1. Background

In early March, Williams F1 intended to have an Augmented Reality (AR) unveiling for their 2021 F1 car, the FW43B, where fans would download an app on their phone that would allow them to view a 3D model of the car at the time of the unveiling. Unsurprisingly, the app was quickly unpacked by people on the internet, leaving us with the 3D assets for the car. This isn’t an issue by itself, other models have been acquired for the 2019 Mercedes and 2021 AlphaTauri, however those were coarse models that have been simplified beyond use. The issue is that the Williams surfaces have a pretty decent resolution, even good enough for computational fluid dynamics (CFD). Shortly after the app was unpacked, the AR unveiling was called off, and the apps were pulled from all app stores. While many people have used the term “hacked”, nothing was stolen from Williams servers. Williams released the app themselves, and people just knew how to extract the models.

You can find the model downloads in the original Reddit thread by u/Astorphobis.

I’m honestly a bit surprised that this wasn’t foreseen by the people responsible for the app, but this incident shouldn’t cause any competitive damage, so long as the rest of the paddock keeps it clean. Talking to a couple F1 Aerodynamicists, they received company emails addressing the matter, ranging from reminders that they can’t be influenced by images from outside of FIA sanctioned events, to more strict instructions to not even look at them.

Thankfully I’m outside of those restrictions, but I can’t assume the model is proper either, as there’s a chance they used early/immature/wrong geometry in places. Further, there’s parts of the car missing, and the parts that exist still have some issues with tesselation. These big caveats are why I’m referring to this geometry as the “FW43B(AR)”, as I don’t want it to make the hard claim that it is the FW43B. Given the above, the geometry isn’t perfect, but it’s certainly the best F1 model the public has ever gotten a hold of.

2. About this article

This is the first of three planned articles, and is entirely on the methodology I’m using to simulate this car. The purpose of this is to receive feedback on my methodology to work towards trustworthy results in later articles, as I’d like to treat this project with caution to avoid presenting anything misleading.

Since I’m not qualified to say where my CFD is right or wrong, I’ve consulted with a number of former F1 Aerodynamicists on the geometry, setup, and results, and have shared their feedback within the article. Since they’re sharing more info than their former employers would likely prefer, they will be kept anonymous, and will be referred to as Aerodynamicist 1, 2, 3, etc.

CFD is a complex beast, especially when you combine it with complex aerodynamics such as those in Formula 1. So, before anybody gets wooed by my pretty pictures, I’d like to bring up a quote that originated in statistics, and is often used within the context of CFD:

Strictly speaking, my CFD is wrong, so it’s just a matter of doing my due diligence to make it as not wrong as possible, and knowing where to place skepticism in my results. That being said, my setup is fairly similar to run-of-the-mill F1 CFD, so if it can be useful at the F1 level, it can be useful here.

Aerodynamicist 2: “This is absolutely spot on. CFD is wrong, and we knew it, we just strove to make sure it was still useful to us. With the new regulations, doing that will be more important than ever.”

For this first article, I’ll be keeping the model quite similar to the original geometry from the app, with only minor fixes to make the model behave in CFD, and a few replicable things like the driver model, wheel MRF volumes, and porous brake rotors. This is mainly to provide results that others can replicate and compare against their own attempts at simulating this geometry. For article 2, I’ll be redrawing as much of the missing features, and implementing any feedback from this article. Finally, article 3 will present CFD results that will be our best shot at having “real” F1 CFD results.

The audience of this article will include a wide range of CFD knowledge, ranging from F1 Aerodynamicists to aero-interested F1 fans, so while I’m getting into the nitty-gritty, a bit of technical language is worded down for the public as necessary.

3. Geometry

First, a rundown of the model, covering what is missing from the model relative to a full geometry, and issues with the models that had to be fixed to run CFD. Since the model only needed to be used for rendering, it’s quite “dirty”, requiring many hours of surface preparation to create a proper model. Shown below is my CFD software’s STAR-CCM+’s) surface repair tool, where red errors indicate faces that intersect each other, green lines indicate free edges that result from unclosed surfaces, and blue errors indicate non-manifold errors, where edges or vertices (points) are shared by multiple surfaces. All of these are critical errors that should be fixed to generate a proper mesh.

3.1. Tessellation

The foremost thing to note is that the geometry was uploaded to the app as a mesh body, meaning it has already been pre-tessellated from the spline driven CAD. As such, there’s a limit on the curvature that can be resolved. Here’s some 8K screenshots giving a rough idea on what we’re working with, open in a new tab and zoom in:

This tessellation has a larger impact on smaller geometries, an example of which can be seen in some example pressure profiles for the front and rear wings, both using a 5mm surface sizing. This is caused by the tessellated surface having inconsistent curvature, where the flat faces of the tessellation will have a lower pressure magnitude due to less curvature, and the edges will have a higher pressure magnitude due to high curvature. This is much more significant for smaller features like the bargeboards and diffuser elements.

Aerodynamicist 2 tells me that this level of tessellation looks perfectly acceptable (with the exception of the cake tin internals below), even better than theirs was at times, and that the pressure curves look fine to them. This surprised me, since better tessellation is a non-issue to fix. Perhaps coarser tessellation saves significant time during the tessellation and meshing stages.

3.1.1. Front Corners

The front and rear uprights / cake tins are the only parts of the car where tessellation creates real problems. I’ll try to cover most of the issues, but it’s hard to give the full picture without navigating through them yourself.

The most glaring issue is that the main structure of the front wheel package is coarsened beyond use, which is an issue because it’s required to seal the body into a closed volume that can be used for CFD.

I deleted this surface and manually sealed off the volume. Because of this, some of the brake ducts are a bit shorter than they should be, and the overall packaging inside of the cake tin is more spacious as a result.

Without seeing the inside of the real FW43B’s cake tin, I have no idea how many more issues are present within this area. What I do know, however, is that the brake calipers shouldn’t be intersecting the cake tin.

Aerodynamicist 2: “As you aren’t looking at brake cooling or anything like that, I would expect that the brake disc internals won’t matter too much as long as you get the mass flow coming out of the wheel in the right positions and amounts.”

3.1.2. Rear Corners

The rear corners are the most difficult part of the car in terms of cleanup, as a large amount of geometry errors can be seen.

We can also see that the rear cake tin cascade is something of a Picasso, with nearly diamond shaped airfoils. These will stay for now, but will definitely be reworked in the future.

Taking off the rear wheels, the cake tins and wheel gap vanes are quite rough.

Without attempting to show what’s inside of the cake tin, believe me when I say it’s not pretty, so the internal flow here won’t be of much value.

3.2. Geometry deviations from reality

With the aid of some handy track photos from pre-season testing (big thanks to James Moy and F1Technical.net), I can make a few overlays comparing the models to the real thing. First off, I’ll just say that the model is pretty spot on, it’s 90%-95% the same thing! Below the images is a numbered list of everything on the car that I’m aware is different from the real car.

1. Front wing strakes are missing

Aerodynamicist 2: “The differences in the wake and vortex structures because of the missing (or eventually in your case different) strake and caketin geometry will likely overshadow any modelling issues. “

Aerodynamicist 3: “Without some extra details such as front wing strakes and resurfaced rear brake duct winglets there will likely be some aerodynamic issues that will be larger in magnitude than changes in your modelling approach.”

2. Front wing flap angle set to minimum value

Just a setup change that will result in less downforce and a more rearward aerobalance (the distribution of aerodynamic loading between the front and rear tires).

3. Nose camera is lower

These are supposed to be ‘non-aerodynamic devices’, but they can be used for a minor effect.

4. Front brake ducts are different

5. Front suspension strake is missing

6. Last J-vane is more aggressive

7. Bargeboard footplate winglets are less aggressive, although this could be the lighting

In this case, opening up the winglets is more aggressive since they’re more aligned with the flow rotating about the Y250 vortex.

8. Additional bargeboard strut

Non-aerodynamic change.

9. Missing skid block

10. Missing chassis internals

In order to still have airflow through the car, I’ve closed off the chassis inlets/outlets and have specified the mass flow rate through them. My largest concern here is not resolving the proper flow out the back of the chassis, since I’ve only been able to specify a constant velocity profile.

Aerodynamicist 3: “Adding some body internals may also be something worth considering, although that is not absolutely critical for what you are doing. “

11. Missing winglet on sidepod

12. Missing winglets near the rear of the floor

13. Modified rear wheel cascade

14. Modified chassis outlet

The model is consistent with races 1-4, however not with pre-season testing. This could just be a cooling modification, and both designs are equally valid.

15. Shorter rear wing mounts

Non-aerodynamic change.

16. More aggressive rear wing

This change is much more significant in the rear-view picture than the front-view picture, however they were taken on different days of pre-season testing, so it may just be a spec change. Both designs are valid.

17. Smaller slot-gap cutout on the rear wing flap

Minor aerodynamic change.

18. Missing vortex generators on the ‘hull’ (bottom-most part of the car)

19. Missing diffuser strakes

Aerodynamicist 2: “The strake outwash and vorticity is absolutely critical to managing the behaviour of the diffuser and especially the rear tyre wake. There’s a reason that the 2022 regulations ban most devices in that area.”

20. Additional wing on the rear crash structure

21. Likely different ride height (rake) value

I’m using the ride height of the car as-given, and while it’s a ride height of the car, it may not be representative of track conditions. My best guess is that these ride heights represent the car at rest.

3.3. Geometry Modifications

While I want to keep the geometry replicable for others, I’m making a few modifications that are either quite easy, or that I wish to obtain early feedback on.

3.3.1. Driver Model

A driver model of P̶i̶e̶r̶r̶e̶ George was obtained from the AlphaTauri website, which only required slight modification around the neck area to work in CFD.

After running all of my simulations, I made the above image comparisons and realized George is sitting low in the car. This won’t be a huge change, but I’ll fix it for the future.

3.3.2. Wheel MRF Volumes

In order to better capture the effects of the wheel rotation in a simulation where the wheel geometry doesn’t move, a moving reference frame (MRF) approach is used which applies an acceleration to a portion of the domain. In order to do this, those portions of the domain must be contained in their own volume so that I can specify them as their own entity in the simulation. These volumes only need to contain geometry that isn’t a simple revolution around the axis of rotation. For example, the tire surfaces do not need to be contained inside of the MRF volume, but the wheel spokes and ridges do. In the below cross-sections of the front and rear tires, the MRF volumes are the blue and yellow areas, respectively.

3.3.3. Porous Brakes

F1 brake rotors contain over 1000 small holes in order to aid in cooling, however this adds simulation complexity that can be avoided without too much issue.

To work around this, I’ll be replacing these complex brakes with simplified brakes using a porous media approach, where the brakes are replaced with a ‘foam’ that has a specified resistance to airflow. This calibration comes from a separate set of simulations that I ran on an isolated brake rotor. This wasn’t rigorous, but it’s better than nothing.

3.3.4. Actuating Suspension

While this article won’t take advantage of actuating suspension, I may as well mention it in the CFD methodology article. I’ve parameterized the suspension motion using a series of transform operations in STAR-CCM+, estimating the pivot points as wherever the suspension terminates into the chassis. Since I have no information about the tire camber/toe gains, the wheels only moved upwards/downwards. With the default front and rear ride heights (measured from the reference plane to the ground) of 35mm/160mm, the minimum allowable ride heights before interference with the chassis are 10mm/100mm. The actuation of the suspension through the default to minimum range can be seen below:

4. CFD Setup

All CFD was meshed, solved, and post-processed using STAR-CCM+ 2021.2.

4.1. Geometry

For now I’ll be doing a straight line symmetry case, with the default front/rear ride heights of 35mm/160mm (1.99 deg rake).

For the tires, a 5mm intersection depth with the ground was eyeballed to give an appropriate contact patch size when paired with a 1mm tire plinth used to improve the contact mesh quality (more on this later).

One important thing to note is that my tire geometries are non-deformed, meaning they’re perfectly round, without accounting for how they’re being pushed into the ground. Ideally, you’d do some sort of FEA on the tires to get a more accurate geometry, but that’s not possible here.

(Image: https://polymerfem.com/tire-deformation/)

4.2. Meshing

For meshing, I’ll be using a trimmed cell mesh, with polyhedral meshes for the wheel MRF volumes. Aerodynamicist 1 tells me that “a proper half car CFD of a car geometry like this is somewhere on the order of 200M trimmer cells”. After a discussion about mesh sizing, this was my target when using an 8mm base sizing, where the base size is the maximum cell size on the car surface (most of the surface is much smaller due to automatic curvature refinements and the specified refinements below). All said and done, an 8mm mesh ends up at 224M cells, however note that my simulation also lacks any internal geometry. As a result of my mesh independence tests, I ended up with a 10mm mesh with 146M cells.

I took some lessons learned from my article on output-based AMR in STAR-CCM+. Specifically the importance of refining the incident flow, and refining the ‘circulation region’ around the geometry. That being said, output-based AMR was not used here.

I have a lot of mesh controls, so buckle up…

4.2.1. Relative Size Controls

All of these scale during the mesh independence study. Given values are for a 10mm base size:

• Target surface size = 10mm
• 5mm sizing -> front wing, rear wing, tires+wakes, furniture

(tire wake refinement volumes in pink, recirculation regions in blue)

• Undertray surface sizing (swept downwards) = 5mm in x, 2.5mm in y/z
• 2.5mm sizing -> bargeboards, rear furniture:

• 1.25mm sizing on the yaw probe, front cake tin strakes, and undertray rear elements
• Anisotropic vortex sizing = from 2.5mm to 5mm
• Anisotropic wake sizing = from 10mm to 160mm
• 10mm/20mm/40mm sizings for the incoming flow 1.4m/2.8m/25m in front of the car

4.2.1. Absolute Size Controls

All of these do not scale during the mesh independence study.

• Minimum surface size = 1mm
• Surface curvature = 48 pts/circle
• Wheel MRF sizing = 2mm (front/rear MRF cell counts = 1.4M/0.95M)
• Tire plinth sizing = 0.25mm (4 cells across)
• Tire contact sizings, using offset volumes of 10mm/40mm/160mm from the tire plinth = 0.5mm/1.0mm/2.0mm

• Trailing edge sizing = 0.25mm (4 cells across)

I had the pleasure of manually splitting each trailing edge from the model into their own surface so that I could apply this mesh control. There are a lot of trailing edges:

4.2.3. Prism Layer Settings

I’m told the top teams can be “pretty cavalier” in their usage of wall modelling, so that’s what I’ll be using for the majority of the car, except for the front wing, undertray, rear wing, and rear caketin cascade, as they all either have high pressure gradients or flow separation that I want to capture as best as possible.

Front wing prism layer mesh:

Rear wing prism layer mesh:

Diffuser prism layer mesh:

Anything wall modelled was kept somewhat between 30

Anything wall resolved was kept within Y+<3, with a stretching ratio of ~1.3:

Here are the distributions of wall Y+:

4.2.4. Anisotropic Wake Refinement

To refine t