NUMERICAL SIMULATION AND WIND TUNNEL MEASUREMENTS OF
LATERAL AERODYNAMIC CHARACTERISTICS ON SIMPLIFIED
AUTOMOTIVE MODEL
MUHAMMAD RIZA ABD RAHMAN
A thesis submitted in fulfillment of the requirement for the award of the degree of
Master of Mechanical Engineering
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
December 2010 v

vi
A thesis submitted in fulfillment of the requirements for the award of the degree of
Master of Mechanical Engineering

viii
DEDICATION
Dengan nama Allah yang Maha Pengasih lagi Maha Penyayang..
Teristimewa buat ibu dan ayah yang tersayang, Zainab Mustafa dan Abd Rahman
Arifin seluruh keluarga dan sahabat...
Terima kasih atas sokongan kalian sehingga aku mampu mencapai hingga ke tahap ini. Hanya Allah s.w.t sahajalah mampu membalas jasa kalian..
Amin..
Motivator terbaik adalah diri sendiri…

ix
ACKNOWLEDGEMENT
All praise to Allah S.W.T, the Almighty God and the Lord of the Universe, the Merciful and Gracious. Salam to our beloved prophet, Nabi Muhammad s.a.w for
His mercy has given me the strength, blessing and time to complete this project.
Words cannot express my thankfulness to my supervisors PM. Dr. Ir.
Shuhaimi Mansor who guided me through the whole study with his knowledge and great patience. His excitement and curiosity toward science inspired me a lot. His encouragement has been with me all the time during the years of my study. Without his endless support and guidance, this thesis would not have been very well presented as for now.
I extend my gratitude to En. Iskandar Ishak and Yaheyia Aldreany, who shared their experience and knowledge in simulation and wind tunnel test analysis. I express my deep sense of gratitude and indebtedness to our engineer, Abd Basid Abd
Rahman and all staff of Aeronautic laboratory especially Airi Ali for their guidance, advices and motivation while completing this project.
Last but not least, the biggest appreciation to my parents and family and also to everyone for their precious contribution as being supportive for all the time.
Thank you…

x
ABSTRACT
Computational Fluid Dynamic (CFD) has become an important tool to solve various engineering problems related to aerodynamics. One such growing interest in
CFD is to correlate results between CFD and wind tunnel tests. The accuracy of CFD has improved considerably over the years but still large errors are present and lateral aerodynamic characteristics such as drag, side force and yaw moment due to yaw angle are often poorly predicted especially on bluff body shapes. Due to this, comparison between CFD and wind tunnel measurements has become more on demand. The main goal of this research is to investigate the capability of CFD to determine aerodynamic characteristics of simple automotive type bodies and its effect on crosswind stability. An investigation was performed both experimentally and computationally to analyze the main characteristics of flow past a 1:6 scale wind tunnel model of a simplified automotive body shape with different rear slant angles.
The investigations were focused on the prediction and measurement of drag, side force, yawing moment and flow characteristics around the model in Reynolds number range of 1.29x10
6
to 2.14x10
6
at various yaw angles. The wind tunnel measurements were performed to provide aerodynamic data on vehicle stability and also to build a database for validating the numerical simulation model. The CFD solver FLUENT 6.3 was used to simulate incompressible three dimensional flow with the standard k turbulent models. The result of the wind tunnel tests and the numerical simulations were found to be in good agreement. The results show that the rear slant angles have significant effect on aerodynamics lateral derivatives.

xi
ABSTRAK
Simulasi Dinamik bendalir berkomputer (CFD) telah menjadi satu alat yang penting dalam menyelesaikan pelbagai permasalahan kejuruteraan yang berkaitan dengan aerodinamik. Antara penggunaan yang semakin meluas pada masa kini adalah mencari perhubungan antara keputusan yang didapati dari CFD dengan ujian terowong angin. Ketepatan CFD semakin baik dari tahun ke tahun tetapi masih terdapat lagi ralat yang besar wujud dan pekali-pekali cirian aerodinamik seperti daya seret, daya sisi dan momen rewang terhadap sudut rewang biasanya kurang tepat terutama bagi bentuk jasad tubir. Oleh kerana itu, perbandingan antara CFD dan ujian terowong angin amat diperlukan. Matlamat utama kajian ini adalah untuk menyelidik kebolehan CFD dalam menentukan ciri-ciri aerodinamik dan kestabilan angin lintang ke atas badan automotif yang dipermudah. Kajian dilakukan secara ujikaji dan simulasi berkomputer bagi menganalisis ciri-ciri utama aliran yang melepasi model badan automotif yang dipermudah berskala 1:6 yang mempunyai sudut belakang yang berbeza-beza. Kajian memfokuskan kepada jangkaan dan pengukuran daya seret, daya sisi, momen rewang dan ciri-ciri aliran udara di sekeliling badan dalam julat nombor Reynolds 1.29x10
6
hingga 2.14x10
6
pada sudut rewang yang berlainan. Pengujian terowong angin dijalankan bagi mendapatkan data aerodinamik bagi kestabilan kenderaan dan juga digunakan untuk mengesahkan simulasi yang dibuat ke atas model. FLUENT 6.3 menggunakan model gelora kdalam simulasi aliran tiga dimensi tak termampat. Keputusan yang diperolehi menunjukkan kaitan yang baik antara pengujian terowong angin dan simulasi.
Keputusan kajian ini juga menunjukkan sudut belakang memberikan kesan yang jelas signifikan ciri-ciri aerodinamik.

xii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
DEDICATION viii
ACKNOWLEDGEMENT ix
ABSTRACT x
ABSTRAK xi
TABLE OF CONTENTS
LIST OF FIGURES xii xv
LIST OF TABLES xviii
NOMENCLATURE xix
1.
INTRODUCTION 1
1.1
Introduction 1
1.2
Problem Statement
1.3
Research Objective
1.4
Scope of Work
1.5
Research Methodology
1.6
Organization of The Thesis
2.
LITERATURE REVIEW 7
3
4
2
3
5
2.1
Introduction 7
2.2
Aerodynamic Characteristic 9
2.2.1
Forces and Moments
2.2.2
Aerodynamic Derivative
9
11
2.2.3
Pressure Distribution
2.2.4
Crosswind Sensitivity
2.2.5
The Angle of Side Slip for Crosswind
11
12
12

xiii
2.2.6
Center of Pressure
2.3
Vehicle’s Crosswind Stability
2.4
Bluff Body Type
2.5
Computational Fluid Dynamic Simulation
2.5.1
Review of Previous Related CFD Study
3.
COMPUTATIONAL FLUID DYNAMICS 23
3.1
Introduction 23
3.2
Pre-processing 24
3.2.1
Selection Grid
3.2.2
Size Function
3.2.3
Computational Domain
3.2.4
Grid Generation Using GAMBIT
3.2.5
Three Dimensional (3D) Modeling Mesh
25
25
27
28
28
3.2.6
Independent Meshing
3.3
Solver Setup for Simulation
3.3.1
CFD Simulations Using FLUENT 6.3
3.3.2
Solver Setup
3.3.3
Boundary Conditions
3.3.4
Fluid Properties
3.3.5
Solution Control 40
3.4
Post-Processing 42
43 3.5
Assumption of The Simulation
4.
WIND TUNNEL TEST 44
30
31
31
36
37
40
4.1
Introduction 44
4.2
Wind Tunnel Specification
4.3
Model specification
4.4
Measurement Method
4.5
Solid Blockage
4.6
Experiment Setup
44
45
46
47
48
4.6.1
Comparison with Loughborough Wind Tunnel Test Results
4.7
Results from 20
0
Rear Slant Angle
4.7.1
Side Force and Yaw Moment Derivatives of 20
0
Slant
4.8
The Effect Rear Slant Angle
4.9
Side Force and Yaw Moment Derivatives of Various Slant
48
50
51
52
55
13
14
14
15
18

xiv
5.
RESULTS AND DISCUSSION 58
5.1
Introduction 58
5.2
Detailed Simulation Results 58
5.3
Drag Force
5.4
Side Force Coefficient and Derivative
59
65
5.5
Yawing Moment Coefficient and Derivative
6.
CONCLUSION AND RECOMMENDATION
70
77
6.1
Conclusion 77
6.2
Recommendations 78
REFERENCES 80
APPENDIX A 84
APPENDIX B 93

LIST OF FIGURES xv
2.6
2.7
2.8
3.1
3.2
3.3
3.4
3.5
3.6
4.1
4.2
4.3
4.4
slants angle of Ahmed model after Gillieron and Chometon 19
Instantaneous streamwise velocity fields in the symmetry plane, for different time of simulation. Hinterberger et.al. (2004)
Surface mesh of Ahmed model with 30° rear slant angle, after
20
Francis T. Makowski and Sung-Eun Kim (2000)
Time-study of C
D
(DES) Figure (a) and Time -Study of C
D
(RANS) Figure (b) after Sagar Kapadia et.al. 2003
21
(a) & (b). Grid generation using size functions
Computational domain size
Davis model configuration
Computational meshing model
Drag coefficient versus number of meshing element (Mesh
22
26
27
29
30 independent study) 31
Graph drag coefficient versus yaw angle for different turbulence model for 20
0
rear slant angle 35
Universiti Teknologi Malaysia Low Speed Tunnel (UTM-LST) 45
General dimensions of baseline shape (rear slant angle 20
0
) of
Davis model. All edge radii 10 mm.
Model with different rear slant angles. All edge radii 10 mm.
46
46
Aerodynamic coefficient against yaw angle at wind speeds 40 m/s of 20
0
slant. (a) drag force, (b) side force ,(c) yaw moment 49

4.9
4.10
4.11
5.5
5.6
5.7
5.8
5.1
5.2
5.3
5.4
5.9
5.10
5.11
5.12
4.5
4.6
4.7
4.8
5.13
5.14
5.15
xvi
Model slant angle 20
0
setup for static test
Aerodynamic coefficients against yaw angle at different wind speeds of rear slant angle 20
0
. (a) side force, (b) yaw moment
50
51
Aerodynamic coefficient versus yaw angle for different rear slant angles at 40 m/s. (a) drag, (b) side force, (c) yaw moment 53
Side force, yaw moment coefficient and centre of pressure for various rear slant angles for 10
0
yaw and drag
Static aerodynamic derivatives of different slant angles at 30 to
54
50 m/s. (a) side force, (b) yaw moment
Static side force derivatives versus Reynolds number for
56 different rear slant angles.
Static yaw moment derivatives versus Reynolds number for
57 different rear slant angles. 57
(a) and (b): Velocity vector and contours in the wake of 0
0
slant 60
(a) and (b): Velocity vector and contours in the wake of 10
0 slant 61
(a) and (b): Velocity vector and contours in the wake of 20
0
slant 62
(a) and (b): Velocity vector and contours in the wake of 30
0
slant 63
(a) and (b): Velocity vector and contours in the wake of 40
0
slant 64
Graph side force coefficients versus yaw angle for slant 0
0
65
Graph side force coefficients versus yaw angle for slant 10
0
65
Graph side force coefficients versus yaw angle for slant 20
0
66
Graph side force coefficients versus yaw angle for slant 30
0
66
Graph side force coefficients versus yaw angle for slant 40
0
66
Graph side force coefficients versus yaw angle at different slant angle 67
Graph side force coefficients versus rear slant angle at yaw angle 10
0
68
Static side force derivatives versus Reynolds number for different rear slant angles. 68
Comparison experimental and CFD static side force derivatives versus rear slant angles for 40 m/s. 69
Graph yawing moment coefficients versus yaw angle for rear slant 0
0
70

5.19
5.20
5.21
5.22
5.23
5.24
5.16
5.17
5.18
xvii
Graph yawing moment coefficients versus yaw angle for rear slant 10
0
70
Graph yawing moment coefficients versus yaw angle for rear slant 20
0
71
Graph yawing moment coefficients versus yaw angle for rear slant 30
0
71
Graph yawing moment coefficients versus yaw angle for rear slant 40
0
71
Graph yaw moment coefficients versus yaw angle at different rear slant angle 72
Graph yawing moment coefficients versus rear slant angle at yaw angle 10
0
73
Static yawing moment derivatives versus Reynolds number for different rear slant angles.
Comparison experimental and CFD static yaw moment force derivatives versus rear slant angles for 40 m/s.
73
73
Velocity vector at plane behind the model 75

xviii
LIST OF TABLES
TABLE NO. TABLE PAGE
2.1
Forces and moment.
3.1
Default values of in FLUENT
4.1
Balance load range and accuracy.
4.2
Comparison aerodynamic derivative UTM-LST and
Loughborough University wind tunnel test
8
41
47
50
4.3
4.4
Static measured derivatives of Cy and Cn for 20 slant.
Side force and moment derivative at different rear slant angle
52
56
5.1
The drag force and the coefficient of drag for the Fluent and wind tunnel test result. 59
5.2
5.3
Tabulated data experimental and CFD static yaw moment force derivatives versus rear slant angles for 40 m/s. 69
Tabulated data experimental and CFD static yaw moment force derivatives versus rear slant angles for 40 m/s. 74

xix
NOMENCLATURE
A - frontal m
2
As - m
2
Cd - aerodynamic drag coefficient cg - centre of gravity
Cn - aerodynamic yaw moment coefficient cp - centre of pressure e
0 e s
- distance center of aerodynamic to center wheel base
- distance center of aerodynamic to center wheel base
Cy E
- aerodynamic side force derivative m m rad
-1
Cn E
- aerodynamic yaw moment derivative rad
-1
Cy - aerodynamic side force coefficient
- dissipation rate
I zz
- model rig yaw moment of inertia kg.m
2 k kinetic energy
" model
" cp distance between cp and cg
m m
" wb base m l
F
distance between front axle to cg
" r distance between rear axle to cg m m m - kg
N a
Re
- Reynolds Number moment Nm
N f u , v , w
V
V x
-1 wind m.s
wind axial
-1
-1 wind lateral
-1
V y
V z
V f wind
- vertical velocity
m.s
-1
m.s
-1
-1
V w
E - yaw deg
E w crosswind deg
U air kg.m
-3
T
I
- model angle of rotation deg
- deg
\ - crosswind angle with respect to vehicle forward speed deg

1
CHAPTER 1
1.
INTRODUCTION
1.1
Introduction
Currently, a new environment exist in the industry that want to produce a new design or model in short period and want to reduce cost. One of the best solution for this problem is by using computational fluid dynamic (CFD) simulation. Therefore, computational fluid dynamic is becoming more important and in high demands. Computational fluid dynamic and experiments have their own strengths and limitations. CFD can provide a very detailed view of the flow field, generating velocities, pressure and densities at every point in the domain where it would be very expensive to measure experimentally. However, calculations always approximate the flow in some way, either by solving a simplified equation or by introducing approximations through the numerical method itself. Besides that, the wind tunnel test has the advantage of dealing with a real fluid and measuring the correct physics, though usually not at perfect real conditions (Reynolds number differences) or the right geometry (because of model support interference or wall effects). It often provides good measures of integrated flow properties such as total forces and moments acting on a body.
The aerodynamic characteristics of passenger cars have been a fruitful area of research for several decades, and continue to this day. However, it is well appreciated that there still remains much more things to be learned in this area, and for that purpose, further research is required to understand the complex aerodynamic and flow around the model.

2
Crosswind stability is an important area of study in vehicle aerodynamic design since it leads to safety issues. The main concern in aerodynamic design for years has been concentrated on reducing the drag for fuel efficiency. Later on, it was found that the streamlined vehicle shapes are sensitive to crosswind disturbance. The styling trend towards rounder shapes especially at the rear of the vehicles and a continuing reduction in aerodynamic drags are suspected to contribute to the crosswind sensitivity (Howell, 1993).
Crosswind sensitivity was one of the major concerns in the design stage process. But this area is still not fully understood. In practical, this behavior sometime will be happen after production. Previously, CFD is used to predict the aerodynamic loads and flow characteristics around the model only but now this research also to predict and see the aerodynamic derivatives.
The ability of computational fluid dynamic (CFD) to predict critical flow characteristics has always been questionable. The accuracy of CFD, has improved considerably over the years but still large errors are present and vehicle parameters such as drag and lift are often poorly predicted. Due to this, comparison between computational fluid dynamic and wind tunnel testing has become demanding. The main goal of this research is to investigate the capability of CFD to determine aerodynamic characteristics on simple automotive type bodies and its effect on crosswind sensitivity. Numerical analysis using CFD modeling and simulation will be compared with experimental results in the wind tunnel.
1.2
Problem Statement
Currently, during the design of a new model both wind tunnel test and computational fluid dynamic will be used. In real application wind tunnel test will consume more cost and time and have limitation in data requirement. To overcome this problem all designer try to change to simulation but the confident

3 level of simulation prediction is still not too accurate compare to wind tunnel test results. In current practice CFD has been used to predict aerodynamic loads and flow field around the model. However, there are few researchers focus on aerodynamic derivatives (side force and moment derivatives) which is very important to estimate the stability of model. The stability of the model play the important role to make sure the shape of the vehicle can be optimized.
1.3
Research Objective
1. To investigate the capability of CFD to determine lateral aerodynamic characteristics on simple automotive type body.
2. To determine the aerodynamic derivative characteristics of a bluff body with various rear slant angles.
1.4
Scope of Work
The current research work is limited to the following:
1. Computational Fluid Dynamic (CFD) simulation using FLUENT
6.3 and wind tunnel test on a bluff body
2. The study is based on a Davis model with different rear slant angles (0
0
, 10
0
, 20
0
, 30
0
and 40
0
).
3. Air velocity between 30 to 50 m/s which corresponds to a range of
Reynolds number based on model length between 1.29 x 10
6
and
2.49 x 10
6
.
4. The yaw range was between -16
0
and 16
0
with increment of 2
0
.

4
1.5
Research Methodology
This research comprises of two main parts, Computational Fluid Dynamic
(CFD) simulation using Fluent 6.3 and wind tunnel test measurement. In both parts, Davis model with five different rear slant angles (0
0
, 10
0
, 20
0
, 30
0
, and 40
0
) were test and simulate in various wind speeds ranging from 30 m/s to 50 m/s with interval of 5 m/s. Wind tunnel test has been conducted at Universiti Teknologi
Malaysia Low Speed Tunnel (UTM-LST) and forces and moments subjected to the models were measured using six component external balances. In this research, Davis model with rear slant angles of 20
0
become a base model for
Validation of simulation and experimental verification with Mansor (2006) works before other rear angles being tested. Both results are then compared to find any correlation between experiment and simulation. The overall flow chart of the research methodology is shown in Figure 1.1.

5
Literature x
Problem statements x
Define objectives x
Determine scopes x
Design research
Preparation for CFD
Results
Simulation
CFD simulation validate with Mansor 2006
CFD simulation for all configurations
Simulation Analysis
Design and fabrication of model and test rig
Wind Tunnel Test verify with Mansor 2006
Wind tunnel test for all configurations
Wind Tunnel Static
Analysis
Comparison CFD and wind tunnel test results
Figure 1.1
Flow chart for research methodology
1.6
Organization of The Thesis
This dissertation is structured in six chapters. The background, a short description of the methodology, motivation and objectives has been presented in this chapter. Chapter 2 is devoted to literature survey, a detailed review of the research work conducted in the area. Chapter 3 briefly discusses the numerical

6 tools, solution procedure and turbulence modeling that are being used in this dissertation. Then, Chapters 4 and 5 investigate bluff body aerodynamics on Davis model. Presented in Chapter 4 are the experimental measurements of drag, side force and yaw moment at various yaw angle from the static wind tunnel tests, and in Chapter 5 the numerical results and their comparison with experimental measurements are provided. Finally, conclusions of the present study and recommendations for future enhancement of the work are given in Chapter 6.

7
CHAPTER 2
2.
LITERATURE REVIEW
2.1
Introduction
Vehicle aerodynamics comprise several categories such as vehicle stability due to directional and crosswind sensitivity, vehicle performance due to aerodynamic drag, and vehicle cooling. For vehicle stability, the flow pass by a vehicle will responsible to straight line stability, dynamic passive steering and vehicle response due to crosswind which is the external flow. In a stable crosswind situation in term of time and position, the yawing moment and side force are compensated by stable steering control angle. Meanwhile a small crosswind will slightly handle by the driver. However, problem do occur when strong crosswind exist that lead to driver lost control and uncomfortable driving condition.
The crosswind stability for ground vehicle is an important factor in car handling since it leads to safety issues. For a car traveling along the road and subjected to crosswind disturbances, the ride and handling characteristic of the vehicle is affected. Analysis produced by Baker and Reynolds (1992) shows that accidents may occur when the vehicle is subjected to crosswind disturbances. Not many wind-induced accidents involve overturning because passenger cars are unlikely to blow over (Barnard, 1996). Rather, the accidents are mostly associated with excessive path deviation that results in impact with other vehicles or roadside objects. Overturning is usually associated with trucks, busses and light vans and

8 for passenger cars it may occur as an indirect result of very large course deviations when experiencing sudden side-wind.
The air flow around the vehicle becomes asymmetrical under natural crosswind or overtaking a vehicle condition. This will create a lateral force which is known as a side force and it will affect the yawing moment, rolling moment and the pitching moment. Design or study about the appropriate shaping of the vehicle body is the task of the aerodynamicist to influence the forces and moments. The aerodynamicist not only focuses on the basic shape of the vehicle, but also includes those aerodynamic effects created from tires, spoilers, roof loads, and cooling.
Figure 2.1
SAE vehicle body axes.
Table 2.1: Forces and moment.
Direction Force, Moment
Longitudinal
Lateral
Vertical
Drag, x
Side Force, y
Lift, z
Rolling, p
Pitching, q
Yawing, r
An important factor in crosswind stability analysis is the rate at which the forces and moments vary with yaw angle, and it is necessary to measure quantities known as the aerodynamic derivatives such the side force derivative. The dCy/d

9 is commonly written as Cy , where Cy is the coefficients of side force and is the yaw angle. A large value of aerodynamic derivatives means that the force or moment changes rapidly with angle, hence the vehicle is sensitive to yaw angle changes.
This chapter starts with the review on the aerodynamic parameter, background of the ground vehicles crosswind stability study and the following development in wind tunnel test to determine the aerodynamic effects on vehicle body in crosswind condition. The next section reviews on the available computational fluid dynamic (CFD) method to estimate the aerodynamic characteristics. The aim is to give an overview on the investigation of crosswind stability and the role of computational fluid dynamic to estimate the lateral aerodynamic characteristics. Since the identification of aerodynamic derivatives in automotive application is determine from experimental approach, the CFD simulation tools should have potential to estimate an accurate result as the experimental results.
2.2
Aerodynamic Characteristic
2.2.1
Forces and Moments
Focusing on the crosswind condition, the airflow will be asymmetrical.
This condition will lead to an asymmetrical pressure distribution in the typical horizontal cross section. The pressure distribution results in a lateral force and a yawing moment which can be reduced to side forces at the front and rear axle. The direction of the airflow relative to the vehicle movement and the direction of the resulting aerodynamic force are not the same. Based on the angle of yaw, it is smaller than the angle between the x-axis and the resulting aerodynamic force. In strong crosswind condition, the side force can easily reach higher level than drag

10 force. The side force, Y and yawing moment, N can be expressed as following equation:
ܻ ൌ ܥݕ
ஒ
ߚ
ߩ
ʹ
ݒ ଶ ܣ
(2.1)
ܰ ൌ ܥݕ
ఉ
ߚ
ߩ
ʹ
ݒ ଶ ܣ݈
(2.2)
The pressure forces will be produced by the airflow around a vehicle and it is acting towards the vehicle surface. This condition will create a force and a moment at each direction for the vehicle. Difference in pressures between the vehicle upper side and underside will produce a lift force (L), and a pitching moment (M) or the difference lift force in front and rear axle. The lift force and pitching moment are expressed as following equation:
ܮ ൌ ܿ
௟
ߩ
ʹ
ݒ ଶ ܣ݈
(2.3)
ܯ ൌ ܿ
௠
ߩ
ʹ
ݒ ଶ ܣ݈
(2.4)
Pressures difference between windward side and leeward side will also produces a rolling moment, R and it can be expressed as:
ܴ ൌ ܿ
௥
ߩ
ʹ
ݒ ଶ ܣ݈
(2.5)
For the vehicle directional stability, the rolling moment only has a comparatively limited effect. It mean whether it is significant depends on the roll steering characteristics of the chassis where a lower rolling moment improves the steering characteristics in crosswind gust (Hucho,1998).

2.2.2
Aerodynamic Derivative
The aerodynamic derivative is the gradient of forces and moment versus yaw angle. The side force and yaw moment derivatives are given by:
11
Side force derivative: dCy d
E
Cy E
Yaw moment derivative: dCn d
E
Cn E
2.2.3
Pressure Distribution
Pressure distribution for a vehicle under crosswind will affect the centre of gravity and the centre of pressure of the aerodynamic forces which are not located in the same position. This means that the wind effect will create a lateral force plus a significant bending moment. The aerodynamic forces and moments depend on the longitudinal velocity of the vehicle, the yaw angle respect to the wind source, and obviously the lateral shape of the vehicle (Punset and Catala,2002).
Figure 2.2 Pressure distribution on a horizontal vehicle section at 20
0
yawing angle.

12
2.2.4
Crosswind Sensitivity
Crosswind sensitivity generally refers to the lateral and yawing response of a vehicle in the presence of transverse wind disturbances which affect the driver’s ability to hold the vehicle in position and on course. Crosswind sensitivity is dependent on more than just the aerodynamic properties of the vehicle; many other elements do play a role in the crosswind influence on forward-moving vehicle. There are several important elements such as:
1. Vehicle dynamic properties
2. Aerodynamic properties
3. Steering system characteristic
4. Driver closed-loop steering behavior
2.2.5
The Angle of Side Slip for Crosswind
Crosswind influence on the side slip terms, by vector addition it combines with the vehicle’s velocity to produce a resultant relative wind. The velocity of the relative wind and the velocity of the crosswind is a length proportional to the velocity it represents and the arrows are drawn at angles corresponding to their respective wind directions by follow the velocity vector. The resultant of the velocity vector can be expressed as follow: cp
Figure 2.3 The angle of side slip for crosswind

13
2.2.6
Center of Pressure
The side force and drag acting together called as center of pressure is a point where both factors join together. Generally, in wind tunnel tests the yawing moment is related to the center of the wheelbase. The consequence of the crosswind effect on center of pressure will leads to values which are independent from the load condition of the vehicle thus providing a basis for a strictly aerodynamic evaluation of different shapes. For evaluation in vehicle dynamic the yawing moment can also be represent as a side force acting at a specific point with a distance from the center of the wheelbase. This point is called the pressure point.
A small distance the pressure point and the center of gravity have the ability to results in a small yawing moment. The pressure point distance can be expressed as:
݁
଴
ൌ
ܿ
௡
ܿ
୷
Ǥ ݈
Hence, the distance of the pressure point to the center of gravity of the vehicle is most significant for the directional stability:
(2.6)
݁
௦
ൌ ݁
଴
െ ൬
݈
ʹ
െ ݈
ி
൰
(2.7)
Figure 2.4
The center of gravity and center of pressure, (Hucho, 1998)

14
2.3
Vehicle’s Crosswind Stability
The dominant factors that affect the crosswind characteristics can be categorized mainly into three categories (Yoshida et al., 1977):
1. The aerodynamic characteristics determined by the body shape of the vehicle
2. Characteristics of the body structural system determined by the basic dimensions of the vehicle
3. Characteristics of the mechanical systems including suspensions, steering, tires, etc.
2.4
Bluff Body Type
Currently, there are several simple bluff body type has been used by most researchers to investigated and determined the aerodynamics characteristics of the ground vehicle. A review by Le Good and Garry (2004) has listed three categories of vehicle shapes that have been used in experimental and computational research in automotive aerodynamics: Simple bodies that are mainly for research purpose.
Basic car shapes used for calibration, correlation and research. The production
(series) cars that are used for variety of specific investigations and correlation studies.
The Davis model that has been used in Mansor’s (2006) work is one of simple body type. The model was originated from PhD work by Davis (1983) to investigate the road vehicle wake. A research conducted by Bearman and
Mullarkey (1994) using Davis model with systematic changes of backlight angle in investigating the effects of side winds and gusts leads to the result that suggested the measurement of steady forces and moments at fixed yaw angles and assuming quasi-steady flow are conservative estimations of unsteady quantities.
Other simple body types are e.g. the Ahmed model, NRSCC/SAE model,
Rover model and Docton model. The usage of Ahmed model in aerodynamic

15 research was among the first study to investigate the significance of the backlight angle on aerodynamic characteristics (Ahmed et al., 1984). The NRSCC/SAE geometry was devised to approximate the overall dimensions of the average North
American automobiles and to exhibit the main characteristics of flow-fields associated with temporary cars and trucks. The Rover model devised by Windsor and Howell in late 1980s was to assist in fundamental investigations of shape effects while the Docton model devised by researchers at Durham University to investigate transient effects (Le Good and Garry, 2004). The complete review of all these models and other type of models used can be accessed in Le Good and
Garry (2004).
2.5
Computational Fluid Dynamic Simulation
The traditional predictive tools used in the industry to evaluate aerodynamic performance of automobiles are wind tunnel tests and road tests
(W.H Hucho 1998). Wind tunnels are expensive to build and operate. They require a large amount of area for accommodating all components even though the test section might be only a small portion of it. Wind tunnels in automotive industries are often big enough to test their full sized vehicles. In spite of the possibility of testing real full-size vehicles, the finite size of the test section, complexities of operating moving ground rigs, and inadequacy of testing under side wind conditions, etc., impose limitations on simulating realistic flow conditions. On the other hand scaled models of vehicles are used for flow replication of full sized vehicles. These models may not possess the realistic characteristics of a complete vehicle, for example these models may not have engine cooling systems, cabin ventilation systems. In addition wall boundary layer and model support interference effects, model & wake blockage effects, effects of flow-intrusive probes, etc., would be present while testing these scaled models and measures has to be taken to overcome these difficulties before they are subjected to tests (W.H Hucho 1998).

16
In order to meet the consumer’s demand and to reduce cost and time-to market, automobile manufacturers have to develop more economical, safer and more comfortable vehicles at an increasingly rapid pace. Traditional wind tunnel testing and road testing techniques takes long development cycle times. In order to overcome these difficulties and to stay in the competitive market automotive manufacturers started concentrating on computational techniques to simulate wind tunnel tests called Computational Fluid Dynamics (CFD). CFD and model scale tests are used increasingly in car development with full-size wind tunnels used for validation and refinement parameter study as in the current industrial practice
(W.H. Hucho, 1998).
CFD simulations are well suited to analyze a wide range of shape options.
These simulations are most useful in predicting trends of how shape changes will affect flow field features of vehicles. Sometimes a CFD simulation permits the investigation of simulations that cannot be realistically duplicated in a wind tunnel. For example most tunnel test sections are designed for development on single vehicles thus studying several vehicles in a platoon is difficult. The aerodynamics of two or more vehicles at very close proximities in passing or overtaking mode, poses a difficult problem for wind tunnel tests. Positioning
(aligning) the model at extremely close proximities is a problem before performing a wind tunnel test.
The commercial suppliers of general-purpose CFD packages have led the developments in software that has enabled such applications to become commonplace. These tools are now used extensively throughout the automotive and aeronautical industries by various departments not only to study external aerodynamics but also to study engine cooling systems, cabin ventilation, etc. It is only in the largest companies that any significant development of CFD software continues, usually where customized coding can offer advantages in efficiency or accuracy for a particular, usually narrow application, such as wing design.

17
The study on aerodynamic characteristics can give the knowledge on vehicles behavior in crosswind condition. The study requires the knowledge of aerodynamic side force and yaw moment and usually are given in terms of aerodynamic coefficient or aerodynamic derivative. There are mainly three available approaches in identifying the aerodynamic derivatives; the theoretical approach and computational fluid dynamics (CFD), and the experimental approach. The identification of aerodynamic derivatives of ground vehicles is still new relative to the aircraft identification. The subject of ground vehicle aerodynamics does not lend itself readily to the mathematical analysis. There are no straightforward methods to predict airflow behavior around a given vehicle shape. The difficulty in the analysis is due to the highly three-dimensional flow around ground vehicle, the air does not follow the contours of the body everywhere, and there is almost always an unsteady wake (Barnard, 1996). The ground vehicle aerodynamic designer has very few mathematical tools and depends highly on experimental approach, which is still superior to the theoretical and computational fluid dynamics (CFD) approaches till now (Hucho, 1997).
Hucho and Emmelmann (1978) and Tran (1991) have developed theoretical predictions for lateral aerodynamic coefficients. Both techniques attempted to predict the transient aerodynamic derivatives. Hucho and
Emmelmann (1978) make the first approach in applying the slender body theory simulated by a flat plate to enable the engineering estimates to transient effects.
Tran (1991) derived the calculation method on the basis of a plate model and took into account to some extent the influences of partial flow, vehicle side area and pressure distribution over the vehicle length. Both of the calculation techniques make considerable simplifications in developing the model and could not account to the effect of styling details or for a unique vehicle shape. This theoretical approach based on the theoretical knowledge of fluid flow around flat plate is too constrained and limited to be applied to various vehicle shape which the fluid flow is highly three dimensional and the flow field dominated by the effects of separation.

18
Barnard (1996) dedicated the last chapter in his book discussing the computational fluid dynamics (CFD) method in the application of ground vehicles aerodynamics. Developed from the theoretical knowledge of fluid dynamics, CFD offers a number of numerical approaches to determine the fluid flow around vehicles model. However the results from the CFD can sometimes be misleading and it is found to be sensitive to the numerical scheme used and the turbulence model and choice of parameters used in it. In practice, the use of CFD requires a great deal of experience and specialist knowledge in the area of automotive application.
2.5.1
Review of Previous Related CFD Study
Gillieron and Chometon (1999) used the Ahmed car models of 25° and 35° rear slant angle configurations for analyzing the turbulent flow structures. A numerical scheme was used to validate the experiments that were carried out on using Ahmed model in a wind tunnel. The model was surrounded by 15000 triangular elements constructed using version 7.2 of ANSA software. Volume meshing was obtained using version 3.0 of the Fluent T-grid 3D software. Across all geometrical configurations, the model had a total of around 300,000 prism and tetrahedral volume cells. Computations were performed using version 4.2 of
Fluent software and the turbulence model used was k- turbulence model with a logarithmic law on the wall.
The ground effect that causes the vortex systems to develop into two counter rotating horse shoe vortices near the base of the Ahmed model were replicated. The computed results obtained on the Ahmed model were found to be in agreement with the experimental results obtained from the wind tunnel. In particular, the computations had successfully reproduced changes in vortex wake flows and aerodynamic drag coefficients. It was concluded that the over predicted computed drag values in Figure 2.5 were because of the code’s tendency to

19 overesti imate base pressure dr esults also r revealed tha are pr romising t techniques a in aut tomotive
Figure 2.5
Com experiment efficients fo r various reear h 25
0 nstruction t technique w nd computa tionally. results.
Exa-Power r FLOW th the exper rimental ttom of the model’s rear ‘C ’ pillar vort experiment tally and comput tationally a d that the oscillation correspon ds to a based on free stream and the square r root of the m tal area. models at a Reynolds n
S on 25
0
0
5
which res sulted in higher e = 7.68 x 10
5
). Their t for the

20 existing geometry the external vehicle flows at high Reynolds number becomes insensitive to Reynolds number. It was found that the geometry rather than the viscosity dictates the character of the flow and the positions of flow separations.
Also it was observed that while using lower Reynolds number the near wall energy carrying coherent structures can be resolved and the flow could be predicted more accurately. This observation raised hope that flow around real cars could be simulated with LES at reduced Reynolds numbers.
C. Hinterberger et.al (2004) conducted experiments on 25
0
rear slant
Ahmed models and concluded that the results obtained through Large Eddy
Simulation (LES) are promising. The comparisons with the experiments showed well captured flow structures.
Figure 2.6
Instantaneous streamwise velocity fields in the symmetry plane, for different time of simulation. Hinterberger et.al. (2004)
R.K. Strachan et.al. (2004) compared Laser Doppler Anemometry (LDA) data to a CFD solution run on Fluent 6.0 employing k- RNG turbulence model for a transverse plane one model length downstream of an Ahmed reference model. The CFD model predicted the counter-rotating vortices at this point in the flow very well. However there was a discrepancy in the position of the vortices between experimental and computational data. This discrepancy was thought in part to be caused by an alignment error in the model during testing. The CFD model was also compared to a previous study employing a Detached Eddy

21
Simulation (DES) turbulence model in the near wake of the Ahmed body. The correlation between the two models proved to be good, as the different ground simulations employed could account for most differences between them. Force measurements were also taken from the current experiment and these as well as
CFD force values were compared against a previous study. It was concluded that computational drag force predictions fluctuated within 3%. In addition comparison of the CFD model with Ahmed’s original experiment showed small discrepancies between the predicted drag coefficients over each part of the model.
Francis T. Makowski and Sung-Eun Kim (2000) worked on the numerical prediction of the aerodynamics around cars using Reynolds Averaged Navier
Stokes equations and unstructured mesh. From their research they concluded that the unstructured hybrid mesh with a solution adaptive mesh refinement capability was of great benefit to predict external aerodynamic flows around ground vehicles. In particular the meshing strategy of using tetrahedral elements in combination with prismatic near–wall elements was a viable approach for significant reduction of meshing time; also its flexibility was useful in dealing with complicated geometry and its ability to resolve widely-varying scales in the flow. Reynolds Averaged Navier Stokes Equation (RANS) simulation in combination with second moment turbulent closure and wall functions represents a cost effective strategy for modelling turbulent flows past ground vehicles like the strong streamline curvature, cross flow, three dimensional flow separation, vortex generation and flow reversals.
Figure 2.7
Surface mesh of Ahmed model with 30° rear slant angle, after
Francis T. Makowski and Sung-Eun Kim (2000)

22
They conducted experiments on Ahmed car model with critical rear slant angle of 30°, shown in Figure 2.7 and the simulations were performed for two different turbulence models; the Standard k- model and the Reynolds Stress
Model (RSM). They concluded that the Standard k- model over predicts the effective viscosity in regions where the turbulence is anisotropic and the RSM was able to demonstrate all the salient flow features observed in the experiments.
Kapadia and Roy (2003) performed the wake flow simulation of Ahmed reference model with 25
0
rear slant using DES as a turbulence model. Further, results are obtained using RANS model for same time -steps and were compared with DES results at a particular time-step. Their comparison showed the ability of
DES in capturing unsteady structure of the flow with minor flow details was better than RANS. Drag coefficient was calculated in both simulations and compared with the established results. Their comparison found similarity between DES results and experimental work by Ahmed et al 1984 and similarity between RANS results and numerical results of Gillieron and Chometon (1999).
Figure 2.8
Time-study of C
D
(DES) Figure (a) and Time -Study of C
D
(RANS) Figure (b) after Sagar Kapadia et.al. 2003

23
CHAPTER 3
3.
COMPUTATIONAL FLUID DYNAMICS
3.1
Introduction
Computers have been used to solve fluid flow problems for many years.
Numerous programs have been written to solve either specific problems or specific classes of problems. From the mid-1970s, the complex mathematics required to generalize the algorithms began to be understood, and general-purpose
CFD solvers were devoted. The first commercial CFD software packages began to appear in the early 1980s and required what were then very powerful computers, as well as an in-depth knowledge of fluid dynamics and large amounts of time to set up simulations.
Computational Fluid Dynamics (CFD) is one of the most powerful and useful tools for predicting the external flow behavior over ground vehicles. The emergence of CFD has made the use of wind tunnels only during the initial stages of a vehicle design (aerodynamic) program and once these initial experimental results are validated by the CFD code, the further extensions of work can be performed computationally. Thus the time involved for model making, mounting and testing at each and every stage can be neglected through these computational methods. Any design modification required can be performed with the available
CAD software and can be analyzed again with the available CFD tool. Thus repeating this cycle enables to reach an optimized design with less running cost.

24
The current study on the effects of vehicle slant angle and the influence of rear end geometries of vehicle on their aerodynamic coefficients are analyzed using CFD. The study is divided into four different phases, initially the models to be analyzed (The Davis car models) are solid modeled using a solid modeling package (Solid Works 2007) and export to *.SAT files. These models are then imported to GAMBIT where test domains are created around them. The domain along with the mode is meshed and respective boundary conditions are assigned and saved as *.msh file. As a final stage these mesh files are exported to Fluent to perform the CFD analysis and predict the aerodynamic behavior of the models.
The process is repeated for various rear slant angle 0
0
, 10
0
, 20
0
, and 30
0
.
Thus, the current chapter deals with the grid generation using the available commercial software GAMBIT followed by CFD analysis using the available commercial CFD tool, FLUENT 6.3.
As in every CFD-package, the solution procedure of Fluent can be divided into three parts:
1. Pre-processing,
2. Solver setup for simulation
3. Post-processing.
3.2
Pre-processing
The most important part of a CFD analysis is the pre-processing of the problem. This is not simply done by setting up geometry and activating some toggle switches in the GUI (Graphical User Interface) of the program.

25
3.2.1
Selection Grid
FLUENT can use grids that comprises triangular or quadrilateral cells (or a combination of the two) in 2D, and tetrahedral, hexahedral, pyramid, or wedge cells (or a combination of these) in 3D. The choice of which mesh type to use will depend on the application. When choosing the mesh type, the following issues should be considered,
1. Accuracy
2. Setup time
3. Computational expense
4. Numerical diffusion (post processing)
3.2.2
Size Function
A size function allows controlling the size of mesh intervals for edges and meshing elements for faces or volumes. Size functions are similar to boundary layers in that they control the mesh characteristics in the proximity of the entities to which they are attached. They differ from boundary layers with respect to the manner in which they are defined and the manner in which they control the mesh.
Whereas boundary layers prescribe specific mesh patterns and the sizes of mesh elements within those patterns, size functions control the following properties:
1. Maximum mesh-element edge lengths (fixed-type size function)
2. Angles between normal for adjacent mesh elements (curvature-type size function)
3. Number of mesh elements employed in the gaps between two geometric entities (proximity-type size function)
The “Create Size Function” command creates a size function and attaches it to a specified entity. A size function allows controlling the size of the mesh in

26 regions surrounding a specified entity. Specifically, they can be used to limit the mesh interval size on any edge or the mesh-element size on any face or volume.
An example of the effect of size functions on the current study is shown in the
Figure 3.1 (a) & (b) below,
(a) Fine cells surrounding the model
(b) Larger cell size away from the model
Figure 3.1
(a) & (b). Grid generation using size functions
In this example, a size function has been attached to the volume and defined with respect to the faces of the Davis model. When the volume is meshed using tetrahedral elements, the size function restricts the size of the element edges in proximity to the source faces. As a result, the tetrahedral elements in the region surrounding the source faces are small in comparison to those used to mesh the volume as a whole, and the mesh-element edge length increases with distance from the source face.

27
3.2.2.1 Size-Function Specifications
To create a size function, the following specifications must be defined:
1. Type
2. Entities
3. Parameter
The type specification determines the algorithm used by the size function to control the mesh-element edge size. The entities specification determines the geometric entities that are used as the source and attachment entities for the size function. The size function parameters define the exact characteristics of the size function.
3.2.3
Computational Domain
Domain size influence on the results is not desired in any CFD calculation.
Therefore, computational domain needs to be defined carefully. Domain size not only has an effect on numerical results, it also changes the mesh size. Size of the domain in current calculations is primarily base on Universiti Teknologi Malaysia
Low Speed Tunnel test section size 2 m X 1.5 m X 5.8 m as shown in Figure 3.2.
Dimension in mm
Figure 3.2
Computational domain size

28
3.2.4
Grid Generation Using GAMBIT
This section presents the use of mesh generator, GAMBIT, to develop 3D mesh for Davis car models. GAMBIT is a single, integrated pre-processor for
CFD analysis. It has ACIS solid modeling capabilities, which enable the user to import CAD solid model files directly. It has the capability of reading IGES CAD format, which has only the information of the vertices and surfaces. GAMBIT enables the user to cleanup and modifies the geometry for grid generation purposes. This software can generate mesh for FLUENT solvers. It enables the user to generate a grid in structured and unstructured hexahedral, tetrahedral, pyramid, and prisms and assign boundary zones to the grid.
Different CFD problems require different mesh types, and GAMBIT gives user all the options needed for these applications. Meshing toolkit in GAMBIT lets user decompose geometries for structured hex meshing or perform automated hex meshing with control over clustering. Triangular surface meshes and tetrahedral volume meshes can be created within a single environment, along with pyramids and prisms for hybrid meshing.
3.2.5
Three Dimensional (3D) Modeling Mesh
As an initial stage the computational results are required to be validated with the available experimental and literature data. In-order to accomplish this task, to study the effects of rear slant angle on vehicle aerodynamics, a systematic procedure for analyzing the aerodynamic behavior was planned. Davis models are validated initially before studying the effects of vehicle rear slant angle. Since, meshing plays a very important role in the final solution, a careful selection of meshing has to be made, before extending the study with the same type of meshing to all the cases (for different slant angle 0
0
, 10
0
, 20
0
, 30
0
and 40
0
) Hence, initially Davis models are validated, and once the validation is accomplished the same meshing technique is extended to all other cases.

29
To mesh a 3D model in gambit, the model can be either created in
GAMBIT or can be imported from other CAD packages. For the current study, solid models of Davis car model are created using the commercial CAD package,
Solid Works 2007. The model is saved as *.SAT files and imported to GAMBIT for meshing. A standard unstructured meshing technique using tetrahedral cells is followed owing to the complex geometry with fillet at the edge of the model and extended to the entire domain using size functions. The same technique is followed for all other cases that are discussed below.
The Davis car model is analyzed for various rear slant angle geometry of
10
0
, 20
0
, 30
0
and 40
0
. A three dimensional view of the Davis model with its variable rear slant angle configuration is shown in Figure 3.3 below.
10 o
slant
SL10
30 o
slant
SL30
40 o
slant
SL40
0 o
slant
SL00
All edge radii 10 mm
20 o
slant
SL20
Figure 3.3
Davis model configuration
Unstructured meshing technique is followed owing to the fillet geometry at the edge of the model. A four layer triangular boundary layer elements are created to capture the boundary layer resolution and more accurate predictions on the separation of flow at the rear slant angle.

30
Figure 3.4 Computational meshing model
The entire domain encloses approximately 4.2 million tetrahedral cells.
The domain is created in such a way that the inlet, out let, sides and ceiling are placed far away that it does not affect the flow predictions. Two sub domains are created surrounding the Davis car model, the smaller domain (Interior 1) just surrounding the model is created to have extremely fine meshes of four layers to record the boundary layer flow behavior, the separations from the rear slant and also to achieve respectable wall y+ range. The facet averaged y+ value was 70, which is within the limits for Standard k– turbulence model. Near around the model have finer tetrahedral elements in order to simulate and capture the strong vortices beginning to develop for 20
0
,30
0
and 40
0
rear slant angle and to predict the quasi-static two dimensional vortices formed at the base. The increase in mesh sizes from the model to the outermost domain is carried out by using the size function option available in the GAMBIT software [GAMBIT user manual].
3.2.6
Independent Meshing
Meshing optimization is a process to find the desire number of meshed element which it can come out with the most accurate results in Fluent software.
The meshing optimization process was successfully conducted with the simulation in Fluent software with several difference number of meshed elements by using

31 the model rear slant angle 20
0
at the zero degree of yaw with the inlet velocity is
40 m/s. The coefficient of drag is used for the comparisons for accuracy of the result. From Figure 3.5, Grid refinement tests indicate that a grid size of approximately 3 Million cells provide sufficient accuracy and resolution to be adopted as the standard for all future simulation case.
0.25
0.2
0.15
0.1
0.05
0
0 1 2 3 4
Number of Meshing Element (Million)
5
Figure 3.5 Drag coefficient versus nu ber of meshing element (Mesh independent study)
3 .3
Solver Setup for Simulation
3 .3.1
CFD Simulations Using FLUENT 6.3
This part of the chapter describes the general theory upon which the
FLUEN T algorithm is based for this particular numerical model. It includes a discussion about the governing partial differential equations, turbulence models, boundary conditions, and solution techniques.

32
3.3.1.1 Introduction
FLUENT is a computer software package developed to model fluid flow in a wide range of applications. Using this CFD package, the governing equations of fluid motion and the given boundary conditions can be discretized and solved for the velocity, temperature and pressure distributions throughout the domain.
FLUENT provides comprehensive modeling capabilities for a wide range of inco mpressible and compressible, laminar and turbulent fluid flow problems.
Steady state or transient analyses can be performed. In FLUENT, a broad range of mathematical models for transport phenomena (like heat transfer and chemical reactions) is combined with the ability to model complex geometries. Examples of
FLUENT applications include external aerodynamics study on ground vehicles; conjugate heat transfer in automotive engine components; laminar non-Newtonian flows in process equipment; pulverized coal combustion in utility boilers; flow through compressors, pumps, and fans; and multiphase flows in bubble columns and fluidized beds.
Robust and accurate turbulence models are a vital component of the
FLUEN T suite of models. The turbulence models provided have a broad range of applicability, and they include the effects of other physical phenomena, such as buoyancy and compressibility. Particular care has been devoted to addressing issues of near-wall accuracy via the use of extended wall functions and zonal models.
3 .3.1.2 Basic Governing Equations
For all flows, FLUENT solves conservation equations for mass and mom en tum. For flows involving heat transfer or compressibility, an additional equation for energy conservation is solved. Additional transport equations are also solved when the flow is turbulent.

33
The equation for conservation of mass, or continuity equation, can be written as follows:
߲ߩ
߲ݐ
൅ ׏ ȉ ሺߩݑሬԦሻ ൌ ܵ
௠
Equation above is the g eneral form of the ma ss conservation equation and is valid for incompressible as w ell as compressible f lows. The , t, and u represent the flow density, time, and velocity, respectively. The source S m
is the mass added to the continuous phase from the dispersed second phase (e.g., due to vaporization of liquid droplets) and any user-defined sources. In our application, S m
is zero.
3 .3.1.3 Turbulence Models
There are two method s being employed to transform the Navier-Stokes e quations in such a way that the small-scale turbulent fluctuations do not have to be dire ctly simulated: "Reynolds averaging" and "filtering". Both methods introduce additional terms in the governing equations that need to be modeled in order to achieve "closure".
The Reynolds-aver aged Navier-Stokes (RANS) equations represent transpo rt eq uations for the mean flow quantities only, with all the scales of the turbule nce being modeled. The approach of permitting a solution for the mean flow variables greatly reduces the computational effort. If the mean flow is steady, the governing equations will not contain time derivatives and a steady-state solution can be obtained economically. A computational advantage is seen even in transient situations, since the time step will be determined by the global unsteadiness in the mean flow rather than by the turbulence. The Reynoldsaveraged approach is generally adopted for practical engineering calculations, and it uses turbulence models such as Spalart-Allmaras, k- and its variants, k- and its variant and the RSM (Reynolds Stress Model).

34
Large eddy simulation (LES) provides an alternative approach in which the larg e eddies are computed in a time-dependent simulation that uses a set of
"filtered" equations. Filtering is essentially a manipulation of the exact Navier-
Stokes equations to remove only the eddies that are smaller than the size of the filter, which is usually taken as the mesh size. Like Reynolds averaging, the filtering process creates additional unknown terms that must be modeled in order to achieve closure. Statistics of the mean flow quantities, which are generally of most engineering interest are gathered during the time-dependent simulation. The attraction of LES is that by modeling less of the turbulence (and solving more), the error induced by the turbulence model will be reduced. However, this turbulence model required high performance computer.
Therefore, Reynolds-averaged approach is employed in this dissertation.
The LE S approach, briefly described in here, should become more feasible for industrial problems when the computational resources become significantly more powerful than what is available here today.
F or most engineering applications, the time-averaged or spatial filtered propert ies of the flow are of interest, thus the time-averaged transport equations, such as the Reynolds-averaged Navier-Stokes (RANS) equations, are established.
3.3.1.3.1 Turbulence Model Validation
Although FLUENT provides reasonable accuracy of the physical flow behav ior, it still needs experimental results for proper validation. Hence the computational results are initially compared with the published experimental data before any further extensions to study the effects of rear slant angle is made. For

35 the current research, the base rear slant angle of 20
0
was used to compare with experimental data published by Mansor (2006).
0.30
Experimental
KeStandard
(Mansor2006)
KeRNG
KeRealizable
0.25
0.20
0 2 4 6 8 1 0
YawAngle(deg)
Figure 3.6
Graph drag coefficient versus yaw angle for different turbulence model for 20
0
rear slant angle
The results for the Davis model and the effects of different turbulence model on drag coefficient using base rear slant angle 20
0
models are shown in
Figure 3.6. Figure shows the prediction of drag coefficient by CFD simulation for
Davis model geometry have good agreement with the experiments conducted in low speed tunnel at Loughborough University up to yaw angle of 8
0
. At yaw angle before 2
0
, simulation results were close to experimental results and the difference increases as yaw angle increases. Simulation and experimental lines intercept at 8
0 yaw angle. After this angle, simulation seems to over predict the coefficient, this is due to unsteady flow structure around the model has become more complex and thus required high number of meshing element. The maximum error percentage for the Davis model case is less than 16%. The predictions of coefficient of drag shows some discrepancies, but have the same trends as been observed in the experiments conducted by Mansor (2006). This study clearly demonstrates that

36
CFD is capable to deliver useful predictions on vehicle’s aerodynamics behavior at different rear slant angle.
The results show that k- Standard has a good agreement with the experimental result. For this reason, this turbulence model approach is employed in this dissertation. The simplest “complete models” of turbulence are twoequation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined. The standard k- model in FLUENT falls within this class of turbulence model and has become the workhorse of practical engineering flow calculations. Robustness, economy, and reasonable accuracy for a wide range of turbulent flows explain its popularity in industrial flow and heat transfer simulations.
The standard k- model is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate
(). The model transport equation for k is derived from the exact equation, while the model transport equation for was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart. In the derivation of the k- model, it was assumed that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard k- model is therefore valid only for fully turbulent flows (Fluent Inc. Manual,2009).
3.3.2
Solver Setup
FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the governing equations about each control volume, yielding discrete equations that conserve each quantity on a control-volume basis.

37
The finite volume discretisation of the governing equations in time and space is described here. The numerical scheme is fully implicit and can accommodate both structured and unstructured grids with cells of arbitrary topology. The numerical implementation of the initial and the wall boundary conditions is also explained.
The segregated approach is used to solve the resulting set of coupled non- linear algebraic equation systems. This leads to a decoupled set of linear algebraic equations for each dependent variable. These equations are solved by an iterative conjugate gradient solver, which retains the scarcity of the coefficient matrix, thus achieving the efficient use of computer resources.
3.3.3
Boundary Conditions
3.3.3.1 Velocity Inlet Boundary Condition
Velocity inlet boundary conditions are used to define the flow velocity, along with all relevant scalar properties of the flow, at flow inlets. The total (or stagnation) properties of the flow are not fixed, so they will rise to whatever value is necessary to provide the prescribed velocity distribution.
The values of velocity inlet boundary conditions in FLUENT are given in the Figure 3.7 below.

38
Figure 3.7
Velocity inlet boundary condition
This boundary condition is intended for incompressible flows, and its use in compressible flows will lead to a nonphysical result because it allows stagnation conditions to float to any level. While assigning the boundary condition for velocity inlet, it should be noted that it is not positioned too close to the model, since this could cause the inflow stagnation properties to become highly nonuniform. Hence for the current case the inlet is positioned well ahead of the model so that the flow is fully developed before it reaches the model and the stagnation properties are not affected.
3.3.3.2 Pressure Outlet Boundary Condition
Pressure outlet boundary conditions require the specification of a static
(gauge) pressure at the outlet boundary. The value of static pressure specified is used only in subsonic flow. Should the flow become locally supersonic, the specified pressure is no longer used; pressure will be extrapolated from the flow in the interior. All other flow quantities are extrapolated from the interior.

39
A set of “backflow” conditions is also specified to be used if the flow reverses direction at the pressure outlet boundary during the solution process.
Convergence difficulties will be minimized if you specify realistic values for the backflow quantities. The default values of pressure outlet boundary conditions in
FLUENT are shown in the Figure 3.8 below,
Figure 3.8
Pressure outlet boundary conditions
The above default values shown are used for the current study. The outlet is positioned sufficiently at a far distance from the model so that the rear wake region information is recorded and moreover the back flow is avoided.
3.3.3.3 Wall Boundary Condition
The Davis models and ground plane are assigned the no-slip wall boundary conditions. These conditions are used to bound fluid and solid regions.
In viscous flows, the no-slip boundary condition is enforced at walls by default.
The same is used for the current study on external aerodynamics. No modified

40 effects are used i.e. default values are used and very fine meshes around the model are used to record the viscous effects.
3.3.4
Fluid Properties
The medium flowing through the system is air. The properties of air for this analysis are taken at an ambient temperature. Having a viscosity of 1.7894 X
10
-5 kg/m.s and Standard Sea level density of 1.225 kg/m
3
, for all the models involving energy calculations, they are assumed to be constant. Due to the high flow rates through the system and limited range in temperature, buoyancy driven flows due to density differences in the air are not significant. Hence, this assumption will have a minimal effect.
3.3.5
Solution Control
3.3.5.1 Under-Relaxation Factors
Because of the nonlinearity of the equation set being solved by FLUENT, it is necessary to control the change of primary variable (ø). This is typically achieved by under-relaxation, which reduces the change of ø produced during iteration. In a simple form, the new value of the variable ø within a cell depends upon the old value, ø old
, the computed change in ø, ø, and the under-relaxation factor, , as follows:

41
Table 3.1: Default values of in FLUENT
Properties Default values
Pressure 0.3 momentum 0.7
Turbulence Kinetic Energy 0.8
Turbulence Dissipation Rate 0.8
Turbulent Viscosity 1
Because the computational domain comprises very small gap between the model and the ground, a high velocity gradient persists at separation regions, it is important to reduce the values of in order to get the result converged. However, it was found that the change did not affect the final result on drag coefficient.
Hence, the default values were used for the entire study.
3.3.5.2 Pressure Solution
The pressure interpolation schemes available in the FLUENT are listed:
1. Standard
2. Presto
3. Linear
4. Second order
5. Body-force-weighted
The linear scheme uses an averaged pressure for the face value of the two adjacent cells. This is the most robust scheme; however, the performance of this scheme drops off when there are large local gradients in pressure. But, for this investigation the default scheme is used as no large pressure gradients are involved, hence the current model is good enough to predict the pressure drop at

42 the base of the Ahmed car model (Ahmed et al., 1984), which in turn in proportional to the drag coefficient of the model.
3.3.5.3 First Order and Second Order Upwind Schemes
For the interpolation for all scalar variables except pressure in the governing equations, FLUENT provides a number of different schemes. The two options relevant to this work are first-order upwind and second-order upwind schemes.
In using these schemes, when the flow regimes are aligned to the grid, the first-order upwind scheme gives comparable results to that of the higher order.
However, when the flow is not aligned with the grid, thus increasing numerical discretization errors, the second-order upwind schemes give superior results.
Hence, for the current study we used second order upwind scheme.
3.4
Post-Processing
In this stage, the desire outcome was the converged solution for the simulation model and it was examined by graphical contour and graph plotting which the Fluent software could give the air flow pattern, the static pressure contour. Besides, it could also give the numerical results such as drag force, side force, and lift force, coefficient of drag, coefficient of lift and coefficient of side force. In this study, the effect of drag force, side force and the effect of the position of center of pressure which it produced the yaw moment was emphasized and it was interpreted in the following chapter.

43
3.5
Assumption of The Simulation
There were some assumptions had to be made due to the simulation model simplification. These simplifications were important when the simulation model had computerized analysis and it also needed for the calculation process. The assumptions were stated as followed:
1. The simulation condition was in the steady state condition
2. The material was a ideal gas which was the air
3. The air flow was in a uncompressed condition
4. The model was studies in 3D view
5. The vehicle model had no ventilation system
6. The vehicle model did not have the side mirror and spoiler
7. The under part of the vehicle model was flat
8. The radius of the curvature for the edges of vehicle model was 10mm which obtained from the experimental testing
9. The center of the moment for the vehicle model was at the center of the vehicle model

44
CHAPTER 4
4.
WIND TUNNEL TEST
4.1
Introduction
Davis Body is one of bluff body model in ground vehicle aerodynamics.
Detailed geometry definition and easy manufacturability made it the final choice for the benchmark study in this dissertation. In this chapter, we describe the experimental measurements and demonstrate the results from Davis model experiments.
4.2
Wind Tunnel Specification
Measurements for Davis model were performed at Universiti Teknologi
Malaysia Low Speed Tunnel (UTM-LST). This facility is currently the largest
Wind Tunnel Facility in the Malaysia in terms of test section size (2 m X 1.5 m X
5.8 m) and maximum wind speed 80 m/s. The wind tunnel is shown in Figure 4.1.
In the empty working test section, the average turbulence intensity at the centre of the working test section is 0.06% measured at 40 m/s. The boundary layer thickness at the centre of the working test section of the floor is 40 mm at 40 m/s. The wind tunnel has a working range of speeds 0 m/s to 80 m/s.

45
Figure 4.1
Universiti Teknologi Malaysia Low Speed Tunnel (UTM-LST)
4.3
Model specification
The model employed in the study is a simplified bluff body that represents a road vehicle shape, called the Davis model. This model was constructed from fiberglass material with a scale of approximately 1:6 scale when compared with an average road car. The model dimensions are as shown in Figure 4.2. Davis model is able to produce the same main flow characteristics as a real car. The flow remains largely attached over the fore body. The rear section has a variable geometry that, when altered, is capable of generating all the primary rear end flow fields seen on road vehicles.

46
Figure 4.2
General dimensions of baseline shape (rear slant angle 20
0
) of
Davis model. All edge radii 10 mm.
In order to investigate different rear slant angle effects on the aerodynamic behavior of the model, there were four different models (0
0
, 10
0
, 30
0
, and 40
0
) was constructed as shown figure below.
Figure 4.3 Model with different rear slant angles. All edge radii 10 mm.
4.4
Measurement Method
Force and moment coefficients at various wind speeds from 30 m/s to 50 m/s were measured for all different rear slant angle angles: 0
0
, 10
0
, 20
0
, 30
0
, and

47
40
0
. The tunnel is equipped with a precision six-component external balance located under the working section. A turntable attached to the balance is fitted flush to the floor and rotates together with the model. All forces and moments are measured in the body axis.
The loads are measured by load cells and the calibration matrix converts them into three forces (lift, drag and side force) and three moments (pitch, yaw and roll). The software saves the data as force and moments. The balance is operated using a dedicated program that also allows the user to choose a suitable sampling rate and data averaging time. The accuracy of the six-component balance as specified by the manufacturer is summarized in the Table 4.1.
Table 4.1 Balance load range and accuracy.
Component
Drag
Side Force
Lift
Roll Moment
Balance Load Ranges
± 1200 N
± 1200 N
± 4500 N
± 450 Nm
Accuracy (% Full Scale)
0.04
0.04
0.04
0.04
Pitch Moment ± 450 Nm 0.04
Yaw Moment ± 450 Nm 0.04
4.5
Solid Blockage
A 2 m x 1.5 m wind tunnel test section results in a solid model blockage ratio of 1.2%, based on maximum projected frontal area of the Davis model. This value was deemed insignificant in that relevant flow structures would not be notably affected by the presence of the wind tunnel walls. Hence blockage corrections were not applied for the current experimental analysis (Barlow,1999).

48
4.6
Experiment Setup
The static yaw aerodynamic derivatives were obtained from a conventional yaw test with the model mounted on the six-component balance. The model was mounted using a single circular rod at the mid-wheel-base, mid-track that passed through a hole on the floor of the test section to a plate attached to the external balance
Tests were conducted between 30 to 50 m/s which corresponds to a range of
Reynolds numbers based on model length between 1.29x10
6
and 2.14x10
6
. The yaw range was between -16
0
and 16
0
with an increment of 2
0
.
The aerodynamic derivatives of side force and yaw moment was determined from the gradient of the coefficient versus yaw angle calculated over a yaw angle range.
4.6.1
Comparison with Loughborough Wind Tunnel Test Results
To verify that the experimental setup is correct, comparison was done with a similar test carried out by Mansor(2006) at Department of Aeronautic and
Automotive Engineering, Loughborough University ( test wind speed 40 m/s,
Reynolds number of 1.71 x 10
6
and the yaw angle range (-16
0
to 16
0
).
16 12 8
C
D
0.5
0.4
0.3
4
0.2
0.1
0
0 4 8 12
YawAngle(deg)
16
(a)

49
16 12 8
Cy 1
0.8
0.6
0.4
0.2
0
4
0.2
0.4
0.6
0.8
1
0 4 8 12 16
YawAngle(deg)
Cn 0.3
(b)
0.2
0.1
16 12 8
0
4
0.1
0
0.2
4 8 12 16
YawAngle(deg)
Loughborough
Experimental
0.3
(c)
Figure 4.4 Aerodynamic coefficient against yaw angle at wind speeds 40 m/s of 20
0
slant. (a) drag force, (b) side force ,(c) yaw moment
Figure 4.4 shows that both tunnel results are in a good trend and agreeable with each other. Nevertheless, it is noticed that the graphs are not really coincide as one line. The aerodynamics derivative comparison is shown in Table 4.2. From the table indicate that the error between experimental and Loughborough wind tunnel test results 7.3% for side force derivative and 6.4% for yaw moment derivative. This discrepancy is due to the two tunnels are in different types, hence the parameter such as turbulence intensity and boundary layer for each tunnel is going to be different. Furthermore, although the model dimensions are same but the surface roughness due finishing may also have some influence.

50
Table 4.2
Comparison aerodynamic derivative UTM-LST and Loughborough
University wind tunnel test
Aerodynamic
Derivative
UTM Wind
Tunnel
Cy (rad
-1
) 1.6041
Loughborough
Univesity Wind Tunnel
1.4954
Cn (rad
-1
) 0.3380 0.3610
Error
(%)
7.3
6.4
4.7
Results from 20
0
Rear Slant Angle
Figure 4.5 shows the 20
0
slant model mounted on the floor turntable for static tests.
Front view Side view
Figure 4.5
Model slant angle 20
0
setup for static test
As the 20
0
slant was the baseline model, extensive tests and more results were produced from the model such as the effect of ground clearance and measurement of all three forces (lift, drag and side force) and three moments
(pitch, yaw and roll). However in this work only the drag, side force and yaw moment are presented.

51
4.7.1
Side Force and Yaw Moment Derivatives of 20
0
Slant
Figure 4.6 shows the side force and yaw moment coefficients versus yaw angle for 20
0
slant model at four different wind speeds of 30, 35, 40, 45 and 50 m/s.
Cy
0.6
30m/s
35m/s
40m/s
45m/s
50m/s
0.4
0.2
16 12 8 4
1E15
0
0.2
4 8 12 16
YawAngle(deg)
0.4
0.6
(a)
Cn
0.1
16
30m/s
35m/s
40m/s
45m/s
50m/s
12 8
0.05
4
0
0
0.05
4 8 12 16
YawAngle(deg)
0.1
(b)
Figure 4.6
Aerodynamic coefficients against yaw angle at different wind speeds of rear slant angle 20
0
. (a) side force, (b) yaw moment

52
The side force and yaw moment derivatives were determined from the gradient of side force and yaw moment coefficient in the yaw angle range ±10
0
.
The results are shown in Table 4.3. The side force derivative Cy slightly reduces as the Reynolds number increases. The side force derivative at the highest
Reynolds number is 3.89% less than the one at low Reynolds number. The yaw moment derivative Cn seems to have less effect with Reynolds number when compared to side force. The yaw moment derivative at highest Reynolds number is 2.8% less from the maximum yaw moment derivatives.
Table 4.3: Static measured derivatives of Cy and Cn for 20
0
slant.
Wind Speed
(m/s)
Cy E
(rad
-1
)
Cn E
(rad
-1
)
4.8
The Effect Rear Slant Angle
Tests were conducted to measure the static coefficient of side force, yaw moment and drag for various rear slant angles at 40 m/s (Re=1.71x10
6
). The results are shown in Figure 4.7.

16
16
12
12
8
8
C
D
0.6
0.5
0.4
0.3
0.2
0.1
0
4 0 4
YawAngle(deg)
(a)
Cy
1
0.8
0.6
0.4
0.2
0
4 0.2
0
0.4
0.6
0.8
1
4
8 12 16
8 12 16
YawAngle(deg)
Cn
0.15
(b)
0.1
0.05
0
16 12 8 4
0.05
0 4 8 12 16
YawAngle(deg)
0.1
0.15
Slant0
Slant10
Slant20
Slant30
Slant40
(c)
Figure 4.7 Aerodynamic coefficient versus yaw angle for different rear slant angles at 40 m/s. (a) drag, (b) side force, (c) yaw moment
53

54
Figure 4.8 shows the summary of static measured coefficients of drag, yaw moment, side force, and center of pressure coefficient for various rear slant angles at 10
0
yaw and 40 m/s (Reynolds number of 1.71x10
6
). The figure shows all the coefficients for different rear slant angle presented at 10
0
yaw except for drag coefficient where zero degrees is also added to the plot. A 10
0
slant has the lowest drag coefficient compared to other models at both zero and 10
0
yaw. While a 30
0 slant has the greatest drag at both zero and 10
0
yaw. From zero to 10
0
yaw, the drag coefficient of 30
0
slant decrease by 1.7%, compared to others slant have increment.
0.5
0.4
0.3
0.2
0.1
0
0
Yaw0 Yaw10
0.1
0.08
0.06
0.04
0.02
0
0 10 20 30
RearSlantAngle(deg)
40 10 20 30
RearSlantAngle(deg)
4 0
20
0.6
0.5
0.4
0.3
0.2
0.1
0
15
10
5
0
0 10 20 30
RearSlantAngle(deg)
40 0 10 20 30
RearSlantAngle(deg)
Figure 4.8 Side force, yaw moment coefficient and centre of pressure for various rear slant angles for 10
0
yaw and drag (zero and 10
0
yaw) at 40 m/s
(Re=1.71x10
6
).
4 0
From the Figure 4.8 shows that, zero and 40
0
slant angle exhibit very small yaw moment but high side force and the 30
0
shows a large yaw moment.
Furthermore, at 10
0
yaw, the 20
0
and 30
0
slant have a yaw moment five times higher than the 40
0
slant indicating that the 20
0
and 30
0
slant have the greatest susceptibility to crosswind. However, the location of the centre of pressure from

55 the centre of the model of the 20
0
slant which is much further forward than the other models could be the main cause of why the 20
0
slant is more susceptible to crosswind.
4.9
Side Force and Yaw Moment Derivatives of Various Slant
Figure 4.9 shows the side force and yaw moment derivatives for different rear slant angles. The results are presented in the form of side force and yaw moment derivatives for wind speeds between 30 to 50 m/s, representing a
Reynolds number in range of 1.29x10
6
to 2.14x10
6
. Data for this figure are tabulated in Table 4.4. This figure indicates that variation of wind speeds has no effect to side force derivative. However, yaw moment derivative is influenced by wind speeds especially at 10
0
rear slant angle. This finding shows contradiction with previous work by Mansor (2006) that 30
0
yaw moment derivative is most affected by wind speeds. Therefore, further research need to be conducted to investigate this behavior.
4
Cy
(rad -1 )
3
2
1
30m/s
35m/s
40m/s
45m/s
50m/s
0
0 4 0 10 20
RearSlantAngle(deg)
30
(a)

56
0.4
Cn
(rad -1 ) 0.3
0.2
0.1
30m/s
40m/s
50m/s
35m/s
45m/s
0
0 10 20 30 4 0
RearSlantAngle(deg)
(b)
Figure 4.9
Static aerodynamic derivatives of different slant angles at 30 to 50 m/s. (a) side force, (b) yaw moment
Table 4.4
Side force and moment derivative at different rear slant angle
Rear Slant
Angle
Side force derivative,
Cy
(rad
-1
)
Yaw Moment Derivative,
Cn
(rad
-1
)
0 3.1583 0.0911
10 2.5539 0.2332
20 1.9949
30 2.1919
40 3.0500
0.3351
0.3134
0.1278
To have a clear trend on how these derivatives vary with Reynolds number, the side force and yaw moment derivatives can be plotted against
Reynolds number as shown in Figure 4.10 and Figure 4.11. The results show, all model are not function of Reynolds number except for rear slant angle 10
0
model where yaw moment derivative is slightly increase with Reynolds number.

57
Cy
( rad 1 )
4
3
2
1
Slant0
Slant10
Slant20
Slant30
0
1.07E+06 1.29E+06 1.50E+06 1.72E+06 1.93E+06 2.14E+06
ReynoldsNumber
Figure 4.10
Static side force derivatives versus Reynolds number for different rear slant angles.
Cn
(rad -1 )
0.4
0.3
0.2
0.1
Slant0 Slant10 Slant20 Slant30 Slant40
0
1.07E+06 1.29E+06 1.50E+06 1.72E+06 1.93E+06 2.14E+06
ReynoldsNumber
Figure 4.11 Static yaw moment derivatives versus Reynolds number for different rear slant angles.

58
CHAPTER 5
5.
RESULTS AND DISCUSSION
5.1
Introduction
In this chapter, the vehicle aerodynamics characteristics under the crosswind disturbances are discussed in-term of the effect of the coefficient of drag, the effect of the side force coefficient, the yaw moment and the lateral derivative effect. Besides that, the flow characteristics around the model from the simulation would also be discussed in this section. Simulated and measured results are compared to examine the compatibility of CFD in lateral aerodynamic characteristics determination.
.
5.2
Detailed Simulation Results
The accuracy of CFD analysis is driven largely by the quality of the physical models in the software and the ability of the software to closely match the true geometry of the physical item that we wish to model. FLUENT features unstructured modeling technique which enables one to build mesh which wraps around curves, inclined planes, and other complex surfaces. It also offers the ability to fine-tune the computational mesh in areas of importance.
As mentioned in Chapter 3, the Standard k- model was selected in this investigation to be the turbulence model. The boundary conditions at inlet and outlet are velocity inlet and pressure outlet conditions, Davis car models, floor,

59 sides and ceiling are considered wall conditions, the flow behaviors, obtained from numerical simulation from three-dimensional models, are presented in the sections below.
5.3
Drag Force
Table 5.1
The drag force and the coefficient of drag for the Fluent and wind tunnel test result.
Rear Slant Angle
(deg)
Coefficient of drag, C
D
CFD Wind tunnel testing
The drag coefficient was found to be the maximum for the 0° rear slant configuration and then it gradually decreased to 0.221 for the 20° rear slant configuration. The drag coefficient started to increase after 20° rear slant angle to
0.2656 at 40° rear slant angle.
Figure 5.1 to Figure 5.5 show velocity vector and contour on the model symmetrical plane. Based on Bernoulli principle, the pressure and velocity are inversely related. Throughout this section, the discussion will also include pressure based observation using velocity contour; this principle will be used to relate these parameter. The 0° degree configuration of Davis model is shown in
Figure 5.1 (a) & (b). It can be seen that flow after reaching the front part stays attached on the body and separates at the sharp rear end leaving a large recirculation region behind the base, refer to Figure 5.1 (a). This resulted in the increase of base pressure drop as shown in Figure 5.1 (b), which constitutes the

60 main reason for its highest drag coefficient among various rear slant configurations.
(a)
(b)
Figure 5.1
(a) and (b): Velocity vector and contours in the wake of 0
0
rear slant angle
Figure 5.2 (a) and (b), shows the 10° rear slant configurations exhibited more similar flow characteristics to that of the 0° rear slant configuration, except for the reduction of drag coefficient. This reduction in drag coefficients was mainly due to the reduced recirculation region, caused by the down wash created by the rear slant region of the Davis model.

(a)
(b)
Figure 5.2
(a) and (b): Velocity vector and contours in the wake of 10
0
rear slant angle
Figure 5.3 (a) and (b) shows velocity flow lines and pressure contours in the wake of 20
0
rear slant angle. The 20
0
rear slant configuration, showed a considerable reduction in the size of the recirculation region. Hence the pressure recovery at the base was expected to be improved, thus ended in the reduction of drag coefficient.
61

(a)
62
(b)
Figure 5.3
(a) and (b): Velocity vector and contours in the wake of 20
0
rear slant angle
The drag coefficient immediately started to increase with an increment or decrement of 10
0
from this base 20
0
rear slant angle. An increase of angle contributed to the increase of drag coefficient which was observed for the 30
0
, and
40
0
rear slant configurations. At 30
0
rear slant angle, the drag coefficient increased, by the direct flow separation on the edge of the rear slant as shown in
Figure 5.4 (a). Thus the recirculation region appears to have increased in size which would be expected to result in a pressure loss as shown in Figure 5.4 (b).

63
(a)
(b)
Figure 5.4
(a) and (b): Velocity vector and contours in the wake of 30
0
rear slant angle
The effects observed on a 40
0
rear slant configuration are shown in Figures 5.5 (a) and (b). The flow structures started to behave like those observed in models with rear slant angles 0
0
.
The flow that was attached before for the 20
0
rear slant configuration was not attached anymore and the flow separated directly from the leading edge of the rear slant. As a result, the recirculation region was increased since the rear slant did not support to have the flow attached to it. Also, this effect resulted in the increase of

64 pressure drop and high drag coefficients as shown in Figure 5.5 (b) for the 40
0
rear slant configuration.
(a)
(b)
Figure 5.5 (a) and (b): Velocity vector and contours in the wake of 40
0
rear slant angle
Although the drag predictions of the current CFD simulations are higher than the experiments, a similar trend is observed when compared to the previous studies as discuss in chapter 2. At the rear slant angle of 20
0
, the prediction of drag coefficient is more accurate, than for other rear slant angles. The CFD predicted a drag coefficient of 0.2210 when compared to experimental value of 0.2300 with an error percentage of approximately 4%. This could be due to the two dimensionality of the k- turbulence model.

65
5.4
Side Force Coefficient and Derivative
Figure 5.6 to Figure 5.10, each curve represents the comparison results of the Fluent software and experimental for side force coefficient for all rear slant angle (0
0
, 10
0
, 20
0
, 30
0
, and 40
0
) model. The rear slant 0
0
and 20
0
for the simulation have good agreement with experimental results. Besides that, rear
Slant 10
0
, 30
0
, and 40
0
shows poor agreement with experimental results. But, the gradient of the curve for all simulation results show same trend with the experimental results.
0.90
0.70
0.50
0.30
experimental cfd
0.10
0.10
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.6 Graph side force coefficients versus yaw angle for slant 0
0
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
experimental cfd
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.7 Graph side force coefficients versus yaw angle for slant 10
0

1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
experimental cfd
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.8
Graph side force coefficients versus yaw angle for slant 20
0
1.00
0.80
experimental cfd
0.60
0.40
0.20
0.00
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.9 Graph side force coefficients versus yaw angle for slant 30
0
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
experimental cfd
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.10
Graph side force coefficients versus yaw angle for slant 40
0
66

67
Figure 5.11 and Figure 5.12 show side force coefficient at different yaw angle and rear slant angle. From the plot, the rear slant 0
0
has the greater value of the coefficient of side force compare with other model and it follow by the rear slant 10
0
. The smallest value of the coefficient of side force is the rear slant angle
20
0
. At rear slant angle of 20
0
, the prediction of drag coefficient is more accurate compare to other rear slant angles. This error could be due to the two dimensionality of the k- turbulence model and the number and distribution density of meshing element. However, simulation results show good agreement in trend compared to experimental results.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0 2
Slant0
Slant10
Slant20
Slant30
Slant40
4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.11 Graph side force coefficients versus yaw angle at different slant angle

68
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Experimental CFD
0 10 20 30 4 0
RearSlantAngle(deg)
Figure 5.12
Graph side force coefficients versus rear slant angle at yaw angle
10
0
The results are presented in the form of side force derivatives for five wind speeds between 30 to 50 m/s, representing a Reynolds number range of 1.29x10
6 to 2.14x10
6
. The aerodynamic derivative was determined from the gradient of the coefficient versus yaw angle within ±10
0
. To have a clear trend on how these derivatives vary with wind speeds, the side force derivatives was plotted versus wind speeds as shown in Figure 5.13.
Cy
(rad -1 )
4
3
2
1
0
1.07E+06
Slant0
1.29E+06
Slant10
1.50E+06
Slant20
1.72E+06
Slant30
1.93E+06
Slant40
2.14E+06
ReynoldsNumber
Figure 5.13
Static side force derivatives versus Reynolds number for different rear slant angles.

69
Cy
( rad 1 )
4
3
2
1
Experimental CFD
0
0 10 20 30 4 0
RearSlantAngle(deg)
Figure 5.14 Comparison experimental and CFD static side force derivatives versus rear slant angles for 40 m/s.
Figure 5.14 shows the comparison of CFD and experimental result for static side force derivative versus rear slant angle. CFD results can predict the same trend with experimental results except for rear slant angle 40
0
. The differences of the vehicle shape for each type of vehicle model have given different flow separation at different yaw angle. For the rear slant angle 40
0
, the
CFD simulation cannot capture the flow behavior around the model. This occurs due to slant angle 40
0
have more complex unsteady flow and vortex behavior compare to other models. Data for Figure 5.14 are shown in Table 5.2.
Table 5.2
Measured and simulated static side force derivatives versus rear slant angles for 40 m/s.
Rear Slant
Angle
(deg) CFD
Side Force Derivative
Cy
(rad
-1
)
Experimental
0 2.6467 3.1583
10 1.5926 2.5539
20 1.2718
30 1.3748
40 1.5181
1.9449
2.1919
3.0500

70
5.5
Yawing Moment Coefficient and Derivative
Figure 5.15 to Figure 5.19, each curve represents the comparison results of the Fluent software and experimental for yawing moment coefficient for the all rear slant angle (0
0
, 10
0
, 20
0
, 30
0
, and 40
0
) model. The rear slant 0
0
and 20
0
for the simulation have good agreement with experimental results. Besides that, rear Slant
10
0
, 30
0
, and 40
0
shows poor agreement with experimental results. But, the gradient of the curve for all simulation results show same trend with the experimental results.
0.15
0.10
Experimental cfd
0.05
0.00
0.05
0 2 4 6 8 10 12 14 16
0.10
YawAngle(deg)
Figure 5.15 Graph yawing moment coefficients versus yaw angle for rear slant
0
0
0.15
Experimental
0.10
cfd
0.05
0.00
0.05
0 2 4 6 8 10 12 14 16
0.10
YawAngle(deg)
Figure 5.16
Graph yawing moment coefficients versus yaw angle for rear slant
10
0

71
0.15
0.10
0.05
0.00
0.05
0 2
Experimental cfd
4 6 8 10 12 14 16
0.10
YawAngle(deg)
Figure 5.17
Graph yawing moment coefficients versus yaw angle for rear slant
20
0
0.15
0.10
Experimental cfd
0.05
0.00
0.05
0 2 4 6 8 10 12 14 16
0.10
YawAngle(deg)
Figure 5.18
Graph yawing moment coefficients versus yaw angle for rear slant
30
0
0.15
Experimental
0.10
cfd
0.05
0.00
0.05
0 2 4 6 8 10 12 14 16
0.10
YawAngle(deg)
Figure 5.19 Graph yawing moment coefficients versus yaw angle for rear slant
40
0

72
0.12
0.1
0.08
0.06
0.04
0.02
Slant0
Slant10
Slant20
Slant30
Slant40
0
0 2 4 6 8 10 12 14 16
YawAngle(deg)
Figure 5.20
Graph yaw moment coefficients versus yaw angle at different rear slant angle
From Figure 5.20 it shows that rear slant angle 0
0
has different trend compared to other rear slant angles. This indicates that CFD has limited capabilities to captured highly unsteady wake vortices behind the model. Due to that, the yaw moment coefficient seems to deviate from actual trend. This occurs due to the complexity of the wake vortices flow structure on rear slant angle 0
0
is much more unsteady compare to other rear slant angle. It is clearly shown in
Figure 5.24 where there is no absolute pattern of wake vortices structure forming behind the model. This explained why RANS gives different yaw moment coefficient trend for rear slant angle 0
0
.
Figure 5.21 shows yawing moment coefficient at different yaw angle and rear slant angles. From the figure, the rear slant 0
0
has the greater value of the coefficient of side force compare to other model and it follow by the rear slant
10
0
. The smallest value of the coefficient of side force is at the rear slant angle
20
0
. At the rear slant angle of 20
0
, the prediction of drag coefficient is more accurate, than for other rear slant angles. This error could be due to the two dimensionality of the k- turbulence model and the number and distribution density of meshing element. However, simulation results show good agreement in trend compared to experimental results.

0.1
0.08
0.06
0.04
0.02
0
Experimental CFD
0 10 20 30 4 0
RearSlantAngle(deg)
Figure 5.21
Graph yawing moment coefficients versus rear slant angle at yaw angle 10
0
Cn
(rad -1 )
0.5
0.4
73
0.3
0.2
0.1
Slant0 Slant10 Slant20 Slant30 Slant40
0
1.07E+06 1.29E+06 1.50E+06 1.72E+06 1.93E+06 2.14E+06
ReynoldsNumber
Figure 5.22
Static yawing moment derivatives versus Reynolds number for different rear slant angles.
Cn
(rad -1 )
0.4
0.3
0.2
0.1
CFD Experimental
0
0 10 20 30 4 0
RearSlantAngle(deg)
Figure 5.23
Comparison experimental and CFD static yaw moment force derivatives versus rear slant angles for 40 m/s.

74
Figure 5.22 and Figure 5.23 show the comparison CFD and experimental static yawing moment derivative rear slant angles at 40 m/s. CFD results can predict the same trend with experimental results. However, CFD results cannot predict close to experimental especially at rear slant angle 40
0
. The differences of the vehicle shape for each type of vehicle model have given difference flow separation at different yaw angle. For the rear slant angle 40
0
, the CFD simulation cannot capture the flow behavior around the model. This due to slant angle 40
0 have more complex unsteady flow and vortex behavior compare to others model.
Data for Figure 5.23 are shown in Table 5.3.
Table 5.3
Measured and simulated static yaw moment derivatives versus rear slant angles for 40 m/s.
Rear Slant
Angle
Yaw Moment Derivative
Cn
(rad
-1
)
(deg) CFD Experimental
0 0.1480 0.0911
10 0.3667 0.2332
20 0.3351
30 0.3437
0.3351
0.3134
40 0.3723 0.1278
Basically the coefficient of yaw moment is a function of the longitudinal distribution of side force on a vehicle, those factors determining the coefficient of side force will also influence coefficient of yaw moment to a greater or lesser degree according to the distance from the moment axis at which their effects are applied. The incremental side force acting upstream of the moment center (center of gravity) will cause increase in coefficient of yaw moment and those acting downstream will cause decrease in coefficient of yaw moment which it is actually the effect of the position of the center of pressure. Hence, for this problem the incremental side forces for the rear slant angle 0
0
are acting downstream on the moment center which the highest value of the coefficient of side forces will give lowest value of the yaw moments and the hatch back model is acting upstream on the moment center. So, it is a function of the vehicle shape which the shape will

75 determine the position of the center of pressure. This means the rear slant 0
0 model is less sensitive to cross wind disturbance.
Figure 5.24 shows positions of plane behind the model that were used to capture the contour and vector of wake structure. x is the distance plane from the model and l is the height of model.
Figure 5.24
Velocity vector at plane behind the model
Figure above shows the velocity vector plane behind the model from the left is rear slant angle 0
0
, 10
0
, 20
0
, 30
0
and 40
0
. Model slant angle 20
0
, 30
0
and 40
0 shows the trailing vortices start to develop at plane x/l = 0.04%. Model slant 10 degree shows the trailing vortices start at plane x/l = 0.12% and for model slant 0
0 shows that trailing vortices not occur.

76
The separation that occurs at the blunt rear ends of a passenger vehicle is often accompanied by a set of longitudinal steam-wise vortices, called the C-pillar vortices. These vortices are highly three dimensional in nature and are rich in kinetic energy. They create down wash by pulling the surrounding air to the model’s rear slant by reducing the size of the model’s wake region. The strength to these vortices is mainly supplied by the flow separating from the sides of the vehicle’s rear slant. Therefore, the rear slant angle of a vehicle plays a vital part in determining the strength of these C-pillar vortices. Additionally, this behavior could be contributed to yawing moment value. But, it need further research to investigate this behavior.
There are some factors worth to be discuss here which will affect the accuracy of the simulation result such as the number of meshed elements, the roughness of the wall of the vehicle model, the turbulence model and the quality of the meshed elements. The fine meshing will give the good accuracy of the result and the coarse meshing will give the poor result which in this study the meshing can consider as fine meshing with the number of the meshed elements about 4.2 million, but it also has to improve the number of meshing which it has not achieve the optimum. This because of the computer capability only is able to solve the problem at this meshing or below.
In the wall roughness point of view, the simulation software assumes the walls were smooth but in the reality of experimental testing, the wall of the vehicle model cannot achieve this smoothness. The roughness of the model will affect the air flow separation on the back part of the vehicle which it will give the effect on the position of the center of pressure that produces the yaw moment. The quality of the meshed elements also will affect the accuracy which the accuracy will reduce in the region of the poor quality of meshing in the simulation model.

77
CHAPTER 6
6.
CONCLUSION AND RECOMMENDATION
6.1
Conclusion
Simulations and wind tunnel test for Davis model with five different rear slant angles (0
0
, 10
0
, 20
0
, 30
0
, and 40
0
) in various wind speeds ranging from 30 m/s to 50 m/s with interval of 5 m/s and yaw range was between -16
0
and 16
0
with increment of 2
0 have been conducted. The simulation was done using the k- turbulence model while the wind tunnel test was carried out in the Universiti
Teknologi Malaysia Low-speed Wind Tunnel facility. The forces and moments on the model were measured. The results from both experimental and computational methods were presented for different rear slant angles and compared with each other.
As the conclusion of this study, the objective which is to determine lateral aerodynamic derivatives using simulation and wind tunnel has is achieved. The
CFD simulation results show a good agreement with the wind tunnel test results for rear slant angle 20
0
. Further, CFD results also show good agreement with experimental in the determination of lateral aerodynamic derivatives. However for rear slant angle of 10
0
and 30
0
CFD results have a reasonable match while for rear slant angle 0
0
and 40
0
, the results are not too promising where it is poorly matches with experimental. However, simulation results still follows the same trend as measured from wind tunnel test. As an example both results shows lateral aerodynamic derivatives increase with the increment of yaw angle. However, at 0
0 yaw angle simulation results for drag, yaw and moment coefficients are closed to

78 experimental for all models with maximum error of 18% and minimum error of
4%.
Although the Standard k- turbulence model in prediction of lateral aerodynamic derivatives are still not accurate, but at certain rear slant angle (10
0 and 30
0
) this turbulence model is capable to provide better results. Hence, there is still potential for RANS turbulence to investigate unsteady behavior analysis. It should be noted that turbulence model is not the only factor that would affect the
CFD simulation performance. In order to obtain good simulation results domain and mesh distribution modeling is the most important aspect. Besides that, a good modeling requires high performance computer to enable it to capture all the flow structure (flow around the model) and analyses the complexity of unsteady wake vortices behind the model for a better approximation of real condition.
Therefore, further investigation should be conducted to determine the limitation of
RANS turbulence model in lateral motion study.
6.2
Recommendations
To improve the accuracy of the result which offers further research on this crosswind condition are suggested. Some recommendations are :
1. Investigation of Reynolds number effects to aerodynamic derivatives especially at 10
0
and 30
0
rear slant angle using computational fluid dynamics and wind tunnel test.
2. Investigate the effect of sharp edges to lateral aerodynamic characteristics.
3. Conduct simulation using high performance computer to have high number of element meshing in order to examine the capability of

79
RANS turbulence model to determine lateral aerodynamic characteristics.
4. Conduct simulation using others type of bluff body models such as
Dominy, MIRA and Windsor.

80
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81
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Simplified Car Model”, SAE Paper 2003-01-0656, 2003.
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83
Sims-Williams, D.B., Dominy, R.G. and Howell, J.P., “An Investigation into
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APPENDIX A
Rear Slant Angle 0
84
Contour of Static Pressure at 0
0
Yaw
Contour of Static Pressure at 16
0
Yaw

85
Pathline of Velocity at 0
0
Yaw
Pathline of Velocity at 16
0
Ya

Rear Slant Angle 10
86
Contour of Static Pressure at 0
0
Yaw
Contour of Static Pressure at 16
0
Yaw

87
Pathline of Velocity at 0
0
Yaw
Pathline of Velocity at 16
0
Yaw

Rear Slant Angle 20
88
Contour of Static Pressure at 0
0
Yaw
Contour of Static Pressure at 16
0
Yaw

89
Pathline of Velocity at 0
0
Yaw
Pathline of Velocity at 16
0
Yaw

Rear Slant Angle 30
90
Contour of Static Pressure at 0
0
Yaw
Contour of Static Pressure at 16
0
Yaw

91
Pathline of Velocity at 0
0
Yaw
Pathline of Velocity at 16
0
Yaw

Pathline For Slant Angle 30
92
0 Yaw Angle
8 Yaw Angle
16 Yaw Angle

APPENDIX B
DAVISMODEL
93
SlantAngle=30
0
SlantAngle=0
0
SlantAngle=40
0
SlantAngle=10
0
SlantAngle=20
0