Computational fluid dynamics (CFD) is a powerful numerical tool widely used to simulate many processes in the racecar environment. Recent progression in computing efficacy, coupled with a reduction in the cost of CFD software packages and the advent of cloud-based CFD operation, has advanced CFD as a viable tool to provide effective and efficient investigations for the full spectrum of motorsport.
In this article we will discuss the fundamentals involved in developing a CFD solution and provide a state-of-the art insight into various CFD developments applicable to the motorsport industry, as well as illustrate some of the physical models most commonly used in these applications.
CFD is a computer investigation into fluid dynamics. Personal computers can run CFD for moderate problems. However, the higher echelons of motorsport use clusters with up to thousands of cores and terabytes of memory as the complexity of the flow fields are immense.
The fluids under investigation can be either a gas or a liquid. When you're working with water, it's called hydrodynamics, and when you're working with air, it's called aerodynamics. The dynamics element refers to the fact the fluid is in motion, which can be caused by an object moving through them, or a thermal effect driving the flow.
There are three main steps to the CFD process – modelling, discretisation and iteration. Modelling involves the continuous mathematical functions you use to describe the real flow. In reality, that flow is the result of many different laws of physics working together. As CFD is a tool, you must tell it how you want it to work. Wouter Remmerie, founder of AirShaper, explains: 'To focus the investigation, it's a matter of selecting only the areas of a study that have a substantial impact on your flow topic. If you're calculating the aerodynamic force on a wing, for example, there's little use in taking the gravitational pull of the moon into account, as the effect is negligible. So, defining correct and relevant models is important to limit the modelling errors.'
In the case of fluid mechanics, the essential model is a set of partial differential equations called the Navier-Stokes equations. These apply the laws of Newton to each fluid element, stating the dynamic balance between the forces acting on it and the change in its momentum. This conservation of momentum, together with the conservation of mass, allows you to describe the flow field.
'For some straightforward cases, like laminar flow through a pipe, there are analytical solutions. One can describe the entire flow field using continuous mathematical functions,' continues Remmerie. 'These allow you to calculate exact velocity and pressure for any given location in the flow field at an infinite resolution. However, for anything more complex, there is no such analytical solution. That means we need to break down reality into small blocks for which we do have a solution.'
These blocks can be finite elements or volumes, known as cells. The process of breaking down a large continuous flow field into cells is called meshing. For each cell in a mesh, we can approximate the continuous Navier-Stokes equations by discrete algebraic equations. These allow us to calculate the pressure and velocity at the centre of each cell, called the node, based on values of velocity and pressure of the surrounding nodes.
‘The higher the order of these discrete approximations, the more surrounding nodes are included,' notes Remmerie. 'The reach of this technique is known as the computational molecule, resulting in a set of algebraic equations for each node. As the value of one node depends on the value of neighbouring nodes and vice versa, the equations are connected. To solve them simultaneously, they are collected together in a matrix.'
To solve a matrix, the discretisation error, which is the difference between the exact solution of the governing equations and the exact solution of the discrete approximation, must be understood. The more cells applied, the smaller this error. However, the more cells, the more equations need to be solved. High-density meshes typically contain millions of cells, and this quickly becomes very computationally expensive. As such, most CFD engineers apply high-density mesh to locations where the flow is complex, and lower density, larger cells where the flow is less so, typically further away from the object under investigation.
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