Making simulations better

I'll start here by bringing in the image from the previous post, but this time overlaid with the original CFD output:

Simplifying the problem

There are three main differences shared by both locations between the original simulation and the measured values:

• Simulated upper wake is too high, and too narrow

• Simulated inboard lower wake is too large, extending further inboard towards the chassis than it should

• Simulated inboard mid wake is too narrow, not extending enough towards the chassis

Immediately, thoughts come to  mind on where we should start looking to tackle the first two issues but the third issue might required some exploration and a bit of trial and error. The first issue simply suggests the upper wake is separating too soon from the tyre surface and not being pulled down behind the tyre. Meanwhile, the lower wake appears to merge with the tyre squirt and inherit its lateral momentum, so tyre squirt (tyre contact patch, more specifically) is a good place to start looking there. On the side of setting up the CFD environment for streamlining validation, I noticed the shape of the tyres we are using in CAD looked a bit strange. Some quick measurements and overlaid images later and some quite obvious shape and curvature differences were found between the CAD model and the real tyre, which needed to be addressed given most of our attention for the next couple of weeks was going to be focussed almost entirely on airflow around said tyres. Combined with previous observations of how sensitive tyre squirt behaviour is to small changes in tyre camber and contact patch size, and a realisation that we might expect significant tyre deformation under cornering, I decided we should put a bit of effort into really modelling the tyres properly before continuing with validation. This process consisted of taking various measurements for sizes and deflections of the real tyres under different loads and calibrating an FEA simulation accordingly, that will now spit out deformed tyre shapes for different load cases we feed into it. I'll cover this process in a short post of its own soon. 

We immediately saw minor changes in the right direction for CFD correlation after implementing the new deformed tyre model, being a slight reduction in lower wake size, and a lower-positioned upper wake structure. This was only a small step though, so we had to go deeper and move beyond geometric changes (I'll come back to some geometry details later, as different challenges come up). Before going any further though, I'll mention our approach to validation, and what our targets were.

Changes made to the setup should be made to target noticeable improvement in the three aforementioned main discrepancies. These changes should focus on local adjustments first before shifting to global parameters (i.e. settings that directly affect the whole flow field throughout the domain) if necessary. These coarse changes were to be guided by simplified wake maps such as seen in Figure 1. Once satisfied that the three issues have been addressed, focus will shift to direct numerical correlation on a point-wise basis to fine-tune the location of the wake perimeter based on the exact measured total pressure values. Whether the setup is deemed successfully validated will ultimately be a qualitative decision, however two quantitative targets were put in place to inform this decision:

• Total pressure discrepancy for a given point should be equal to or less than the combination of both experimental and numerical uncertainty, OR

• XY distance from a given point to a coordinate with a simulated equal total pressure value should be 10 mm or less (twice the mesh size present around most of the total pressure gradient at the wake perimeter)

Surface roughness

The first physics-based change to the simulation was adjusting the y+ values and general distribution on the tyre tread and sidewalls. This wasn't expected to result in significant changes and indeed it didn't. Had it made a significant change, we would probably have needed to reconsider how we set up prism layers over other surfaces on the car with a lot more care. Moving past this, the first change that came to mind to target the upper wake issue was to create a smoother surface that the flow could follow and remain attached to more easily. The most local way to achieve this is by simply adjusting the surface roughness for the tyre tread to a lower value to reduce the boundary layer energy loss from excessive friction. The next week was a cat and mouse game of making adjustments to tread, sidewall, and ground surface roughness values, learning how each affects different parts of the wake and the enhancement or weakening of different flow structures. Along the way, we found that the default R+ limiter for surface roughness was getting in the way, so we disabled it. Theoretically this is fine to do as we were using the k-omega turbulence model, but we nonetheless conducted regular checks for solution stability/sensitivity and generally refrained from going overboard with high roughness values just in case. Satisfyingly, the best result was given by three seemingly realistic roughness values; 0.15 mm for tread, 1.0 mm for sidewall, and 2.0 mm for ground (a decrease, increase, and increase respectively over the original estimates). The general surface finish of the sidewall is smoother than the tread in reality, however the presence of raised lettering and "hairs" makes the higher overall representative roughness value of 1 mm believable. Tyre surface details are shown in Figure 2, and the improved simulation results obtained by using these values are shown in Figure 3. 

Solution instability

While the results in Figure 3 show an overall good improvement in correlation over the original simulation, there are a few important notes:

• Upper wake is still too high at Z=0.35, but is now also too low at Z=-0.11

• Second point from the bottom on the left at Z=-0.11 is also not correlating well when considering the exact numerical value and XY distance as per the validation requirements

• These above two points are potentially acceptable, if not for the fact that this solution has uncovered an instability in the simulation, with slight changes in results depending on the initial condition (i.e. whether we started with a uniform domain condition, or continued directly using the results field of a previous simulation)

This was pretty annoying as we got so close to an acceptable correlation in a time much shorter than expected, by using just roughness adjustments. Over the next week we identified the source of the instability as the geometry surrounding where the upright interfaces with the wheel hub (whub) retaining plate in the front wheel. There were no obvious geometric issues here though, so we worked through a few options to iron out the issue. After rigorous testing to ensure stability, the following changes were permanently implemented as the solution:

• Adjusted mesh size at the MRF boundary to maintain a more constant cell volume on either side of the interface

• Removed prism layers from the upright and brake calliper geometries, which were causing cell distortions in areas of complex geometry (the highly disorganised flow inside the wheel meant physics were more dominated by static pressures and geometric blockages rather than viscous phenomena)

• As an extension on the above, a free-slip condition was given to the upright and brake calliper surfaces (which in isolation caused negligible changes to the results)

• Applied a hard limit to minimum cell size of 25% in the interior wheel area to avoid overly small cells (spawning from auto curvature or proximity surface refinements) where they did not appear to be needed

Turbulence physics

At this point we had a stable solution again, but we had also lost some correlation in the results. Further adjustments to surface roughness gave no improvement, so we shifted attention to global physics models. Adjustments to the k-omega a1 and realisability coefficients that were originally set according to generic recommendations only made the results worse (by generally increasing tyre separation and/or depowering flow structures that appeared critical to achieving correlation at both planes simultaneously). Nice to know though that the recommended values were a suitable option and provided noticeable improvement over the software defaults. Eventually it was two other k-omega parameters that provided a boost back to good results, even improving on the best results achieved with the unstable setup. These parameters where constitutive turbulence anisotropy (switching from linear to quadratic), and enabling curvature correction, which both control how small-scale turbulence (typically on the scale of individual mesh cells or smaller) interacts with primary and secondary flow and vice-versa, particularly in areas with high flow curvature...such as the wake region behind a wheel. Changing physics parameters such as these is always risky and I'm still not super comfortable changing them based on just one source of correlation data. I accepted them for now, noting a minimal change to predicted vehicle forces and moments, but I plan on revisiting these settings as more correlation data becomes available. 

Now that we were hyper-aware of potentially instabilities, this setup was tested with numerous initial conditions and even small mesh changes, but thankfully produced the same result to within the previously calculated simulation uncertainty every time. On that note, we should really run a verification study again, but given this is the last time we hope to be dealing with EV23 in simulation, there was minimal justification to do so. The final accepted results (based on both location and numerical criteria) are shown in Figure 4. 

After going back and fine tuning roughness values, tyre deformation, and contact patch size (to target per-point magnitude correlation), an acceptable result was produced (Figure 4). 

Key features compared to the original results in Figure 1:

• Much smaller tyre squirt and downstream lower wake growth

• Much larger inboard mid-wake structure achieved through powering up the clockwise rotation by increasing upper wake attachment (lower tread roughness) and enabling curvature correction

• Flatter and wider upper wake structure (although still not quite matching track data; location-based correlation remained marginally outside the original goal bounds. I suspect the tyre tread may not have been quite stiff enough and was able to flex more than it should in the FEA model). Failing that, we could just be hoping for too much without looking into more fundamental physics changes, which we are strongly against investigating this early in development of our simulation tools. 

• A much smaller outboard lower wake and squirt, which was not explicitly validated due to no probes being placed here, but it seems logical based on camber and inboard wake/squirt behaviour

• Thinner bridge between lower and mid-wake structure, providing better numerical correlation at Z=0.35

• Significant downstream persistence of the rotational structure, almost forming two completely separate wake regions at Z=-0.11, giving overall very good numerical correlation at this plane

Obviously these results still aren't perfect, particularly the shape of the upper wake structure, and the fact that these changes are only targeting one particular parameter (total pressure) in one particular location, but it's a good start and some pretty big advances were made. I don't want the team spending too much time diving into all sorts of obscure settings to improve any further until we have significantly more data to go off, such as different rake locations, setting different camber, tyre pressure, and toe at track tests, including aerodynamic surfaces to introduce more complex pressure gradients, and including different aspects of validation, such as surface flow and forces/moments. 

Surface flow

Of course, as mentioned in the previous post, we also had some wool tufts to go off for surface flow validation. The tufts were pretty low resolution and the surface flow was expected to be pretty simple, so really we were just looking to make sure nothing completely unexpected was happening. I won't show the close-up photo as it's a little hard to look at with all the sponsors and logos on the same panel, but Figure 5 shows the extracted averaged tuft positions overlayed on the CFD output. Unfortunately it was raining during this test, so some of the tufts ended up sticking to the bodywork and were discounted (shown in orange). The rest show a good agreement, especially considering the wool we had was not as flexible as I would have liked. Some good notes for next time at least. Based on the poor test setup and conditions but otherwise general agreement of the results, I decided not to implement any specific changes to improve correlation in this area.