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Aerodynamics of cars, An experimental investigation- A synergy of wind tunnel
& CFD
Book · November 2017
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Table of Contents
Sr No
Description
Page Numbers
1
List of Tables
2-3
2
List of Figures
4-6
3
Abbreviations & Symbols
7-8
4
Index
9 - 12
5
Main Text
13 - 111
6
Refrences
112 - 120
1
List of Tables
Chapter No
Table
Description
Page
No
No
3
I
Generic Shapes-Exptl Details
29
Literature Survey
II
Drag Breakup – Ahmed et al
30
III
Yunlong Lieu & Alfred Moser- Exptl Details
31
IV
Drag Values of 3 Shapes- Han et al
32
V
Effect of Mesh Refinement-Han et al
32
VI
Emmanuel Gilmaneau – Exptl Details
33
VII
Drag Values Modelwise & Regionwise-
34
Ramnefors et al
4
I
Drag Coefficient Computed-FLUENT
51
`11Methodology
II
CFD Simulation Model (3D , Pressure based
52
, FVM )
III
Drag with Different Turbulence Models
53
IV
Drag of Sedan at 3 Velocities
54
V
Drag Values from Force Report –FLUENT
65
VI
Drag from CFD & Pressure Coeff from Wind
67
Tunnel Expt
VII
Correlations
67
VIII
Review of Pressure Coefficient
69
IX
Comparison
of
Drag
computed
with
72
Hatchback-Breakup of Drag & Validation
73
Literature
X
with Morel/Ahmed et al Values
XI
Sedan-Breakup of Drag & Validation with
2
74
Morel/Ahmed et al Values
5
I
Summary of
Findings
II
Parameters Influencing Aerodynamic Drag &
87 –
other Properties ( Literature )
88
Analysis of Hatchback ,Hatchback with front
90
Spoiler,Sedan & Sedan with Rear Spoiler
III
Drag Coefficient Modelwise
IV
Drag
Values
with
Different
92
Turbulence
92
Drag from CFD & Pressure Coeff from Wind
93
Models
V
Tunnel Expt
VI
Correlations
94
VII
Review of Pressure Coefficient
94
VIII
Hatchback-Breakup of Drag & Validation
95
with Morel/Ahmed et al Values
IX
Sedan-Breakup of Drag & Validation with
Morel/Ahmed et al Values
3
96
List of Figures
Chapter No
Figure
Description
No
2
1
Statement of the
Page
No
Zonal Approach for Computing Flowfield
20
around the Cars
Problem
1
Pro-e Model 1 Squareback
50
2
Pro-e Model 2 Squareback with Front
50
Spoiler
4
3
Pro-e Model Notchback
50
Methodology
4
Pro-e Model 1 Notchback with Rear
50
Spoiler
5
Skin Friction Coefficient Model 1
54
6
Static Pressure Coefficient Model 1
54
7
Skin Friction Coefficient Model 2
54
8
Static Pressure Coefficient Model 2
54
9
Skin Friction Coefficient Model 3
54
10
Static Pressure Coefficient Model 3
54
11
Skin Friction Coefficient Model 4
55
12
Static Pressure Coefficient Model 4
55
13
Velocity Vectors Model 1
55
14
Velocity Vectors Model 2
55
15
Velocity Vectors Model 3
55
16
Velocity Vectors Model 4
55
17
Low Speed Automotive Wind Tunnel
64
4
4
Methodology
18
1:10 Wooden Scale Model in Place
64
19
Static Pressure Contours at 27 M/S
64
20
Skin Friction Coefficient at 27 M/S
64
21
Velocity Vectors at 27 M/S
64
22
Pressure Coefficient Distribution along
65
the Symmetry Plane ( Top & Base )
23
Pressure Coefficient as a Function of
66
Static Pressure
24
Pressure Drag , Viscous Drag & Total
Drag
&
Pressure
Coefficient
66
versus
Velocity
25
Pro-e Model Hatchback
71
26
Pro-e Model Sedan
71
27
Classification of Hatchbacks
71
28
Generic Shapes
71
29
Drag Analysis - Hatchback
74
30
Drag Analysis - Sedan
75
31
Hatchback - Drag Breakup
75
32
Sedan - Drag Breakup
76
33
Static Pressure Contours – Hatchback
77
34
Static Pressure Contours – Sedan
77
35
Skin Friction Coefficient – Hatchback
77
36
Skin Friction Coefficient – Sedan
77
37
Velocity Vectors– Hatchback
77
38
Velocity Vectors – Sedan
77
5
6
39
Hatchback – Vortices in the Rear Slant
78
40
Sedan – No Vortices in the Rear Slant
78
1
Optimization Loop ( Simulation Based
101
Optimization
9
Recommendations
Optimization )
1
Half Rankine Oval – Equivalence to
Hatchbacks.
6
108
Abbreviations & Symbols
CFD
–
Computational Fluid Dynamics
RANS
–
Reynold’s Averaged Navier Stoke’s Equations
DNS
–
Direct Numerical Simulation
LES
–
Large Eddy Simulation
RSM
–
Reynold’s Stress Model
SST
–
Shear Stress Transport
RNG
–
Renormalized Group Theory
DOT
–
Department of Transportation
DOE
–
Department of Energy
PSD
–
Probability Spectrum density
Hatchback –
Two Box Model of a Car (Also Fastback & Squareback)
Notchback –
Three Box Model of a Car (Separate Dicky outside)
Ahmed Body –
Generic Shape of a Car referred to as for Analysing Flow over
surface.
Morel Body -
Generic Shape of a Car referred to as for Analysing Flow over
surface
K
-
Turbulent kinetic energy

-
Isotropic dissipation rate

-
Specific dissipation rate
U
-
Conservation flow variable
-
Aerodynamic Drag coefficient
CP
–
Pressure Coefficient
A
-
Frontal area
V
-
Vehicle speed
-
Aerodynamic lift coefficient
C
C
D
L
7
C

Y
Ψ
AA
-
Cross wind force coefficient
-
Probability Spectrum Density Function
–
Yaw Angle
C LO & C DO -
Baseline Drag & Lift Coefficients
Re
–
Reynold’s Number
Sr
-
Strouhal Number
Pc
-
Peclet Number
Other symbols and abbreviations are defined at appropriate places.
8
Index
Chapter 1 . Introduction to Road Vehicle Aerodynamics
1.1
Introduction to Road Vehicle Aerodynamics
1.2
Industry Scenario 14
1.3
External Flow Over Cars
13
16
Chapter 2 . Statement of the Problem
2.1
Problem Definition / Statement
18
2.2
Objective
2.3
Reynold’s Number as a function of Strouhal Number , Peclet
21
Number & Schmidt Number 23
Chapter 3 Literature Survey
3.1
Sources 26
3.2
DOE Statistics
3.3
Drag Reduction Technologies
3.4
Generic Shapes
3.5
Experimental Investigation
3.6
Engine Cooling Drag
27
28
29
29
35
9
3.7
Cross Winds
37
3.8
Underside Flows
39
3.9
Detail Optimization
40
3.10 Effect of Wheel Rotation
3.11 Wind Tunnel Issues
40
41
3.12 Noise Control 43
3.13 CFD Considerations 44
Chapter 4 Methodology
4.1
The Synergy 48
4.2
Image Based Modelling of a Mid Segment Car and CFD
Analysis using FLUENT 50
4.3
Wind Tunnel Experiment for Measurement of Pressure
Coefficient and CFD Simulation of by fine tuning the flow Regime 61
4.4
Hatchback versus Sedan – CFD Analysis of Drag and other Issues 70
4.5
Results & Discussion
4.6
Conclusion
81
4.7
Overall Results
81
79
Chapter 5 Summary of Findings
5.1
Tools for Measurement of Aerodynamic Properties
10
83
5.2
Limitations of Wind Tunnel
84
5.3
Limitations of CFD
84
5.4
Detail Optimization
86
5.5
Parameters affecting Aerodynamics
5.6
Other Design Modifications 93
5.7
Design Stage Measures
5.8
CFD Analysis of Hatchback, Hatchback with Front Spoiler,
86
95
Sedan & Sedan with Rear Spoiler 90
5.9
Wind Tunnel Experiment for Measurement of Pressure
Coefficient & CFD Simulation by Fine Tuning the Flow Regime.
Computation of Pressure and Viscous Drag. 93
5.10 Hatchback versus Sedan Analysis ( CFD – FLUENT )
Chapter 6 Optimization
6.1
Introduction to Simulation based Optimization 98
Chapter 7 Present Status
7.1
Wind Tunnel & CFD
102
Chapter 8 Future Scope
8.1
Wind Tunnel & CFD
104
8.2
Digital Physics
105
11
95
8.3
Digital Processing / Reconstitution
106
Chapter 9 Recommendations
9.1
Idealisation of flow over Hatchbacks to Half Rankine Oval &
Notchbacks separations to Doublets
12
107
Chapter 1 . Introduction to Road Vehicle Aerodynamics
1.1
Introduction to Road Vehicle Aerodynamics
Aerodynamic drag or the wind resistance is considered to be of prime concern in
vehicle design. The other important issues being the vehicle weight & fuel
efficiency . The twentieth century in particular has witnessed refinement in vehicle
design in terms of issues mentioned above. However the focus in this project is on
drag & related issues. It is worth noting that reduction of one count of drag i.e.
ΔC D = 0.1 translates into an improvement of mileage of 2.60 k m/ lit. As per DOT
figures India has approximately 13 million cars plying on the roads as recorded
during 2008. Further few hundreds are added every day. It is also worth noting
from the statistics given by DOE, that 16 % of the energy produced in USA is
consumed in overcoming drag of road vehicles .The Indian scenario is not much
different. Therefore there is enormous scope for improving aerodynamics of cars in
order to conserve depleting oil reserves.
Aerodynamic Design of cars is crucial as it directly affects the fuel economy &
stability in motion .Therefore it is necessary to have a clear understanding of
external aerodynamics of road vehicles which are nearer to bluff bodies and
moreover the flow over them is complex owing to its nonlinear and stochastic
nature (Partly attached & partly separated).Norbert Grun (1996)[65] Also wind
resistance is amongst the three significant factors (Efficiency of engine , weight &
aerodynamic drag ),which influence the fuel efficiency .Therefore needs a proper
focus in the early stage of design At a vehicle speed of 70 kmph & above the
prominence of air/wind is the major factor affecting fuel economy / stability . Wolf
.Heinrich . Hucho (1998). [99] Six degrees of freedom are assumed for a road
vehicle, for investigating the influence of various aerodynamic forces & moments.
These forces and moments are namely drag, lift, crosswind force & rolling
13
moment, pitching moment, yawing moment respectively. Amongst these “drag” is
found to be the most prominent factor affecting the fuel consumption at higher
speeds although other factors also need to be tackled in an integrated manner.
It is worth noting from the statistics given by DOE, that 16 % of the energy
consumed in USA is consumed in overcoming drag of road vehicles ,Richard .M
.Wood (2004) [78] This fact emphasizes the need and scope for reduction of
aerodynamic drag of road vehicles. As per the data available from DOE (Dept. of
Energy) at present US consumes 35 % more energy than it produces and it is
anticipated that by 2020 the energy imbalance may reach 65 %. A more dramatic
trend is noted for the transportation sector where US oil consumption will exceed
US oil production by 85 % in years to come and it is projected that by 2020 oil
consumption will exceed US production by 140 %.To address these issues DOE
(Dept. of Energy) and DOT (Dept. of Transportation) have a number of
programmes investigating a variety of technologies including American fuels and
advanced manufacturing processes.
This fact is equally applicable to Indian Scenario as the number of road vehicles
plying on the roads is multiplying in millions every year & the transportation sector
consumption of oil is likely to overshoot .Conservative estimates state that the
conventional fuels are going to deplete by 2050.Therefore to conserve the fuel/oil
reserves we need to go for appropriate drag reduction technologies.
1.2
Industry Scenario
Also, the Auto industry has seen a continual increase in the level of global
competition. The growth in the complexity of vehicle design and content has led to
expensive and time – consuming development processes. The large cost and long
gestation implies very significant risk for the automaker. At the same time, it is
clear that technology will play an ever increasing role as the basis of this global
14
competition, requiring high quality products that are safe to use, and economical to
design and manufacture. The climate has been favorable for the increasing use of
Computer-Aided Engineering (CAE) tools for math-based analysis of candidate
designs and product features. The objectives of math-based analysis include:
1.
Shortening the product development process and reduce some hardware
testing.
2.
Developing high quality products through the evaluation of more design
alternatives.
The availability of a reliable numerical prediction method could greatly reduce
design costs by reducing the amount of wind-tunnel testing required.
Computational Fluid Dynamics, as one of the CAE tools, a virtual testing bench has
been adopted to serve this role for an increasing number of applications. When one
examines the aerodynamic development of vehicles, there are many reasons why
CFD is expected to play an even more important role in future years. Traditional
aerodynamic development employs the use of partial-scale or full-scale clay
models of the proposed vehicle configuration. To ensure geometric fidelity, these
models include much of the vehicle’s details. As a result, they are expensive to
build and take considerable time to complete. Extensive use of large wind tunnels
for testing them is expensive and requires planned scheduling. Furthermore, certain
desired data may not be obtained from such models. For example, early assessment
of the potential of a shape for aerodynamic noise cannot be determined very
accurately due to the need for model construction. Finally in the process of detailed
development of a model in a wind tunnel, very elaborate flow measurement
techniques may be required so that diagnosis (e.g. for drag reduction) is possible.
CFD, with its ability to display flow properties in great detail, offers this additional
capability.
15
1.3
External Flow over Cars
The flow over Cars can be broadly classified as under . The values of drag / lift
change ±Δ corresponding to each of the following is given in summary of findings.
1.
Flow over surface – The flow in the case of Road Vehicles is mostly partly
attached and partly separated as road vehicles / cars come under the category
of bluff bodies.
2.
Side / Cross Winds - As we know that road vehicles operate entirely in the
unsteady transient conditions created by the natural wind and the wake s of
other vehicles .This is time dependent and turbulent environment
which
differs from the conditions simulated in the wind tunnels .To asses the
aerodynamic characteristics in crosswinds conditions , wind tunnel testing is
done on yawed vehicle .However it should be noted that such an investigation
can only act as an indicator of crosswind performance as it is essentially a
steady state simulation of a transient event .The other tool available to the
aerodynamicist is the crosswind generator where the prototype vehicles can
be assessed for behavior under severe single gust inputs .Also these tests are
carried out at the end of development process to ensure that these
demonstrate competitive characteristics in extreme conditions .Therefore they
are not considered suitable for subjective assessment as the gust duration is
too short .In general however generators do not indicate how the vehicle
behaves in normal windy conditions .While they may provide useful
information regarding vehicle behavior in sudden short period gusts as the
vehicle response to the normal windy conditions requires longer exposures
which can only be obtained in the natural environment. The unsteady
aerodynamic loads acting on a road vehicle are evaluated in power spectral
density terms.
16
3.
Engine Cooling Drag - Engine cooling drag is defined as the increase in
vehicle drag from a closed front end reference condition .It consists of two
parts namely the internal drag (Internal momentum loss ) of the cooling air
flow and the external interference to vehicle pressure distribution both at
inlet and exit .The integration of cooling system into a vehicle creates these
unavoidable interferences which are an integral part of what is called cooling
drag in the automotive industry.
4.
Underhood / Underside flows - The flow along the underside of the vehicle
can be compared with that of a rough plate or flow in a narrow channel with
one very rough wall .The drag of a plate increases by moderate roughness
Complete paneling of the underside provides a reduction of drag .
5.
Effect of Wheel Rotation - Wheels and wheel housing drag is about 30 % of
the total drag. However wheel rotation reduces the drag but there is slight
increase in the lift.
17
Chapter 2 Statement of the Problem
2.1
Problem Definition / Statement
Aerodynamic drag (Wind resistance) which is directly proportional to the square of
the speed and is also a function of shape, becomes a major factor influencing the
fuel economy at speeds beyond 70 Km /Hr .The drag, lift, t he crosswind force act
simultaneously on the vehicle when it is in the motion & these forces also cause
pitching moment, rolling moment & yawing moment .Therefore these need to be
dealt in an integrated manner. However drag is considered as major factor
influencing the fuel economy. In general Aerodynamic force can be represented as
follows
F  f (  , V , D, ,  )
i.e F  f (  ,V 2 , D2 ,
V *D

,M)
i.e. F  f (  ,V 2 , D2 , Re , M )
Where  = Fluid density
 = Kinematic viscosity
V = Stream speed
D = Charecteristic length
R
e
 Reynold’s Number
M = Mach Number
 = Bulk elasticity
From above set of equations it is evident that the Aerodynamic force is a function
of Fluid density, Square of the velocity, Square of the characteristic length,
Reynold’s number & Mach number.
18
The density & Length are constant .Reynold’s number depends upon the type of
flow i.e Turbulent / Laminar. Mach number matters when the flow is compressible.
i. e for M > 0.3
Also since there is relation between Strouhal Number & Reynold’s Nunber, it is
found that At Strouhal Number of 0.2 the laminar to Turbulent transition takes
place.
Therefore to reduce the aerodynamic force Reynold’s number should be such that
the flow is laminar and streamlined .To achieve this the shape of the car body
should be streamlined so that the flow remains attached throughout the profile..For
road vehicle applications the flow is incompressible & M< 0.3. Also following
dimensionless constants play important role in analyzing the flow phenomena.
Reynold’s number , Re 
 *V * L V * L
,where L is characteristic length (span) V is



velocity &  is knematic viscosity , Strouhal number ,
frequency of vortex shedding & Peclet number
Schmidt number given by
S
c


D


*D
P
e

S
r
L *V

D
f *L
, where f is
V

R *S
e
c
Where
S
c
is
where D is Mass diffusivity.
As the flowfield around the car is complex owing to its partly attached and partly
separated nature, the zonal approach is required to simulate it which is also
assumed to be steady & incompressible .At high Reynold’s numbers flowfield
domains can be classified as
(Refer Fig 1)

Potential flow in the fore or front side, where inertial effects dominate.

Boundary layer zone, in the middle portion of roof, where viscous effects are
to be accounted.

Wake zone which is also dominated by inertial effects, and is a separated
flow downstream of the vehicle’s base by means of free shear layer.
19
Each of these zones is governed by simplified versions of equations of motions
which need to be solved separately using second order upwind schemes .Also their
physical interaction has to be accounted for in an iterative process with simpler
couplings for zonal solutions .Norburt Grun (1996)[65]
Fig1 Zonal approach for flowfield around the car
BOUNDARY LAYER
P
POTENTIAL FLOW
B
W
WAKE
P -Potential Flow , B- Boundary Layer , W- Wake
Now, it is not possible to make the car body shape adaptive to cope with the flow
regime therefore it is advisable to make the body streamlined & avoid separation
which causes pressure drag. This is because mesh of the car surface which is a set
of Bezier points and a connectivity matrix is completely determined through a
deterministic spline algorithm. Therefore to change the frontal area or the shape of
the car the Bezier points need to be displaced in a prescribed way to alter the
geometry G. Lombardi, S. Carmassi, F .Beaux (2002)[25]This is possible only
with state of the art CAE tools like simulation based optimization modules.
Neverthless it is impossible to design adaptive car shape/surface mechanism to
minimise drag in the transient wind conditions. However it is p ossible to analyse
the flow over generic shapes of car and evaluate aerodynamic properties.
20
It is also found that separation in cars is unavoidable which makes the car a bluff
body having pressure drag & viscous drag. (Total drag = pressue drag +viscous
drag)
Therefore to reduce the drag to minimum the body shape should be nearer to the
generic shapes which have proven optimum aerodynamic characteristics .It is also
found that major component of drag which is pressure drag stems out from the base
/ rear slant from where the separation takes place .Therefore by properly modifying
the base / rear slant reduction in drag can be achieved. i.e by wake control. Also by
providing necessary aerodynamic features like air dams, spoilers, stabilizer fins the
flow control can be achieved and thereby the desired downforce also can be
obtained.
Also it is the need of the hour to have schemes/models which can capture the flow
physics appropriately, the algorithms & the software codes to solve the PDE’S with
speed to comply with the ideal transient road conditions.
2.2
Objectives
To investigate into the phenomenon of External Aerodynamics of Cars through
Synergy of Numerical & Wind Tunnel Experiments.
1.
To generate the surface or solid models of the car body with proportionate
Overall dimensions / Image tracing & using Pro-e Software.
2.
To analyse the CAD models using Fluent CFD Softwares (3D, Pressure
based, Finite Volume, RANS solvers) with virtual cuboidal wind tunnel of
21
appropriate size. (5L/3B/3H) made in GAMBIT Preprocessor of Fluent &
with appropriate surface and Volume meshing schemes for the domain.
Determine Aerodynamic drag, Lift, analyse pressure contours, Velocity
vectors from graphic images. Study the flow patterns in the wake / Separation
region.
3.
Analyse the effect of rear & front spoiler /stabilizer on Notchback version of
model.
4.
Validate the drag values ,Wake structures with baseline drag values & Wake
structures of generic shapes .( Morel body / Ahmed body ) Ascertain the
features of Squareback , Fastback & Notchback shapes from graphic images
of Pressure contours ,Drag , Streamlines & Velocity vectors .
5.
Conduct an experiment on 1:10 scale wooden model of a car using win d
tunnel. Determine /
Measure pressure coefficient distribution along the
symmetry plane and an offset plane with straight wind speed for different
permissible velocities .Determine pressure coefficient .Establish a correlation
between static Pressure & Pressure coefficient .Pressure coefficient
distribution also
gives an indication of regions of high & low pressures
along the symmetry plane & thus stability .Thus the pressure coefficient
distribution gives an idea of how the aerodynamic forces act in an integrated
manner.
6.
Find out drag ( Total drag = Pressure drag + Viscous drag ) values of the
corresponding CAD model from CFD analysis by fine tuning the flow regime
by equating the length based Reynold’s Numbers , using SST K -ω
22
Turbulence model. Visualise the meaning of pressure coefficient alongwith
with Drag values obtained from CFD.
7.
Analyse drag values & flow pattern of Hatchback & Sedan versions of CAD
models using CFD.
2.3
Reynold’s Number as a function of Strouhal Number , Peclet Number &
Schmidt Number
Aerodynamic force is given By
F  f (  , V , D, ,  )
i.e F  f (  ,V 2 , D2 ,
V *D

,M)
i.e. F  f (  ,V 2 , D2 , Re , M )
Where  = Fluid density
 = Kinematic viscosity
V = Stream speed
D = Charecteristic length
Re  Reynold’s Number
M = Mach Number
 = Bulk elasticity
From above set of equations it is evident that the Aerodynamic force is a function
of Fluid density, Square of the velocity, Square of the characteristic length,
Reynold’s number & Mach number.
However there exists a relation between Reynold’s Number and Strouhal Number,
which is given as below.
23
Re  S r *
V2

And Re 
Pe
Sc
Where Re is Reynold’s Number given by Re 
VL VL
= Inertial forces /Viscous



force
S r is Strouhal Number given by S r 
fL
, where f is frequency of vortex shedding
V
.Defined as a dimensionless Number describing oscillating flow mechanisms.
S c is Schmidt Number given by S c 

D


*D
where D is Mass diffusivity. Defined
as ratio of viscosity and mass diffusivity.
Pe is Peclet Number given by Pe 
LV
 Re * S c Defined as the rate of advection of its
D
flow to its diffusion.
The density of air & Length are constant. Reynold’s number depends upon the
type of flow i.e Turbulent / Laminar. Mach number matters when the flow is
compressible. i.e for M > 0.3
Also since there is relation between Strouhal Number & Reynold’s Nunber, it is
found that At Strouhal Number of 0.2 the laminar to Turbulent transition takes
place.
Therefore to reduce the aerodynamic force Reynold’s number should be such that
the flow is laminar and streamlined. To achieve this the shape of the car body
should be streamlined so that the flow remains attached throughout the profile. For
road vehicle applications the flow is incompressible & M< 0.3.
Therefore by keeping the Strouhal Number below 0.2 , the attached flow can be
maintained. For the purpose any method of energizing of the external flow can be
24
used .Subsequently if Strouhal Number is below 0.2 diffusion is also less ,
therefore Schmidt Number is higher and therefore Reynold’s Number is again low.
These characteristics are achievable with generic shapes like airplane win gs and
pontoons. Therefore it is desirable to have car shapes nearer to these shapes.
25
Chapter 3 Literature Survey
3.1
Sources
The literature for the topic is found from SAE transactions, Sciencedirect, Elsavier
journal & e-books on the topic of Aerodynamics, Computational fluid dynamics,
Turbulence modeling, Fluid dynamics, Numerical methods & Measurements.
Wind force is considered as one of the dominating forces of nature which has
influence on road vehicle aerodynamics & therefore on the vehicle stability & fuel
economy. Also wind resistance is amongst the three significant factors (Efficiency
of engine, weight & aerodynamic drag) which influence the fuel efficiency . S.R
Ahmed (1984)[81], Wolf Heinrich Hucho (1998)[99] Therefore needs a proper
focus in the early stage of design. CAE/CFD serves the purpose of analyzing the
design variants using virtual prototypes & virtual flowbench thus reducing the
development cycle time. Generally for research purpose modifie d Ahmed body S.
R. Ahmed (1984)[81] / Morel body Morel .T. (1976)[92] (simplified car body /
Generic shape) is analysed which is considered as generic shape of a car, as
adaptive designs which can counteract or nullify the aerodynamic forces are not
practically possible.
The mesh of the car surface which is a set of Bezier points and a connectivity
matrix is completely determined through a deterministic spline algorithm.
Therefore to change the frontal area or the shape of the car the Bezier points need
to be displaced in a prescribed way to alter the geometry G. Lombardi, S.
Carmassi, F. Beaux (2002) [25]This is possible only with state of the art CAE
26
tools like simulation based optimization modules. Neverthless it is impossible to
design adaptive car shape/surface mechanism to minimise drag in the transient
wind conditions. However it is possible to analyse the flow over generic shapes of
car and evaluate aerodynamic properties.
From first principle, streamlined bodies will have minimum drag but however d ue
to practical difficulties of asthetics, operational safety , service accessibility &
design of the layout constraints the shape of an automobile has evolved over the
years. It is necessary to have a clear understanding of external aerodynamics of
road vehicles which are nearer to bluff bodies as the flow over them is complex
owing to its nonlinear and stochastic nature (Partly attached & partly separated).
Assuming six degrees of freedom for a road vehicle various investigations have
been carried out to analyse three forces & three moments namely drag, lift,
crosswind force & rolling moment, pitching moment ,yawing moment respectively
.Amongst these “drag” is found to be the most prominent factor affecting the fuel
consumption at higher speeds although other factors also need to be tackled in an
integrated manner.
Ground vehicles fall in the category of bluff bodies which move in close proximity
of the road surface. Also with the introduction of more refined & powerful engines
used for cars it has become imperative that aerodynamic parameters like drag/lift
be optimized so that the engine power is properly utilized.
All transportation systems involve either the movement of solid structures through
fluids or movement of fluids past sold structures.
3.2
DOE Statistics
27
It is worth noting from the statistics given by DOE, that 16 % of the energy
consumed in USA is consumed in overcoming drag of road vehicles Richard M.
Wood (2004).[78] This fact emphasizes the need and scope for reduction of
aerodynamic drag of road vehicles.
As per the data available from DOE (Dept. of Energy) at present US consumes 35
% more energy than it produces and it is anticipated that by 2020 the energy
imbalance may reach 65 %. A more dramatic trend is noted for the transportation
sector where US oil consumption will exceed US oil production by 85 % in 2004
and it is projected that by 2020 oil consumption will exceed US production by 140
%.To address these issues DOE (Dept. of Energy) and DOT (Dept. of
Transportation) have a number of programmes investigating a variety of
technologies including American fuels and advanced manufacturing processes.
3.3
Drag Reduction Technologies
It is shown that the majority of the energy consumed by ground transportation is
used to overcome pressure drag rather than skin friction (Viscous) drag. Following
are some of the pressure drag reduction Technologies used for ground vehicles .To
be specific these Technologies are as under

Surface shaping – for attached flows

Surface shaping - for separated flows

Surface motion

Surface permeability

Mass addition

Energising the external flow
This review gives an account of work done in the field of external aerodynamics
from time to time. Details of experimental investigations( Wind tunnel testing ),
road testing and numerical simulations using CFD are outlined .Also the main
28
factors affecting the road vehicle aerodynamics like effect of engine cooling air
flow, crosswinds, effect of simulation of road and wheel rotation & detail
optimization have been discussed which would describe aerodynamics in total.
Unlike streamlined bodies with attached flows, the flows over automobile are
complex. The key feature of the flowfield around an automobile are the regions of
separated flow/wakes. Even simple basic vehicle configuration free of all add ones
and having smooth surfaces generate a variety of quasi two-dimensional and fully
three dimensional regions of separated flow Ahmed et al ( 1984).[81]
3.4
Generic Shapes
There are three generic shapes in all namely Squareback , Fastback & Notchback
(Three box version) depending upon the base / rear slant angle . Squareback &
Fastback are also known as hatchbacks where the rear luggage boot ( Dicky ) is
taken inside.
3.5
Experimental
Investigations
Thomas
Morel
(1978)[92] investigated
experimentally using wind tunnels the effect of base slant (rear -end surface over
which the flow is separated) on the drag generated.
Table – I Generic Shape –Exptl Details
Experimental Model
Details
Vehicle like bluff body ( Morel Larger
body )
wind
tunnel
-
scale
models
of
automobiles ,L/B/H vehicle body 3.33 : 1.5 :
1( Roughly ¼ th size of a typical auto ),
Reynold’s Number 1.4*10 6 ,
Exptl velocity
58 m/s, Interchangeable afterbodies - slant
angles from 0 0 to 90 0 .Total 19 models spaced
10 0 in the regions of lesser importance and 5 0
& 2.5 0 in the regions of rapid changes ,Critical
angle 30 0 , Drag max/min 0.41/0.25
29
The experiments were performed to study the effect of ground proximity
,Reynold’s number , free stream turbulence and rounded upper edge of slanted
surface .The results of these experiments showed that inspite of variation in these
factors which changed critical slant angle ,the drag overshoot the basic critical
beheaviour remained same. Similar exercise was also done by Janssen & Hucho
(1974)[99]
S.R.Ahmed, et al (1984)[81] investigated the flow phenomena experimentally over
a similar generic shape of the car. In his work he varied the geometry by varying
the rear slant angle in steps of 5 0 and found the results. He observed that the slant
angle in the rear determines the characteristics of the flow. The large recirculation
region behind the body seen is due to flow separation, which results in higher drag
coefficients owing to lower base pressures at the rear .The separat ed flow is
observed to be two dimensional wake for low incidences of rear slant angle upto
20 0 where the drag is low and as the rear slant angle approaches 30 0 the wake
becomes three dimensional with steady increase in drag with sudden fall of drag at
30 0 .Subsequently beyond 30 0 the flow again reverts to two dimensional wake and
the drag again increases. He also observed that for the vehicle under consideration
(Bluff body ) 85 % of the total drag is of pressure type & remaining 15 % is of
friction ( viscous ) type. He also studied the break up of drag on the forbody, rear
slant & rear vertical face.
Table – II Drag break up(Ahmed et al-1984)[81]
Rear slant angle( ø)
C TOTAL
C K *(Forebody)
C S *(Slant0
C B *(Base)
50
0.231
0.016
0.010
0.158
12.5 0
0.230
0.016
0.037
0.122
30 0 (High drag )
0.378
0.016
0.213
0.092
30 0 ( Low drag )
0.260
0.019
0.089
0.101
30
Lienhart & Becker (2003) [31]conducted experiments with two rear slant angles
25 0 & 35 0 and studied turbulence, velocities and static pressure measurements in
the wake structure, as losses in the wake region make a major contribution to the
aerodynamic drag. Laser Doppler anemometry & Hot wire anemometry was used to
measure velocities and turbulence scales at different locations. The reason for
choosing the above two angles is that because they are around the angle 30 0 at
which pronounced shift in the topology of the separated flow occurs.
Yunlong Lieu & Alfred Moser[104]investigated the flow over Ahmed body using
CFD numerical simulations with different Turbulence Models.
Table – III (Yunlong Lieu & Alfred Moser)[104]
C K (Forebody)
C B ( Base )
C S ( Slant )
C TOT
Error %
Ahmed
0.020
0.095
0.090
0.260
-----
LSTM
-----
0.129
0.121
-----
-----
K-ε+WF
0.026
0.105
0.111
0.242
-6.8
K-ε-V 2
0.020
0.124
0.120
0.264
+1.5
SSG
0.010
0.102
0.098
0.210
-19.2
RSM
0.013
0.093
0.178
0.282
+8.5
SST
0.026
0.107
0.108
0.241
-7.3
In their investigations they have also used Lienhart & Backer (2003) [31] data
for validation .They used Ahmed body with rear slant angle of 35 0 and a free
stream velocity of 40 m/s for which the Reynold’s number is 7.68 * 10 5 .
Han et al, Ramnefors and Ichinose and Ito Saeyoung. Han, V. Sumantran,
Clark. Harris, Ted .Kuzmanov, Mark.Huebler & Thoma.Zak (1996)[82]
investigated the flow over three simplified car shapes of 1:12 scale models namely
31
squareback, Fastback & optimized afterbody or fast boat tail ramp (F -B-R) with 21 0
rear slant angle.
The validation of code GMTEC with experimental results yielded following
outcome. The tests were carried out at a freestream speed of 51 m/s , at turbulence
intensity of 0.6 %,turbulence scale of 0.01 &1,50,000 cell mesh .The results are as
under,which give drag with respect to the value of 1.0 for Square -back version.
Table – IV Drag values for three shapes- Han et al
Expt type
S-B
F-B
F-B-R
Experimental
1.0
0.815
0.44
150 (K-ε )
1.0
0.82
0.43
150 ( RNG K-ε)
1.0
0.83
0.435
Also the effect of mesh size is given in the following table.
Table -V . Effect of mesh refinement on drag- Han et al
Drag
Drag
Drag
(K-ε)
(RNG- K-ε)
( Experimental )
75K
0.18
0.18
0.148
150K
0.177
0.158
0.148
300k
0.175
0.152
0.148
The following observations were made.
32
In general the Square back ( No slant in the rear) design suffers from a large
recirculation region behind the body due to flow separation, which results in higher
drag coefficients owing to lower base pressures at the rear.
In case of Fast back (Boat tail ramp in the rear) designs the flow is complex due
to interaction of the longitudinal vortices and separation in the rear. The slant angle
of the fast back determines the characteristics of the flow.
The Notchback design of car bodies refers to the three box version which has a
boat tail ramp to accommodate streamlines behind the body and minimal shedding
of vortices and thus avoid separation. Such designs have a low value of drag
coefficient owing to high pressure recovery at the base. This version is said to be
the optimized version of all.
Emmanuel Guilmaneau (2007)[21] in his study revealed the following results
Table -VI (Emmanuel Guilmaneau)(2007)- Expts[21]
Model
35 0
W/O Stilts
SST K-ω
0.2895
Ahmed et al ----
25 0
With
W/O
With Stilts
Stilts
Stilts
0.3133
0.3074
----
0.260
----
0.285
Exptl ,1984
C.P.Van Dam (1999)[14] in his article has given an overview of various drag
prediction methods employed by various researchers for road vehicles. C.P.Van
Dam (1999)[14] also proposed two methods of calculating aerodynamic force
namely from 1) Body perspective 2) Fluid flow prespective.
33
F
b

  p.n   : n ds
SBody

& D    p nx  vvn   xx nx   xy n y  xz nz ds

S
Ramnefors et al (1996)[59]conducted detailed study of computations of flow over
a basic car shape (Volvo environmental concept car) using a RANS solver using
CFDS-FLOW3D with several turbulence models. Drag was computed by
integrating surface and shear stresses and compared to wind tunnel measurements
.The difference form the previous studies was use of large mesh size ,wind tunnel
walls modeled solid inviscid , and floor modeled as solid viscous. The following
table gives details of drag values found.
Table - VII Drag Values Modelwise& Regionwise-Ramnefors et al
C DTOTAL
C DFRONT
C DREAR
C Pstgn
C pbase
K-ε
0.127
0.119
-0.007
1.032
0.116
RSM(IP model)
0.088
0.098
-0.010
1.012
0.082
RSM(GL model )
0.109
0.098
-0.010
1.010
0.134
Low Re K-ε
0.122
0.110
0.008
1.023
0.065
Two layer K-ε
0.141
0.120
0.009
1.040
0.069
Experiment
0.141
-----
-----
1.00
0.003
The table above gives drag contributions from front and aft sections as well as
pressure coefficients of stagnation point and base .The drag contribution of mid
section (mainly skin friction ) can be found out by subtracting the front and aft
contributions.
Shinsuke Kowata , Jongsoo Ha , Shuya Yoshioka , Takuma Kato , Yasuaki
Kohama .(2008)[86] Studied the effect of underbody slants & rear flaps. Since the
upward flow from the slanted underbody was blocked by the rear flaps, the vortex
shedding into wake was repressed. In conclusion, in order to reduce the drag force
34
of a bluff-body with the underbody slant, it is important to suppress the trailing
vortex formation at the slanted underbody and the vortex shedding into wake as
well as to raise the lowered pressure.
Andy Lawson , David Sims-Williams , Robert Dominy (2008) [7]Compared
surface pressures on side glass of hatchback with MIRA wind tunnel & on road test
results. The on-road data corresponds to relatively calm, low yaw conditions and
the time-averaged pressure distributions on-road and in the wind tunnel at zero yaw
were very similar. Variations in instantaneous aerodynamic yaw angle produces
fluctuations in surface pressures but the sensitivity of instantaneous pressures to
yaw angle was lower for the on-road measurements compared with steady state
wind tunnel tests. Also, surface pressure unsteadiness was larger than could be
attributed to yaw angle fluctuations alone. The response of instantaneous surface
pressures to yaw angle fluctuations is reduced for higher frequency fluctuations as
small-scale turbulence gusts are less able to modify the flow over the entire
vehicle. Examination of the spectral relationship between surface pressur e and yaw
angle indicates that the impact of yaw angle fluctuations at is reduced by a factor
of 2 for reduced frequencies above unity
3.6
Engine Cooling drag
Jack Williams(2003)[43] studied the aspect of engine cooling drag.(Prior
references / Investigations – Renn & Gilhaus (1985), Carr (1995), Hoerner(1965),
Wiedeman (1987),
Soja (1987) , Kuchman & Weber (1953), Hucho (1998),
Oshima. (1998)).
Engine cooling drag is defined as the increase in vehicle drag from a closed front
end reference condition. It consists of two parts namely the internal drag (Internal
35
momentum loss) of the cooling air flow and the external interference to vehicle
pressure distribution both at inlet and exit. The integration of cooling system into a
vehicle creates these unavoidable interferences which are an integral part of what is
called cooling drag in the automotive industry.
An analytical expression for cooling drag is introduced by author to help the
understanding and interpretation of cooling drag. The analysis shows th at the
reduction in the inlet spillage drag from the closed front end reference condition is
the primary reason why cooling drag measurements are lower than would be
expected from free stream momentum considerations.
Barnard’s (2000)[43] ducted model is an example of cooling system installation
with no inlet interference and several alternatives for exit thrust recovery . Barnard
(2000) modified Ahmed model with internal ducting for expt.
The equation for cooling drag as proposed by the author is as follows

D
q A
cooling
0
r
V
 2 C tinlet 1  x m 

V
 
   2
C texit
 
0

r
A
A
r
6
 V
COS 

 V



0
2
r
This equation is derived from the physical law which can be stated as under
Cooling drag = Freestream momentum (Ram drag)+Interference to the exterior
pressure distribution around the inlet – Exit momentum recovery of the cooling
airflow.
Where
x
m
=Inlet flow leakage fraction,
 = Inclination angle of exit flow.
C
texit
=Exit thrust recovery coefficient. And
q = Freestream dynamic pressure. Vr/V 0 =
0
Cooling system resistance. A 1 =Area of engine bay exit
A 2 =Area of radiator, Vr=Velocity at radiator, V 0 = Freestream velocity
Therefore A 1 /A 2 = Exit or Nozzle area ratio
36
In general the free stream momentum ( ram drag ) is the upper limit and overstates
the cooling drag penalty .The interference is caused by exterior flow separation
underneath the front end-bumper spoiler ,cooling air dam , tires , and underbody
.In general , ram drag ( the free stream momentum of the cooling airflow ) is the
upper limit for cooling drag .Using this value for fuel economy trade –off studies
against fan power will overstate the penalty.
3.7
Cross Winds
An estimation of unsteady aerodynamic loads on a road vehicles in windy
conditions is made by Jeff Howell (2004) [46](Also researched by Watkins. S &
J. W. Saunders – (1995) & (1997), C.J.Baker, (1991)
As we know that road vehicles operate entirely in the unsteady transient conditions
created by the natural wind and the wakes of other vehicles .This is time depe ndent
and turbulent environment which differs from the conditions simulated in the wind
tunnels .To asses the aerodynamic characteristics in crosswinds conditions , wind
tunnel testing is done on yawed vehicle . However it should be noted that such an
investigation can only act as an indicator of crosswind performance as it is
essentially a steady state simulation of a transient event hicles can be assessed for
beheaviour under severe single gust inputs .Also these tests are carried out at the
end of development process to ensure that these demonstrate competitive
characteristics in extreme conditions .Therefore they are not considered suitable for
subjective assessment as the gust duration is too short .In general however
generators do not indicate how the vehicle beheaves in normal windy conditions
.While they may provide useful information regarding vehicle beheaviour in
sudden short period gusts as the vehicle response to the normal windy conditions
requires longer exposures which can only be obtained i n the natural environment
.The steady state aerodynamic force characteristics like drag ,lift and side force are
determined from wind tunnel testing as a function of yaw angle for a small SUV.
37
In the present case unsteady aerodynamic loads acting on a road vehicle are
evaluated in power spectral density terms.
The overall aerodynamic load PSD

AA

 T  u
2
 
 uu  T  v
2

AA
as given by Jeff Howell (2004)[46] is

 vv  X  
2
Where T   is a transfer function relating aerodynamic load to an unsteady wind
input and
is an aerodynamic admittance function which accounts for the
X
attenuation of aerodynamic loads under high frequency inputs. uu &

vv
are
longitudinal and lateral turbulence PSD functions. Also the lift and drag
coefficients proposed are as under as a function of yaw.
C
 C LO  2.8   AND  C D  C D 0  1.0 
2
L
2
The turbulent wind energy PSD at low level is known from the field of build ing
aerodynamics ,although the spectra needs to be extrapolated into the near ground
domain occupied by road vehicles. This data is then converted to give the
longitudinal and lateral turbulence components in the resultant velocity frame for a
moving
vehicle.
Then
using
a
quasi
steady
analysis
the
aerodynamic
characteristics, as determined from wind tunnel tests are used to derive the
unsteady aerodynamic loads experienced by a typical road vehicle subjected to a
random wind input. The wind energy spectrum is assumed to be of Von
Karman(2003) type as defined by ESDU (Engineering sciences data unit,
Characteristics of atmospheric turbulence near the ground, 85020, London,1985 )
and also the turbulence is assumed to be isotropic .Subsequently the effects of
vehicle speed ,wind speed and wind direction on lift and side force spectra.
38
As per the analysis, the side force is linear over the yaw range of interest, but
however drag and lift are of parabolic nature.
A. Ryan, R. G. Dominy (1998) [1]Investigated the effect of cross wind at an angle
of 30 0 with second jet on a stationary model .Data was captured using pressure
tappings. It was found that in transient conditions pressure force & moments
coefficients i.e. side force & lift which were measured were highe r by 10 % to 20
% than steady state values at corresponding yaw angle.
3.8
Underside flows [All ref in 99]
The flow along the underside of the vehicle can be compared with that of a rough
plate or flow in a narrow channel with one very rough wall .The dra g of a plate
increases by moderate roughness .Reduction of drag by panelling has been
explained by Carr (1996) and also by Buchheim et al. (1980) Complete paneling
of the underside provides a reduction of drag amounting to -0.045.When the rear is
designed as diffuser it is possible to achieve a value of ΔC D =-0.07
The flow of air around an isolated rotating wheel was investigated by Morelli
(2001) and Stapleford, Carr, Scribor - Rylski (1970)
and
Cogotti (1987)
investigated the effect of faired wheel.(Drag =-0.014 7 Lift = -0.090 )Wheels also
influence mud deposition on the vehicle body Lajos et al, (1984 )
important elements of the underbody flows. (Wiedemann
and are
(1996), Lajos et al
(1988)
Wheels and wheelhouses account for 30 % to 40 % of the total aerodynamic drag
and lift of a modern car. Wickern & Zwicker ,(1995), Eloffson et al (2002),
Mercker and Berneberg (1992 )
39
The effect of wheelhouse geometry was also investigated by Fabijanic, (1996) and
Hanjalic (2005). Due to complexity of the flow, insight on integral parameters
only was available.
3.9
Detail optimization [ All ref in 99]
Carr(1996)
investigated
the
effect
of
optimization
of
forebody /
nose
,windshield/A-pillar Scribor- Rylski (1970 ),vehicle rear end , roof , sides,
undersides, wheels and wheel wells,rear spoilers .The improvement in drag and lift
for each variant due to change of flow was analysed.
L.J.J anssen & H .J .Emmelman (1978) also studied aerodynamic improvements
by optimizing frontal area of a car .They also found relationship between fuel
economy and aerodynamics/other influencing factors like weight. The potential for
fuel economy increases resulting from aerodynamics is significant as contrasted
with the potential given by reduction of weight or installed engine horse power
.Full size cars show greater potential compared to subcompact cars .Also for diesel
powered cars the improvements lead to higher potentials.
3.10 Effect of wheel rotation
Joechen Weidman & Juergen Potoff (2003) [48] investigated the effect of road
rolling and wheel rotation experimentally. Large number of vehicles are tried and
tested over the floor plate of IVK wind tunnel without boundary layer control &
with simulation of road driving through boundary layer suction, moving centre belt
& wheel rotation.
Results show that by introducing road simulation higher ( ΔC D upto 0.017 ), but
predominantly smaller C D values by -0.002 to -0.024 are obtained .The change of
lift coefficients ΔC L at +0.035 to -0.085 are also observed .These facts prove that
effects of wheel rotation and rolling road are not constant quantities.
40
Alexander Wäschle (2007) [3] Investigations of the aerodynamic influence of
rotating wheels on a simplified vehicle model as well as on a series production car
are presented. For this research CFD simulations are used together with wind
tunnel measurements like LDV for aerodynamic forces. Several wheel rim
geometries are examined in stationary and in rotating condition. A g ood agreement
could be achieved between CFD simulations and wind tunnel measurements. Based
on the CFD analysis the major aerodynamic mechanisms at rotating wheels are
characterized. The flow topology around the wheels in a wheel arch is revealed. It
is shown, that the reduction of drag and lift caused by the wheel rotation on the
isolated wheel and the wheel in the wheel arch are based on different effects of the
airflow. Though the forces decrease at the front wheel due to the wheel rotation
locally, the major change in drag and lift happens directly on the automotive body
itself. This increase of aerodynamic efficiency of the automotive body caused by
the wheel rotation is attributed to a changed interaction between the wakes of the
rear wheels and the car's rear end. These results emphasize that wheel rotation is
essential for aerodynamic shape optimization of production cars.
3.11 Wind tunnel issues
The conventional method of testing aerodynamic properties of the vehicle has been
“wind tunnel testing.” However it is associated with some minor inherent
limitations as it represents steady state simulation of unsteady transient road
conditions, which are discussed below. Zhigang Yang, Max Schenkel, Gregory J
Fadler (2003) [106] Sometimes it is necessary to apply corrections to account for
differences which are as follows.

Control of boundary layer on the wind tunnel
41

Pressure gradient in the test section- Its reduction/elimination

Wind tunnel blockages
To arrive at the correction factor of pressure gradient the physical phenomena
which are responsible are studied and are pointed below Gerhard Wickern,
Schwartekopp (2004)[28,29]

Local dynamic head

Horizontal buoyancy

Viscous effect

Cooling flow

Solid wall blockage
The different methods of boundary layer control as per Gerhard Wickern, Stefen
Dietz & Ladger Luehrman (2003)[28,29] are

Tangential blowing

Boundary layer scoops

Boundary layer suction
Conventionally wind tunnels are used to analyse aerodynamic properties of
vehicles .However this analysis is performed in the controlled low turbulence
environment provided by the wind tunnels .Such conditions are rarely encountered
on the road where the local atmospheric wind conditions give rise to velocit y
fluctuations and changes in turbulence characteristics.
42
The use of surface pressure tappings mounted around the nose of the vehicle have
been used as probes to investigate the results .Andrew Lawson, Robert. G.
Dominy, Andrew Sheppard (2003)[5,6]
It has been found that there are opportunities of drag reduction by injecting low
velocity air into the base region. The wind tunnel tests have shown favourable
results. This flow in the base is known as base bleed. Base bleed has been
extensively investigated for missile aerodynamics, and subsequently applied for
cars. It was found that the drag could be reduced upto 30 % .Jeff Howell &
Andrew Sheppard, Alex Blackmore (2003)[47]
3.12 Noise Control
Ye Li, Takashi Kamioka, Takahide Nouzawa, Takaki Nakamura & Yoshihiro
Okada& Nariyoshi Ishikawa.(2003) [102]Investigated noise generated in
production vehicles using experimental and numerical simulations. FDM & FEM
were applied to analyse flow. Lighthill analogy is also applied to conduct acoustic
analysis. S.Haruna, Takahide Nouzawa, Ichiro Kamioka (1990). [82]
Atsushi Nashimoto, Tsuneo Akuto, Yuidri Nagase & Nobuyuki Fujisawa
(2003)[8] Investigated the effect of installing a winglet on each blade of an
automobile engine cooling fan experimentally .Following observations have been
made.
i)
It reduces the noise by 1 db as measured by sound level meter
ii)
Flow visualization and PIV measurements showed strong tip vortex in case of
blade without winglets downstream & with winglets the tip vortex decreas ed.
iii)
Hence it reduces noise by app 15 %
iv)
Such change in the flowfield corresponded to change in the noise spectrum
and indicated that the noise reduction effect was brought about by the flow
control through the installation of winglets.
43
3.13 CFD Considerations:
CFD which is basically a finite volume pressure or density based RANS solver is
becoming
a
popular
tool
nowadays
for
analyzing
external
aerodynamic
characteristics of a car, owing to its capability of analyzing more number of design
variants in shorter time Also with CAE/CFD we can achieve required
geometric/dynamic similarities in the model
It has been observed that the accuracy of CFD based analysis depends on the
following factors C.P.Van Dam (1999)[14]

Geometric/Dynamic similarity

Flow solver

Convergence level

Transition prediction

Turbulence model
Mats Ramnofors, Ricard Bensry, Elna Holmberg, Sven Perzon (1996)
[59]Investigated the effect of grid refinement and turbulence model. They found
that grid refinement investigations and computations of truncation errors indicate
that with considerable attention to detail the mesh related error can be reduced to
about 0.002 for a mesh of 2.7 million cells on a basic car body. Also by doing
Richardson extrapolation this error may be virtually eliminated.
It is found that the accuracy of the nearfield flow predictions like surface pressure
and shear stress is necessary for prediction of nearfield force prediction as well as
accurate farfield flow and wake predictions .It is also found that most of the mesh
points tend to be concentrated near the body for most of the CFD problems.
44
However in subsonic flows one should not underestimate the effect of farfield flow
developments on nearfield flow properties .Therefore to capture the details (such as
vertical wake and wake based predictions) in the far field denser meshes may be
required.
The various fluxes appearing in the descretised equation are built using centred
and/or upwind schemes .Normally convective fluxes are obtained by two kinds of
upwind schemes. A first one is hybrid differencing which is a combination of
upwind and centred schemes .Unlike practical approaches
where centre
differencing/upwind differencing blending is fixed with global blending factor for
all faces of the mesh, the hybrid differencing scheme Spalding, (1972)[88] results
from a local blending factor based on the signed Peclet number at the face .Another
popular scheme which is implemented is the gamma differencing scheme.
A pressure equation is obtained in the spirit of the Rhie & Chow (1983)
[77]procedure, Momentum and pressure equations are solved in a segregated
manner in the well known simple coupling procedure of, Patankar, (1980.)[70]
The temporal descretisation is based on a three step scheme ensuring a second
order accuracy. All spatial terms are descretised with time step yielding an implicit
scheme.
For nearing the exact solution the descretisation schemes should posses the
following properties.

Conservativeness

Boundedness

Transportiveness
The governing equations which are nonlinear partial differential in nature are
normally solved in an iterative manner .Now for the convergence to take place the
45
iterative process of solving the equations has to continue for a certain period for
the results to be accurate.
It is a practice to concentrate on parameters rather than force, moment coefficients
to monitor the convergence level of flowfield situation.
Laminar to turbulent transition is one of the most important issues to be considered
while doing aerodynamic analysis. Often this problem of transition is associated
with low Reynold’s numbers. Also it is important that boundary layer be predicted
not only for drag prediction but also for guaranteeing uniqueness of the flow.
Great deal of development has been done in the area of turbulence model for time
averaged/Reynold’s averaged Navier-Stoke’s equations .These models range from
simple algebraic zero equation ,half equation ,one equation and two equation
models.Of these the K-ε , Realisable K-ε , RNG K-ε , K-ω , and SST K-ω models
with empirical coefficients are used for automotive applications .However as per
Bradshaw(1990)[90] “The present state is that the most sophisticated turbulence
models are based on brutal simplifications of N-S equations, and can not be relied
on to predict large range of flows with a fixed set of empirical coefficients.”
Moreover these models are caliberated for particular flow. Also when the flow
solvers use unstructured meshes/multigrid blocks the implementation of tuebulence
model into solver is crucial .Therefore there are significant differences in the
predictions from different turbulence models especially for complex flow with
steep pressure gradients.
X .Q. Xing., M.Damodaran (2002) [101]Analysed application of inverse airfoil
for obtaining the required downforce.
46
Ilhan Bayraktar, Tuba Bayraktar (2006)[41]Provided guidelines for CFD
simulations
of
ground
vehicles.
Different
aspects
of
linking
advanced
computational tools and aerodynamic vehicle design challenges are discussed. Key
technologies like parallel computation, turbulence modelling and CFD/wind tun nel
compatibility issues are presented.
Andrew
Anagnost,
Ales
Alajbegovic,Hudong
Chen,David
Hill,Chris
Teixeira,Kim Molvig.(1997)[6] Introduced Digital Physics application.“ Digital
Physics .” a descrete particle method has been used to study the flow ove r Ahmed /
Morel body in the ground proximity .Digital Physics extends to allow application
of the method to high Reynold’s Number flows over external geometries.
Tools based on digital processing of the information resulting from wall flow visualisations and tomographies of total pressures in the wake , to validate and
quantify results which were otherwise based on visual analysis have been
instrumental in providing the experimentalist with new interpretation and decision
making methods. Francis Chometon , Patrick Gillieron (1996)[24]
47
Chapter 4 Methodology
4.1
The Synergy
The research work done mainly consists of CAD modeling from the image of the
car with Pro-e & CFD simulation of these models using Fluent software. The wind
tunnel experiment for measuring pressure coefficient distribution is also carried
out. The experiment on pressure coefficient distribution was chosen as it gives the
distribution of pressure coefficient around the vehicle body .Therefore the regions
of high & low pressures are known & therefore the stability of the vehicle. CFD
exercise (Numerical Experiments) gives an insight into drag values , pressure
contours and velocity vectors for analyzing flow over surface & also nature of
wake.
The importance of aerodynamic design has been discussed earlier .The
conventional tool used for determining aerodynamic properties is wind tunnel.
However the measurement procedures and hardware testing involved are
cumbersome. Therefore wind tunnels are used nowadays for validating the CF D
codes developed. CFD has been complementing wind tunnel testing these days. In
the present case the basic CAD model was made from the image of a car and
pressure coefficient distribution measurement along the symmetry plane & an
offset plane of a wooden 1:10 scale model, was carried out in the low speed
automotive wind tunnel.
The measurement of aerodynamic characteristics like drag, lift, downforce yawing
moment etc using scale models in wind tunnels & extrapolating these
measurements to the full scale conditions have become a subject of debate, as for
accurate results corrections for boundary layer control , pressure gradients
48
,blockages & real turbulence are required. Therefore in the present work it is aimed
to have a synergy of wind tunnel pressure distribution & CFD simulation which
will yield more meaningful &
accurate results rather than validation of CFD
results with wind tunnel measurements .The primary goal of this work is to carry
out static pressure measurement on the 1:10 scale wooden mode l of a car in a wind
tunnel (2ft *2 ft*6 ft, low speed ),compute pressure distribution coefficient &
simulate the similar flow conditions/regime using Fluent-6.3 finite volume code
(3D,Pressure based RANS solver) with SST, K   turbulence model.
Secondly, the CFD analysis results are also compared with literature values
available with regards to generic shapes of Ahmed et al[81] / Thomas Morel
[92]etc .The pressure distribution, Velocity vectors, pressure coefficients & wake
structures are also ascertained from generic shapes.
From first principle , if the flow over the body is controlled & made streamlined
the aerodynamic resistance or the drag is reduced .To do so the separation / wakes
should be avoided as far as possible , which is possible in case of Notchback
version of cars.
(Three box). However it is a matter of requirement of downforce for particular
application. Flow can be controlled by detail optimization of shape in the fore and
aft. . Basic versions of cars are analysed i.e Hatchback & Notchback.
Following figure 1 shows CAD model of a car generated from the image of a car,
and the Fig 2-4 are modifications of the same car for analyzing the effect on three
box version and spoilers.
49
4.2
Image based Modelling of a mid-segment car & CFD Analysis using
Fluent, (3D, Pressure based, RANS Solver.)
Fig.1 (Model-1.) Pro-e model of Fig.2
Squareback version
Fig.3
(Model-3.)
Threebox version )
(Model-2.)
Squareback
version with front spoiler
Notchback
( Fig.4 (Model-4.) Notcback with
rear spoiler.
The above models were generated in Pro-e Wildfire 2.0 & imported to Gambit preprocessor of Fluent for making the final simulation model. The necessary cuboidal
wind tunnel is made around the model , surface & volume meshing is done &
necessary boundary conditions like inlet wind velocity , outlet pressure ,wa ll
movement , wheel rotation etc are applied , before the model is post -processed &
the results are read. The drag values are found from the graphic images at 3
strategic locations for the four models are as given under in Table – I The three
strategic locations are namely nose, bonnet-wind shield junction and roof top.
50
Table-I Drag Coefficient Computation - FLUENT
Model 1
Model 2
Model
3
- Model 4 -
Actual
With additional 3box
3-box
(existing)
front spoiler
spoiler
Notchback
Hatchback
with
(Notchback)
Drag
0.62 / 0.36 / 0.71 / 0.38 / 1.2
0.40 / 0.35 / 0.43 /0.50 /0.64
coefficient
0.92
0.69
(
Average
C
D
)
rear
Average = 0.76
=
Average
0.63
Average = 0.52
=
0.48
Similar exercises are carried out using other Turbulence models namely RNG K-ε ,
K-ω , SST K-ω . Refer Table III.
Similarly, the pressure contours & Velocity vectors from the graphic images is also
analysed from the graphic images .This analysis gives information about regions of
high & low pressures over the body and also the wake structure behind the model
.Refer Fig 5 to 16
51
The Simulation model used for analysis is as given below in the Table -II below
Table – II CFD Simulation Model ( 3D , Pressure based , Finite Volume )
Space
3D
Time
Steady
Viscous- Model
Standard K – ε
Wall treatment
Standard wall treatment
Boundary conditions/ Zones
Fluid
Airdensity-1.225 Kg/m3 , Viscosity –
1.7894e -04
Solid
AL OR MS (For wheels)
Velocity inlet
19.45 M/S ( 70 Km/Hr )
Wall
NA
Wall
NA
Symmetry
NA
Pressure outlet
Ambient ( Gauge 0 )
Default interior
Interior
Solver details
Equations
Solved
Flow
YES
Turbulence
YES
Descretization schemes ( Finite volume CFD )
Pressure
Standard ( Patankar )
Momentum
Second order upwind
Turbulent kinetic energy
Second order upwind
Turbulent dissipation rate
Second order upwind
Wind tunnel
Cuboidal ( 5L/3B/3H)
52
Wall motion wrt adjacent cells
Yes
Mesh
Teetrahedral-T Grid Hybrid, Mesh size
30
Table –III Drag values found for the four models with different
Turbulence models.
Turbulence Model
Car Model Drag ( Max / Min )
K-ε , Standard WF
1
0.62 / 0.36 / 0.92
0.63
2
0.71 / 0.38 / 1.2
0.76
3
0.40 / 0.35 / 0.69
0.48
4
0.43 / 0.5 / 0.640
0.52
1
0.35/0.26/0.59
0.40
2
0.41/0.24/0.59
0.41
3
0.18/0.31
0.24
4
0.11/0.27/0.5
0.29
K-ω , Standard WF 1
0.70/0.55/1.28
0.84
2
0.95/0.39/1.69
1.0
3
0.62/0.54/0.95
0.70
4
0.16/0.63/0.90
0.56
RNG K-ε
53
Average Drag
Table –IV Drag values found for Sedan model (Three box) with four
velocities.Model-3.
Turbulence
Inlet
Model
m/s
K-ε
WF
,
Velocity Drag ( Max / Min Average
)
Drag
Standard 19.44
0.40/0.35/0.69
0.48
22.22
0.51/0.43/091
0.61
25.00
0.62/0.54/1.14
0.76
27.00
0.72/0.63/1.3
0.88
Fig 5. Skinfriction coefficient ( Fig 6. Static pressure contours
Model-1 )
(Model-1)
Fig 7. Skinfriction coefficient ( Fig 8. Static pressure contours
Model-2 )
(Model-2)
Fig 9. Skinfriction coefficient ( Fig 10. Static pressure contours
Model-3 )
(Model-3)
54
Fig 11. Skinfriction coefficient ( Fig 12. Static pressure contours
Model-4 )
(Model-4)
Fig 13 Velocity vectors ( Model-1 )
Fig 14 Velocity vectors ( Model-2
)
Fig 15 Velocity vectors ( Model-3 )
Fig 16 Velocity vectors ( Model-4
)
In road vehicles which are bluff bodies the flow around them is partly attached and
partly separated & therefore complex .The total drag comprises of viscous drag in
the attached flow & pressure drag in the separation regions.
55
In general there are three generic shapes of cars Designed to suit the applications.
Notchback (Three box), Hatchback & Fastback .Hatchback can be Squareback or
Fastback.
In general the Square back design suffers from a large recirculation region behind
the body due to flow separation, which results in higher drag coefficients owing to
lower base pressures at the rear, as seen in the graphic image.
In case of Fast back designs the flow is complex due to interaction of the
longitudinal vortices and separation in the rear. The slant angle of the fast back
determines the characteristics of the flow & therefore the drag.
The Notchback design of car bodies refers to the three box version which has a
boat tail ramp to accommodate streamlines behind the body and minimal shedding
of vortices and thus avoid separation. Such designs have a low value of drag
coefficient owing to high pressure recovery at the base. This version is said to be
the optimized version of all .Refer Table IV.
To improve the aerodynamic drag of ground vehicles the different parameters of
which it is constituted should be identified so as to minimize their effects .As of
today a better understanding of the aerodynamic phenomena which generate drag is
made possible by extensive measurements done in wind tunnel with improved
techniques based on the numerical processing of experimental data .Schematically ,
drag reduction is obtained by minimizing the vortices carried in the boundary
layers by controlling their separation by minimizing the intensity of the vortices
emitted in the wake when separation can not be avoided and by optimizing the
56
geometry of the zones of separation in such a way that the loss of tota l pressure in
these zones becomes minimal.
The Notchback (Three box version) design is the one where the loss of pressure in
the wake region in the rear is minimum and therefore the drag of this model is
minimum.
Hatchbacks derive their origin from estate cars, which have longer wheelbase
generally and therefore are having a flow pattern of half Rankine body.
(Semiinfinite body) & therefore the horseshoe vortices in the rear do not meet in
the wake region .However there is loss of pressure in the base, which can be
reduced by providing a spoiler in the rear edge of roof .Another aspect of looking
at hatchback is from overall dimensions (Package ) of the vehicle & convenience of
luggage boot which is inside in the rear which provides the downforce require d for
stability.
Fastbacks are the models compromising between the Hatchbaks & Notchbacks on
flow modification as well as Design of layout.
In the present problem the chosen midsegment car is of Hatchback type, which is
modified to Notchback version to Analyse the drag & lift. Also spoiler has been
added on the rear on the Notchback version and in the front in case of Hatchback
model to analyse the effect.
As discussed above the drag value of the three box version is lowest, as the
separation is avoided in this case.
57
Static pressure contours show the regions of high and low pressures thus indicating
the stability due to lift acting.
The velocity vectors indicate the flow patterns and details of wake formation in the
separation zone in the rear .From these details the loss of pressure in the base can
be ascertained. The Htachback versions show prominent vortex formation in the
rear.
The static pressures and the velocity vector images complement each other.
The addition of spoilers adds to the downforce & reduces the lift but however at
the cost of increased drag.
Also the model which is simulated for flow with four velocities shows increase in
drag velocitywise i.e. from 0.48 to 0.61 to 0.76 to 0.88.as the drag is proportional
to the square of velocity.
Effect of Turbulence Closures / Models on measured drag values. [Ref 71 ,90]
All the four models were analysed with different turbulence closure schemes as
mentioned above in table III. Following are the comments on differing values of
drag predicted by these turbulence schemes.
The overall accuracy of numerical predictions of external aerodynamics depends
both on the “Numerical schemes” and the robustness of the “Turbulence model”
used to solve the Navier-Stoke’s equations .While numerical scheme is said to be a
source of error in overall predictions, “Turbulence model “becomes equally
important for accurate prediction of three dimensional boundary layer growth and
therefore the strength of the trailing vortices and the resulting base pressure.
58
Most of the CFD analyses make use of two equation turbulence models called
(   )Model ,
enhanced (   )Model , & RNG (   )Model . Standard (   )Model have
been shown to cause unrealistically high generation of turbulence energy in
conditions where the flow experiences high normal strain.i.e. In the location like
stagnation point. As a consequence the overprediction of forebody drag is
attributed to the excessive turbulent viscosities predicted near the stagnation point.
The (   )Model is the most widely employed two equation eddy viscosity model. It
is based on the solution of equations for turbulent K.E. & turbulent dissipation rate
.The (   )Model requires addition of the so called damping functions in order to
stay valid through the viscous sublayer to the wall. The aim of the damping
function is to ensure proper limiting beheaviour of  &  at the wall .The damping
functions lead to turbulence equations with stiff source terms .This aspect and
necessary high grid resolution nearby walls ( in order to resolve the viscous
sublayer) requires the utilization of atleast point implicit or better f ull implicit time
stepping schemes .The accuracy of
(   )Model degrades
for flows with adverse
pressure gradients.
The    standard model differs from   
inverse time scale  


in using the model equation for the
with units same as vorticity. In fact omega expresses the
fractional rate at which energy is dissipated in the flow .The    model assumes,
eddy viscosity

T


The modeling of  and  equations differs primarily in the transport

term, and the consequences for the prediction are not significant .The greatest
practical difference between the two models lies in their near wall beheaviour
where it is found and demonstrated that    has better numerical properties
59
SST    model of Menter merges the    model of Wilcox (1993) and high
Reynold’s number (   )Model .The SST model seeks to combine the positive
features of both models .Therefore    approach is employed in the sublayer of
the boundary layer .The reason is that the    model needs no damping function.
This leads to similar accuracy to significantly higher nu merical stability in
comparison to (   )Model .Furthermore    model is also utilized in logarithmic
part of the boundary layer where it is superior to the (   )Model approach in
adverse pressure flows and in compressible flows .On the other hand the
(   )Model is
employed in the wake region of the boundary layer because the   
model is strongly sensitive to the freestream value of  . The (   )Model is also
used in free shear layers since it represents a fair compromise in accuracies for
wakes, jets and mixing layers.
One distinct feature of SST turbulence model is the modified turbulent visc osity
function .The purpose is to improve the accuracy of prediction of flows with strong
adverse pressure gradients and of pressure induced boundary layer separation. The
modification accounts for the transport of the turbulent shear stress .It is based o n
the observation of Bradshaw (1990)[90]
RNG (   )Model has many advantages over standard models .These pertain to
scale invariant phenomenon lacking externally imposed characteristic length and
time scales.
The concept is to remove a narrow band of high wave number nodes. When the
high wave number nodes are removed the resulting equations of motion for the
remaining nodes is a modified system of Navier-Stoke’s equations that allow
computations on relatively coarser grids at high Reynold’s numbers Therefore the
60
main physical effect of removing the small scale eddies from the dynamics is to
introduce an effective eddy viscosity into the Navier-Stoke’s equations.
RNG theory results in decreasing the turbulent Kinetic energy and increasing rate
of turbulent dissipation leading to a smaller value of eddy viscosity value.
4.3
Wind Tunnel Experiment and CFD Simulation. (Pressure coefficient
distribution & computation of drag from CFD.)
The primary goal of this work is to carry out static pr essure pressure measurement
on the 1:10 scale model of a car in a wind tunnel (2ft *2 ft*6 ft, low speed),
compute
pressure
distribution
coefficient
&
simulate
the
similar
flow
conditions/regime using Fluent-6.3 finite volume code (3D, Pressure based RANS
solver) with SST, K   turbulence model for aerodynamic analysis.
In the present work a CAD model is generated in Pro-e, wildfire 2.0 using its image
tracing on the graph paper & then plotting co-ordinates and curves .Then by using
variable section sweep command the model is extruded.
Similarly 1:10 scale wooden model is also made for wind tunnel pressure
distribution testing .The low speed wind tunnel at I.I.T, Bombay, Aerospace dept.
having following specifications & instrumentation is used for the experiment. Refer
Fig 17 and 18.

2 ft*2 ft *6 ft wind tunnel test section

25 HP motor for suction blower.

DC control panel

20 way single selection box- 3 Nos

Micrmanometer-For pressure tapping.
61

Pitot tube-for stastic & total pressure

Sonic ( Mach < 0.3 )
The physical model for wind tunnel testing are provided with 2 mm dia holes on
the symmetry plane longitudinally as shown through which the pressure tappings
are taken for the wind tunnel exptl set up .In all 53 tappings were taken except two
for pitot tube readings for measuring freestream velocity. Pitot tube is fitted ahead
of the model in the wind tunnel to measure free stream velocity of the wind
(V∞).The pressure measurements for three velocities are noted & then the pressure
distribution coefficient is computed .The car model is screwed in the centre of the
test section so as not to have distortion during testing .The freestream velocity is
given as
V
2Totalpr  Staticpr


m/s
& Pressure coefficient is given by
CP 
P  P

2
2
*V 
Similarly for CFD exercise the CAD model of the car in .igs form is imported in
Gambit preprocessor of Fluent where the following operations are done before
running simulations.

Stitch surfaces

Surface meshing

Appropriate size virtual wind tunnel ( shell ) around

Volume meshing of the domain

Boundary conditions

Specify zones.

Export mesh to Fluent for solving- Numerical solution.
62

Turbulence model SST K-ω
For fine tuning the flow conditions / regime of wind tunnel, velocity /length based
Renold’s Numbers are tuned (Turbulence range) as matching the pressure contour
point to point was not possible with Fluent. However the values fairly match .In the
experiment three velocities of 9.31 m/s , 12.25 m/s , & 15.1 m/s were set
considering the limitations of the wind tunnel .Therfore to match the conditions
with CFD the velocities were tripled as the CAD model is of scale 1:32. By doing
so the Reynold’s Number of both flow conditions is matched to app 1.7 * 10 4 .
Reynold’s Number is calculated using the formula
R
e

U *L

Where U is velocity & L is the model length.
Pressure drag & viscous drag are calculated as per the formulae
Pr essure  drag 
Pr essureforce
0.5 *  * A *V
2
& Viscous  drag 
Viscousforce
0.5 *  * A *V
2
.
Where the pressure & viscous force & the projected frontal area are read from
Fluent results (Force report – Table V) In the same table the analytical values of
drag found by integrating the axial component of pressure are also mentioned
.Ahmed et al (1984)[81]
Pressure coefficient distribution curves for all the three velocities are plotted
.However one curve corresponding to 19.45 m/s is shown .The graphic images of
static pressure contours, skin friction drag, & velocity vectors are obtained for each
velocity Refer fig 19 ,20 , 21 .Pressure contours & Pressure coefficients give fair
amount of matching on strategic locations.
The Fluent force report also gives the breakup of pressure force & viscous force
from which the corresponding drag values are calculated knowing the area.(
Report-projected area )( Refer Table –V )
63
Fig.17.Low speed automotive wind Fig. 18. 1: 10 Scale model in test section
tunnel
of wind tunnel
Fig.19 Static Pressure contours at 27 Fig 20. Drag( Skin friction coefficient)
m/s
Fig 21 Velocity vectors showing separation behind.
64
Table – V Drag values calculated as per force report of Fluent
Velocit
Pressure
y m/s
force
Pressur
( e
N)
Pressure
Viscous
drag(D P )
force (N) s drag force
drag(D P (Analytical
)
Viscou Total
(D F )
Tota
( l
N)
drag
)( Ahmed et
( D=
al 1984)
DP
+
DF )
27.00
1428220.
0.62
---
930298.0
0.41
0
36.00
2358518.
1.03
0
1084201.
0.47
----
1297746.
0
0.56
6
2381947.
1.03
4
45.00
578075.0
0.25
----
125407,5
0.55
677332.5
0.80
60.0
1444793.
0.63
0.321
1770340.
0.77
3215133.
1.40
1
5
6
Fig 22. Pressure Coefficient Distribution along Symmetry Plane (Top &Base )
Pressure coefficient along X-Distance
2.5
2
Pressure coefficient
1.5
Top profile
Base profile
1
0.5
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
-0.5
X-Distance
65
Fig 23. Pressure Coefficient as a Function of Static Pressure
Pr Coeff as a Function of Static Pressure
1.6
P
r
e
s
s
u
r
e
C
o
e
f
f
i
c
i
e
n
t
1.4
1.2
1
0.8
0.6
Pr Coeff
0.4
0.2
0
2.16
1.89
1.84
1.8
1.75
1.66
1.56
1.32
1.29
1.23
1.16
1
0.99
0.96
Static Pressure
Pr Coeff 1.48
1.33
1.3
1.28
1.25
1.2
Static Pressure
Fig 24. Pressure Drag, Viscous Drag, Total Drag & Pressure Coefficient versus
Velocity.
1.6
Pressure Drag , Viscous Drag , Total drag & Pressure Coefficient versus
Velocity
2
Total Drag y = 0.15x - 0.662x + 1.595
R² = 0.696
1.4
1.2
1
Pr Drag
0.8
Vis Drag
D
r 0.6
a 0.4
g
0.2
Tot Drag
Pr Coeff
Poly. (Tot Drag)
0
-0.2
27
36
45
60
Poly. (Pr Coeff)
-0.4
-0.6
Pressure Coeff y = -0.28x2 + 0.92x + 0.46
R² = 1
Velocity M/S
66
Table – VI Drag from CFD & Pressure coefficient from Experiment
Velocity(m/s)
Wind Pr drag ( Viscous drag( Total drag
Tunnel air speeds
CFD)
CFD )
( CFD )
C
9.31
0.62
0.41
1.03
1.1
12.25
0.47
0.56
1.03
1.18
15.10
0.25
0.55
0.80
0.70
P
Table VII Correlations
Sr No
Parameter
Correlation
1
Pressure Coefficient
Y=-0.28x 2 +0.92x+0.46
R² = 1
2
Total Drag
y=0.15x 2 -0.662x+1.595
R² = 0.696
3
Viscous Drag
y=0.017x 2 +0.019x+0.392
R² = 0.884
4
Pressure Drag
y=0.132x 2 -0.681x+1.202
R² = 0.762
Analysis of C P  Plots:
Refer fig 22.
These are the plots of pressure distribution coefficient versus X-distance along the
vehicle length on a symmetry plane. From these plots the critical areas of drag can
be located for the purpose in all 53 pressure tappings are taken plus two more for
pitot tube for measuring free stream velocity.
At X=0 the COP is higher as this situation refers to a flow perpendicular to plate
surface. Thereafter due to curvature on the front there is interference and flow gets
67
bifurcated into vertical and horizontal components. Thereby the COP dips down
upto the nose /stagnation point. Again at stagnation point there is slight rise in the
COP due to change of topology of the body profile. The rise in COP at stagnation
point can also be supported by theory of presence of artificial viscosities. This rise
continues till the bonnet windshield junction.
At this junction there is again interference and the COP dips slightly and rises
subsequently upto roof top at the end of wind shield.
Thereafter there is decline in COP as from this point the velocity increases and the
situation refers to flow past flat plate where viscous drag dominates.
Next at the rear end due to separation the COP falls and remains more or less
constant in the rear vertical.
Similarly for the base profile the COP remains steady throughout the length and
there is very small decline in the value till end.
For establishing linear and second order relation between COP and pressure values
ten points including minimum and maximum are considered
Fig 23 shows the relations between Static Pressure and Pressure Coefficient, which
seems to be linear.
Fig 24 shows Pressure Drag, Viscous Drag, Total Drag & Pressure Coefficient
plotted against Velocities alongwith trendlines of total drag and pressure
coefficient.
68
Table VI shows the drag values computed from FLUENT and Pressure Coefficients
computed from wind tunnel experiment. These two parameters give us an insight
into the beheaviour of a car in windy atmosphere.
Table VII shows correlations obtained from the graph fig 24. Polynomial fitting has
been done as the R 2 values are better.
Table –VIII
Review of Pressure Coefficients
Sr
Author
Details
Remarks about Cp
No
1
2
Mat Ramnofors,
Basic car
-1.0 to + 1.0
1996 [59]
shape Volvo
Stagnation value = 1.032 , Base value =
ECC
0.116
Norbert Grun
Basic car
Found that (Asep / Aref =0.5 for fastbacks
,1996 [65]
shape
& 1.0 for vans) Also Cp decreases as free
stream velocity increases.
3
4
B.Basara ,2001 , Basic car
Compared Numerical simulation ( k-ε , &
[9]
shape
RSM ) results with exptl. Cp = + 0.5 to -1.2
Andrew
Morel Body
+1.0 to -1.5 , For slant angle 5 0 No
Anagnost , 1997
separation.For slant angles 30 0 & 35 0
,[6]
separation.
The above table VIII shows pressure coefficient values found by various
researchers.
69
4.4 Hatchback versus Sedan – Analysis of Drag
Aerodynamic drag or the wind resistance is considered to be of prime concern in
vehicle design. The other important issues being the vehicle weight & fuel
efficiency. The twentieth century in particular has witnessed refinement in vehicle
design in terms of issues mentioned above. However the focus in this paper is on
drag & related issues. It is worth noting that reduction of one count of drag i.e.
ΔC D = 0.1 translates into an improvement of mileage of 2.60 km/ lit As per DOT
figures India has approximately 13 million cars plying on the roads as recorded
during 2008.Further few hundreds are added every day. .
It is observed that
Hatchbacks or the two box version of cars are becoming popular than contemporary
Sedan or the three box version inspite of lower drag value of Sedans. Thus creating
a conflict of choice amongst customers. The reasons cited are convenience of
luggage boot space inside, smaller and compact size due to reduction in wheel
base, better power to weight ratio, better manovurability and lesser parking space.
In the present work a midsegment Hatchback and its sedan version are modeled
form its image and CFD analysis is done to predict drag and other aerodynamic
characteristics such as lift, flow over the car and analysis of wake / separation in
the rear slant. Refer fig 25 and 26.The results of Hatchback and Sedan are
compared and it is ascertained that the drag value of Sedan is lower t han
Hatchback. The drag values are also compared with those of generic shapes from
literature.
Broadly cars are classified as Hatchbacks –Two box & Notchbacks (Sedans) Three box based on their generic shapes. Hatchbacks are further sub classified as
Fastbacks & Square backs as per the rear slant angle as shown in Fig 28. As seen in
the Fig 27 the angle 30 0 is critical angle at which the drag is maximum & it is
70
found that the drag value is minimum at an angle of 12.5 0 which increases up to 30 0
and again for greater angles the drag value decreases.
Fig 25 Pro-e Model of Hatchback
Fig 26 Pro-e Model of Sedan
Fig 27 Sub Classification of Hatchbacks
Figure
28
Generic
shapes-
Based on Rear Slant Angle Wolf Heinrich Wolf Heinrich Hucho (1998)Hucho 1998[99]
Rear[99]
a)
Squareback
b)
Fastback
d) Notchback
71
a
b
c
d
and
c)
Table-IX Comparison of drag values computed with literature.
Version /Drag Author
Values
CFD-
( Experimental
(
Literature
–
– Vehicle like bluff body)
Image Literature
based model)
( CFD
Vehicle like bluff
body)
Hatchback-Two
1.40
Box
(
Rear
angle 30 0 )
0.378
Ahmed etal 0.240 Yunlong Lieu &
slant (1984)
Rear slant Alfred
angle 30 0 [81]
0.41
Moser
,
Rear
slant angle 35 0 [105]
T.Morel 0.2895
&
0.3074
(1978) Rear slant Emmanual Guilmaneau (
angle 30 0 [92]
2004)[21] for Rear slant
angle
25 0
&
35 0
respectively
Sedan
Box
–Three 0.44
Rear 0.44
Han
et
al 0.435 Han et al 1996)
slant angle 30 0 (1996) Rear slant Rear slant angle 21 0[82]
angle 21 0 [82]
72
Table X ( HATCHBACK ) Breakup ( Total Drag = Pressure Drag + Viscous
Drag ) from CFD & validated with Ahmed et al and T.Morel expt values
Velocit
Pressure
Pressur
y m/s
force ( N) e
Viscous
Viscou
force (N)
s drag force ( N) l
et al
(D F )
( Exptl
drag(D P
Total
Tota
drag
)
Ahmed
( D= )
DP
+
DF )
T.More
l
( exptl )
27.00
1428220.
0.62
930298.0
0.41
0
36.00
1084201.
2358518.
1.03
0
0.47
0
1297746.
0.56
6
2381947.
/0.260
1.03
578075.0
0.25
125407,5
0.55
677332.5
0.80
60.00
1444793.
0.63
1770340.
0.77
3215133.
1.40
5
6
73
High /
Low
4
45.00
1
0.378
0.41
Fig 29. Drag Analysis of Hatchback
Drag Analysis of Hatchback
1.6
y = 0.15x2 - 0.662x + 1.595
R² = 0.6962
1.4
1.2
D
r
a
g
1
0.8
0.6
Pr Drag
0.4
Vis Drag
0.2
Total Drag
0
27
36
45
60
Pr Drag
0.62
0.47
0.25
0.63
Vis Drag
0.41
0.56
0.55
0.77
Total Drag
1.03
1.03
0.8
1.4
Poly. (Total Drag)
Velocity m/s
Table XI ( SEDAN ) Breakup ( Total Drag = Pressure Drag + Viscous Drag )
from CFD & validated with Ahmed et al and T.Morel expt values
Velocit
Pressure
Pressur
y m/s
force ( N) e
Viscous
drag force (N)
(D P )
Viscou
Total
Tota
Ahmed
s drag force ( N)
l
et al (
(D F )
drag
Exptl )
( D= T.More
DP
+
DF )
27.00
561505.6
0.18
0
36.00
613300.0
629972.0
0.20
0.21
614830.4
0
638065.8
0.21
1251365.9
660149.0
0.22
1290121.4
0.378
0.41
1
0.24
1343121.0
0
74
/0.260
High /
0.42
0
728290.6
( exptl )
0.38
0
0
0.20
1180957.1
0
0
0
60.00
0.20
5
0
45.00
619451.4
l
Low
0.41
0.44
Fig 30. Drag Analysis of Sedan
Drag Analysis of Seadan
D
r
a
g
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
y = -0.0025x2 + 0.0315x + 0.3525
R² = 0.976
Pr Drag
Vis Drag
Total Drag
27
36
45
60
Pr Drag
0.18
0.2
0.21
0.2
Vis Drag
0.2
0.21
0.22
0.24
Total Drag
0.38
0.41
0.42
0.44
Poly. (Total Drag)
Velocity m/s
Fig 31 . Hatchback Drag breakup
Breakup of Pressure Drag & Viscous Drag Hatchback
0.9
0.77
0.8
0.7
0.6
D
r 0.5
a 0.4
g 0.3
0.63
0.62
0.56
0.55
0.47
0.41
Pr Drag
0.25
Vis Drag
0.2
0.1
0
27
36
45
Velocity m/s
75
60
Fig 32. Sedan Drag breakup
Break-up of Pressure & Viscous Drag Velocitywise - Sedan
0.3
0.24
0.25
0.2
0.2
D
r
0.15
a
g 0.1
0.2
0.21
0.21
0.22
0.2
0.18
Pr Drag
Viscous Drag
0.05
0
27
36
45
Velocity m/s
76
60
Graphic Images of Static Pressure , Skin Friction Coefficient &
Velocity Vectors at 27 m/s
Fig 33 Static Pressure Contours
Fig 34 Static Pressure Contours
( Hatchback)
( Sedan)
Fig 35 Skin Friction Coeficient
( Hatchback)
Fig 36 Skin Friction Coefficient
( Sedan)
Fig 37 Velocity Vectors
(Hatchback)
Fig 38 Velocity Vectors (Sedan)
77
Fig 39 Hatchback - Vortices in the rear slant / Wake region in the lower
region creating loss of pressure.
Fig 40 Sedan – No Vortices seen in the rear slant / Wake region & there
is a downwash providing downforce.
78
4.5
Results and Discussion
As Fluent is simulation software it outputs results in the form of graphic images
and tables. The graphic images shown above give static pressure contours, drag,
skin friction coefficient & velocity vectors for Hatchback and Sedan respectively.
.Figs 33 to 38 . From skin friction coefficient images it is observed that the drag
value for Hatchback lies between 1 to 1.20 and for Sedan it lies between 0.6 to 1.
However these figures pertain to skin friction coefficient i.e. only viscous part of
drag due to profile . The total drag values found from force report are 1.40 and 0.44
for Hatchback and Sedan respectively. The discrepancies are explained as under.
Generally skin friction coefficient is computed for fully attached flows in
Aerospace applications. Automotive shapes being bluff bodies therefore do not
give realistic values of drag as a whole. Therefore the total drag values obtained
from force report can be assumed as the realistic. The drag values for Hatchback &
Sedan as compared with literature are given in the following Table – X and XI. The
drag values of Hatchback are not much in agreement with those of literature for
generic shapes. The reason for this disparity is the inability of the turbulence model
to track the separation accurately in the wake region & as a result the higher drag
value predicted by CFD. The other reasons being translation of accurate CAD
geometry for the model, wind tunnel corrections and use of robust Numerical
scheme. An accurate CAD model through digital reconstitution is po ssible .The
process of white light scanning for mapping to the vehicle points in Cartesian
coordinates system followed by conversion of these points to surface possible.
These surfaces are then stitched to form panels for numerical simulation .
79
However it is found that the computed Sedan values of drag are realistic as they
are nearer to literature values. These are compared with the available literature
values for 21 0 rear slant angle.
The Sedan values of literature are mentioned only to demonstrate the ir lower drag
compared to Hatchbacks. It is also observed that for Hatchbacks the CFD values
are little lower.
Static pressure contour images indicate the regions of high & low pressures along
the symmetry plane. These images enable us to track excessive lift, which is not
desirable. The images of velocity vectors enable us to analyze the flow over body
& separation in the wake region. These images indicate how pronounced the
trailing vortices are. Also depending upon the up wash / downwash observed the
necessary down force can be visualized. It is also observed that the static pressure
and velocity values complement each other. Refer fig 39 & Fig 40 which show
details of separation / wake regions. It is seen that in Fig 39 of Hatchback trailing
vortices are prominent, whereas in Fig 40 of Sedan there are no vortices seen as
there is no separation of flow and as a result there is downwash which also
provides necessary down force.
Refer Figs 29 and 30 which indicate that the total drag increases as the speed
increases.
Figs 31 and 32 indicate breakup of Pressure drag & viscous drag for Hatchback and
sedan respectively.
However the total drag is a polynomial as seen from the trendlines. For Sedan the
pressure and viscous drag are almost 50 % each at all speeds, however for
Hatchback there is variation owing to flow separation in the rear and also due to
possible reversal of flow.
80
4.6
Conclusion
The important conclusion which can be drawn is that the drag of Sedan (Three box
version) is lower than Hatchback (Two box versions) for the same car front , which
is ascertained from values computed.
The Hatchback has large recirculation of vortices in the separated / wake region in
the rear & therefore gives rise to additional pressure drag. The Sedan or the three
box version has a boat tail ramp which avoids separation and therefore the pressure
drag reduces. The Sedan version is said to be an optimized version.
4.7
Overall Results
The research work mainly consists of image based CAD modeling with Pro -e &
CFD simulation of these models using Fluent software .The wind tunnel
experiment for measuring pressure coefficient distribution is also carried out. The
experiment on pressure coefficient distribution was chosen as it gives the
distribution of pressure coefficient around the vehicle body .Therefore the regions
of high & low pressures are known & therefore the stability of the vehicle.
The first exercise which consists of four CAD models & their analysis with Fluent ,
in which one is Hatchback and one is Notchback .The drag , the pressure
distributions around , and the wake structures are compared with those of generic
shapes & ascertained that these parameters match with the generic shapes .The
effect of front spoiler on the Squareback model shows that due to the spoiler in the
front the drag value is increased but at the same time the downforce is available
which provides the required traction & stability .The effect of rear spoiler on the
81
Notchback model shows that due to the rear spoiler there is downforce available in
the rear which provides the traction & stability.
The wind tunnel experiment is conducted to perform pressure distribution around
the 1:10 scale wooden model of the car body .This distribution also ascertains the
regions of high & low pressures and thus it provides information about drag & lift
in an integrated manner.
Subsequently the same model is tested with CFD simulation package . For
determining the drag the similar flow conditions / regime is obtained by fine tuning
the length based Reynold’s Number .The CFD simulation with Fluent gives
breakup of drag as Total drag = Pressure drag + viscous drag .
82
Chapter 5
5.1
Summary of Findings
Tools for Measurement of Aerodynamic Properties
Automotive body shapes which move in close proximity of ground are nearer to
bluff bodies where the flow over them is partly attached & partly separated
.Therefore to tackle this problem zonal approach is required.
Also to track the flow physics appropriately the validated software codes are
required. Generally the validated software codes are customized for specific
application and may not respond accurately in variety of applications. i.e. Codes
developed for internal flows may not work for external flows .With the availability
of CFD software codes it is possible to model & simulate the flow conditions.
Another conventional tool for analysis is the wind tunnel .However the constrain ts
/ limitations associated with these tools are as under.
The aerodynamic forces like drag , lift ,crosswind force & the corresponding
moments i.e. rolling , pitching & yawing act in an integrated manner generating
trade-off’s between force-moment
parameters .The most crucial amongst these
being drag and downforce.
In addition the effect of wheel rotation and generated noise are also to be
addressed.
As the nature of flow over ground vehicles is partly attached & partly separated the
total drag contains two components namely Pressure drag & Viscous drag. In case
of bluff bodies the pressure drag is prominent.
83
The conventional tool i.e. Full scale wind tunnel are expensive to build and operate
where as scale model tests results are subjected to numerous doubts associated with
realistic simulation of Reynold’s Number, surface an underbody details, engine
cooling, passenger compartment flows, tunnel wall boundary layer and model
support, interference effects, model & wake blockage effects, effect of flow
intrusive probes etc .Road tests represent the most realistic simulation of the
environment in which the vehicles operate .However the difficulties associated
with ever changing environments often make the results obtained open to debate.
5.2
Limitations of Wind Tunnel
Inspite of the fact that the wind tunnel results are accurate within 0.001 -0.002
sometimes it is necessary to apply corrections to account for differences which are
as follows.

Control of boundary layer on the wind tunnel

Pressure gradient in the test section.

Wind tunnel blockages
5.3
Limitations of CFD
CFD as a CAE tool which has emerged as an efficient virtual work bench is found
to be accurate within – 2.7 % with 95 % confidence band of 13 %.However there
are also limiations of computational methods , which are as given below.
Modelling Error
84
Translation of the real geometry into the CAD form is crucial for accuracy
.Secondly the modeling of virtual wind tunnel, inlet conditions of velocity ,
turbulence and also boundary layer development in the wind tunnel has to be
matched.
Descretisation Error
While solving continuous derivatives of the governing equations using finite
difference schemes such as higher order upwind schemes Taylor series expansion is
generally used. In such cases Descretisation error may be seen as the effect of
truncating the higher order terms.
Turbulence modelling Error
Modelling of complex flow physics of the flow has been a real challenge. DNS &
LES need high resolution & computational speeds which limits the application
.Therefore for computing the flow around the car Turbulence models are required
in which the time averaged Navier-Stoke’s equations are solved instead of real time
equations .These models which are used for complete closures are however not
very accurate in describing the flow .i.e. Separation, Pressure distribution etc .The
intricacies of boundary layer development needs to be properly addressed in order
that the near wall stresses are properly modeled.
Residual Errors
These errors can be attributed to the accuracy of the computations. i.e Convergence
criteria. Generally the convergence criteria employed is of the order 10 -4 to 10 -5
85
.However to have minimum residual error the convergence of 10 -7 to 10 -8 is
required & which in turn needs double precesion solver.
5.4
Detail Optimization
Numerical simulations are the most useful techniques in predicting trends of how
shape changes will affect flow field features & it is most suitable tool used during
early design stage & therefore provides options in identifying the optimum shapes
.Therefore this process enables to find shapes
having favourable aerodynamic
characteristics with minor geometric modifications .The main objective is to find
out rapidly the best configurations within certain small range of shapes, which are
considered to be acceptable.
Taking into account the effect of various parameters, Multidesciplinary design &
optimization (MDO) is employed, which is basically simulation based optimizer
module. Refer the optimization loop depicted in next chapter on optimization.
5.5
Parameters affecting Aerodynamics
The following table-I gives details of Modifications, Measures & their effect on
aerodynamic properties of a vehicle.
86
Table – I Parameters influencing the Aerodynamic Drag & Other Properties.
( From Literature )
Sr
Parameter
Modification / Effect
No
1
Contribution
drag ±ΔC D =0.14 ( S.R.Ahmed )[81]
Total Drag - Lower
Rear
slant upto 20 0 & then
rises upto 30 0
angle
and
again
decreases
beyond 30 0
2
Engine
Cooling
Drag
to ±ΔC D =0.19 ( Jack Williams )[43]
Baseline
–
Air Optimum
-Inlet Inlet
cooling
Outlet
air Configuration
configuration
3
Crosswinds.
Lift & Drag –
function
C C
L
 2.8   AND  C D  C D0  1.0 
2
LO
2
of (Jeff Howell )[46]
yaw.(Ψ)
4
5
Underside
i) Panelling
ΔC D = -0.045 (Wolf Heinrich Hucho )[99]
flows
ii) Diffuser
ΔC D = -0.07
Wheel
Simulation.
ΔC D = -0.002 to 0.024
ΔC L = + 0.035 to - 0.085
rotation
(Wolf Heinrich Hucho )[99]
6
Noise control
Through
flow 15 % Reduction.
control
& (Atsushi Nashimoto)[8]
avoidance
of
87
separation
7
8
Surface
Attached
& Overall 15 % Reduction , More than 30 %
Shaping
Separated
for
flows
% for separated flows.(Richard Wood)[78]
attached
flows
,
Surface
NA (only for ------.(Richard Wood)[78]
Motion
aerospace
More
than
2-5
appn)
9
Surface
Porosity
15 % Redction.(Richard Wood)[78]
Permeability
10
Addition
of ----
Mass
11
.(Richard
Wood)[78]
Energising the Ground vehicle Only Marginal.(Richard Wood)[78]
external flow
5.6
More than 10 % reduction.
application
Other Design Modifications [ Ref 99]
Following are some of the Design modifications which influence the Drag.

Lowering the vehicle height by 30 mm – ( App – 5 % )

Smooth wheel covers – ( -1 to -3 % )

Wide tyres – (+ 2 to + 4 % )

Windows flush with exteriors – ( App -1 % )

Sealing body gaps – ( -2 to -5 % )

Underbody panels /trays – ( -1 to -7 % )
88

Concealed headlamps – ( + 3 to +10 % )

Outside rearview mirrors – ( + 2 to +5 % )

Air through radiator and engine compartment – ( 4 to 14 % )

Brake cooling devices – ( +2 to +5 % )

Interior ventilation – ( App +1 % )

Open windows – ( App 5 % )

Open sunroof – ( App +2 % )

Roof mounted surf board rack – ( +40 % )
5.7
Design Stage Measures
Following are some of the Design measures which can be incorporated during the
Design stage.

Weight reduction

Frontal Area – Minimum

Other prominent areas- Radiator grill,Wind shield

Location of air inlets / outlets

Shortest transverse span

Largest possible side radii

Slight nose down of the undertray

The stagnation point

Closed integral body structure

Side windows sloped inwards

Front shape – Wedge or Rounded

Spoilers /Stabilizer fins, Air dams, Vents.

Multielement airfoils / Gurney flaps

Laminar flow control for – Reduction of skin friction coefficient

Use of compliant walls ( Artificial Dolphin skin )
89

Riblets
Other observations based on the experimental work done are as under
In the present work mainly the external flow, effect of spoilers and effect of
differing turbulent closure schemes is analysed.
5.8. Analysis of Hatchback, with Front spoiler on Hatchback , Sedan
(three box ) & with Rear spoiler on sedan
The following table gives modelwise drag.
Table - II
Drag
k-epsilon
RNG K-epsilon
k-Omega
Model-1
0.63
0.40
0.89
Model-2
0.76
0.41
1.00
Model-3
.048
0.24
0.70
Model-4
0.52
0.29
0.56
From the above table it is clearly seen that the sedan (Three box version, Model 3
and 4) has the minimum Drag. Also it is noticed that by adding a spoiler either
front or rear the Drag value increases. There is also variation in the Drag with
differing Turbulence models.
 
Turbulence model (Jones & Launder) is the most popular model used by the
CFD community .However the predictions made by this model are on the higher
side as compared to RNG    ( Yakhot & Orszag ) predictions. The reason being
the standard wall function which is based on constant pressure hypothesis and
90
therefore modeling of eddy viscosity needs corrections .These corrections are
found in RNG    model which has a low Reynold’s version for near wall
stresses & it uses the usual wall law at higher Reynold’s numbers .Also it is
observed that this turbulence model does not predict the separation accurately as it
is ideally not suited to complex geometry .k-ω model predicts higher values of
Drag compared to others .i.e. Lower base pressures.
In general the Square back (Hatchback) design suffers from a large recirculation
region behind the body due to flow separation, which results in higher drag
coefficients owing to lower base pressures at the rear, as seen in the graphic image.
In case of Fast back (Hatchback) designs the flow is complex due to interaction of
the longitudinal vortices and separation in the rear. The slant angle of the fast back
determines the characteristics of the flow & therefore the drag.
The Notchback design of car bodies refers to the three box version which has a
boat tail ramp to accommodate streamlines behind the body and minimal shedding
of vortices and thus avoid separation. Such designs have a low value of drag
coefficient owing to high pressure recovery at the base. This version is said to be
the optimized version of all.
Following table III shows drag values at three strategic locations for models 1 -4
with k-ε model.
91
Table-III Drag Coefficient Modelwise - FLUENT
Model 1
Model 2
Model
3
- Model 4 -
Actual
With additional 3box
3-box
(existing)
front spoiler
spoiler
Notchback
Hatchback
with
(Notchback)
Drag
0.62 / 0.36 / 0.71 / 0.38 / 1.2
0.40 / 0.35 / 0.43 /0.50 /0.64
coefficient
0.92
0.69
(
Average
C
D
)
Average = 0.76
=
Average
0.63
Average = 0.52
=
0.48
Table –IV Drag values found for the four models with different
Turbulence models.
Turbulence Model
Car Model Drag ( Max / Min )
K-ε , Standard WF
1
0.62 / 0.36 / 0.92
0.63
2
0.71 / 0.38 / 1.2
0.76
3
0.40 / 0.35 / 0.69
0.48
4
0.43 / 0.5 / 0.640
0.52
1
0.35/0.26/0.59
0.40
2
0.41/0.24/0.59
0.41
3
0.18/0.31
0.24
4
0.11/0.27/0.5
0.29
K-ω , Standard WF 1
0.70/0.55/1.28
0.84
2
0.95/0.39/1.69
1.0
3
0.62/0.54/0.95
0.70
4
0.16/0.63/0.90
0.56
RNG K-ε
92
Average Drag
rear
5.9
Wind Tunnel experiment of pressure coefficient distribution & CFD
simulation, by fine tuning the flow regimes .Computation of Pressure &
Viscous Drag.
The results of Wind Tunnel expt for Pressure Coefficient and Drag measurement
from CFD are as under .Results are already discussed in Methodology.
Table – V
Drag from CFD & Pressure coefficient from
Experiment
Velocity(m/s)
Pr drag
Viscous drag
Total drag
C
9.31
0.62
0.41
1.03
1.1
12.25
0.47
0.56
1.03
1.18
15.10
0.25
0.55
0.80
0.70
The correlations obtained are as under
Table VI Correlations
Sr No Parameter
Correlation
1
Y=-0.28x 2 +0.92x+0.46
Pressure Coefficient
R² = 1
2
Total Drag
y=0.15x 2 -0.662x+1.595
R² = 0.696
3
Viscous Drag
y=0.017x 2 +0.019x+0.392
R² = 0.884
4
Pressure Drag
y=0.132x 2 -0.681x+1.202
R² = 0.762
93
P
The following table VII shows the literature values of pressure coefficient.
Table – VII
Review of Pressure Coefficients
Sr
Author
Details
Remarks about Cp
No
1
2
Mat Ramnofors,
Basic car
-1.0 to + 1.0
1996 [59]
shape Volvo
Stagnation value = 1.032 , Base value =
ECC
0.116
Norbert Grun
Basic car
Found that (Asep / Aref =0.5 for fastbacks
,1996 [65]
shape
& 1.0 for vans) Also Cp decreases as free
stream velocity increases.
3
4
B.Basara ,2001 , Basic car
Compared Numerical simulation ( k-ε , &
[9]
shape
RSM) results with exptl. Cp = + 0.5 to -1.2
Andrew
Morel Body
+1.0 to -1.5 , For slant angle 5 0 No
Anagnost , 1997
separation.For slant angles 30 0 & 35 0
,[6]
separation.
From pressure coefficient distribution areas of positive & negative pressures can be
located & the force report function of Fluent gives break up of pressure & viscous
Drag. i.e. Total Drag = Pressure Drag + Viscous Drag.
The wake analysis is also done from velocity vector diagrams which indicate
downwash, and therefore the car is stable and pressure loss at the base is moderate.
Tools based on digital processing of the information resulting from wall flowvisualisations and tomographies of total pressures in the wake , to validate and
quantify results which were otherwise based on visual analysis have been
94
instrumental in providing the experimentalist with new interpretation and d ecision
making methods. Francis Chometon , Patrick Gillieron (1996)[24]
5.10 Hatchback Versus Sedan Analysis
Table VIII ( HATCHBACK ) Breakup ( Total Drag = Pressure Drag + Viscous
Drag ) from CFD & validated with Ahmed et al and T.Morel expt values
Velocit
Pressure
Pressur
y m/s
force ( N) e
Viscous
Viscou
force (N)
s drag force ( N) l
et al
(D F )
( Exptl
drag(D P
Total
Tota
drag
)
Ahmed
( D= )
DP
+
DF )
T.More
l
( exptl )
27.00
1428220.
0.62
930298.0
0.41
0
36.00
1084201.
2358518.
1.03
0
0.47
0
1297746.
0.56
6
2381947.
0.378
1.03
/0.260
High /
4
45.00
578075.0
0.25
125407,5
0.55
677332.5
0.80
Low
60.00
1444793.
0.63
1770340.
0.77
3215133.
1.40
0.41
1
5
6
95
Table IX ( SEDAN ) Breakup ( Total Drag = Pressure Drag + Viscous Drag )
from CFD & validated with Ahmed et al and T.Morel expt values
Velocit
Pressure
Pressur
y m/s
force ( N) e
Viscous
Viscou
force (N)
drag(D P
Total
Tota
Ahmed
s drag force ( N)
l
et al
(D F )
drag
(Exptl )
(D=
T.More
)
DP
+
DF )
27.00
561505.6
0.18
619451.4
0
36.00
613300.0
5
0.20
629972.0
614830.4
0.22
0
0.20
0.378
0.41
1290121.4
0.24
1
1343121.0
/0.260
High /
0.42
0
728290.6
0
1251365.9
( exptl )
0.38
0
660149.0
0
60.00
0.21
0
0.21
1180957.1
0
638065.8
0
45.00
0.20
l
Low
0.41
0.44
0
The above tables VIII & IX give drag values computed from Fluent and also
reference values from literature for comparison.
The important conclusion which can be drawn is that the drag of Sedan (Three box
version) is lower than Hatchback (Two box versions) for the same car front, which
is ascertained from values computed.
The Hatchback has large recirculation of vortices in the separated / wake region in
the rear & therefore gives rise to additional pressure drag. The Sedan or the three
box version has a boat tail ramp which avoids separation and therefore the pressure
96
drag reduces. The Sedan version is said to be an optimized version. The Results are
discussed in Methodology.
97
Chapter 6 Optimization
6.1
Introduction to Simulation based Optimization
Unlike streamlined bodies with attached flows, the flows over automobile are
complex. The key feature of the flowfield around an automobile are the regions of
separated flow/wakes. Even simple basic vehicle configuration free of all add ons
and having smooth surfaces generate a variety of quasi two-dimensional and fully
three dimensional regions of separated flow. The major contribution to the drag of
a vehicle stems from the pressure drag which is a consequence of flow separation
& it makes the drag prediction difficult Also this drag scales in a different way
with Reynold’s number & Mach number defining the flow regimes. It is also
difficult to establish complex interrelation between wake structure, pressure
distribution of body surface, drag and geometry as the flow regime to which the
road vehicle is subjected is turbulent which is nonlinear & stochastic. Extensive
research is going on in the field of automobile aerodynamics, especially of cars,
and there is a clear indication of the ever increasing popu larity of numerical
techniques and CAE tools such as CFD to predict automobile characteristics in
comparison to the typical wind tunnel test methods. With the rapid progress of
computer hardware and software components, these simulation methods will
become more predictable and accurate and may replace wind tunnel testing in
future.
The complete expression for drag is given by
D  0.5C D AV
2
Drag = f(Shape, Velocity of wind +Velocity of vehicle ,
Rear slant angle )
From the above expression it is clear that the drag depends on the frontal area, &
velocities. To be more specific the drag is a shape function defined by Bernstein
polynomial for Bezier curves as given below The Bezier curve P(t) based on (L+1)
points P 0 ,P 1 ,P 2 -----P L is given by
98
L
P t   
k 0
p B t 
L
K
K
Where the blending function is
L
B  t    K  1  t  t
L K
L
K
K
and ( L / K ) is the binomial coefficient function, the number of ways of choosing
K items from a collection of L items.
L!
L
 
 K  K ! L  K  !
for L  K or 0 otherwise.
Where P  t  is a position vector and
t is any single parameter which can take
values between k  0 to L .
On the same lines two sets of orthogonal Bezier curves can be used to design an
object surface by specifying an input mesh of control points. The parametric vector
function for the Bezier surface is formed as the Cartesian product of Bezier
blending functions.
M
L
P  t , s    P j ,k B j ,m  s  B k , L  t 
j 0 k 0
With
P
j ,k
specifying the location of the  M  1 by  L  1 control points .Where t
and s are the parameters which can take values from k  0 to L & j  0 to M
respectively.
The mesh of the car surface which is a set of Bezier points and a connectivity
matrix is completely determined through a deterministic spline algorithm.
Therefore to change the frontal area or the shape of the car the Bezier points need
to be displaced in a prescribed way to alter the geometry
. G.Lombardi,F.
Beaux,S . Carmassi [25].This is possible only with state of the art CAE tools like
simulation based optimization modules Neverthless it is impossible to design
99
adaptive car shape/surface mechanism to minimise drag in the transient wind
conditions .Therefore for automotive applications simplified/modified Ahmed body
(Simplified car body) is used as reference to study and investigate the flow &
optimization of drag.
The following block diagram Fig 1 . shows how simulation based optimization loop
works with the help of an aerodynamic solver and an optimizer module .With the
help of library of acceptable variant surface shapes the optimized can be found out.
100
IGES format file
Wake definition
Wake node
Mesh generation
Aerodynamic
SOLVER
GEOMETRICAL
CHANGES
FAIL
Constraint
definitioin
CONSTRAINTS
CHECK
PARTS
INTERNAL
FILE
REBUILDING
Cost
function
evaluation
OPTIMIZER
Human evaluation
Fig 1 THE OPTIMIZATION
LOOP
101
Chapter 7 Present Status
7.1
Wind Tunnels and CFD
All major Automotive manufacturers in the world have wind tunnels for
determining the Aerodynamic characteristics of vehicles. However wind tunnel
procedures are cumbersome owing to complexities of measurements and hardware
testing involved. Therefore many of the companies are using computer simulations
using validated CFD codes. The problem definition is given to various vendors &
the results are compared for optimum performance.
The last four dacades have witnessed an exponential growth in the speed of
arithmetic operations which can be performed on the computers .Therefore
numerical solution of PD’S with robust numerical schemes and Turbulence
closures is possible .Turbulence models like K-ε , RNG K-ε , K-ω , SST K-ω ,
RSM , DNS (Direct Numerical simulation) & LES ( Large Eddy simulation ) have
been successfully used to track the flow physics invovlved . However there are
hardware limitations as the number of operations grows as (Re) 3 . The complex
domains can be mapped by unstructured mesh generation which is known as
numerical grid.
New cars like Opel Astra , Honda civic , Honda City , Toyota Altis have been able
to achieve a drag coefficient of C D = 0.25 App .which is far better than the values
of C D = 0.45 / 0.50 of old cars of sixties.
It is observed that all these cars are Notchback versions, however hatchback
versions are more popular even though these have little higher values of drag. The
obvious reason is their maneuverability in traffic.
102
The use of CFD to predict internal and external flows has risen dramatically in the
past few years. The availability of workstations together with efficient solution
algorithms & sophisticated pre & post processing facilities enable the use of CFD
codes for development and design tasks of industry.
Following are the advantages of CFD over experiment based approaches for fluid
systems designs.

Substantial reduction of lead time & cost of new designs.

Ability to study systems where controlled experiments are difficult or
impossible to perform, (Very large systems.)

Ability to study the systems under hazardous conditions at and beyond their
normal performance limits. ( Safety & accident related issues)

Practically unlimited level of detail of results.
CFD Codes can produce very large volumes of results at virtually no additional
costs.
CFD Technology can be integrated into design, R & D and Manufacture .These
CFD codes are structured around numerical algorithms that can tackle fluid flow
problem. Efforts are under way to develop CFD codes having self a daptive meshing
capability.
103
Chapter 8
Future Scope
8.1 Wind Tunnel and CFD
As discussed in the earlier chapter, use of CFD has become popular with
availability of sophisticated and fast computational facilities.
The availability of high end computing and advanced manufacturing techniques in
future will help development of vehicles to be faster.
The use of CFD to predict internal and external flows has risen dramatically in the
past few years. The availability of workstations together wit h efficient solution
algorithms & sophisticated pre & post processing facilities enable the use of CFD
codes for development and design tasks of industry.
Following are the advantages of CFD over experiment based approaches for fluid
systems designs.

Substantial reduction of lead time & cost of new designs.

Ability to study systems where controlled experiments are difficult or
impossible to perform, (Very large systems.)

Ability to study the systems under hazardous conditions at and beyond their
normal performance limits. ( Safety & accident related issues)

Practically unlimited level of detail of results.
CFD Codes can produce very large volumes of results at virtually no additional
costs. CFD Technology can be integrated into design , R & D and Manufactu re
.These CFD codes are structured around numerical algorithms that can tackle fluid
104
flow problem .Efforts are under way to develop CFD codes having self adaptive
meshing capability.
8.2
Digital Physics
“ Digital Physics” a descrete particle method has been used to study the flow over
Ahmed / Morel body in the ground proximity .Digital Physics extends to allow
application of the method to high Reynold’s Number flows over external
geometries .The lattice gas automata ( LGA) method can be viewed as a descr ete
version of kinetic theory for a dense gas. The mean beheaviour of microscopc
model of a digital fluid can be shown rigorously to agree with the macroscopic
governing equations of fluid dynamics, the Navier-Stoke’s equations .The motion
of particles is simulated on a face centred hyper cubic lattice (FCHC) which
ensures macroscopic isotropy. Andrew Anagnost (1997) [6]
Han (1996)[82] used K-ε model to compute flow over Ahmed body .The deviation
between the predicted and measured drag was 30 % for the slant angles between 0
to 30 0 . However the computational approach completely failed to predict the
phenomena of vortex breakdown and formation of large separation bubble for slant
angles beyond 30 0 . There was also an extensive experimental & computational
effort at MIRA to investigate the flow over Ahmed body. They obtained excellent
experimental results which were reproduced using CFD codes. Drag coefficients
were qualitatively predicted but the values were 30 % high in the sub critical &
critical regimes .Several mesh resolutions were used with limited success.
Therefore the results showed strong dependence on grid structures and questioned
the generality of the scheme.
105
Therefore the Digital Physics has demonstrated its capability to simulate high
Reynold’s Number external fluid flows.
The scope for use of these technologies and initiatives required to reduce energy
consumption in overcoming aerodynamic drag of road vehicles has already been
discussed in scope in the begining.
8.3 Digital Processing / Reconstitution
Tools based on digital processing of the information resulting from wall flow visualisations and tomographies of total pressures in the wake, to validate and
quantify results which were otherwise based on visual analysis have been
instrumental in providing the experimentalist with new interpretation and decision
making methods. Francis Chometon, Patrick Gillieron (1996)[24]
106
Chapter 9 Recommendations
9.1 Idealisation of Flow Over Hatchbacks – Equivalence to Half Rankine Oval
& Notchbacks – Equivalence to Doublets.
Theoretical interpretation of flow over “Hatchbacks” has been explained as
minimum pressure drag is evident in this case .This theoretical aspect can be
leveraged in Deign of Hatchbacks, which are gaining popularity nowadays.
A geometry based view point is to distinguish the contributions upstream and
downstream of the maximum cross section of a vehicle i.e. forebody drag C DF &
afterbody drag C DA .
In the ideal case of inviscid flow i.e. potential flow the suction forces on fore and
after body cancel exactly and the total drag vanishes , independent of the body’s
shape .Viscous effects in real fluids disturb this balance and even without
separation the displacement effect of the boundary layer causes a lower pressure
level on the afterbody , leading to a resulting force pointing downstream i.e.
friction induced pressure drag .If separation can be avoided on the forebody then
the theoretical lower limit of forebody drag is nearly reached , because boundary
layer displacement effects are very small in this region .Independent of geometry
details the forebody pressure drag depends on only the length -diameter ratio of the
whole body and is always
C
DF , P
≤ 0. The possible maximum of
C
DF , P
= 0 is
reached for semiinfinite bodies.
On road vehicles which are bluff bodies
massive separation occurs on the
afterbody and leads to a drastic deviation of the pressure distribution compared to
inviscid flow, also upstream of separation .The forebody drag is also affected by
107
separation , because the wake increases the effective length-diameter ratio towards,
a semiinfinite body.
A Semi infinite body or Half Rankine Oval which is theoretically assumed to have
formed around the vehicle body is as shown in the Fig.1. below in which the
extended body shape is also shown.
Fig 1. Half Rankine Oval around the car body .
It is called half body because it has only the leading point and it trails to infinity at
the downstream end .As shown in the above figure it is a combination of plane
source and uniform flow.
108
The plane half body is described by dividing the streamlines .Where  is stream
function & q is the source strength.
q
2
q q
Uy 

2 2
Or
 
 
q 1  

y  rSin  
2U
At
q
2U

q
  ,y 
2
4U
  , y  0
  0, y max 

3
q
,y 
2
4U
Therefore velocity component anywhere,
1 
q
 UCos 
r 
2r
u  USin
ur 
And the resultant velocity,
u res  u r  u
2
2
These components vanish at stagnation point .Therefore equating the radial and
tangential components to zero.
109
ur  0
Or
q
0
2r
q
rCos 
2U
i.e.
UCos 
x
q
, Also
U
u  0
Or
USin  0
Where
  0,  , y  0
 q 
,0  Which is the leading point of the half
 2U 
Therefore the stagnation point is 
body.
Also the position of the maximum velocity on half body is found at
  67 0
and
  67 0
These values are obtained by substituting r from equation
 
q 1  

y  rSin  
2U
inequation
u res  u r  u
2
2
& Setting
u res
0

Norburt Grun (1996) [65] Explained the equivalence of Doublets and vorticity
associated with separation zones in cars on the aft side .Also included in literature
review.
110
In the separation zone there is formation of free shear layer which contains
vorticity & can be compared with a doublet for determining boundary of the
flowfield.
111
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