Tutorial: Simulation of Transitional Flow over an Aerospatiale-

A Airfoil

Introduction

Transitional boundary layer flows are important in many CFD applications of engineering interest such as airfoils, wind turbines, ship hulls and turbomachinery blade rows. An ANSYS proprietary empirical correlation (Langtry and Menter) has been developed to predict standard bypass transition as well as flows in low free-stream turbulence environments. The transition model is based on the coupling of the SST k- model transport equations with two other transport equations, one for the intermittency and one for the transition onset criteria, in terms of momentum-thickness Reynolds number.

This tutorial will teach you the basic setup and solution procedures for transitional flow over the Aerospatiale-A airfoil. The objective of this tutorial is to perform a validation study that examines the accuracy of ANSYS FLUENT 13 for computation of two-dimensional transitional flows

In this tutorial you will learn how to:

Use the FLUENT 13 GUI Model compressible flow (using the ideal gas law for density) Set boundary conditions for external flows Use the Transition SST turbulence model Use Full Multigrid (FMG) initialization to obtain better initial field values Post-process the results and compare them with experimental data Do an additional exercise comparing the results against the (fully turbulent) SST

k-w model

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface and that you have a good understanding of the basic setup and solution procedures. This is an advanced tutorial and should only be attempted after you have mastered the introductory tutorials.

Problem Description

The problem considers flow around the Aerospatiale-A airfoil at 13.1 and 13.3 angles of attack with free stream Reynolds numbers of 2.07 x 106 and 2.10 x 106, respectively. The chord length is 1 m. The geometry of the airfoil is shown in Figure 1

Figure 1: Problem Description

A 2D domain is created for the problem. The leading edge of the airfoil is located at the origin of the global coordinate system. The computational domain extends from -18 m to 25 m in the x-direction and from -18 m to 21.56m in the y-direction. A quadrilateral mesh is created, with very fine mesh spacing close to the airfoil surface. The total mesh count is 65,536 quadrilateral cells.

Mesh Requirements

The recommended mesh guidelines for predicting boundary layer transitional flow are a maximum y+ value of 1 in the wall adjacent cell, an expansion ratio no greater than 1.1 for the wall normal mesh spacing and sufficient grid points in the streamwise direction. These requirements are needed to ensure proper resolution of the flow in the viscous sublayer and proper resolution of streamwise changes in geometry, for instance where there is high surface curvature, or flow, for instance near separation or reattachment points.

Setup

Start the 2D, double precision version of FLUENT

Step 1: Mesh

1.1 Read the mesh file

File --> Read --> Mesh

Select the file a_airfoil.msh.gz by clicking on it under Files and then clicking on OK

1.2 Check the grid.

Mesh -->Check

Fluent will perform various checks on the mesh and will report the progress in the console. A message will appear warning of potential problems that might result from high aspect ratio cells near the surface of the airfoil. In this case, the warnings can be ignored as the wall distance calculation is unaffected by the high aspect ratio cells but in general it is recommended to confirm the wall distance is correct by displaying contours of Cell Wall Distance as suggested by the warning message.

1.3 Display the mesh (Figure 2)

Display --> Mesh Make sure that all the surfaces are selected and click Display

Figure 2: Mesh Display

You can use the middle mouse button to zoom into the area around the airfoil and view the mesh around the pressure and suction sides more closely.

Step 2: Materials

2.1 Define the Materials

Define -->Materials In Properties, select Ideal-Gas for Density, specify the other material properties as shown in

Figure 3 and click on Change/Create and Close the panel. The selection of the ideal gas model will automatically enable the energy equation.

Figure 3: Materials Panel

Step 3: Models

3.1 Select the Pressure-Based solver

Define --> General

In Solver, select Pressure-Based under Type, Absolute under Velocity-Formulation, Steady under Time, and Planar under 2D Space as shown in Figure 4.

Figure 4: General Panel

3.2 Specify the turbulence model. This tutorial will be solved using the Transition SST turbulence model

Define -->Models -->Viscous

Select Transition SST (4 eqn) under Model and Viscous Heating under Options as shown in Figure 5.

Figure 5: Viscous Model panel

Note: The transition model is based on coupling of the SST k-omega transport equations with two other transport equations, one for the intermittency, and one for the transition onset criteria, in terms of momentum thickness Reynolds number. Because the model requires the solution of the additional equations, there are additional CPU costs associated with using it

Step 4: Operating Conditions

Define --> Operating Conditions

Set the Operating Pressure to 59607.1 Pascals.

Step 5: Boundary Conditions

Define --> Boundary Conditions

The inputs in Table 1 will be specified at the inlet boundary for the simulation

Free Stream Conditions F1 wind tunnel data F2 wind tunnel data

Angle of attack 13.1 13.3

Static pressure (Pa) 59607.1 59607.1

Static temperature (K) 273 273

Mach number 0.148 0.150

Cos (AoA) 0.97398 0.97318

Sin (AoA) 0.22665 0.23005

Intermittency 1 1

Turbulent intensity 1 1

Turbulent viscosity ratio 15 15

Table 1. Inputs for Inlet Boundary Conditions

Specifying Inlet Turbulence Levels

It has been observed that the turbulence intensity specified at an inlet can decay quite rapidly depending on the inlet turbulent viscosity ratio. As a result, the local turbulence intensity downstream of the inlet can be much smaller than the inlet value. Typically, larger values of inlet turbulent viscosity ratio result in a smaller turbulent decay rate. However, if the specified turbulent viscosity ratio is too large (i.e. greater than 100), the skin friction on the airfoil surface can deviate significantly from the laminar value. For this reason, it is desirable to have a relatively low (i.e. 1 -10) inlet turbulent viscosity ratio and set the turbulence intensity value at the inlet such that it decays to reach the actual experimental value at the leading edge of the airfoil.

5.1 Specify the inputs for the F2 wind tunnel data

Select inlet under Zone, select pressure-far-field under Type and click on Edit. Specify the inputs as shown in Figure 6 below. In the Thermal tab, specify a temperature of 273 K. If the inlet temperature is not specified correctly, the results will not match the data.

Figure 6. Inlet boundary condition settings

5.2 Set the Boundary Condition for outlet by selecting it in Zone, select pressure-outlet as the Type and click on Edit. Enter values in the panel as shown in Figure 7 below. In the Thermal tab, specify a value of 273 K for Backflow Total Temperature.

Figure 7. Outlet boundary condition settings

5.3 The boundaries bottom-airfoil and top-airfoil are walls. They require no changes to be made from the default wall boundary condition settings.

Step 6: Solution Methods/Controls

6.1 Set the Solution Methods

Solve --> Methods

Set up the parameters as shown in Figure 8 below. Select Coupled under Scheme, Least Squares Cell Based under Gradient, Second Order under Pressure, and Second Order Upwind for all other equations.

Figure 8. Solution Methods settings

6.2 Set the solution controls

Solve --> Controls

Enter the values shown in Figure 9. For the equations that do not appear in the figure, use values of 0.8 for Momentum Thickness Re, and 1.0 for both Turbulent Viscosity and Energy.

Figure 9. Solution Controls settings

Step 7: Solution Monitors

7.1 Residual Monitoring

Solve --> Monitors --> Residuals --> Edit

Enable Plot under Options. Change Convergence Criterion from absolute to none.

Figure 10. Residual Monitors panel

7.2 Drag Coefficient Monitoring

We will monitor the drag coefficient on the bottom-airfoil and top-airfoil wall zones.

Solve --> Monitors --> Drag --> Edit

Select both walls under Wall Zones. Turn on Print to Console and Plot under Options. Select 2 under Window. Under Force Vector enter x=0.97318 and y=0.23005.

Figure 11. Drag Monitor panel

Step 8: Initializing the Solution

8.1 Initialize the solution

Solve --> Initialization

Use the inlet boundary conditions to initialize the flow. Select inlet under Compute From and then click on Initialize

Figure 12. Solution Initialization panel. Values will be automatically populated after selecting inlet under Compute From.

8.2 Apply FMG initialization (Text User Interface command)

/solve/initialize/fmg-initialization yes

Note: The Full Multigrid (FMG) initialization can provide a better initial solution for complex problems at a minimal cost compared to the overall computational expense. The use of FMG initialization will accelerate the convergence of the problem.

8.3 Set the reference values used to compute the coefficients of drag, pressure and skin friction

Report --> Reference Values

In the Compute From drop-down list, select inlet. FLUENT will update the Reference Values based on the inlet boundary conditions.

Figure 13. Reference Values panel.

Note: The default value of 1 m2 is kept for Area. In reality, one should calculate the appropriate area (typically the projected area) for accurate computation of the drag coefficient, Cd. In this tutorial, Cd is used only to monitor the convergence.

Step 9: Save Case and Data

File --> Write --> Case & Data

Enter a_airfoilf2_transition_fmg.cas.gz under Case/Data File and click OK.

Step 10: Iterate

10.1 Start the solution

Solve --> Run Calculation

Figure 14: Run Calculation panel

Monitor the scaled residuals (Figure 15) and the drag convergence history (Figure 16). The drag is converged within one drag count (1e-4).

Figure 15: Scaled Residuals History

Figure 16: Drag Convergence History

10.2 Save case and data files

File --> Write --> Case & Data

Save the case and data files as a_airfoil_f2_transition_2000.cas.gz

Step 11: Post-processing

11.1 Enable Double Buffering in Display Options

Display --> Options

11.2 Set the color map

Display --> Colormap

Select float under Type and 3 under Precision.

11.3 Display contours of Mach Number, Static Pressure, Static Temperature and Intermittency

Display --> Graphics and Animations --> Contours

Select Filled under Options and Velocity/Mach Number under Contours of. It will be necessary to zoom to a smaller region close to the airfoil.

Figure 17: Contours of Mach Number

Figure 18: Contours of Static Pressure

Figure 19: Contours of Intermittency

Figure 20: Velocity Vectors Colored by Velocity Magnitude (m/s)

Observation: Transition on the suction surface is triggered by a laminar separation bubble which results in a turbulent boundary layer downstream. If difficulties are experienced locating the separation bubble shown in the figure, open the Camera panel ( Display --> Views --> Camera) and enter the values (0.113,0.086,0.445) for Position, (0.113,0.086,0) for Target, (0,1,0) for Up Vector, (0.005,0.005) for Field and increase the value of Scale in the Vectors panel from 1 to 10.

11.4 Experimental F2 wind tunnel data is available for the skin friction coefficient on the top-airfoil surface

Display --> Plots --> XY Plot

Figure 21: Solution XY Plot Panel

Deselect Node Values under Options.

Select Wall Fluxes/Skin Friction Coefficient in Y Axis Function.

Select top-airfoil under Surfaces.

Click on Load File to load the experimental data file Exp-F2-CF.xy.

Click on Plot to plot both the simulation and experimental results.

Figure 22: Comparison of Skin Friction Coefficient with F2 Wind Tunnel Data

11.5 The pressure coefficient from the experimental F2 wind tunnel data is available

Display --> Plots --> XY Plot

Deselect Node Values under Options.

Select Pressure/Pressure Coefficient in Y Axis Function

Select top-airfoil and bottom-airfoil under Surfaces.

Click on Free Data to unload the skin friction coefficient data file, then click Load File and load the experimental data file Exp-F2-Cp.xy.

Click on Plot to plot both the simulation results and the experimental data

Figure 23: Comparison of Pressure Coefficient with F2 Wind Tunnel Data

Step 12: Additional Exercise

A comparison has been made between CFD results obtained using the Transition SST turbulence model and the experimental F2 wind tunnel data. Next we will make the following additional comparisons

12.1 Comparison of results from the SST k-omega model with the Transition SST model results and the F2 wind tunnel data. 12.2 Comparison of results from the Transition SST and SST k-omega models with experimental F1 wind tunnel test data

12.1.1 Enable the SST k-omega turbulence model.

Define --> Models --> Viscous

Select k-omega under Model, SST under k-omega Model and Viscous Heating under Options.

Be sure Compressibility Effects is not selected in k-omega Options.

Figure 24: Viscous Model Panel after activating SST k-omega Model

12.1.2 Repeat the operations described in Steps 8-10 of this tutorial, then save the case and data files as a_airfoil_f2_sst_2000.cas.gz.

12.1.3 Quantitative comparison with F2 wind tunnel data

Figure 25: Skin friction coefficient predictions with SST k-omega and Transition SST models compared with experimental F2 wind tunnel data

Figure 26: Pressure coefficient predictions with SST k-omega and Transition SST models compared with experimental F2 wind tunnel data

12.2 Comparison of results from the SST k-omega model with the Transition SST model results and the F1 wind tunnel data.

Open a_airfoil_f2_transition.2000.cas.gz, change the inlet boundary conditions to reflect the F1 experimental conditions.

After changing the inlet boundary conditions, repeat Steps 8 10 and save the case and data files as a_airfoil_f1_transition_2000.cas.gz.

Change the turbulence model to SST k-omega, repeat Step 12.1.2, and save the case and data files as a_airfoil_f1_sst_2000.cas.gz.

Figure 27: Comparison of Transition SST and SST k-omega model skin friction coefficient predictions with experimental F1 wind tunnel data

Figure 28: Comparison of Transition SST and SST k-omega model pressure coefficient predictions

References:

Chaput, E., Chapter 3: Application-Oriented Synthesis of Work Presented in Chapter II, Notes on Numerical Fluid Mechanics, Vol. 58, Vieweg Braunschweig, Wiesbaden, 1997, pp. 327-346

Langtry, R.B. and Menter, F.R., Transition Modeling for General CFD Applications in Aeronautics, AIAA 2005-522.