Making simulations better

To start with, here's the image from the previous post, but this time overlaid on the original CFD output:

Simplifying the problem

There are three main differences between the CFD and experimental results, common to both planes:

• Simulated upper wake is too high, and too narrow

• Simulated inboard lower wake extends too far inboard towards the chassis

• Simulated inboard mid wake does not extend far enough inboard 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 suggests the upper wake is separating too soon from the tyre tread surface. Regarding the third issue, the inboard lower wake appears to merge with the tyre squirt and inherit its lateral momentum, so tyre squirt and therefore the tyre contact patch is a good place to start looking there. 

Only now did I notice the shape of the tyres we are using in CAD looked a bit strange. Some quick measurements and photo-CAD overlays revealed some major shape and curvature differences between the CAD model and the real tyre. This 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 these tyres. We had seen previously during first tests of the CFD setup just how sensitive tyre squirt was to both camber and tyre-ground intersection distance, so I decided we should put a bit of effort into accurately modelling the tyres as the first step. This process consisted of taking various measurements of shapes and deflections of the real tyres under different loads and using them to calibrate an FEA simulation that spits out deformed tyre shapes for different load cases we feed into it. This process is covered in the next post. 

We immediately saw moderate positive changes in correlation after implementing the new deformed tyre model:  a slight reduction in lower wake size, and a lower-positioned upper wake structure. This was only a step though, so we had to go deeper and move beyond geometric changes. 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. physics/turbulence settings) 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 and the CFD results match the simplified maps, focus will shift to pressure magnitudes on a point-wise basis to fine-tune the location of the wake perimeter. 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 magnitude error for a given point should be equal to or less than the combination of both experimental and numerical uncertainty, OR

• Distance from a given probe point to a location in the CFD results with equal magnitude should be 10 mm or less (twice the local mesh size)

Surface roughness

The first physics-based change to the simulation was adjusting the target y+ values on the tyre tread and sidewalls. I didn't expect this to have a big influence and indeed it didn't, which was a good result. The first major change that came to mind was reducing the surface roughness for the tyre tread to reduce the boundary layer losses and delay separation. This evolved into a series of trial-and-error simulations, making adjustments to tread, sidewall, and ground surface roughness values, and learning how each affects different parts of the wake. We figured out that the default R+ limiter for surface roughness was getting in the way, so we disabled it. Theoretically this is fine to do as the y+ > R+ requirement is only enforced for the k-epsilon model, while we use the k-omega SST model. We still closely monitored affected areas for sensitivities. 

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 setup estimates). The general surface finish of the real sidewall is smoother than the tread in reality, however the presence of raised lettering and mould hairs makes the higher overall representative roughness believable. While this sort of surface detail is not correctly represented with these uniform sand-grain roughness values, it was preferrable to approximate it as such (if suitably accurate results were achieved) than to physically model disruptive bumps on the surface. 

Solution instability

While the results in the image above 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

• Upper wake is too far outboard at Z=-0.11

These two discrepancies would have potentially been acceptable, if not for the fact that an instability had been discovered, with changes in results (particularly the inboard mid-wake position showing noticeably worse correlation) depending on the initial condition used.

We occasionally test for sensitivities by running an identical case with three different initial conditions for the velocity field:

• Uniform value with magnitude of 0 m/s

• Uniform value with magnitude equal to the target freestream velocity

• Using the field from a previously converged solution

Now we had caught one, and this was pretty annoying as we got so close to an acceptable correlation with less than a week of running simulations. We identified the source of the instability near the geometry surrounding the upright/wheel hub interface on the inboard side of the upright. There were no obvious geometric or mesh issues here though, so we worked through a few options to iron out the issue. After finding success using the following changes, they were permanently implemented into our main CFD setup definition:

• Adjusted mesh sizing within the front wheel shell bounds to a uniform size of 5mm, removing local surface refinements and applying a hard limit to minimum cell size to avoid tiny cells forming in corners and interfaces

• Removed prism layers from the upright and brake calliper geometries that were causing cell distortions, with the mesher obviously struggling to satisfy its prism layer quality requirements

• As an extension on the above, a zero-shear/free-slip condition was given to the upright and brake calliper surfaces (both this and the prism layer removal caused negligible changes to the results since the effect of these parts is primarily just a blockage to mass flow moving laterally through the wheel shell)

Turbulence settings

At this point we had a stable solution again, but we had also lost some correlation in the results. Further adjustments to surface roughness returned no further improvements, so we shifted attention to global physics models. Adjustments to the k-omega SST a1 parameter and realisability coefficient only made the results worse, but this was a pleasing result as it proved that the recommended values we had set for them were a suitable option and provided improvement over the software defaults. 

Eventually it was two other turbulence parameters that provided the improvement we wanted, even improving slightly on the best results achieved with the unstable setup. These parameters where constitutive turbulence anisotropy (switching from linear to quadratic) and enabling curvature correction, both of which 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 validation data. I accepted them for now, noting a minimal change to predicted forces and moments, but I plan on revisiting these settings during future validation to continually check that they offer improvement. 

After these turbulence changes, alternative roughness settings were again tested, and again yielded no further improvements. The final accepted results for the EV23 validation at the two rake planes are shown at the end of this post. 

Having changed all these settings to reduce sensitivity and improve correlation, we should have run a verification study again, but given this is the last time we hope to be dealing with EV23 in simulation, it would wait until we had an EV24 setup with an initial floor design. 

Obviously these results still aren't perfect, particularly the upper wake structure, but it's a good start and some pretty big advances were made. It still won't be (and probably never will be ) treated as "validated" in the sense that it's a perfect replication of reality, both because this is probably impossible, and because so far all we've used is cross-sectional total pressure planes at two locations during one driving scenario, so there's a chance we could be over-fitting the data with the changes we have made.