Mathematical Modeling of Europa Aerodynamics

Yes, I have tried to do some fluid flow modeling of the Europa body shape. Through my work I have access to Fluent, a commercial fluid flow package. Always on the look out for ways to speed up my car I wanted to look at the aerodynamics and so I decided to have a go.

Those familiar with this sort of technique will appreciate that the first requirement is to generate a geometrical model of the car. This can then be meshed and the flow then modeled. In the absence of any other information (do you know of a full set of 3-D surface co-ordinates? - if so please e-mail me with details), I decided that a 2-D slice along the centre line of the car would do, at least as a starting point. I did this by fixing a straight edge to the rafters of my garage and measuring the height of the top body surface from this datum at regular intervals along the length, approximately every 100mm. I then did a similar thing using the floor to measure the underside profile. Hardest part was the windscreen, because it slopes so much. Finally, I used a profile measurer (one of those things with lots of sliding needles) to do all the twiddly bits such as the bumpers, windscreen surround etc. These were traced onto graph paper and the coordinates recorded. The measurements were put into a data file on my computer. To gain more access underneath, the car was up on dollies so I used a Visual Basic programme to convert the measurements to real x,y values as if the car was sitting on the ground. Eventually I want to look at ride height effects so this will also be useful.

The modeling was carried out using Fluent/UNS, an unstructured code. The model was built as if the car were sat in a moving floor wind tunnel. The domain was extended 10m up and 40m from the back of the car. A uniform inlet velocity of approximately 60mph was used with the same floor speed. The grid was adapted according to the velocity gradient and finished with around 150000 cells (I can see why full body 3-D models are so huge). The computational grid after adaption is shown below.

The contours of velocity magnitude around the body are shown below.

 Note the way that the rear lip on the engine cover has no effect at all and would have to stick up miles before it had an effect. There is a sharp increase in velocity at the top of the windscreen. My car has a plastic sun roof which probably magnifies the effect. I will try blending in this area. Note the low velocities at the bottom of the windscreen which gives a high pressure area, used by many car manufacturers to act a a source for the ventilation system. This is typical of all cars and explains why you have to have the ventilation fan on if the heater inlets are positioned in this area. On my car I have removed the fibre glass from behind the rear number plate and fitted an oil cooler. There seems to be plenty of air flow through it.

Below is an enlarged image of the front of the car.

Of particular interest is the high velocity region under the floor where there is a lip at the rearward end of the chassis plate where the pedal box bolts down. Mine is a Spyder chassis and it seems to be causing some problems in this area.

I have used the model to calculate the downforce and drag. In fact there is a quite large upward lift on the body - ie there is negative down force.

Next stage is to look at alterations to the shape to improve things, in order to reduce drag and to reduce the upward lift.

Following this work in 1998 I am now taking the opportunity to report some more modeling that I have done. Since starting the work there has been a new version of the Fluent preprocessor so it seemed a good idea to use this for practice. Note also the newer version of Fluent.

The following picture shows the base case, i.e. of the original car.

Next with the silly Spyder lip under the bottom of the car removed.

You can clearly see how the air flow under the car has been cleaned up.

Next I tried adding a rear diffuser. This was easy to on the model - simply add a wall from the back of the chassis to the bottom of the rear vallance. I used a straight line:

Air velocities under the car are much high, suggesting lower pressures and a bit of downforce.

As an alternative I tried a big front air dam to stop the air getting underneath:

This has obviously stopped the air flow quite well.

Finally I tried the air dam and the diffuser together:

The following table shows the calculated lift forces:

Model	Lift Force
Base	+657
Bottom lip removed	+382
Bottom lip removed + diffuser	-469
Bottom lip removed + air dam	+298
Bottom lip removed + diffuser + air dam	+240

The absolute values of these numbers should probably be taken with a pinch of salt but their relative ranking appears to be highly significant.

Even a small change like grinding off a half inch lip can make an appreciable difference. However, look at the huge effect that the diffuser has had, potentially changing lift into downforce. It is clearly much better than those big old fashioned air dams. It can be seen that adding an air dam in front of the diffuser stops it working, which is, perhaps, not surprising.

The use of diffusers is now very widespread - see for example the Lotus Elsie. Graham Oates has added one to his sprint and hill climb Lotus Europa. The engineering looks fairly simple but I am sure the simple design shown here can be further refined. The sharp angle between the floor and the diffuser will almost certainly give detachment of the air stream. It may be possible to use a curved or stepped profile to prevent this.

Watch this space.

If anyone has a set of nodal coordinates for the whole body surface I should be pleased to hear from you. Contact me on

keithwilford@lotuseuropa.freeserve.co.uk