice, arithmetic averages can beused in most applications without any repercussion on accuracy or convergence. Arithmetic averag-ing has the advantage that it is computationally less expensive.

Different upwind schemes result, depending on the expression for α. In EURANUS a TVD version

of the Flux Difference Splitting scheme (FDS TVD), Roe (1981), and Symmetric TVD (STVD),Yee (1987), are available.

For both schemes can be expressed as:

(9-16)

where represents the eigenvalues of the Jacobian matrix and is a limiter function,

ensuring monotonicity.

Both the FDS TVD and STVD scheme do not have a built-in entropy criterion, which would guar-antee that the 2nd law of thermodynamics is satisfied. These schemes therefore may allow unphys-ical solutions, such as expansion shocks.

In order to avoid unphysical solutions an entropy fix is used. The eigenvalue in Eq. 9-16 is

replaced by :

. (9-17)

Eq. 9-17 limits the minimum value of to . In subsonic and transonic cases a small con-

stant value (<1.) for the entropy fix suffices (choose the input variable ENTRFX < 1.). For flowsimulations in high speed regime, it is advised to scale the entropy fix with the spectral radius, bychoosing the input variable ENTRFX > 1, e.g. ENTRFX=1.05 or 1.1. The scaling factor is thenENTRFX-1., i.e.:

. (9-18)

The latter choice also increases the robustness, at the expense of a slightly increased dissipation.

Two values for ENTRFX are to be specified. The first one applies to the linear field (the character-

istic variables that propagate with speed ), the second value to the non-linear field (the charac-

teristic variables that propagate with speed ).

For first-order upwind schemes, the limiter vanishes and both FDS TVD and STVD reduce to thesame first-order accurate upwind scheme.

ρi 1 2⁄+ ρi ρi 1+=

vi 1 2⁄+vi ρi vi 1+ ρi 1++

ρi ρi 1++----------------------------------------------=

Hi 1 2⁄+

Hi ρi Hi 1+ ρi 1++

ρi ρi 1++-------------------------------------------------=

c2

i 1 2⁄+ γ 1–( ) Hi 1 2⁄+ v2

i 1 2⁄+–=

α

αi 1 2⁄+ λi 1 2⁄+ 1 Qi 1 2⁄+–[ ]=

λi 1 2⁄+ Qi 1 2⁄+

λi 1 2⁄+

λ i 1 2⁄+

)

λ i 1 2⁄+λ2

i 1 2⁄+ δ2+2δ

------------------------------if λi 1 2⁄+ δ≤=

λi 1 2⁄+ if λi 1 2⁄+ δ>=

)

λi 1 2⁄+ δ

δ

δ ENTRFX 1.–( ) λ*i 1 2⁄+=

un

un c±


9-12 FINE™

For second-order upwind schemes, the limiter is activated.

The limiter acts on ratios of variations of the characteristic variables, defined as:

(9-19)

For the FDS TVD scheme, Q is function of only one of the ratios, according to the sign of theeigenvalue:

(9-20)

The following limiters are available:

, (9-21)

(9-22)

, (9-23)

, (9-24)

which represent respectively the Min Mod limiter (LIMITE=1), the Van Albada limiter (LIM-ITE=2), the Van Leer limiter (LIMITE=3) and the Super Bee limiter (LIMITE=4). The functionminmod chooses the value with the minimum module.

In the STVD scheme, the check on the eigenvalue sign is avoided by choosing as a function of

the two ratios and

. (9-25)

Since the 'classical' limiters such as Van Leer, Van Albada, Min Mod, Super Bee are defined as afunction of one ratio, Eq. 9-25 would exclude these limiters in a STVD context.

A new family of non-separable limiters, containing also smooth limiters, is proposed within EURA-NUS, Lacor et al. (1993).

The classical limiter functions are applied to a so-called effective ratio , which is an average of

and :

. (9-26)

The same functions as given in Eq. 9-21 to Eq. 9-24 can be chosen, where the ratio is replaced

by the effective ratio (the same limiters as for the FDS scheme are used).

The following possible choices for the effective ratio are proposed:

Qi 1 2⁄+ ri 1 2⁄+

ri 1 2⁄+- δi 1 2⁄– W

δi 1 2⁄+ W--------------------- ri 1 2⁄+

+ δi 3 2⁄+ W

δi 1 2⁄+ W---------------------=,=

Q Q ri 1 2⁄+-( )= λi 1 2⁄+ 0>

Q Q ri 1 2⁄++( )= λi 1 2⁄+ 0<

Q r( ) minmod 1 r,( )=

Q r( ) r r2+

1 r2+--------------= r 0>

0= r 0<

Q r( ) r r+1 r+--------------=

Q r( ) max 0 min 1 2r( , ) min 2 r( , ),,[ ]=

Q

r- r+

Q Q ri 1 2⁄+-

ri 1 2⁄++,( )=

r*

r-

r+

Q r-

r+,( ) Q r*( )=

Q r

r*


FINE™ 9-13

. (9-27)

It can be shown that these new limiters guarantee monotonicity provided that:

, (9-28)

which is easily achieved by switching the limiter off for negative .

The effective ratios in Eq. 9-27 are given in order of increasing magnitude. It can be shown that the

lower , the more diffusive the resulting limiter is. The choice of effective ratio is governed by theinput parameter IRATIO. IRATIO=1 corresponds to the smallest value in the list of Eq. 9-27, IRA-TIO=2 to the 2nd smallest value, and so forth, with IRATIO=6 corresponding to the maximumvalue.

For both the FDS and the STVD scheme, different limiters can be applied to the linear field (the

characteristic variables that propagate with speed ) and to the non-linear field (the characteristic

variables that propagate with speed ). In addition, for the STVD scheme, a different specificratio can be chosen for both fields.

To this end, the input variables LIMITE (corresponding to the type of limiter selected in the Numer-ical Model page) and IRATIO are vectors of length two. The first component determines the choiceof limiter, respectively the effective ratio for the linear field, the second component for the non-lin-ear field.

In general, robustness is increased by applying a more diffusive limiter. By applying this limiteronly to the non-linear field, and a compressive one to the linear field, a good compromise betweenrobustness and accuracy can be obtained.

The upwind dissipation can also be reformulated to let the limiter act on ratios of variations of theprimitive variables.

Combining Eq. 9-9 to Eq. 9-11 the limiter function can be moved outside the diagonal matrix andput in front of the primitive variable variation:

. (9-29)

The limiter function is the same as before and acts on ratios as in Eq. 9-19 or Eq. 9-27 where thecharacteristic variable variations are replaced by primitive variable variations.

Eq. 9-29 can be simplified to

. (9-30)

The Jacobian matrix in Eq. 9-30 is the Jacobian with respect to the primitive variables :

. (9-31)

9-4.2 Multigrid Strategy

EURANUS uses multigrid for efficiency and fast convergence. The input variable given by the user(Numerical Model page: Number of Grid(s)) denotes the number of grid levels to be used. Thecoarser grids are automatically created within EURANUS by dropping nodes in each direction. If in

min r+ r-( , )r

+r

-( )2

r-

r+( )

2+

r+( )

2r

-( )2

+--------------------------------------- 2r

+r

-

r+

r-+

--------------- r+r-

.5 r+ r-+( ) max r+ r-( , )≤ ≤ ≤ ≤ ≤

r* 0≥

r*

r*

un

un c±

di 1 2⁄+12---Ri 1 2⁄+ diag λi 1 2⁄+

1( )Li 1 2⁄+1– 1 Qi 1 2⁄+–[ ]δi 1 2⁄+ V=

di 1 2⁄+12--- An i 1 2⁄+ 1 Qi 1 2⁄+–( )δi 1 2⁄+ V=

∂ Fn( )∂V

---------------

An RΛL1–=


9-14 FINE™

a certain direction, the grid can not be coarsened any more (because of an odd number of cells)before reaching the desired number of grid levels, EURANUS will create the missing grids bycoarsening only in the remaining directions.

FIGURE 9.4.2-4 Scheme of the multigrid strategy

The multigrid method is based on the Full Approximation Storage (FAS) approach. V (input param-eter MGRSTR=1), W (MGRSTR=2) and F-cycle (MGRSTR=3) can be chosen by the user, or ifpreferred their sawtooth variant (MGRSTR =4,5,6 for respectively V,W,F sawtooth). In the saw-tooth variant no smoothing (i.e. Runge-Kutta solver or implicit solver) will be applied in the coarse-to-fine part of the cycle. As a result, the solution is only prolonged when passing from coarse tofine.

FIGURE 9.4.2-5 Scheme of the multigrid method

Consider a set of meshes denoted with an index l = 1,...,L with L being the finest level. The Navier-Stokes problem on the finest level can be written as:

, (9-32)

where is the spatial discretization of the Navier-Stokes operator on the finest mesh . The

problem is then approximated on coarser levels l as:

, (9-33)

with the forcing function, defined recursively as:

, (9-34)

MG Cycle

Finest level : 000

Coarse level : 111

Coarse level : 2 2 2

Coarsest level : 3 3 3

Finest level : 000

Coarse level : 111



∂UL

∂t---------- NL UL( )+ 0=

NL UL( ) L

∂Ul

∂t--------- Nl U

l( )+ Fl=

Fl

Fl Nl Il 1+l Ul 1+( ) Il 1+

lFl 1+ Nl 1+ Ul 1+( )–[ ]+=


FINE™ 9-15

where and represent restriction operators of respectively the unknowns and the residu-

als. If the input variable IRESTR=0, they are defined as:

, (9-35)

, (9-36)

where is defined as:

(9-37)

and Ω represents the cell volume. The summation in Eq. 9-35 and Eq. 9-36 is over the 8 fine cellscontained within a coarse cell.

If IRESTR=1 a more complicated quadratic restriction is used both for the residuals and theunknowns.

After temporal discretization, Eq. 9-33 becomes:

. (9-38)

is the current solution on mesh l, around which the equations have been linearized (in animplicit method) and which has to be smoothed. One has:

(9-39)

is an update of and is to be calculated.

S is the smoother. It is the operator that corresponds to the chosen time integration method.

In EURANUS, an explicit multi-stage Runge-Kutta time-marching scheme has been implemented, see below.

The linear problem Eq. 9-38 can be solved for . The updated solution will be smoothed(provided S is a good smoother) and can be restricted to the next coarser level, according to Eq. 9-39 with l replaced by l-1.

Note that the number of smoothing sweeps (i.e. the number of times the Runge-Kutta operatorrespectively the chosen relaxation operator is applied) can be chosen by the user for each grid level(Numerical Model page in Expert Mode: Scheme definition and Number of sweep on successivegrid levels) as described in section 9-3.1.1.

Once the solution on the coarsest mesh is smoothed, the coarse-to-fine sweep of the multigrid cycleis initiated. The current solutions on finer grids are updated with the solution on the next coarserlevel:

(9-40)

The operator is a prolongation operator, which may be of zero- (i.e. piecewise constant, input

parameter IPROLO=0) or first-order (IPROLO=1).

Il 1+l

Il 1+l

Il 1+l

Rl 1+

Rl 1+

∑=

Il 1+l Ul 1+

Ωl 1+ Ul 1+

∑Ωl 1+

∑---------------------------------=

Rl+1

Rl 1+ Fl 1+ Nl 1+ Ul 1+( )–=

S∆Ul

Nl Ul 0( )( )+ Fl=

Ul 0( )

Ul 0( )

Il 1+l

Ul 1+=

∆Ul Ul 0( )

∆Ul

Ul

Ul= Ul + Il-1l (Ul-1 - Il

l-1 Ul)

Il-1l


9-16 FINE™

In the basic V,W,F cycle (MGRSTR = 1,2,3 respectively) the new solution on the finer mesh is

smoothed before proceeding to the next finer level, by solving Eq. 9-35, with . Thenumber of sweeps of the smoothing operator is user input (Numerical Model page in Expert Mode:Scheme definition and Number of sweep on successive grid levels).

In the sawtooth type cycles (MGRSTR=4,5,6) the system of equations is not solved in the coarse-to-fine part of the multigrid cycle.

The user also has the possibility to smooth the corrections after prolongation (2nd term in the right-hand-side of Eq. 9-40) before adding them to the current finer grid solution, by applying the resid-ual smoothing operator to the corrections. This is governed by the input parameter SMCOR whichhas the same definition as RSMPAR, see below, and allows to calculate the smoothing parameter,according to the chosen type of residual smoothing (parameter IRSMCH), see below.

In EURANUS, the computing cost of a multigrid cycle is significantly reduced by using simplify-ing assumptions on coarser (i. e. all levels but the finest) grids (input parameter MGSIMP). IfMGSIMP=1, a first-order accurate upwind scheme is used on coarser levels (if Upwind spatial dis-cretization scheme is selected in the Numerical Model page in Expert Mode), else a more diffusivecentral scheme is used on coarser levels (if Central spatial discretization scheme is selected in theNumerical Model page in Expert Mode). If MGSIMP=2 in addition to the changes for MGSIMP=1also viscous terms as well as source terms (of turbulence and chemistry) are omitted on coarser lev-els.

9-4.3 Full Multigrid Strategy

In order to create a good initial solution, Full Multigrid is also available.

The structure of Full Multigrid can be well explained through Figure 9.4.3-6. One starts an iterationmethod, such as a multi-stage Runge-Kutta explicit scheme, on the coarsest grid. The solution onthat level will not be interpolated to the next finer grid until it converges to a certain accuracy level.Then the solution on the finer grid is taken as the initial solution for further iterations run on thatgrid level. The process is recursively used until the finest grid is reached. The initial solution on thefinest grid is called the solution obtained by a Full Multigrid method.

FIGURE 9.4.3-6 Scheme of the full multigrid strategy

It should be mentioned that there are two different kinds of prolongation in Full Multigrid. One isthe same as that used in the standard multigrid cycle, the other is the prolongation of solutions,which replaces corrections in a standard multigrid prolongation. The latter could be different fromthe former. Normally a zero-order prolongation is often used for the solution interpolation in a fullmultigrid cycle.

Based upon numerical experiments, it has been found out that it is very important to check the con-vergence level of solutions on the coarser grid before switching to the next finer grid. The reason

Ul 0( )

Ul

=

Prolongation of solutionProlongation of correction

FMG Cycle

Finest level : 000

Coarse level : 111



Finest level : 000

Coarse level : 111




FINE™ 9-17

for this is that if solutions do not converge on the coarser grid, it may cause divergence on the nextfiner grid.

In addition, an initial solution on coarse grids is less sensitive to multigrid convergence than on thefinest grid. A large cell size makes solutions converge easily and fast. Hence it takes much lesscomputational time and risk of blowing up to get reasonable solutions on the finest grid, when com-pared to the start directly on the finest grid. A full multigrid method can therefore improve therobustness and efficiency of numerical iterations methods.

9-4.4 Time Discretization: Multistage Runge-Kutta

An explicit q-stage Runge-Kutta scheme for the equation

(9-41)

can be written:

(9-42)

The coefficients determine the stability area and the order of accuracy of the Runge-Kutta

scheme. They can be chosen in such a way that they suit the problem to be solved.

For inviscid calculations the local (i.e. for each cell) inviscid time step is calculated as:

. (9-43)

CFL is the user specified CFL number (variable CFL on the Numerical Model page). The vectors Sare cell normals at the cell centre (obtained by averaging the normals on the cell faces) in respec-tively i,j and k-direction. The module corresponds to the cell face area.

For viscous calculations one also calculates a local viscous time step in each cell.

If a viscous CFL number (expert parameter CFLVIS by default set at -1) is specified by the user inthe Control Variables page, i.e. the input variable CFLVIS > 0, the following formula is used for theviscous time step:

, (9-44)

with the local laminar viscosity (laminar simulation) or the sum of local laminar and turbulentviscosity (turbulent simulation).

The actual local time step is then the minimum of both time steps:

TddU

F U( )=

u1

un α1 tF u

n( )∆+=

u2

un α2 tF u

1( )∆+=

…

uq

un

tF uq 1–( )∆+=

un 1+

uq=

αi

t∆Ω-----

⎝ ⎠⎛ ⎞

I

CFL

wSi wSj wSk c Si Sj Sk+ +[ ]+ + +--------------------------------------------------------------------------------------------------=

t∆Ω-----

⎝ ⎠⎛ ⎞

ν

CFLVISΩρ

8µ Si2

Sj2

Sk2

2 SiSj SiSk SkSj+ +[ ]+ + + -------------------------------------------------------------------------------------------------------------------------=

µ


9-18 FINE™

. (9-45)

If the input variable CFLVIS < 0 (Default) the viscous CFL number, CFLVIS, is replaced by theinviscid CFL number, CFL in Eq. 9-44. The actual local time step is then obtained by weighting theinviscid and viscous time step according to a harmonic mean formula:

(9-46)

If local time stepping is used i.e. each cell in the computation domain has its own time step given byEq. 9-43, for inviscid calculations and Eq. 9-45 or Eq. 9-46 (depending on CFLVIS) for viscouscalculations.

If global time stepping is used, i.e. in all cells the same time step is used, which is, for stability rea-sons, the minimum of the local time steps. This option is only to be used for unsteady simulationswhen the dual time stepping approach (default) is not selected. For steady simulations, it is recom-mended always to choose local stepping, as it will increase the convergence rate.

In practice, 4 or 5 stage Runge-Kutta schemes are mostly used. In EURANUS the following coeffi-cients are default for 4 and 5 stage schemes:

For central schemes

(9-47)

For first-order upwind schemes:

(9-48)

For second-order upwind schemes:

(9-49)

The user has the possibility to provide the Runge-Kutta coefficients through the expert parameterIRKCO. The first element of IRKCO corresponds to the first coefficient, the 2nd element to the sec-ond, and so forth. A maximum of 10 coefficients (i.e. a 10-stage scheme) is foreseen. If all elementsof IRKCO are zero the default values are used as listed in section 9-3.2.3.

In Jameson (1985) the dissipative terms are calculated only once or a few times in a q-stage Runge-Kutta scheme. This approach reduces the computational cost substantially.

The disadvantage is that the dissipative terms need to be stored separately. For the laminar Navier-Stokes equations with 5 equations, 5 extra arrays are required to store the dissipative residuals fromthe artificial dissipation.

The residual is split into a convective and a dissipative part:

(9-50)

The artificial (central or upwind) dissipation terms, cf. Eq. 9-2, are accounted for either in the con-vective part (parameter IBOTH = 0) or in the dissipative part (parameter IBOTH = 1).

t∆Ω-----

⎝ ⎠⎛ ⎞ min

t∆Ω-----

⎝ ⎠⎛ ⎞

I

t∆Ω-----

⎝ ⎠⎛ ⎞

ν,

⎩ ⎭⎨ ⎬⎧ ⎫

=

t∆Ω-----

⎝ ⎠⎛ ⎞

t∆Ω-----

⎝ ⎠⎛ ⎞

I

t∆Ω-----

⎝ ⎠⎛ ⎞

ν

t∆Ω-----

⎝ ⎠⎛ ⎞

I

t∆Ω-----

⎝ ⎠⎛ ⎞

ν+

--------------------------------=

α1 = .125; α2 = .306 ; α3 = .587 ; α4 = 1.α1 = .0814 ; α2 = .191 ; α3 = .342 ; α4 = .574 ; α5 = 1.

α1 = .0833 ; α2 = .2069 ; α3 = .4265 ; α4 = 1.α1 = .0533 ; α2 = .1263 ; α3 = .2375 ; α4 = .4414 ; α5 = 1.

α1 = .1084 ; α2 = .2602 ; α3 = .5052 ; α4 = 1.α1 = .0695 ; α2 = .1602 ; α3 = .2898 ; α4 = .5060 ; α5 = 1.

F U( )

F(U)=Q(U)-D(U)


FINE™ 9-19

The expression for F in Eq. 9-42 at any stage m is then

(9-51)

where m is the current stage and r is the latest stage at which the dissipative residuals have beenevaluated.

The recalculation of the dissipative residuals is governed by the (vector) variable ISWV. For a m-stage Runge-Kutta scheme the m first elements of this vector are used, the first element correspond-ing to the 1st stage, the 2nd element to the 2nd stage and so on. If the element of ISWV is 0 it meansthat the dissipative residual should not be calculated at the corresponding stage, and the latest avail-able dissipative residuals will be used; if it is 1, D will be calculated.

Note that for consistency reasons, the first value of ISWV should always be one.

For upwind schemes, in order to run at high CFL numbers, it is advised to recalculate the upwinddissipation at every stage. The best strategy is to chose IBOTH=0 (upwind dissipation put in con-vective residuals, and hence calculated at each stage). ISWV monitors then only the recalculation ofthe physical dissipation (i.e. Navier-Stokes terms) and a calculation on the first stage only is usuallyenough (ISWV=1 0...0).

Central schemes are usually less sensitive to the recalculation of the artificial dissipation, so thatIBOTH=1 can be used. The recalculation of artificial dissipation is then also governed by ISWV.However only one calculation (ISWV=1 0...0) may not be enough; a better choice is for instancerecalculation once every 2 stages, e.g. ISWV= 1 0 1 0 1 for 5-stage Runge-Kutta.

For IBOTH=2 (Default), the same strategy as for IBOTH=1 is used but in addition the physical vis-cous terms are evaluated only once per iteration.

For non-equilibrium real gas calculations (ITYGAS=4 in corresponding ’.run’ file) the input varia-ble ISWS governs the recalculation of the source terms of the species equations. Apart from thesource terms, ISWS also governs the recalculation of the diagonal terms of the Jacobians of thesource terms (which are used in the point implicit procedure).

From Eq. 9-42 it can be seen that, after the update in the last stage, the residual is normally not re-calculated any more. Strictly spoken however, within a multigrid approach, one should use in thecalculation of the forcing function for the coarser level, Eq. 9-34, the residual corresponding to thelatest solution. For single grid computations, re-calculation is never done.

Within multigrid, the Runge-Kutta operator can be applied more than once on each grid level, toensure a better smoothing. The parameter "Number of sweeps on successive grid levels" give thenumber of times the Runge-Kutta operator has to be applied to each grid level during the fine-to-coarse - respectively the coarse-to-fine - part of the multigrid cycle. They can take different valueson each grid level.

Within the explicit Runge-Kutta approach, the source terms of the two-equation turbulence modelsand of the chemistry equations (non-equilibrium real gas) are treated in a point implicit way.

For the k-ε equations the Jacobian of the negative part of the source term is diagonalized by assum-ing that the turbulent viscosity is approximately constant. This leads to the following relations

between and :

. (9-52)

Fm= F(Um) = Q(Um) – D(Ur)

ρk ρε

ρkµtρεCµfµ-----------=

ρε Cµfµρk( )2

µt

-------------=


9-20 FINE™

For instance, for the Chien model, this results in the following diagonal terms of the Jacobian,including the compressibility corrections of Sarkar and of Nichols, cf. Eq. 4-75, on page 4-37,Eq. 4-77, on page 4-37:

, (9-53)

. (9-54)

Note that in the equations above the damping function is not taken into account.

9-4.5 Implicit residual smoothing

Implicit residual smoothing can be used in combination with Runge-Kutta to speed up the conver-gence to steady state.

One stage in the explicit Runge-Kutta scheme Eq. 9-41 might be written:

(9-55)

The residual R may then be smoothed first, before applying the update of Eq. 9-55. The smoothing

may be obtained by applying a central type operator leading to a smoothed residual :

(9-56)

with the operator

(9-57)

and similar for the operators in the directions j and k.

is a smoothing parameter on which the stability criterion is:

, (9-58)

where are the CFL numbers of the smoothed and unsmoothed Runge-Kutta scheme respec-tively. The result of the residual smoothing is thus that one can run at higher CFL numbers: choose

> 1 and by an adapted choice of ε, according to Eq. 9-58, the scheme remains stable. Though

theoretically Eq. 9-58 guarantees stability for any value of , in practice this is not the case. A

good practical value is =2. The parameter is user input (RSMPAR).

Different types of residual smoothing, corresponding to different definitions of ε are available.Each one corresponds to a different value of the input parameter IRSMCH.

For IRSMCH = 1 the definition of Eq. 9-58 is used, with the restriction that ε should be positive.

For higher values of IRSMCH, the definition of ε also takes the mesh aspect ratio into account.

For IRSMCH = 2 one uses, after Radespiel & Rossow:

ρk( )∂∂Sk

-

2Cµ

µt

------–= ρk 112---αMt

2+⎝ ⎠⎛ ⎞ 2

µρy

2--------– 2

Cp1 γ 1–( )Mk

ρka2

---------------------------------Pk–

ρε( )∂∂Sε

-32---Cε2f2

Cµρεµt

-------------– 2µy

2----e

0.5y+––=

fµ

um 1+ un αm tF um( )∆+ un αmR um( )+= =

R

I εi∆i2–( ) I εj∆j

2–( ) I εk∆k2–( )R R=

∆i2

∆i2R Ri 1– 2Ri– Ri 1++=

ε

ε 14--- σ*

σ-----

2

1–>

σ* σ,

σ*/σ

σ*/σ

σ*/σ σ*/σ


FINE™ 9-21

, (9-59)

with the spectral radius (scaled with the cell face area), e.g.:

. (9-60)

A similar definition as Eq. 9-59 holds for ε in the directions j and k.

For IRSMCH = 3, after Swanson & Turkel, one has:

(9-61)

IRSMCH=4 is also after Swanson & Turkel but for viscous flows. First Eq. 9-61 is applied. Denot-ing the obtained value as ε*, the final value is:

. (9-62)

Finally, for IRSMCH = 5, one has, after Martinelli & Vatsa:

. (9-63)

εi14--- σ*

σ------

1 max λj* λi*⁄( ) λk* λi*⁄( ),( )+

1 max λj* λi*⁄ λk* λi*⁄,( )+---------------------------------------------------------------------------------------

2

1–=

λi* un c+( ) S⋅[ ]i=

εi14--- σ*

σ------

11 0.0625 λj* λi*⁄( ) λk* λi*⁄( )+( )⋅+--------------------------------------------------------------------------------------------

21–=

εi max ε*14---

10 λd⋅λi* λj* λk*+ +-------------------------------------[ , ]=

εi14--- σ*

σ------

1 λj* λi*⁄( ) λk* λi*⁄( )+ +

1 λj* λi*⁄ λk* λi*⁄+ +--------------------------------------------------------------------------

2

1–=


9-22 FINE™

FINE™ 10-1

CHAPTER 10:Initial Solution

10-1 OverviewFINE™ provides the possibility to start a computation from an initial solution. The following initialsolution types are available:

• constant values,

• from file,

• for turbomachinery,

• from throughflow.

Each of these types is described in the next sections.

FINE™ allows to define a different initial solution type for each block or group of blocks. Such ablock dependent initial solution provides more flexibility in the restart of previously computedsolutions. The next section describes how to set up a block dependent solution.

10-2 Block Dependent Initial SolutionThis procedure permits to initiate the calculation of some of the blocks with the results of a previ-ous calculation, whereas the other blocks are started from a uniform flow. Another possibility is toinitiate one new calculation with the results of several previous calculations. This is for instance thecase if a multistage turbomachinery calculation is preceded by the calculation of the separatestages.

The flow solver can start from files resulting from calculations performed on different grid levels.Only the grid levels that are used in the multigrid cycle are considered here. For instance, a compu-tation of a three-stage turbine can start from three solutions for each stage, each one on a differentgrid level.

Furthermore, the full multigrid cycle is automatically removed when at least one file is provided onthe finest grid level.

Initial Solution Block Dependent Initial Solution

10-2 FINE™

10-2.1 How to Define a Block Dependent Initial Solution

The Initial Solution page is divided in two parts. On the left, a tree displays the structure of thegroups of blocks. On the right, four buttons allow the user to choose the type of initial solution:constant values, turbomachinery oriented, restart from a solution file or restart from a throughflowfile. At the bottom two buttons allow to modify the group(s). It is possible to create new groups ofblocks in the same way as for the groups of patches on the boundary conditions page (see section 8-1). Different initial solutions can be assigned to these groups of blocks.

By default, all the blocks are grouped in one group named "MESH" and constant values areselected. In the constant values page, the toggle button Cylindrical is set on.

FIGURE 10.2.1-1Default settings of the initial solution page

10-2.2 Examples for the use of Block Dependent Initial Solution

The block dependent initial solution is helpful in many industrial cases. The following are two sce-narios in which this capability is very useful:

1. A solution has been calculated for a turbine including 10 stages. A new stage is added. Now theturbine has 11 stages. The designer does not want to begin a computation from scratch for theturbine with 11 stages. He can take advantage of the solution that has been found for the 10 firststages. The new computation will contain one group with the 10 stages and one group with thelast stage. The first group will be assigned to a from file initial solution and the second group canbe assigned to another type of initial solution.

Initial Solution Defined by Constant Values Initial Solution

FINE™ 10-3

2. A turbine includes 10 stages. Even with the turbomachinery-oriented initial solution, the codedoes not succeed to converge properly. The designer could split the turbine in several parts andcalculate the solution for each of these parts. Then a global project is created. In the Initial Solu-tion page, a from file initial solution is assigned to each part of the project. The computation willhave a far better chance to succeed.

10-3 Initial Solution Defined by Constant ValuesWhen selecting on the Initial Solutions page constant values the user can modify the physical val-ues used as initial solution on the page as shown in Figure 10.2.1-1. The physical values are uni-formly used as initial solution all over the selected group of blocks, except on the boundaries. Thevariables for which initial values need to be specified are the static pressure, the static temperature,the velocity components and the turbulence-based variables k and ε, if a two-equation turbulencemodel is used. Note that the velocity components specified by the user are the Cartesian (cylindri-cal) ones for a Cartesian (cylindrical) case.

The lower part of the page allows for a further control of the initial field. First, for both Cartesianand cylindrical projects, the velocity direction can be fitted along the I, J or K mesh lines. Thereverse option determines whether the velocity vectors will point in the I (J or K) increasing ordecreasing direction. By default, no specific velocity direction is set and the input box is set to“None”.

For the cylindrical projects only, an option for the fitting method can be chosen. The first option fits

Vm, the meridional velocity (defined as ), and uses Vθ to set the azimuthal absolute

velocity. The second option fits W, the relative velocity, to the mesh lines.

Furthermore, for the cylindrical projects only, it is also possible to act on the initial pressure field.To this end, two options are available: constant pressure field (default) and a radial equilibriumpressure gradient. In a rotational machinery for instance, a radial equilibrium pressure gradient isoften closer to the physics than a constant field. The radial equilibrium factor allows to adjust theinfluence of the pressure gradient (its default value is 1.0).

Vm Vr2

Vz2

+=

Initial Solution Initial Solution from File

10-4 FINE™

10-4 Initial Solution from File

10-4.1 General Restart Procedure

FIGURE 10.4.1-1Restarting from a file

To continue on the result of a previous computation the user must simply select the solution. Click-ing on the Open browser button will open a File Chooser window to select the ’.run’ (or ’.cgns’)file of a computation.

To restart from a solution the computation definition file with extension ’.run’ is not

sufficient. It is required that the solution file with extension ’.cgns’ is present, which con-tains all the saved and requested quantities.

The toggle button Reset convergence history can be selected. When selecting this button the ’.res’file, which contains all the residuals from the previous computation, will be erased. The new resid-uals will be calculated with respect to the first iteration of the new computation. If the from filesolution is already very close to the exact solution, the normalized residuals will decrease slowly. Itis just because the starting state is already a good approximation of the solution.

When all the blocks are grouped in only one group, the user is able to unselect the button Reset con-vergence history. In this case, the new residuals are appended to the ’.res’ file and are calculatedwith respect to the first iteration of the old computation.

If only one group of blocks exists the button to Reset convergence history can be set

on or off. If several groups of blocks exist, the button is disabled and automatically theconvergence history is reset.

There is a limitation in the current version of the FINE™ interface: if the user wants to keep theconvergence history, the ’.run’ file MUST belong to the active computation. The following steps

1. Compute a solution.

Initial Solution from File Initial Solution

FINE™ 10-5

2. Create a new computation.

3. In this new computation, select a from file initial solution.

are not compatible with the Reset convergence history option. Whatever the user selects, the togglebutton Reset convergence history will be set ON automatically.

If, for some reason, the user still wants to keep the convergence history in a new computation, theonly workaround is to copy all the files from the old computation directory to the new computationdirectory and to rename them with the name of the new computation. Then the File Chooser willpoint to a ’.run’ file belonging to the active computation and the convergence history will not bereset.

The initialization of the flow computation from a solution file is currently limited to

CGNS files.

As the initial pressure and temperature fields are block dependent, discontinuities in

these quantities can be present at block connections and the flow solver could have diffi-culties to converge in that case. Therefore boundary conditions should be carefullychecked in order to avoid any important discontinuity at block connections.

The flow solver can start from files resulting from calculations performed on different grid levels.Only the grid levels that are used in the multigrid cycle are considered here. For instance, a compu-tation of a three-stage turbine on 0/0/0 with 3 grid levels can start from three solutions for eachstage, each one on a different grid level (0/0/0, 1/1/1, and 2/2/2). Furthermore, the full multigridcycle is automatically removed by the flow solver when at least one file is provided on the finestgrid level.

10-4.2 Restart in Unsteady Computations

To allow a second order restart for unsteady computations it is necessary to set in the ComputationSteering/Control Variables page Multiple Files in the Output Files. This parameter allows to havemultiple output files: for each saved time step also the solution of the previous time step is saved.

To perform a second order restart for an unsteady computation select in the Initial Solution pagefrom file. Using the File Chooser select the solution file with extension ’.cgns’ at a certain step(’_ti.cgns’). EURANUS will automatically find the solution of the previous time step if present(’_ti-1.cgns’). If EURANUS can not find the solution of the previous time step a message willappear in the Task Manager to indicate that a first order restart will be performed.

10-4.3 Expert Parameters for an Initial Solution from File

There is no current limitation to start a k-ε computation from a Baldwin-Lomax solution. In thiscase, the turbulent quantities are estimated from the friction velocity if the expert parameter INIKEis set to 2 (default value) or from the turbulent viscosity field µt if INIKE = 1. In the latter case, theturbulent viscosity is initialized or read from file depending on the value of the expert parameterIMTFIL (default value IMTFIL = 0 to initialized µt or IMTFIL = 2 to read µt from file).

Initial Solution Initial Solution for Turbomachinery

10-6 FINE™

10-5 Initial Solution for TurbomachineryThis type of initial solution respects the inlet and outlet boundary conditions and assumes a constantrothalpy along the axisymmetric grid surfaces typical of the turbomachinery oriented meshes (e.g.,created by AutoGrid). In addition, the velocity field is automatically aligned with the blade pas-sages.

When using the turbomachinery-oriented initial solution, make sure that the INLET

boundary condition is set in cylindrical mode and not in Cartesian mode. This last modeis not compatible with the turbomachinery initial solution in the present version.

FIGURE 10.5.0-1Example of Turbomachinery-oriented initial solution

The turbomachinery-oriented page displays two major panels: one for the inlet patches and one forthe Rotor/Stator interfaces (see Figure 10.5.0-1). On the left of each panel, a tree shows the namesof the patches. If no patch name has been given in IGG™, the default name will be a concatenationof the name of the block, the index of the face and the index of the patch.

The Inlet Patches grouping displayed in this initial solution page is identical to the Inlet Patchesgrouping created under the INLET thumbnail of the Boundary Conditions page. Similarly, theRotor/stator interface grouping displayed in the initial solution page is based on the ID given in theRotor-Stator thumbnail of the Configuration/Rotating Machinery page. There is no way to modifythe groups of patches in the Initial Solution page. If the user wants to edit the groups of patches, theuser must go back to the Boundary Conditions and the Rotating Machinery pages.

An input dialog box is provided per group of patches in order to select the type of static pressurespecification: constant distribution or radial equilibrium. One or two input boxes are provided pergroup of patches in order to define the static pressure value to be used and, if radial equilibrium ischosen, the radius on which this radial equilibrium will be based.

Provided that a k-ε turbulence model is selected, a third panel is displayed that requires the initialvalues for the turbulent kinetic energy (k) and the turbulent dissipation rate (epsilon). For advice onthe initial values to choose for k and epsilon see section 4-3.5.4.

Make sure that there is an inlet patch among the blocks for which a Turbomachinery

initial solution has been chosen. If there is no inlet patch for the selected group of blocks,a warning message is displayed in the FINE™ interface asking the user either to edit the

Throughflow-oriented Initial Solution Initial Solution

FINE™ 10-7

group or to change the type of initial solution.

10-6 Throughflow-oriented Initial SolutionThis type of initial solution, of interest in turbomachinery calculations, allows to get an initial fieldon the basis of an axisymmetric throughflow solution. The initial solution is defined through anexternal file created by the user. The file contains 2D data in the format described hereafter. Thesolver will use data to generate an initial throughflow-oriented solution.

Note that there is no direct link between the throughflow module integrated in the

FINE™ interface and the format currently available. Work is in progress to make thebridge between both tools.

The solver will create a virtual mesh based on the hub and shroud definitions, forcing points on thedata points. Two additional stations will be created, at the inlet and outlet, respectively. The inletdata are extrapolated from the first spanwise station while the outlet data come from the last station.It is therefore recommended that the inlet and outlet boundaries of the mesh lie outside the meridi-onal domain covered by the throughflow data.

The meridional velocity is based on the mesh direction.

10-6.1 File Format

The file will include three parts, that must be separated by a blank line:

• solution definition,

• hub definition,

• shroud definition,

Once it is created, the file is selected in the FINETM interface through a File Chooser click on theOpen browser button in the Initial Solution/from throughflow page.

10-6.1.1 Solution Definition

The first part of the file contains the values of the flow variables throughout a meridional structuredmesh covering the entire machine. For each node of the meridional mesh, the (R,Z) coordinates arespecified together with the pressure, temperature and velocity components.

Here an axial case is taken as an example:

Throughflow Axial Stator #Comment lineRZ #Type of data (ZR or RZ are accessible)4 3 #Number of spanwise and streamwise stations

0.246 -0.025 150000 0 0 0

0.275 -0.025 150000 0 0 0

0.29 -0.025 150000 0 0 0

0.246 -0.0 130000 0 0 0

0.275 -0.0 130000 0 0 0

1st spanwise section close to inlet at Z=-0.025

2nd spanwise section at Z=-0.0

Initial Solution Throughflow-oriented Initial Solution

10-8 FINE™

0.29 -0.0 130000 0 0 0

0.246 0.025 100000 0 0 0

0.275 0.025 100000 0 0 0

0.29 0.025 100000 0 0 0

0.246 0.05 90000 0 0 0

0.275 0.05 90000 0 0 0

0.29 0.05 90000 0 0 0

There are 4 spanwise stations in this example (Z=-0.025, Z=0.0, Z=0.025 and Z=0.05), each with 3points in spanwise direction (R direction). The point order in a streamwise and spanwise stationgoes respectively from hub to shroud and from inlet to outlet.

Each data line is made of the two (R,Z) coordinates (in m), the static pressure (in Pa), the static tem-perature (in K), the meridional velocity and the tangential velocity (in m/s).

10-6.1.2 Hub Definition

The hub definition uses the same format as for AutoGrid. The first line must be HUB. The secondline specifies the type of coordinate (ZR or RZ) and the third line the number of hub points. Thenext lines correspond to the hub coordinates.

Taking again the example of the case above:

HUBRZ #Type of data (ZR or RZ are accessible)2 #Number of points on hub0.245 -0.02 #Point coordinates (in m)0.245 0.051

The hub is described in increasing Z coordinate from -0.02 to 0.051. The first column contains theR coordinate for each of the two points on the hub.

10-6.1.3 Shroud Definition

The shroud definition is similar to the hub definition, except for the first line that will be replacedby SHROUD and the points coordinates.

SHROUDRZ #Type of data (ZR or RZ are accessible)2 #Number of points on hub0.3 -0.02 #Point coordinates (in m)0.3 0.051

3rd spanwise section at Z=0.025

4th spanwise section close to outlet at Z=0.05

Throughflow-oriented Initial Solution Initial Solution

FINE™ 10-9

FIGURE 10.6.1-4 Throughflow-oriented Initial Solution

Meridional Average View

3D View

INLET OUTLET

BLADE

1st spanwisesection

4th spanwisesection

2nd spanwisesection

3rd spanwisesection

HUB

SHROUD

Initial Solution Throughflow-oriented Initial Solution

10-10 FINE™

FINE™ 11-1

CHAPTER 11:Output

11-1 OverviewWith the EURANUS flow solver in the FINE™ environment the user has the possibility to specifythe content of the output generated by the solver. The output does not only contain the flow varia-bles for which the equations are solved (density, pressure, velocity components), but also other var-iables such as the temperature, the total conditions, the Mach number, customized velocityprojections, etc...

Furthermore CFView™ allows to calculate derived quantities, which permits to limit the memorysize of the output and to avoid re-launching the flow solver in case one quantity of interest is notavailable. With this functionality the user can find the compromise between an acceptable memorysize for the output and the ease of having all flow quantities of interest immediately available forvisualization.

In the next sections the way to control the output from the EURANUS flow solver is described inmore detail:

• field quantities: calculated at all the mesh nodes (see section 11-2.1),

• solid data: calculated along the solid wall boundaries (see section 11-2.1.5),

• customized averaged data:

— the evolution of some averaged quantities can be provided along the streamwise direction asdescribed in section 11-2.2,

— for turbomachinery applications, a pitchwise averaged output can be created for visualiza-tion as described in section 11-2.3,

• global performance output (see section 11-2.5),

• additional output for the ANSYS code, a widely used finite element code for structural analy-sis (see section 11-2.4).

The global performance output is written in a ASCII file with the extension ’.mf’. All other outputgenerated by the solver is written in one single ’.cgns’ file, compatible with the CFView™ visuali-sation software. It is also possible to request for the output to be written in Plot3D format asdescribed in section 11-2.6.

Output Output in FINE™

11-2 FINE™

11-2 Output in FINE™

11-2.1 Computed Variables

Using the Outputs/Computed Variables page, the user can choose which physical variables have tobe included in the output generated by the flow solver EURANUS, see Figure 11.2.1-1 toFigure 11.2.1-6. All the selected variables will then be automatically available when launchingCFView™ in order to visualize the results.

11-2.1.1 Thermodynamics

FIGURE 11.2.1-1 Thermodynamics computed variables page (for cylindrical projects)

Table 11-1 and Table 11-2 give the formulae used to calculate the thermodynamic quantities.

Cartesian and cylindrical casesQuantity Incompressible Compressible

Static pressure

Total pressure

Static temperature

Total temperature

Density

Entropy

Dynamic viscosity

TABLE 11-1 Thermodynamics quantities generated by EURANUS

n

PstatPstat

Ptot Pstat ρV2

k+2

---------------+=Ptot Pstat

Ttot

Tstat-----------

⎝ ⎠⎛ ⎞

γγ 1–-----------

=

Tstat Tstat

Pstat

ρrgas-------------=

Ttot TstatV

2k+

2Cp---------------+= Ttot Tstat

V2

k+2Cp

---------------+=

ρ ρ

s Cp

Tstat

Tstatinlet

---------------------ln= s Cv

Pstat Pstatinlet⁄( )

ρ ρinlet⁄( )γ------------------------------------------ln=

µ µ

Output in FINE™ Output

FINE™ 11-3

Furthermore five definitions of the pressure coefficient are available: CP1, CP*1, CP2, CP*2, CP3:

— ,

— ,

— ,

— ,

— .

where Xinlet corresponds to the mean value of the variable X on the inlet, and where Uref is definedas:

• RLEN in cylindrical cases, with RLEN, the reference length given in the Flow Model page,

and ω, the rotational speed (defined block per block),

•UENTR (Cartesian case) to be specified in the expert parameters list of the ComputationalSteering/Control Variables page.

When applying FINE™ to external flow situations (expert parameter IINT set to 0), only the quan-tity CP2 is well-defined. In external flows this pressure coefficient is defined in terms of the Refer-ence values and Reynolds Number Related Info specified in FINE™ on the Flow Model page:

.

The user must then ensure that the far field or free stream quantities set on the Boundary Conditionspage as well as the initial solution values (set on the Initial Solution page) are fully consistent withthe reference values specified on the Flow Model page.

Cylindrical cases onlyIncompressible Compressible

Relative total pressure

Relative total temperature

Rothalpy

ω is the angular rotation speed and r, the distance from the rotation axis

TABLE 11-2 Thermodynamic quantities generated by EURANUS in cylindrical cases

Ptotr

Pstat ρW2

k+2

----------------+=Ptot

rPstat

Ttotr

Tstat-----------

⎝ ⎠⎜ ⎟⎛ ⎞

γγ 1–-----------

=

Ttotr

TstatW

2k+

2Cp----------------+= Ttot

rTstat

W2

k+2Cp

----------------+=

I CpTstat

Pstat

ρ----------- W

2k ω2

r2

–+2

----------------------------------+ += I CpTstatW

2k ω2

r2

–+2

----------------------------------+=

CP12 P Ptinlet–( )

ρinletUref2

--------------------------------=

CP∗1Ptinlet Pt–

Ptinlet

--------------------------=

CP22 P Pinlet–( )

ρinletWinlet2

------------------------------=

CP∗22 Ptinlet Pt–( )

ρinletWinlet2

----------------------------------=

CP32 P Pinlet–( )

ρU2

------------------------------=

ω

CP22 P Pref–( )

ρrefUref2

---------------------------=


11-4 FINE™

Finally, when a condensable fluid is selected in the Fluid Model page, new quantities at the bottomof the page will appear. Those variables are defined using the thermodynamic tables defining thecondensable gas (see section 3-2.3.4 for more details).

When the condensable fluid option is used, 6 flow variables are stored at all mesh cell centersinstead of 5 for a perfect gas or liquid. These variables are the following: density, velocity compo-

nents, static pressure and total energy ( ). The static and total enthalpy can easily be

derived using:

• static enthalpy .

• absolute total enthalpy .

• relative total enthalpy .

The dryness fraction permits to evaluate the location of the local thermodynamic state with respectto the saturation curve. For each value of the pressure an interpolation from the saturation table(’PSA.atab’) permits to determine the saturated liquid (ρl) and gas (ρv) values of the density. Thedryness fraction is then computed by:

• dryness fraction .

The generalised dryness fraction directly results from the above expression whereas the standarddryness fraction is bounded in the [0,1] interval.

It should be mentioned that the presence of the saturation table (’PSA.atab’) is

required in order to allow the calculation of the dryness fraction, although this table isnot required by the solver itself (unless an inlet boundary condition based on drynessfraction is used).

11-2.1.2 Velocities

FIGURE 11.2.1-2 Velocities computed variables page (for cylindrical projects)

ρE ρ eV

2

2------+

⎝ ⎠⎛ ⎞=

h epρ---+⎝ ⎠

⎛ ⎞=

Ha hV

2

2------+

⎝ ⎠⎛ ⎞=

Hr hW

2

2-------+⎝ ⎠

⎛ ⎞=

Xρ ρl–( )ρvρv ρl–( )ρ

--------------------------=


FINE™ 11-5

The velocity quantities that can be selected are described below.

Both for Cartesian and cylindrical cases:

•Absolute velocities: Vx, Vy, Vz, Vxyz, V.

•Velocity projections: Vi, Vj, Vk, |Vi|, |Vj|, |Vk|,Vis,Vjs,Vks.

with , surface vector of the i surface,

.

•Absolute Mach Number, only for compressible fluids:

.

For cylindrical projects only:

•Absolute velocities in the rotating frame:|V|, Vr, Vθ, Vm:

,

,

.

•Relative velocities: Wx, WY, Wxyz, W, Wθ:

,

.

•Relative velocity projections: Wi, Wj, Wk, |Wi|, |Wj|, |Wk|, Wis, Wjs, Wks

with , surface vector and

.

•Relative Mach Number:

.

11-2.1.3 Vorticities

FIGURE 11.2.1-3 Vorticities computed variables page

The vorticity is calculated according to the following expression:

Vi V·

Si⋅⎝ ⎠⎛ ⎞ Si⋅= Si

Vis V V·

Si⋅⎝ ⎠⎛ ⎞– Si⋅=

Mabs VγPstat

ρ--------------

⎝ ⎠⎛ ⎞⁄=

Vr Vx θ Vy θsin+cos=

Vθ Vy θ V– x θsincos=

Vm Vr2

Vz2

+=

W V ω r×–=

Wθ Wy θ W– x θsincos=

Wi W·

Si⋅⎝ ⎠⎛ ⎞ Si⋅= Si

Wis W W·

Si⋅⎝ ⎠⎛ ⎞– Si⋅=

Mrel WγPstat

ρ--------------⎝ ⎠

⎛ ⎞⁄=


11-6 FINE™

,

where is the gradient operator. From the above expression, ζx, ζy, ζz, ζxyz, and ζ are available.

11-2.1.4 Residuals

FIGURE 11.2.1-4 Residuals computed variables page

The residuals are computed in FINE™/Turbo by a flux balance (the sum of the fluxes on all the facesof each cell). The absolute value |RES| resulting from the flux balance is written as output for eachcell. The residuals for the following quantities can be selected:

• density ρ,

• energy E,

• velocity component Wx,

• velocity component Wy,

• velocity component Wz,

• turbulent kinetic energy k for two equations turbulence models,

• turbulent energy dissipation rate ε for two equations turbulence models.

11-2.1.5 Solid Data

FIGURE 11.2.1-5 Solid data computed variables page

The solid wall data refer to quantities that are estimated at the solid boundaries:

• static pressure at walls (see section 11-2.1.1).

• static temperature at walls (see section 11-2.1.1).

• normalized tangential component of the viscous stress at walls, where is the vis-

cous stress, V is the reference velocity and ρ is the reference density defined in Flow Model page.

• heat transfer at walls in general and for k-ε extended wall function

where and are coming from page 4-34.

ζ ∇ V×=

∇

Cfτ

ρV2

2⁄----------------= τ

qw KDT

Dn--------⋅=

qw ρCpuτTτ= uτ Tτ


FINE™ 11-7

• relative velocity at walls (see section 11-2.1.2).

• viscous stress at walls.

• y+ (in first inner cell).

11-2.1.6 Turbulence

FIGURE 11.2.1-6 Turbulence computed variables page.

The following quantities can be stored:

• y+ (3D field)

,

•wall distance (i.e. closest distance to the wall: ywall),

• turbulent Viscosity (µt/µ),

• production of kinetic energy (Production),

• k and ε for two equation turbulence models.

11-2.1.7 Throughflow

For the output specific for Throughflow computations see Chapter 6.

11-2.2 Surface Averaged Variables

This option is customised for turbomachinery applications and displays in a Cartesian plot the evo-lution of surface-averaged variables along the streamwise direction. The user should select blocksalong the streamwise direction. A surface averaging is performed on the grid surfaces perpendicularto the streamwise direction. Computation on each block will be performed to create the plot.

The Surface Averaged Variables page is modified according to the type of project as defined in theMesh/Properties... menu. For a Cylindrical project the page looks like shown in Figure 11.2.2-7.In this case the streamwise direction (by default K) is defined on the Rotating Machinery page ofthe FINE™ interface. The blocks to include in the averaging can be selected from the list of blocksby left-clicking on them. Selected blocks appear highlighted. This selection acts as a toggle whereclicking ones on a block name selects the block and clicking a second time deselects the block. Toselect multiple blocks it is sufficient to left-click on each of them.

The variables available for averaging are listed on this page and a averaging method can be selectedfor each variable independently. The turbulent quantities k and ε only appear for selection if a two-equations turbulence model is used.

τxyz

yρywalluw

µ----------------------=+


11-8 FINE™

FIGURE 11.2.2-7 Surface averaged variables page for a Cylindrical project

Since the integration is performed on mesh surfaces, some differences could appear.

For example, in a case with splitter, two curves will be generated and a sum on this curveshould be performed to see the evolution of the quantity in streamwise direction of onechannel.

Since the surface averaging is performed on grid surfaces this option is mainly suita-

ble for H-topology meshes. Especially computing the evolution of the mass flow instreamwise direction with HOH mesh topology is not correct.

For Cartesian projects as defined in the Mesh/Properties... menu the Surface Averaged Variablespage is displayed as shown in Figure 11.2.2-8. In this case the streamwise direction needs to beselected directly in this page by selecting to average on surfaces of constant index (in the exampleof Figure 11.2.2-8 surfaces of constant k). The blocks to include in the averaging need to beselected in the same way as for a cylindrical case as described before. Contrary to a cylindricalproject, in this case no relative quantities are available.

Like for a cylindrical project the surface averaged evolution of the quantities is shown

for each block separately.


FINE™ 11-9

FIGURE 11.2.2-8 Surface averaged variables page for a Cartesian projects

11-2.3 Azimuthal Averaged Variables

The FINE™/Turbo environment provides the user with a specific turbomachinery output, i.e. thetwo-dimensional meridional view of the circumferentially-averaged results. Note that this function-ality is also available in CFView™.

Using the Azimuthal Averaged Variables page, the user can choose which physical variables have tobe included in the pitchwise-averaged output generated by the flow solver. This page is thereforeonly accessible if the project is of the cylindrical type. The azimuthal averaging of the variables iscalculated at the end of the computation. The results will be displayed as a 2D case in CFView™.The name of the file from which CFView™ can read which variables have been averaged in the azi-muthal direction has the extension .me.cfv.

The choice is left to the user to apply mass or area averaging, and to merge into one patch the aver-aging patches. This last option (Merging of meridional patches) simplifies the meridional view butthe patches are merged in increasing order one after another, which is not suitable for all topologies.

If Surface of revolution mesh (Autogrid) option is activated, a specific algorithm will be applied toenhance azimuthal averaging of the solution performed on revolution surfaces.

The Parameters area is divided into five ’notebook pages’ which can be selected by clicking on oneof the five corresponding thumbnails: Thermodynamics, Velocities, Vorticities, Residuals and Tur-bulence in the same way as for the control variables.

Figure 11.2.3-9 shows an example of the corresponding information page for thermodynamics vari-ables. Other pages are similar to those described in section 11-2.1.

At the bottom of Figure 11.2.3-9 in expert mode the user can define the meridional patches for azi-muthal averaging. See section 11-3.1 for more detail on this possibility. By default meridional aver-aging patches are set.

Automatic setting of the meridional averaging patches only works if no manual action

is involved (like renaming of some patches).


11-10 FINE™

FIGURE 11.2.3-9The thermodynamics azimuthal averaged variables page

11-2.4 ANSYS

The FINE™/Turbo environment provides the user with a specific ANSYS output. The objective isto export results of the CFD computation on solid surfaces (nodes and elements) into ANSYS as aboundary condition for the finite element model. This approach is called FEM loading method forloading the CFD results on a Finite Element Model. The transferred results on the interface fluid-structure can be the pressure field for a structural analysis and the temperature field or the heatfluxes for a thermal analysis in the structure.

The FEM approach needs to have the finite element mesh of ANSYS. If this mesh

does not exist before the CFD computation, it is impossible to create directly a file thatcan be imported in ANSYS to apply the suitable boundary condition. Consequently thebest way to manage the interface between FINE/TURBO and ANSYS can be a new post-processing tool. The post-processing tool is needed with the specification of the ANSYSmesh, the common surfaces where the data must be interpolated and the type of bound-ary condition on each surface. The transfer will be carried out through the ANSYS filesaved with the command CDWRITE ("project_ANSYS.cdb") in ANSYS. This file willbe modified and read again in ANSYS to impose the CFD results as boundary conditions(see Figure 11.2.4-10).


FINE™ 11-11

FIGURE 11.2.4-10Data transfer of CFD results into the ANSYS project

11-2.4.1 ANSYS Pre-Processing

Before completing the Outputs/ANSYS pages, the user must create the file ’project_ANSYS.cdb’with the command CDWRITE in ANSYS. Furthermore before the save in ANSYS, some opera-tions needs to allow the identification of the common surface between the fluid model and the struc-tural model. The ANSYS project must be completely defined with a special treatment for thesurface loads that will be replaced by the interpolated CFD results. On each common surface, acoded constant value is specified. The default coded values are given in the table 11-3 for the differ-ent types of boundary condition. The value is incremented by one for each different surface so thatfor example the pressure imposed on the first surface is set to 1000001 and it is set to 1000002 onthe second, ...

TABLE 11-3 Default code for different type of boundary condition imposed from CFD results

The coded value can be modified in order to avoid confusion with physical values.

Note that the surface must be relatively flat or smooth (without sharp angle) so that the

six surfaces define a cube. Moreover the surface closed on itself as a cylinder or a blademust be divided into two parts.

Validation tests are performed with ANSYS release v8.0. Please refer to ANSYS user

manual for more details on the ’.cdb’ file format

Boundary Condition Code

Pressure field 1000001

Temperature field 2000001

Temperature field for heatflux by convection

3000001

Heat flux 4000001


11-12 FINE™

11-2.4.2 Global Parameters

The user can complete the Outputs/ANSYS pages when the file ’project_ANSYS.cdb’ has been cre-ated (refer to section 11-2.4.1 for more details).

FIGURE 11.2.4-11General Parameters of ANSYS outputs

Firstly, the user needs to specify under the thumbnail Global Parameters in Boundary Conditions(Figure 11.2.4-11 - (1)) the coded constant value used in the file ’project_ANSYS.cdb’. The defaultcoded values are given in the table 11-3 for the different types of boundary condition. Furthermore,the user has to specify the required units of the data for each type of boundary condition. The unitswill be specified next to the coded value.

Then, the user needs to load the file ’project_ANSYS.cdb’ (Figure 11.2.4-11 - (2)) created inANSYS (refer to section 11-2.4.1 for more details) in Input File.

The data transfer between the CFD mesh and the structural mesh is possible if the commongeometries are matching. It is possible that this condition is not fulfilled and the causes can bediverse.

• the units: a first difference can come from the units of the meshes. Consequently the units usedin the ANSYS mesh must be specified in ANSYS Mesh Units. The conversion Factor will bededuced automatically (Figure 11.2.4-11 - (3)).

• the coordinate system: the second cause of mismatching is the use of different coordinate sys-tems (Figure 11.2.4-11 - (3)). For example, the original geometry can be only rotated for theCFD model so that the axial direction corresponds to the Z axis. The necessary change of coor-dinate will be done through the specification of the position of the coordinate center of theANSYS mesh in the coordinate system of the CFD mesh and the specification of the locationof three common points in both meshes in Reference System.

Note that these points cannot be located on a line or a plane including the zero point

(not linearly dependent). The coordinates are specified in their respective units.

(2)

(1)

(3)

(4)

(5)


FINE™ 11-13

The origin of the ANSYS mesh should be at (0,0,0).

Finally in Output File, the user specifies the new output file ’project_CFD.cdb’ (Figure 11.2.4-11 -(4)) containing the transferred CFD results on the solid boundaries coded in ANSYS (refer to sec-tion 11-2.4.1 for more details).

In order to create the new output file, the user has to complete the page under the Surface Selectionthumbnail before clicking on the Create Output File button (Figure 11.2.4-11 - (5)).

11-2.4.3 Surface Selection

After completion of the page under Global Parameters thumbnail, the user can complete the pageunder Surface Selection page (refer to section 11-2.4.2 for more details) before creating the ANSYSoutput file.

When the ANSYS input file is read in Input File, the common surfaces where data must be trans-ferred are identified in the ANSYS mesh. The interface FINE™ lists each surface with the corre-sponding coded value (Figure 11.2.4-12 - (1)).

For each detected surface of the structural ANSYS mesh, by clicking on Selected Surface Proper-ties button (Figure 11.2.4-12 - (2)), a new window (Figure 11.2.4-13) allows the user to specify thesolid patches from which the data will be interpolated and some interpolation parameters: interpola-tion type (Interp Type) and the allowed maximal distance (Max Dist).

FIGURE 11.2.4-12Surface Selection of ANSYS outputs

(2)

(1) (3)(4)


11-14 FINE™

Two different interpolation types (Interp Type) are proposed: a conservative and a non-conserva-tive. The suitable interpolation scheme is dependent on the type of boundary conditions. The spatialfield of pressure or temperature can be interpolated from cell faces to nodes whereas a conservativetransfer of the heat fluxes can be preferred.

An allowed maximal distance (Max Dist) can be used to control the interpolation process by ensur-ing that it is performed in the nearest element of the selected solid CFD patches.

FIGURE 11.2.4-13Add Solid Patches to ANSYS surface

Then, the user specifies the solid CFD patches in the list of Solid Patches by <Ctrl> or <Shift> andleft-click. To add or remove solid patches linked to the highlighted ANSYS surface, the buttonsAdd Selection and Remove Selected are respectively used. When the solid patches are well selected,the window has to be closed (Close) and the patches will appear in the list Selected Solid Patchesand Groups (Figure 11.2.4-12 - (3)).

Note that the ANSYS surface must be completely overlapped by the selected IGG

solid patches in order to ensure a complete data transfer.

The area of the selected IGG solid patches can be larger than the area of the ANSYS

surface.

Since the IGG™ solid patches defining a periodic structure can be divided (Figure 11.2.4-14), aperiodic shift can be required to match the common ANSYS surface. This shift must be specifiedfor each solid patch, highlighted in Selected Solid Patches and Groups list, in Periodicity by acti-vating Rotation and Translation (Figure 11.2.4-12-(4)). The rotation and translation shifts arerespectively specified degrees and IGG™ units mesh.

FIGURE 11.2.4-14Mesh differences IGG™ vs. ANSYS


FINE™ 11-15

Moreover one ANSYS surface can be covered by a group of solid patches and by the same grouprotated (or translated). Consequently, a duplication of the periodic solid patches is possible by acti-vating Duplicate patch(es) after applying a Rotation and Translation to the highlighted solid patch(Figure 11.2.4-12-(4)).

FIGURE 11.2.4-15Duplicate Option Utility

Finally, the new output file can be created by clicking on the Create Output File button (Figure11.2.4-11 - (5)).

11-2.5 Global Performance Output

The main results for global performance are summed up in a file with extension ’.mf’. Inlet and out-let averaged quantities, pressure ratios and efficiency are computed and stored in this file. The usercan select which and what kind of information is stored using expert parameters as described in sec-tion 11-3.2. In this section the default contents of the global performance output is described.

11-2.5.1 Solid Boundary Characteristics

This part of the file gives the characteristics of the quantities that are estimated at the solid bounda-

ries. Those quantities are inferred from the global force exerted by the flow

at a given point. This force can be estimated from the pressure and velocity fields at each point. Thecalculated quantities for an internal configuration are:

•Axial thrust, i.e. the projection of the global force on the rotation axis: .

• The projection of the torque along a given direction , i.e. the couple exerted by the global

force along direction . This direction is given through the expert parameter

IDCMP, the default value of which is (0,0,1).

For external flow configurations the expert parameter IINT must be set to 0 and the output file willcontain the quantities as described in section 11-3.2 instead of the axial thrust and the torque

F Fpressure Fviscous+=

F nz⋅S∑

z

r F×S∑

⎝ ⎠⎜ ⎟⎛ ⎞

z⋅ z


11-16 FINE™

11-2.5.2 Global Performance

Global performance data, available in the ’.mf’ file, are calculated using the results at the inlet andoutlet boundaries of the computational domain. The ’.mf’ file also provides global averages at eachrotor/stator interface. If the project does not involve any of these boundaries or interfaces, the ’.mf’file is empty.

For turbomachinery cases, the output includes an efficiency. Several definitions are available,selected through the expert parameter EFFDEF (default: 1).

For projects with a rotor, the expressions proposed in table 11-4 are used (index 1 and 2 refer to theinlet and exit sections respectively).

The same definitions can be applied to the real gas in the case IRGCON=0 but with instead of γ.

EFFDEF Compressors Turbines

1

2

3

TABLE 11-4 Isentropic and polytropic efficiency definitions for perfect gases

Compressors Turbines

TABLE 11-5 Isentropic efficiency definition for real gases with ct r (IRGCON=1)

The definitions in Table 11-5 correspond to real gases with IGRCON=1. The value of is

obtained from the temperature by using the isentropic relation: .

pt2>pt1 pt2<pt1

ηis

pt2

pt1

------⎝ ⎠⎛ ⎞

γ 1–γ

-----------

1–

Tt2

Tt1

------- 1–

-----------------------------= ηpolRcp

----

pt2

pt1------

⎝ ⎠⎛ ⎞ln

Tt2

Tt1-------

⎝ ⎠⎛ ⎞ln

------------------⋅= ηis

1Tt2

Tt1

-------–

1pt2

pt1

------⎝ ⎠⎛ ⎞

γ 1–γ

-----------

–

-----------------------------= ηpol

cp

R----

Tt2

Tt1-------

⎝ ⎠⎛ ⎞ln

pt2

pt1------

⎝ ⎠⎛ ⎞ln

------------------⋅=

ηis

p2

pt1

------⎝ ⎠⎛ ⎞

γ 1–γ

-----------

1–

T2

Tt1

------- 1–

-----------------------------= ηpolRcp

----

p2

pt1

------⎝ ⎠⎛ ⎞ln

T2

Tt1

-------⎝ ⎠⎛ ⎞ln

------------------⋅= ηis

1T2

Tt1

-------–

1p2

pt1------

⎝ ⎠⎛ ⎞

γ 1–γ

-----------

–

-----------------------------= ηpol

cp

R----

T2

Tt1

-------⎝ ⎠⎛ ⎞ln

p2

pt1

------⎝ ⎠⎛ ⎞ln

------------------⋅=

ηis

p2

p1

-----⎝ ⎠⎛ ⎞

γ 1–γ

-----------

1–

T2

T1

----- 1–

----------------------------= ηpolRcp

----

p2

p1

-----⎝ ⎠⎛ ⎞ln

T2

T1

-----⎝ ⎠⎛ ⎞ln

-----------------⋅= ηis

1T2

T1

-----–

1p2

p1

-----⎝ ⎠⎛ ⎞

γ 1–γ

-----------

–

----------------------------= ηpol

cp

R----

T2

T1

-----⎝ ⎠⎛ ⎞ln

p2

p1

-----⎝ ⎠⎛ ⎞ln

-----------------⋅=

γ

pt2>pt1 pt2<pt1

ηis

h02is

h01–

h02 h01–--------------------= ηis

h02 h01–

h02is h01–

--------------------=

h02is

T02is Cp

T0------ T0d

1

2 is

∫r

P0------ P0d

1

2is

∫=


FINE™ 11-17

Expressions involving the Torque in Table 11-6 are computed only if the user activates the optionCompute force and torque in the Boundary Condition page devoted to solid surfaces.

For non rotating projects (pure stator), the following expression is used to define the efficiency:

. (11-1)

Finally, relative and absolute flow angles are derived from the averaged velocity components:

, (11-2)

. (11-3)

11-2.6 Plot3D Formatted Output

On the Computed Variables page it is possible to select Plot3D output to be created according to thefile format described in Appendix B. The user may select between a ASCII format or Fortran unfor-matted format.

When selecting the Unformatted file (binary) option use the corresponding option in

CFView™ to open the file: click on the File Format... button in the menu File/OpenPlot3D Project... and select Unformatted. Do not select Binary format. In CFView™ theuser needs to select also little endian or big endian formats. On PC platforms (Windowsand LINUX) select binary low endian and on all other platforms select binary bigendian.

EFFDEF Pumps Turbines

1

2

3

TABLE 11-6 Efficiency definitions for liquids (incompressible flows)

pt2>pt1 pt2<pt1

η∆ptm·

ρω Torque⋅-------------------------------= η ρω Torque⋅

∆ptm·-------------------------------=

η ∆pm·

ρω Torque⋅-------------------------------= η ρω Torque⋅

∆pm·-------------------------------=

η∆ptm·

ρCp∆Tt

--------------------= ηρCp∆Tt

∆ptm·--------------------=

ηpt2 p2–

pt1 p2–------------------=

α arcvθ

Vm

------⎝ ⎠⎛ ⎞tan= β arc

wθ

Vm

------⎝ ⎠⎛ ⎞tan= cylindrical

α arcvy

vx

----⎝ ⎠⎛ ⎞tan= β arc

wy

wx

------⎝ ⎠⎛ ⎞tan= cartesian

Output Expert Parameters for Output Selection

11-18 FINE™

11-3 Expert Parameters for Output Selection


In expert mode the user may specify on the bottom of the Azimuthal Averaged Variables page the‘averaging patches’ of the 3D mesh used to define the mesh surface that will be projected onto themeridional plane in order to support the azimuthal averaged variables. A default selection is auto-matically presented for AutoGrid meshes. Four input boxes are provided to enter the number ofpatches, the index of the patch being defined, the block number and six indices to define the patch.For instance, the six indices: 1 1 1 65 1 129, define a patch of a given block corresponding to a faceI = 1 and for J =1 to 65 and K=1 to 129.

The same system is used to define blade patches that will simply be projected in the meridionalplane to visualize the variables on the blade pressure side or suction side.

The indices must be defined on the finest mesh.

MERMAR: Safety margin for azimuthal averaged CFView™ solution. The mesh is shrunkwith a factor of 1.- MERMAR.

1st entry = axial safety margin 2nd entry = radial safety margin

The purpose of these two margins is to avoid points near the boundaries for which the azimuthalaveraging can not be performed. In general the azimuthal averaging is performed by taking a pointon the defined patch and to average the values for points in azimuthal direction starting from thispoint. If there is not a sufficient amount of points in azimuthal direction the average is not com-puted for that point and therefore the value for this point is not represented in CFView™. To avoidsuch ’blank’ points near the edges of the patches it may be necessary to take a certain margin fromthe edges of the patches.

The default values for the safety margins are appropriate for meshes on surfaces of revolution. Ifthe mesh is not a mesh on surfaces of revolution higher margins may be required. See section 11-4.3 for more detailed information on the methods available for azimuthal averaging and the use ofthese margins.

Use of the 3rd and 4th entry is not supported.


To influence the type of output written in the file with extension .mf the following expert parame-ters can be used:

EFFDEF: Efficiency definition for projects with at least one rotating block:

= 1: total to total,

= 2: total to static,

= 3: static to static.

OUTTYP: Select the type of output:

= 1: torque and drag,

= 2: heat flux and energy,

Expert Parameters for Output Selection Output

FINE™ 11-19

IINT: Type of flow:

= 0: internal flow,

= 1: external flow.

For external cases the following output is written in the global performance output file:

•Drag coefficient, i.e. normalized projection of the global force in a chosen direction:

.

• Lift coefficient, i.e. normalized projection of the global force in a chosen direction, generally

perpendicular to that used for the Drag coefficient: .

•Momentum, i.e. normalized projection of the torque in a chosen direction (default 0, 0, 1):

.

In the above equations, S is the surface of the selected patch(es), and are user defined ref-

erence density and velocity (see the Flow Model menu of the FINE™ interface). is a surface of

reference for which the default value SREF is set to 1 m2 and is a length of reference for which

the default value CREF is set to 1. are normalized vectors used for the Drag, Lift and

Momentum coefficient and defined through the expert parameters IDCDP, IDCLP and IDCMP.Their default value is (0., 0., 1.). r is the distance from the reference point IXMP (default value: 0.,

0., 0.). is the normalized vector directed along the rotation axis. The parameters mentioned herecan be changed in the Computational steering/Control variables page in expert mode.

IWRIT: Add some additional output on all block faces such as mass flow through these faces:

= 0: deactivated,

= 1: mass flow through rotor/stator interfaces,

= 3: summarizes the mass flow through different boundary types (SOL, ROT, INL,...),

= 4: mass flow through all block faces.

SREF: Reference area to non-dimensionalize the lift, drag and momentum, to get respectively thelift coefficient, drag coefficient, moment coefficient. The default SREF=1.

CREF: Reference chord to non-dimensionalize the calculated moment, to get the moment coeffi-cient.

IDCDP: This parameter gives the direction (i.e. 3 values) on which the body force has to be pro-jected to give the axial thrust or the drag component. E.g. 1,0,0 means that the drag is the x-component of the body force.

IDCLP: For flows around bodies this parameter gives the direction (i.e. 3 values) on which the bodyforce has to be projected to give the lift component. E.g. 1,0,0 means that the lift is the x-component of the body force. For internal (IINT=1) cylindrical cases this parameter is notused.

F n1 0.5ρrefUref2

Sref( )⁄⋅S∑

F n2 0.5ρrefUref2

Sref( )⁄⋅S∑

r F×S∑

⎝ ⎠⎜ ⎟⎛ ⎞

n3⋅⎝ ⎠⎜ ⎟⎛ ⎞

0.5ρrefUref2

SrefCref( )⁄

ρref Uref

Sref

Cref

n1 n2 n3, ,

nz

Output Theory

11-20 FINE™

IDCMP: This parameter gives the direction (i.e. 3 values) on which the moment vector on the bodyhas to be projected to give the moment. E.g. 1,0,0 means that the moment is the x-compo-nent of the moment vector.

IXMP: Specifies the x,y,z coordinate of the point around which the moment has to be calculated.

11-4 Theory

11-4.1 Computed Variables

The flow solution is stored in the .cgns file and will be used for the 3D CFView™ output.CFView™ requires a cell-vertex representation of the flow solution, i.e. the flow variables need tobe provided at the mesh nodes. Since EURANUS considers the flow variables at cell centres, aninterpolation process is performed by the flow solver in order to compute the flow variables at themesh nodes.

The required interpolation of the flow solution is done by arithmetic averaging. If represents one

of the primitive variables and the interpolated value,

, (11-4)

where the summation is over the eight surrounding original locations of the respective variable. Thebasic flow variables are calculated at the mesh nodes using the above procedure. Derived quantities

are computed from this consistent representation of solution and geometry. By

contrast, if a quantity involves the surface normals, these are first calculated on the cell faces of theoriginal mesh and then averaged to the required location. Other exceptions are quantities involvinggradients or which are provided by the code:

• The Cartesian components of are computed in the cell corners,

. (11-5)

• If a cylindrical component is requested, transformation to cylindrical coordinates is done at the

cell corners, as is the calculation of . Only then are the requested component, the vec-tor or its magnitude interpolated to the desired mesh.

• Some of the variables used in the turbulence models are provided by the code in the cell cor-

ners and treated in the same way as the coordinates (wall distance, , ).

If a two equation turbulence model is used, and are additional variables treated in the sameway as the primitive variables. The residuals too, are provided by the code in the cell centres andtherefore treated in the same way as the primitive variables, with the difference that they are onlydefined in the interior and thus copied to the dummy cells as described above.

The above described arithmetic averaging process used to construct the CFView™ solution is firstorder accurate, which has an important consequence if the user wants to extract quantitative globalquantities:

u

ρ wx wy wz p, , , , u

u18--- ui

i 1=

8

∑=

vr pt H s ..., , , ,( )

∇ W×

∇ V× ∇ W× 2ωsystem+=

∇ W×

y+ µt

k ε

Theory Output

FINE™ 11-21

In case of high flow gradients the calculation within CFView™ of the average (sur-

face integral) of a given quantity throughout an I, J or K=constant surface of the mesh ora cutting plane will be performed with an error with respect to the flow solution calcu-lated by the flow solver.

11-4.2 Surface Averaged Variables

The procedure generates a multi-column file with indices, coordinates and the streamwise evolutionof the requested variables, averaged on mesh surfaces normal to the streamwise direction. This filecan be processed for plotting versus the index, the coordinates , or and the meridional dis-tance.

Mass or area averaging can be requested for each variable individually.

FIGURE 11.4.2-16 Stencil for 1D averaged flow. The numbers are the relative weight of each cell in the contribution of the central cell to the surface average.

The weight coefficients are computed on the cell face centres (index ), since this is the naturallocation of the required surface normals, yielding:

. (11-6)

The surface average is then calculated as

, (11-7)

where or . The stencil shown in Figure 11.4.2-16 illustrates that the contributions

from the cell face centre at a boundary contain some influence from the lateral dummy cells (weight1/4).


Exact azimuthal-averaging for general configurations requires a mechanism that is independent ofthe computational grid. First a meridional mesh must be defined to support the azimuthal-averagedsolution. Secondly, the latter must be extracted from the 3D computational mesh. The 2D mesh isprovided by the meridional projection of any suitable contiguous set of sub-surfaces contained in

x r z

F

m· F14--- qcorner

four corners

∑=

q1

wF

cell face centres

∑--------------------------------------- wFqF

cell face centres

∑=

wF m· F= AF

Output Theory

11-22 FINE™

the volumetric mesh. The domains and indices defining these sub-surfaces are provided in the inputfile. Choosing sub-surfaces of the actual 3D mesh ensures that the resolution of the meridionalmesh is commensurate with the accuracy of the numerical solution.

Starting from each point of the meridional mesh, the solution is defined by the primitive var-

iables averaged along a circular arc passing through that point,

(11-8)

where denotes the azimuthal-average of the generic variable and where

(11-9)

is the meridional velocity. Either mass or area averaging can be requested, but the

same type of averaging will be used for all the primitive variables.

The integrals in Eq. 11-8 are approximated by trapezoidal sums. Practically, the -constant line

along which the integration proceeds may be composed of fragments of data points,

, so that Eq. 11-8 is evaluated as:

, (11-10)

with

(11-11)

and

(11-12)

All requested variables are derived, if possible, from the azimuthal-averaged primitive variables.Those variables that can not be computed from the azimuthal-averaged primitive variables are com-puted first. The fact that they are computed by the same routines that are used for generating 3DCFView™ output ensures consistency. The suction and pressure side of the blades can be superim-posed on the azimuthal averaged view.

For meshes that do not lie on surfaces of revolution the accuracy of the averaged solution isdecreased close to curved boundaries (see Figure 11.4.3-17). Although all boundary grid points lieon the same surface of revolution, the straight line segments forming the cell edges do not. The

-constant ray associated with point 1 will therefore miss some cell faces or pick values from theinside instead of boundary values. In the worst case it will not encounter any cell faces at all. Strongcurvature and cells with high aspect ratio increase the inaccuracy.

This problem has been addressed in two ways. First, meridional grid points encountering fewer thantwo cell faces are set to zero (a message printed to the screen indicates for how many points this

r z,( )ρ wr wθ wz p, , , ,

u1

w θd∫-------------- wu θd∫=

u u

wρVm for mass averaging

1 for area averaging⎩⎨⎧

=

Vm vr2

vz2+=

r z,k n j( )

j 1 ...,k,=

u aijuij

i 1=

n j( )

∑j 1=

k

∑=

aij bij

Σi 1=n j( )

bij

Σj 1=k Σi 1=

n j( ) bij

-------------------------------=

bi

2wi θ2 θ1–

wi θi 1+ θi 1––

2wi θn θn 1––⎩⎪⎨⎪⎧

=

i 1=

i 2 ..., n-1,=

i n=

r z,

Theory Output

FINE™ 11-23

was necessary). Secondly, the possibility is provided to shrink the meridional mesh by a smallamount to avoid the outermost regions of the volumetric mesh as shown in Figure 11.4.3-18. Inde-

pendent shrink factors can be specified in the streamwise and spanwise directions using theexpert parameter MERMAR. Figure 11.4.3-18 illustrates the global effect. Each mesh line is shrankindividually by uniformly contracting towards its centre. The grid points thereby slide along thesegments of the original line (dashed line in Figure 11.4.3-18).

FIGURE 11.4.3-17Azimuthal-averaging along circular arcs at curved boundary (light lines = meridional mesh supporting the azimuthal-averaged solution, heavy lines = an arbitrary

cell face of the computational mesh), situation (a) before shrinking and (b) after shrinking.

FIGURE 11.4.3-18: Shrinking of the meridional mesh, schematic illustration of (a) the global effect and (b) the modification applied to each mesh line (dashed line and circles = original

line, solid line and squares = shrank line, C = centre point of the original line)

k

a) b)1

2

1

2

kh/2

h

a

b

Output Theory

11-24 FINE™


The surface integrals are approximated by rectangular sums: for any vector quantity and scalar

quantity ,

(11-13)

The index B indicates a boundary cell face centre value, obtained by averaging the coordinates

of the four corners:

(11-14)

and the solution in the first inner (index 1) and first outer cell (index 0):

. (11-15)

All variables except flow angles are first computed locally from this consistent representation ofsolution and geometry and then summed, multiplied by the appropriate weight factor

or . Averages are calculated for the following variables:

.

Static pressure is area averaged, all other variables are mass averaged. Explicitly, representing

any of the enumerated scalars (other than ) and its average:

. (11-16)

The mass flow is obtained from Eq. 11-13 with , the area with . The values

of are also computed from and the averaged velocity components

to be compared with the directly averaged values.

Q

q

Q Sd

surface1/2

∫ QBSB

cell faces

∑= q Sd

surface1/ 2

∫ qB SB

cell faces

∑=

r x y z, ,=( )

rB14--- ri

i 1=

4

∑=

U ρ wx wy wz p, , , ,=( )

UB12--- U0 U1+[ ]=

m· B ρWS( )B= AB S B=

wx wy wz wr wt vx vy vz vr vt W VVS

S------- p ρ pt rel, pt abs, pt rot, Tt rel, Tt abs, Tt rot,, , , , , , , , , , , , , , , , , , , ,

q

p q

q1m·---- m· BqB

cell faces

∑= p1A--- ABpB

cell faces

∑=

m· Q ρW= A q 1=

pt rel, pt abs, Tt rel, Tt abs,, , , p ρ,

FINE™ 12-1

CHAPTER 12:Blade to Blade Module

12-1 OverviewThis chapter describes the quasi-three-dimensional Blade-to-Blade Module for turbomachinery cas-cade analysis. The module is fully automatic and can be used (and acquired) independently fromthe other NUMECA tools.

Furthermore, an additional module is associated with the present one, called FINE™/Design2D,which permits to redesign the blades for an improved pressure distribution on the blade surfacesand is presented in Chapter 13.

The module assumes that the flow in the turbomachinery cascade remains on an axisymmetricstreamsurface, whose shape and thickness can either be provided by the user, or automatically con-structed by the module (using the given hub and shroud walls).

The geometrical input data required from the user can be:

1. The streamsurface and the blade section on this last surface or,

2. The whole three-dimensional blade shape and the hub and shroud walls.

The module comprises a fully automatic mesh generator (which is able to treat any type of meridi-onal configuration) and a customised version of NUMECA’s turbulent Navier-Stokes flow solver.

In the next section the interface is described in detail including advice for use of the Blade-to-BladeModule. The theoretical background for the mesh generator and the flow solver is described in sec-tion 12-4. Finally, the Blade-to-Blade Module requires geometrical data files and generates output,which are detailed in section 12-5.

The Design 2D module can not be used with:

• other turbulence models than Baldwin Lomax turbulence model,

• upwind scheme,

• real gas,

• unsteady computations,

• azimuthal averaged output.

Blade to Blade Module Blade-to-Blade in the FINE™ Interface

12-2 FINE™

12-2 Blade-to-Blade in the FINE™ InterfaceThe Blade-to-Blade Module is proposed under the FINE™/Design 2D interface through the menuModules/Design 2D., which permits a very rapid, easy and interactive use of the solver. All theparameters can be selected interactively through this user interface, which automatically creates theinput files and permits to launch the solver.

A monitoring tool, called the MonitorTurbo, can be launched to verify the convergence and resultsduring and after the computation. It permits to observe the evolution of the convergence history, ofthe pressure distribution along the blade surface, and of the blade geometry.

The results can be analysed with the NUMECA CFView™ post-processing software, whose con-nection with the Blade-to-Blade Module is automatically provided.

The geometrical data are specified in ASCII input files, whereas the definition of the flow solverparameters and of the boundary conditions are specified via the interface.

This section describes the creation of the solver input files using the interactive menus included inthe FINE™/Design2D interface. Further details concerning the input and output files are providedin section 12-5.

12-2.1 Start New or Open existing Blade-to-Blade Computation

When starting the interface a Project Selection window allows to Create a New Project or to Openan Existing Project. To create a new Blade-to-Blade project:

1. click on the button Create a New Project.

2. Browse to the directory in which the new project directory needs to be created and enter a namefor the project.

3. Close the Grid File Selection window since no grid file is associated to a Design 2D project.

4. Switch to the Blade-to-Blade module through the menu Modules/Design 2D.

When an existing Blade-to-Blade project should be opened click on the button Open an ExistingProject in the Project Selection window and select the project in the File Chooser window. Themost recently used projects can also be selected from the list of recent projects. If the selectedproject was saved in the Design 2D module, the FINE™ interface is automatically switched to thismodule showing the interface as in Figure 12.2.1-1.

It is not possible to have Blade-to-Blade and three-dimensional computations in one

project. A project is either a Blade-to-Blade project or a FINE™/Turbo project. The typeof the project is determined by the module in which it is saved.

The FINE™/Design 2D interface is the same as the FINE™/Turbo interface and contains a menubar, an icon bar, a computations definition and a parameters area. The menu bar is the same in bothmodules, except for the Modules menu that allows to switch to the other available modules. Theicon bar in the Design 2D module contains only the icons applicable for a 2D computation. The listof Parameters pages on the left of the interface is updated according to a 2D computation. Most ofthe pages are the same as in a FINE™/Turbo project. The only differences are in:

• the Flow Model page: the Design 2D module can not be used in unsteady,

• the Boundary Conditions page as described in section 12-2.3,

• the Blade-to-blade Data pages as described in section 12-2.2,

• the Initial Solution page as described in section 12-2.5.

Blade-to-Blade in the FINE™ Interface Blade to Blade Module

FINE™ 12-3

FIGURE 12.2.1-1 Design 2D in the FINE™ interface

12-2.2 Blade-to-Blade Data

Three specific menus appear in the Blade-to-blade Data page:

• Blade Geometry, see section 12-2.2.1,

•Mesh Generation Parameters,

• Inverse Design: parameters that are only used in 2D design but not in blade-to-blade analysis.Inverse design is described in Chapter 13.

The blade geometry and the axisymmetric streamsurface (or hub and shroud walls) are specifiedunder the form of a series of data points given in ASCII files, whose structure is described in sec-tion 12-5.

All geometrical data has to be given in the same length unit (which can be chosen arbitrarily). Thechosen length unit is defined under the Blade geometry thumbnail on the Blade Geometry page.

12-2.2.1 Blade Geometry Definition

Three types of geometrical input data are possible:

- 2D type: This first option is valid only for purely axial cases, in which the stream surface is a cyl-inder (constant radius). The blade geometry is then given on the cascade plane (cylinderdeveloped to generate the cascade).

- Q3D type (quasi 3-dimensional): The axisymmetric stream surface is given (including its thick-ness), and the blade geometry is specified on the given surface.

- 3D type (from hub to shroud): The whole 3D blade geometry is given under the form of a series ofblade sections (minimum 2, ordered from the hub to the shroud). The hub and theshroud walls are also specified. The stream surface can either be specified by the user(the lower and the upper axisymmetric surfaces have to be specified), or can be automat-ically constructed by the solver (geometrical division). In the latter case, the user onlyhas to specify the spanwise position of the stream surface and its relative thickness.


12-4 FINE™

- 3D type (from .geomTurbo file): The whole 3D blade geometry is given under the form of ageometry turbo file containing the hub, shroud and blade definition (more details inAutoGrid User Manual). The stream surface can either be specified by the user (thelower and the upper axisymmetric surfaces have to be specified), or can be automati-cally constructed by the solver (geometrical division). In the latter case, the user onlyhas to specify the spanwise position of the stream surface and its relative thickness.

a) Streamsurface Data

Figure 12.2.2-2 shows the Parameter area for entering Stream surface data. The following streamsurface data files have to be specified, depending on the type of input data:

• 2D or Q3D types: stream surface definition file name,

• 3D case: hub and shroud file names or .geomTurbo file name.

When the 3D type of input data is selected additional parameters have to be defined:

• - Geometrical division or streamtube provided by the user.

• - If geometrical division: spanwise position between 0 (hub) and 1 (shroud).

• - If streamtube provided: lower and upper surfaces file names (2 lines).

FIGURE 12.2.2-2 Streamsurface parameters area

In both cases the module automatically calculates the intersection of the 3D blade with the consid-ered stream surface.

2D&Q3D:

3D:


FINE™ 12-5

In a 3D case with geometrical division, the streamtube height defines the thickness of the stream-tube (the recommended value is 1%).

In a 2D, Q3D or 3D case with streamtube provided, the blockage ratio permits to scale the stream-tube thickness distribution.

For all types of input data the number of points along meridional stream surfaces has to be speci-fied. This input data is the number of points that the module will generate along the streamsurfacein order to obtain an accurate calculation of the meridional coordinate (default: 300).

b) Blade Geometry Data

Selecting the Blade geometry thumbnail allows to define the characteristics of the blades and thefiles where the data is stored:

•Blade geometry file names.

— 2D or Q3D: suction and pressure side file names,

— 3D case (from hub to shroud): number of spanwise section and for each section, suction andpressure sides file names.

— 3D case (from .geomTurbo file): the whole 3D blade geometry is given under the form of ageometry turbo file (more details in AutoGrid User Manual).

•Blunt leading edge: if active, indicates that the leading edge is blunt.

•Blunt trailing edge: if active, indicates that the trailing edge is blunt.

• Splitter blades:

— If the "splitter" button is selected, the blade geometry input file names have to be given forthe splitter blades. In a 3D case (from hub to shroud), the number of spanwise sectionsshould be identical for the main and splitter blades, and is not repeated here.

• Length unit: The user can define the geometrical data in any length unit, and simply has todefine by means of this scale the ratio between the meters and the chosen unit length (if theinput is in millimetres, the ratio must be 0.001). All the geometrical data must be given in thesame unit length chosen by the user.

•Number of blades or pitch distance. In a 2D input type, this input is the pitch distance (in theunit length chosen by the user), whereas in a Q3D or 3D case (from hub to shroud), it must bethe number of blades (Figure 12.2.2-3).

FIGURE 12.2.2-3 Blade geometry information page for 3D cases (from hub to shroud)

3D


12-6 FINE™

c) Blade Data Edition

Selecting the Blade data edition thumbnail permits to edit the position of the leading and/or trailingedge among the data points provided by the user in the input files (see Figure 12.2.2-4).

For both leading and trailing edges the user has to specify if the leading or trailing edge is on thesuction side or pressure side, and to give also its position (starting from the initial position). There-fore a value of 1 will not modify the edge position.

In a 2D or Q3D case this operation is performed on the data points provided by the user, whereas ina 3D case it is performed on the blade points resulting from the 3D interpolation process. In anycase the data points can be visualised by plotting the "projectname.b2b.geoini" file using the Moni-torTurbo. The way to visualise the data points in order to decide whether the position of the edges isacceptable is to launch the analysis module and to visualise the ".geoini" file.

FIGURE 12.2.2-4 Blade data edition thumbnail

12-2.2.2 Mesh Generation Parameters Page

The different Mesh generation parameters (as shown in Figure 12.2.2-5) do not necessarily have tobe modified by the user. They have been set to default values, which have shown to be efficient inmany cases.

The available Mesh generation parameters are:

•H(periodic)- or I(non periodic) -type mesh: The user defines if the upstream and/or the down-stream region should be inclined (non periodic, which permits to improve the orthogonality ofthe mesh cells to the flow) or not.

•Generation mode: fully automatic or semi-automatic:

— In the fully automatic mode, the user only has to specify the number of points along the suc-tion side. The number of points in the other segments are then calculated in order to ensurethe smoothness of the mesh (the number of cells in each patch is always a multiple of 8, sothat 4 multigrid levels are available for the solver).

— In the semi-automatic mode, the user decides to specify the inclination angles of theupstream/downstream boundaries (radians), as well as the number of cells in each of the seg-ments of the mesh. The number of input data depends on the number of segments, which canbe 3 if the upstream/downstream boundaries are not inclined, 4 if one of them is inclined,and 5 if both are inclined. The number of cells in each segment should be chosen so that theyare always a multiple of 8 (four multigrid levels are available for the flow solver). In a casewith splitters the number of segments is 4 or 5 (if the downstream periodic boundaries arenon periodic), and the numbers of cells should be specified for both blade passages.


FINE™ 12-7

.

FIGURE 12.2.2-5 Mesh generation parameters information page

•Number of points in the pitchwise direction: The number of cells should better be a multiple of8, so that four multigrid levels are available.

• Periodic boundaries type: the user defines if the periodic lines should be straight or curved. Inthe default configuration the periodic lines are curved.

• Five thumbnails give access to parameters to influence the mesh quality and points distributionas described in the next paragraphs.

a) Inlet

The inlet location of the mesh is imposed on the hub and the shroud. The position is specified inmeridional coordinates (Z, R) or in spanwise coordinate (S).

b) Outlet

The outlet location of the mesh is imposed on the hub and the shroud. The position is specified inmeridional coordinates (Z, R) or in spanwise coordinate (S).

c) Clustering

The clustering coefficient in streamwise direction can be imposed from 0.0 to 1.0. A value of 1.0gives a uniform distribution, whereas a 0.0 value concentrates all the points at the edges.

The second input defines if an Euler (no clustering in pitchwise direction) or a Navier-Stokes mesh(with clustering to capture the boundary layer) should be generated. For a Navier-Stokes mesh thefollowing parameters should be specified:

• Size of the first mesh cell in the pitchwise direction (in meters).

•Number of constantly spaced cells in the pitchwise direction.


12-8 FINE™

•Constant or decreasing clustering from the blade edges to the inflow/outflow boundaries.

d) Smoothing

An elliptic smoother can be used in order to improve the quality of the mesh. In case the smoothingis selected, the user has to specify if the smoothing should be performed with or without the controlof the clustering along the walls, and the number of smoothing steps (sweeps) to be performed (seeFigure 12.2.2-6).

FIGURE 12.2.2-6 Smoothing page of the Mesh generation parameters page

e) Local Pre-smoothing

A local pre-smoothing can be performed in the leading and trailing edge regions, which can beappropriate in cases of thick rounded leading and/or trailing edges (Figure 12.2.2-7).

FIGURE 12.2.2-7 Local pre-smoothing page of the Mesh generation parameters page

12-2.2.3 Inverse Design Menu

This menu concerns the inverse design module. The parameters included in this menu do not haveto be specified when performing a flow analysis. A description on the Inverse design module is pro-vided in Chapter 13.

12-2.3 Boundary Conditions

The Boundary Conditions page allows to define the boundary conditions at the inlet and the outletas well as the rotational speed.

The Rotational speed must be given in RPM (revolutions per minute, positive if oriented in the θ-direction, see Figure 12.5.1-12 on page 15)

12-2.3.1 Inlet Boundary Conditions

Eight inlet boundary conditions are available:

•Direction of absolute velocity (radians) + absolute total conditions (Pa, K).

•Direction of relative velocity (radians) + relative total conditions (Pa, K).

•Absolute Vθ velocity component (m/s) + absolute total conditions (Pa, K).

•Relative Wθ velocity component (m/s) + relative total conditions (Pa, K).


FINE™ 12-9

•Mass flow (kg/s) + direction of absolute velocity (radians) + static temperature (K).

•Mass flow (kg/s) + direction of relative velocity (radians) + static temperature (K).

•Mass flow (kg/s) + absolute Vθ velocity component (m/s) + static temperature (K).

•Mass flow (kg/s) + relative Wθ velocity component (m/s) + static temperature (K).

Selecting one of these options activates a submenu in which the user can set the inlet values. Anexample corresponding to a ’Direction of absolute velocity + absolute total conditions’ is shown infigure 12.2.3-8.

FIGURE 12.2.3-8 Inlet boundary conditions information page

12-2.3.2 Outlet Boundary Conditions

Three outlet boundary conditions are available at the outlet (Figure 12.2.3-9):

• exit static pressure imposed (Pa),

•mass flow imposed (kg/s) (+ exit static pressure required to initiate the calculation),

• supersonic exit (exit static pressure required to initiate the calculation).

FIGURE 12.2.3-9 Outlet boundary conditions information page

Both zero and first order extrapolation techniques are available, and can be selected in the Expertmode (the default technique is the zero-order one).


12-10 FINE™

It should be mentioned that the inverse design method is more stable when the mass flow is explic-itly imposed as a boundary condition. Therefore it is recommended to impose the mass flow duringthe analysis also. The recommended strategies are therefore the one imposing the mass flow at theinlet and the pressure at the outlet, or the one imposing the total conditions at the inlet and the massflow at the outlet.

12-2.4 Numerical Model

In general the default values for the Numerical Model parameters are appropriate.

In the blade-to-blade module it is not possible to perform the calculations on a coarser mesh levelas it is the case with 3D projects.

12-2.5 Initial Solution Menu

A turbomachinery-oriented initial solution construction strategy is automatically used, whichrequires an approximation of the inlet static pressure to be provided by the user or an Initial solu-tion file provided by the user (Figure 12.2.5-10)

FIGURE 12.2.5-10 Initial solution page

12-2.6 Output Parameters

This menu permits to select the different flow variables to be included in the output. The moduleautomatically creates the outputs for a 3D and a 2D (in the m,θ plane) CFView™ project. Furthercomments about this menu are provided in section 12-5.2.

12-2.7 Control Variables Page

On the Control Variables page the user defines if a flow analysis or an inverse design should beperformed (Figure 12.2.7-11).

All other parameters on this page are the same as for a FINE™/Turbo computation as described inChapter 15.

FIGURE 12.2.7-11 Run type page of the information area

Expert Parameters Blade to Blade Module

FINE™ 12-11

12-2.8 Launch Blade-to-Blade Flow Analysis

Once the ".run" has been correctly created through the menu File/Save Run Files, a flow analysiscan be started, by pressing the Start button in the Solver menu.

A restart from a previous calculation is also possible by pressing the Start button in the Solver menuand selecting an initial solution file in the page Initial Solution. As calculations on coarser grid lev-els are not possible, a restart can never be performed with the full-multigrid option.

12-3 Expert ParametersA series of expert parameters can be specified in Expert Mode on the Control Variables page.:

ITFRZ: the number of iterations after which the turbulent viscosity field is frozen. It is recom-mended to use this option (ITFRZ=200 for instance) in order to eliminate the spuriousresidual oscillations due to the turbulent quantities fluctuations.

IATFRZ: this switch is related to the previous one. It should usually be set to 1 (default value).However in the case of a restart and if the turbulent viscosity field has been frozen in theprevious calculation, this switch should be to 2, so that the previous turbulent viscosity fieldis read from the previous calculation and kept unchanged.

In the case the initial solution has been obtained with a frozen turbulent viscosity field

(using the ITFRZ expert parameter), the parameter IATFRZ should be set to 2 in order toread the turbulent viscosity field from a file and to keep this field unchanged.

12-4 TheoryThe main characteristics of the mesh generation tool and of the blade-to-blade flow solver are pro-vided in this section.

12-4.1 Mesh Generator

The mesh generator is a fully automatic tool customised for blade-to-blade applications, generatingH(periodic)- or I(non periodic)-type grids (see the AutoGrid manual) starting from a minimumamount of information from the user.

Contrary to many quasi-3D methods that solve the flow equations on a 2D mesh constructed on theaxisymmetric streamsurface, the mesh generated here is a 3D-mesh with only 1 cell in the spanwisedirection. This approach permits to use a 3D flow solver without major adaptation. Another advan-tage is that the effects of the eventual streamtube thickness variations are then implicitly taken intoaccount, and do no longer have to be introduced under the form of additional source terms in theequations.

The main characteristics of the generator are the following ones:

• can be applied to any type of meridional configuration (axial, radial and mixed flow machines,return channels...),

• treatment of blunt leading and trailing edges,

Blade to Blade Module Theory

12-12 FINE™

• splitters can be modelled,

• generation of H- and I-type (H non periodic) meshes,

• possibility to have an inclined mesh (non periodic) in both upstream and downstream regions,or only in the upstream or downstream region,

• general mesh generation process, which allows to consider the real leading and trailing edgesof the blade as the edges of the mesh, whereas in a classical H-mesh generator the edges (thepoints where the upstream/downstream boundaries intersect with the blade) are respectivelythe points located at the minimum and maximum x-position.,

• fully automatic tool: the only information required from the user is the number of points alongthe suction side and along the pitchwise direction. The number of points in the different seg-ments of the mesh as well as the inclination angles of the upstream and downstream regionsare calculated automatically.

12-4.2 Flow Solver

The flow solver included in the blade-to-blade module is a customised version of the EURANUSflow solver, with restricted functionalities in order to optimize the efficiency. The module can beapplied to compressible and incompressible flows.

The space discretization of the governing flow equations is based on a cell-centered control volumeapproach. To compute the various fluxes, a central scheme has been adopted, using Jameson typedissipation with 2nd and 4th order derivatives of the conservative variables. Turbulence of the flowis accounted for by means of the Baldwin-Lomax model.

The system of flow equations is solved explicitly using the 4-stage Runge-Kutta method. To accel-erate the flow solver convergence, various strategies are used:

•multigrid approach (V-cycle),

• full multigrid strategy, to initiate the resolution process,

• local time stepping,

• implicit residual smoothing.

A turbomachinery-oriented initial solution is automatically constructed to provide a fast and robustcalculation.

A particular boundary condition is applied along the upper and lower sides of the axisymmetricstreamtube, in order to force the flow to follow the streamsurface. For this purpose a spanwise pres-sure gradient is computed according to:

, (12-1)

where n is the spanwise direction, Vm and Vθ are respectively the meridional and tangential compo-nents of the absolute velocity, and δ and Rc are respectively the slope and the curvature radius ofthe meridional trace of the streamsurface.

A procedure is applied to the numerical scheme in order to force the flow to be aligned to thestreamsurface. This procedure eliminates the momentum residual in the direction normal to thestreamsurface. In case of multigrid the same procedure is applied to the flow solution after restric-tion and prolongation of the solution.

∂p∂n------ ρ

Vθ2

r------ δcos ρ

Vm2

Rc-------–=

File Formats used by Blade-to-Blade Module Blade to Blade Module

FINE™ 12-13

12-5 File Formats used by Blade-to-Blade Module

12-5.1 Input Files

The input files required for running a blade-to-blade study can be split into 3 categories:

• The geometrical input files, defining the blade geometry.

• The solver input file (.run), where the solver parameters and the fluid and flow conditions aredefined.

• The inverse design input files that allow to define an inverse problem.

The geometrical input files have to be created by the user, and are compatible with the AutoGridinput file formats.

The solver and inverse design input files are automatically created by the FINE™/Design 2D envi-ronment, the user has to set the parameters and flow conditions in the FINE™ interface. The nextsection describes the geometrical input files.

12-5.1.1 Geometrical Input Files

The blade geometry and the axisymmetric streamsurface (or hub and shroud walls) are specifiedunder the form of a series of data points given in ASCII files.

Three types of geometrical input data are possible:

• 2D type: This first option is valid only for purely axial cases, in which the streamsurface is acylinder (constant radius). The blade geometry is then given on the cascade plane (cylinderdeveloped to generate the cascade).

•Q3D type: The axisymmetric streamsurface is given (including its thickness), and the bladegeometry is specified on the given surface.

• - 3D type (from hub to shroud): The whole 3D blade geometry is given under the form of aseries of blade sections (minimum 2, ordered from the hub to the shroud). The hub and theshroud walls are also specified. The streamsurface can either be specified by the user (thelower and the upper axisymmetric surfaces have to be specified), or can be automatically con-structed by the solver (geometrical division). In the latter case, the user only has to specify thespanwise position of the streamsurface and its relative thickness.

• 3D type (from .geomTurbo file): The whole 3D blade geometry is given under the form of ageometry turbo file containing the hub, shroud and blade definition (more details in AutoGridUser Manual). The stream surface can either be specified by the user (the lower and the upperaxisymmetric surfaces have to be specified), or can be automatically constructed by the solver(geometrical division). In the latter case, the user only has to specify the spanwise position ofthe stream surface and its relative thickness.

All geometrical data has to be given in the same length unit (which can be chosen arbitrarily).

a) Streamsurface Data:

For the 2D and Q3D types, one ASCII file defining the surface and its thickness is required. For the3D type (form hub to shroud), 2 files are required to define the hub and shroud walls separately andfor the 3D type (from .geomTurbo), 1 file is required to define the hub, shroud and the blade. Incase the user wants to specify the streamsurface, 2 additional files are required to define the lowerand upper axisymmetric surfaces of the streamtube.

The structure of the streamsurface data file is the following:

Blade to Blade Module File Formats used by Blade-to-Blade Module

12-14 FINE™

— line 1: title of the input file

— line 2: coordinate system: ZRB (for 2D and Q3D types)ZR, RZ or XYZ (for 3D type)

— line 3: number of data points N

— lines 4 to 3+N: data points in 2 or 3 columns (ordered from the inlet to the outlet)

— line 4+N: character line (facultative)

— line 5+N: Zin, Zout, Rin, Rout, specifying the inlet/outlet positions of the mesh (facultative).

(X,Y,Z) are the Cartesian coordinates (Z being the axial coordinate along the axis of rotation), R isthe radius, and B is the streamtube thickness.

The inlet/outlet positions of the mesh can either be specified:

• in the above streamsurface data file(s) (lines 4+N and 5+N)

• through the FINE™ interface through the thumbnails Inlet and Outlet in the Mesh GenerationParameters page.

In both cases the inlet/outlet positions along a given surface are specified by four real data, i.e. Zin,Zout, Rin, Rout. No extrapolation is allowed, which implies that these positions should be locatedinside the meridional curve formed by the data points.

In a 2D or Q3D case, one single meridional position is required for both inlet and outlet boundaries,which are applied to the given streamsurface. These positions are either specified in the streamsur-face data file or through the 4 first real data contained in the expert parameter B2BLIM.

In a 3D case, two positions should be specified for the inlet/outlet positions. They are applied alongthe hub and shroud walls (geometrical creation of the streamtube), or along the upper/lower sur-faces of the streamtube (streamtube specified by the user). These positions can be given in the 2corresponding input files, or through the thumbnails Inlet and Outlet in the Mesh GenerationParameters page.

b) Blade Geometry Data

The blade geometry is specified by a series of sections (1 for 2D and Q3D cases, minimum 2 for a3D case) or by a ".geomTurbo" file. When the blade is defined by sections, each section comprises2 input files, respectively for the suction and the pressure sides.

The structure of the blade geometry data file is the following:

— line 1: title of the input file

— line 2: coordinate system: ZTR, ZTHR, RTZ, RTHZ, YXZ, ZXY or XYZ

— line 3: number of data points N

— lines 4 to 3+N: data points in 2 or 3 columns (ordered from the leading to the trailing edge)

(X,Y,Z) are the Cartesian coordinates (Z being the axial coordinate along the axis of rotation), R isthe radius, TH is the circumferential position (in radians) and T is the circumferential coordinatemultiplied by the radius (Rθ).


FINE™ 12-15

FIGURE 12.5.1-12 Coordinate system and reference for flow angles and speed of rotation

In a 2D case, if the ZTR coordinate system is used, the radius does not have to be specified in theblade geometry input file. The number of columns can be 2 or 3, the third column being not read bythe solver (the radius is automatically set to the value given in the streamsurface data input file).

The suction side is by convention located above the pressure side in the θ-direction

Figure 12.5.1-12. It does not necessarily have to be the physical suction side.

12-5.2 Output Files

Several output files are generated by the blade-to-blade module:

12-5.2.1 Geometry Files

a) ’project_computationname.geoini’ and ’project_computationname.geo’

These files contain the blade shape in the (m,θ) plane. The ’.geoini’ file contains the initial bladeshape as given in the input files (or resulting from the 3D interpolation process in a 3D case),whereas the ’.geo’ file contains the blade discretization points used in the computation.

These files can be read and plotted by the NUMECA MonitorTurbo (Blade profile menu).

b) ’project_computationname.merdat’, ’project_computationname.mer.ori’ and ’project_computationname.mer’

These files contain respectively the hub and shroud walls and the streamtube projection onto themeridional plane. The ’.merdat’ file contains the hub and shroud walls (3D case only), whereas the’.mer’ and ’.mer.ori’ files contain the streamtube.

These files can be read and plotted by the NUMECA MonitorTurbo (Blade profile menu).

c) ’project_computationname.ps.ori’ & ’project_computationname.ss.ori’

These files contain respectively the pressure side and the suction side of the blade.

W

RPM (<0)

z

θ

α < 0

β>0

V


12-16 FINE™

d) ’project_computationname.split.ps.ori’ & ’project_computationname.split.ss.ori’ (if splitter blades)

These files contain respectively the pressure side and the suction side of the splitter blade.

12-5.2.2 Quantity Files

a) ’project_computationname.cgns’

This file contains the results of the calculation, i.e. the five flow variables (density, x-y-z componentsof the relative velocity and the static pressure) at all the mesh cell centers (including the dummy cellsgenerated by the boundary conditions). It also contains all output variables to be displayed byCFView™.

b) ’project_computationname.mf’

This file is a summary file containing the averaged flow quantities at the inlet and the outlet bounda-ries.

c) ’project_computationname.mfedge’

This file is a summary file containing the averaged flow quantities at the leading and trailing edgeplanes.

d) ’project_computationname.2d.cfv’ & ’project_computationname.3d.cfv’

The blade-to-blade module automatically creates all the files required by the NUMECA CFView™post-processing tool. Two projects are created, the first one being named ’***.3d.cfv’, allowing a 3Dvisualization of the case, the second one being named ’***.2d.cfv’, allowing a 2D visualization in the(m,θ) plane.

e) ’project_computationname.velini’ & ’project_computationname.vel’

These files contain the isentropic Mach number and the pressure coefficient distributions along theblade surfaces. The two quantities are plotted along the curvilinear abscissae measured along the bladesurface (non-dimensionalized by the blade chord).

The isentropic Mach number is calculated (for compressible flows only) using the inlet relative totaltemperature and pressure, which are not necessarily imposed (depending on the choice of the inletboundary condition). In case the total conditions are not imposed, the values are the ones resultingfrom the calculation (average along the inlet boundary).

, (12-2)

where p is the local static pressure, and p0 is the local relative total pressure calculated assuming a con-stant rothalpy and a constant entropy in the field.

The pressure coefficient is defined by:

, (12-3)

where pexit is the exit static pressure, and p is the local static pressure.

Mis2

γ 1–-----------

p0

p-----

⎝ ⎠⎛ ⎞

γ 1–γ

-----------

1–⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

=

Cpp p– exit

pexit

-------------------=


FINE™ 12-17

These files can be read and plotted by the NUMECA MonitorTurbo (Loading diagram menu). The’.velini’ file contains the initial distributions, whereas the ’.vel’ contains the actual ones, and is iter-atively updated during the resolution process.

f) ’project_computationname.split.velini’ & ’project_computationname.split.vel’ (if splitter blades)

These files contain the isentropic Mach number and the pressure coefficient distributions along thesplitter blades. These files can be read and plotted by the NUMECA MonitorTurbo (Loading dia-gram menu).

g) The ’project_computationname.loadini’ & ’project_computationname.load’

Provided that the parameter ISQUEL specified in the ’.run’ file is different from 0, these files areautomatically generated, and contain the distributions of the suction-to-pressure side Mach numberand pressure coefficient difference and average. These distributions can be superimposed to thesuction and pressure side distributions.

These files can be read and plotted by the NUMECA MonitorTurbo provided with the FINE™ userinterface (Loading diagram menu). The ’.loadini’ file contains the initial distributions, whereas the’.load’ contains the actual ones, and is iteratively updated during the resolution process.

h) ’project_computationname.split.loadini’ & ’project_computationname.split.load’ (if splitter blades)

These files contain the same results as the ’.load’ and ’.loadini’ files along the splitter blades. Thesefiles can be read and plotted by the NUMECA MonitorTurbo provided with the FINE™ user inter-face (Loading diagram menu).

12-5.2.3 Numerical Control Files

a) ’project_computationname.log’ & project_computationname.std’

These files contain all the informations written by the solver during its execution. When the solverfails for any accidental reason, the explanation can usually be found in these files.

b) ’project_computationname.res’

This file contains the evolution of the mean and maximum residuals and of the inlet and outlet massflows. This file can be read and plotted by the NUMECA MonitorTurbo (Convergence historymenu).


12-18 FINE™

FINE™ 13-1

CHAPTER 13:Design 2D Module

13-1 OverviewThis chapter describes the new quasi-three-dimensional FINE™/Design 2D Module for turboma-chinery cascade inverse design. This module is associated with the FINE™/Design 2D Blade-to-Blade module presented in Chapter 12. In addition to the mesh generator and the flow solver, theFINE™/Design 2D module includes one of the latest inverse methods for the redesign of the bladeswith improved performance. Such a method permits to redesign the blade shape for a target pres-sure distribution along the blade surfaces. The use of the design method requires a license for blade-to-blade simulation.

The FINE™/Design 2D module can be used (and acquired) independently from the otherNUMECA tools.

In the near future NUMECA intends to extend the FINE™/Design 2D environment to other typesof applications and to other design techniques. This first version is limited to the inverse design ofturbomachinery cascades, and has therefore been integrated with the Blade-to-Blade method in theFINE™/Design 2D user environment.

Both analysis and design modules are based on the assumption that the flow in the turbomachinerycascade remains on an axisymmetric streamsurface. The geometrical inputs required from the userto perform an inverse design are not different from the ones required to perform an analysis (asdescribed in Chapter 12).

For more information about the Blade-to-Blade method, see the description provided in theChapter 12. In the next section the interface is described in detail including advice for use of theinverse design method. The theoretical background for the inverse method is described in section13-3. Finally, the Design 2D Module requires geometrical data files and generates output asdetailed in section 13-4.

Design 2D Module Inverse Design in the FINE™ Interface

13-2 FINE™

13-2 Inverse Design in the FINE™ InterfaceThe Blade Design module is proposed under the new NUMECA FINE™/Design 2D environmentpresented in Chapter 12, which permits a very rapid, easy and interactive use of the solvers. All theparameters can be selected interactively by means of this user interface, which automatically cre-ates the input files and permits to launch the analysis and inverse solvers.

A graphical control software, called MonitorTurbo, is provided. It permits to observe the evolutionof the convergence history, of the pressure distribution along the blade surface, and of the bladegeometry (case of an inverse design). It also permits to create the target pressure distribution inter-actively.

The results can be analysed with the NUMECA CFView™ post-processing software, whose con-nection with the blade-to-blade module is automatically provided.

The geometrical data are specified in ASCII input files, whereas the definition of the flow solverparameters and of the boundary conditions are specified via the interface.

This section describes the creation of the inverse design input files using the interactive menus pro-vided in FINE™/Design 2D. Further details concerning the input and output files are provided insection 13-4.

The next sections provide information concerning:

• The starting of a new or an existing blade-to-blade project.

• The creation of the solver input files required for a flow analysis.

• The launching of a blade-to-blade flow analysis.

13-2.1 Start New or Open Existing Design 2D Project

To start the FINE™/Design 2D module from the FINE™ interface select the menu item Modules/Design 2D.

When launching the FINE™ interface a Project Selection window allows to Create a New Projector to Open an Existing Project. To create a new Blade-to-Blade project:

1. Click on the button Create a New Project.

2. Browse to the directory in which the new project directory needs to be created and enter a namefor the project.

3. Close the Grid File Selection window since no grid file is associated to a Design 2D project.

4. Switch to the Design 2D module through the menu Modules/Design 2D.

When an existing Design 2D project should be opened click on the button Open an Existing Projectin the Project Selection window and select the project in the File Chooser window. The mostrecently used projects can also be selected from the list of recent projects. If the selected projectwas saved in the Design 2D module, the FINE™ interface is automatically switched to this moduleshowing the interface as in Figure 12.2.1-1.

It is not possible to have Design 2D and three-dimensional computations in one

project. A project is either a FINE™/Design 2D project or a FINE™/Turbo project. Thetype of the project is determined by the module in which it is saved.

The interface in the Design 2D module is described in Chapter 12. The only difference with ablade-to-blade analysis computation is the use of the Inverse Design page. This page is described inmore detail in the next sections.

Inverse Design in the FINE™ Interface Design 2D Module

FINE™ 13-3

13-2.2 Creation of Inverse Design Input Files

An inverse design calculation should always start from the converged flow analysis of the initialgeometry.

Once a converged flow solution for the blade-to-blade analysis has been obtained, the user can pro-ceed with a modification of the blade using the inverse method. For this purpose the two input files"project_computationname.req" and "project_computationname.run" have to be prepared, in addi-tion to the files required for the analysis ("project_computationname.run" and the geometrical inputfiles).

13-2.2.1 Recommendations

It is often useful to save the results obtained after the analysis computation. Therefore it is recom-mended to perform the inverse design in a new computation. With the analysis computationselected in the Computations area on the top left of the FINE™ interface click on the New button. Anew computation is created with the same parameters as the initial computation. The Rename but-ton may be used to rename the new computation.

FIGURE 13.2.2-2 Computations area

The expert integer parameter IATFRZ is usually set to 2 during the inverse design procedure inorder to freeze the computation of the turbulent viscosity. The consequence of this is to drasticallyreduce the computational time per inverse design iteration.

13-2.2.3 The Input File "project_computationname.req"

The ’project_computationname.req’ file has exactly the same format as the ".vel" or ".load" outputfiles automatically generated by the blade-to-blade analysis module. The most appropriate way togenerate this file is to modify the ’projectname.b2b.vel’ or ’projectname.b2b.load’ file resultingfrom the flow analysis of the initial geometry, using the MonitorTurbo.

In order to create a target with the MonitorTurbo, the following operations should be made:

1. Start the ’MonitorTurbo’.

2. Select the "Loading diagram" menu.

3. Open the ’project_computationname.vel’ or ’project_computationname.load’ file.

4. Choose between the ’Mis’ or ’Cp’ distributions (in case the inlet total conditions are notimposed as boundary conditions, the inverse problem has to be formulated in terms of Cp). Thedefinition of Mis and Cp are provided in Eq. 13-1 and Eq. 13-2 presented in section 13-4.

5. Activate the ’Markers’ to distinguish the discretization points.

6. Activate the Edit a curve button.

7. Choose the suction or the pressure side curve, by placing the cursor on the corresponding leg-end, and typing <s> to select. The activated curve changes color.

analysis

inverse design


13-4 FINE™

8. Modify the curve using the middle button of the mouse:

a. Choose the left point where the modification will start (click on the middle button).

b. Choose the right point where the modification will end (click on the middle button).

c. Choose control points between the left and the right points (click on the middle button).

d. Displace the control points.

— Select the control point by placing the cursor on the point.

— Press <Ctrl> on the keyboard, and displace the point vertically.

The exact position of the point can be specified by pressing the right button of the mouse.

e. Save the new curve by clicking on the Save button, and giving the name of the new curve, or cancel the modifications by clicking on the Cancel button.

At any moment, a zoom of the curves can be obtained by defining a new rectangular

window, using the left button of the mouse. The previous unzoomed view can beretrieved by pressing the right button of the mouse.

13-2.2.4 Input File "project_computationname.run"

The "project_computationname.run" input file is created via the Inverse design page included in theFINE™/Design 2D interface (Figure 13.2.2-1).

One of the three possible inverse formulations should be chosen:

• Pressure and suction side distributions or classical formulation: both suction and pressure sidesof the blade are modified for an imposed pressure distribution along the whole blade contour.If this formulation is used the profile closure constraint has to be activated.

• Suction side distribution or mixed formulation: only the suction side is modified for a pre-scribed suction side pressure distribution. The profile closure conditions should also be acti-vated, so that the pressure side follows the suction side modifications.

•Blade loading or loading formulation: the camber line of the blade is modified for a prescribedloading (suction-to-pressure side pressure difference) distribution from the leading to the trail-ing edge. The blade thickness distribution is maintained constant and therefore the profile clo-sure condition does not need to be used.

The target of the inverse design computation may either be constructed in terms of isentropic Machnumber (Mis) or pressure coefficient (Cp) (see Eq. 13-1 and Eq. 13-2 in section 13-4). The isentro-pic Mach number formulation is limited to compressible flows.

Control of the leading and trailing edges is provided. The inverse method permits to maintain someparts of the blade unchanged, such as the leading and trailing edge regions. The number of frozenpoints along the suction and the pressure sides should be specified for each edge by the user. Thedefault value is 1. However in many cases it is recommended to freeze the leading edge regionwhere no modification is imposed. At the trailing edge it is highly recommended to freeze theregions where a flow separation appears in the analysis of the initial blade.

Two relaxation factors are available:

• The first relaxation factor (default value = 1.0) permits to consider an intermediate targetbetween the one present in the ".req" file and the initial distribution present in the ".vel" file.This factor is not often used.

• The second relaxation factor (default value = 0.05) permits to under-relax the geometry modi-fications. The range of variation of this factor is from 0.01 to 0.1. Higher values than 0.1 arenot recommended for reasons of stability, whereas lower values than 0.01 usually mean thatthe inverse problem can not be treated.

Inverse Design in the FINE™ Interface Design 2D Module

FINE™ 13-5

The following geometry constraints are available:

• the profile closure constraint should always be used, unless:

— the blade thickness is automatically controlled ("loading" formulation).

— the trailing edge of the blade is blunt, and the trailing edge thickness does not need to bemaintained.

•Constant stagger angle is not often used.

•Constant blade chord: this constraint permits to maintain the blade chord (measured on thetransformed m-θ plane). This constraint should not be used together with the constant radiusoption, as the two constraints are contradictory.

•Constant radius: this option is recommended for radial machines, as it permits to guarantee anunchanged meridional position of the leading and trailing edges. The points are displacedalong the circumferential direction. This option is not recommended for large rounded leadingedges.

•Reference point: the fixed reference point can be either the leading edge (by default) or thetrailing edge (if the corresponding button is selected).

FIGURE 13.2.2-1 Inverse design page

Finally, the number of iterations performed for the inverse design calculation.

13-2.3 Initial Solution Menu

An inverse design calculation should always start from the converged flow analysis of the initialgeometry.

Once a converged flow solution for the blade-to-blade analysis has been obtained, the user can pro-ceed with a modification of the blade using the inverse method. (Figure 13.2.3-2)


13-6 FINE™

FIGURE 13.2.3-2 Initial solution page

13-2.4 Launch or Restart Inverse Design Calculation

Once the ’.req’ and ’.run’ input files have been correctly created, an inverse design can be started,by selecting the Inverse design option in the "run type" parameter included in the Control Varia-bles page, and by pressing the Start button in the Solver menu.

FIGURE 13.2.4-3 Run type page of the information area

Exactly as in the case of the restart of a flow analysis the user has to specify the name

of the initial solution file. It is recommended to save the results of the flow analysisunder a different name, so that several inverse design calculations can be performed suc-cessively, starting from the same initial solution.

An interrupted inverse design calculation can be "restarted". For this purpose the user

should set the expert parameter INVMOD to 1 instead of 0. This implies that in additionto the correct flow solution file, the actual blade geometry will be read by the solver andconsidered as the initial one.


13-2.5.1 Using a Parametrised Target Distribution

Using a parametrised target distribution is possible through the two expert parameters IADAPT andRADAPT, that can be accessed via the Control variables page. The expert mode must be activatedin the top right corner of the interface.

The integer variable IADAPT contains 6 values:

• Type of parametrisation

— 0: parametrised distribution is not used

— 1: suction side (or loading) distribution is parametrised

— 2: pressure side distribution is parametrised.

Theory Design 2D Module

FINE™ 13-7

•Number of iterations after which the adaptation process will start.

• Index of starting (left) point of the parametrised target. The user specifies the position withrespect to the leading edge (typically about 10 points).

• Index of the ending (right) point of the parametrised target. The user specifies its position withrespect to the trailing edge (typically about 10 points).

• Turning angle is imposed value (0) or the change of swirl RVθ between inlet and outlet (1).

• Imposed turning or swirl is taken from the analysis solution (0) or set by the user (1).

The real variable RADAPT contains 4 values:

•Reduced curvilinear position of the free parameter between 0. (left point) and 1.0 (right point(default: 0.5).

•Relaxation factor governing the amplitude of successive updates of the parameter (default:0.25)

•Range of variation of the free parameter (in isentropic Mach number or pressure coefficient,depending on previous choice of the user) (default: 0.2).

•User imposed value of the turning angle (in deg.) or swirl RVθ (m2/s) (used if the last integerof IADAPT is set to 1).

INVMOD: set this parameter from 0 to 1 to allow the restart of an inverse design computation.

13-2.5.2 Splitter Blades Design

Centrifugal compressors with splitters can be redesigned with FINE™/Design 2D. It is possible tomodify either the main blades or the splitter blades. The choice is made through the expert variableINVSPL (accessed in the "Computation Steering" menu of the FINE™ interface):

• INVSPL= 1: main blades are modified

• INVSPL= 2: splitter blades are modified

The target should be constructed from the ’project_computationname.vel’ or’project_computationname.load’ files if the main blades are modified, or from the’project_computationname.split.vel’ or ’project_computationname.split.load’ files if the splitterblades are modified.

13-3 TheoryThe purpose of an inverse method is to redesign the blade shape in order to obtain a prescribedpressure distribution along the blade surfaces. This provides a detailed control of the boundarylayer behaviour, by limiting the amount of diffusion and by eliminating the eventual spurious accel-eration and deceleration detected along the initial blade profile. Such a method also offers an indi-rect control of the secondary losses, as a control of the blade loading distribution can be obtained.

The inverse design method adopted in FINE™/Design 2D consists of modifying iteratively theblade geometry, until a target pressure distribution is reached on the blade surfaces. The geometrymodification algorithm is based on the permeable wall concept. Each iteration of the process iscomposed of 2 separate steps, respectively related to the geometry and to the flow field updates.Both viscous and inviscid problems can be treated with this approach.

Three formulations of the inverse problem are possible:

Design 2D Module File Formats used for 2D Inverse Design

13-8 FINE™

• the classical formulation, in which both suction and pressure sides are redesigned in order toobtain a pressure distribution prescribed along the whole blade surface.

• the mixed formulation, in which the suction side is redesigned in order to obtain a pressure dis-tribution specified along the suction side only. This formulation is for instance interesting forrotor blades on which strict mechanical constraints are imposed. In those cases the classicalinverse formulation may be less efficient because the blade thickness is a result of the calcula-tion, and it is often difficult and time consuming to find an appropriate target leading to a bladewith an acceptable thickness distribution.

• the loading formulation, in which the distribution of blade loading (pressure-to-suction sidepressure difference) from the leading to the trailing edge is prescribed, and in which the cam-ber line of the blade is redesigned (the blade thickness distribution being kept unchanged).This approach is interesting especially for radial machines. This is due to the fact that in radialmachines, the average velocity level in the blade channel is mainly controlled by the shape ofthe hub and shroud endwalls, and therefore a modification of the blade shape mainly influ-ences the loading distribution. The "loading" formulation is therefore more appropriate andefficient for radial machines. However no general rule can be set, and improvements can bereached in many cases using the second formulation.

Several geometrical constraints and options have been implemented, to increase the flexibility ofthe method:

•Control of the leading and trailing edges: several points can be kept unchanged in the leading/trailing edge regions.

•Constant blade chord.

• Specification of the fixed reference point (leading or trailing edge).

• Inverse problem formulated in terms of isentropic Mach number or of pressure coefficient.

•Constant meridional position of leading and trailing edges (recommended for radialmachines): with this option, the points are displaced along the circumferential direction, whichguarantees that their meridional position is unchanged.

An important advantage of the present method is the possibility to control the outlet flow angle orswirl. A major drawback of most inverse methods is the lack of control of the turning angle or workexchange in the cascade. The user does not have the guarantee that the specified target pressure dis-tribution will lead to an unchanged turning angle. This implies that several iterations are sometimesrequired before finding the target leading to an acceptable design.

FINE™/Design 2D offers a unique solution to that problem, allowing the control of the turningangle or of the change of swirl from inlet to outlet. A degree of freedom is introduced in the targetpressure distribution, that is automatically modified in order to respect the outlet flow angle con-straint. A part of the target pressure distribution is defined using a fourth order polynomial curve.The parameter defines the vertical position of a point of this polynomial curve. A smooth transitionis ensured between the fixed part of the target and variable one. The parameter is iteratively andautomatically adjusted in order to respect the outlet flow angle or the outlet swirl RVθ.

13-4 File Formats used for 2D Inverse Design

13-4.1 Input Files

The input files required to run a blade-to-blade study can be split into 3 categories:

File Formats used for 2D Inverse Design Design 2D Module

FINE™ 13-9

• The geometrical input files, defining the blade geometry.

• The solver input files, which define the solver parameters and the fluid and flow conditions.

• The inverse design input files, which permit to define an inverse problem.

The geometrical and solver input files have been described in Chapter 12. The inverse design input filescan be interactively created with the FINE™ environment, and are described in this section.

13-4.1.1 Inverse Design Input Files

In order to perform an inverse design problem, 2 additional input files are required:

— The ’project_computationname.req’ file, which defines the target pressure distribution. This file canbe interactively created using the MonitorTurbo.

— The ’project_computationname.run’ file, which specifies the parameters for the inverse design(automatically written by the user interface when saving the ’.run’ file).

It should be mentioned that an inverse design always starts from a converged analysis of the initial geome-try. The target pressure distribution can be generated by modifying the pressure distribution resulting fromthe analysis of the initial geometry.

13-4.2 Output Files

Several output files are generated by the blade-to-blade module, which have been described in Chapter 12.The inverse design method produces additional output files which are presented in this section.

13-4.2.1 Geometry Files

a) ’project_computationname.geoini’ & ’project_computationname.geo’

These files contain the blade shape in the (m,θ) plane. The ’.geoini’ file contains the initial blade shape,whereas the ’.geo’ file contains the actual one.

These files can be read and plotted with the NUMECA MonitorTurbo (Blade profile menu). In the case ofan inverse design the visualization of the two files permits to compare the initial and the new geometry.

b) ’project_computationname.split.geoini’ & ’projectname_computationname.split.geo’ (if splitter blades)

These files contain the splitter blade shape in the (m,θ) plane. The ’.geoini’ file contains the initial bladeshape, whereas the ’.geo’ file contains the actual one.

These files can be read and plotted with the NUMECA MonitorTurbo (Blade profile menu). In the case ofan inverse design the visualization of the two files permits to compare the initial and the new geometry.

c) ’projectname_computationname.ss.ori’ ,’projectname_computationname.ps.ori’ & ’projectname_computationname.mer.ori’

These three files are automatically generated at the beginning of the solver execution, and contain respec-tively the suction side, the pressure side and the axisymmetric streamsurface on which the calculation isperformed. These files are especially interesting in a 3D input type, with which this blade section resultsfrom the 3D interpolation procedure between the 3D blade and the streamsurface. These files have thesame format as the blade geometry and streamsurface data input files.

The coordinate system for the blade data is always XYZ, which makes these files compatible with IGG™or AutoGrid. The coordinate system for the streamsurface is always ZRB (B is the streamtube thickness).


13-10 FINE™

The coordinates are given in the same unit length chosen by the user for the input data.

d) ’project_computationname.ss.new’ & ’project_computationname.ps.new’

After an inverse design stage, these two files are automatically generated, and contain the new suc-tion and pressure sides. These files have the same format as the blade geometry data input files.

The coordinate system is always XYZ, which makes them compatible with IGG™ or AutoGrid.The coordinates are given in the same length unit chosen by the user in the input.

In the default configuration of the solver the points included in these files are the mesh points alongthe blade walls. The number of points can be different and controlled by the user through the expertparameter NPTB2B. If this parameter is set to a value N different from 0, the number of pointsdescribing both suction and pressure sides will be N.

13-4.2.2 Quantities Files

a) ’project_computationname.velini’ & ’project_computationname.vel’

These files contain the isentropic Mach number and the pressure coefficient distributions along theblade surfaces. The two quantities are plotted along the curvilinear coordinate measured along theblade surface (non-dimensionalized by the blade chord). The ’.velini’ file contains the initial distri-bution, whereas the ’.vel’ file contains the actual one.

The isentropic Mach number is calculated using the inlet relative total temperature and pressure,which are not necessarily imposed (depending on the choice of the inlet boundary condition). Incase the total conditions are not imposed, the values are the ones resulting from the calculation(average along the inlet boundary).

The isentropic Mach number is defined by:

(13-1)

where p is the local static pressure, and p0 is the local relative total pressure calculated assuming aconstant rothalpy and a constant entropy in the field.

The pressure coefficient is defined by:

(13-2)

where pexit is the exit static pressure and p is the local static pressure.

These files can be read and plotted by the NUMECA MonitorTurbo (Loading diagram

menu). In the case of an inverse design the visualization of the two files permits to com-pare the initial and the new pressure distributions.

b) ’project_computationname.loadini’ & ’projectname_computationname.load’

Provided that the parameter ISQUEL specified in the ’.run’ file is different from 0, these files areautomatically generated and contain the distributions of the suction-to-pressure side Mach numberand pressure coefficient difference and average. These distributions are useful when the ’loading’

Mis2

γ 1–-----------

p0

p-----

⎝ ⎠⎛ ⎞

γ 1–γ

-----------

1–⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

=

Cpp p– exit

pexit

-------------------=

File Formats used for 2D Inverse Design Design 2D Module

FINE™ 13-11

formulation of the inverse design method is selected. The ’.loadini’ file contains the initial distribution,whereas the ’.load’ file contains the actual one.


menu). In the case of an inverse design the visualization of the two files permits to comparethe initial and the new distributions.

c) ’project_computationname.split.loadini’ & ’project_computationname.split.load’ (if splitter blades)

Provided that the parameter ISQUEL specified in the ’.run’ file is different from 0, these files are auto-matically generated and contain the same quantities as the ’.load’ and ’.loadini’ files calculated alongthe splitter blades (Loading diagram menu).

d) ’project_computationname.tarini’ & ’project_computationname.tar’

The inverse solver automatically generates these two output files, which contain respectively the initialand actual target pressure (or loading) distributions.


menu). The comparison of the .tarini and ’.velini’ (or ’.loadini’) permits to observe theinverse problem to be solved, whereas the comparison of the ’.tar’ and ’.vel’ (or ’.load’)files permits to verify the correct convergence of the inverse design.


13-12 FINE™

FINE 14-1

CHAPTER 14:The Task Manager

14-1 OverviewUsing the Solver menu in FINE™/Turbo computations can be started, suspended or killed. Forbasic task management these menu items are sufficient.

The Task Manager provides more advanced features for the management of (multiple) tasks. Itallows to manage tasks on different machines on a network, to define parallel computations or todelay tasks to a given date and time.

Before using the Task Manager for the first time it is important to read the next section first. Thissection provides important information for getting started with the Task Manager. Read this sectioncarefully to fully benefit of the capabilities of the Task Manager.

From FINE™/Turbo the Task Manager can be accessed by the Modules/Task Manager menuitem. The interface as shown in Figure 14.3.1-1 will appear.

In section 14-3 the Task Manager interface is described in detail including a description of all capa-bilities. The current limitations of the Task Manager are listed in section section 14-6.

To manage tasks through the use of scripts is also possible and has the benefit that it is not neces-sary to stay logged in on the machine on which the tasks are launched. See section 14-5 for moredetail on the scripts to use to launch NUMECA software.

14-2 Getting Started

14-2.1 The PVM Daemons

The Task Manager is based on the PVM library. It allows FINE™ to control processes and commu-nication between processes on all the machines available by the user. PVM works with a virtualmachine managed through a pvm daemon. In this section the way PVM daemons are working andits limitations under Windows are described.

The Task Manager Getting Started

14-2 FINE

14-2.1.1 What PVM Daemons Do.

If a user starts the FINE™ interface on a given computer where no PVM daemon is running,FINE™ will start the process pvmd on this machine that becomes the virtual machine server for theuser. When adding a host in the Task Manager (on the Hosts definition page) a pvmd is started onthe remote computer that is added to the virtual machine. If after that the user logs on the secondcomputer and starts the FINE™ interface this second computer belongs also to the virtual machinewhose server is the first pvmd started.

If after that the user logs on a third computer on which no pvmd is running and starts the FINE™interface, FINE™ will start a pvmd that becomes the server of a new virtual machine. When tryingto add a host belonging the first virtual machine (containing the two first computers), he will see thea warning message that he cannot connect to the virtual machine because a pvmd is already run-ning.

If the user wants to have the three computers in the same virtual machine, one of the virtualmachines must be shut down (on the Hosts definition page) and add the corresponding computersfrom the second one.

14-2.1.2 Limitation under Windows

On windows only one pvmd can run and hence, only one single user can connect to the virtualmachine. If an other user wants to use the NUMECA software on the PC as server (FINE™) or asclient (EuranusTurbo), the first one needs to shut down the pvm daemons on this machine. To shutdown go to the Hosts definition page and click on Shutdown. This will close the interface andremoves all the pvm daemons on the machine. Remove the files pvml.<userID> andpvmd.<userID> from the directory defined by the PVM_TMP (by default C:\tmp).

14-2.2 Multiple FINE™ Sessions

During a FINE™ session all the tasks defined by the user are stored in the tasks file in theNUMECA tmp directory. This directory is in the .numeca/tmp directory below the home directory.On UNIX the home directory corresponds to the HOME environment variable. This is also true onWindows if this variable is defined and, if it is not the case, it is set to the concatenation of HOME-DRIVE and HOMEPATH environment variables.

When FINE™ is started more than once at the same time, a warning indicates to the user thatFINE™ is already running and can enter in conflicts with the other FINE™ sessions. Indeed, theuser can define tasks in both interfaces but the task definitions saved when exiting FINE™ will beoverwritten by the other sessions. Therefore, it is not advised to open multiple FINE™ sessionswhen the Task Manager must be used.

14-2.3 Machine Connection from UNIX/LINUX Platforms

The Task Manager allows the user to control processes on all the machines connected to the net-work. The rsh command is used by the PVM library to access the machines. Before using theTask Manager, the following actions must be done:

1. Modify the .rhosts file in the home directory by introducing all the machines which can be usedby the Task Manager. i.e.: if the machines machine1 and machine2 will be used by the user’stasks, the .rhosts file must be modified as follows:

line1: machine1 <login1>line2: machine2 <login2>where machine1 and machine2 are the host names.

Getting Started The Task Manager

FINE 14-3

login1 and login2 are optional. They must be set if the login on remote host is different fromthe login on the local host.

The .rhosts file needs to be ended by a blank line.The .rhosts file permission must be set to ’rw’ (chmod 600 ~/.rhosts).

2. Test the rsh command on the desired machine: an external check that the .rhosts file is set cor-rectly is to enter the following command line:

% rsh remote_host ls <Enter>

where remote_host is the name of the machine to connect to. If the login on the remote host is notthe same, ensure that the .rhosts file contains the line:

remote_host local_login

and in this case the command line is:

% rsh remote_host -l local_login ls

If the .rhosts is set up correctly, a listing of the files is shown on the remote host.

Due to a limitation of the PVM library, FINE™ can not be connected to a machine

where FINE™ has already been started. When PVM tries to establish the connection, itdetects that a server FINE™ is already running and/or pvm daemons are still running andfinally refuses the connection with a warning. To solve this problem, the PVM daemonsmust be stopped on the machine on which FINE™ must be connected:

1. Log on the machine where the connection must be established.

2. Start FINE™ and open the Task Manager through Modules/Task Manager and use the buttonShutdown of the page Hosts definition. The button Shutdown can be used to switch off all thePVM daemons of all the machines connected to FINE™. This action will stop all the daemonson all the machines connected, kill all the tasks and finally exit FINE™.

3. On UNIX: remove all the /tmp/pvmd.<userID> and /tmp/pvml.<userID> files. Under Windowsthese files should be removed from the directory defined by PVM_TMP (by default this direc-tory is C:\tmp).

4. Repeat this operation for all the machines on which the problems appear.

The operations 2 and 3 can be done automatically using the script

NUMECA_INSTALLATION_DIRECTORY/COMMON/cleanpvmd provided with theNUMECA software.

5. If PVM still has a problem to get the connection, it will print an error message either to thescreen, or in the log file /tmp/pvml.<userID> (on UNIX) or in the directory defined by the envi-ronment variable PVM_TMP (by default C:\tmp) in the log file called: pvml.<userID>. Pleasesend this log file to NUMECA support team ([email protected]).

All these operations apply only to the user’s daemons and user’s files. Multiple users

can use the Task Manager simultaneously. No interaction appears between PVM dae-mons and PVM log files of different users.

The Task Manager does not allow to launch processes from a UNIX platform to a

Windows platform.

The Task Manager Getting Started

14-4 FINE

14-2.4 Machine Connection from Windows Platforms

When a user stops the pvmd on a remote host (using Remove Host button on the Hosts definitionpage) and immediately try to restart it (using the Add Host... button), a message will appear statingthat it is not possible to connect. This problem does not occur in general since there is no need toremove a host and add it immediately after. When it occurs the only solution is to wait until the hostis available again (after 5 to 10 minutes).

From time to time, when a user tries to connect on a remote host, an error message can

appear very briefly: "Can not connect to RSH Port!!!" This may happen on Win-dows connecting to a host, disconnecting, and trying to reconnect again to the same host.It has the inconvenience to stop the interface FINE™. There is a socket release timeparameter which keeps the connection for some time.

14-2.5 Remote Copy Features on UNIX/LINUX

All the tasks defined by the user are associated with files used or created by the NUMECA’s soft-ware. When the files are not visible from the machine on which the task must be launched (i.e. thefiles are on the local disk of the host where FINE™ is running), the user can use the remote copyfeature proposed in the Task Manager. All the files needed by the tasks will be transferred into adirectory (specified by the user) of the remote machine and at the end all the created or modifiedfiles are transferred back to the host machine from which the task has been launched. By default,the available remote directories are "/tmp". The user can also specify any other directory, as long asit is visible from the remote host and has writing permission. This feature uses the rcp UNIX com-mand. Before using the remote copy feature, it is advised to first check if the rcp command workscorrectly between the machines:

— First try the rsh.exe command (see section 14-2.3).

— Type the command: touch test;rcp -p -r test destination_machine:/tmp/test. If no error isreturned by the system, the remote copy works between the local host and thedestination_machine. Errors may appear if the .cshrc file contains an stty command. In orderto be able to use the remote copy feature, remove all the stty commands from the .cshrc file.

— If the login on the local host is different from the login on the remote host, type the com-mand:

touch test;rcp -p -r test remote_login@destination_machine:/tmp/test.

14-2.6 Remote Copy Features on Windows

As files located on the local disk are not visible from a UNIX machine, this feature is proposed tobe able to launch tasks on remote UNIX platforms. The principle is the same as the one described inthe previous section: local files are copied in the remote directory specified by the user, then thetask starts. When it terminates, all results files are transferred in the original directory. This featureuses rcp.exe windows command. Before using the remote copy feature, it is advised to first check ifthis command works properly:

— First try the rsh.exe command (see section 14-2.3).

— Create a file test, then type the command: rcp -b test destination_machine:/tmp/test. If noerror is returned by the system, the remote copy works between the local host and thedestination_machine. Errors may appear if the .cshrc file contains an stty command. In orderto be able to use the remote copy feature, remove all the stty commands from the .cshrc file.

— If the login on Windows is different from the login on the remote host, type the command:

The Task Manager Interface The Task Manager

FINE 14-5

rcp -b test destination_machine.remote_login:/tmp/test

rcp.exe is provided with FINE™ and is located in the same directory as rsh.exe.

14-3 The Task Manager Interface

14-3.1 Hosts Definition

On the Hosts definition page hosts in the virtual machine, the operating system of the machine andtheir connection status are visualized. For an explanation of the virtual machine see section 14-2.1.1. If the connection is not OK, it means that the corresponding computer is no more in the vir-tual machine. This may occur for example if the computer has been rebooted.

FIGURE 14.3.1-1Hosts definition page

14-3.1.1 Add Host

When the user clicks on the Add Host... button, the interface asks for a host name and a login name.The login name is optional. It is needed only if the user login on the local host and the one on theremote host are different.

When the user accepts (Accept), the host name appears in the host list, with type of operating sys-tem and its connection status. At this point, the host is in the virtual machine, and is ready to receivea task.

if the connection can not be established, check for more detail in section 14-2.1, sec-

The Task Manager The Task Manager Interface

14-6 FINE

tion 14-2.3 and section 14-2.4.

14-3.1.2 Remove Host

When the user clicks on Remove Host button, the selected host is removed from the list, and is notin the virtual machine any more. This operation is not allowed when a task is running on the host tobe removed, or when the selected host is the local one.

14-3.1.3 Shutdown

When the user clicks on Shutdown button, all hosts in the virtual machine are removed. FINE™exits and the virtual machine halts. All running tasks are killed. This option is useful when the userwants to change the machine on which FINE™ is running. See section 14-2.1.1 for more detail onvirtual machines and when to change this.

14-3.2 Tasks Definition

A task is a collection of subtask where a subtask is one of the program with its arguments (’.run’file for EURANUS and Design3D, template ’.trb’, geometry ’geomTurbo’ and mesh ’.igg’ files forAutoGrid and macro file .py and ’.run’ file for CFView™). The different subtasks of a given task

can be run simultaneously if the output of one subtask is not needed by other ones (for example:several CFView™ subtasks with different macro ’.py’ files or several EURANUS subtasks withdifferent ’.run’ files started on different computer). If the output of one subtask is needed by otherones, it must be run sequentially. For example: AutoGrid generates the mesh that is used for startingan EURANUS computation whose output is used for starting CFView™.

14-3.2.1 Task List

In this section, the user can visualize the defined tasks and their status. To create a task, just click onNew Task button. The defaults task name can be modified by clicking on Rename Task button. Theselected task can be removed by clicking on Remove Task button.

Once a task is created and defined (see following section), it can be started or stopped just by click-ing respectively on the Start, or Stop button.

A task can be delayed: click on Delay button and enter the date and time for the moment the taskneeds to be launched in the dialog box. The delayed task can be disabled using the button Cancel.

When the user validates the data, a little watch in the task list indicates that the task is scheduled:

FIGURE 14.3.2-2Task List with Delay window to start a task at a later moment

When exiting FINE™, all the delayed tasks are automatically started and stay in sleep

mode until their starting dates are reached. When starting FINE™ again, all the task


FINE 14-7

manager related to the delayed tasks still in sleep mode are killed and FINE™ Task Man-ger gets back the control of these tasks.

14-3.2.2 Task Definition

In this section the subtasks of the selected task of the Task List are listed. A subtask is defined by itstype (euranusTurbo, AutoGrid, CFView™ or Design3D), their status and the host on which they arelaunched. To add a subtask click on the New Subtask. Select the executable name (EURANUS,AutoGrid, CFView™ or Design3D) and the host on which the process should be started in the twolists. The host name list contains the hosts that are in the virtual machine. They are set in the Hostdefinition page.

14-3.2.3 Subtask Arguments

a) Definition of Input and Output

Once a subtask is created, input and/or output files must be defined in the Subtask arguments sec-tion:

— The flow solver EURANUS and Design3D requires one argument file: the name of the run-file. This files is created using the menu File/Save Run Files in the FINE™/Turbo module.

— The mesh generation system AutoGrid requires three files as arguments: the trb file, thegeomTurbo file and as output the grid file name (see the AutoGrid manual for more details)


14-8 FINE

— The flow visualization system CFView™ requires two files: the run file and a macro file(see CFView™ manual for more details)

The run file is automatically opened by CFView™ before starting the macro. The macro filemay open other ’.run’ files to perform flow comparisons (see CFView™ manual for moreinformation about the macro ’.py’ file).

b) Simultaneous or Sequential Mode

Moreover, a process can be executed simultaneously with the other subtasks (by selecting RunSimultaneously with Previous Subtask) or sequential (by selecting Run After Previous Subtask). Inthis last case, the process waits the previous subtask to be finished before starting. This is onlyavailable for AutoGrid, Design3D and EURANUS subtasks. Only a certain amount of tasks can beperformed at the same time depending on the available licenses. The subtasks related to post-processing with CFView™ are always executed in sequential mode.

c) Remote Copy

The Remote copy to button allows the user to specify that the files are not visible from the remotemachine and must be transferred. This is only available for AutoGrid, Design3D and EURANUS.

d) Parallel Computations.

d.1) MPI system

The flow solver euranusTurbo has integrated multiprocessor machine concept. The button ParallelComputation can be activated to specify that the parallel version of the flow solver can be used forthis computation.

The button Flow solver parallel settings gives access to the dialog box used to set up a parallelcomputation.

When the dialog box is opened, the block list displayed all the block of the mesh. The user candefined new processes on all the available machines and defined manually or automatically the loadbalancing (using the Automatic Load Balancing button).

The parallel processing can only be used on multiprocessor machine (shared memory

mode) or on machines with the same operating systems (homogenous distributed mem-ory mode)

See section 14-4 for more detailed information on parallel computations.


FINE 14-9

d.2) SGE system

Within the Task Manager provided in FINE™/Turbo v6.2-7, the parallel process can be set usingthe SGE (Sun Grid Engine) batch system.

This last sytem includes the possibility to add a SGE type host and to define arguments needed tolaunch the computation within the Task Manager.

Host Definition

In the page Hosts definition the user needs to add host. When adding the host, automatic checks are performed:

1. it will detect if the "sge_qmaster" is running on the platform. If not, it means that the platformdoes not have SGE capabilities or the platform is not the SGE master processor.

2. it will detect all parallel environment defined in SGE.

3. it will detect all parallel environment that the user is allowed to use. If no parallel environmentcould be accessed by the user, his login should be added to the user list by the SGE administra-tor.

When all checks are successfull, the SGE capability of the added host is activated and the user cansee if the host added is a SGE paltform within the Task Manager GUI (Figure 14.3.1-1).

Task Definition

In the page Tasks definition, if the user select a SGE platform when launching an EURANUS taskin parallel, he has the access to the MPI system or the SGE system (Figure 14.3.2-3).

When the SGE system is used, the number of processor and the SGE environment have to be speci-fied. Depending on the number of processor, an automatic load balancing is performed to updatethe block distribution and the process needs only to be started by the user.

Processes list with the load balancing of the cells

Buttons used to removeor add new processes on the specified machine

List of the block in the associated mesh

Button used to link theselected block with a process

Default block distribution


14-10 FINE

FIGURE 14.3.2-3Tasks Definition - SGE inputs

Process Management

Once the process is starting, the ".run" file is modified automatically depending of the number ofprocessor. Then a script file ".sge" is created at the same time as the ".p4pg" file when using MPIsystem.

The name of the SGE job is limited to 8 characters and the following format is thus

chosen "comp#000" where 000 stands for a any number depending of the number ofSGE jobs already running under the same environment.

To test if a computation is running, because there are no communication with the task managersince EURANUS has not been launched using PVM daemon, the "qstat" command with the job-IDnumber of the SGE job is used.

To suspend the SGE job, the user could use the Suspend function of the Task Manager. It will createautomatically a ".stop" file in the running computation directory that will enable EURANUS to sus-pend after saving the solution at the next iteration or after the full multigrid initialization.

To kill the SGE job, the user could use the Stop function. The Task Manager will then use the SGE’sfunction "qdel" to kill the computation without saving the solution.

To kill EURANUS properly, the SGE’s "execd parameters" variable should be set to

"NOTIFY_KILL=TERM" and the "notify time" variable of nodes should be set to a suf-ficient value to allow EURANUS to exit properly. We invite the user to ask the SGEadministrator to check these variables.

e) Message Window

When a task is started, a Task Manager process is launched to take care about the task management:process communication, automatic launching of the sequential and parallel subtasks. A messagewindow linked to the Task Manager is opened. In this window the user can follow the evolution ofthe status of all the subtasks of the current task. In case of flow solver computations the iterationsare also displayed in this window as shown in Figure 14.3.2-4.

At the bottom of the Task Manager window a Refresh Rate can be chosen. This rate determines howfrequently the Task Manager window is updated. A higher refresh rate will update the informationin the window more frequently but will use more of the available CPU.

Parallel Computations The Task Manager

FINE 14-11

FIGURE 14.3.2-4Task Manager information window

If the user quits FINE™, all the message windows will stay open and the tasks will

continue. Closing a message window will immediately kill all the subtasks of the corre-sponding task.

14-4 Parallel Computations

14-4.1 Introduction

Parallel computations can be defined through the FINE™ interface as described in section 14-3.2.3.Parallel processing relies on the distribution of independent tasks among several processors usingcommunication protocols to transfer data from one processor to another whenever this is necessary.This induces of course an acceleration of the computation itself but it also makes possible verylarge computations that would not fit on a single processor.

The present parallel processing relies on the block structure of the flow solver EURANUS. Eachprocess is assigned a given number of blocks. As a consequence, the number of processors cannotexceed the number of blocks. Boundary data are exchanged between processors each time anupdate of the flow solution is required.

The parallel version makes use of MPI (Message Passing Interface) libraries. MPI was chosenamong other tools such as PVM or Open MP for its high communication performances (high band-width, low latencies). Although Open MP has better performance on shared memory configura-tions, i.e. on a given computer with single global memory and several processors, it is not designedfor distributed memory configurations (several computers with their own memory).

The parallel version is implemented for UNIX, LINUX and Windows platforms.

The Task Manager Parallel Computations

14-12 FINE

The present MPI implementation is based on a host/node approach. One host process is dedicated toinput/output management. The host reads the mesh and input files, sends the data to the computa-tion processes (the nodes), receives the computation results from the nodes and writes the outputfiles. Figure 14.4.1-5 shows the task distribution on a 4 processors configuration. Note that the host/node implementation will be replaced progressively as parallel MPI input/output functionalities arenow available.

FIGURE 14.4.1-5Tasks in a parallel computation

14-4.2 Modules Implemented in the Parallel Version

The following flow solver functionalities are already available in the parallel version:

•All turbomachine boundary conditions (including Phase-lagged). These include rotor/statorinterfaces, non matching boundaries and the fully conservative non matching boundary treat-ment (FNMB),

• Turbomachinery initial solution,

•Baldwin-Lomax, Spalart-Allmaras and k-ε turbulence models,

•Real gases,

• Preconditioning (low Mach number and incompressible fluids),

•Cooling holes,

•Outputs including pitchwise averaged output. No solid data nor surface averaged outputs areavailable yet.

The lagrangian module is not available for parallel computations.

14-4.3 Management of Inter-block Communication

The block structure of the solver allows to distribute blocks across processors or computers (in caseof a cluster). Each processor will handle an integer number of blocks. The treatment of the bound-ary condition will be replaced by message passing between the processors or remote computers.

Communication optimization

The parallel version of the flow solver is optimized in order to minimize duplicated data as well asthe number and the volume of exchanged messages. A significant improvement of the code per-formance was obtained by grouping small messages into larger buffers: the information containedin small messages is usually shared by a large number of blocks, leading to frequent messages of

Input data base Host

Output data base

Node 1 Node 2 Node 3

reading writing

boundary conditions boundary conditions

Parallel Computations The Task Manager

FINE 14-13

that type. This is the case for block edges data that are exchanged several times during each itera-tion. Significant latency times are induced by these communication processes and message group-ing highly reduces the number of such messages.

Large message limitation

Very large messages are usually exchanged during initialization and at the end of the computationbetween the nodes and the host. These also need to be avoided as they can cause important memoryneeds and eventually lead to system failure. Messages are split into buffers of maximum sizeMXBFSZ (see section 14-4.4) in order to avoid excessive MPI memory requests.

14-4.4 How to Run a Parallel Computation

The setting of a parallel run using the FINE™ interface is described in section 14-3.2.3. The userselects the number of nodes, making sure it is smaller than the number of blocks. A balanced distri-bution of the blocks among the various processes is automatically performed by the FINE™ inter-face but the user can also define its own load balancing, i.e. process distribution.

Memory allocation

Memory allocation is performed as follows:

• The integer data structure is duplicated for all processes. Since the integer data structure size isabout a tenth of the real data structure, this does not lead to high memory overload when thenumber of processes is less than 10.

• The real memory allocation is performed for each process. It should be set to the minimalamount of memory necessary to hold the data structure on the process that has most gridpoints. When the load is well balanced, the real memory overload is due to face and edge datastructures. These data need indeed to be duplicated when two processors are involved in thesame block connection.

The total memory need Mtotal for a parallel computation involving n ( ) processors can be esti-

mated as:

where Mreal and Minteger are the real and integer memory needed for the same computation insequential mode.

From a practical point of view, the user does not specify the total memory needed but the integer

and real memory required per processor. This can be estimated as for the real mem-

ory and Minteger for the integer memory.

In case of parallel calculation the estimated number of real memory displayed by

FINE™ on the page Control Variables shall not be followed but the formula shownabove shall be respected.

n 2≥

Mtotal M real 1 2n

n 1–------------ Minteger n⋅+⋅,⋅=

Mreal

n---------------- 1 2,⋅

The Task Manager Task Management Using Scripts

14-14 FINE

The following table states the total memory need for a parallel computation using respectively 4and 6 and 8 processors. The values of Mreal and Minteger are set to 10 Mb and 1 Mb respectively.

The equivalent memory request on a single processor is thus 11Mb.

In the present implementation, the presence of the host processor increases the global memoryrequest. It also reduces the overall speed-up of the computation as it is mainly dedicated to I/Omanagement and no computation is affected to it. Future versions of EURANUS will optimize thisaspect by removing gradually the need of a host processor.

Message size limitation

During initialization and final steps, large messages are usually exchanged between the nodes andthe host process. In order to avoid any system failure, messages are split into buffers of maximumsize. This size is set to 100000 by default but the user can eventually tune this value through theexpert parameter MXBFSZ.

14-4.5 Troubleshooting

If the computation is interrupted for an unknown reason, more detailed information is provided inthe ’.std’ and ’.log’ computation files. The file contains all relevant informations including MPIerror messages and should be sent to the NUMECA support team.

14-4.6 Limitations

• The distributed memory mode is restricted to homogeneous (i.e. with the same operating sys-tem) clusters.

• The number of processors should not exceed the number of blocks.

14-5 Task Management Using ScriptsThis section provides all available information to launch installed NUMECA Software from a shell,without using IGG™, AutoGrid, FINE™ or CFView™ interfaces. Every time a task is started ascript file is automatically created. On UNIX the name of this file has the extension .batch andunder Windows the extension is .bat. Such files contain text lines with the commands to launch thesoftware with the appropriate command arguments. To launch a task from a shell simply executethe automatically generated file by typing its name in a shell.

In the next sections the available commands to launch NUMECA software are described in moredetail.

Please notice that the capability to launch in batch is currently not supported for

EURANUS in Parallel Mode on PC.

n Mtotal (Mb) Parallel overhead (Mb)

4 20 9

6 20.4 9.4

8 21.7 10.7

TABLE 14-1 Parallel memory request

Task Management Using Scripts The Task Manager

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14-5.1 Launch IGG™ Using Scripts

14-5.1.1 How to Launch IGG™ on UNIX

To launch IGG™ without use of the interface the commands to perform must be written in a macroscript file. To create such a file:

1. Create a script file *.py. For more details on the commands that can be included in such a scriptfile see the IGG™ manual.

2. Set permission for execution for the script by using the command: "chmod 755 *.py".

3. Launch the macro script in a shell by typing:

igg -script /user/script.py -batch -niversion 62_7

The command line to start the grid generator IGG™ contains its name, the full path name of thescript "*.py" file to launch and the IGG™ release that will be used. The "-batch" option avoids thedisplay of the IGG™ graphical user interface.

"igg SCRIPT_PATH/script.py -batch -niversion <version>"

14-5.1.2 How to Launch IGG™ under Windows

1. Create script file "*.py". For more detailed information on the commands to include in a macroscript see the IGG™ manual.

2. Set permission for execution of the file *.py

3. Launch the macro script *.py by typing in a shell:d:\NUMECA_SOFTWARE\fine62_7\bin\igg.exe -script d:\user\test.py -batch

The command line to start the grid generator IGG™ contains its full path name and the full pathname of the script "*.py" file to launch. The "-script" & "-batch" options respectively permits tolaunch the script and avoids to display the IGG™ graphical user interface.

"IGG_PATH\igg.exe -script SCRIPT_PATH\script.py -batch"

REMARKS:

• The full path name of the executable (igg.exe) has to be specified.

• The full path name of the script has to be specified.

• If there is a segmentation fault at exit (due to an incontrollable "opengl" problem), it is possi-ble to avoid it by adding -driver msw option:

d:\NUMECA_SOFTWARE\fine62_7\bin\igg.exe -script d:\test.py -batch -driver msw

14-5.2 Launch AutoGrid using Scripts

14-5.2.1 How to Launch AutoGrid on UNIX

1. Create a template and geometry files (*.trb and *.geomTurbo) using the AutoGrid interface.

2. Start AutoGrid to create a mesh from these files by typing:igg -batch -autoGrid /user/test.trb /user/test.geomTurbo /user/test.igg -niversion 62_7

The command line to start the grid generator AutoGrid contains its name, the full path name of thetemplate, of the geometry files, the full path name of the mesh that will be saved and the IGG™release that will be used. The "-batch" option avoids the display of the IGG™ graphical user inter-face.


14-16 FINE

14-5.2.2 How to Launch AutoGrid under Windows

1. Create a template and geometry files (*.trb and *.geomTurbo) using the AutoGrid interface.

2. Start AutoGrid to create a mesh from these files by typing on one line:d:\NUMECA_SOFTWARE\fine62_7\bin\igg.exe -batch -autoGrid c:\users\template.trb c:\users\tem-plate.geomTurbo c:\users\mesh.igg

The command line to start the grid generator AutoGrid contains its full path name, the full path name ofthe template, of the geometry files and the full path name of the mesh that will be saved. The "-batch"option avoids the display of the IGG™ graphical user interface.

14-5.3 Launch EURANUS in Sequential using Scripts

14-5.3.1 How to Launch EURANUS in Sequential on UNIX

1. Create a script file (for example, with the name ’batch.sh’). Such a script file (e.g. ’batch.sh’) must becreated with permission for execution to launch a series of computations. An example of a ’batch.sh’file for a series of computations on UNIX:

#! /bin/csh

euranusTurbo /users/project/project_computation_1/project_computation_1.run -niversion 62_7

euranusTurbo /users/project/project_computation_2/project_computation_2.run -niversion 62_7

The script is started in a C-shell that is obtained by having as its first line: " #! /bin/csh". The com-mand line, to start the flow solver EURANUS, contains its name, the full path name of the ’.run’ fileto launch and the FINE™ release that will be used:

"euranusTurbo COMPUTATION_PATH/computation.run -niversion <version>"

2. Set Permission for execution for the script file ’batch.sh’ by typing the command: "chmod 755batch.sh".

3. Create an input file (’.run’) for each computation. To create those files through the FINE™ interface,click on the File/Save Run Files menu in order to save the ’.run’ file of the activated computation,after opening the corresponding project.

4. Launch the script ’batch.sh’ by typing the script file name: ’./batch.sh’.

When saving the ’.run’ file of the computation (File/Save Run Files) and launching the

computation (Solver/Start...) killed just afterwards (Solver/Kill...), a new script ’.bat’ onWINDOWS (’.batch’ on UNIX) is created in the corresponding computation subfolder thatenables the user to launch the same computation in batch.

14-5.3.2 How to Launch EURANUS in Sequential under Windows

1. Create Script File ’.bat’. An example of ’.bat’ file for a series of computations on Windows:

C:\NUMECA_SOFTWARE\fine62_7\bin\euranus.exe \\C:\users\project\project_computation_1\project_computation_1.run -seq

C:\NUMECA_SOFTWARE\fine62_7\bin\euranus.exe \\

C:\users\project\project_computation_3\project_computation_3.run -seq


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C:\NUMECA_SOFTWARE\fine62_7\bin\euranus.exe \\

C:\users\project\project_computation_2\project_computation_2.run -seq

The command line, to start the flow solver EURANUS, contains its full path name, the full pathname of the ’.run’ file to launch and the sequential mode selection:

INSTALLATION_DIRECTORY\fine62_7\bin\euranus.exe \\COMPUTATION_PATH\project_computation_1.run -seq

2. Set Permission for Execution ’.bat’

3. Create an input file (’.run’) for each computation. To create those files through the FINE™interface, click on the File/Save Run Files menu in order to save the ’.run’ file of the activatedcomputation, after opening the corresponding project.

4. Launch the script ’.bat’ by typing the script file name: ’.bat’ in a shell or double click on the’*.bat’ file from the Windows Explorer.

When saving the ’.run’ file of the computation (File/Save Run Files) and launching

the computation (Solver/Start...) killed just afterwards (Solver/Kill...), a new script’.bat’ on WINDOWS (’.batch’ on UNIX) is created in the corresponding computationsubfolder that enables the user to launch the same computation in batch.

14-5.4 Launch EURANUS in Parallel using Scripts

14-5.4.1 How to Launch EURANUS in Parallel using MPI on UNIX

1. Create a script file ’batch.sh’ with permission for execution. An example of a ’batch.sh’ file fora parallel computation on UNIX:

#! /bin/csh

euranusTurbo_parallel /users/project/computation/computation.run -niversion 62_7 -p4pg /users/project/hosts.p4pg

The script is started in a C-shell that is obtained by having as its first line: " #! /bin/csh". Thecommand line, to start the flow solver EURANUS in parallel, contains the script name that ena-bles parallel computation, the full path name of the ’.run’ file to launch, the FINE™ release andthe full path name of the file ’hosts.p4pg’ containing the definition of the machines that will beused to launch the computation in parallel:

"euranusTurbo_parallel COMPUTATION_PATH/computation.run -niversion <version> -p4pgHOST_PATH/hosts.p4pg"

The name of the executable is different from the one for sequential computations.

2. Create Hosts Definition File ’hosts.p4pg’. A file needs to be created to define the hosts (e.g.’hosts.p4pg’). This file specifies the machine information regarding the various processes. Anexample of a ’hosts.p4pg’ file:

Example 1:

Hostname1 4 euranusTurbo62_7(master host on Hostname1 and 4 processes on Hostname1)Hostname2 2 euranusTurbo62_7(2 processes on Hostname2)


14-18 FINE

Example 2:

Hostname1 0 euranusTurbo62_7 (master host on Hostname1 and no other process on Hostname1)Hostname2 2 euranusTurbo62_7 (2 processes on Hostname2)

For each machine, a line must be added consisting of the machine name (the machine hostname), thenumber of processes to run on the machine, the name of the executable and the FINE™ release:

"hostname 4 euranusTurbo<version>"

If additional machines are to be used, subsequent lines are required for each one. If the number of proc-essors is set to 0 for the first machine (first line of the ’hosts.p4pg’ file), only the master host processwill run on that machine while the nodes will run on the next machines declared in the following lines.

The first machine (hostname) specified in the file ’hosts.p4pg’ should be the one from which

the script will be launched.

The total number of processes defined in the file ’hosts.p4pg’ should be equal to the number

of nodes running.

3. Set permission for execution ’batch.sh’ by using the command: "chmod 755 batch.sh"

Create input files ’.run’ to launch the computation. The parallel settings of the computational file (’.run’)are managed by the Task Manager. Therefore before launching the parallel computation script, the follow-ing steps must be performed through the FINE™ interface:

4. Create computational file (’.run’) by activating the corresponding computation and clicking on the File/Save Run Files menu in the interface.

5. To set the final parallel settings:

— create a task in the Task Manager,

— define the parallel settings of EURANUS subtask (parallel computation),

— launch the task through the Task Manager by clicking on Start,

— kill the task when EURANUS flow solver starts by clicking on Stop. This operation is mandatory inorder to have all the parallel settings correctly imposed in the computation file (’.run’).

6. Launch the script ’batch.sh’ by typing the script file name: "./batch.sh".

When saving the ’.run’ file of the computation (File/Save Run Files) and launching the com-

putation in parallel as explained in step 5 through the Task Manager (Modules/Task Manager)and killed it just afterwards, a new script ’.batch’ and a file ’.p4pg’ are created in the correspond-ing computation subfolder that enable the user to launch the same computation in batch and inparallel.

14-5.4.2 How to Launch EURANUS in Parallel using MPI on Windows

1. Create a script file ’batch.bat’ with permission for execution. An example of a ’batch.bat’ file for a par-allel computation on Windows:

D:\NUMECA_SOFTWARE\Fine62_7\bin\mpirun.exe /"D:\test\test_computation_1\test_computation_1.p4pg" /"D:\test\test_computation_1\test_computation_1.run"

The command line, to start the flow solver EURANUS in parallel, contains the script name that enablesparallel computation, the full path name of the ’.run’ file to launch and the full path name of the file’.p4pg’ containing the definition of the machines that will be used to launch the computation in parallel:


FINE 14-19

"NUMECA_RELEASE_PATH/mpirun.exe HOST_PATH/hosts.p4pg COMPUTATION_PATH/computa-tion.run "

2. Create Hosts Definition File ’.p4pg’. A file needs to be created to define the hosts (e.g. ’hosts.p4pg’).This file specifies the machine information regarding the various processes. An example of a’hosts.p4pg’ file:

Example 1:

Hostname1 5 D:\NUMECA_SOFTWARE\Fine62_7\bin\euranus.exe (master host on Hostname1 and 4processes on Hostname1)

Hostname2 2 D:\NUMECA_SOFTWARE\Fine62_7\bin\euranus.exe(2 processes on Hostname2)

Example 2:

Hostname1 1 D:\NUMECA_SOFTWARE\Fine62_7\bin\euranus.exe (master host on Hostname1 and noother process on Hostname1)

Hostname2 2 D:\NUMECA_SOFTWARE\Fine62_7\bin\euranus.exe (2 processes on Hostname2)

For each machine, a line must be added consisting of the machine name (the machine hostname), thenumber of processes to run on the machine, the name of the executable and the FINE™ release:

"hostname 4 NUMECA_RELEASE_PATH\bin\euranus.exe"

If additional machines are to be used, subsequent lines are required for each one. If the number of proc-essors is set to 1 for the first machine (first line of the ’.p4pg’ file), only the master host process will runon that machine while the nodes will run on the next machines declared in the following lines.

The first machine (hostname) specified in the file ’.p4pg’ should be the one from which the

script will be launched.

The total number of processes defined in the file ’.p4pg’ should be equal to the number of

nodes running.

3. Set permission for execution ’batch.bat’

Create input files ’.run’ to launch the computation. The parallel settings of the computational file (’.run’) aremanaged by the Task Manager. Therefore before launching the parallel computation script, the followingsteps must be performed through the FINE™ interface:

4. Create computational file (’.run’) by activating the corresponding computation and clicking on the File/Save Run Files menu in the interface.





— kill the task when EURANUS flow solver starts by clicking on Stop. This operation is mandatory inorder to have all the parallel settings correctly imposed in the computation file (’.run’).

6. Launch the script ’batch.bat’ by typing the script file name: "./batch.bat" in a DOS-shell.

When saving the ’.run’ file of the computation (File/Save Run Files) and launching the com-

putation in parallel as explained in step 5 through the Task Manager (Modules/Task Manager)and killed it just afterwards, a new script ’.bat’ and a file ’.p4pg’ are created in the correspondingcomputation subfolder that enable the user to launch the same computation in batch and in paral-lel.


14-20 FINE

14-5.4.3 How to Launch EURANUS in Parallel using SGE on UNIX

1. Create a script file ’batch.sge’ with permission for execution. An example of a ’batch.sge’ file for aparallel computation on UNIX:

#! /bin/csh

#$ -S /bin/sh

#$ -o /home/sgeuser/parallel_sge/parallel_sge_computation_1/ parallel_sge_computation_1.std -j y

#$ -N comput1

#$ -pe numecampi 3

#$ -notify

P4_GLOBMEMSIZE=15000000

Export P4_GLOBMEMSIZE

NI_VERSIONS_DIR=/usr/numeca

MPIR_HOME=$NI_VERSIONS_DIR/_mpi

cd /home/sgeuser/parallel_sge/parallel_sge_computation_1

$MPIR_HOME/bin/mpirun -np $NSLOTS -machinefile $TMPDIR/machines \

$NI_VERSIONS_DIR/bin/euranusTurbo62_7 \

/home/sgeuser/parallel_sge/parallel_sge_computation_1/parallel_sge_computation_1.run

where:

#$ -S /bin/sh requires Bourne shell to be used by SGE for job submission and hence, only the .profile fileof the user is executed if exists on each computation host. There is nothing specific to Numeca softwarethat must be written . the .profile file.

#$ -o /home/sgeuser/parallel_sge/parallel_sge_computation_1/ parallel_sge_computation_1.std -j ytells SGE system that the standard output has to be redirected in the ".std" in the computation directory,the option "-j y" indicates that the standard error is redirected into the same file.

#$ -N comput1 is the name of the job given to SGE and that will be seen when monitoring the job with thegraphical monitoring utility qmon (Job Control button ) or with the qstat SGE command. SGE has a limi-tation of 8 characters for the job name.

#$ -pe numecampi 3 requests 3 slots (processors) to the SGE system for executing the job using thenumecampi parallel environment described in chapter 2.1. This must correspond to NTASK +1 whereNTASK is the number of computation processes in the ".run" file, the "+1" being the host process thatmanages inputs/outputs.

#$ -notify gives a delay between the send of the SIGKILL signal and SIGUSR2 signal. The delay isdefined in the SGE interface.

P4_GLOBMEMSIZE=15000000

Export P4_GLOBMEMSIZE

NI_VERSIONS_DIR=NUMECA_RELEASE_PATH

MPIR_HOME=$NI_VERSIONS_DIR/_mpi

are the environment variables indicating respectively the Numeca software installation directory and thempi directory that are used in the following command:


FINE 14-21

$NSLOTS is the number of slots (processors) that have been allocated by SGE for the job, $TMP-DIR is generated by SGE for providing the machines file used by the mpirun script.$NI_VERSIONS_DIR/bin/euranusTurbo is a symbolic link to the numeca_start startup script forall Numeca softwares and 62_7 is the version of the code that will be used and requires that it isinstalled under /NUMECA_RELEASE_PATH/fine62_7.

/home/sgeuser/parallel_sge/parallel_sge_computation_1/parallel_sge_computation_1.run is theargument to the euranusTurbo executable.

For sequential runs, the line "#$ -pe numecampi 3" must be removed and the final

command must be: $NI_VERSIONS_DIR/bin/euranusTurbo62_7 \ /home/sgeuser/parallel_sge/parallel_sge_computation_1/parallel_sge_computation_1.run -seq

2. Set permission for execution ’batch.sge’ by using the command: "chmod 755 batch.sge"

Create input files ’.run’ to launch the computation. The parallel settings of the computational file(’.run’) are managed by the Task Manager. Therefore before launching the parallel computationscript, the following steps must be performed through the FINE™ interface:

3. Create computational file (’.run’) by activating the corresponding computation and clicking onthe File/Save Run Files menu in the interface.





— kill the task when EURANUS flow solver starts by clicking on Stop. This operation is man-datory in order to have all the parallel settings correctly imposed in the computation file(’.run’).

5. Launch the script ’batch.sge’ by typing the script file name: "./batch.sge".

When saving the ’.run’ file of the computation (File/Save Run Files) and launching

the computation in parallel as explained in step 4 through the Task Manager (Modules/Task Manager) and killed it just afterwards, a new script ’.sge’ is created in the corre-sponding computation subfolder that enables the user to launch the same computation inbatch and in parallel.

14-5.5 Launch CFView™ Using Scripts

14-5.5.1 How to Launch CFView™ on UNIX

1. Create a macro file ’.py’. For more details see the CFView™ for more detailed information onthe format of a macro file and the commands that can be included in a macro file.

2. Launch the macro ’.py’ by typing: cfview -macro /user/test.py -batch -niversion 62_7The command line to start CFView™ contains its name, the full path name of the macro ’.py’ file tolaunch and the CFView™ release that will be used. The ’-batch’ option avoids the display of theCFView™ graphical user interface.

"cfview -macro MACRO_PATH/macro.py -batch -niversion <version>"

14-5.5.2 How to Launch CFView™ on PC under Windows

1. Create a macro file ’.py’. For more details see the CFView™ for more detailed information onthe format of a macro file and the commands that can be included in a macro file.

The Task Manager Limitations

14-22 FINE

2. Launch the macro ’.py’ by typing:d:\NUMECA_SOFTWARE\fine62_7\bin\cfview.exe -macro \user\test.py -batch

The command line to start CFView™ contains its full path name and the full path name of themacro ’.py’ file to launch. The ’-batch’ option avoids the display of the CFView™ graphical userinterface.

14-5.5.3 Command Line Arguments

The command cfview may be followed by a set of command line arguments. Those command linearguments allow to override some system defaults (used driver, display, double-buffering andupdate abort options) or to specify files to be loaded immediately (project, macro, defaults settings,macro module). The supported command line arguments are:

-help prints a summary of the command line arguments,

-version prints the CFView™ version number,

-date prints the CFView™ version date,

-defaults <file name> starts CFView™ with the default settings from the specified file,

-project <file name> starts CFView™ and opens immediately the specified project,

-macro <file name> starts CFView™ and execute the specified macro script,

-macromodule <file name> starts CFView™ and load the specified macro module,

-display <display name> starts CFView™ on the specified display device,

-doublebuffering on (off) activates (disables) double buffering,

-updateabort on (off) activates (disable) update aborting (see the CFView™ manual for moredetail on this option),

-driver <driver name> starts CFView™ with the specified graphics accelerator,

-reversevideo on (off) starts CFView™ with black (white) background color (see the CFView™manual for more detail on this option),

-facedisplacement <n> starts CFView™ with the specified face displacement (see the CFView™manual for more detail on this option),

-loaddata all (none, ask) when opening a project the quantities fields are loaded in the computedmemory (are not loaded, a specific dialog box is raised where the user choose the field variables tobe loaded). The defaults is to load all field quantities. (see the CFView™ manual for a descriptionof the data management facility and of the associated dialog box),

-batch on (off) starts CFView™ without graphical user interface. This mode can be used in combi-nation with the -macro command line option in order to perform the execution of a macro scriptwithout user interaction,

-hoops_relinquish_memory off this option disables the hoops garbage collection feature that isactivated when CFView™ is idle during a long period of time.

14-6 LimitationsThe task manager have some limitations due to the current PVM and MPI libraries:

Limitations The Task Manager

FINE 14-23

• UNIX to PC connections are not allowed.

• The remote copy works only if there is enough disk space on the remote machine. Currently, nocheck is performed to identify the available disk space and the flow solver crashes with "undi-fined reason".

• Parallel computation with distributed memory are only available on homogenous UNIX/Win-dows platforms.

• When a user launches FINE™ on different machines, the connection between these machines isnot allowed as described in section 14-2.1.1.

The Task Manager Limitations

14-24 FINE

FINE™ 15-1

CHAPTER 15:Computation Steering and Monitoring

15-1 OverviewThis chapter describes the Computation Steering pages and the additional tool MonitorTurbo.

First section 15-2 describes the Computation Steering/Control Variables page. Furthermore thischapter is completely dedicated to the monitoring tools available in FINE™ to monitor the globalsolution during and after a computation:

•Computation Steering/Convergence History and Task Manager/Convergence History, see sec-tion 15-3 and

•MonitorTurbo, see section 15-4.

In section 15-5 advice is provided on how to use the monitoring tools in analysing the progress of acomputation.

15-2 Control VariablesThe Computation Steering/Control Variables page allows to define some global parameters for theselected computation:

• the Maximum Number Of Iterations on the finest grid level (i.e. not including the iterationsperformed during coarse grid initialization).

• the Convergence Criteria corresponding to the (negative) number of orders of magnitude thenorm of the residuals must decrease before stopping the calculation. If this criterium is notreached the calculation proceeds until the maximum number of iterations is performed.

• The frequency for saving output (Save Solution Every): every x iterations the solver saves theflow solution and creates the output files to be read in CFView™(where x is the number ofiterations defined in the FINE™ interface).

•When the option Mimimum output is selected the solution is only saved at the last iteration.

• the Memory Requirements for the computation. By default an estimation is given for therequired memory. Depending on the parameters defining the computation additional memorymay be needed. For example, more memory is required when full non-matching connections

Computation Steering and Monitoring Convergence History

15-2 FINE™

or a k-ε turbulence model is used. Also the amount of selected output may require more mem-ory. To allocate more memory for the computation select the button Set the requested memory.This will allow to define the amount of memory in Mb used for reals and integers.

For unsteady computations the Control Variables page is updated to give access to

additional parameters as described in section 4-2.1 and section 4-2.3.

Furthermore this page contains in expert mode two lists of expert parameters. Only the expertparameters that are described in the manual are supported. Use of the other parameters is not rec-ommended. For a summary of all supported expert parameters see Appendix C.

15-3 Convergence HistoryThe Computation Steering/Convergence History or Task Manager/Convergence History pageallows the user to define quantities to be followed during the convergence process of the flowsolver EURANUS. This pages is divided in 5 areas as shown in Figure 15.3.0-1:

1. The steering files selection (Select Computations) and the curves export (Export Curves ToFile...) only available in Task Manager/Convergence History page.

2. The available variables (Available Variables).

3. The parameters (Parameters type).

4. The selected variables (Selected Variables).

5. The graphics view (Convergence History).

FIGURE 15.3.0-1The five areas of the Convergence History page

(2) (3) (4)

(5)

(1)

Convergence History Computation Steering and Monitoring

FINE™ 15-3

When the flow solver EURANUS is invoked, a communication is automatically established withFINE™ allowing the user to follow the selected quantities. Two representations of the quantities arecurrently available: the convergence curves displayed in the area 5 and the quantity value at the lastiteration in the area 4. All these data are stored in files with extension .steering and .steering.binary.These files are created and managed automatically by FINE™

If the communication between the flow solver and FINE™ is interrupted (i.e.: net-

work problem), parts of the convergence curves can be lost.

15-3.1 Steering Files Selection and Curves Export

Different mode exists for the selection of the current steering results stored in the steering files:

1. When a project is opened, the active computation steering files is automatically selected andappears in the Add or select computations window (a) appearing when clicking on Select Com-putations button. Each time a new computation is selected, the associated steering file is auto-matically loaded and becomes the active one.

FIGURE 15.3.1-2Steering files selection area

2. All the steering files already loaded can be selected by <Ctrl>-leftclick and <Shift>-leftclick inthe list of available computations.

3. The file can also be loaded manually using the button Add Computation (c). A file chooserprompts the user to select the file.

4. The button Remove Computation allows the user to remove from the memory the selected com-putation (the file is not removed and remains available for selection).

5. Additionally, when a task is started, the steering files of the flow solver computation called inthe task are automatically loaded and become available through the list (b).

The Export Curves To File... button enables the user to save in an ASCII file ’.cvh’ all the curvesplotted in the Graphics View.

15-3.2 Available Quantities Selection

The available quantities selected by default are linked to the type of computation. For example,when launching a turbomachinery computation, the global residual, the inlet and outlet mass flow,the efficiency, the pressure ratio, the axial thrust and the Torque are computed during the conver-gence process. The Available Quantities list (b) allows the user to select and add (c) new quantitiesto the computed list

(b)

(c)

(a)

(d)


15-4 FINE™

.

FIGURE 15.3.2-3Available quantities selection area

All the quantities can be added before or during the computation.

When a quantities has been added, it appears in the selection list and becomes the selected quantity.If the flow solver is running, the value and the convergence curve of the new quantities is displayedafter a few seconds. The convergence curve begins at the iteration corresponding to the momentwhen the new quantity has been added in the Selected Variables list.

When a quantity is added for selection it appears in the selection list with a number behind thename. This number is only added to avoid to have two times the same variable name in the list. Thisis especially necessary when, for example, the static pressure is monitored at two different points inthe domain.

15-3.3 New Quantity Parameters Definition

When a new quantity has been added, it becomes available for selection in the Selected Variableslist (area 4 in Figure 15.3.0-1). The user can select the way the flow solver computes the quantitythrough the parameter type area (area 2 in Figure 15.3.0-1). Several types of parameters can be cho-sen through the parameter type list box (a in Figure 15.3.3-4).

The available types of parameters that can be defined to computed the selected quantities:

1. global: the computed variable is averaged over all the domain.

2. local 3d grid point: the user specify the grid point indices (I,J,K) and the block index (block id)where the quantity must be computed.

FIGURE 15.3.3-4Parameter type definition

Care should be taken when using the steering of a parameter on a local 3d grid point. It

should be carried out in the following way:

- select the parameter (relative velocity u, static pressure...).

- add for selection. It becomes available for the selected variables.

(a)

(c)

(b)

(a)

Convergence History Computation Steering and Monitoring

FINE™ 15-5

- set the block id and the I,J,K indices of the grid point on which the evolution of theselected parameter will be visualized.

All the user modifications (I,J,K indices...) can also be done (and modified) during the

computation run.

15-3.4 Quantity Selection Area

When a quantity has been added, it becomes available for selection in the Selected Variables list.The list is divided in 3 columns as shown in Figure 15.3.4-5: the variable name (a) which can bechanged using the button rename (d) , the quantity value (b) which displays the last computed valueand the units (c) of the variable. The button remove (e) is used to remove the first selected variable.

.

FIGURE 15.3.4-5Selected variables area

When a quantity is not yet computed, the value indicated is undefined.

Selecting a quantity will show its history in the graphics view as described in the next paragraph. Toselect multiple quantities click on them (with the left mouse button) in the list while holding the<Ctrl> or <Shift> key. To select quantities that are next to each other in the list simply click on thefirst one and keep the mouse button pressed while moving to the last variable.

15-3.5 Definition of Global Residual

The residuals are computed by EURANUS as a flux balance (the sum of the fluxes on all the facesof each cell):

. (15-1)

The root mean square of the residuals is computed with the following formula:

, (15-2)

and the maximum of the residuals in the same way:

, (15-3)

(a) (b)

(d) (e)

(c)

RES fluxes∑=

RMSRES RMSRES

cellvolume-----------------------------

⎝ ⎠⎛ ⎞

⎝ ⎠⎛ ⎞log=

MAXRES MAXRES

cellvolume-----------------------------

⎝ ⎠⎛ ⎞log=


15-6 FINE™

with log the logarithm to the base ten.

On the Computation Steering/Convergence History or Task Manager/Convergence History page,the global root mean square of the residuals normalized by its value at the first iteration is shown.These values are stored in the file with extension .steering.binary. Additionally the global residualsare shown in numerical values in the Task Manager window (3rd column). The RMS value listed inthe Task Manager window is the global root mean square normalized by its value at the first itera-tion: RMSRES-(RMSRES)it=1. The maximum value (4th column) is the maximum residual at a cer-

tain iteration normalized by the RMS residual at the first iteration: MAXRES-(RMSRES)it=1.

FIGURE 15.3.5-6Task Manager window

15-3.6 The Graphics View

FIGURE 15.3.6-7Graphics view area in Computation Steering/Convergence History page

(b)

(a)

MonitorTurbo Computation Steering and Monitoring

FINE™ 15-7

The convergence history of the selected curves are displayed inside the graphics view.

In the Computation Steering/Convergence History page, the color of the curves is different (up to 8selected quantities). The automatic chosen curves colors are also used for the displayed value (a).Additionally, the error between the two first selected quantities is also indicated (b). This is espe-cially important for checking the difference between the mass flow at inlet and outlet(Figure 15.3.6-7).

In the Task Manager/Convergence History page, the color of the curves is the same (but with differ-ent markers) if related to the same computation and is different for each curves if related to different computations (up to 10 selected quantities).

FIGURE 15.3.6-8Graphics view area in Task Manager/Convergence History page

15-4 MonitorTurbo

15-4.1 Introduction

The MonitorTurbo can be launched independently from FINE™ in order to facilitate the batchmode control. It is a separate graphic control window in which the user can visually monitor:

• the convergence history of one or several computations (Convergence history),

• the blade loading distribution (Loading diagram available with FINE™/Design 2D only),

• the blade profile (Blade profile available with FINE™/Design 2D only).

The two last displays are only available under the FINE™/Design 2D environments, as described inChapter 12 and Chapter 13. This section only describes the functionalities of the convergence his-tory display.

Computation Steering and Monitoring MonitorTurbo

15-8 FINE™

On UNIX and LINUX platforms type: monitorTurbo -print <Enter>

When multiple versions of FINE™ are installed the installation note should be con-

sulted for advice on how to start FINE™ in a multi-version environment.

On Windows click on the Monitor icon in Start/Programs/NUMECA software/fine#. Alterna-tively FINE™ can be launched from a dos shell by typing:

<NUMECA_INSTALLATION_DIRECTORY>\fine#\bin\monitor <Enter>

FINE™ allows multi-process analyses. Therefore, the convergence histories of multiple (running)projects can be visualized at the same time. It is also possible to compare the convergence historyassociated with different computational parameters for the same project.

The monitored variables are displayed as a x-y graph in the upper part of the window (a). The x-axis represents the number of multigrid cycles or work units (see section 15-4.3.3 and Section B-4.3) achieved by the flow solver. The y-axis is a logarithmic axis representing the power of ten ofthe residual values. The user can choose the residual of any of the equations solved and some globalparameters using the buttons visible in the lower right part of the graphic control window (b) asshown in Figure 15.4.1-9.

The lower part of the graphic control window contains four boxes. The small box (c) located on theleft side contains a Print button (which allows to save the current graph as a postscript file) and aQuit button (which allows to close the MonitorTurbo window). The three other boxes are describedin the next sections.

.

FIGURE 15.4.1-9The monitorTurbo window

(a)

(b)(c)

MonitorTurbo Computation Steering and Monitoring

FINE™ 15-9

15-4.2 The Residual File Box

Three buttons are provided in this box to Add, Remove or Activate residual files through a filechooser. The residual files describe the iteration process of previous or current computations. Theycontain the history for internal flow of the axial thrust, mass flow, torque, efficiency, pressure ratio(lift, drag and momentum coefficients if external flow) and the residuals of five (seven or six ifrespectively the k-ε or the Spalart-Allmaras turbulence model is used) physical variables.

The activation of a part of the residual files ’.res’ has the effect of deactivating the other loadedresidual files. When a residual file is deactivated, its associated convergence history is not dis-played. The selective activation of residual files allows thus to display only the convergence histo-ries of some of the loaded residual files ’.res’.

The input boxes File and Block, visible just below the three buttons Add, Remove and Activate,allow to select for which file and block the choice of the monitored variables performed in theQuantities to display menu should be applied.

15-4.3 Quantities to Display

15-4.3.1 Residuals

Buttons are provided to select the type of residuals: rms or maximum as shown in Figure 15.4.1-9on the right. The residuals relative to all transport equations of the problem are available: these arethe continuity, the momentum, the energy, and eventually the turbulent kinetic energy k and the tur-bulent dissipation ε (if the turbulent computation is using a k-epsilon model, e.g. not for BaldwinLomax), and the turbulent kinematic viscosity nu (if the Spalart-Allmaras model is used) or theblade force for a throughflow application.

While the Computation Steering/Convergence history or Task Manager/Convergence History pagedisplays only the global residual, the MonitorTurbo gives the RMS and maximum values per block.Computation of the RMSRES and MAXRES values is done according to Eq. 15-1 to Eq. 15-3. Thevalues shown in the MonitorTurbo for the RMS are normalized by the value of RMSRES at the firstiteration: RMSRES-(RMSRES)it=1. The values shown for the maximum residuals are normalized bythe maximum residual at the first iteration: MAXRES-(MAXRES)it=1.

Since the RMS and maximum residuals are normalized differently it may occur that

the RMS value shown in the MonitorTurbo is higher than the maximum residual.

15-4.3.2 Global Quantities

Several buttons are provided to visualize the additional global quantities available under the envi-ronment FINE™/Turbo:

• Internal flow problems (expert parameter IINT=1): The axial thrust, the (inlet and outlet) massflows, torque, pressure ratio, and efficiency.

• External flow problems (expert parameter IINT=0): The drag, the lift and the momentum coeffi-cients. The user has to specify the axis that has to be taken into account for these global quanti-ties as described in section 11-3.

If several computations are performed at the same time, the curves associated with the different projects are drawn in different colors. The buttons of the present box act only on the curves of the file and block selected through the File and Block menu.

Computation Steering and Monitoring Best Practice for Computation Monitoring

15-10 FINE™

15-4.3.3 Display Options

The Legend button is used to display which files are currently activated. In addition, if the mass flow button is activated, the relative errors between the inlet and the outlet are indicated.

The Work Unit button is provided to set the type of unit used on the horizontal axis in the Monitor-Turbo window: multigrid cycles or work units. If Cycles option is chosen (Work Unit button deacti-vate), the abscissa will show the number of iterations, Work Unit option will adapt the values on the horizontal axis with respect to the grid levels (if 3 grid levels are used, one iteration on 222 and 111 is taking respectively 1/64s and 1/8s considering that one iteration on 000 is taking 1s.

The Update now button updates the graph for the active residual file and the selected block.

The Auto update button can be switched on to follow the iteration processes automatically. It ishowever a rather time-consuming option and this button is not active by default.

15-4.3.4 Zooming Option

This option allows to interactively zoom in and out:

1. In the drawing window, press the left mouse button to initiate a zooming operation,

2. Then drag the mouse to the left or to the right to zoom in, the zooming window number is dis-played on the screen,

3. Click again on the left button when finished,

4. To zoom out, click on the right button of the mouse.

15-5 Best Practice for Computation Monitoring

15-5.1 Introduction

Several tools are available in the FINE™/Turbo package to follow the evolution of a calculation:

• the Convergence History page available in FINE™/Turbo and in the Task Manager module,which allows to follow the evolution of a calculation easily and to compare globally the evolu-tion of multiple computations.

•Another useful tool is the MonitorTurbo to compare per equation the evolution of multiplecomputations and per block in the domain.

•CFView™ to enter even into more detail.

Each of them has its own specific features, but they are very complementary. This section describeshow to use those tools to monitor a computation. For a detailed description of the use of CFView™see the separate CFView™ user’s guide.

When a computation has just been launched for the first time, and initialization steps have beenproperly passed, the solver writes a first solution file. In fact it is not yet a solution but only theresult of the initialization. Still this first output is interesting to check if all boundaries conditionshave been set correctly. Especially think to have a look at the rotating elements of the machine, theprofiles of velocities at inlet and at outlet. This operation aims to detect a user mistake, which couldcause a loss of time, like for example, a forgotten patch. To check this first output use CFView™.To check the rotating part of the machine, select the rotating walls (hub or shroud for rotating walls)using the menu item Geometry/Select Surfaces and select for the quantity the velocity. Using the

Best Practice for Computation Monitoring Computation Steering and Monitoring

FINE™ 15-11

Representation menu the velocity will be displayed on the selected patches and this will be therotation speed everywhere.

15-5.2 Convergence History

The global residual on the Convergence History page allows to see quickly whether the computa-tion is iterating properly. The residuals should go down first on the coarser grid levels of the FullMultigrid strategy as shown in Figure 15.5.2-10. See Chapter 9 for more detail on Full Multigrid.When going to a finer grid level the global residual increases suddenly to decrease immediatelyafter. When the computation reaches the finest grid, the curve of the global residual should nor-mally decrease gradually. In general a fall of 3 orders with a stabilization of this curve is consideredas a good convergence. But it is important to check if other global quantities like mass flow, effi-ciency, pressure ratio are also stabilized and to compare the differences between massflow at inletand outlet (in general a difference of less than 5% is acceptable).

FIGURE 15.5.2-10Example of convergence history for global residuals

15-5.3 MonitorTurbo

The MonitorTurbo follows the same quantities as the Convergence History, but its main interest isto offer the possibility to follow the convergence block by block. Thus, one can localize problemsand, if necessary, modify the mesh in the region associated to the block, or change a boundary con-dition.

Finally, coming back to the Task Manager, it is possible to get a deeper control, locally, by addingcontrol points (local 3d grid point). These points allow to track in important parts of the domain,the speed, the pressure and turbulent quantities, which could be a requested information sometimes.In the case of steady computations, the values associated to these points should converge to a con-stant value.

One additional advice is to use CFView™ during the computation with intermediate and non-con-verged solutions. When having convergence problems for example CFView™ may be used to lookfor the zones were the residuals have too high values compared to other regions or an incorrect tur-bulence field. To know in which block(s) the residuals start to increase first in case of divergenceproblem, the MonitorTurbo may already give an indication. Combining the information from the

Computation Steering and Monitoring Best Practice for Computation Monitoring

15-12 FINE™

MonitorTurbo and CFView™ allows to find the cause of convergence problems in the computa-tions.

15-5.4 Analysis of Residuals

In some cases it may occur that the MonitorTurbo shows high RMS and maximum values of theresiduals in a certain block while CFView™ shows high residuals in a different block. This differ-ence between the two tools is caused by the different ways of representing the residuals. InCFView™ the absolute values of the residuals resulting from the flux balance are directly plottedfor each cell. In CFView™ the residuals are not scaled with the cell volumes and no normalizationwith values at the first iteration is applied. This explains why some high maximum residuals inscaled mode can be invisible in CFView™ because they occur in small cells. Also the fact that theresiduals are computed on the cell centers in the solver and shown in CFView™ on the cell cornersmay lead to some, minor, interpolation differences.

FINE™ A-1

APPENDIX A:Governing Equations

A-1 OverviewThe flow solver integrated into the FINE™ user environment is named EURANUS ("EURopeanAerodynamic NUmerical Simulator"). EURANUS is a multipurpose code for 2D and 3D flows incomplex geometries, using the latest numerical developments in CFD. A structured mesh isrequired and complex geometries can be easily handled through a flexible multiblock meshing pro-cedure.

This appendix describes the basic governing equations solved in EURANUS. For more detailedinformation on the different aspects like turbulence, fluid modeling, multi grid strategy etc., see therelated chapters in this manual.

A-2 Reynolds-Averaged Navier-Stokes Equations

A-2.1 General Navier-Stokes Equations

The general Navier-Stokes equations written in a Cartesian frame can be expressed as:

, (A-1)

where is the vector of the conservative variables:

, (A-2)

and are respectively the inviscid and viscous flux vectors:

t∂∂ U FI∇ FV∇+ + Q=

U

Uρ

ρv

ρE

=

FI FV

Governing Equations Reynolds-Averaged Navier-Stokes Equations

A-2 FINE™

and , (A-3)

where the stress and the heat flux components are given by:

(A-4)

and . (A-5)

contains the source terms:

, (A-6)

with expressing the effects of external forces and the work performed by those external

forces: . Other source terms are possible, like gravity, depending on the chosen func-

tionalities.

A-2.2 Time Averaging of Quantities

The Navier-Stokes equations are averaged in time. The density and the pressure are time averagedrelated to the instantenous value through:

(A-7)

where where is the time averaged value and the fluctuating part and

(A-8)

The energy, velocity components and temperature are density weighted averages defined as:

(A-9)

A-2.3 Treatment of Turbulence in the Equations

Except for the non-linear k-ε turbulence model, a first-order closure model based on Boussinesq'sassumption, is used:

(A-10)

Fli

ρvi

ρv1vi pδ1 i+

ρv2vi pδ2 i+

ρv3vi pδ3 i+

ρE p+( )vi

= F– vi

0

τi1

τi2

τi2

qi vjτi j+

=

τi j µ µt+( ) ∂wi

∂xj

--------∂wj

∂xi

-------- 23--- ∇w( )δi j–+=

qi κ κt+( )xi∂∂ T=

Q

Q

0

ρfe

Wf

=

fe Wf

Wf ρfe v⋅=

q q q'+=

q q'

q' 0=

qρq

ρ------=

ρwi″wj″– µt xj∂∂wi

xi∂∂wj 2

3--- w∇( )δi j–+

23---ρkδi j–=

Formulation in Rotating Frame for the Absolute Velocity Governing Equations

FINE™ A-3

with the xi component of the relative velocity. In this equation is the turbulent kinetic energy

and is defined as:

. (A-11)

In contrast to the laminar case, both the static pressure and the total energy contain contributionsfrom the turbulent kinetic energy and are defined as:

, (A-12)

(A-13)

Note that Eq. A-13 does not contain a term in the angular velocity. This term is accounted for in thesource term, and assuming stationary flow, corresponds to the last term of Eq. A-15.

A-2.4 Formulation in Rotating Frame for the Relative Velocity

The resulting time averaged Navier-Stokes equations for the relative velocities in the rotating frame of reference become:

(A-14)

where the shorthand notation , i, in the Fvi expression, is used to denote derivatives with respect to

. The source term vector Q contains contributions of Coriolis and centrifugal forces and is given

by:

(A-15)

with the angular velocity of the relative frame of reference.

A-3 Formulation in Rotating Frame for the Absolute VelocityAlthough the governing equations for rotating systems are usually formulated in the relative systemand solved for the relative velocity components, the formulation retained for ship propeller applica-tions or ventilators are often expressed in the relative frame of reference for the absolute velocity

wi k

k12---ρwi″wi″ ρ⁄=

k

p* p23---ρk+=

E e12--- wiwi k+ +=

U

ρρw1

ρw2

ρw3

ρE

= FIi

ρwi

p*δ1 i ρwiw1+

p*δ2 i ρwiw2+

p*δ3 i ρwiw3+

ρE p*+( )wi

= Fvi–

0

τi1

τi2

τi3

qi wjτi j+

=

xi

Q

0

ρ–( ) 2ω w× ω ω r×( )×( )+[ ]

ρw∇ 0.5ω2r2( )

=

ω

Governing Equations Formulation in Rotating Frame for the Absolute Velocity

A-4 FINE™

components. This formulation is different from the one generally used to solve internal turboma-chinery problems, where the equations are solved for the relative velocity. The two formulationsshould lead to the same flow solution. However, experience shows that the solution can be differ-ent, especially in the far field region. For propeller problems, the formulation based on relativevelocities has the disadvantage that the far field relative velocity can reach high values. Thisinduces an excess of artificial dissipation leading to a non physical rotational flow in the far fieldregion, this dissipation being based on the computed variables.

This formulation is controlled by the expert parameter IVELSY=0.

This formulation is valid only if all boundary conditions are uniform in the azimuthal

direction. If the flow field boundary conditions are not uniform in the azimuthal direc-tion, the boundary conditions expressed in this formulation must be unsteady. In thiscase, the formulation for the relative velocity is suggested.

Except for the non-linear k-ε turbulence model, first-order closure, based on Boussinesq's assump-tion, is used for the Reynolds stress:

(A-16)

with the xi component of the absolute velocity. The flux vectors are decomposed into Cartesian

components:

(A-17)

and

(A-18)

where the shorthand notation , i, in the Fvi expression, is used to denote derivatives with respect to

. The velocity is the xi component of the relative velocity. This formulation envolves thus

both the absolute and the relative velocity components.

The source term vector Q is given by:

, (A-19)

with the angular velocity of the relative frame of reference. Other source terms are possible, likegravity, depending on the chosen functionalities.

ρvi″vj″– µt xi∂∂vi

xi∂∂vj 2

3--- v∇( )δij–+

23---ρkδi j–=

vi

FI fI11x fI21y fI31z+ +=

Fv fv11x fv21y fv31z+ +=

U

ρρv1

ρv2

ρv3

ρE

= FIi

ρwi

p*δ1i ρwiv1+

p*δ2i ρwiv2+

p*δ3i ρwiv3+

ρEwi p*vi+

= Fvi–

0

τi1

τi2

τi3

qi vjτij+

=

xi wi

Q

0

ρ ω v×( )–

0

=

ω

Formulation in Rotating Frame for the Absolute Velocity Governing Equations

FINE™ A-5

The averaged Navier-Stokes equations are obtained by the Favre averaging as described in sectionA-2.2.

In contrast to the laminar case, both the static pressure and the total energy contain contributions

from the turbulent kinetic energy and are defined as:

, (A-20)

. (A-21)

The stress and the heat flux components are given by:

(A-22)

and , (A-23)

k

p* p23---ρk+=

E e12---wiwi k+ +=

τij µ µt+( ) ∂vi

∂xj

-------∂vj

∂xi

------- 23--- ∇v( )δi j–+=

qi κ κt+( )xi∂∂ T=

Governing Equations Formulation in Rotating Frame for the Absolute Velocity

A-6 FINE™

FINE™ B-1

APPENDIX B:File Formats

B-1 OverviewThis Appendix describes the files used by FINE™ and the flow solver EURANUS. It is divided intwo parts. The first one gives the file format information needed to use FINE™, while the secondone describes the format of the files used and produced by EURANUS. As FINE™ is intended tohandle the file treatment for the user, knowing the exact format of all the files used in a simulationprocess is not required. This Appendix is therefore written for advanced users.

In the following description, it is assumed that all the files are related to a generic project called'project'. The chapter is divided in five sections:

• files produced by IGG™,

• files produced and used by FINE™,

• files produced and used by the flow solver EURANUS,

• files used as data profile,

• resource files used to control the layout and which contain default values and reference infor-mation.

To simplify the notations, it is assumed that the related mesh has a topology of one block.

B-2 Files Produced by IGG™This section describes the files produced by the grid generator IGG™ and used by FINE™:

• the identification file project.igg,

• the binary file project.cgns,

• the boundary conditions file project.bcs,

• the geometry file project.geom.

File Formats Files Produced by FINE™

B-2 FINE™

B-2.1 The Identification File: project.igg

This file contains all the mesh geometric and topologic information. It is used by FINE™ to iden-tify the mesh topology. A complete description of this file is given in the IGG™ User’s Guide.

B-2.2 The Binary File: project.cgns

When the mesh is created and saved in IGG™, the binary file project.cgns containing the grid pointcoordinates is created. Later on, the solver will store the wall distances used for the different turbu-lence models in the same file.

B-2.3 The Geometry File: project.geom

When the mesh is created and saved in IGG™, the geometry file project.geom containing the wholegeometry (curves, surfaces and cartesian points) is created.

B-2.4 The Boundary Condition File: project.bcs

As described in Chapter 8, the settings of the boundary condition type have to be set inside IGG™while the physical boundary condition parameters are set in FINE™. The settings of IGG™ arestored in the file project.bcs. This files is used by FINE™ to initialize the boundary condition typesfor each patch. They are updated each time the boundary condition type is changed inside IGG™.

B-3 Files Produced by FINE™This section describes the files produced and used by FINE™ (or used by the flow solver EURA-NUS launched from FINE™). Please note that FINE™ acts as a file manager between differentsoftware systems. Therefore, it is important that the read, write and execute permissions are setproperly for all the files and directories used by FINE™.

Manual modification of these files is not supported since it may corrupt the file or pro-

vide incorrect results. Such a modification should only be done on explicit advice ofNUMECA support team ([email protected]).

B-3.1 The Project File: project.iec

This file contains all the information related to the project. It is used by FINE™ to save and recoverall the user settings. This file is subdivided into several blocks. Each block contains data and/orother blocks. The beginning of the blocks is identified by the key word NI_BEGIN and by a nameand the end of the block is identified by the key word NI_END and by the name of the block.

a) File Header

The file always has the following header containing the version number and the project type:

NUMECA_PROJECT_FILE VERSION 5.0PROJECT_TYPE STRUCTURED

After the header, 3 new lines are used to store the name of the files linked to the project:

Files Produced by the Flow Solver EURANUS File Formats

FINE™ B-3

GRID_FILE /usr/_turnkey_tutorials/_rotor37/rotor37/_mesh/rotor37.iggTRB_FILE /usr/_turnkey_tutorials/_rotor37/rotor37/rotor37.trbGEOMETRY_FILE /usr/_turnkey_tutorials/_rotor37/rotor37.geomTurbo

These are respectively the mesh, the template and the geometry files. The template and the geome-try files are not used by FINE™/Turbo and are only there for backward compatibility reasons.

b) The Computation Block

The project file contains the settings of all the computations defined by the user. Each computationblock is identified by the following keywords:

NI_BEGIN computation...NI_END computation

The computation block contains the following subblocks:

• The Solver Parameters Section block containing all the parameters of the solver EURANUS.

• The Initial Solution & Boundary Condition Section block containing the initial solution andthe boundary conditions.

• The Blade-to-Blade Parameters Section block containing all the parameters of the blade-to-blade module.

• The Grid Parameters Section block containing the topology of the mesh.

• The Fluid Properties Section block containing the fluid properties.

B-3.2 The Computation File: project_computationName.run

When the solver is started, FINE™ creates a new directory using the name of the active computa-tion. A subproject file (’.run’ extension) containing the settings of the active computation is savedinto this new directory. This file is used as input by the flow solver EURANUS and by the flow vis-ualization system CFView™.

The menu File/Save Run Files enables to save the ’.run’ file without starting the

solver EURANUS.

B-4 Files Produced by the Flow Solver EURANUS This section describes the files produced and used by the flow solver EURANUS. The flow solveruses most of the files described above and produces the following files:

B-4.1 The cgns file: project_computationName.cgns

This binary file contains the flow solution. It is used to restart the solver and also by CFView™ tovisualize the flow field. The data structure is the following:

1. For block i= 1 to n:

The primitive flow variables: density, velocity components, pressure. These are computed at cellcenters and are used for restart. Depending on the type of computation, temperature or turbulentquantities such as k, ε or µt are also stored.

File Formats Files Produced by the Flow Solver EURANUS

B-4 FINE™

2. For block i= 1 to n:

The grid point coordinates and the 3D output flow variables as selected by the user through FINE™(see Chapter 11). This data will be read by CFView™. Flow quantities are interpolated at meshnodes by the flow solver as required by CFView™ (see section 11-4 for mathematical details).

If the user selected solid data output, azimuthal averaged output or surface averaged output (seeChapter 11), the corresponding mesh coordinates and computed quantities are added to the corre-sponding ’.cgns’ file.

B-4.2 The mf file: project_computationName.mf

This ASCII file contains averaged quantities over the inlet, outlet and rotor-stator sections. It is gen-erated only if both inlet and outlet boundary conditions are present.

B-4.3 The res file: project_computationName.res

This file contains the residual values for all blocks for each iteration of a computation as describedin section 15-4.3.1. It is continuously updated during the computation. It is used by the Monitor-Turbo to visualize the convergence history.

The format of this file is the following:

• line 1: Version line.

• line 2: Number of blocks.

• line 3: 3D or 2D.

• line 4: NO-K-EPS or K-EPS or SPL-ALM.

• line 5: Number of chemistry species (not used, for backward compatibility only).

• line 6: STEADY or UNSTEADY.

• line 7: TURBO (not used, for backward compatibility reasons only).

• For iteration i=1 to itmaxIteration number, Total iteration number (for unsteady computations only), Work unit, CPUtime, Physical time (for unsteady computations only), Lift, Drag, Torque, Qmax, Tmax,Mass flow in and out.For block j = 1 to n:

RMS residual for the density ρ, the 3 momentum components (ρvx, ρvy, ρvz), the energy

e, the turbulent variables k, ε and υ, and the same data for the maximum residual.

Where:

Iteration number = the number of iterations. For unsteady computations it includes the number ofiterations performed in stationary mode to initialize the unsteady computation.

Total iteration number = the total number of iterations including the dual-time step sub-iterationsand the initial stationary iterations.

Work unit: for single grid computations, one work unit is equal to one iteration, while in multigrid,the work unit corresponds to the computing effort of the multigrid run to the single grid run. For 3D

cases it is computed as follow: WU = 1 + n2(1/2)3 + n3(1/2)6 +...

While for 2D: WU = 1 + n2(1/2)2 + n3(1/2)4 +...

where nx is the number of iteration done on the xth multigrid level

Files Produced by the Flow Solver EURANUS File Formats

FINE™ B-5

RMS is the root mean square of the residual, defined by (see section 15-4.3).

Physical time = the physical time step.

Lift, Drag and Torque are scalar values corresponding respectively to the projection of the forcevector along a lift direction (IDCLP), a drag direction (IDCDP) and a torque direction (IDCMP).These directions are controlled by the real expert parameters "IDCLP", "IDCDP", "IDCMP" inFINE™ (on the Computation Steering/Control Variables page in expert mode) as described in sec-tion 11-2.5.1 and section 11-3.2.

For internal flows (expert parameter IINT=1):

•Qmax = efficiency between inlet and outlet,

• Tmax = total pressure ratio between inlet and outlet.

For external flows (expert parameter IINT=0):

•Qmax = maximum heat flux on surface = k*Grad T*n,

• Tmax = maximum static temperature.

Mass flow in/out = total mass flow for both inlet and outlet boundaries. When no inlet or outlet ispresent in the computation, the corresponding mass flow is set to zero.

Finally, the ".res" file is given with the CPU time included. In case of parallel computations the wallclock time will be given instead of the CPU time.

B-4.4 The log file: project_computationName.log

This ASCII file contains all the information related to the current computation. It contains a sum-mary of the computation variable as well as warnings and error messages. If the flow solverencounters a problem, the latter is described in the ’.log’ file. This file is for support purposes only.When a problem appears please send this file together with a detailed problem description toNUMECA support team at [email protected].

B-4.5 The std file: project_computationName.std

This ASCII file contains all the information related to the current computation. It contains thewhole content of the Task Manager window as well as warnings and error messages. If the flowsolver encounters a problem, the latter is described in the ’.std’ file. This file is for support purposesonly. When a problem appears please send this file together with a detailed problem description toNUMECA support team at [email protected].

B-4.6 The wall file: project_computationName.wall

This self-explained ASCII file gives information about forces and torques on the patches for whichthe Compute force and torque button is activated on the Boundary Conditions page in the Solidthumbnail (see section 8-2.4).

ΣRes2

n---------------------

File Formats Files Produced by the Flow Solver EURANUS

B-6 FINE™

B-4.7 The aqsi file: project_computationName.aqsi

This ASCII temporary file is created and read by the code to ensure a smooth restart in the presenceof quasi-steady rotor-stator interfaces.

B-4.8 The Plot3D files

The Plot3D output module of EURANUS creates 4 files.

• The project_computationName.g file contains the grid data.

• The project_computationName.q file contains the conservative variables.

• The project_computationName.f file contains additional variables.

• The project_computationName.name file contains the names of the additional variables.

The first 3 files can be written in ASCII or binary format, the binary format being the Fortran unfor-matted format. The .name file is always written in ASCII.

When the "Unformatted file (binary)" FORTRAN format is selected in FINE™:

the user has to make sure that the file format is also correctly defined in CFView™.When opening the Plot3D project in CFView™ through the menu File/Open Plot3DProject... , click on the File Format... button and select Unformatted. Do not selectBinary as it corresponds to binary files generated by C programs. Once this is done, theuser also needs to check the "binary low endian" or "binary big endian" format on thesame page. On PC platforms (Windows or LINUX) make sure to use "binary lowendian" format whereas "binary big endian" is mandatory on all other platforms.

1. The project_computationName.g file format:

• Line1: number of blocks,

• Line2: the 3 dimensions of each block,

• for each block, the coordinates of the mesh points.

2. The project_computationName.q file format:


• Line2: the 3 dimensions of each block,

• for each block:the free stream mach number, the flow angle, the Reynolds number and the time,the 5 conservative unknowns: density, the 3 momentum components and energy.

3. The project_computationName.f file format:


• Line2: for each block, the 3 dimensions and the number of additional variables selected by theuser,

• for each block: the additional flow variables.

4. The project_computationName.name file format:

This file contains the names of the additional variables stored in the ’.f’ file, one name per line. Ifthe quantity is a vector, it will be written on 3 different lines like in the following example:

Files Used as Data Profile File Formats

FINE™ B-7

Velocity-X

Velocity-Y

Velocity-Z

B-4.9 The me.cfv file: project_computationName.me.cfv

This ASCII file contains data required for the visualization of the meridional averaged output underCFView™. It is created whenever the user specifies variables in the Outputs/Azimuthal AveragedVariables page of the FINE™ interface.

B-5 Files Used as Data ProfileThis section describes the files created by the user and used as input data for the boundary condi-tions and for the fluid model. Once these files are read by the interface, they are imported in the’.iec’ file described in section B-3. The flow solver does not read these files, it retrieves the profilesfrom the computation definition file with extension ’.run’. Profiles may also be specified by enter-ing the coordinates directly into the profile viewer, as described in section 2-12.

The imported values will be interpreted in the current project units. These values

would change (in the database) if the user changes the corresponding units. Therefore allvalues will be converted for the flow solver EURANUS in SI system units (in radians forthe angles).

The values for 1D profiles should be given in increasing order of the x-coordinate. For example,when entering a profile of temperature as a function of R, FINE™ checks whether the two firstpoints are in increasing order. If this is not the case, the profile will be inverted automatically in

order to ensure compatibility with the flow solver. The next time the Profile Manager ( ) isopened, the profile will be shown in increasing order, contrary to what was initially entered.

For 2D profiles there is no such constraint except for profiles as a function of r-θ (see section 4-2.3.2).

B-5.1 Boundary Conditions Data

When defining the inlet (or outlet) boundary condition parameters, the user has the option of speci-fying one or several input files containing each a data profile. These profiles are used to compute byinterpolation the corresponding physical variables at the inlet (or outlet).

The file containing the profile must be created by the user and its name must possess the ’.p’ exten-sion. The values of the physical variable stored in this file can come from any source: experiments,previous computations, etc.

The format used to create this file contains:

• Line 1: Two strings defining the name of the coordinate axes.

• Line 2: Type of interpolation and number of points of the profile curve.The types are: 0 for data given at each cell centre

1,2,3,4 and 5 for 1D interpolation respectively along x, y, z, r and θ.51 for 2D interpolation along x and y.52 for 2D interpolation along x and z.

File Formats Files Used as Data Profile

B-8 FINE™

53 for 2D interpolation along y and z.54 for 2D interpolation along r and θ.55 for 2D interpolation along r and z.56 for 2D interpolation along θ and z.

The theta angle is defined as θ = arctg (y/x). The θ profile should cover the patch

geometry, so it may take negative values. For unsteady calculations with profile rotationthe θ profile must be given form 0 to 2π (see section 4-2.3.2).

For time dependant profiles the interpolation type is 100.

• The next lines contain the coordinate(s) of each point with the associated physical value.

Example 1:

r pressure4 50.5 1010000.6 1020000.6 1030000.7 1020000.8 101000

This example is related to the interpolation of the pressure along the radius. There are 5 point coor-dinates in the file. This is a space profile.

FINE™ uses the same file formats to import space, time, and space and time profiles. Thus if thereis only one profile in the file, it will be interpreted as a space profile, if a second profile exists,FINE™ will recognize it as a time profile. Following is an example of a space and time profile:

Example 2:

R Pt 4 6 .3 95600.13 .251765 98913.46 .248412 100909.6 .24445 101527.6 .240182 101740.4 .23622 101811.4

100 10.216713 101811.4 .210922 101872.1 .205435 101872.1 .199644 101872.1 .195682 101872.1 .191414 101872.1 .187452 101872.1 .18349 101740.4 .179222 99946.98 .1 99946.98

Files Used as Data Profile File Formats

FINE™ B-9

The two profiles are separated by an empty line. The interpolation type in time is specified as 100.

If this file is imported with the profile viewer invoked as "fct(space)"- only the first part will betaken into account. If "fct(time)" is specified - only the second part will be read by the flow solver.Both profiles will be imported if "fct(space-time)" is specified for the variable type.

If there are less coordinates supplied than the number of points specified, FINE™ will put zero forthe missing coordinates.

B-5.2 Fluid Properties

Fluid properties like Cp or Gamma or the viscosity can be input in the solver as constant but canalso be input as variables in function of the temperature.

The format used is the following:

• Line 1: Two strings: "T" and the name of quantity considered ("P" and "Density" for baro-tropic law).

• Line 2: Contains two integers:

— the first number is the type of interpolation: 11 for Temperature and 12 for Pressure (baro-tropic profiles only),

— the second one defines the number of points on the profile curve.

• The next lines list the data of each point: temperature and the fluid property.

Example 1:

T Mu11 5270 6e-5275 3e-5280 2e-5290 1.5e-5300 0.9e-5

It is recommended to cover the whole temperature range of the problem.

The format for the Cp and Gamma profiles is slightly different because the two profiles are speci-fied in the same file (with extension .heat_capacity). It is as shown in the example below:

Example 2:

T Cp11 4295 1004.9298 1005.3301 1010.8318 1011.0

11 3296 1.31298 1.34303 1.36

File Formats Resource Files

B-10 FINE™

The first set of points is for the Cp profile, the second is for the Gamma profile as functions of thetemperature.

B-6 Resource FilesAll the resource files are located in the same directory, which is ~/COMMON under UNIX and~\bin under Windows. It is not possible to start FINE™ if any of these files is missing.

B-6.1 Boundary Conditions Resource File euranus_bc.def

This file contains the default values for all parameters of the available boundary conditions. Thesame file is also used to create the graphical layout of the page Boundary Conditions in FINE™.FINE™ only reads from this file so this file is not modified while using FINE™.

B-6.2 Fluids Database File euranus.flb

This file contains all the data relative to the fluids created by the users in the page Configuration/Fluid Model. This file is overwritten each time a user quits FINE™ after modifying the fluids data-base (add, remove, or modify a fluid). All the users should have read and write permissions for thisfile. It is not recommended to modify this file manually.

B-6.3 Units Systems Resource File euranus.uni

This file contains the conversion factors for all physical quantities used in FINE™ for all possiblecombinations between existing systems of units. To add a new units system the user should add thecorresponding conversion factors following the existing format shown in the extract below:

...

# new units can be added by respecting the format

# for UNITS NAMES AND CONVERSION FACTORS

# NOTE: VALUE_UNITS_NAME value should NOT begin with capital letter !

# -----------------------------------------------------------------------

# -----------------------------------------------------------------------

# these are the names of the systems

# used to change all the quantities at the same time

DEFAULT_SYSTEM SI

DEFAULT_SYSTEM Default

DEFAULT_SYSTEM American 1

DEFAULT_SYSTEM American 2

# -----------------------------------------------------------------------

# -----------------------------------------------------------------------

Resource Files File Formats

FINE™ B-11

# this is the system that will be taken as default

# when creating a new project

NEW_PROJECT_DEFAULT_SYSTEM Default

# -----------------------------------------------------------------------

# --------------------- UNITS NAMES AND CONVERSION FACTORS ---------------

NI_BEGIN UNITS_RECORD

NUMBER_OF_SYSTEMS 4

VALUE_UNITS_NAME length

UNITS_NAME 1 [m]

CONV_FACTOR 1 2 1.

CONV_FACTOR 1 3 3.280839895

CONV_FACTOR 1 4 39.37007874

UNITS_NAME 2 [m]

CONV_FACTOR 2 1 1.

CONV_FACTOR 2 3 3.280839895

CONV_FACTOR 2 4 39.37007874

UNITS_NAME 3 [ft]

CONV_FACTOR 3 1 0.3048


CONV_FACTOR 3 4 12.

UNITS_NAME 4 [in]



CONV_FACTOR 4 3 0.08333333333

NI_END UNITS_RECORD


NUMBER_OF_SYSTEMS 4

VALUE_UNITS_NAME mass

UNITS_NAME 1 [kg]

CONV_FACTOR 1 2 1.

CONV_FACTOR 1 3 0.06852176586

CONV_FACTOR 1 4 0.005710147155

UNITS_NAME 2 [kg]

CONV_FACTOR 2 1 1.

CONV_FACTOR 2 3 0.06852176586

CONV_FACTOR 2 4 0.005710147155

UNITS_NAME 3 [lbf s2/ft]


B-12 FINE™

CONV_FACTOR 3 1 14.59390294

CONV_FACTOR 3 2 14.59390294

CONV_FACTOR 3 4 0.08333333333

UNITS_NAME 4 [lbf s2/in]

CONV_FACTOR 4 1 175.1268352

CONV_FACTOR 4 2 175.1268352

CONV_FACTOR 4 3 12.

NI_END UNITS_RECORD

......

If, for example, a new system is added on the fifth position, the user should supply the factors toconvert the physical quantities from all the existing systems (1, 2, 3, and 4) to the fifth, and backfrom the fifth to all the others as shown below:


NUMBER_OF_SYSTEMS 5

VALUE_UNITS_NAME length

UNITS_NAME 1 [m]

CONV_FACTOR 1 2 1.

CONV_FACTOR 1 3 3.280839895

CONV_FACTOR 1 4 39.37007874

CONV_FACTOR 1 5 new_factor_value_from_1_to_5

UNITS_NAME 2 [m]

CONV_FACTOR 2 1 1.

CONV_FACTOR 2 3 3.280839895

CONV_FACTOR 2 4 39.37007874


UNITS_NAME 3 [ft]



CONV_FACTOR 3 4 12.


UNITS_NAME 4 [in]



CONV_FACTOR 4 3 0.08333333333


UNITS_NAME 5 [new_units_name]





NI_END UNITS_RECORD

Resource Files File Formats

FINE™ B-13

The default units sytem can be changed by modifying the line

NEW_PROJECT_DEFAULT_SYSTEM Default

with the name of the desired system.

The first (SI) and the second (default) systems are identical except for the rotational

speed units (RPM vs. radian).


B-14 FINE™

FINE™ C-1

APPENDIX C:List of Expert Parameters

C-1 OverviewOn the Control Variables page under Expert Mode a list of non-interfaced expert parameters isavailable. As stated in the interface these parameters should not be used unless explicitly stated inthis manual. This chapter contains a list of all non-interfaced expert parameters that are described inthis manual. For each parameter a reference is given to the corresponding section. If more informa-tion is desired on another parameters please contact NUMECA support at [email protected].

C-2 List of Integer Expert ParametersCLASID: class of particles for CFView™ output section 7-2.5COOLFL: select cooling/bleed through external file and version section 7-4.3EFFDEF: efficiency definition section 11-3.2I2DLAG: simplification of Lagrangian module section 7-2.5IADAPT: parametrised target distribution section 13-2.5IATFRZ: mutligrid parameter for Baldwin Lomax section 4-3.4IBOTH: time discretization section 9-3.2IBOUND: reflection treatment of particles on solid wall section 7.2-2ICODKE: activation of compressible dissipation section 4-3.4ICOPKE: pressure gradient velocity model section 4-3.4ICYOUT: solution overwritten every NOFROT timesteps section 4-2.2IFACE: spatial discretization section 9-3.2IFNMB: transform PERNM boundaries in FNMB section 4-2.2IFNMFI: reading full non-matching data from file section 5-4.3.4IFRCTO: activate partial torque output section 8-2.4.3IHXINL: inlet boundary condition for condensable fluid section 3-2.9IINT: internal or external flow section 11-3.2IKELED: activation of LED scalar scheme for k-ε section 4-3.4IKENC: non-conservative approach for k-ε section 4-3.4IMASFL: mass flow extrapolation at inlet instead of velocity section 8-3.2IMTFIL: initial solution for k-ε section 10-4.3INEWKE: definition of high Reynolds k-ε model section 4-3.4

List of Expert Parameters List of Float Expert Parameters

C-2 FINE™

INIKE: initial solution for k-ε section 10-4.3INVMOD: restart of inverse design section 13-2.5INVSPL: inverse design of splitter blades section 13-2.5IOPTKE: optimized implementation for k-ε section 4-3.4IPROLO: multigrid prolongation order section 9-3.2IRESTR: multigrid restriction order section 9-3.2IRGCON: real gas modelling section 3-2.9IROEAV: upwind discretization section 9-3.2IRSMCH: residual smoothing section 9-3.2IRSNEW: rotor-stator interaction section 5-4IRSVFL: viscous fluxes treatment at R/S interface section 5-5.4ISIDAT: rotor-stator connectivity structure section 5-4ITFRZ: freezing of turbulent viscosity section 4-3.4ITHVZM: definition of flow angle in throughflow section 6-4ITRWKI: wake induced transition through AGS model section 7-5.3ITYSTO: storage of the energy section 3-2.9IUPWTE: upwind discretization for turbulence equations section 4.3.4IVELSY: relative frame of reference section A-3IWAVVI: spatial discretization section 9-3.2IWRIT: writing of global performance data section 11-3.2IYAP: Yap’s modification for turbulent length scale section 4-3.4KEGRID: switch from Baldwin-Lomax to k-epsilon model section 4.3.4KOUTPT: particles trajectories output section 7-2.5LIPROD: linear production term section 4-3.5LMAX: maximum number of segments in Lagrangian module section 7-2.5MAXNBS: maximum number of injection sectors section 7.4-3MGRSTR: multigrid strategy section 9-3.2MGSIMP: multigrid strategy section 9-3.2MXBFSZ: maximum buffer size section 14-4.4NIBOUND: reflection treatment of particles on solid wall section 7-2.5NCLASS: maximum nuber of classes section 7-2.5NPERBC: inlet/outlet signal periodicity section 4.2-2NQSTDY: update rotor-stator boundary condition section 5-4NREPET: calculation of the wall distance section 4-3.4NSUBM: number of subdomains in calculation of wall distance section 4-3.4NTUPTC: number of patches in calculation of wall distance section 4-3.4OUTTYP: select type of output section 11-3.2THINI: throughflow under-relaxation section 6-4VISNUL: central discretization section 9-3.2ZMNMX: indication of injector positions in cooling/bleed section 7-4.3

C-3 List of Float Expert ParametersALF: constant for compressible dissipation section 4-3.4ALPHAP: preconditioning parameter section 4-3.8ANGREL: relative angles for the inlet boundary conditions section 8-3C3: constant for k-ε model section 4-3.4CDIDTE: central discretization section 9-3.2CE1: constant for k-ε model section 4-3.4CE2: constant for k-ε model section 4-3.4

List of Float Expert Parameters List of Expert Parameters

FINE™ C-3

CMU: constant for k-ε model section 4-3.4COOLRT: reduction of mass flow in cooling holes section 7-4.3CP1: constant for compressible dissipation section 4-3.4CREF: reference chord for non-dimensionalizing section 11-3DDIMAX: tolerance factor for Lagrangian module section 7-2.5DIAMR: diameter ratio for Lagrangian module section 7-2.5EKCLIP: clipping value for turbulent kinetic energy section 4-3.4ENTRFX: upwind discretization section 9-3.2EPCLIP: clipping value for turbulent kinetic dissipation section 4-3.4EXPMAR: central discretization section 9-3.2FTRAST: forbid transition before FTRAST*chord with AGS model section 7-5.3GAMMAT: turbulence time scale section 4-3.4IDCDP: direction of drag or axial thrust section 11-3.2IDCLP: direction of lift section 11-3.2IDCMP: direction of moment or torque section 11-3.2IRKCO: Runge-Kutta coefficients section 9-3.2ISWV: Runge-Kutta dissipative residuals section 9-3.2IXMP: definition of point for moment or torque section 11-3.2LTMAX: maximum turbulent length scale section 4-3.4MAVREM: control of multigrid correction for k and ε section 4-3.4MAVRES: update control of k and ε section 4-3.4MUCLIP: clipping value for Mut/Mu for k and ε and Spalart-Allmarassection 4-3.4NUTFRE: initial value of turbulent viscosity for Spalart Allmaras section 4-3.3PRCLIP: turbulence parameter section 4-3.4PRT: turbulent Prandtl number section 4-3.4RADAPT: parametrised target distribution section 13-2.5RELAXP: under-relaxation for mass flow imposed at outlet section 8-3RELPHL: relaxation factor for Phase-Lagged section 4.2.2RESFRZ: freeze turbulent viscosity field section 4-3.4RGCST: value of the gas constant section 3-2.9RSMPAR: residual smoothing parameter section 9-3.2RTOL: maximum angle for normals in calculation wall distance section 4-3.4SIGE: constant for k-ε model section 4-3.4SIGK: constant for k-ε model section 4-3.4SIGRO: constant for k-ε model section 4-3.4SMCOR: residual smoothing section 9-3.2SREF: reference surface to non-dimensionalize coefficients section 11-3TEDAMP: damping for k-e model section 4-3.4THFREL: throughflow under-relaxation section 6-4VELSCA: maximum value allowed for velocity scaling section 8-3VIS2: central discretization section 9-3.2VIS2KE: central discretization section 9-3.2VIS4: central discretization section 9-3.2VIS4KE: central discretization section 9-3.2

List of Expert Parameters List of Float Expert Parameters

C-4 FINE™

FINE™ D-1

APPENDIX D: Characteristics of Water (steam) Tables

D-1 OverviewAs described in section section 3-2.3.4, the Condensable Fluid module aims at the modelling of thereal thermodynamic properties of a given fluid by means of interpolation of the variables from ded-icated tables.

The approach that has been adopted in EURANUS consists of using a series of thermodynamictables, one table being required each time a thermodynamic variable must be deduced from twoother ones. This implies the creation of many tables as input, but presents the advantage that no iter-ative inversion of the tables is done in the solver, with as a consequence a very small additionalCPU time.

Information related to

• the range of variation of admissible values for thermodynamic variables

• the discretization of the grid

• the nature of the interpolation algorithm selected

• the relative mean error (mean and maximum) on thermodynamic variables

• the size of the table

is discussed here below for water (steam) tables.

D-2 Main CharacteristicsWater (steam) tables come in the form of 11 tables, described as follows:

TER: interpolates static temperature as a function of internal energy and density PER: interpolates static pressure as a function of internal energy and density RPT: interpolates density as a function of static pressure and temperature EPT: interpolates internal energy as a function of pressure and static temperature SHP: interpolates entropy as a function of total enthalpy and static pressurePHS: interpolates static pressure as a function of entropy and total enthalpy

Characteristics of Water (steam) Tables Main Characteristics

D-2 FINE™

RHS: interpolates static pressure over density as a function of entropy and total enthalpyHSP: interpolates total enthalpy as a function of entropy and static pressureMER: interpolates dynamic viscosity as a function of internal energy and densityKER: interpolates thermal conductivity as a function of internal energy and densityPSA: defines the saturation line

Table 1 on page 2 lists the range of admissible variations for the thermodynamic variables, in thedifferent tables proposed. Ranges have been extended from the default tables proposed up toFINE™ /Turbo v6.2-7, especially at low pressures (< 1000 Pa). Significant improvements, both interms of robustness and accuracy, are expected in that area.

Tables Variables Minimum Maximum

TER / PER Energy [J/kg] 500,000 4,000,000

Density [kg/m3] 0.001 1,020

Pressure [bars] 0.0003 26,600

Temperature [K] 237 1,630

RPT / EPT Pressure [bars] 0.002 24,000

Temperature [K] 250 1,350

Density [kg/m3] 0.00032 1,432

Energy [J/Kg] -187,568 4,212,000

Enthalpy [J/kg] -99,726 5,500,000

SHP Enthalpy [J/kg] 1,500,000 4,500,000


Entropy [J/kg/K] -1,582 12,733

PHS / RHS Enthalpy [J/kg] 1,850,000 4,500,000

Entropy [J/kg/K] 2,000 10,500


HSP Enthalpy [J/kg] -1,655 50,000,000

Entropy [J/kg/K] 0 13,000


MER / KER Energy [J/Kg] 500,000 4,000,000

Density [kg/m3] 0.001 500

Viscosity [Pa.s] 0.0000085 0.00013

Conductivity [W/m/K] 0.015 0.58

TABLE 1. Admissible range of variations for thermodynamic variables

Main Characteristics Characteristics of Water (steam) Tables

FINE™ D-3

Both RMS (root mean square) and maximum errors should be interpreted as relative errors. RMSerror does not exceed 2%, while in most tables it is ranging from 0.0001% to 0.1%. Maximum rela-tive errors are located nearby the saturation line, where the interpolation naturally degrades despitethe use of bi-cubic double precision algorithms.

Tables RPT and EPT have been tuned so as to guarantee maximum accuracy in the vapor phase (<0.1% at maximum). However, run performed in the liquid phase are consequently prohibited sincethey would lead to large relative errors (> 100%) in that area. A dedicated set covering RPT andEPT tables balancing maximum relative errors both on vapor and liquid phases can however beobtained upon request. Please take direct contact at [email protected] for any question on thispurpose.

Tables Grid Interpolation ErrorRMS [%]

Error Max-imum [%]

Size[Mb]

PER 71 x 71 bi-cubic (double precision) 0.02 80.7 3.2

TER 71 x 71 bi-cubic (double precision) 0.014 1.7 3.2

RPT 101 x 101 bi-cubic (single precision) - < 0.1 3.3

EPT 101 x 101 bi-cubic (single precision) - < 0.1 3.3

SHP 41 x 41 bi-cubic (single precision) 0.0015 0.008 0.5

PHS 81 x 81 bi-cubic (single precision) 0.005 5.8 2.1

RHS 81 x 81 bi-cubic (double precision) 0.026 9.7 4.2

HSP 81 x 81 bi-cubic (single precision) 0.0003 0.01 2.1

MER 41 x 61 bi-cubic (double precision) 0.126 8.7 1.6

KER 41 x 61 bi-cubic (double precision) 2.02 27.2 1.6

PSA 120 cubic - - 0.1

TABLE 2. Main characteristics of water (steam) thermodynamic tables

Characteristics of Water (steam) Tables Main Characteristics

D-4 FINE™

Index

FINE™ i

INDEX

AAbu-Grannam-Shaw Model 7-41

Add Fluid 3-3ANSYS

Outputs 11-10

AutoBlade 2-3, 2-10

AutoGrid 1-2, 2-3, 2-5, 2-10

Axial Thrust 8-11, 11-15

Azimuthal Averaged Output 11-9

BBackground Color 1-7Barotropic Liquid, see Fluid, Barotropic LiquidBenedict-Webb-Rubin 3-13

Blade To Blade 12-1–??Boundary Conditions 12-8

File Formats 12-13–12-17

Flow Solver 12-12

Geometrical Data 12-3

Initial Solution 12-10, 13-5

Input Files 12-13–12-15

Inverse Design 12-8

Mesh Generator 12-6, 12-11

New Project 12-2

Numerical Model 12-10

Open Project 12-2

Output Files 12-15–12-17

Stream Surface Data 12-4

Theory 12-11Bleed flow

Data file 7-33

Flow Parameters 7-29

Outputs 7-31

Positioning 7-18

Visualization 7-30

Wizard 7-16Block

Conjugate Heat Transfer 7-12

Throughflow 6-2–6-3

Boundary Conditions 8-1

Blade To Blade 12-8

Lagrangian Module 7-4, 7-4–7-6

Rotor/Stator 5-17–5-19

Throughflow 6-7–6-8

Turbulence 4-16

Unsteady 4-2

Boussinesq 4-47

CCFD

Governing equations A-1

Introduction 1-1

CFL Number 7-12, 9-2, 9-17

CFView™ 1-3–1-4, 2-10

CGNS B-3Characteristic Values, see Reference ValuesComputation Definition Area 2-12Condensable fluid

Boundary conditions 8-20

Outputs 11-4Condensable Fluid, see Fluid, CondensableConductivity 3-3–3-5

Laminar 3-10

Turbulent 3-10

Turbulent, Condensable Fluid 3-15

Conjugate Heat Transfer 7-11–7-15

Blocks Types 7-12

Theory 7-13–7-15

Control Variables 15-1

Unsteady 4-4

Convention 1-5

Convergence History 10-4Cooling

Theory 7-32, 7-33Cooling flow

Bleed flow 7-15

Data file 7-33

Flow Parameters 7-29

Outputs 7-31

Positioning 7-18

Visualization 7-30

Wizard 7-16Create

Grid File 2-3

Project 2-2, 2-4, 12-2, 13-2

Run Files 2-6

DDelete Fluid 3-7

Design 2D 2-10, 13-1–??Formulation 13-4, 13-7

Input Files 13-3, 13-8

Interface 13-2

Output Files 13-9

Start 13-6

Theory 13-7–13-8

Design 3D 1-2, 2-3, 2-10

ii FINE™

Index

INDEX

DiscretizationCentral Scheme 9-9–9-10

Limiters 9-12

Spatial 9-4, 9-7–9-13

Temporal 9-4

Time 9-17–9-21

Upwind Scheme 9-10–9-13

Drag 8-11

Drag Coefficient 11-19

Driver 1-6

Dryness Fraction 3-15

Duplicate Active Project 2-6

EEdit Fluid 3-7

Efficiency 11-16

Enthalpy 3-11, 3-15

Entropy 3-14

Euler 4-15

2D 6-1

Equations 6-13

EURANUS 1-3EuranusTurbo

Parallel Computation 14-8, 14-17

Expert Mode 2-12

Expert Parameters C-1, D-1

External Boundary Condition 8-13

FFile Chooser 2-19

File Format 6-9, B-1

File Management 1-3

File Menu 2-4

File Names, Limitations 2-7Fluid

Add 3-3

Condensable 3-13–3-16

Delete 3-7

Edit 3-7

Incompressible 5-18

Interface 3-2

Liquid 3-12

List 3-2

Models 3-1–3-16

Perfect Gas 3-10

Real Gas 3-11Fluid-Particle Interaction. See Lagrangian Module.Force 8-11

Blade 6-14

Friction 6-15

Forced Transition 7-38, 7-40

Formula Editor 3-6

Full Non-matching 5-20

Fully Laminar 7-40

Fully Turbulent 7-40

GGauss Theorem 9-8

Global Layout 2-7

Global Performance 11-15, B-4

Graphics 1-6

Graphics Area 2-16

Gravity 3-5, 4-41Grid

Create Grid File 2-3

Grid Generation 1-2–1-4

Units 2-4, 2-8Group

Block Rotation 5-2

Boundary Conditions 8-2

Rotor/Stator 5-3

HHand Symbol 1-5

Host Definition 14-5

Hybrid Analysis 6-3

IIcon Bar 2-10

IGG™ 1-3, 2-3, 2-5, 2-10Incompressible

Fluid Model, see Fluid Model, IncompressibleLocal Conservative Coupling 5-18

Initial Solution 10-1–10-8

Blade To Blade 12-10, 13-5

Block Dependent 10-1–10-3

Coarse Grid 9-3

Constant Values 10-3

File 10-4–10-5

Full Multigrid Strategy 9-16

Throughflow 6-8–6-9, 10-7–10-8

Turbomachinery 10-6–10-7

Turbulence 4-16

Unsteady 10-5Initialization

Full Multigrid Strategy 10-1

Unsteady 4-4

Index

FINE™ iii

INDEX

Installation 1-6

Interface 1-7

General Description of FINE™ Interface 2-1–2-19

LLagrangian Module

Boundary Conditions 7-4, 7-4–7-6

Global Strategy 7-3

Interaction With Turbulence 7-10

Outputs 7-6

Particles Traces 7-7

Theory 7-9–7-11

Laminar 4-15

Layout 2-7

License 1-8

Lift 8-11

Lift Coefficient 11-19

Light Bulb 1-5

Limitations 2-7, 2-8Limiter

Lacor 9-12

Minmod 9-12

Superbee 9-12

Van Albada 9-12

Van Leer 9-12

Linearization 4-27

LIPROD 4-27Liquid, see Fluid, LiquidLocal Conservative Coupling 5-17–??Loss Coefficient 6-6

Low Speed Flow 4-42

MMach Number

Absolute 11-5

Condensable Fluid 3-15

Isentropic 13-4, 13-10

Relative 11-5

Mathematical Model 4-15Menu

File 2-4

Menu Bar 2-4

Mesh 2-8

Modules 2-10

Solver 2-9Merge

Merge Mesh Topology 2-11

Patch For Azimuthal View 11-9

Mesh 1-2–1-4

Information 2-15

Properties 2-8

Selection 2-11

Toggles 2-14

View 2-8, 2-16–2-18

View Area 2-13

Modules 2-10

Moment 8-11

Momentum 11-19Monitor

Convergence History 15-11

Display 15-10

Quantities 15-3

Residual File Box 15-9

Solution 15-1–15-12

Steering File 15-3

Zoom 15-10

MonitorTurbo 15-7

MSW Driver 1-6

Multigrid 9-2

Full 9-16

Prolongation 9-16

Strategy 9-3, 9-13–9-17

NNew Project 2-4, 12-2, 13-2

Numerical Model 9-1

Blade To Blade 12-10

OOpen

Project 2-3, 2-5

OPENGL Driver 1-6

Outputs 3-15, 11-1–11-24

3D Quantity 11-2–11-7, 11-20

Azimuthal Averaged 11-9, 11-18, 11-21–11-23

Lagrangian Module 7-6

mf File 11-15, 11-18

Particle Traces 7-7

Surface Averaged 11-8, 11-21

Theory 11-20–11-24

PPair of Scissors 1-5

Parallel Computation 14-13

Parameter Button 2-13

Parameters Area 2-2

Particles 7-1Perfect Gas, see Fluid, Perfect Gas

iv FINE™

Index

INDEX

Performance 11-15, B-4

Periodic Boundaries 6-7, 8-9

Phase Lagged 4-3, 4-13

Plot3D 11-17, B-6

Post Processing 1-3–1-4

Prandtl Number 3-10

Preconditioning 4-42

Parameters 4-45, 9-3

Preferences 2-6

Profile Manager 2-19, 3-3–3-6

File Formats B-7Project

Configuration 2-4

Creation 2-2

Duplicate 2-6

Management 1-3

New 2-4

Open 2-3, 2-5

Save 2-6

Units 2-6Properties

Fluid 3-1

Mesh 2-8PVM

Daemons 14-1–14-5

QQuit 2-7

RReal Gas, see Fluid, Real GasReference

Density 3-9, 4-47

Length 4-47

Pressure 3-5, 4-45

Reference Values 4-47

Temperature 3-5, 3-9, 4-45

Velocity 4-45, 4-47

Residual 11-6, 15-5, B-4

Implicit Smoothing 9-20

Radespiel & Rossow 9-20

Swanson & Turkel 9-21

Vasta 9-21

Restart 2-10

Design 2D 13-6

Unsteady 4-5

Reynolds Number 4-47Rotation

Blocks 5-2–5-3

Rotor/StatorDomain Scaling 5-11–5-12, 5-21–5-24

FNMB Mixing Plane Coupling 5-19–5-21

Frozen Rotor 5-9–5-10, 5-24

Initial Solution 10-6

Interface 5-3–5-5

Local Conservative Coupling 5-17–5-18

Mixing Plane Coupling 5-5–5-8, 5-16–5-21

Phase Lagged 5-13

Pitchwise Rows Coupling 5-18–5-19

Steady 5-5–5-8, 5-9–5-10, 5-16–5-21, 5-24

Theory 5-15–5-24

Unsteady 5-11–5-12, 5-13, 5-21–5-24

Rough Wall 4-35

Run File 1-3, 2-6Runge-Kutta

Scheme 9-17

SSave

Intermediate Solution 2-9

Project 2-6

Scripts 14-14

Second Order Restart 4-5

SI System 2-6

Smooth Wall 4-35

Solid Data 11-6

Solver Menu 2-9

Specific Heat 3-10–3-12, 3-15

Standard Mode 2-12

Start Flow Solver 2-9Stator

Rotor/Stator Interface. See Rotor/Stator.Steady

Rotor/Stator 5-5–5-8, 5-9–5-10, 5-16–5-21, 5-24

Stop Flow Solver 2-9

Surface Averaged Output 11-7

Suspend Flow Solver 2-9

Sutherland 3-9

Sutherland Law 3-9

TTask Definition 14-6

Taskmanager 14-1–14-23

Add Host 14-5

Delay 14-6

Limitations 14-22

Parallel Computation 14-8

PVM 14-1–14-5

Index

FINE™ v

INDEX

Remove Host 14-6

Scripts 14-14–14-22

Shutdown 14-6

Subtask 14-7–14-11

Task Definition 14-6–14-11

Tear-off Graphics 2-8Temperature

Reference 3-9

Sutherland 3-9

Thermal Connections 7-12

Thermodynamic Tables 3-13

Throat Control 6-3Throughflow

Analysis Mode 6-3

Blade Geometry 6-3–6-5

Block Type 6-2

Boundary Conditions 6-7–6-8

Expert Parameters 6-12

File Format 6-9–6-11

Flow Angle/Tangential Velocity 6-5–6-6

Global Parameters 6-2

Initial Solution 6-8–6-9, 10-7–10-8

Loss Coefficient 6-6

Mesh 6-6

Model 6-1–6-15

Theory 6-13–6-15

Time Configuration 4-2Time Step

Global Time 9-4

Local Time 9-4

Physical 4-14

Torque 8-11, 11-15

Transition Model 7-37

Abu-Grannam-Shaw Model 7-41

Forced Transition 7-38, 7-40

Fully Laminar 7-40

Fully Turbulent 7-40Turbulence

Boundary Condition 4-16


Linearization 4-27

Output 11-7Turbulence Models

Baldwin-Lomax 4-28

k-epsilon 4-31

Non Linear k-epsilon 4-33

Spalart-Allmaras 4-29

TVD 9-11

UUnits

Grid 2-4, 2-8

Project 2-6

Unload Mesh 2-8

Unsteady 4-2

Boundary Conditions 4-2, 4-6, 4-12

Control Variables 4-4

Create 4-6


Initialization of 4-7

Phase Lagged 4-3

Rotor/Stator 5-11–5-12, 5-21–5-24

Rotor/Stator Phase Lagged 5-13

Second Order in Time 4-5

Turbomachinery 4-12

User Mode 2-12

VVander Waals 3-13Velocity

Absolute 11-5

Friction 4-21

Local Scaling 4-46

Projections 11-5

Reference 4-47

Relative 11-5

Relative Projections 11-5

View Area 2-13

View Manipulation 2-16

View On/Off 2-8, 2-13Viscosity

Inviscid Flux 9-8

Laminar 3-9

Turbulent 3-10, 4-39

Viscous Flux 9-8

Vorticity 11-5

WWall

Rough 4-35

Smooth 4-35

Work Unit B-4

XX11 Driver 1-6

ZZoom In/Out/Region 2-18

user manual fine turbo v6.2-9

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