Overview

Topic 1 – Basic aerodynamic principles

Let us begin by examining the effects of Bernoulli’s Principle as applied to an airfoil.  Bernoulli demonstrated that as a fluid (such as air) travels faster, the pressure it experiences is lower.  Consider two air molecules approaching an airfoil along the streamlines shown in the figures below.   One travels along the bottom side of the airfoil, and the other along the top side.  Continuity says that they must reach the back of the airfoil at the same time.  However, the molecule on the top side has travel further.  Thus, it must have been traveling faster to have arrived at the same time.  This means the velocity of air on the top side of the airfoil is faster than the bottom side, and thus the pressure on the top surface is lower than on the bottom surface, producing a net upward force, or Lift. 

Comparing velocity

However, Lift is not the only force which is important to us, either on an airplane or on a racecar.  As an object moves through the air (or any fluid), there is a resistance to its motion, due to the fact that it must push air molecules out of the way in order to move.  The force of resistance is called Drag.  We must be careful to realise that even as we create Lift, the shape that we are pushing through the air, also experiences a Drag force, resisting its motion.

Just as the shape of the airfoil influences the difference in velocity over the top versus the bottom surface, and thus effects the Lift, the shape of the object as it moves through the air influences the Drag.  It is obvious, as we look at different shapes (such as the two vehicles shown below) that some are more aerodynamically shaped than others, and thus create less resistance to the air moving around it, and therefore, less Drag.

Any body moving in a fluid experiences forces caused by the action of that fluid.

• Drag is the force on the body caused by the fluid which resists the motion of the body
  • Drag forces are expressed by  F_D = C_D(ρv²/2)A
  • C_D is the drag coefficient, based on the object’s shape
  • ρ is air density
  • v is the velocity of the air moving past the object
  • A is the projected frontal area

• Lift is the force caused by the fluid in a direction perpendicular to the Direction of travel of the body
  • Lift forces are expressed by  F_L = C_L(ρv²/2)A
  • C_L is the drag coefficient
  • The other parameters are the same as above

Topic 2 - Simple aerodynamic analysis

Earliest aerodynamic analyses came from empirical data gathered through testing of a simple shape moving through a fluid.  What follows is a simple Drag Coefficient Chart from such early work, where data was gathered by actually measuring the force required to move a shape through a fluid.  The horizontal axis is the Reynolds Number, N_R, of the fluid flow:   $N_g=\rho \nu D/\mu$

Where

$D$ = diameter of the body  
$\mu$ = air viscosity  
$\nu$ = velocity of the flow
$\rho$ = fluid density

The next step forward in aero analysis was to create a test rig where the air moved around the object.  This permitted larger objects to be tested.  The result is what we call a wind tunnel, where the test object sits still, and air is blown around it.

The following shows early wind tunnel data examining the effect of a Rear Spoiler on a vehicle.  Remember that reduced vehicle Lift leads to the production of Downforce.

The data shows that both spoilers very significantly reduce the Lift on the nearest axle.  Also note that the effect is greatest as speed is higher.  This makes sense when we revisit the Lift force equation, $F_L=C_L\left(\rho {\nu }^2/2\right)A$, which shows that the force should increase with the square of the speed.

The next example shows how addition of a pure airfoil, mounted inverted on the vehicle, can produce very large increases in Downforce.  Jim Hall’s Chaparral 2G racecar introduced movable wings to motor racing.  It featured a two-position high mounted wing.  It operated in either a “trimmed” or “spoiled” condition.  Trimmed, the wing produced minimum drag for maximum straightaway speed.  Spoiled, (tilted at 12 degrees angle of attack) it produced Downforce and Drag, to assist cornering.  This had the impact of assisting to slow the car (by increased Drag force) and improving cornering via increased traction through Downforce.  It was, without a doubt, the most innovative racecar of its time and it ushered in a new era of vehicle aerodynamics. 

Topic 3 - 3D modelling and computational fluid dynamics (cfd)

One of the things that we seek to do in aerodynamic analyses is to ascertain the flow around an object, and how changes in that flow affects Lift and Drag.  The next figure was created using a flow analysis programme on the three-part racecar wing shown at the top of the figure.  The wing was examined at various angles of attack (the orientation of the wing relative to the airflow, and this is plotted on the horizontal axis in degrees) and also with and without end plates on the end of the wing.   Two dependent parameters, the Lift and Drag Coefficients, are both plotted on the vertical axis.

Graph showing lift and drag coefficients (Milliken 1995:p516)

This study shows that both Drag and Downforce (i.e. negative Lift) are greater for the wing with end plates.  The increase in Drag makes sense, because the plates are an additional surface which must be pushed through the air.  So, it is not surprising that they generate more drag.   But the gain in Downforce seems a bit counter intuitive.  Upon closer examination, however, it turns out that when the air traveling over the wing surface is very near the end of the wing, it has a tendency to “slip off” the end of the wing, rather than traveling along the entire wing contour.  This “lost” air thus fails to contribute to the increased top surface pressure that creates the Downforce.  Adding the end plates prevents this air from “slipping off” the end of the wing, but rather, keeps it traveling along the wing contour.  

Sometimes very subtle changes to an airfoil system can make a difference which is more significant that none might expect.  The next figure indicates how the Drag coefficient and Downforce (negative Lift) coefficient can change by the addition of very small fin or flap appendages.

Graph showing drag coefficient and downforce coefficient (Milliken 1995:p520)

Similarly, small changes in the angle of the nose wing on a formula racecar can significantly affect the Downforce generated at the front of the vehicle.

Small changes in the angle of the nose wing (Milliken 1995:p518)

The time and expense involved in running a full-scale wind tunnel test in order to gather empirical test data to distinguish the effects of such subtle changes can be very time consuming and expensive.  Even scale-model tests take a great deal of effort and are costly.   Therefore, as computer analysis technologies have advanced, it has become more cost effective to run Computational Fluid Dynamics (CFD) computer analyses.  Of course, we have to ask ourselves if these computer models generate accurate results.  As the figure below indicates, they are certainly capable of generating results adequate to assess comparisons between different configurations, such that only those configurations which show significant promise can be taken to the wind tunnel, thus greatly reducing the time and expense of actual testing.

Computational Fluid Dynamics (CFD) computer analyses (Milliken 1995:p518)

CFD allows us to look at any surface of a vehicle to examine the aerodynamic effects.  By properly shaping the underside of the vehicle, it is possible to create a “ground effect” where the volume beneath the car becomes a low pressure area, created by the vortex of air flowing through the venturi shaped passages on the underside of the car.

Underside of an hovercraft (Milliken 1995:p534)

Topic 3 - Application 1

Advances in Computational Fluid Dynamics have made computer analysis of racecar aerodynamics much easier to perform than actual testing.  Let us examine a study performed to evaluate how the Downforce of a formula car front wing was impacted by how high above the track surface it was located.  One might assume that we would want to have our wing as close to the ground as possible, right?  However, that is not what the CFD results say. 

CL versus ground clearance
(For a dual-element front wing)

Lift coefficient as affected by height above road surface for various airfoils

Topic 3 - Application 2

CFD effects can be surprising when compared to our assumptions. These figures below display the change in pressure due to an increase the flap angle of the front wing.  The red on the color gradient indicates the highest increase in pressure, and yellow a lesser increase, but still an increase.  While the blue indicates the greatest decrease in pressure, and the green a slightly lesser decrease, but still a decrease.   Gray indicates no change in pressure.

Change in pressure due to flap angle

Topic 3 - Application 3

The figure right plots the free stream energy in the air flowing around the car.  Red indicates high free stream energy, while purple indicates low free stream energy, i.e. the energy is being gobbled up by turbulence. 

The top 4 figures show different vertical cross sections, at different distances from the vehicle centerline.  You can see the effects of cockpit, mirrors, wheels, etc.  The bottom figure is a horizontal cross section at the height of the rear wing mainplane. 

From this, could we assess whether widening the wing would provide a benefit on this car?

Clearly CFD is a very useful tool for improving our vehicle aerodynamics.  The next figure shows air flow streamlines.  What does the up-turn behind the car cause?  Would it be of interest to the racecar following behind? 

Air flow streamlines on a racing car

The next figure shows the surface pressure on the front of the car, here the red zones represent the highest pressure.

Surface pressure on the front of the car

Effects on individual components like the front wing or brake duct can be easily studied as shown in the next figures.

Front wing and break duct

Topic 3 - Application 4

Topic 4 - Other advanced flow modelling

CFD analysis can be applied to other things that we have examined during this module.  For example, the cooling flow through a turbine blade which is used to keep the temperatures manageable.  By use of CFD analysis in conjunction with FEM analysis we can determine how the air flows though the blade and its impact on the temperatures of the blade.

CFD analysis can tell us many things about air flow around turbine aerofoils.

(Youtube, 9 secs)

The diagrams below can also be used to examine the flow in the cylinder of an IC engine.

Topic 5 – CFD analysis routines for student use

Another FEM routine which has a free student version is ANSYS through its Fluent CFD option.  Here are links to videos showing how to use that routine:

Youtube, (12:21)

Youtube, (21:35)

Youtube, (16:50)

Reference

Gillespie, T. (2000). Fundamentals of Vehicle Dynamics.  Detroit,

          USA: SAE International.

Seward, D.(2014). Race Car Design.  London: MacMillan.

Milliken, W. & Milliken, D. (1995).  Race Car Vehicle Dynamics. Detroit,

          USA: SAE International.

Milliken, W. (2006). Equations of Motion.  Cambridge, USA: Bentley.