CALIFORNIA STATE UNIVERSITY NORTHRIDGE

Evaluation of Ground Effect on the Drag on an HPV Fairing Using CFD

A thesis submitted in partial fulfillment of the requirements

For the degree of Master of Science in Engineering, Mechanical Engineering

By

Dimitry Tsybulevsky

May 2012

ii

The Thesis of Dimitry Tsybulevsky is approved:

Susan Beatty, Eng. Date

Mike Kabo, Ph.D. Date

Robert G Ryan, Ph.D., Chair Date

California State University, Northridge

iii

Acknowledgements

I would like to thank Dr. Robert Ryan for being my graduate advisor and

supporting me throughout this thesis. My thesis never would have been completed

without his help. I would also like to thank Professor Susan Beatty for helping me during

my time in California State University Northridge (CSUN) and being on my thesis

committee. Additionally, special thanks goes to Dr Mike Kabo for assisting me with the

application process for the graduate program in CSUN and being on my thesis

committee. Lastly, I would like to thank the Department of Mechanical Engineering at

CSUN for the encouragement and help to complete my Masters Degree in Mechanical

Engineering.

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Table of Contents

Signature page.ii

Acknowledgements....iii

List of Tables.................................vii

List of Figures...............................viii

Abstract.......................................xi

Chapter 1: Introduction1

1.1. Problem Statement..........1

1.2. Purpose of the Thesis.......1

1.3. Background Information..........3

1.3.1. Definition of Drag.....3

1.3.2. Definition of Ground Effect..................4

1.3.3. Definition of CFD and CFD History.....5

1.3.4. Drag Measurement Techniques Using CFD Approach.................6

1.3.5. Theoretical Values of Drag on the Ellipsoid body .......7

1.3.6. Drag Values on Variation With Ground Clearance....................12

1.4. HPV Fairing Geometry Description..... ....15

1.5. Organization of the Thesis.....16

Chapter 2: Importation of Solid Model into ANSYS and Mesh Definition..18

2.1. Meshing and Preprocessing...............18

2.2. Modeling of the HPV Fairing and Ellipsoid Geometries in SolidWorks..20

2.3. Importing the Model into ANSYS WORKBENCH from SolidWorks.22

2.3.1. Extracting A Fluid Volume for the Models.....24

v

2.3.2. Opening the Models in ANSYS ICEM CFD..31

2.3.3. Preparing the Geometry for Meshing......32

2.3.4. Generating the Initial Mesh Using Octree Mesh Approach and Applying

the Correct Mesh Size.........34

2.3.5. Generating the Tetra/Prism Mesh Using Delaunay Mesh Approach......40

2.3.6. Smoothing the Mesh to Improve Quality........41

2.4. Exporting the Mesh into ANSYS FLUENT..........43

Chapter 3: FLUENT Setup and Application of Spalart-Allmaras Turbulence Model..47

3.1. Background Information in Computational Software and Methodology..47

3.2. Turbulence Model..48

3.2.1. Spalart Allmaras Turbulence Model...........49

3.3. Application of FLUENT Setup......55

3.3.1. Initial Setup.........55

3.3.2. Boundary Condition........59

3.3.3. Solution Setup and Mesh Adaption.................64

3.4. Solution to the Problem............70

3.4.1. Graphical and Numerical solutions.........71

3.5. Drag Calculation....71

Chapter 4: Baseline Solution and Calibration of FLUENT.......75

4.1. FLUENT Calibration Using Flat Plate......76

4.2. FLUENT Calibration Using Oblate Ellipsoids..80

4.2.1. Results for Oblate Ellipsoids.......83

4.3. Comparison between Hoerners data and CFD data......88

vi

Chapter 5: HPV Fairing Results....93

5.1. HPV CFD Test Results......93

5.1.1. HPV Fairing Benchmark Results .......94

5.1.2. HPV Fairing at Different Ground Proximities Results.................106

5.1.3. Ground Clearance Effect on Pressure and Skin Frication.....................113

5.1.4. Ground Clearance Effect on Drag and Lift .....119

5.2. Estimation of Discretization Error...124

5.2.1. Discretization Error Calculation........126

5.3. Tradeoff Study Between Ground Clearances Drag and Stability for a Typical

HPV.....128

Chapter 6: Conclusion..133

References........135

Appendix A......138

Appendix B......148

Appendix C......163

vii

List of Tables

Table 2-1....30 Table 3-1....60 Table 3-2....61 Table 3-3....62 Table 3-4....65 Table 3-5....66 Table 4-1....78 Table 4-2....79 Table 4-3....89 Table 4-4....89 Table 4-5....89 Table 4-6....90 Table 4-7....92 Table 5-1....97 Table 5-2....98 Table 5-3......108 Table 5-4......124 Table 5-5......124 Table 5-6......128 Table 5-7......132 Table C-1.....163 Table C-2.....164 Table C-3.........165 Table C-4.....166 Table C-5.....167 Table C6......168 Table C7......169 Table C-8.....170 Table C-9.....171 Table C-10...172

viii

List of Figures

Figure 1-1.4 Figure 1-2.9 Figure 1-3...10 Figure 1-4...12 Figure 1-5...14 Figure 1-6...15 Figure 2-1...19 Figure 2-2...20 Figure 2-3...21 Figure 2-4...23 Figure 2-5...24 Figure 2-6...25 Figure 2-7...26 Figure 2-8...26 Figure 2-9...27 Figure 2-10.....28 Figure 2-11.....29 Figure 2-12.....30 Figure 2-13.....31 Figure 2-14.....32 Figure 2-15.....32 Figure 2-16.....35 Figure 2-17.....36 Figure 2-18.....36 Figure 2-19.....38 Figure 2-20.....39 Figure 2-21.....41 Figure 2-22.....42 Figure 2-23.....43 Figure 2-24.....44 Figure 2-25.....45 Figure 2-26.....45 Figure 2-27.....46 Figure 3-1...56 Figure 3-2...57 Figure 3-3...58 Figure 3-4...59 Figure 3-5...63 Figure 3-6...64 Figure 3-7...67 Figure 3-8...69 Figure 3-9...69 Figure 3-10.....70 Figure 3-11.....72 Figure 4-1...77

ix

Figure 4-2...79 Figure 4-3...80 Figure 4-4...82 Figure 4-5...84 Figure 4-6...85 Figure 4-7...86 Figure 4-8...87 Figure 4-9...88 Figure 4-10.....91 Figure 5-1...95 Figure 5-2...96 Figure 5-3...96 Figure 5-4...97 Figure 5-5...98 Figure 5-6...99 Figure 5-7.....100 Figure 5-8.....101 Figure 5-9.....101 Figure 5-10...102 Figure 5-11.......103 Figure 5-12...103 Figure 5-13...104 Figure 5-14...105 Figure 5-15...106 Figure 5-16...107 Figure 5-17...108 Figure 5-18...109 Figure 5-19...110 Figure 5-20...................111 Figure 5-21...................112 Figure 5-22...................112 Figure 5-23...................114 Figure 5-24...................115 Figure 5-25...................116 Figure 5-26...................117 Figure 5-27...................118 Figure 5-28...................119 Figure 5-29...................120 Figure 5-30...................122 Figure 5-31...................123 Figure 5-32...................130 Figure 5-33...................131 Figure 5-34...................132 Figure A-1....................122 Figure A-2....................138 Figure A-3....................141

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Figure A-4....................144 Figure B-1....................148 Figure B-2....................148 Figure B-3....................149 Figure B-4....................149 Figure B-5....................150 Figure B-6....................150 Figure B-7....................151 Figure B-8....................151 Figure B-9....................152 Figure B-10..................152 Figure B-11..................153 Figure B-12..................153 Figure B-13..................154 Figure B-14..................154 Figure B-15..................155 Figure B-16..................155 Figure B-17..................156 Figure B-18..................156 Figure B-19..................157 Figure B-20..................157 Figure B-21..................158 Figure B-22..................158 Figure B-23..................159 Figure B-24..................159 Figure B-25..................160 Figure B-26..................160 Figure B-27..................161 Figure B-28..................161 Figure B-29..................162 Figure B-30..................162

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Abstract

Evaluation of Ground Effect on the Drag on an HPV Fairing Using CFD

By

Dimitry Tsybulevsky

Master of Science in Mechanical Engineering

The purpose of this study was to evaluate the ground effect on the Human

Powered Vehicle (HPV) Fairing with different ground clearances, and its effect on drag

using Computational Fluids Dynamics (CFD) software. The short term goal of this thesis

was to use the CFD software package ANSYS FLUENT, to find how the ground

clearance of the 2010 version of the HPV fairing affects the overall drag and to an

optimal ground clearance for the vehicle. The long term goal was to create a guide to help

future students use ANSYS FLUENT and other ANSYS software to create mesh and

CFD studies to find external forces such as drag and lift coefficients on objects moving

through a fluid.

In order to create a good computational mesh for the HPV fairing flow field, the

mesh was first created for standard geometries, i.e. flat plate and oblate ellipsoids. Drag

values computed for various meshes were compared to known drag values for those

geometries. The results for the flat plate matched within 3.5% of the theoretical results,

and for the oblate ellipsoids the difference was less than 5.6% from experimental values.

This process helped to optimize the final mesh settings for the HPV fairing and find

acceptable results for the drag coefficient with the fairing at different ground clearances.

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As mentioned previously, a long term goal for this thesis was to create a tutorial

on how to use ANSYS and FLUENT to create good CFD studies. The tutorial can be

used with future California State University, Northridge (CSUN) senior design teams to

create body geometries and effectively to accurate results for drag and lift on various

bodies. This tutorial can also help with regard to importing the geometry from CAD

software and performing the correct model setup in ANSYS.

The study for the HPV was conducted as a function of h/L, where h is the ground

clearance and L is the length of the HPV fairing. (L= 99 inches and was constant). The

ground clearance ranged from 3 to 18 inches including two baseline tests, at 30 and 297

inches away from the ground. All of the results are provided in terms of the streamlines,

pressure and velocity magnitude fields, and vorticity contours.

The goal was to see how high the body had to be off the ground to eliminate the

drag ground effect. It was found that the fairing had to be at least 18 inches of from

ground in order to see a significant reduction in ground effect. Additionally a trade off

analysis was conducted on the HPV fairing to balance the speed benefit from high ground

clearance with vehicle stability during cornering. However, the height required to

minimize the ground effect was impractical for the HPV competition due the Center of

Gravity (CG) considerations.

1

Chapter 1: Introduction

1.1. Problem statement

The aerodynamics of human powered vehicles (HPVs) is greatly influenced by

the shape of the body and the proximity of the ground to the surface of the HPV

bodywork. In most cases the airflow between the ground and HPV bodywork results in a

drag increase known as the ground effect. Approaches to lessen this effect fall into two

categories: a) creating a specialized fairing skirt which helps to direct the airflow away

from the underside of the vehicle; or b) increasing the height of the vehicle from the

ground. Neither of those strategies is perfect; each strategy has its upside and its

downside with respect to vehicle performance.

1.2. Scope of the Thesis

The main goal of this thesis is to conduct a computational fluid dynamics (CFD)

study on an HPV fairing by using ANSYS 12.1 and FLUENT in the Mechanical

Engineering Design center at California State University Northridge (CSUN). This study

analyzes airflow around a typical HPV fairing geometry and assesses the impact of the

ground effect at typical HPV speeds. In addition, this study is designed to use the oblate

ellipsoid and the flat plate as a calibration tool for the HPVs fairing mesh, boundary

conditions and FLUENT setup. Then the experimental results found in Fluid Dynamics

of Drag by Hoerner [11]

are compared to the CFD results from FLUENT for the oblate

ellipsoid to make sure that the software computationally precise.

To accomplish these objectives the SolidWorks model created by 2010 CSUNs

HPV design team was imported into ANSYS 12.1 and modified to be used within

ANSYS-FLUENT. The geometry was cleaned within ANSYS 12.1 WORKBENCH

2

Geometry Design-Modeler; then the model was imported into ANSYS ICEM to create

the mesh that was used by FLUENT. The mesh incorporates an estimation of boundary

layer thickness to insure that sufficient points were used near the HPVs fairing surface to

accurately predict velocity gradients in this region.

Initially a study was performed on an ellipsoid geometry, which is somewhat

similar to the shape of an HPV, and for which published drag data is available. In

addition, velocities were chosen to match Reynolds numbers with available data. Using

the ellipsoid geometry, a strategy was developed to optimize the program settings to get

an effective convergence and solution accuracy in terms of drag force. This included

running inviscid flow cases, using coarser mesh for the preliminary calculations, and then

using FLUENT mesh refinement capabilities. In addition, different turbulence models

such as the Spalart-Allmaras turbulence (SA) model and k- model within FLUENT were

tried to assess the turbulence models effect on solution convergence and drag

calculations. This study was conducted using several different flow conditions and mesh

configurations to determine their effect on the calculated drag values.

The analysis was conducted on the 2010 HPV geometry at several different flow

velocities with a maximum flow velocity of approximately 40 mph (58.67

). These

speeds corresponded to a Reynolds number range of approximately 5 105 to 3 106. That means the majority of the flow over the HPV fairing after the expected boundary

layer transition point was in the turbulent region.

Finally, a study was conducted to assess the impact of geometry changes on

computed drag, i.e. changing the proximity of the HPV fairing to the ground surface.

3

Analyses were run for ground clearance of 3, 6, 9, 12, 15, 18, 30 inches and a freestream

case of 297 inches above the ground.

1.3. Background Information

1.3.1. Definition of Drag

Drag refers to the forces that oppose the relative motion of an object through a

fluid, either gas or liquid. Drag forces only act in the direction opposite to velocities not

the oncoming flow velocity (or upstream velocity U). For a 3-D object moving through a

fluid, the drag is the sum of forces due to pressure differences in the flow field (pressure

drag) and shear forces on the objects surface (friction drag).

Drag force has been found to be dependent on a fluids density (), object area

(A), flow velocity (U) and a dimensionless drag coefficient (CD), expressed by the

following drag equation:

= 122 (1-1)

The drag coefficient is a function of object shape and Reynolds number, and is

usually determined experimentally or by CFD analysis. The area can either be the surface

or wetted area, or the projected frontal area depending on the source of the drag

coefficient values. Generally the wetted area is used if the total drag is dominated by

friction drag.

4

Figure 1-1 a shows basic example of drag generated by a solid body moving

through a fluid.

1.3.2. Definition of Ground Effect

Ground effect is a term applied to a series of aerodynamic effects that are

important in the automotive and aerospace industries. These effects usually cause an

increase in drag force and a decrease in lift force (i.e. increase down force). Ground

effects relevant to the automotive industry are due to the proximity of the underside of

the moving vehicle to the stationary road surface. The ground effect is easily visualized

by taking a canvas tarp out on a windy day and holding it close to the ground; when the

canvas gets close enough to the ground it will suddenly be sucked downward due to the

lowered pressure in the flow between the tarp and the ground. Some vehicle body

components, such as a splitter and a diffuser, can be found under the vehicles body to

help increase the ground effect and improve the downforce of the vehicle. This helps it

travel faster through the corners by increasing the vertical force on the tires.

Figure 1-1: Example of drag generated by solid object

(Adapted from http://www.grc.nasa.gov/WWW/K-12/airplane/drag1.html )

5

Ground effects in aerospace applications are due to the proximity of the flying

body to the ground. The most important of these effects is the wing in ground (WIG).

This is due to the reduction in lift experienced by an aircraft as it approaches a height of

roughly the aircrafts wingspan above the ground. Those effects increase as the aircraft

approaches the surface, which can lead to loss of control and crashes.

1.3.3. Definition of CFD and CFD History

Computational Fluid Dynamics (sometimes referred to as CFD) is a branch of

fluid mechanics which uses complex algorithms in conjunction with numerical methods

to solve the partial differential equations describing fluid flow. Advances in CFD

software make it possible to perform complex calculations to simulate the interaction of

gases and liquids with each other and geometric surfaces defined by Computer Aided

Design (CAD) software. Yet even with modern high speed computers, only approximate

solutions can be achieved in most cases, particularly for flows involving turbulence and

flow separation around blunt bodies because CFD solution is a numerically based.

CFD originated in the early part of the 20th century, marked by initial attempts to

solve differential equations found in physics and engineering. The main equations

governing fluid flow behavior are the Navier-Stokes equations, developed in the early

part of the 19th century by George Stokes and Claude Navier. Although the Navier-

Stokes equations were a significant development, the analytical mathematical solution of

those equations proved untenable at that time period. This led to the development of a

large number of simplified equations derived from the Navier-Stokes equation for special

cases, which can be tackled analytically using pen and paper or a simple calculator.

6

However, these special cases were very limited in terms of describing practical

applications. [36]

The invention of digital computers led to many changes in solving the

complicated Navier Stokes equations. In the late 1940s, John von Neumann led a group

of scientists and engineers to develop modern CFD. The digital computing machines

have the analytical solutions of simplified flow equations with numerical solutions of full

nonlinear flow equations for arbitrary geometries. Modern day CFD uses high-speed

computers to achieve better solutions and improve accuracy of known exact and non-

exact solutions to the Navier-Stokes equations such as nonlinear partial differential

equations and turbulence analysis. [36]

Common CFD codes have a specific structure that revolves around a numerical

method or numerical algorithm able to undertake complex fluid flow studies. Most of the

CFD codes currently on the market have only three basic elements, which divides the

complete simulation to be performed on the specific domain or geometry. The basic three

elements are the following: 1. Pre Processor, where the solution domain is defined and

the mesh is generated; 2.Solver where the flow equations are solved for the previously

defined mesh and domain; and 3. The Post-Processor, where the numerical results are

displayed and analyzed.

1.3.4 Drag Estimation Techniques Using CFD Approach

There are several approaches to calculate the drag on a 3-D geometry using the

CFD approach. Perhaps the most common and widely used approach to finding drag

using CFD is solving the Reynolds Averaged Navier-Stokes (RANS) equations, or the

surface integration of stresses, i.e. near field methods. There are several problems with

7

this approach to solving CFD problems. For the near field method the problem is usually

insufficiently accurate results, for example even if the flow solution is locally accurate in

terms of pressure and velocity profile. As for RANS, the problem is mainly related to the

numerical solution that generates the drag coefficient. A second problem for the RANS is

near field drag computation; it only allows for distinction between pressure and friction

drag. [26]

Due to the mentioned problems above with the RANS methods, the following

approach is used in this thesis to find the drag coefficient of the HPV fairing. This

approach is to use the oblate ellipsoid to determine computational precision of FLUENT

by finding the proper mesh parameters and turbulence model to provide accurate drag

estimates. This approach establishes how fine the mesh should be in order to acquire

proper results for drag forces over the HPV fairing. This mesh incorporates estimation of

the boundary layer thickness to ensure that there are enough points used near the body

surface to accurately predict the velocity gradient within the boundary layer, and the

related friction drag. Using the ellipsoid body geometry, a strategy is developed to

optimize the program settings within the FLUENT solver for effective convergence and

solution accuracy.

1.3.5 Experimental Values of Drag on the Ellipsoid Bodies

An oblate ellipsoid is a disk shaped spheroid where a=b>c, and prolate ellipsoid is

a rugby ball shaped spheroid where a=b

8

setup of the CFD approach. However, there is a lot of literature that discusses drag

information on similar types of bodies, such as prolate ellipsoids and spheroids. This may

be used as a baseline reference for the work being performed in this study. The

information in Figure 1-2 comes from a well-known drag expert, Dr. S.F Hoerner. In his

book Fluid-Dynamic Drag (1965), Hoerner presents the drag coefficient of numerous

shapes such as oblate ellipsoids, prolate ellipsoids, and spheroids in both 2-D and 3-D

flow fields. Figure 1-2 presents the wetted area drag coefficient of an oblate ellipsoid

with different fineness ratios of body of revolution over a range of Reynolds number

(Re). The d is the diameter of the ellipsoid at its widest part, and l is the length of the

ellipsoid. The points that are shown in Figure 1-2 are the experimental data that were

found for those bodies, and the dashed lines represent the theoretical drag for fineness

ratio and is given with the following equation. [6, 11, 12]

= , + . + . (1-2)

9

Figure 1-2 represents the effect of Reynolds number on the drag of the ellipsoid

with different fineness ratios of . In the laminar region where the Reynolds number is

less than 105 the drag coefficients tend to be higher. When the Reynolds number reaches

between 105 and 106, the boundary layer flow begins to transition from laminar to

turbulent, and a significant drop is seen in the drag coefficient. After the drag reaches its

minimum value, the drag begins to rise slightly as the boundary layer transition point

continues to move forward. Finally, when the Reynolds number reaches 107, the flow is

fully turbulent and the drag starts to decrease again. In reference to Figure 1-2 the higher

the Reynolds numbers, the lower the drag at the fineness ratios. Additionally, the higher

the fineness ratio the lower the drag coefficient will be.

Figure 1-2: Drag Data on 3-D Bodies of Revolution Aligned Straight-and-Level (Adapted from Hoerner Fluid Dynamics of Drag, 1965, 6-16)

10

To define the fineness ratio that is used in Figure 1-3 and its relationship to the

friction drag coefficient Cf the following equation is employed.

= + .. +

(1-3)

To find the correct ratio of wetted area to frontal area for streamline

bodies, the wetted area can be approximated as = (0.7 0.8) , where the perimeter is equal to , and the frontal area is equal to 2

4. The ratio of

wetted area to frontal area is equal to:

= .

= .

=

This expression is then substituted into equation 1-3 to find the

for the frontal

area coefficient and curve fit for Figure 1-3 as derived by Hoerner.

= 3 + 4.5

0.5 + 21

2 (1-4)

Figure 1-3: Drag coefficient of streamlined bodies as a function of their thickness ratio (Adapted

from Hoerner Fluid Dynamics of Drag, 1965, 6-19)

11

Figure 1-3 illustrates the drag coefficients based on frontal area of streamline

bodies as a function of their fineness ratio, the points in Figure 1-3 are the experimental

data and the dashed lines are evaluated from equation 1-4. When the fineness ratio

increases, the drag coefficient also increases expect for low fineness ratios.

The drag coefficient for the HPV fairing based on its frontal fineness ratio of 3.53

is between 0.02 and 0.065 for Reynolds numbers 105-107. This was found using Figure 1-

3 and equation 1-4.

It is difficult to isolate the critical Reynolds number on the oblate ellipsoid where

the transition will occur from laminar to turbulent flow with estimated Reynolds numbers

from 500 to 600 thousand for that geometry. Figure 1-4[8]

shows the wetted area drag

coefficient for the

= . prolate spheroid for several different surface roughnesses. The roughness has an enormous effect on the drag coefficient in the low Reynolds numbers.

This is because the flow is not fully developed and this adds to the total skin friction

coefficient as illustrated in figure 1-4. During Dr. Dresss study the critical Reynolds

number reached about 800 thousand where the transition from laminar to turbulent region

occurs, and the minimum drag coefficient happened at a Reynolds number of almost 1.2

million for a fine grit of 80. The different types of runs show the effect of skin roughness

from laminar to turbulent flow, and the effect on the wetted drag.

12

1.3.6. Drag Values on Variation With Ground Clearance

Once the potential of using aerodynamic downforce in automotive racing

applications was realized, many teams started to experiment with other methods to

increase aerodynamic downforce other than simply attaching inverted wings. It was

found that with a larger underbody area of the vehicle, significant levels of downforce

could be generated. This kind of effect was first seen in 1935 in the racing circuit with

early wing prototypes used in ground effect models. [13]

Figure 1-4: Drag Data from a

= . Prolate Spheroid Aligned Straight-and-Level free transition

is the base run, 80 is the fine grit, and 40 is the rough grit (Adapted from Dress, NASA Technical Paper 2895 1989, 29)

13

Figure 1-5 illustrates a basic principle of ground effect on typical car shapes

represented by an oblate ellipsoid and half streamlined body. However, to understand

ground effect the nature of the flow under the vehicle must be considered. The top part of

the Figure, shows an oblate ellipsoid that is approaching the ground. The flow under the

oblate ellipsoid and the downforce (CL) are increasing as distance to the ground reduces

and creates low pressure. If one looks at the bottom part of the Figure and closely

examines the half streamlined body, the drag coefficient is seen to be nearly the same as

the oblate ellipsoid. The lift force is opposite due to the reduced flow under the body,

with the result of increased lift due the reduced ground clearance. In both Figures the

transition to significant ground effect starts to occur at

< 0.05. However, this only applies to these specific geometries. The transition point can shift to either left or right

depending on the fineness ration and overall shape of the geometry.

There are several options for the car body shape to generate lower pressure under

the body. Option one is to streamline the underbody to create low pressure. Option two is

to create a seal between the underbody of the car and the ground and only leave the rear

portion of the car open. Then the low pressure behind the car would dictate the pressure

under the car. [14, 15]

14

Figure 1-5: Effect of ground Proximity on the lift and drag of two streamline bodies (Adapted from Race Car Aerodynamics by Joseph Katz 1995)

15

1.4. HPV Fairing Geometry Description

Figures 1-2 and 1-3 are used as a reference to estimate the expected drag

coefficient for the HPV fairing. If one assumes the HPV fairing is a body of revolution

then the oblate ellipsoid can be used as a computational precision tool for the mesh setup,

turbulent model selection, and optimize FLUENT parameters. To apply Figures 1-2 and

1-3 one needs to estimate an equivalent fineness ratio for the HPV fairing, and a range of

drag values can then be estimated for the HPV fairing in freestream flow. This is used as

a benchmark for the HPV fairing analysis.

Figure 1-6 shows the dimensions of the HPV fairing; this data can then be used to

find the fineness ratio based on the height of the HPV fairing which is equal to 3.53 for

half of a body of revolution. However, because the HPV fairing is assumed to be a body

of revolution the height needs to be doubled to get the correct fineness ratio

= 1.76. the resulting wetted area drag coefficient value for = 3 106 is approximately CD,Wetted=0.009 and CD,surface area=0.091.

Figure 1-6: Dimensions of the HPV fairing from SolidWorks 2010 where l= 98.93 inches, h=d= 28.03 inches

16

1.5. Organization of the Thesis

The remainder of this thesis will be organized as follows. Chapter 2 describes the

model design and importation of the model into ANSYS WORKBENCH and fluid

volume extraction. It also explains how to import the model in to ANSYS ICEM and the

mesh setup and creation. Lastly, it will be explained how to import the mesh from

ANSYS ICEM to ANSYS FLUENT.

Chapter 3 explains how to operate FLUENT using ANSYS WORKBENCH and

apply FLUENT setups as an initial setup, materials for the fluid and geometry, dynamic

mesh, and boundary conditions. It will demonstrate how to use FLUENT to generate

numerical and graphical solutions for the HPV fairing geometry with different ground

clearances ranging from 3 inches to 18 inches away from the ground.

Chapter 4 presents the results of the baseline solution of the oblate ellipsoid with

= 2&4 and results for the flat plate. This chapter also compares the CFD results of the

baseline solution to the results found in Chapter 6 in Fluid Dynamics of Drag by

Hoerner. [11]

Chapter 5 presents the results of the HPV fairing with different ground clearances

ranging from 3 inches to 18 inches away from the ground. Then the results from the HPV

fairing CFD analysis are compared to the benchmark results (freestream and 30 inch

ground clearance). In addition, the results for drag and lift are discussed, and calculations

of discretization error are presented. Then the final part of Chapter 5 will include the

trade-off study regarding the optimum vehicle height while considering both vehicle

stability and aerodynamic drag.

17

Chapter 6 is the conclusion and the summarization of the study. It is based on the

results shown in Chapters 4 and 5. References and an appendix follow the conclusion.

18

Chapter 2: Importation of Solid Model into ANSYS and Mesh Definition

2.1.Meshing and Preprocessing

The pre-processing of a CFD procedure consists of several inputs for the flow

problem that are done by the user in CFD software. For this study the pre-processing

software is ANSYS ICEM CFD, and the solver software is ANSYS FLUENT. The inputs

are then transferred into a form made suitable for use by the solver. The pre-processor is

the main connection between the CFD solver and the user. The user has to complete

several significant steps in the pre-processing stage of the CFD problem. A schematic of

the process is shown in Figure 2-1.The following definition, gives a brief explanation of

these steps.

1. Define the geometry of interest: This step uses ANSYS DesignModeler CAD

software within ANSYS WORKBENCH to help design and model the topology of

the fluid flow domain inside or outside the geometry. This domain is defined and

optimized for the best CFD results.

2. When the geometry preparation is defined within the pre-processor software, the fluid

domain and every surface affected by the fluid is then also defined. Each fluid and

surface has its own distinct property; those properties are used in the CFD process

and must be defined at this stage. The output of the DesignModeler software is a

xxxx.agdb file.

3. Meshing is the third step. Because the CFD process uses a finite volume method, the

domain of interest has to be divided into structured and unstructured elements. All the

elements are connected to each other through nodes to and from the flow domain. For

this study ANSYS ICEM CFD software is used to create the mesh in the form of a

19

xxxx.mesh file. The quality of the mesh contributes to the accuracy of the final

results.

4. Definition of boundary conditions is the final step at the pre-processing stage. Each

CFD domain needs an initial condition to begin calculations, which is defined by the

users input. In addition, the CFD code implements the boundary conditions at a

specific locations.

The following few sections will explain these four steps in complete detail and

explain how to use ANSYS 12.1 for external flow problems. Lastly, Figure 2-1 illustrates

how the files from the different software packages move through the overall solution

process.

Figure 2-1: Block Diagram illustrates where each file type goes to

ANSYS DesignModeler

ANSYS FLUENT

ANSYS WORKBENCH

.wbpj

SolidWorks .SLDPRT

ANSYS ICEM CFD .agdb .mesh

20

2.2. Modeling of the HPV Fairing and the Ellipsoid Geometries in SolidWorks All of the solid models that were used in this study were designed and drafted

using SolidWorks Computer-Aided Design (CAD) software, using inches for dimensions.

The fairing was originally designed and modeled by the 2009-2010 California State

University Northridge (CSUN) Human Powered Vehicle (HPV) Team for their

competition in April 2010. An ellipsoid model was also designed to represent a simpler

geometry and was used as the baseline for this thesis. The ellipsoid model establishes the

mesh fineness requirements to acquire good results for the drag force, based on

comparison with published results from Fluid Dynamics Drag by Hoerner data. [11]

The modeling of the ellipsoid geometry in SolidWorks was a little challenging,

because the ellipsoid had to represent the fairing shape as closely as possible. The

ellipsoid was created using the lofted boss/base tool in SolidWorks. However, before that

could be done, several planes were created so that a 2-D ellipse could be drawn on each

plane with different chord lengths A and B. This is illustrated in Figure 2-2.

After all of the 2-D schematic geometries were drawn, the lofted boss/base tool

was used to create the 3-D ellipsoid body that can be seen in Figure 2-3. The ellipsoid

Figure 2-2: Representation of an ellipse geometry B=99in and A=49.5in

B

A

21

model dimensions are: the chord length (l) is 99 inches; height(x) is 49.5 inches, and the

diameter (d) of the ellipsoid is 24.75 inches. The fineness ratio of is then can be found

as 9949.5 = 2. This ratio is then used to find the drag of a non-oblate ellipsoid body.

Additionally, another ellipsoid was created in SolidWorks with a fineness ratio of

= 4, and was used as a baseline test in FLUENT. Additional comparisons were made with a

flat plate geometry which is useful because the drag force on a flat plate is completely

due to surface stresses.

There are a few reasons why two oblate ellipsoids are used to calibrate FLUENT

and set correct mesh parameters for the HPV fairing. The first reason is to match the

results from FLUENT runs to the known results from Fluid Dynamics Drag by Hoerner.

The second reason is to find the limitation of FLUENT on predicting drag on similar

geometries with different fineness ratios, as the flow behaves differently for a Falter

shape. Generally, a smaller ratio will have a larger contribution of pressure forces to

the overall drag, especially if the boundary layer separates on the rear portion of the

body.

Figure 2-3:

3-d Ellipsoid body from SolidWorks

22

After the models were created and saved in SolidWorks, one needed to import

those models into ANSYS 12.1 for geometry calibration and model clean up before the

models were meshed and used within ANSYS FLUENT.

2.3. Importing Model into ANSYS WORKBENCH from SolidWorks

ANSYS WORKBENCH is a Computer Aided Engineering (CAE) software

package that is used in engineering simulation and analysis. It is an innovative project

organizer that ties together the entire simulation process. It helps the user go through

several complex studies at once with drag and drop menus. It also has powerful user

controls, automated meshing abilities, project level update mechanisms, and integrated

optimization tools, which enable complex simulation and product optimization. [40, 37]

The next few Figures show a step by step explanation process to import any

SolidWorks model into ANSYS WORKBENCH, and clean up the geometry so it can be

properly meshed. Figure 2-4 shows how to load the geometry in ANSYS

WORKBENCH. In order to load the SolidWorks model in ANSYS WORKBENCH, the

user first has to open ANSYS WORKBENCH, then go to the component systems and

select Geometry (A). Then the geometry tab is placed on the main WORKBENCH

screen, and it then becomes a cell. In order to load the geometry, the user must right-click

the Geometry..? tab, and then scroll down until import geometry has been reached.

After left-clicking on this item, a new window will open. Then user must left-click

browse tab and load the specific geometry (B) to be modified.

After the geometry is loaded into the WORKBENCH, the user must double click

with the left mouse button on the geometry cell number 2, and ANSYS DesignModeler

23

will load. The user then is able to clean, modify, edit and fix the geometry so a better

mesh can be created for future analysis of the model. This is explained in Section 2.3.1.

Figure 2-4: ANSYS WORKBENCH front screen; A- geometry is selected first; B-geometry cell where geometry is going to be imported

A

B

24

2.3.1. Extracting a Fluid Volume for the Models

The next few Figures will show step by step how to extract the fluid volume

around the imported geometry. The fluid volume must be extracted because one must

correctly define the volume that is being occupied by the fluid around a specific solid

model.

Figure 2-5 illustrates how once the geometry is loaded into ANSYS

DesignModeler the user can then begin to select what kind of fluid volume to apply to the

specific model, such as internal or external fluid volume. For this study an external fluid

volume is being used. This is because the imported geometry represents a solid body and

the air flow is external to the body surface.

Figure 2-5: Ellipsoid model with in ANSYS DesignModeler and the selection of the external flow.

25

Figure 2-6 illustrates the shape and the cushion size of the fluid volume enclosure.

The cushion size is also known as the domain size. For this study the shape of the fluid

volume is the box shape, since it is convenient for generating the mesh around the solid

body. Since the CFD process is a numerical approximation approach that uses the finite

volume method to solve the NavierStokes equations, the fluid volume domain is going

to be composed of an Octree Mesh, sometimes referred to as an unstructured mesh. In

order to create the fluid volume domain, the user must set the cushion size and select

either uniform or non uniform size. For this thesis the non-uniform cushion size will be

used on all the models. This is done to make a more efficient study that does not require a

large quantity of computing power.

The ellipsoid model was run in freestream condition without any ground plane

representation. The HPV fairing simulation consisted of eight different cases. The first

two cases are set as benchmarks, where one is in freestream condition and the other one

simulation a ground clearance of 30 inches. The other six cases will simulate the HPV

fairing with ground clearances ranging from 3 to 18.

Figure 2-6: Selection of shape and cushion type

26

Figures 2-7 and 2-8 illustrate the generated fluid volume enclosure for the solid

model, and the editing process for the fluid enclose based on model symmetry about the

XY plane. This makes the computation more efficient because it only has to analyze half

Figure 2-7: Generated enclosure for the oblate ellipsoid in freestream

Figure 2-8: Editing of the enclosure based on symmetry

27

of the model to achieve the same results. In order to create the symmetric model, the user

must right click on the Enclosure tab in the tree outline, and then select the edit

selection tab. After the user has selected the previous command, the model enclosure can

then be edited to the users specifications and the correct symmetry plane.

The user can then select up to three planes of symmetry. As mentioned earlier this

model is only symmetric to one plane, the XY plane. In order to select the symmetry

plane, the user must left click on the not selected tab and then the user must select the

corresponding plane from the tree outline, then press apply. In order to generate the new

model, the user must press the Generate tab to create the symmetric model about the

XY plane. This is illustrated in Figure 2-9 where one can see the selection of the total

number of planes that can be used at the same time, and the symmetry plane selection.

Figure 2-9: Selection of symmetry planes. For this study it is the XY plane.

28

Figures 2-10 and 2-11 show the final view of the oblate ellipsoids model and

fluid enclosure, and the HPV fairing within the non-uniform fluid volume box. The

oblate ellipsoid fluid volume box is X+=Y+=Y-=Z=3 times chord length, and X-=6 times

chord length. The fairing fluid volume box is X+=Y+=Z=3 times chord length, X-=6 times

chord length, Y-=3 to 18 inches for the test cases, and for the benchmarks it is 30 inches

and 297 inches. The domain size was selected to help decrease the total computing power

while maintaining accuracy. The optimal domain size for a wing was found by Amir

Mohammadi in his thesis and this data is being used as a reference for the domain size

used here. [21]

Before the mesh can be created, the model needs to be exported as an

xxxxxx.agdb file. In order to save the ANSYS DesignModeler file, the user must do the

following steps; File>Export> xxxxxx.agdb> then Save. Once the file is saved, it then

can be opened by ANSYS ICEM CFD, and a proper mesh can be applied to the solid

model and the fluid volume box.

Figure 2-10: Fluid volume for the ellipsoid model

Y+=3x

X-=6x X+=3X

Z=3x

Y-=3x

29

In addition to creating the fluid volume, naming the surfaces that represent the

boundary conditions will help later with ANSYS FLUENT setup and the meshing

process in ANSYS ICEM CFD. In order to name the different surfaces, the user must

right click on the surface and then click edit to name the surface. For the oblate ellipsoid

and the HPV fairing model, the surfaces that are created are the inlet velocity, outlet,

boundary volume box, and symmetry plane. The boundary volume box for the oblate

ellipsoid is made out of three surfaces that surround the geometry. However, for the

fairing the bottom surface is named ground plane and the volume box is made only of

two adjacent surfaces. This is illustrated in Figure 2-12 and Table 2-1.

Z=3X Y-=3 to 18 inches

X-=6X X+=3X

Y+=3X

Figure 2-11: Fluid volume for the Fairing model

30

Plane Name Surface Name For Ellipsoid Surface Name For HPV

Right (YZ plane @ X+) Velocity Inlet Velocity Inlet

Left (YZ plane @ X-) Outflow Outflow

Top (XZ plane @ Y+) Fluid Volume Box Fluid Volume Box

Bottom (XZ plane @Y-) Fluid Volume Box Ground plane

Far side (XY plane @ Z+) Fluid Volume Box Fluid Volume Box

Symmetry (XY plane @Z-) Symmetry Plane Symmetry Plane

Table 2-1: Surface names for ellipsoid and HPV Fairing

Figure 2-12: Plane location and names

Ground plane

Symmetry

Fluid Volume

Box

Outflow

Velocity Inlet

31

2.3.2. Opening the Models in ANSYS ICEM CFD

Before the meshing procedure can begin, the file that was saved by

DesignModeler must be opened in ANSYS ICEM CFD. In order to do that, the user must

do the following steps; File>WORKBENCH Reader>select xxxxxx.agdb file> then

Open. Prior to the file being completely loaded into ANSYS ICEM CFD, the user has to

go to the scroll down menu below and select the options that are illustrated in Figure 2-

13. Then the user must press apply.

Figure 2-13: Importing an xxxxxx.agdb file into ANSYS ICEM CFD CFD (A). Opening the xxxxxx.agdb in ANSYS ICEM CFD CFD (B)

A B

32

2.3.3.Preparing the Geometry for Meshing

Figure 2-14: Extracting the feature curve from the symmetry plane

Figure 2-15: Demonstration the correct location

Select those locations for the fluid volume area

33

Figure 2-14 illustrates how to prepare the geometry that was loaded into ANSYS

ICEM CFD so that the correct mesh and grid can be generated. In order to extract the

curves from the surface, the user must do the following steps: Geometry tab > Create/

Modify Curve icon> Extract Curves from Surfaces icon, then select the surface on the

screen. The user has to click on the glass icon to select all appropriate visible objects, or

use the following shortcut key v. The plane that is selected for this study is the

symmetry plane. After all the correct surfaces are selected, the user must click apply or

OK.

Following the Extract Curves procedure, the body for the fluid has to be created.

In order to do that, the user must start with the Geometry tab again, and then the user

must click the Create Body icon. Following that, name the part as the fluid name; any

name can be used to name the region. For this study the name that is used is Fluid

Volume. In order to name the fluid region, the user must select Centroid of 2 points for

the location and the Material Point icon to select the location of the fluid volume. Then

the user must click the two screen locations to select the fluid body region as

demonstrated in Figure 2-15. Following that, the user must click OK to finish creating

the fluid volume area and proceed to the meshing setup. In addition, the user must create

parts from the Subsets by selecting the inlet velocity, outlet, and the fluid volume

boundary, and then right click on the Subsets to create parts. These names, are used

when meshing in ANSYS ICEM CFD, and setting the boundary conditions and

parameters in ANSYS FLUENT.

34

2.3.4. Generating the Initial Mesh Using the Octree Mesh Approach and Applying the Correct Mesh Size The strategy that is used for the mesh process is to have a prismatic or structured

mesh around the solid model and then transition to an unstructured mesh. The prismatic

mesh represents the boundary layer and is defined as a stair step mesh to decrease the

required computing power. The height and the mesh density of the prismatic layer was

set to represent the estimated boundary layer thickness around the solid models, i.e.

oblate ellipsoids, flat plate and HPV fairing. Then the prismatic mesh transitions to an

unstructured mesh to create a hybrid mesh around the solid model and inside the fluid

region.

Assigning the correct mesh for each model was a trial and error method. The

reason behind this is that each model used slightly different mesh parameters, and it also

varied from robust to fine mesh. It also depended on the size and shape of the geometry.

The Scale Factor multiplies other mesh parameters to globally scale the model, for

example if a Max Element Size of a given entity is 64 units and the Scale Factor is 0.3

units, then the actual maximum element size will be 64 0.3 = 19.2 . After countless tries, the correct scale factor was found to be approximately 0.3 for all the

models. For that reason, all the models used a proper mesh for balancing accuracy with

computed memory requirements.

The maximum element size that was selected ranged from 64-128. This value was

selected due to the fact that an Octree Mesh scales by a power of two, and the Octree

algorithm is limited to datasets of resolution of power of two. For that reason our values

range from 26-27 (or 64-128). This is very important because all other values that will be

input into the maximum scale factor will be rounded off to the closest power of two. In

35

order to set the parameters, the user must select Mesh tab> Global Mesh Setup icon >

Global Mesh Size. After the correct input is input the user must click apply/ok. This is

demonstrated in Figure 2-16. Lastly, the general grid topology will be talked in chapter 3.

After the meshing sizing is completed, the user must select the Part Mesh Setup

icon. This icon is selected in the Mesh tab area to specify the mesh parameters. In order

to create the prism mesh, the user must first select the prism option in the mesh parameter

area, only for the solid model and the symmetry plane. The prism height is set to 0.1-0.2,

depending on the model, so it can build the correct boundary layer as learned in ME692.

For the ellipsoid and fairing geometry surfaces the maximum size is set in the range of

2.5-3; this creates a proper surface mesh for the solid geometry. Also the user needs to

input at least 90 for number of prism layers of to be created, and a height ratio of 1.06-1.1

for the growth factor. This corresponds to the maximum thickness () in the turbulent

boundary layer, which is approximately 2 inches. This number was found using the

Figure 2-16: Meshing sizing with ellipsoid of ratio l/d=2

36

calculations that can be seen in appendix A for the boundary layer thickness for the

laminar, turbulent, and transition layers on a flat plate with a length equal to that of the

ellipsoid and the fairing models.

For the fluid volume box (inlet velocity, outlet, symmetry and open domain) the

maximum size is set to 64 to allow create an appropriate volume mesh. After the mesh

parameter setting are complete, the user must press apply. This is shown in Figure 2-17

for the ellipsoid and HPV fairing models.

The density box is created to represent the wake region of recirculation flow

immediately behind the model. The wake region is chaotic due to boundary layer

separation on the rear portion of the body. The density box allows local control over the

mesh density in the wake region to correctly represent the flow.

Figure 2-17: Mesh parameters step for the ellipsoid

A B

Figure 2-18: Mesh density box setup (a). Shifting of mesh density box to refine wake region (b)

37

In order to create the density box that represents the wake region, the user must

first select the Mesh tab> Create Mesh Density icon, then select the size of the density

box. For this study the size was selected at 32, and the ratio and width were left at zero.

The user then must select the density location as an entity. After the density box is

selected, the user must click OK to generate it. Note that at this point the box surrounds

the solid body. In order to shift the density box to the expected wake region location, the

user must click Geometry tab>Transform Geometry icon >Translate Geometry icon,

then select the density box and keep the translation method as explicit. Before the density

can be shifted the model needs to be measured by the Measure Distance feature.

Following that the density box is shifted by half of the model length. In this study the

model was 99 inches long so the density box was shifted 44.5 inches in the negative X

direction to represent the True Wake region. This is illustrated in Figure 2-18.

Following the completion of the creation and shifting of the density box, to

generate the mesh, the user must first click the Mesh Tab>Compute Mesh icon, then

the user must select the Create a Prism Layers and click Compute, as Figure 2-19

illustrates. Following that another mesh has to be defined to refine the present mesh of

the model that can be correctly analyzed within ANSYS FLUENT. This is the Delaunay

mesh step, and it will be discussed later in the chapter. The reason why an Octree Mesh

was used as opposed to a Delaunay Mesh is to minimize the numerical error as much as

possible. This also helps to minimize the total computing power needed to create a solid

mesh.[39]

38

Figure 2-20 illustrates the cut plane that allows the examination of the prism

layers in the mesh around the solid model. Please note that the prism height floats, as the

height was initially set to 0.05-0.1. These numbers illustrate that the first few prism layers

start growing very slowly and there after grow exponentially. The variation in layer

thickness (float) is not significant for the model because the surface mesh size is

relatively uniform. The mesh density near the solid body does not vary with axial

position as defined in ANSYS ICEM CFD, note that the mesh is adjusted during the

analysis in ANSYS FLUENT with mesh adaption.

Figure 2-19: Computing the initial mesh

39

The mesh process is completed by performing a check done on the mesh to find

any errors that may cause problems during the analysis in FLUENT. In order to check the

mesh, the user must do the following steps; Edit Mesh tab > Check Mesh tab. The

user needs to keep the default settings and then click OK.

Figure 2-20: Mesh analysis using a cut plane in the XY plane (A); YZ plane (B); XZ plane (C)

A

B

C

40

2.3.5. Generating the Tetra/Prism Mesh Using the Delaunay Mesh Approach Once an Octree Mesh has been checked and no errors have been found, the

Delaunay Mesh can be generated. The Delaunay Mesh more efficiently fills the volume,

and it has a smoother volume transition. This kind of mesh works a lot better with

FLUENT to help calculate better results for drag for all the models according to the

ANSYS ICEM CFD user manual.[39]

Figure 2-21 displays the steps to generate the

Delaunay Mesh within ANSYS ICEM CFD.

In order to generate the Delaunay Mesh, the user must do the following steps:

click on Mesh tab>Global Mesh Setup>Volume Meshing Parameters, and select the

Delaunay option from the drop down menu. The user must enter a scale factor of 1.2,

memory scaling factor of 1 and the Delaunay Scheme must be T-Grid according to the

ANSYS ICEM CFD user manual. [39]

After all the correct options have been selected, the

user must click Apply. In order to start the computing process, the user must click on

the Compute Mesh icon and select the Delaunay method from the drop-down menu, and

then disable the Create Prism Layers option. The user must make sure that the Existing

Mesh option is selected from the drop-down menu because the mesh is generated based

on the Octree Mesh; then finally click Compute

.

41

2.3.6. Smoothing the Mesh to Improve Quality

The smoothing of the mesh is done to improve its quality. The smoothing

approach involves the initial smoothing of the interior elements without adjusting the

prism elements. After the initial smoothing is complete, the prism elements then will be

smoothed by themselves.

In order to smooth the mesh, the user must click the Edit Mesh tab > Smooth

Mesh Globally tab. To smooth the mesh that was generated using the Delaunay

Approach the user first has to smooth the interior elements without touching the prism

elements. This is done by opening the Smooth Elements Globally control panel. The

first step that the user must do in this process is to set the number of smoothing iterations;

this number was set to 25. The second step is to enter the Up to Value; this value

Figure 2-21: Delaunay Mesh Setup

42

specifies the quality level up to which the program will attempt to smooth the mesh. It

was set to 0.5 this was based on ANSYS ICEM CFD settings. [39]

Then for the criterion

the user must select the quality option from the drop down menu. Lastly the user must set

all the elements to get smooth except for PENTA_6 which was set to freeze.

The reason why PENTA_6 was set to freeze is because it is a five sided element

with six nodes as a prism element. These elements are usually perfect, but they may be

damaged by the smoother as it adjusts to optimize the nearby tetra elements. By selecting

the freeze option in the Smooth Mesh type for the PENTA_6 elements, it protects them

from being damaged. When smoothing those kinds of elements the values for the Up to

Value should be reduced to 0.01 so only the worst of the PENTA_6 elements are

adjusted, and the number of smoothing iterations should be dropped to 2. Figure 2-22

illustrates how the smoothing step is setup and the quality Histogram for the mesh

elements. [39]

Figure 2-22 Mesh smoothing setup and quality histogram.

43

2.4. Exporting the Mesh into ANSYS FLUENT

When the mesh process is finally completed, checked, and smoothed, the user has

to then save the project and transfer the mesh into ANSYS FLUENT. This procedure

applies to all the models for this thesis and can be used as a general guideline for future

CFD projects.

There are several steps in this procedure of transferring the mesh file from

ANSYS ICEM CFD to FLUENT. The first step is to save the ICEM project by clicking

on File>Save Project As, which creates a xxxx.uns file. The second step is to go to the

Output tab and select the red tool box (Select Solver). After the Select Solver is clicked

a menu will appear on the screen with two drop down lists. The first list is Output Solver;

the user must select the FLUENT_V6 option in order to produce a mesh file that is

compatible with FLUENT. The second drop down list is the Common Structural Solver;

the user must select ANSYS option, and then click Apply; as illustrated in Figure 2-23.

Figure 2-23: Output step and solver selection

44

Following the Output Solver and the Common Structual Solver selection, the user

then can apply the boundary conditions to mesh. The boundary conditions are located in

the Output tab, where the user can apply the boundary conditions and check that all the

surfaces are defined and represented correctly. This is illustrated in Figure 2-24.

After all the the above steps are completed the user can then write the input file

for ANSYS FLUENT. This is done in the Output tab once again. In order to write the

mesh as a FLUENT compatable file, the user must select the Write Input tab. First the

correct ANSYS.uns file for the project, (that was saved in the first step) must be opened.

Then the FLUENT_V6 window will appear. Following the windows appearance a name

for the file must be entered in the Output File line. All other options can remain as the

defult values; the step is completed by clicking Done. This is all illustreted in Figures 2-

25 and 2-26 below.

Figure 2-24: Boundary condition step.

45

After the mesh is saved as a FLUENT file (.msh file) the user then can close

ANSYS ICEM CFD, and open ANSYS WORKBENCH. In order to load the mesh into

Figure 2-25: Opening of the ANSYS .uns File

Figure 2-26: Fluent_V6 window that appears after the ANSYS .uns file is selected.

46

FLUENT, the user must select the mesh option from the component systems list and drag

it to the WORKBENCH. The same thing is then done for the FLUENT option. After the

two boxes appear on the WORKBENCH, the user must right click on the mesh cell in the

mesh box and load the FLUENT mesh, as illustrated in Figure 2-27.

After the mesh has been loaded in the ANSYS WORKBENCH, it then can be

loaded in FLUENT. This is done by dragging the Mesh cell from the Mesh box to Setup

cell in FLUENT Box.

Figure 2-27: Loading of the .msh file in ANSYS WORKBENCH

47

Chapter 3: FLUENT Setup and Application of Spalart-Allmaras Turbulence Model

3.1. Background Information in Computational Software and Methodology

The major reason behind the growth of CFD usage in various industries is due to

its accuracy, reliability, and replacement for running experimental tests. There is also

much more advanced computing technology available today for much less cost than

running a physical experiment, which may require major equipment such as a wind

tunnel. This kind of software is capable of solving large two and three dimensional

problems numerically in a short period of time.

The accuracy and reliability of a CFD simulation depends on the numerical

algorithms employed by the software. This means selecting the appropriate options such

as a turbulence model, appropriate spatial and temporal discretization scheme, and

correct computational grid topology. The grid topology can have significant weight on

the final results of the CFD simulation. Each one of the options mentioned earlier can

have either a positive or negative effect on the simulation.

With reference to the grid topology, structured grids are more common, preferred,

and efficient in the boundary layer region along the model surface for the simulation of

the flat-plate, oblate ellipsoid and HPV fairing. In addition, structured grids allow more

efficient computations and parallelization. However, an unstructured grid requires less

grid points outside the boundary layer region. Considering the oblate ellipsoid geometry,

the unstructured grid was a lot easier to generate; it also adapted to the flow gradients

more easily. However, the structured grid was much harder to generate around the model

within the boundary layer. The reason why all the models use hybrid grids is to simplify

the mesh creation and provide accurate and reliable results.

48

FLUENT is a finite-volume solver that is based on the full Navier-Strokes

equations with a Blasius assumption for turbulence. FLUENT works on structured and

unstructured grids. As noted above, the mesh for each model is composed of both kinds

of grids. Various grids were examined in order to find the optimum size grid to use for

this study. In the thesis Computation of Flow Over a High Performance by Amir

Mohammadi, [21]

grid optimization was considered, and some of those findings, have

been used here.

The following section discuss the way FLUENT solves the grid and provides the

user with the proper results. FLUENT uses cell faces to integrate for a solution, since the

software must handle both structured and hybrid meshes. The hybrid mesh contains many

different types of cells such as TETRA_4 (Tetrahedral), TRI_3 (Triangles), PENTA_6

(Prisms), QUAD_4 (Quadrilateral) and PYRA_5 (Pyramids) cells. The structured mesh is

a uniform mesh, composed entirely of QUAD-4 cell.

3.2. Turbulence Model

Turbulence modeling is the construction and use of a model such as Spalart-

Allmaras (SA), k-epsilon (k-), or k-omega (k-) to predict the effects of turbulence

around or inside blunt objects.[33]

Averaging is used to simplify the solution of the

governing equations of turbulence; hence the models are required to represent different

scales of the flow that are not resolved.

Consideration of turbulent flows phenomena includes transport properties,

boundary layer separation, and other major phenomena; because of this, the most recent

work focuses on different types of turbulent models that consist of one or two equation

49

models. For instance, examples of two-equation models are the k- and k- models, and

the most popular one-equation model is the SA model. For this thesis, the SA model is

being used because of its strong performance in the baseline studies versus the k- and k-

turbulent models.

3.2.1. Spalart-Allmaras Turbulence Model

The SA model was developed in 1992 by Dr. Steven R. Allmaras and Dr. P.R

Spalart. The SA model is an approach for modeling different types of turbulent flows,

specifically aerodynamics flows with a high Reynolds number. This model is basically a

transport equation for the eddy viscosity , or a parameter that is proportional to the turbulent viscosity. The main idea that Spalart and Allmaras used to develop this model

was very similar to the Nee & Kovasznay (NK) model, which was developed in 1969,

and more recently the Baldwin & Barth (BB) in 1990. However, all one-equation models

have been based on the turbulent kinetic energy equation.[42]

It was discovered during the preliminary and baseline tests on the flat and

ellipsoid models that the SA model provided better results for drag forces and prediction

of flow separation, compared to other options such as the k- and k- models. Due to its

performance during these tests for different flow conditions, the SA model was selected

as the main turbulent model for this thesis. As noted above the SA model employs only

one-equation, which is a partial differential equation for the modified eddy viscosity. The

basic equation is setup as:

=

+ ( ) = + (3-1)

50

This can be written as:

+ = 1(1 2) 1 12 2 2 + 1 ( + ) +

2 (3-2)

Equation 3-2 can be simplified and the term by term explanation will be given

over the next few paragraphs.

+ = 1 + 1 ( + ) + 2

[1] 2 (3-3)

Or

+ = 1 + 1 [ () + cb2()2] [1] 2 (3-4)

Or in words:

The production, diffusion, and destruction terms that were defined in the SA

model were based on the NK model. The production term defined by NK was based on a

statement that was made by Nee & Kovasznay about what defines eddy viscosity and

turbulent flow. The eddy viscosity can be regarded as the ability of turbulent flow to

transport momentum. The ability must be directly related to the general level of

activity, and therefore, to the turbulent energy". [28]

+ = + - Rate of change of

viscosity parameter

Transport of by

convection

Transport of by turbulent

diffusion

Rate of dissipation

of

Rate of production

of

51

Based on the above argument, NK defines the production term analogous to the

production of turbulent energy. Based on this assumption, NK then assumed that the

production term must increase monotonically with magnitude of the mean vorticity

and the increase of the total viscosity.

The SA model is slightly different in defining the production term in terms of its

consideration of the appropriate form of mean vorticity. Since the NK model focuses on

the simulation of the turbulent shear flow, then the mean vorticity form of was the

best choice. However the SA models emphasis is on high Reynolds number

aerodynamic flow in which turbulence is found only where the vorticity is located.

Consequently the SA model uses only magnitude of the vorticity.

The diffusion term that was defined in NK used a general definition of diffusion

of a scalar F based on the general diffusion equation:

= (3-5)

Here is the flux of F due to diffusion and it can be rewritten as = , where DF is the coefficient of diffusion. In addition to the diffusion assumption by NK,

they also considered the total viscosity = + as a portable quantity, where is the molecular viscosity and is the eddy viscosity. NK also assumed that turbulent motion

diffuses by itself; for that reason the coefficient of diffusion is assumed to be Dn=n, and

henceforth the turbulent Prandtl and Schmidt numbers are approximately one and 1.

Based on all the above NK assumptions for the diffusion term, the equation is given as:

= (nn) (3-6)

52

The SA model is still slightly different than the NK model for the diffusion term.

SA considers the general diffusion operator as ([ ]), where is the eddy viscosity and is the Prandtl number. In the SA model, the molecular viscosity does not

play a major role, and the Prandtl number is still about one. The main difference between

the SA and NK models comes in the conservation of the integral. Spalart and Allmaras

pointed out that manipulation of two-equation models such as the k- model often brings

out diffusion terms that are not conserved. For example, if a cross product of k is calculated, a non conservative diffusion term will then be allowed in the equation.

[28, 42]

Lastly, the destruction term in the SA model is very similar to the NK approach.

NK again uses the same assumptions as the production term for the eddy viscosity to

construct the destruction term. NK states that the rate of decay of the energy of high-

intensity uniform turbulence is a very rough approximation, and it is inversely

proportional to the square of the energy:

2

= (2)2 (3-7)

Separating the terms and then integrating both sides will then get the decay law:

2 1 (3-8)

Since Equation (3-1) considers the quantity F to be the total viscosity n, if the

production and the diffusion terms are removed from Equation (3-1), it will then reduce

to:

= (3-9)

53

Based on the NK assumption of similar behavior of total turbulent energy and

viscosity, it can be assumed that 2. Finally, based on dimensional analysis, the final form of the destruction term is given as:

= 2( ) (3-10)

The term B is a universal constant for the turbulence production and L is the

characteristic length. The L term was introduced in order to make B a non-dimensional

term. Usually L is a function of y, but in this area of the outer edge of the turbulent flow,

L is assumed to be equal to the boundary layer thickness (). However, when L is

analyzed closer to the wall, it can be assumed that L=y. In addition, the destruction term

depends on the distance from the wall. This accounts for the high rate of dissipation in

nearness of solid boundaries. It is very important to note that the maximum dimension of

the dissipating eddies in the direction perpendicular to the flow must be equal to the

distance from the wall.

As mentioned earlier, the SA model for the destruction term is very similar to the

NK approach. The major difference in the derivation of the destruction term is the way

SA defines the non-dimensional function beside the constant in the term. The SA model

assumes that the blocking effect on the wall in the boundary layer is felt at a distance

through the pressure term. The pressure term acts as the main destruction term in the

Reynolds shear stress. For that reason the first term of the destruction term can be written

as; 1(/ )2 , where cw1 is constant and d is the distance to the wall. To overcome the problem with slow decay in the outer region, SA multiplied the destruction term by a

54

non-dimensional function fw which is equal to 1 in the log layer near the wall.

Consequently the new destruction term then becomes:

= 1( )2 (3-11)

Now that the production, diffusion, and destruction terms are defined, the rest of

the SA model will be explained. The relationship between all the working terms in the

equation and the turbulent kinematic eddy viscosity is = 1 = and the wall function fv1 is defined as:

1 = 33+13 = (3-12)

The term is defined as the modified Vorticity magnitude that is maintained in

the buffer layer with log behavior. This is defined as:

+ 22

2 , = 2 , = 12 2 = 1 1+1 (3-13)

The destruction term function fw is:

= 1+366+36 16 , = + 2(6 ), = min 22 , 10 (3-14)

2 = 3exp (42) (3-15)

Now that the SA model is completely defined as a one-equation model. SA

suggests the following constants to be used with its equation to do numerical simulation.

The suggested values for the constants are:

55

1 = 0.1355; 2 = 0.622; 1 = 12 + 1 + 2 ; 2 = 0.3; 4 = 2 ; 1 = 7.1

3 = 1.2 ; 4 = 0.5 ; = 23 ; = 0.41 3.3. Appling FLUENT Setup

All of the modeling and analysis was done using ANSYS FLUENT. Before all

this could be done the software had to be calibrated and initial parameters had to be

applied to the model within FLUENT. The following section will explain the setup,

application of boundary conditions to each model, and application of the mesh

refinement.

3.3.1. Initial Setup

In order to open FLUENT and start the CFD analysis, the user first has to open

ANSYS WORKBENCH as illustrated in Figure 2-27 and load the mesh from ANSYS

ICEM CFD. In order to do that, the user has to drag the correct cells in ANSYS

WORKBENCH to the workbench window. The cells are the geometry block and the

FLUENT block. The user must right click on the mesh cell to load the ANSYS ICEM

CFD mesh to the workbench. Then to load the mesh into FLUENT, the user must drag

the mesh cell to the FLUENT block and then double click on the setup cell to open

FLUENT. However, the FLUENT Launcher window will open first, and the user must

select the following options that are illustrated in Figure 3-1. Then press OK to start

FLUENT.

56

As soon as FLUENT opens the user needs to set up the problem. Almost all the

steps are the same for each simulation except for the boundary condition setup that will

be discussed later. Figure 3-2 shows how to apply the problem setup within FLUENT to

get the best results.

The first thing that is done in the Problem Setup is the General setup. This is

where the mesh is checked; after that is completed the correct scale and the units are then

selected for the model. The reason why the correct scale and the units are selected is

because the model is in SI units and it needs to be converted to British units and scaled to

the correct size. In order to convert the units from SI to British units, the user must click

on the General tab and then select the Units menu. After that task is completed, the

user must scale the model to the correct size. In order to scale the model, the user must

click on the Scale menu and select ft for the View Length Unit In and then in the

Figure 3-1: Fluent Launcher option selection

57

scaling region the user must select the Convert Units option and units of inches. This is

illustrated in Figure 3-2. Then press Scale and close the dialog box by clicking Close.

After the General setup is completed, the user must select the following steps to

complete Problem Setup. The steps are: Models, Materials, Cell Zone Conditions,

Boundary Conditions and Reference Values setups. The Model setup allows the user to

set various flow model options, e.g. phase change, mass transfer, etc. For this study, the

Viscous model is the only one selected. In the Viscous model option the SA turbulent

model is selected and the SA model uses the constants that are explained in Section 3.2.

This is illustrated in Figure 3-3.

Figure 3-2: General setup step in Fluent

58

The next step is the Materials setup where the user must select the fluid and solid

materials. As mentioned earlier, the outside fluid (fluid box) for this thesis is going to be

air, and the solid will be set as aluminum in the Materials setup. The reason why

aluminum was set as the solid material, and not carbon fiber, is due to two reasons. First

FLUENT does not have carbon fiber in its data base. The second reason is because the

wall is assumed to be smooth and an arbitrary material is used.

The next steps in the Problem Setup are the Cell Zone Conditions and the

Reference Values setup. The Cell Zone Condition task allows setting the type of cell zone

condition parameters for each zone i.e. fluid domain is set as fluid. The Reference Value

Task page allows setting the reference quantities that are used for computing different

variables after the solution process has finished. Figure 3-4 illustrates the reference

values that are being used for the HPV model; however, the reference values for the other

Figure 3-3: The Viscous Model Dialog box displaying the SA model setup

59

models such as the oblate ellipsoid and the flat plate are all the same except for the area

and the velocity values that change with each simulation.

3.3.2. Boundary Conditions

The following discussion summarizes the Boundary Conditions task in FLUENT,

and Boundary Conditions for each simulation, are shown in Tables 3-1 and 3.2. Recall

that while creating the mesh in ICEM, the boundary types were then set for each face in

the domain. The right boundary plane (YZ plane in the positive X direction) is the inflow

of the flow field ( = ), and the left boundary plane is the outflow. The top and bottom planes, and the XY plane in the positive Z direction are set as Symmetry planes, as well

Figure 3-4: Reference Values task for the HPV model

60

the Symmetry plane for the fluid boundary. The exception is the simulation of the

moving ground plane as shown in Table 3-2, the bottom plane is defined as a wall for

these cases.

Symmetry boundary conditions are used when the physical geometry and the

expected pattern of flow solution have mirror symmetry in order to reduce the total

computational time and power needed for the simulation. In addition, symmetries are also

used to model zero-shear slip walls in viscous flow.

In the Problem Setup a Boundary Conditions Task can be opened and this where

the boundaries are specified for each region, this is done according to Tables 3-1 and 3-2

for the flat plate, oblate ellipsoid and the HPV fairing simulations.

plane Position Name Type

Right (YZ plane @ X+) Inflow Velocity

Inlet Left (YZ plane @ X-) Outflow Outflow Top (XZ plane @ Y+) Top of the outer volume Symmetry

Bottom (XZ plane @Y-) Bottom of the outer volume Symmetry Far side (XY plane @

Z+) Far side of outer volume Symmetry Symmetry (XY plane

@Z-) Symmetry Symmetry Model Model Wall

Table 3-1: Boundary type for the Flat Plate, Oblate Ellipsoid, and HPV fairing run without a

ground plane

61

plane Position Name Type

Right (YZ plane @ X+) Inflow Velocity

Inlet Left (YZ plane @ X-) Outflow Outflow Top (XZ plane @ Y+) Top of the outer volume Symmetry

Bottom (XZ plane @Y-) Ground Plane Wall Far side (XY plane @

Z+) Far side of outer volume Symmetry Symmetry (XY plane

@Z-) Symmetry Symmetry Model Model Wall

Figures 3-5 and 3-6 illustrate the velocity inlet and the outflow setup. This step is

performed on all the models. A Velocity Inlet boundary condition is used to define the

velocity and the scalar properties of the flow at the inlet. By clicking on Velocity Inlet

and setting the momentum parameter. In the momentum parameter the user must select

the following options; the Velocity Specification Method is set to the Magnitude,

Normal to Boundary, the Reference Frame setting is set as Absolute, and the

Velocity/Magnitude setting is set to the freestream velocity. As the Velocity Magnitude

varies the Modified Turbulent Viscosity varies with it. The following equations are used

to find the values that are illustrated in Table 3-3.

= 0.1618 (3-16)

= 0.07 (3-17)

= 32

() (3-18)

Table 3-2: Boundary type for the HPV fairing model with moving simulation ground plane

62

In these equations I is the turbulence intensity, is the root-mean-square of the

turbulent (defined as; = 132 + 2 + 2 , and is the mean flow velocity. The

turbulence intensity can be also found using the Reynolds number. The turbulence length

l is a physical quantity related to the size of the large eddies that contain the energy in

turbulent flow, and L is the length of the model. In order to find the modified turbulent

viscosity , the user must use Equations 3-16 and 3-17 to find I and l then plug these

values into Equation 3-18 to get the value for as illustrated in Table 3-3

uavg (f/sec) I l (ft) Re

modified turbulent viscosity

[],(ft2/sec)

modified turbulent viscosity

[],(m2/sec) 6.562E+00 3.268E-02 5.775E-01 3.301E+05 1.517E-01 1.409E-02 1.312E+01 2.997E-02 5.775E-01 6.602E+05 2.782E-01 2.584E-02 1.969E+01 2.849E-02 5.775E-01 9.903E+05 3.966E-01 3.685E-02 3.281E+01 2.673E-02 5.775E-01 1.650E+06 6.202E-01 5.761E-02 3.937E+01 2.612E-02 5.775E-01 1.981E+06 7.274E-01 6.758E-02 4.593E+01 2.562E-02 5.775E-01 2.311E+06 8.325E-01 7.734E-02 5.249E+01 2.520E-02 5.775E-01 2.641E+06 9.356E-01 8.692E-02 5.867E+01 2.485E-02 5.775E-01 2.951E+06 1.031E+00 9.581E-02 6.562E+01 2.451E-02 5.775E-01 3.301E+06 1.137E+00 1.057E-01

Table 3-3: Change in modified turbulent viscosity () with velocity.

63

The outflow boundary condition is used to define the flow that exits the region. At

this plane, the details of the pressure and the flow velocity are unknown before the

solution has been generated by FLUENT. The pressure outlet is set to outflow and the

flow rate weighting parameter is set to one; this specifies that 100% of the outflow is

leaving the bounded area. These steps are illustrated in Figur