How F1's processing-intensive development tool really works 

One of the great challenges for Formula 1 engineers in modern times has been the growing necessity for accurately relating experimental aerodynamics to what is happening to the physical car on track and how our tools for aerodynamic research all have their limitations. 

A key part of this is computational fluid dynamics - or CFD - but what is it?

Physical processes such as the bouncing of a car on its springs or the flow of air around a car, and the consequential forces that those systems exert on the car, can be described mathematically by a series of equations. The big difference between the two examples given is that while the motion of a car on its springs is relatively easy to write the equations for, and hence to solve, those determining the flow of air are extremely complex and require vast computing power to solve. Even then, they’re subject to some approximations. 

While many people may have heard of Daniel Bernoulli and his equations of fluid flow, the work of Claude-Louis Navier and George Stokes in the early nineteenth century is the basis for the majority of CFD codes. The theory of how a wing develops downforce is often incorrectly explained by use of Bernoulli’s theorem. In what’s called the equal transit theory it’s said that particles of air travelling a greater distance over the curved surface of a wing will travel faster than those travelling on the less curved surface, the top surface in a vehicle wing. This is incorrect – there is nothing to say
that two particles of air arriving at the front of a wing need to join up again when they get to the trailing edge of a wing. 

The real answer to this relatively simple example of fluid flow relies on understanding the momentum of the air particles and how they’re affected by pressure, temperature density and the viscosity of the air. Rather than just assuming the relationship between velocity and pressure is all that matters, as Bernoulli proposes, CFD ensures the rules governing conservation of mass, conservation of momentum and conservation of energy are all respected – and therefore Newton’s second law and the first law of thermodynamics aren’t broken. It’s this need to consider many aspects that leads to the complexity we need to use partial differential equations, the manipulation of which needs to take into account the many variables simultaneously. This makes solving the equations rather complex. 

The way they’re solved is to consider the total flow field as a huge number of much smaller flow fields, and solving for each of these while acknowledging the effect each of these small cells has on its neighbour. In practical terms, we take a CAD model of the car, and we surround it with a virtual mesh. The size of the cells in the mesh can be variable. They will be fine where there are rapid changes in flow properties and coarser where the flow is better conditioned. One can imagine that the flow around an open-wheel race car is far more complex than around, say a sleek glider, and hence the number of cells needed is vastly increased. 

When running in the wet, the spray F1 car's generate visually demonstrates the turbulent air they create

Photo by: Sam Bloxham / Motorsport Images

Once this mesh is established, we use our computer code to solve the many equations. But, since the solution for each cell will affect the initial conditions for its neighbour, we need to run the simulation multiple times with the answer changing each time. Eventually, the result will tend to converge – in other words, it will stop changing significantly. At this point, we may believe we’ve achieved a solution. This may occur after many more than one thousand iterations solving each of the many thousand cell equations. One can understand how this eats computer power. It’s similar to a sculptor chipping away at a piece of stone until a form of what they’re aiming at emerges. The more stone they remove, the nearer the stone becomes to the final image until the sculptor decides that their creation is recognisable to others, even if not
photo-realistic, and at this point they stop. 

It would be nice to think that after such a complex mathematical manipulation we fully understood the flow around our car. Unfortunately, that’s not completely true: there are various simplifications and assumptions that have to be made in order to be able to solve our problem, and by far the most troublesome is turbulence. A Formula 1 car has far more turbulent flow around it than it does laminar, or smooth, flow. Turbulent flow is even more complex. Just look at the water vapour from a car exhaust as you follow it on a cold morning. It appears to be completely random and never following a repeatable pattern. The modelling of this, even after 30 years of commercial CFD development, is still hotly debated with various solutions in use even in F1. 

A big advantage of CFD over other experimental techniques is that it produces a vast amount of data which can aid understanding of how the forces are developed

The Navier-Stokes equations are aimed at getting a pragmatic solution to an extremely complex physical problem and they do this by using some approximations, and above all by time averaging the results. This type of solution is known as RANS or Reynolds Averaged Navier Stokes. It’s attractive in that it is reasonably accurate and efficient on computer core hours. A half car can be simulated assuming symmetry, and a model with around 100 million cells will solve in around five hours on a 192-core cluster. But for a better understanding of turbulent flow, other methods are favourable from a point of view of accuracy, if not computing time. 

Large Eddy Simulations (LES) and Detached Eddy Simulations (DES) will give better solutions but will require around 300 million cells and, on the same machine, will take 35 hours to solve. For this reason, they’re used sparingly.   

A big advantage of CFD over other experimental techniques is that it produces a vast amount of data which can aid understanding of how the forces are developed. The real strength of the analytical approach is when multi-physics can be explored. Imagine the wind blowing through a tree. The airflow moves the leaves, and the moving leaves affect the airflow. Ideally, we would model the structure of the tree as well as the air movement. This is multi-physics and can take simulation to new areas of fidelity. It’s complex but enables investigations and understanding beyond those achieved with physical scale modelling in a wind tunnel. 

CFD modelling has provided F1 teams with greater understanding of how its cars behave, but still leaves some variables unanswered

Photo by: Shishir Gautam (Shutterstock)