Simplified (un)Steady Slaloms

A final-year student (non-team-member) came to me looking for a project in vehicle aerodynamics for a class, and I saw this as a good opportunity to try something that I had otherwise been assuming wasn't worth the time of the current aero team. That is, to see if the vertical motion of the side-mounted floors induced by vehicle roll during highly transient cornering scenarios (such as slaloms) significantly effects the downforce and general flow characteristics of the diffuser and tunnel. 

I would expect some difference due to an effective angle-of-attack change, as well as a change of effective curvature of the floor profile experienced by the flow's frame of reference. These effects would quickly become negligible with higher speeds though, for the same reason that seemingly wobbly wings on F1 cars don't affect their performance. An additional potential difference would be that created by the floor's vertical motion contracting or expanding the volume underneath it, creating changes in overall static pressure. This too would become insignificant compared to the pressures otherwise generated by the diffuser as speed increases, but I didn't know at what speed this would occur.

Given the limited time for the project, and that the student had all of one hour of prior CFD experience, I simplified the problem to be 2D, thus ignoring any effects of finite width and vehicle roll angle. This would create a worst-case scenario for any transient effects to show themselves. If nothing significant came up here, we could be confident that there would be nothing of interest to see in 3D either. Since I'm no longer on the team after graduating, a simplified project setup like this that requires no direct interaction with the car or team works well for me to supervise without getting in anyone's way.

A representative slalom case was taken from suspension positions from previous track data. The first few short slalom sections I found while scrolling through plots were all consistently between 0.65-0.7s duration from peak to peak, as shown below at a plotted resolution of 25 Hz. The low resolution combined with temporary 3D-printed mounts for the sensors left a fair bit of noise but that didn't matter given our macro-level interest. Speeds were typically around 10 to 10.5 m/s. 

Unsurprisingly but conveniently, the motion was somewhat sinusoidal. A a reasonably accurate velocity function for CFD use was therefore easily created, knowing the expected roll angle of the car and assuming the 2D slice to be simulated is taken at the outer edge of the floor where vertical motion is maximised. A motionless period at the start and end was included to allow the solution to settle first, and to see how long it takes to return to static performance after motion ceases. The main point of interest is when vertical velocity is at a maximum, so to best capture these two instances, the simulations were run with the floor starting at its highest position (i.e. the inboard floor at the apex of a slalom).  

In case the results were interesting, I wanted some context in the form of an alternative floor profile. This would also help reduce some of the over-reliance on assumptions and simplifications by allowing a relative rather than absolute assessment of transient performance. My criteria was for them to find something with similar total downforce and flow separation behaviour. Using Javafoil, they selected a NACA 4412 profile which had total downforce within 5% (as predicted by Javafoil, still in 2D) and a similar flow separation point, albeit with a slightly thinner recirculation region. 

The two profiles are shown below. Given only the suction side was being analysed, the pressure side of the custom 2024 profile was replaced with a most flow-aligned surface to avoid separation off the back of the leading edge. 

Below are the Javafoil pressure distribution estimates for (top) the custom 2024 floor profile, and (bottom) a NACA 4412 profile at equal ground clearance (55 mm) and Reynolds number.  

2D sims were then run in Ansys for each of the two floors at three positions; maximum height (78 mm), ride height (55 mm), and minimum height (32 mm). One transient simulation was run per floor. I had specified 5 key results that should be analysed:

• Total downforce at each position, making comparisons between static and transient performance of each floor, and of the transient performance between the two floors

• Pressure distribution and centre of pressure location, making the same comparisons

• Location of flow separation and maximum thickness of the recirculation region, making the same comparisons

• Confirmation that the above three metrics have the same values between static and transient simulations at the maximum height before motion starts, and have similar values at the minimum height when vertical velocity is 0, to confirm the transient simulation results were behaving and converging as expected.

• Time taken for total downforce values to return to steady-state after the floors return to maximum height and motion ceases. 

After confirming the 4th point to within 2% and 5% for the maximum and minimum heights for both floors, the transient results as the floor passed down and up through the central (ride height) position were analysed in more detail. The results I found most interesting were the pressure distributions for each floor. 

In the above images, "zone" was used to refer to one of twenty sampling points evenly spaced between the leading and trailing edges, along the suction surface of both profiles. 

Common between both floor profiles was a forward shift in COP during upward motion, and a rearward shift during downward motion. This was more exaggerated for the 2024 profile, suggesting its aero balance was more sensitive to vertical motion than the NACA 4412 profile, although the difference was minor. Interestingly, the peak pressure magnitudes during the downward motion were vastly different between the two profiles, not only in absolute magnitude but also relative to their respective static values. The negative pressure increase for the 2024 profile here may not best represent what is expected to happen in reality though, as it appeared to have been a result of reduced flow separation (observable in the top plot above as the increase in negative pressure near the trailing edge relative to the other two cases), which was already the point of biggest discrepancy to previous 3D CFD results for this floor profile in full-car context. All other results at ride height for both profiles showed similar separation behaviour between all cases. 

Total downforce during upward motion showed negligible difference to static values for both profiles (<5%). During downward motion, the 2024 profile showed negligible difference to the equivalent static value, but 30% total downforce was lost on the NACA 4412 profile during the same scenario. As mentioned above, the 2024 profile might be artificially overperforming here relative to its static results, but it seems unlikely even with more representative flow separation behaviour that it would see such a significant deficit. 

Finally, when it came to settling back to steady-state flow, the NACA 4412 profile took 0.05 s to re-establish (equal to the time taken for the accelerated flow to traverse the length of the floor; a satisfyingly logical result), while the 2024 profile took 0.12 s. This suggests unstable flow separation behaviour, but again this is expected to be much less significant in 3D.

While the 2024 floor may have overperformed in some aspects during these 2D simulations, the 30% downforce loss estimate for the NACA 4412 is hard to ignore. Given the 2024 profile has already been optimised and put to use on the real car, there was a good reason here to both keep it, and to not worry about putting any further team time into further investigating or optimising its performance during transient vehicle scenarios. 

I was expecting this conclusion but the results were still interesting to see, especially for the NACA 4412 profile. And I got to help someone else learn about CFD software and workflow. A good little project I think.