final report-desktop

STUDY OF UNDERBODY AERODYNAMICS ON SPORTS CAR

DEPARTMENT OF MECHANICAL ENGINEERING, MIT MYSORE.

CHAPTER-1

Introduction

In earlier years study of aerodynamics had primarily been on the upper surface of the car, this

provided a certain improvement but wasn’t able to completely minimize the drag. Thus study

of underbody aerodynamics gained momentum. Due to increasing demand for higher

performance with lower emission in recent times, underbody aerodynamics of cars are playing

a crucial role in improving the performance characteristics. This trend is seen in all major sport

cars, and many studies have been conducted on the underbody aerodynamic characteristics of

these cars.

In this chapter the basic concepts of the study and the input data for the analysis of the models

are presented.

1.1 Aerodynamics

Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly

when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas

dynamics with much theory shared between them. Aerodynamics is often used synonymously

with gas dynamics, with the difference being that gas dynamics apply to all gases.

Understanding the motion of air around an object enables the calculation of forces and moment

acting on the object. Typical properties calculated for a flow field include velocity, pressure,

density and temperature as a function of position and time by defining a control volume around

the flow field. Aerodynamic problems can be identified in a number of ways, where external

aerodynamics is the study of flow around solid objects of various shapes, and internal

aerodynamics is the study of flow through passages in solid objects. Aerodynamic forces

created by the relative motion of the vehicle are drag force, lift force and down force which

produces noise by the air flowing around the car body. This air flowing within the car’s body

is used for cooling the engine. Influence of drag and lift are the important parameters to study

the aerodynamics of the cars.

Drag is the aerodynamic force that is opposite to the velocity of an object moving through air

or any other fluid. Its size is proportional to the speed differential between air and the solid

object. Drag comes in various forms, one of them being friction drag which is the result of the

friction of the solid molecules against air molecules in their boundary layer. Friction and its



drag depend on the fluid and the solid properties. Some of the different shapes of the geometry

which shows corresponding value of drag coefficient are given below.

Fig 1.1 Drag coefficient values of different shapes

The amount of drag that a certain object generates in airflow is quantified in a drag coefficient.

This coefficient expresses the ratio of the drag force to the force produced by the dynamic

pressure times the area. Therefore, cd=1 denotes that all air flowing onto the object will be

stopped while a theoretical 0 is a perfectly clean air stream. At relatively high speeds of high

Reynolds number (Re> 1000) the aerodynamic drag force can be calculated using the formula

below.

Cd=𝟐𝑭𝒅

𝛒𝒗𝟐𝑨

Where

Fd = drag force

ρ = density of the air

v2= speed of the object relative to the fluid (m/s)

A = reference surface area

Cd= drag coefficient

Lift is the component of the pressure and wall shear force which acts normal to the moving

body. The pressure difference between the top and bottom surface of the object generate an



upward force that tends to lift. For the slender bodies such as wings, the shear force acts nearly

parallel to the flow direction. Thus it contributes that, lift is small. The lift force depends on

the density of the fluid, the upstream velocity, the size, shape and orientation of the body. It is

found convenient to work with appropriate dimensionless numbers that present the drag and

lift characteristics of the body. The aerodynamic lift force is defined by formula

CL=𝟐𝐹𝒍

𝛒𝒗𝟐𝐀

Where,

A= frontal area of the body

½ρv2=dynamic pressure

FL= lift force

1.2 Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical

methods and algorithms to solve and analyse the problems that involve fluid flows.The analysis

of system is associated by means of computer based simulation.

The Industrial and Non-Industrial application areas:

Aerodynamics of aircraft and vehicles: lift and drag.

Power plant: combustion in IC engines and gas turbines.

Turbo machinery: flows inside rotating passages, diffusers, propeller etc…

Electrical and electronic engineering: cooling of equipment including microcircuits.

Chemical process engineering: mixing and separation, polymer molding

Marine engineering: loads on offshore structures.

Environmental engineering: distribution of pollutants and effluents.

Biomedical engineering: blood flows through arteries and veins.



1.3 Main elements of CFD

Pre-processor

Solver

Post-processor

These three modules constitute the core of CFD. The steps involved are briefed in Fig.1.3,

showing its main functions and interconnectivity with other modules.

1.3.1 Preprocessor

It consists of, input of a flow problem to a CFD program by means of an operator-friendly

interface. The subsequent transformation of this input will be in suitable form for the use of

solver. The solution to a flow problem is defined at nodes instead of each cell. The accuracy of

a CFD solution is governed by the number of cells in the grid which leads to accurate solutions.

Both accuracy of a solution and its cost in terms of necessary computer hardware and

calculation time are dependent on the fineness of the grid. Other functions in the pre-processing

stage include specifying of the boundary conditions at various locations in the geometry and

specifying properties for the materials involved.

The user activities at the preprocessing stage involve:

Definition of the geometry of region of interests, the computational domain.

The sub-division of the domain includes a number of smaller, non-overlapping, sub-

domains of grid cells.

Selection of the physical and chemical phenomena that need to be modeled.

Definition of fluid properties.

Specification of appropriate boundary conditions at cells which coincide with the

domain boundary.



1.3.2 Solver

In the solver stage, the transport equations of mass, momentum and energy are solved with

supporting physical models in the background. Also, the solution is initialized by specifying

the convergence criteria, how the solution needs to be monitored, and also by the method in

which the solution is controlled. In outline the numerical methods that form the basis of the

solver perform the following steps.

Approximation of the unknown flow variables by means of simple functions.

Discretization by substitution of the approximations into the governing flow equations

and subsequent mathematical manipulations.

Solution of the algebraic equations.

1.3.3 Post processor

It is one which consists of different visualization techniques which allows the user to read the

analyzed data in different forms.

Domain geometry and grid display

Vector plots

Line and shaded contour plots

2D and 3D Surface plots

Particle tracking

Color post script output.

These variables can be probed at a particular location in areas of interest. All these

features make post-processing and there by CFD very useful



Fig 1.2 Shows main elements of CFD

1.4 Different turbulence models

This provides theoretical background about the turbulence models available in Ansys (fluent)

which provides the following choices of turbulence models:

k-ϵ models

Standard k-ϵ model

Renormalization-group (RNG) k-ϵmodel

Realizable k-ϵ model

k-ω models

Standard k-ω model

Shear-stress transport (SST) k-ω model

v2-f model (add-on)

Reynolds stress models (RSM)

Linear pressure-strain RSM model

Quadratic pressure-strain RSM model

Low-Re stress-omega RSM model

Detached eddy simulation (DES) model, which includes one of the following RANS

models



Transition k-kl-ω model

Transition SST model

Spalart-Allmaras RANS model

Realizable k-ϵ RANS model

SST k-ϵ RANS model

Large eddy simulation (LES) model, which includes one of the following sub- scale

models

Smagorinsky-Lilly sub grid-scale model

WALE sub grid-scale model

Dynamic Smagorinsky model

Kinetic-energy transport sub grid-scale model

The k-Є Models which we use for the analysis are explained below

1.4.1 Standard k-Є Model

The simplest “complete models” of turbulence are the two-equation models in which the

solution of two separate transport equations allows the turbulent velocity and length scales to

be independently determined. The standard k-Є model falls within this class of models and has

become the workhouse of practical engineering flow calculations in the time since it was

proposed by Launder and Spalding. Robustness, economy, and reasonable accuracy for a wide

range of turbulent flows explain its popularity in industrial flow and heat transfer simulations.

It is a semi-empirical model, and the derivation of the model equations relies on phenomenon

logical considerations and empiricism. As the strengths and weaknesses of the standard k-Є

model have become known, improvements have been made to the model to improve its

performance. Two of these variants are available: the RNG k-Є model and the realizable k-Є

model. The standard k-Є model is a semi-empirical model based on model transport equations

for the turbulence kinetic energy (k) and its dissipation rate (Є).

1.4.2 RNG k-Є Model

The RNG k-Є model was derived using a rigorous statistical technique (called

renormalization group theory). It is similar in form to the standard k-Є model, but includes the

following refinements:

The RNG model has an additional term in its Є equation that significantly improves the

accuracy for rapidly strained flows.

The effect of swirl on turbulence is included in the RNG model, enhancing accuracy

for swirling flows.



The RNG theory provides an analytical formula for turbulent Prandtl numbers, while

the standard k-Є model uses user-specified, constant values.

While the standard k-Є model is a high-Reynolds-number model, the RNG theory

provides an analytically-derived differential formula for effective viscosity that

accounts for low-Reynolds-number effects. Effective use of this feature does, however,

depend on an appropriate treatment of the near-wall region.

These features make the RNG k-Є model more accurate and reliable for a wider class of flows

than the standard k-Є model. The RNG-based k-Є turbulence model is derived from the

instantaneous Navies-Stokes equations, using a mathematical technique called renormalization

group methods. The analytical derivation results in a model with constants different from those

in the standard k-Є model, additional terms and functions in the transport equations for k and

Є. A more comprehensive description of RNG theory and its application to turbulence can be

found.

1.4.3 Realizable k-Є Model

The realizable k-Є model is a relatively recent development and differs from the standard k-Є

model in two important ways:

A new transport equation for the dissipation rate, Є, has been derived from an exact

equation for the transport of the mean-square velocity fluctuation.

The term realizable means that the model satisfies certain mathematical constraints on the

Reynolds stresses, consistent with the physics of turbulent flows. Neither the standard k-Є

model nor the RNG k-Є model is realizable. An immediate benefit of the realizable k-Є model

is that it more accurately predicts the spreading rate of both planar and round jets. It is also

likely to provide superior performance for flows involving rotation, boundary layers under

strong adverse pressure gradients, separation, and recirculation.

1.5 Limitations of CFD

CFD solutions rely upon physical models of real world processes.

Solving equations on a computer invariably introduces numerical errors.

Truncation errors due to approximation in the numerical models.

Round-off errors due to finite word size available on the computer.

The accuracy of the CFD solution depends heavily upon the initial or boundary

conditions provided to numerical model.



1.6 Diffuser

A diffuser is a shaped section of the car underbody which improves the car's aerodynamic

properties by enhancing the transition between the high-velocity airflow underneath the car and

the much slower free stream airflow of the ambient atmosphere. It is a design that is installed

under the car at the rear and is considered as a part of underbody tray. This increases the area

gradually at some angle and tends to bring air back to its original velocity at the time of exit. It

works by providing a space for the underbody airflow to decelerate and expand so that it does

not cause excessive flow separation and drag by providing a degree of "wake infill" or more

accurately, a pressure recovery. The diffuser itself accelerates the flow in front of it which helps

to generate downforce. In the diffuser, the cross-section area increases, a bigger area will

decrease the velocity of the fluid and increase the static pressure. A high static pressure

recovery in the diffuser will lead to a higher base pressure. There are three non-dimensional

parameter that affect the properties of a diffuser, the area ratio, the non-dimensional diffuser

length and the diffuser angle.

Fig 1.3 Shows velocity profile of diffuser

Area ratio: h2 / h1

Non-dimensional diffuser length: N

Diffuser angle: θ

The shape of the velocity profile in above figure depends on the underbody’s proximity to the

ground as well as the roughness and the length of the entry section.



CHAPTER-2

Literature Review

The literature review provides background information on issues to be considered in this work

and to emphasize the relevance of the present study.

Aerodynamic analysis of drag reduction devices on the underbody for SAAB 9-3 was

conducted by Johan Levin and Rikardrigdal [1]. The main objective of study is to investigate

the possibility to increase the base pressure and reduce the drag of the vehicles SAAB9-3 sports

sedan and SAAB9-3 sports wagon by designing underbody shapes which is carried out using

commercial CFD codes. The simulation for sports sedan at diffuser angle 8° shows that

reduction in lift force has been achieved as well as reduction in drag force. Similarly for the

drag, result for sports wagon diffuser angle 5°, shows that it had a higher Cd value than the

SAAB9-3 sports sedan model. So it is concluded that flat panels placed over the underbody

together with a diffuser with a sloped angle of 8° showed the best improvement of the sedan

model SAAB9-3.

Xingjun Hu et al [2], Studied the influence of the diffuser angle which is investigated without

separator and the end plates with different diffuser angle varying from 0o, 30, 60, 9.80 and 120

respectively. The numerical simulation was done in the commercial code fluent by choosing

K-epsilon model. By simulation it is seen that with the increase in diffuser angle, a negative

pressure is generated at the underbody interface and the region of the negative pressure become

large and larger. When diffuser angle is changed to 9.8° there is no positive pressure disturbing

at the edge of underbody which is an appropriate diffuser angle at which the drag co efficient

of sedan has a minimum value and concluded that the total aerodynamic drag co-efficient of

sedan first increases and then decreases with increase in diffuser angle and also the lift co-

efficient decreases as the diffuser angle is increased.

Flow and turbulent structures around simplified car models was carried by D.E.Algure et al

[3]. The aim is to study different Large Eddy Simulation models as well as to show their

capabilities of capturing the large scale turbulent flow structures in car-like bodies using

relative coarse grid. The flow around two model car geometries, the Ahmed and the Asmo cars

is simulated. Models are used to study the flow in detail and compare the structures found in

both geometries. When comparing the results obtained in the Ahmed geometry with the

experimental results, it can be seen that the arrangement in the slanted back is acceptable.



Considering the coarse meshes used the rear wake shows good result when compared to the

experimental data. The results of the Asmo car are also in quite good agreement with

experimental results. Though they are not as accurate as results from the literature with finer

meshes, comparisons here presented using such coarse grids are useful to evaluate the potential

of coarse Large Eddy simulations.

Angel Huminic et al [4], presents result concerning the flow around the Ahmed body fitted

with a rear underbody diffuser without end plates to reveal the influence of the underbody

geometry shaped as a Venturi nozzle on the main aerodynamic characteristics. The study is

performed for different geometrical configurations of the underbody. Radius of the front

section length and the angle of the diffuser being the parameters which are varied based on a

theoretical approach came into new aspects concerning the flow around the Ahmed reference

model for 35° angle of the back fitted with a simple rear underbody diffuser. Thus, an

optimization of the flow beneath bodies in ground effect can be performed by dividing, shaped

as a venture nozzle, into the components that permit computational coefficients of aerodynamic

resistance. This approach helps to evaluate the underbody to total drag.

Effect of a moving belt for pressure on the underbody of a competition vehicle was conducted

by Satoshi Yamazaki et.al [5]. Model was examined in a wind tunnel by using two ground

simulation methods, the moving belt and the fixed ground method. In case of a competition

vehicle which has an extremely small ground clearance, the effect of the moving belt was

confirmed that it increases the negative pressure of the underbody surface. By competition

which is cleared that the down force is larger in case of using the moving belt method than in

case of using the fixed ground method.

Ahmed and Chacko [6], focused on the optimization of the aerodynamics with means of some

external tools. Old fashioned cars have been subjected and optimized and the tools used have

been set to their optimum size, shape and angle to achieve the best. Then the drag co efficient

and lift co-efficient has been investigated for better performance. By simulating the domain

with no diffuser drag co-efficient shows positive value which represents the drag force in an

opposite direction to the motion of the car whereas for lift coefficient it represents the vertically

upward acting force. When a diffuser is installed under the car at the rear end it is considered

as a part of underbody tray and the low pressure region is created underneath the car body. It

was found that lift coefficient were acting vertically downward resembles the negative lift of

the body.



Sinisa Krajnovic and Lars Davidson [7], studied the effect of a moving floor on the flow around

a simplified car with typical fastback geometry. Two large-eddy simulations of the flows with

stationary and moving floors are made and both instantaneous and time-averaged results are

compared. It is found that the floor motion reduces the drag by 8% and lift by 16%. Changes

in the qualitative picture of the flow are limited to the flow near the floor and on the slanted

surface of the body.

Zulfaa Mohamed-Kassim and Antonio Filippone [8], in this numerical study the fuel-saving

potentials of drag-reducing devices retrofitted on heavy vehicles are analyzed. Realistic on-

road operations are taken into account by simulating typical driving routes on long-haul and

urban distributions variations in vehicle weight are also considered. Results show that the

performance of these aerodynamic devices depend both on their functions and how the vehicles

are operated. Vehicles on long-haul routes generally save twice as much as the fuel that is

driven in urban areas. The fuel reductions from using selected devices individually on a large

truck ranges from less than 1% to almost 9%.

V.J. Modi et al [9], present results of an organized and extensive wind tunnel test-program,

complemented by flow visualization and full-scale road tests, aimed at assessing the

effectiveness of a boundary-layer control procedure for the drag reduction of a cube-van. Wind

tunnel results, obtained using a scale model, at a subcritical Reynolds number of 105, by

promoting its separation using fences reduces the pressure drag coefficient. The entirely

passive character of the procedure is quite attractive from the economic consideration as well

as the ease of implementation. The road tests with a full-size cube-van substantiated the trends

indicated by the wind tunnel data.

Upendra S. Rohatgi [10], in his study a small scale car model of length 1710 mm of General

Motor’s Sports utility vehicle was built and tested in the wind tunnel for expected wind

conditions and road clearance. Two passive devices, one of which is on the rear screen which

is a plate behind the car and other one on the rear fairing where the end of the car is

aerodynamically extended, were incorporated in the model and tested in the wind tunnel for

different wind conditions. This showed that rear screen could reduce drag up to 6.5% and rear

fairing can reduce the drag by 26%.



2.1 Objectives

The main objective of this work is to investigate the flow past underbody of 2D

geometrical car with and without diffuser, by varying the flow with different velocities

and to observe the flow characteristics (i.e., lift and drag coefficient).

The simulations are carried out by varying diffuser angles 6°, 7°,8°,9° and 10° to

observe it’s influence on the drag and lift ,and also on the wake region, this will be

carried out by using commercial CFD codes.



CHAPTER-3

3.1 Methodology

Numerical simulation of a physical problem involves approximation of the problem geometry,

choice of appropriate mathematical model and numerical solution techniques, computer

implementation of the numerical algorithm and analysis of the data generated by the

simulation. Thus, this process involves the following steps:

Modeling the geometry for the problem identified.

Selection of appropriate mathematical model for the physical problem.

Selection of suitable discretization method.

Generation of a grid, based on the problem geometry and the discretization method.

Selection of suitable solution technique to solve the system of discrete equations.

Setting up the suitable convergence criteria for iterative solution methods.

Preparation of the numerical solution for further analysis.

3.2 Validation

In order to validate the code, two different geometry have been selected

3.2.1 Validation for flow past Cylindrical Geometry

The validation for the present work is done on the flow past cylinder to validate the drag and

lift coefficient. For the validation, numerical approach is followed up with the geometry of 1m

diameter.

The computational domain defined is a rectangular area with dimensions 36m x 7m. The center

of the cylinder is placed at 5.5m from the inlet and placed midway from the top and bottom

edges. The flow studies is carried out for Reynolds number of 100

The analysis of 2-D cylindrical geometric model has been shown in Fig.3.1.



Fig 3.1 Shows geometry of cylinder

3.2.1.1 Meshing and boundary conditions

Meshing is an integral part of the computer-aided engineering simulation process. The mesh

influences the accuracy, convergence and speed of the solution. The arrangement

(Quadrilateral) provides very fine mesh in the regions near the model the capturing more detail

flow information, and a use of coarser mesh in other regions for reducing computational effort.

In this, a fine quadrilateral fine mesh is generated with nodes (173,915) and number of elements

(173,137) used for the simulation. The meshing of cylindrical geometry is as shown in below

Fig 3.2

Fig 3.2 Shows meshing of cylindrical geometry



Any prescribed quantities, such as prescribed displacements and prescribed tractions on the

boundary are called as boundary conditions. The boundary conditions are defined for inlet,

outlet, top, bottom and wall. For inlet, a velocity inlet boundary condition is assigned and the

Velocity is set as, v=0.00149m/s. For outlet, a pressure outlet boundary is defined, and the

value assigned is p=0 Pa. For top and bottom the boundary was defined as symmetry. And

finally for the wall a wall boundary with no slip condition is specified.

Regions Boundary Conditions

Inlet Velocity inlet ,v= 0.00149m/s

Outlet Pressure outlet, reference pressure p=0 Pa

Top Symmetry

Bottom Symmetry

Wall Wall, No slip

Table 3.1 Boundary condition

3.2.1.2 Inference

When fluid flows around a bluff body (cylinder), vortex shedding is in the wake of the body.

Vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows

past a bluff (as opposed to streamlined) body at certain velocities, depending on the size and

shape of the body. In this flow, vortices are created at the back of the body and detach

periodically from either side of the body. This sheet of flow is von Karman vortex sheet, which

is a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid

around blunt bodies.

A vortex street will only form at a certain range of flow velocities, specified by a range of

Reynolds numbers (Re), typically above a limiting Re value of about 90, in our case the

Reynolds number is 100 hence vortex is observed.



Fig 3.3 Shows variation in lift co-efficient of cylinder

For the CFD simulation of a circular cylinder due to the alternating Von Karman vortex sheet,

there exists variation of pressure at the rear end of the cylinder. Due to such oscillation of

values, Cl oscillation occurs and this is plotted in Fig 3.3. The Cl oscillates from the positive

extreme to the negative extreme. As stated earlier there is a variation of pressure in the rear of

the cylinder and it oscillates periodically from one extreme to the other, this can be seen for a

given instance in Fig 3.5. Here the vortex formed is in the upper portion, hence the low pressure

area in pressure contours appears towards the upper segment.

Fig 3.4 Shows variation in drag coefficient of cylinder



When the flow is affected by the alternating vortex a slight oscillation to the drag is observed,

this is due to the varying pressure drag, which is part of the total drag.

Here wave drag is zero (no shock waves), and skin friction drag is constant, thus the varying

value of pressure drag creates small variation of value of drag as observed in Fig 3.4.

Fig 3.5 Shows effect of pressure contour plot on cylinder

The flow patterns of the particles of the fluid at the end of computation can be seen in Fig 3.6

and Fig 3.7. The formation of vortex on the upper side is seen over here. Due to alternating

vortices the pattern of velocity vectors and magnitude oscillates periodically.

Fig 3.6 Shows effect of velocity contour plot on cylinder



Fig 3.7 Shows velocity streamlines flow over cylinder

3.2.2 Validation for flow past on Ahmed body

The validation for the present work is done on the Ahmed car and comparison is to be made of

Cd and Cl with the work done by Huminic A, Huminic G, & Soica, A [4] on the geometry as

shown in Fig 3.8. Validation of numerical approach is carried on the geometry of car domain

as per work.

Fig 3.8 Shows geometry of Ahmed car

The computation is performed on Ahmed body having a rear slanted upper surface of 35°, rear

diffuser angle of 9° with ground clearance of 200mm. The length and height of the car is

4166mm and 1.35m respectively. The length of the diffuser is kept to be 2000mm with the

angle as mentioned earlier. Fig 3.9 is a schematic of a generic Ahmed car.



Geometrical parameters Symbol Dimensions

Length of the car H21 4166 mm

Height of the car V29 1352 mm

Ground clearance hg 200 mm

Length of diffuser L27 2000 mm

Diffuser angle αd 9°

Upper slant angle αld 35°

Table 3.2 Geometrical parameters of Ahmed car

3.2.2.1 Meshing and Boundary conditions

In this a fine quadrilateral fine mesh is generated with nodes (222,197) and number of elements

(220,297) used for the simulation. The mesh around the Ahmed body is dense for the accuracy

of simulation.

Fig 3.9 Shows dense mesh on Ahmed body

Region Boundary Conditions

Inlet Velocity inlet ,v= 25m/s

Outlet Pressure outlet, reference pressure p=0

Top Stationary wall, No slip

Bottom Moving wall, v=25 m/s

Wall No slip

Table 3.3 Parameters of boundary conditions



A uniform and constant velocity (v=25m/s) were imposed at the inlet boundary. Same

conditions were considered for the bottom surface which represents the ground and in addition

the option ‘solid moving wall’ was activated. At outlet boundary a zero pressure condition was

imposed (p=0), no slip condition were imposed on surfaces of Ahmed body.

3.2.2.2 Inference

The influence of the diffuser on the drag and lift was studied for diffuser angle of 9o and upper

slant angle of 35o. The results of both experimental work [4] and our study were compared and

validated.

The Ahmed reference model for 35° angle of the back, fitted with a simple rear underbody

diffuser, without endplates of the lower front section. The influence of the underbody geometry

shaped as a Venturi nozzle on the main aerodynamic characteristics, lift and drag, is revealed.

The study is performed for a single geometrical configuration of the underbody.

The below fig 3.10 to fig 3.11 shows variations of lift and drag coefficient of the Ahmed body,

from fig 3.10 it can be observed that

Fig 3.10 Shows variation in lift Coefficient of Ahmed body



Fig 3.11 Shows the variation in drag coefficient of Ahmed body

Fig 3.12 Shows pressure contour plot at v=25m/s

In the pressure contour as shown in Fig 3.12, the top most surface has least pressure at the

corners of the vehicle, this is due to sudden change in geometry the flow accelerates or

decelerates. This can be seen clearly when we compare the pressure contour with the velocity

magnitude contour shown in Fig 3.13, the flow is almost static at the leading edge due to its

thicker section. The flow then moves towards the corner and accelerates over the corner, this

is due to narrowing of flow area (due to thinner boundary layer at these corners), thus increase

in velocity (continuity principle). At the trailing section of Ahmed body due to large angle of

geometry the flow separates and hence vortices are formed and a wake region is created at the

end.



Fig 3.13 Shows velocity contour plot at v=25m/s

Now a comparison of our study is done with the experimental work to validate the CFD

model, and is as follows

Results obtained from experimental work [4]:

Drag co-efficient = 0.6

Lift co-efficient = -0.5

Results obtained through validation:

Drag co-efficient = 0.6583

Lift co-efficient = -0.5614

The variation of the parameters is under 10% and hence the result is validated with

reasonable error.



3.3 Numerical Simulation of flow past on car geometry without diffuser

The numerical simulation for the car geometry under consideration is carried out for three

different velocities with three different k- 𝜀 models. The three k- 𝜀 models used for

investigation are Standard, RNG & Realizable. The geometry used for present investigation is

shown in Fig.3.14 and dimensions are shown in table 3.4

Fig 3.14 Shows car geometry without diffuser

The geometry of the car consists of different segments, it is a freeform design inspired from

popular sport cars. The dimensions of the car is length, L=4570mm, Height, H=1322mm. The

ground clearance of the vehicle is 80mm and the diffuser angle is set to 0°. Length, height

and ground clearance of the car is kept constant throughout our investigation.


Length of the car L 4570 mm

Height of the car H 1322 mm


Diffuser angle αd 0°

Table 3.4 Geometrical parameters of car

3.3.1 Meshing and boundary condition

Meshing is an integral part of the computer-aided engineering simulation process. The mesh

influences the accuracy, convergence and speed of the solution. In this, a quadrilateral fine

mesh is generated with nodes (225,451) and elements (222,460) for the simulation. For the

present condition standard k-𝜀 model is used for velocity at 20m/s (72kmph) and flow past over

the body is analyzed.



Fig 3.15 Shows mesh generation over car body


Inlet Velocity inlet ,v= 20m/s, turbulence intensity=0.5%


Top Wall, stationary wall , No slip

Bottom Moving wall ,v= 20m/s

Wall Wall, Stationary wall, No slip

Table 3.5 Boundary conditions

The boundary conditions, as specified in Table 3.5, are Inlet set as a velocity inlet with velocity,

v=20m/s. Outlet is set as a pressure outlet with reference pressure P=0. Top is specified as a

stationary wall with no slip condition. Bottom is a moving wall with velocity, v= 20m/s. Finally

wall is also a wall boundary with no slip condition. Similarly, for the different cases of

boundary conditions, inlet velocity is varied for 40m/s (144kmph) and 88m/s (320kmph). Same

condition is considered for the bottom surface which represents the ground and in addition, the

option ‘solid moving wall’ is activated.



3.3.2 Results and discussion

A diffuser angle of zero degree is maintained for all the three cases. For increasing velocities

both Cl and Cd, for our design, decreases. This trend of decrease in Cl and Cd is expected

behavior, as Cl and Cd are both inversely proportional to the square of the freestream velocity.

i.e.,

𝐶𝑑 = 𝐷

𝑞∞𝐴 𝐶𝐿 =

𝐿

𝑞∞𝐴

Where,

𝑞∞, is dynamic pressure equal to 1

2𝜌∞𝑉∞

2

𝑉∞, is freestream velocity

𝜌∞, is freestream density

𝐷, is total drag and L, total lift

Fig 3.16 Shows variation of lift Coefficient without diffuser



Fig 3.17 Shows the variation of drag coefficient without diffuser

Stagnation pressure is seen high at the front where fluid particles flow over the body, a small

recirculation is observed which is a low pressure region. The flow over the car has a steady

pressure and velocity along the underbody surface, this is due to no curvature in the geometry,

whereas the upper surface has a positive curvature. This curvature results in speeding up the

velocity over this surface, (due to smaller boundary layer and continuity principle) thus the

maximum velocity is observed at the topmost curvature in our design. Bernoulli’s principle can

be applied for the regions without unsteady flow and vortices. Thus except for the rear end of

the domain, we see an inverse ratio of pressure and velocity magnitude in Fig 3.18 and 3.19.

Fig 3.18 Shows effect of pressure contour plot on body without diffuser at v=20m/s for

standard k-𝜀 model



This trend of decrease of Cl and Cd is also seen in RNG k-ε and Realizable k-ε. The values of

Cl and Cd for different velocities and different computational models are tabulated in Tables

3.6-3.8. For zero diffuser angle the body experiences positive lift and hence at high velocities

the car may be unstable.

Fig 3.19 Shows effect of velocity contour plot on body without diffuser at v=20m/s for

standard k-𝜀 model

Fig 3.20 Shows velocity streamlines along car at v=20m/s for standard k-𝜀 model

The below table shows variation of three different velocities with increase in velocity of Cd

and decrease in Cl for different models.

Velocity(kmph) Diffuser angle(deg) Drag coefficient(Cd) Lift coefficient (Cl)

72 0 0.1973 2.2579

144 0 0.1874 2.1170

320 0 0.1771 1.9419

Table 3.6 Cd and Cl values of three velocities for Standard k-ε Model



Velocity(kmph) Diffuser angle(deg) Drag coefficient(Cd) Lift Coefficient(Cl)

72 0 0.1993 2.1646

144 0 0.1888 2.0035

320 0 0.1760 1.8365

Table 3.7 Cd and Cl values of three velocities for RNG k-ε model

Velocity(kmph) Diffuser angle(deg) Drag coefficient(Cd) Lift Coefficient(Cl)

72 0 0.2090 1.9397

144 0 0.1936 1.9595

320 0 0.1808 1.7723

Table 3.8 Cd and Cl values of three velocities for Realizable k-ε model

Fig 3.21 Shows the variations in co-efficient of lift for different k-ε models with

respect to velocity without diffuser

2.2579

2.117

1.9419

2.1646

2.0035

1.8365

1.93971.9595

1.7723

1.7

1.8

1.9

2

2.1

2.2

2.3

72 kmph 144 kmph 320 kmph

Coef

ffic

ien

t of

Lif

t(C

l)

Velocity

Coefficient of Lift v/s Velocity

Standard RNG Realizable



Fig 3.22 Shows the variations in co-efficient of drag for different k-ε models

with respect to velocity without diffuser

It is evident that from above table from table 3.6-3.8 and fig 3.21-3.22, as speed

increases the drag and lift has been significantly reduced for all the k-ε models

which an aerodynamic property i.e. lift and drag are inversely proportional also

seen that lift coefficients are positive which reduces the traction and stability of

the vehicle. Realizable k-ε model is chosen for further investigations, since the

values seen to be more practical.

0.1973

0.1874

0.1771

0.1993

0.1888

0.176

0.209

0.1936

0.1808

0.17

0.18

0.19

0.2

0.21


Co

effi

cien

t o

f D

rag(

Cd

)

Velocity

Coefficient of Drag v/s Velocity

Standard RNG Realizable



3.4 Numerical Simulation of flow past on car geometry considering different

diffuser angles

3.4.1 Geometry

The geometry of the car consists of different segments, it is a freeform design inspired from

popular sport cars. The dimensions of the car is length, L=4570mm, Height, H=1322mm. The

ground clearance of the vehicle is 80mm and the diffuser angle is variable with values set to

6°, 7°, 8°, 9° and 10°. Length, height, ground clearance and diffuser length of the car is kept

constant throughout our investigation.

This investigation is carried out for five different cases of the model using Realizable k-ε.

Fig 3.23 Shows car geometry with diffuser angle 7°

6° 7° 8°



9° 10°

Fig 3.24 Variation of diffuser angle at the rear end of the investigation car


Length of the car L 4570 mm

Height of the car H 1322 mm


Length of diffuser ld 830 mm

Diffuser angle αd 60-100

Table 3.9 Geometrical details

3.4.2 Meshing and Boundary condition

In this, a quadrilateral fine mesh is generated with nodes (222,202) and elements (219,387) for

the simulation. The dense mesh is carried around the surfaces of the car.

Fig 3.25 Shows meshing of car body at diffuser angle 7°




Inlet Velocity inlet ,v= 40m/s, turbulence intensity=0.5%


Top Wall, stationary wall ,no slip

Bottom Moving wall ,v= 40m/s

Wall Wall, Stationary wall, no slip

Table 3.10 Boundary conditions

The boundary conditions, as specified in Table 3.10, are Inlet set as a velocity inlet with

velocity, v=40m/s. Outlet is set as a pressure outlet with reference pressure P=0. Top is

specified as a stationary wall with no slip condition. Bottom is a moving wall with velocity, v=

40m/s. Finally wall is also a wall boundary with no slip condition. Similarly, for the different

cases of boundary conditions, inlet velocity is varied for 20m/s(72kmph) and 88m/s(320kmph).

Same condition is considered for the bottom surface which represents the ground and in

addition, the option ‘solid moving wall’ is activated.

3.4.3 Results and discussions

For the above case when compared to zero degree diffuser angles, the cases with positive

diffuser angle have lesser wake region. For increasing velocities both Cl and Cd, decreases as

explained earlier. The flow over the car has a steady pressure and velocity along the underbody

surface till the start of diffuser, this is due to no curvature in the geometry. The presence of

diffuser accelerates the flow and creates lesser pressure on the lower surface. The upper surface

has a positive curvature. The velocity distribution over the geometry can be explained using

boundary layer (area of the flow) and continuity principle. Bernoulli’s principle can be applied

for the regions without unsteady flow and vortices. Thus except for the rear end of the domain,

we see an inverse ratio of pressure and velocity magnitude. Due to which due to the acceleration

of the flow over the diffuser a net lower pressure is generated from the lower surface and this

creates a positive downforce or a negative lift. The plots of pressure contours and velocity

magnitude for the case of v=40m/s is shown in Fig 3.28, Fig 3.29, Fig 3.30.



Fig 3.26 shows variation in co-efficient of lift

Fig 3.27 shows variation in co-efficient of drag



Fig 3.28 Shows effect of pressure contour on car with diffuser at v=40m/s

Fig 3.29 Shows velocity contour of the car at v=40m/s (144kmph)

The pressure recovery is also higher as the flow velocity of lower surface is closer to upper and

also length of separation of the surface is lower. This results in a smaller wake and lesser drag

than zero diffuser angle

Fig.3.30 Shows streamline flow at v=40m/s (144kmph)



For velocity of 40 m/s for different diffuser angles 60, 70, 80, 90 and 100 CFD computation has

been carried out. The results obtained are from the simulation done using Realizable k-ϵ model

and are tabulated below in Tables 3.11-3.13.

Diffuser angles(deg) Drag co-efficient(Cd) Lift co-efficient(Cl)

6° 0.2355 -1.5399

7° 0.2348 -1.1160

8° 0.2374 -0.6345

9° 0.2410 -0.5806

10° 0.2441 -0.1708

Table 3.11 Cd and Cl values for different diffuser angle at 72 kmph


6° 0.2199 -1.7439

7° 0.2283 -1.4250

8° 0.2245 -0.9208

9° 0.2217 -0.8515

10° 0.2299 -0.4136



6° 0.1963 -1.6896

7° 0.2096 -1.5203

8° 0.2118 -1.2113

9° 0.2186 -1.1670

10° 0.2236 -0.8353


Upon plotting these tabulated values for different diffuser angle, we found out that the general

trend line of Cl and Cd with increase in angle of diffuser the values of Cl and Cd increases (downforce

decreases). The plots of different angles v/s Cl and Cd are plotted and are shown in Fig 3.26, and fig

3.27



Fig 3.31 Shows graphical representation of diffuser angle v/s Co-efficient of drag for

Realizeable K-ε model

Fig 3.32 Shows graphical representation of diffuser angle v/s Co-efficient of lift for

Realizable K-ε model

0.2355 0.236 0.23740.241

0.2441

0.2199

0.22430.2265

0.2283 0.2299

0.204

0.20960.2118

0.2186

0.2236

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

5 6 7 8 9 1 0 1 1

CO

EF

FIC

IEN

T O

F D

RA

G(C

D)

DIFFUSER ANGLE

DIFFUSER ANGLE V/S COEFFICIENT OF DRAG


-1.5399

-1.116

-0.6345-0.5806

-0.1708

-1.7439

-1.425

-0.9208-0.8515

-0.4136

-1.86

-1.5203

-1.2113-1.167

-0.8353

-1.9

-1.7

-1.5

-1.3

-1.1

-0.9

-0.7

-0.5

-0.3

-0.1 5 6 7 8 9 10 11

CO

EF

FIC

IEN

T O

F L

IFT

(CL)

DIFFUSER ANGLE

DIFFUSER ANGLE V/S COEFFICIENT OF LIFT




For increasing velocities both Cl and Cd, decreases as explained earlier. The flow over the car

has a steady pressure and velocity along the underbody surface till the start of diffuser, this is

due to no curvature in the geometry. The presence of diffuser accelerates the flow and creates

lesser pressure on the lower surface. The upper surface has a positive curvature. The velocity

distribution over the geometry can be explained using boundary layer (area of the flow) and

continuity principle. Bernoulli’s principle can be applied for the regions without unsteady flow

and vortices. Thus except for the rear end of the domain, we see an inverse ratio of pressure

and velocity magnitude. Due to which due to the acceleration of the flow over the diffuser a

net lower pressure is generated from the lower surface and this creates a positive downforce or

a negative.



CHAPTER-4

Conclusion

When comparing the result obtained in the Ahmed geometry with the investigated result it

can be seen that the drag and lift coefficients of the body is acceptable, as it shows the

nearer results to the Ahmed body.

The results of the numerical analysis for flow past underbody of a car with and without

diffuser lead to the following conclusions

From the investigation it was observed that the change of diffuser angle has a great

influence on wake of the underbody flow. The drag coefficients increases with absence of

diffuser. It decreases with increasing diffuser angle and also lift coefficient decreases as the

diffuser angle is varied. The same trend were observed for different velocities and various

diffuser angles.

The pressure on the underbody surface of the car differs between the case diffuser and

without diffuser. Negative pressure coefficient is obtained in our investigation, which gives

a stable downforce for the car at relatively high speeds.

Due to the aerodynamic characteristics of a car downward thrust is created to allow it to

travel faster through corner by increasing the vertical force on the tires, thus creating more

traction.

Scope of future work

The present analysis of 2-D car geometry can be further extended to 3-D geometrical

car analysis to obtain better results

The parameters of diffuser including diffuser angle, number of guide vanes, shape of

separators and shape of end plate can be included to the 3-D geometrical car



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[8] Mohamed-Kassim, Z., & Filippone, A. (2010). Fuel savings on a heavy vehicle via

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