aerodynamic analysis of a car.pdf

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Aerodynamic analysis of a car using CFD 1

CHAPTER 1

INTRODUCTION

1.1 IntroductionThe 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 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 somehardware testing.

2. Developing high quality products through the evaluation of more design

alternatives. Aerodynamic development of motor vehicles is expensive. Much capital

must be invested in testing facilities such as wind tunnels and climatic tunnels.

Secondly, considerable costs result from the work itself. Finally, the development

time may be lengthened by aerodynamic work. The efforts to improve the

aerodynamics of vehicles are witnessed by the large numbers of wind tunnels

constructed specifically for this purpose. Nearly all major manufacturers have such

facilities at their disposal or are currently building them. Generally, the demands

upon the quality of a wind tunnel increase with the expectations placed upon the

quality and reliability of the results. Similarly the development costs increase steeply

with the quality of the intended results.

The availability of a reliable numerical prediction method could greatly reduce designcosts by reducing the amount of wind-tunnel testing required.

Computational Fluid Dynamics, as one of the CAE tools, has been adopted to serve

this role for an increasing number of applications. When one examines the


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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 measurementtechniques 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.

Extensive research is going on in the field of automobile aerodynamics, especially of

cars, and there is a clear indication of the ever increasing popularity 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 will completely replace wind tunnel

testing in future.


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1.2 Problem definition and objectives

Problem definition: To perform the aerodynamic analysis of the rear part of

different car bodies available on road .

Objectives:

1. To prepare the solid model of the car body with proportionate dimensions

using SOLID WORKS.

2. To find out the aerodynamic drag force and pressure distribution on the car

body in case of front winds at the variable speeds using CFD(Computational

Fluid Dynamics) software ANSYS-FLUENT.

3. To find out the Drag Coefficient of the car body and compare it with

theoretical prescribed values for good aerodynamic behavior.


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1.3 Line of Action

The 3-D model of a car body is generated in solid works. To ensure accuracy,

the outline curves of the car body are traced from a blueprint image of side view.

The co-ordinates of the curves are obtained by tracing the image on a graph

paper. When the modeling is complete, the solid works file has been converted

into .iges and then this .iges file is later on imported into gambit for further

processing. In Gambit, surface mesh of the model and the domain surfaces is

carried out. Further after assigning the boundary zones, the file from gambit is

exported as a .msh file. This .msh file is imported in Tgrid for volume meshing.

Finally the .msh file from Tgrid is imported in Fluent for analysis purpose. In

fluent, after giving suitable boundary conditions, the problem is sent to the solver

that carries out certain numerical calculations.


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CHAPTER-2

LITERATURE REVIEW

2.1 Introduction to Aerodynamics of Vehicles and its Importance :

The performance, handling and comfort of an automobile are

significantly affected by its aerodynamic properties. A low drag is a decisive

prerequisite for good fuel economy. But the other aspects of vehicle aerodynamics

are no less important for the quality of an automobile: side wind stability, wind noise,

soiling of the body, the lights and the windows, cooling of the engine, the gear box

and the brakes, and finally heating and ventilating of the passenger compartment alldepend on the flow field around and through the vehicle.

The flow processes to which a moving vehicle is subjected fall into three categories:

Flow of air around the vehicle;

Flow of air through the body;

Flow processes within the machinery.

Aerodynamic Drag:

The aerodynamic drag D, as well as the other force components and moments,

increases with the square of the vehicle speed V:

D~V2

With a medium size European car, aerodynamic drag accounts for nearly 80 percent

pf the total road resistance at 100 km/h. There is therefore much scope for improving

economy by reducing aerodynamic drag. For this reason drag remains the focal

point of vehicle aerodynamics, whether the objective is speed or fuel economy.


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Drag acts against the cars thrust, and the balance of these forces determines

whether you can accelerate quickly or not at all !! Friction acts with the drag to try to

slow the car down.

There are several factors that affect the drag of a vehicle. We can break this down

into an equation, so we can see exactly how each factor plays its part. The equation

for drag is:

Drag = (.5)x(density)x(speed)x(speed)x(area)x(drag coefficient)

There are a quite a few different terms there, so lets see how these affect the drag in

different circumstances:

Density- The density of air is important. Lower density means lower drag.

Speed- Note that drag is affected by speed times itself i.e. speed square. This

means that if we double the speed the drag goes up by four times. Three times the

speed means nine times the drag, four times the speed means sixteen times the

drag, etc.

Fi 1: Dra orce actin on a vehicle


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Area- The frontal area of the car is considered.

Drag coefficient- This special number characterizes the aerodynamic design of the

vehicle. It encompasses many physical features and can be reduced by good design

of your car.

Lift :The pressure difference between the upper and lower sides of the vehicle

produces a resultant force, at right angles to the direction of motion, which is called

lift.

As a rule the lift is in upwind direction, i.e. it tends to lift the vehicle and therefore

reduce effective wheel loads. It is coupled with a pitching moment, which

differentially effects the wheel loads at the front and rear. Below 100km/h, lift and

pitching moment have only a small-effect upon the vehicle, even in a cross-wind.

They do change the attitude of the car in relation to the road and therefore slightly

affect the aerodynamic drag.

The shape of the car must be such that the additional forces and moments remain

so small that the directional stability is not greatly affected. First, the need to react to

a cross-wind of varying intensity and direction is inconvenient, as the driver must

continually apply steering corrections. Secondly, in very rare cases

there is danger of total loss of control. This can only be countered by suitable

aerodynamic design.

Soiling of the rear of the vehicle can be studied from the flow in the wake region.

Dust or dirty water is whirled up by the wheels and, dust particles and water droplets

distributed throughout the entire wake region by turbulent mixing, and deposited on


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the rear of the vehicle. Since the flow pattern at the rear has a significant influence

upon the aerodynamic drag, soiling at the rear cannot be considered in isolation.

The fresh air fan which must be correspondingly larger, then provides a flow which is

independent of the driving speed(though only when the exit vents in the body are

located in the areas of ambient pressure as well.)

The trend in the aerodynamic development of cars:

Summarized below. Shows how drag decreases between 1920 and the mid

1970s. Owing to the lack of statistical data only a general tendency can be outlined.

The reduction of the drag coefficient from .8 for cars in the 1920s to an average

value of .45 for cars of the 1960s and 1970s occurred in two stages. In the first, theperiod between the two world wars, the cars were stretched and body details were

rounded while maintaining significant characteristics such as projecting fenders and

headlights. In addition to a lower drag coefficient of approximately .55, frontal areas

were decreases, resulting in a considerable reduction of the total aerodynamic drag.

The average drag coefficient began to drop in 1978. the range of data is still

enormous. Even some contemporary cars have drag coefficients worse than .5,

while the best, the opel omega, has Cd=0.28

With concept cars there is still room for further drag reductions. Drag figures of

.14(GM Aero 2002) and .15, established in 1922, at last seems attainable. So that a

drag coefficient of 0.30 is possible for without major and expensive technical

compromise. In the long run 0.20 might be achieved with production cars.

The drag coefficient itself is split into three components:

Skin friction drag

Form or pressure drag

Induced drag

The first two are particularly important for cars, while the third(induced drag) is only

really important for wings, and hence aircraft in the main.


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Skin friction drag(viscous drag):

Skin friction drag occurs due to the air having viscosity. When air is moving past an

object then the air in direct contact with a surface is actually brought to a

stop(relative to the surface). Air slightly off the surface moves slightly faster. If we go

far enough from the surface then the air is moving at its full(or free stream) speed.

The region just above the surface where the air is not moving at its full speed is

known as the boundary layer. Skin friction drag is not dependent on the particular

material that an object is made of, but it is affected by how rough the surface is. As

you might expect, smoother surfaces are better than rough surfaces. Also, theamount of surface in contact with the air is a factor, so minimizing this is

advantageous in reducing skin friction drag.

The entire skin friction drag is created within the boundary layer. Reflection on this

situation tells us that the amount of skin friction will depend on three factors:

1. Velocity of the gas.

2. Viscosity of the gas.

3. Length of the surface over which the gas flows.

This last point mean that more total drag will occur if gas flows for many feets over a

long object than if the same gas flows a short distance over a shorter object.

Therefore, we can say that:

Viscous drag=velocity x viscosity x distance

Viscous drag will have units of Newton, velocity will be in meter/second, and

distance in meters.


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In turbulent boundary layer flow, the friction drag is much higher than in the laminar

case. This is because the turbulent mixing process leads to velocity profiles with

much steeper velocity gradient at the wall than in laminar case.

Form or pressure drag:

While skin friction drag is a function of the surface roughness and the length of

vehicle in contact with the air, the form , or pressure drag, is dependent on the

shape of the vehicle. It is therefore the main way in which designers can reduce

aerodynamic drag. So what causes pressure drag?

The clue is in the name. Depending on the shape of a body moving through the airconcentrations of high and low pressure can form, relative to the background(usually

atmospheric) pressure. These can act to pull the body backwards i.e. causing drag.

In general, the drag of a body may be written as

D=Df + Dp;

For blunt bodies the pressure drag is predominant. Generally, a sudden change of

the drag coefficient of a vehicle as a function of its Reynolds number should be

avoided. For this purpose, flow separation is fixed at certain points, for instance at

the upper edge of the rear sloping window, up to this point the shape of the body

should be designed so that the flow remains attached and the pressure rise is a

large as possible for various free stream conditions. The resulting wake should be as

small as possible to obtain low drag. The drag coefficients achieved by present by

present day European cars range from .30 to .52(excluding sports and racing cars).

In general the dependence of these drag coefficients on Reynolds number is very

small and sudden changes do not occur. This demonstrates that the predominant

part of the drag of these vehicles is the pressure drag. For some unconventional

streamlined body shapes, drag coefficients have been measured in the region .15

to .27. for bodies of this type the portion of pressure drag is relatively small. These


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drag coefficients thus contain a large portion of friction drag and therefore depend

noticeably on the Reynolds number.

Reducing skin friction

To reduce skin friction a laminar flow airfoil should be selected. However, this will

only be helpful if care is taken to keep the surface smooth. Generally this means

using modern materials such as plastic or other moldable substances. Traditional

aluminium bodies, held together with rivets, are unlikely to achieve much laminar

flow, due to roughness of the surfaces. It should be kept in mind also that the

laminar flow airfoil will not achieve laminar flow over its entire length; it simply

achieves more laminar flow than a non laminar airfoil. Additionally, as we discussed

in an earlier chapter, the laminar flow airfoil will achieve laminar flow only when

operated within a narrow range of angles of attack.

Reducing pressure drag:

The first step in reducing pressure drag is to make everything streamlined. It is also

important to remove all non- streamlined shapes protruding from the vehicle body,

and then streamline the rest.


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2.2 Real time examples showing how drag acts on different bodies:

a) Flow past a flat plate.

The picture above shows the flow past a flat plate(like a door) placed

sideways to the wind. Along the center of the plate the air actually comes to a

stop(stagnation point) and this is known as the separation streamline.

According to bernoullis theory, when air is slowed down its pressure

increases, and vice versa. As the air comes to a stop along the centerline,

this creates a high pressure region ahead of the plate pushing it backwards.

Behind the plate the air is not able to follow the surface of the plate and so

large eddies form, swirling around in a random fashion. This is known as

separated flow and creates a low pressure region behind the plate. This acts

like a vacuum cleaner, literally sucking the plate backwards. It is high

pressure in the front of the plate and low pressure behind it that is the

pressure drag.

Resistance 100%

Fi 2 : Flow ast a lat late


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b) Flow around a cylinder

Flow manages to follow the curve of the cylinder before it starts swirling

around. The effect of this is that the low pressure behind the cylinder is not as

low as behind the flat plate. The drag(i.e. the resistance) is about half that of

the flat plate, so a big improvement. It is possible to even better though.

c) Flow around an aerofoil

Below is a picture of an aerofoil. As seen below the streamlines are able to

follow the curve of the upper and lower surfaces and join up towards the

trailing edge. In this case there is still a high pressure region at the front, but

the low pressure at the rear is much closer to atmospheric pressure. Hence

the drag is around 20 times less than the flat plate, and 10 times less than the

cylinder.

Fi 3 : Flow ast a c linder


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d) Flow separation over a moving van.

In the diagram given below a hypothetical flow diagram shows how the air

particles in each streamline, within the boundary layer, should accelerate

around the front of the van and slow around the back.

This leads to the conclusion that an area of low pressure will form over the

windshield. An area of high velocity and low pressure will exist along the top

of the van.

Fi 4 : Flow ast an aero oil

Fi 5 : H othetical low around a van


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The airflow should decelerate as it turns downward along the back of the van.

This would cause the pressure to return to atmospheric pressure behind the

van. The actual flow around the van is more like that shown in fig.6

The air particles in the boundary layer are unable to make the sharp change

in direction and velocity required to negotiate the downward curve at the back

of the van, especially in the presence of the adverse pressure gradient

created by the low pressure along the roof. The result is flow separation. The

air behind the van winds up moving faster than it ideally should. Bernoullis

equation tells us that the higher velocity will be accompanied by a lower

pressure. As a result, the pressure behind the van is much lower than

atmospheric pressure and the air is tumbling in a pattern referred to aseddies.

It is mostly the low pressure behind the van which causes pressure drag(it

also acts like a vacuum cleaner sucking up all the crap from the road,

making the back of the van very dirty) In other words most pressure drag is

due to low pressure behind the object, rather than high pressure ahead of the

object.

Fi 6 : ctual low around a van


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2.3 Flow phenomena related vehicles:

The various flow phenomena related to vehicles can be divided into two groups

these are (a) the external flow around a vehicle, including all details of its surface,

and (b) the internal flow through different systems such as carburetor, engine,

exhaust system, cooling system as well as the flow through the passenger cabin

itself.

External flow:

The external flow around a vehicle is shown in fig .In still air, the

undisturbed velocity V is the speed of the car. Provided no flow separation takes

place, the viscous effects in the fluid are restricted to a thin layer of a few

millimeters thickness, called the boundary layer. Beyond this layer the flow is in-

viscid and its pressure is imposed on the boundary layer.

Within the boundary layer, the velocity decreases from the value of the in-viscid

external flow at the outer edge of the boundary layer to zero at the wall, where

the fluid fulfills a no-slip condition. When the flow separates at the rear part of the

vehicle, the boundary layer is dispersed', and the flow is entirely governed by

viscous effects. Such regions are quite significant compared with the

characteristic length of the vehicle. At some distance from the vehicle, there

exists no velocity difference between the free stream and the ground. Therefore

in vehicle-fixed co-ordinates, the ground plane is a stream surface with constant

Fi 7 : E ternal low around a car


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velocity V and at this surface no boundary layer is present. This fact is very

important for the simulation of flow around vehicles in wind tunnels.

Mechanics of air flow:

The flow around a vehicle is governed by two basic equations. The first equation

is Law of Conservation of mass according to which:

w.s=constant

where, s denotes the local cross section of a small stream tube and w is the local

velocity which is assumed to be constant across s.

The second equation is Newton's Law of momentum conservation. If this law is

applied to an in-viscid flow it turns out that inertia forces and pressure forces are

balanced. The integration of the momentum equation along a streamline forincompressible flow leads to:

g=p+ *w^2/ 2

Above equation is Bernoulli's equation, which relates the pressure p and velocity

w along a streamline(p is static pressure, *w^2/2 is dynamic pressure, and g is

total pressure).

In In-viscid flow ,the sum of static and dynamic pressure is constant along a

streamline. Bernoulli's equation indicates low pressure in regions of high localvelocities and vice versa. If the floe comes to rest, w=0,a so called 'stagnation

point', as on the nose of the vehicle(fig),the static pressure there will be equal to

the total pressure, and this is the highest possible pressure in the flow field.


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This flow is a considerable simplification of the three dimensional flow around a

vehicle. At the lower surface of the vehicle, the pressure is higher than the free

stream pressure, but for very small ground distances, even suction may be present.

At the upper surface, high pressures are observed in the region of the bonnet and

windscreen, where as high suction(negative pressure) is found at the cabin roof.

Negative pressure means high local velocity at cabin roof. On the rear part of the

vehicle's upper surface a steep pressure rise occurs, and it is the region where

considerable differences exist between the real flow of a viscous fluid and the in-

viscid flow. The pressure level on the upper side of the vehicle is much lower than

on the lower side. This means that a net upward lift force acts on the vehicle.

Effects of viscosity and Boundary Layer Development

The occurence of drag in two dimensional incompressible flows can be explained by

the viscous effects. The flow in a boundary layer along a thin plate is shown in fig.The corresponding external flow has parallel stream lines and constant velocity V

and pressure p. The viscous flow within the boundary layer fulfills the no-slip

boundary condition along the wall. in the front part of the plate the boundary layer

flow is steady and(almost) parallel to the wall. This state of the flow is called laminar.

Fig 8 : Simplified three dimensional flow around a vehicle


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The thickness of the boundary layer increases downstream. With increasing

distance x, the boundary layer thickness increases. The laminar state of the

boundary layer flow is stable against disturbances for certain conditions only. At a

distance X=Xtr from the leading edge of the plate ,a transition to the so-called

turbulent state of the boundary layer takes place. The transition between the two

states of the boundary layer flow of largely governed by the value of the Reynolds w

number. For the flat plate transition occurs around.

Rextr=5*10^5

But this value applies only for negligible pressure gradient in the external flow. In

case with a pressure gradient, a pressure decrease in the flow direction leads to a

stabilization of the boundary layer, whereas an adverse pressure gradient cause anearlier transition to the turbulent state. In general, for medium Reynold's numbers

transition from laminar to turbulent occurs in the region of minimum pressure, and

with increasing reynold's number the transition point moves upstream.

Separation

Laminar and turbulent boundary layer flows depend strongly on the pressure

distribution which is imposed by the external flow. For a pressure increase in flow

direction the boundary layer flow is retarded, especially near the wall and even

reversed flow may occur. This behavior is shown schematically in fig. It can be seen

that, between forward and reverse flow, a dividing streamline leaves the wall. This

phenomenon is called separation.


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There are two components of drag; friction drag and pressure drag. If a velocity

gradient du/dy is present in a viscous fluid at the wall, due to molecular friction ashear stress w acts everywhere on the surface of a body. The integration of the

corresponding force components in the free stream direction leads to the friction

drag. Integrating the force components in the free stream direction, resulting from

the pressure distribution, gives the pressure drag. For blunt bodies the pressure

drag is predominant. in turbulent boundary layer flow, the friction drag is much

higher than in the laminar case. This is because the turbulent mixing process leads

to velocity profiles with much steeper velocity gradient at the wall than in laminar

case.

The drag of bodies with finite thickness mainly consists of friction drag which is small

in all cases in which no flow separation occurs. This can be achieved by slender

shapes on the rear of the body which produce only a weak pressure rise in the flow

direction. Shapes of this kind are aero foils and streamlined bodies.

Blunt bodies, such as circular cylinder, a sphere or a flat plate normal to the flow,

show quite different drag characteristics. On the rear part of such bodies in in-viscid

external flow, extremely steep pressure gradients occur which lead to flow

separation.

The pressure distribution is therefore considerably altered when compared with the

theoretical case of in-viscid flow. as an e.g, fig shows the pressure distribution for a

Fi 9 : Laminar and turbulent boundar la er


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circular cylinder. In front part the distribution is similar to that in in-viscid flow, where

as on the rear the flow separation leads to considerable suction.

The pressure distribution is therefore asymmetrical with respect to the y-axis.

Friction drag also results from the wall shear stresses, but for blunt bodies the

pressure drag is predominant.

In general, the drag of a body may written as

D=Df + Dp

generally, a sudden change of the drag coefficient of a vehicle as a function of its

Reynolds number should be avoided .for this purpose, flow separation is fixed at

certain points, for instance at the upper edge of the rear sloping window, up to this

point the shape of the body should be designed so that the flow remains attached

and the pressure rise is as large as possible for various stream conditions. The

resulting wake should be as small as possible to obtain low drag. The drag

coefficients achieved by present day European cars range from .30 to .52(excluding

Fig 10 : Pressure distribution and stream line pattern for a circularcylinder at different Reynolds number (a) inviscid flow

(b) sub-critical flow, boundary layer laminar (c) supercriticalflow, boundary layer turbulent


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sports and racing cars).In general, the dependence of these drag coefficients on

Reynolds number is very small and sudden changes do not occur. This

demonstrates that the predominant part of the drag of these vehicles is the pressure

drag. For some unconventional 'streamlined' body shapes, drag coefficients have

been measured in the region .15 to .27.For bodies of this type the portion of

pressure drag is relatively small. These drag coefficients thus contain a large

proportion of friction drag and therefore they depend noticeably on the Reynolds

number. The flow separation that lead to a pressure drag can be divided into two

different types .as shown in fig, the separation line may be located perpendicular to

the flow direction .

In this case, vortices are generated the axes of which are also perpendicular to the

outer flow. Thus the velocity components parallel to the vortex axes are very small.

A symmetrical flow in the separated region as shown in fig exists only for small

Reynolds numbers. For larger Reynolds numbers, periodic vortex shedding occurs

and flow in the separated region is basically unsteady. The kinetic energy of the

vortex field is rapidly dissipated by turbulent mixing and irreversibly converted intofrictional heat. This leads to a considerable total pressure loss in the region behind

the body and the corresponding deficit in kinetic energy is equal to the work which is

necessary to overcome the pressure drag. Behind the body a wake is formed in

Fig 11 : Flow separation on a bluff body


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which time averaged, relatively uniform suction and very low flow velocities are

present.

The other type of flow separation is characterized by a separation line with respect

to the oncoming flow, see fig .In this case, vortices are shed, the axes of which are

roughly parallel to the separation line. A considerable velocity component, parallel to

the separation line and therefore in direction of the vortex axes, is present. Thus, a

well ordered, steady three dimensional flow separation is found.

On the rearward surface of the body this separated flow induces suction which leads

to a pressure drag. On the inclined base of the body the flow is attached in the

vicinity of the vortices the pressure distribution is characterized by suction peaks.

The flow field of the concentrated vortices, however, contains a lot of kinetic energy

which corresponds to the work necessary to overcome the pressure drag.

Fig 13 shows the three dimensional flow separation at the rear of a vehicle.

Fig 12 : Flow separation on a body with obliqueblunt base ( separation line at an angle to

the flow direction)


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On the drag problem of a body, it might be mentioned finally that the shape of a

body in front of the largest crass-section has only minor influence on the total drag.

The main contribution to the drag force originate from the rear part of the body .It is

not important to find a proper shape to divide the oncoming flow but it is very

important to design a rear body surface which brings the divided streamlines

smoothly together. Optimum shapes are 'streamlined' bodies having a very slender

rear part.

Overall Forces and Moments

In addition to the drag discussed so far, other forces and moments occur on vehicles

which are shown schematically in fig14.In symmetrical flow (=0) the drag D is

accompanied by a lift force L Furthermore, a pitching moment M, with respect to the

lateral axis(y-axis) is present. The three components L,D and M completely

determine the vector of the resulting air force.

Fi 13 : Three dimensional low se aration at rear o the vehicle


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In cross wind conditions (#0) an asymmetrical flow field is present around the

vehicle. In this case, in addition to the forces and moments mentioned so far, a side

force Y is observed. Furthermore, there occur a rolling moment R with respect to the

longitudinal axis (x-axis) and a yawing moment N with respect to the vertical axis (z-

axis). Thus six components L,D,M and Y,R,N determine the vector of the total force.

Expressions for these are given below

(1) D=.5*Cd**A*V2

(2) L=.5*Cl**A*V2

(3) Y=.5*Cy**A*V2

(4) M=.5*Cm**A*V2*l

(5) R=.5*Cr**A*V2*l

(6) N=.5*Cn**A*V2*l

Fig 14 : Forces and Moments acting on a vehicle (c.g.-centre of gravity)


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Here l is the total length of the vehicle . is the air density, V is the free stream

velocity, A is the projected frontal area. Cd , Cl, Cy, Cm, Cr, Cn are corresponding

coefficients.

2.4 Flow Field around a Passenger Car

The flow field around a vehicle is not yet fully understood, so a picture must be

built up from pressure distribution measurements, velocity field measurements

and flow observations of the vehicle surface. There are two types of separation.

The first type has a quasi-two-dimensional character. In this case the line of

separation tends to run perpendicular to the local flow direction .If reattachment

occurs, so-called separation bubbles are formed. Of course the flow inside the

bubble, which is shed from a three-dimensional in nature. However, since the

separation itself is mainly two-dimensional with separation line normal to the flow

and vortex axes parallel to the separation line, it is designated 'quasi-two-

dimensional'. This type of flow can occur at the leading edge of the front hood, at

the sides on the fenders, on the cowl and on the front spoiler, and possibly in thenotch of a notchback (see fig 15).

Fi 15 : uasi 2d se aration


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Wakes also form on the blunt rear of a square back. Depending on the outer flow

field, long wakes are formed, which extend far downstream, or the wakes are short

and closed(see fig).

Fig below shows the counter-rotating vortex pair of a notchback, a fastback and a

square-back. The lower vortex rotates counterclockwise and is responsible for

carrying the contamination of the rear vehicle. The upper vortex rotates in the

opposite direction. After the separation bubble closes , a pair of counter-rotating

longitudinal vortices forms in the trailing wake. This produces an upwash in the case

of a square-back, and induces a downwash in the trailing wake flow on a notchback

or fastback.

Fig 16 : Large,long,open wake of a squqreback and small,short,closedwake of a fastback


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The vector diagrams in fig clearly show the3se vortices. On a square back, the

vortex pair rises in the flow direction and wanders toward the plane of symmetry.

On fastbacks and notchbacks the vortices approach the road downstream and

move to the outside .It can be postulated that these longitudinal vortices are the

continuation of the lateral vortices described above. There is a velocity decrease

toward the center of the vortex. The longitudinal vortices are slowly exhausteddownstream by dissipation.

Fig 17 : Counter rotating transverse vortices in the wake of carsWith three typical rear end configurations


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Fi 18 : Continued on ne t a e


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The second type of separation is three dimensional in nature. Vortex trains are

formed at sharp edges where the flow is oblique, as with a delta wing. Such a vortex

pair is formed on the two A-pillars and is bent back towards the roof at the upper end

of the A-pillars. Its effect on the rear end flow is still unknown. A strong vortex pair

forms at the rear of the vehicle, depending upon the inclination of the rear

end(fig20).

Fi 20 : Three dimensional low se aration

Fig 19 : Transverse velocity vector diagrams for notchback, fastbackand squareback cars


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These rear vortices interact with the external flow field and with the quasi-two-

dimensional wake.

2.5 Design tips for Aerodynamic design:

Design tips- lift and downforce

When designing aircraft we are normally interested in how much aerodynamic lift

we can generate so we can get off the ground. Requirements for cars are quite

different, however. Lift can actually be very dangerous, as car that is lifted off the

ground can no longer be steered, and braking can be tricky if your wheels are off

the ground. So on the whole we try to generate negative lift, which is usually

known as downforce. For road cars we generally want near zero lift, or some

slight downforce. With lift or downforce we will generate some induced drag-

defined as the drag caused by the generation of lift. So minimizing lift/downforce

to minimize drag is generally what we desire.


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A car that generates maximum down-force for minimum drag penalty is what F1aerodynamicists strive for.

Design tips-Aerodynamic design(3-D inverted airfoil shape)

File photo of a fully closed racing car

Fi 21 : File hoto o a racin car


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The 2004 winner from Fruze Platt School, certainly looks aerodynamic, but

what do we mean around, being quite turbulent causing pressure drag. Note

that the car is closely fitted around the driver. This does two things:

Minimizes frontal area.

Minimizes the surface area of the vehicle in contact with the air, hence

reducing skin friction drag.

The front of the cockpit curves very smoothly up and over the drivers head,

without any sharp corners. This is to prevent any flow separation. Note that

the sides also curve smoothly in to a thin vertical trailing edge. The body is

made from smooth material, in order to try and maintain a laminar boundary

layer for as long as possible by that in terms of the discussion of drag above.

The vehicle is completely enclosed. This is good as the airflow can be

controlled by the designer. In open top cars the air will tend to swirl

On the whole this car is pretty close to the aerodynamic ideal. The lap

times certainly are impressive, showing the power of aerodynamics.

2.6 Numerical methods for computation of flow around road

vehicle:

The traditional predictive tools used in the automobile industry to evaluate

aerodynamic performance are the wind tunnel and roads tests. Full-scale wind

tunnel tests are expensive to builds and operate whereas scale model test

results are subjected to numerous doubts associated with realistic simulation of

Reynolds number, surface and underbody details, engine cooling and

passenger compartment flows, tunnel wall boundary layer and model support

interference effects, model and wake blockage effects, effect of flow-intrusive

probes etc.

Road tests represent the most realistic simulation of the environment in which a

vehicle operates. However, the difficulties associated with the ever-changing


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environment often make the results obtained open to debate. Great care is

need to make the results meaningful and conclusive.

Computer, and with them computational fluid dynamics(CFD), are slowly

emerging as additional basic tools in aerodynamic design, Wind tunnels and

computer are both simulators-wind tunnels analogues, computers digital. There

characteristic differences make them complementary rather than completely

competitive. The relative role of the simulation techniques is however changing.

In future, wind tunnel may be used for validation and refinement of the

theoretical predictions or global simulation of the entire flow field rather than for

extensive parameter studies as in the past.

Numerical simulation is well suited to the analysis of a wide range of shape

options for example during an early design stage-thus increasing thus

increasing the prospect that an optimum shape will be identified. Sometimes a

numerical simulation permits the investigation of situations that can not berealistically duplicated in a wind tunnel The aero-dynamics of two vehicles in

the passing for overtaking mode, for example, poses a difficult problem for wind

tunnel tests.

Numerical simulations are most useful in predicting trends of how shape

changes will, affect flow field features. Absolute performance prediction is

usually poor. Computer size and speed limitation, and the lack of information

about the physics involve of the limit the predictive capacity of numerical

methods.

An interesting application of numerical methods is the effectively enhancement

of wind tunnel test through pre-test planning on-line test diagnosis and post-test


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validation. Although this may not lead to reduction in wind tunnel testing, it can

help to ensure that the time spent issued more intelligently.

All numerical methods to computer fluid flow are based on approximations to

the full Navier-Stokes equations. These are second order non-linear partial

differential equations which govern all fluid motion. Except for the simples

approximations, they are solved by techniques such as finite volume of finite

differences to achieve the spatial and temporal detail needed.

In these techniques the physical region of interest is divided up (or discretized)

by a two- or- three dimensional grid. Such grids are in practice complicated

orthogonal or non-orthogonal networks that may originate in the body contour

envelope and have a flow physics oriented spacing. The vast amount of detail

needed to analyze the flow around a real vehicle will limit the use of

computational methods for quite some time to come.

Navier-Stokes Equations:

The Navier-Stokes equations are nonlinear partial differential equations in

almost any real situation (an exception is creeping flow). On this slide we show

the three-dimensional unsteady form of the Navier-Stokes Equations. These

equations describe how the velocity, pressure, temperature, and density of a

moving fluid are related. The equations were derived independently by G.G.

Stokes, in England, and M. Navier, in France, in the early 1800's. The

equations are extensions of the Euler Equations and include the effects of

viscosity on the flow. The equations are a set of coupled differential equations

and could, in theory, be solved for a given flow problem by using methods from

calculus.


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But, in practice, these equations are too difficult to solve analytically. In the past,

engineers made further approximations and simplifications to the equation set until

they had a group of equations that they could solve. Recently, high speed computers

have been used to solve approximations to the equations using a variety of

techniques like finite difference, finite volume, finite element, and spectral methods.

This area of study is called Computational Fluid Dynamics or CFD.

The form most commonly used in CFD is called Reynolds averagedNavier-

Stokes equations (RANS).The Navier-Stokes equations consists of a time-

dependent continuity equation for conservation of mass, three time-dependent

conservation of momentum equations and a time-dependent conservation of

energy equation. There are four independent variables in the problem, the x, y,

and z spatial coordinates of some domain, and the time t. There are six


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dependent variables; the pressure p, density r, and temperature T (which is

contained in the energy equation through the total energy Et) and three

components of the velocity vector; the u component is in the x direction, the v

component is in the y direction, and the w component is in the z direction, All of

the dependent variables are functions of all four independent variables. The

differential equations are therefore partial differential equations and not the

ordinary differential equations that you study in a beginning calculus class.

The symbol is used to indicate partial derivatives.

The symbol indicates that we are to hold all of the independent variables fixed,

except the variable next to symbol, when computing a derivative. Re is the

Reynolds number which is a similarity parameter that is the ratio of the scaling

of the inertia of the flow to the viscous forces in the flow. The q variables are

the heat flux components and Pr is the Prandtl number which is a similarity

parameter that is the ratio of the viscous stresses to the thermal stresses. The

tau variables are components of the stress tensor.

The terms on the left hand side of the momentum equations are called the

convection terms of the equations. The terms on the right hand side of the

momentum equations that are multiplied by the inverse Reynolds number are

called the diffusion terms. Diffusion is related to the stress tensor and to the

viscosity of the gas. Turbulence, and the generation of boundary layers, are the

result of diffusion in the flow. The Euler equation contain only the convection terms of

the Navier-Stokes equations and can not, therefore, model boundary layers.

These equations establish that changes in momentum in infinitesimal volumes

of fluid are simply the sum of dissipative viscous forces (similar to friction),

changes in pressure, gravity, and other forces acting inside the fluid: an

application of Newton's second law. As such, these equations in both full and


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simplified forms, are used in the design of aircraft and cars, the study of blood

flow, the design of power stations, the analysis of the effects of pollution, etc.

The Navier-Stokes equations are differential equations establish relations

among the rates of change. For example, the Navier-Stokes equations for

simple case of an ideal fluid (in-viscid) can state that acceleration (the rate of

change of velocity) is proportional to the gradient (a type of multivariate

derivative) of pressure.

A solution of the Navier-Stokes equations is called a velocity field or flow field,

which is a description of the velocity of the fluid at a given point in space and

time. Once the velocity field is solved for, other quantities of interest (such as

flow rate, drag force, or the path a "particle" of fluid will take) may be found.

PROPERTIES

Non linearity

The non linearity is due to convective acceleration, which is an acceleration

associated with the change in velocity over position. The non linearity makes

most problems difficult or impossible to solve and is part of the cause of

turbulence. Hence, any convective flow, whether turbulent or not, will involve

non linearity.

Turbulence

Turbulence is the time dependent chaotic behavior seen in many fluid flows. It

is generally believed that it is due to the inertia of the fluid as a whole: the

culmination of time dependent and convective acceleration; hence flows

where inertial effects are small


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tend to be laminar. It is believed, though not known with certainty, that the

Navier-Stokes equations model turbulence properly. Though CFD will

theoretically work on any flow, in practice many common flows (such as flow

over a wing) contain so much detail that no computer can handle in any

reasonable amount of time.

Applicability

Together with supplemental equations (for example, conservation of mass)

and well formulated boundary conditions, the Navier-Stokes equations seem

to model fluid motion accurately; even turbulent flows seem (on average) to

agree with real world observations.

Limitations

The Navier-Stokes equations assume that the fluid being studied is a

continuum. At very small scales or under extreme conditions, real fluids made

out of discrete molecules will produce results different from the continuous

fluids modeled by the Navier-Stokes equations. Another limitation is very

simply the complicated nature of the equations. Time tested formulations exist

for common fluid families, but the application of the Navier-Stokes equations

to less common families tends to result in very complicated formulations

which are an area of current research. For this reason, the Navier-Stokes

equations are usually written for Newtonian fluids.

Derivation and description

The derivation of the Navier-Stokes equations begins with the conservation of

mass, momentum, and energy being written for an arbitrary control volume.

The most general form of the Navier-Stokes equations ends up being:


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This is a statement of the conservation of momentum in a fluid, it is an

application of Newton's second law to a continuum. This equation is often

written using the substantive derivative, making it more apparent that this is a

statement of Newton's law:

The right side of the equation is a summation of body forces. is apressure gradient

and arises from normal stresses that turn up in any flow. is representative o f

shear forces in the fluid, normally viscous effects, f represents "other" forces,

such as gravity.

The shear stress term contains too many unknowns, hence the generalform above

isn't directly applicable to any problem. For this reason, assumptions on the

specific shear stress behavior of a fluid are made (based on natural observations)

and applied in order tospecify this quantity in terms of familiar variables, such

as velocity. For example, this

term becomes the usable quantity when the fluid is assumed

incompressible and Newtonian.


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The Navier-Stokes equations are strictly a statement of the conservation of

momentum. In order to fully describe fluid flow, more information is needed

(how much depends on the assumptions made), this may include the

conservation of mass, the conservation of energy, or an equation of state.

Regardless of the flow assumptions, a statement of the conservation of mass

is nearly always necessary. This is achieved through the continuity equation,

given in its most general form as:

Incompressible flow of Newtonian fluids

The vast majority of work on the Navier-Stokes equations is done under an

incompressible flow assumption for Newtonian fluids. The incompressible flow

assumption typically holds well even when dealing with a "compressible" fluid,

such as air at room temperature (even when flowing up to about Mach 0.3).

Taking the incompressible flow assumption into account and assuming

constant viscosity, the Navier-Stokes equations will read (in vector form):

f represents "other" body forces, such as gravity or centrifugal force. It's well

worth observing the meaning of each term:

Numerical methods to solve the Navier-Stokes equations can be classified

into the following four categories, depending upon the degree of approximation

made:

Linearized inviscid flow methods

Non-linear inviscid flow methods

= -


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Methods based on Reynolds-averaged Navier-Stokes equations

Solutions of full Navier-Stokes equations

1. Linearized in-viscid flow methods

These are used routinely in aircraft design and have reached maturity. They are

applicable to subsonic, contour-attached flow. Vortex-lattice and panel method

codes belong to this category. Use of these methods to compute the flow field

around the cars, whose predominant feature is the large separation region at the

vehicle rear, remains severely restricted.

2.Non-linear in-viscid flow methods

The non-linear in-viscid flow methods based on the solution of Euler equations have

established themselves as accurate design tools for the prediction of trans-sonic

flow around a class of aircraft components, e.g. wings. The 'automatic' simulation of

flow kinematics in the subsonic separated flow computationsclaimed by developers

of these codes needs further substantiation. Provided this simulation capability turns

out to be general, a coupling of these methods with boundary layer approaches may

means a significant advance also of benefit to vehicle aerodynamicists.

3. Methods based on Reynolds-averaged Navier-Stokes equations

These methods are still undergoing extensive research and development. These

equations need a turbulent model for closure. The difficulty of modeling turbulence

with sufficient generality and the complex mesh generation needed to resolve flows

such as around road vehicles are the principle difficulty that have to be overcome.

4. Solutions of full Navier-Stokes equations

Methods to solve the full Navier-Stokes equations, which belong to the last category

named above, are practically non-existent. Only very preliminary research is

underway here.


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Some Difficulties of Numerical Simulation of the Road Vehicle Flow Field

Regions of separated flow being the key features of a road vehicle flow field, an

analytical approach is extremely difficult. Even simplified, basic vehicle-like

configurations free of all appendages and having smooth surfaces create 'closed'

separation regions and a large wake. One of the main difficulties encountered in

modeling such flows is the lack of generally applicable information about three-

dimensional separated flows. The variety of separation phenomena that can occur in

three-dimensional flows is a subject of continuing research. Factors governing the

initiation of different types of three-dimensional flow separation, kinematics of the

structures in separated flow, unsteady behavior of bluff body wakes, turbulence, etc.,

are all phenomena not well understood. Modular or sequential approaches similar tothose used in aircraft applications remain inadequate since computational methods

to treat three-dimensional boundary layers, in an adverse pressure gradient and

strong cross flow environment, which is typical of road vehicle flows, are not yet

available. As noted earlier, use of Reynolds-averaged Navier-Stokes equations need

a turbulence model to close the system of equations and make them amenable to

solution. Standard mixing length and eddy viscosity concepts cannot be used to

model complex real turbulent flows. Higher order turbulence models, currently not

available, are therefore needed.

Methods Based on Solution of Navier-Stokes Equations

The Navier-Stokes equations for a homogeneous, incompressible medium, together

with the continuity equation, can be used to describe adequately the laminar flow

around a road vehicle. As these equations represent, in principle, all the physics

involved, no additional assumptions and modeling are needed.

However, the flow around road vehicles is mainly turbulentand Navier-Stokes

equations for turbulent flows need a turbulence 'model', to make the system of


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equations amenable to numerical analysis. The basic equations employed are

averaged over a time interval. This interval is chosen so as to make the equations

independent of the random eddy fluctuations, yet permit a resolution of the unsteady

macro-structures which may be present. The industry standard turbulence model

used most commonly is the k- turbulence model.

K-epsilon Model

Introduction

The K-epsilon model is one of the most common turbulence models. It is a two

equation model, that means, it includes two extra transport equations to represent

the turbulent properties of the flow. This allows a two equation model to account for

history effects like convection and diffusion of turbulent energy. The first transported

variable is turbulent kinetic energy, k . The second transported variable in this case

is the turbulent dissipation, . It is the variable that determines the scale of the

turbulence, whereas the first variable, k , determines the energy in the turbulence.

Usual K-epsilon models

Standard k-epsilon model

Realizable k-epsilon model

RNG k-epsilon model


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Standard k-epsilon model

Transport equations for standard k-epsilon model

For k;

For dissipation

Modeling turbulent viscosity

Where S is the modulus of the mean rate-of-strain tensor, defined as :


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Effect of buoyancy

where Prt is the turbulent Prandtl number for energy and g i is the component of the

gravitational vector in the ith direction. For the standard and realizable - models, the

default value of Prt is 0.85.

The coefficient of thermal expansion, is defined as

Model constants

The Model constants have the following default values:

RNG-k model:

The RNG model was developed using Re-Normalisation Group (RNG) methods by

Yakhot etal to re normalise the Navier-Stokes equations, to account for the effects of

smaller scales of motion. In the standard k-epsilon model the eddy viscosity is

determined from a single turbulence length scale, so the calculated turbulent

diffusion is that which occurs only at the specified scale, whereas in reality all scales

of motion will contribute to the turbulent diffusion. The RNG approach, which is a

mathematical technique that can be used to derive a turbulence model similar to the


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k-epsilon, results in a modified form of the epsilon equation which attempts to

account for the different scales of motion through changes to the production term.

Applicability and Use

Although the technique for deriving the RNG equations was quite revolutionary at

the time, it's use has been more low key. Some workers claim it offers improved

accuracy in rotating flows, although there are mixed results in this regard: It has

shown improved results for modeling rotating cavities, but shown no improvements

over the standard model for predicting vortex evolution (both these examples from

individual experience). It is favoured for indoor air simulations.

2.7 Introduction to CFDComputational fluid dynamics or CFD is the analysis of systems involving fluid flow,

heat transfer and associated phenomena such as chemical reactions by means of

computer-based simulation. The technique is very powerful and spans a wide range

of industrial and non-industrial application areas. Some examples are:

1. Aerodynamics of airc4raft and vehicles: lift and drag.

2. Hydrodynamics of ships.

3. Power plant :combustion in IC engines and gas turbines.

4. Turbo machinery: flows inside rotating passages, diffusers etc.

5. Electrical and electronic engineering: cooling of equipment including micro

circuits.

6. Chemical process engineering: mixing and separation, polymer moulding.

7. External and internal environment of buildings: wind loading and heating

ventilation.

8. Marine engineering: loads on off-shore structures.

9. Environmental engineering :distribution of pollutants and effluents.

10 Hydrology and oceanography: flows in rivers, estuaries, oceans.

11. Meteorology : weather prediction.

12. Biomedical engineering: blood flows through arteries and veins.


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CFD Code workingCFD codes are structured around the numerical algorithms that can tackle fluid flow

problems. In order to provide easy access to their solving power all commercial CFD

packages include sophisticated user interfaces to input problem parameters and to

examine the results. Hence all codes contain three main elements(1)a pre-

processor,(2)a solver and (3) a post processor. We briefly examine the function of

each of these elements within the context of a CFD code.

Pre-processorPre-processing consists of the input of a flow problem to a CFD program by means

of an operator-friendly interface and the subsequent transformation of this input into

a form suitable for use by the solver. The user activities at the pre-processing stage

involve:

1.Definition of the geometry for the region of interest generally known as the

computational domain.

2.Grid generation i.e. the sub division of the domain into a number of smaller, non-

overlapping sub-domains, a grid(or mesh) of cells(or control volumes or elements).

3.selection of the physical and chemical phenomena that needs to be modeled.4.Definition of fluid properties.

5.Specification of appropriate boundary conditions at cells which coincide with or

touch the domain boundary.

The solution to a flow problem(velocity, pressure, temperature etc.) is defined at

nodes inside each cell. The accuracy of a CFD solution is governed by the number

of cells in the grid. In general, the larger no of cells the better the solution accuracy.

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

hardware and calculation time are dependent on the fineness of the grid. Optimal

meshes are often non-uniform, finer in areas where large variations occur from point

to point and coarser in regions with relatively little change.


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SolverThere are three distinct streams of numerical solution techniques Finite difference,

Finite element and spectral methods. In outline the numerical methods that form the

basis of the solver perform the following steps:

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

2. Discretization by substitution of the approximation into the governing flow

equations and subsequent mathematical manipulations.

3. Solution of the algebraic equations.

The main differences between the three separate streams are associated with the

way in which the flow variables are approximated and with the discretization

processes.

Finite Differences Methods

Finite difference methods describe the unknowns () of the flow problem by means

of point samples at the node points of a grid of co-ordinate lines. Truncated Taylor

series expansions are often used to generate finite difference approximations of

derivatives of in terms of point samples of at each grid point and its immediate

neighbors. Those derivatives appearing in the governing equations are replaced by

finite differences yielding an algebraic equation for the values of () at each grid point.

Finite Element Method

Finite element methods use simple piecewise functions(e.g. linear or quadratic) valid

on elements to describe the local variations of unknown flow variables ().the

governing equation is precisely satisfied by the exact solution. If the piecewise

approximating functions for () are substituted into the equation it will not hold exactlyand a residual is defined to measure the errors. Next the residuals(and hence the

errors) are minimized in some sense by multiplying them by a set of weighing

functions and integrating. As a result we obtain a set of algebraic equation for the


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unknown coefficients of the approximating functions. The theory of finite elements

has; been developed initially for structural stress analysis.

Spectral MethodsSpectral methods approximate the unknown by means of truncated Fourier series or

series of Chebyshev polynomials. Unlike the finite difference or finite element

approach the approximations are not local but valid throughout the entire

computational domain. Again we replace the unknowns in the governing equation by

the truncated series. The constraint that leads to the algebraic equations for the

coefficients of the Fourier or Chebyshev series is provided by a weighted residuals

concept similar to the finite element method or by making the approximate unction

coincide with the exact solution at a number of grid points.

The Finite Volume MethodThe finite volume method was originally developed as a special finite difference

formulation. It is central to four of the five main commercially available CFD codes

:CFX,PHOENICS,FLUENT,FLOW3D and STAR-CD. The numerical algorithm

consists of the following steps:

Formal integration of the governing equations of the fluid flow over all the

(finite) control volumes of the solution domain.

Discretization involves the substitution of a variety of finite-difference type

approximations for the terms in the integrated equation representing flow

processes such as convection, diffusion and sources. This converts the

integral equation into a system of algebraic equations.

Solution of the algebraic equations by an iterative method.

The first step, the control volume integration, distinguishes the finite volume method

from all other CFD techniques. The resulting statements express the (exact)

conversation of relevant properties for each finite size cell. This clear relationship


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between the numerical algorithm and the underlying physical phenomena

conversation principle forms one of the main attractions of the finite volume method

and makes its concepts much simples to understand by engineers than finite

element and spectral methods. CFD codes contain discretization techniques suitable

for the treatment of the key transport phenomena, convection(transport due to fluid

flow) and diffusion as well as for the source terms and the rate of change with

respect to time.

The underlying physical phenomena are complex and non-linear so an iterative

solution approach is required. The most popular solution procedures are the TDMA

line-by-line solver of the algebraic equations and the SIMPLE algorithm to ensure

correct linkage between pressure and velocity. Commercial codes may also give theuser a selection of further, more recent, techniques such as Stones algorithm and

conjugate gradient methods.

Post Processing

As in pre-processing a huge amount of development work has recently taken place

in the post-processing field. Owing to the increased popularity of engineering

workstations, many of which have outstanding graphics capabilities, the leading CFD

packages are now equipped with versatile data visualization tools. These include:

Domain geometry and grid display

Vector plots

Line and shaded contour plots

2D and 3D surface plots

Particle tracking

View manipulation(translation, rotation, scaling etc)

Color postscript outputMore recently these facilities may also include animation for dynamic result display

and in addition to graphics all codes produce trusty alphanumeric output and have

data export facilities for further manipulation external to the code. As in many other


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branches of CAE the graphics output capabilities of CFD codes have revolutionized

the communication of ideas to the non-specialist.

Problem solving with CFDPrior to setting up and running a CFD simulation there is a stage of identification and

formulation of the flow problem in terms of the physical and chemical phenomena

that need to be considered. Typical decisions that might be needed are whether to

model a problem in two or three dimensions, to exclude the effects of ambient

temperature or pressure variations on the density of an air flow, to choose to solve

the turbulent flow equations. To make the right choices requires good modeling

skills, because in all but the simplest problems we need to make assumptions to

reduce the complexity to a manageable level whilst preserving the salient features of

the problem in hand.

A good understanding of the numerical solution algorithm is also crucial. Three

mathematical concepts are useful in determining the success or otherwise of such

algorithms: convergence , consistency and stability

Convergence is the property of a numerical method to produce a solution which

approaches the exact solution as the grid spacing, control volume size or element

size is reduced to zero. Consistent numerical schemes produce systems of

algebraic equations which can be demonstrated to be equivalent to the original

governing equation as the grid spacing tends to zero. Stability is associated with

damping of errors as the numerical method proceeds. If a technique is not stable

even round off errors as the numerical method proceeds. If a technique is not stable

even round off errors in the initial data can cause wild oscillations or divergence

Performing the actual CFD computation itself requires operator skills of a differentkind.

Specifications of the domain geometry and grid design are the main tasks at the

input stage and subsequently the user needs to obtain a successful simulation


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result. The two aspects that characterize such a result are convergence of the

iterative process and grid independence.

The solution algorithm is iterative in nature and in a converged solution the so-called

residual measures of the overall conservation of the flow properties are very small.

Progress towards a converged solution can be greatly assisted by careful selection

of the settings of various relaxation factors and acceleration devices. There are no

straightforward guidelines for making these choices since they are problem

dependent.

Optimization of the solution speed requires considerable experience with the code

itself, which can only be acquired by extensive use. Good initial grid relies largely onan insight into the external properties of the flow. A background in the fluid dynamics

of the particular problem certainly helps and experience with grinding of similar

problems is also invaluable.

The only way to eliminate errors due to the coarseness of a grid is to perform a grid

dependence study, which is a procedure of successive refinement of an initially

coarse grid until certain key results do not change. Then the simulation is grid

independent.

Validation of a CFD code requires highly detailed information concerning the

boundary conditions of a problem and generates a large volume of results. To

validate these in a meaningful way it is necessary to produce experimental work may

not(yet) exist in which case the CFD user must rely on (1)previous experience,(2)

comparisons with analytical solutions of simpler flows and (3)comparisons with high

quality data from closely related problems reported in the literature.

CFD computation involves the creation of a set of numbers that constitutes a

realistic approximation of a real time system.

It is clear that there are guidelines for good operating practice which can assist the

user of a CFD code and repeated validation plays a key role as the final quality

control mechanism. However, the main ingredients for success in CFD are


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STRUCTURED

experience and a thorough understanding of the physics of fluid flows and the

fundamentals of the numerical algorithms. Without these it is very unlikely that the

user gets the best out of a code.

A SPECIAL MENTION TO GRIDSThe use of CFD is spreading in all areas of engineering. The flow domains are

usually very complicated, which places high demands on both meshing and solution

methods.

Grids can either be structured(hexahedral) or unstructured(tetrahedral).It

depends upon type of discretization scheme and application.

Scheme

Finite differences: structured

Finite volume or Finite element: structured or unstructured

Thin boundary layers are best resolved with highly-stretched grids.

Unstructured grids are useful for complex geometries

Unstructured grids permit automatic adaptive refinement based on thepressure gradient, or regions interested(FLUENT).

Most flows of engineering interest take place in complex geometries. The flow

domain is in many cases difficult to define: the CAD-data provides a description of

UNSTRUCTUREDFi 23 : Di erent t es o meshes


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parts surrounded by fluid, but the extraction of a closed fluid volume is often a non-

trivial job. CFD-engineers usually spend a large-if not the largest-portion of their

analysis time on this task. The starting point for a CFD simulation is often a CAD-

data, usually provided by designers or analysts from another department; CFD-

engineer has to import this data into one or more tools and work on it until a

satisfactory mesh is created. A tool for the clean-up and repair of CAD-data is

indispensable in the process of grid generation for complex geometries. Not only

that it has to provide the possibility of creating a closed surface enclosing the flow

domain, but it also has to facilitate the desired simplification and removal of

geometry details which are deemed unimportant for the flow analysis. Such details

can make meshing substantially more complicated while having little effect on thecomputed flow; however, one has to be careful as sometimes small geometrical

details can trigger phenomena which otherwise may not be captured in the

simulation(separation, unsteadiness etc.).This step often requires a skilled analyst

who can evaluate the surface and make adequate decisions about the level of detail

that is to be retained in the final closed surface. In addition to flow volume extraction

from exact geometry defined by CAD-data, surface-wrapping techniques are often

used to create an approximated closed surface of the flow domain. This approach

usually leads to small geometry details getting lost during the wrapping process,

whish is often satisfactory; caution is needed in order to ensure that the main flow

features are captured. The advantage of this approach is that it can be fully

automated.

Meshing of complex Flow DomainsSince flow domains can be arbitrarily complex, the meshing procedure should be

fully automatic, as any manual intervention by the CFD-engineer may require bothtoo much time and special skills to produce an optimal result. Therefore, block-

structured grids can seldom be used; unstructured meshes are the only practical

alternative.

The meshing tool-in addition to being automatic-needs to fulfill the following criteria:


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Prismatic layers should be automatically created along walls, if viscous flows are

to be computed. The prisms may have any polygonal base(from triangle

onwards) it is most important that there are enough of cells with two faces

parallel to wall in order to allow for an appropriate treatment of the wall boundary

layer. Also, parts like ducts, pipes, narrow gaps etc. should be recognized and

meshed with prismatic cells, both for accuracy (allowing for an accurate

treatment of parallel flow) and efficiency reasons(allowing for higher aspect

ratios)

The mesh fineness should be controllable, both by the user(who often knows in

advance where the mesh should be finer) and by the solver(for a subsequent

mesh adaptation and error-guided mesh refinement). The mesh quality should be controlled and, where necessary, automatically

repaired. This can be achieved by re-meshing, merging, or splitting of bad cells.

The most widely used unstructured meshes are those made of tetrahedral, usually

with a layer of triangular prisms along walls to allow for an appropriate treatment of

boundary layers. While such meshes are the easiest to generate, their quality is

often inappropriate. The prism layers along walls alleviate the problems associated

with flat tetrahedral near boundary, but the fact that a tetrahedron has only four

faces-and thus only four neighbor cells-makes cells of this type less suitable for

approximation of diffusive fluxes than hexahedra or polyhedra. The problem is that

,in order to compute gradients of dependent variables, the four nearest neighbors of

a given cell are often not sufficient to achieve the accuracy offered by control

volumes with six or more faces. The consequence is that a larger number of

tetrahedral control volumes are needed when computing viscous flows to achieve

the desired accuracy than when hexehedra or polyhedra are used. Hexahedral

control volumes are probably optimal from efficiency and accuracy point of view, but

meshes made of good quality hexahedra are difficult to generate automatically.

Polyhedra meshes, on the other hand, can be generated automatically as easily as

tetrahedral meshes; while they have more neighbors and thus require both more


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storage And computing time per cell, the higher accuracy usually compensates for

the extra effort.

The question often asked is: which grid is optimal for my application? Any grid type

leads asymptotically to the same solution(there are exceptions where the error is not

reduced by grid refinement, but these are not typical and will not be considered

here);however, the effort needed to obtain a solution of a required accuracy depends

largely on the mesh type and quality. A general recommendation is to use prismatic

cells not only along walls but also whenever flow direction is fixed by the

geometry(pipes, channels, ducts, small gaps etc).This means that the side prism

faces should be aligned with the flow while the prism base should be orthogonal to

flow direction. On the other hand, when recirculating flows are encountered,polyhedral cells tend to generally be the most efficient ones. Tetrahedral cells if used

as control volumes-are the least suitable; there are methods, however, which use

tetrahedral meshes but solve on a dual mesh(which is effectively a polyhedral

mesh),thus alleviating the problems associated with tetrahedral control volumes.

Commercially available CFD codes:

Commercial CFD code: FLUENT, Star-CD, CFDRC,CFX/AEA, etc.

Research CFD code: CFDSHIP-IOWA.

Public domain software (PHI3D,HYDRO, and WinpipeD, etc.)

Other CFD software includes the Grid generation software (e.g. Gridgen,

Gambit) and flow visualization software (e.g. Tecplot, FieldView)


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Chapter 3

PROJECT METHODOLOGY

3.1 Geometric modeling

To understand the effect of change in the rear end 3 different car models are being

considered namely :

a. AUDI-A4(notchback)

b. AUDI-Q7 (squareback)

Due to time constraints the hatchback model is not being considered in the analysis.

The 3D-model of the above mentioned cars were generated in SOLIDWORKS. To

have profile accuracy the blueprints of all models were traced on graph paper. Then

from the graphs, co-ordinates of different points through which the curve passed

were obtained. The next step was to scale model by deciding a scale factor between

the traced image dimensions and the actual dimension. The above scale was set

with reference to the wheel base(actual/graph).

Fi 23 : CFD methodolo


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1) Audi A4

Table no : 1Point number X(mm) Y(mm) Point number X(mm) Y(mm)

1 330.1 178.6 15 4990.9 607.2

2 330.1 428.6 16 5088 589.4

3 427.2 714.4 17 5126.9 535.8

4 873.9 821.6 18 5126.9 464.45 1437.1 857.3 19 5058.9 410.8

6 1747.8 1071.6 20 5058.9 330.4

7 2039.1 1214.48 21 4408.3 214.3

8 2427.5 1285.9 22 4408.3 321.5

9 2913 1285.9 23 3981.1 660.8

10 3301.4 1285.9 24 3592 321.5

11 3884 1160.9 25 3592 160.7

12 4408.3 982.3 26 1359.4 160.7

13 4874.4 928.7 27 1359.4 321.5

14 4952.1 785.8 28 97.1 660.8

Fi 24 : Side view ro ile o AUDI A4 on ra h


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The solid models as obtained in solid works is as below:

Fi 25 : Solid model o UDI 4


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2) AUDI Q7

Table no : 2Point number X(mm) Y(mm) Point number X(mm) Y(mm)

1 411.46 971.52 15 5260.81 794.88

2 881.7 1118.72 16 5348.98 706.56

3 1175.6 1148.16 17 5319.59 647.68

4 1557.67 1177.6 18 5202.03 412.16

5 2057.3 1442.56 19 4819.96 323.84

6 2

aerodynamic analysis of a car.pdf

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