Computational fluid dynamics

Definition

Any material which flows, such as air or water, can

be referred to as a fluid; ‘dynamics’ simply means

moving and ‘computational’ is about calculations.

Aerodynamics was for many years about observing

the air flow over a vehicle, with sample calculations

for specific areas of the car; the advent of

computers meant that calculations could be done

many times faster than by long hand. So, it became

possible to carry out calculations for large sections

of the car very quickly.

In the 1970s engineers became interested in

the aerodynamics which were taking place both

underneath and inside the car, places which

could not be seen. More recently software has

been developed, such as AutoCAD, 3D Studio

and Pro/ENGINEER, which allows solid modelling

and the facility to virtually walk through a

40% overlap = 40% of the

width of the widest part of the

car (not including wing mirrors)

540 mm

1000 mm

64 kph (40 mph)

40%

overlap

500 mm

1500 mm

50 kph (30 mph)

R-Point

R-Point = hip point for a 95th

(a) Frontal impact test percentile male

(b) Side impact test

(c) Pole test (d) Pedestrain impact test

Child

head

Adult

head

Upper

leg

Leg

29 kph (17 mph)

Pole Diameter = 254 mm

The history, development and construction of the car body 31

design. This means that there is now no longer

a need to make a buck, or a mock-up, of a car to

be able to visualize the design. As an example,

vehicle body engineers used to use a wooden

buck of an engine to help them to design the

body work, and see if it could be fitted to and

removed from the initial body design. The Rover

75 is the first car to be designed without this; a

solid modelling package was used for a virtual

engine and body design, allowing an onscreen

test fit.

Having designed the virtual car it is possible to

observe it in a virtual wind tunnel and carry out

calculations both internally and externally, this is

what computational fluid dynamics (CFD) is all

about. As you can appreciate, the cost of a virtual

design and aerodynamic testing without a wind

tunnel is only a fraction of the cost of building a

buck and using a real wind tunnel.

The calculations

The following are some of the calculations which

an aerodynamist may be concerned with; it

should be remembered that these calculations are

often carried out on about 10 000 000 (ten million)

individual grid squares, or cells, on the car

body, a slight change of design will need a new

set of calculations. Even using the latest computer

software, the slightest change may take several

days; without CFD it would take months, and the

level of accuracy would be much less. If you

choose to use any of these formulae, remember to

use SI units, metres, newtons and seconds where

appropriate.

Dynamic pressure, which is also a kinetic energy

of unit volume in terms of cubic metres, comes

from the Bernoulli equations. Bernoulli was a scientist

whose fluid flow theories were first used in

the design of ships’ hulls.

Dynamic pressure

_ 1/2 _ air density _ vehicle velocity squared

_ 1/2 _V2

As you can see, the speed (velocity) of the vehicle

is important for these calculations. Of course

velocity is a vector quantity, it is related to the

direction of the wind. Wind is very rarely a

straight-on head wind, so calculations can be done

for any of the 360 degree possible wind directions

for each of the ten million grid squares. Yes, that is

3.6 billion calculations for each speed and of

course the air density varies with altitude; at sea

level the value is 1.226 kilogrammes per cubic

metre.

Reynolds Number is a ratio which gives a good

guide to the air flow pattern and is an important

consideration of what is called scale effect.

Reynolds Number

_ air density _ air velocity

_ length of flow/air Viscosity

Re _ __l__

Drag is the aerodynamic resistance of the vehicle,

its resistance to pass through air. Drag in newtons

force is found by the formula:

Drag _ 1/2 air density _ velocity squared

_ frontal area _ coefficient of drag

_ 1/2_V2ACD

You will see that part of the formula is familiar,

and part of it is the same as dynamic pressure,

therefore:

Drag _ dynamic pressure _ frontal area

_ coefficient of drag

The coefficient of drag is a number which indicates

the resistance of the car to pass through the air,

typical values are between 0.25 and 0.35.

Lift is the force generated by an aerofoil section

normal to the direction of fluid flow. In other

words it is the upward lifting force which is generated

when passing horizontally through air. For

road vehicles wings are used to hold a vehicle on

to the road, this can be called downthrust or negative

lift.

Lift _ dynamic pressure _ wing area

_ coefficient of lift

When working with road vehicles the frontal area is

often used for the wing area figure. On aircraft, the

wing plan area is more appropriate. With advanced

aerodynamic work the plan area is related to a

reference area. For most road vehicles the frontal

area and the plan area are proportional; also the

coefficient of lift and the coefficient of drag are also

proportional.

Lift _1/2_V2ACL

32Repair of Vehicle Bodies

Grid system

The vehicle body shape is broken into grid squares,

or cells, see Figure 1.29. Depending on the shape

of the panel, the grid cells may be of different

shapes between square and oblong.

The squares are then considered as imaginary

cube shapes, see Figure 1.30. A set of calculations

called the Navier–Stokes equations gives a relationship

between pressure, momentum and viscous

forces in three-dimensional space. There is also a

similar set called the Euler equations. The above

calculations covered some of these concepts. The

computer is used to calculate the amount of energy

which is entering each cube and in turn leaving it.

Obviously the two figures should balance and there

will be flow between adjacent cubes.

Ahmed model

For benchmark testing of CFD systems the simplified

vehicle shape, known as the Ahmed model, is

used, see Figure 1.31. This is a simplified model of

a hatchback car. The Ahmed model can be made

from a wooden block and used in any wind tunnel.

1.3 Methods of construction

The steel body can be divided into two main types:

those which are mounted on a separate chassis

frame, and those in which the underframe or floor

forms an integral part of the body. The construction

of today’s mass-produced motor car has

changed almost completely from the composite,

that is conventional separate chassis and body, to

the integral or mono unit. This change is the result

of the need to reduce body weight and cost per unit

of the total vehicle.

Composite construction

(conventional separate chassis)

The chassis and body are built as two separate

units (Figure 1.32). The body is then assembled

on to the chassis with mounting brackets, which

Figure 1.30One cube shape in a grid cell, the CFD

calculates the energy of entering and leaving each

cube (Dr Barnard 1996)

Figure 1.29Grid of cells on a Volvo car (Dr Ramnefors 1994)

The history, development and construction of the car body 33

Figure 1.31The Ahmed Model, a simplified shape of a hatchback vehicle (Dr Ahmed 1984)

Figure 1.32Composite construction (conventional separate chassis)

34Repair of Vehicle Bodies

Figure 1.33Composite construction showing a Lotus Elan chassis before fitting the body (Lotus Engineering)

have rubber-bushed bolts to hold the body to

the rigid chassis. These flexible mountings allow

the body to move slightly when the car is in

motion. This means that the car can be dismantled

into the two units of the body and chassis.

The chassis assembly is built up of engine,

wheels, springs and transmission. On to this

assembly is added the body, which has been preassembled

in units to form a complete body shell

(Figure 1.33).

Integral (mono or unity)

Construction

Integral body construction employs the same

principles of design that have been used for years

in the aircraft industry. The main aim is to

strengthen without unnecessary weight, and the

construction does not employ a conventional separate

chassis frame for attachment of suspension,

engine and other chassis and transmission components

(Figure 1.34). The major difference between

composite and integral construction is hence the

design and construction of the floor (Figure 1.35).

In integral bodies the floor pan area is generally

called the underbody. The underbody is made up of

formed floor sections, channels, boxed sections,

formed rails and numerous reinforcements. In most

integral underbodies a suspension member is

incorporated in both the front and rear of the body.

The suspension members have very much the same

appearance as the conventional chassis frame from

the underside, but the front suspension members

end at the cowl or bulkhead and the rear suspension

members end just forward of the rear boot

floor. With the floor pan, side rails and reinforcements

welded to them, the suspension members

become an integral part of the underbody, and

they form the supports for engine, front and rear

suspension units and other chassis components. In

the integral body the floor pan area is usually of

heavier gauge metal than in the composite body,

and has one or more box sections and several channel

sections which may run across the floor either

from side to side or from front to rear; this variety

of underbody construction is due largely to the

difference in wheelbase, length and weight of the

car involved. A typical upper body for an integral

constructed car is very much the same as the

conventional composite body shell; the major

differences lie in the rear seat area and the construction

which joins the front wings to the front

The history, development and construction of the car body 35

bulkhead or cowl assembly. The construction in the

area to the rear of the back seat is much heavier in

an integral body than in a composite body. The

same is true of the attaching members for the front

wings, front bulkhead and floor assembly, as these

constructions give great strength and stability to

the overall body structure.

Semi-integral methods of

Construction

In some forms of integral or mono assemblies, the

entire front end or subframe forward of the bulkhead

is joined to the cowl assembly with bolts. With this

construction, the bolts can be easily removed and the

entire front (or in some cases rear) subframe can be

replaced as one assembly in the event of extensive

damage.

Glass fibre composite

Construction

This method of producing complex shapes involves

applying layers of glass fibre and resin in a prepared

mould. After hardening, a strong moulding is

produced with a smooth outer surface requiring little

maintenance. Among the many shapes available

in this composite material are lorry cabs, bus front

canopies, container vehicles, and the bodies of cars

such as the Reliant Scimitar. The Italian designer,

Michelotti, styled the Scimitar body so that separately

moulded body panels could be used and

overlapped to hide the attachment points. This

allows the panels to be bolted directly to the supporting

square-section steel tube armatures located

on the main chassis frame. The inner body, which

rests directly on the chassis frame and which forms

the base for all internal trim equipment, is a complex

GRP moulding. The windscreen aperture is

moulded as a part of the inner body, and incorporates

steel reinforcing hoops which are braced

directly to the chassis. The boot compartment is

also a separate hand-laid GRP moulding, as are the

doors and some of the other panels. Most of the

body panels are secured by self-tapping bolts which

offer very positive location and a useful saving in

assembly time (see Figures 1.36 and 1.37).