Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is the method by which fluid flow can be simulated using computational methods. It generally involves discretizing the Navier-Stokes equations (partial differential equations that govern fluid motion) into series of algebraic equations that can then be solved.

In a Formula SAE/Student context, CFD is predominantly used for two purposes; simulating an external aerodynamics package (including radiators and other cooling components) and simulating the intake and exhaust systems of internal combustion engines. While either problem have their unique challenges, the process of running CFD for their simulation it quite similar.

As with all computational simulations (CFD, structural simulation, track time simulators, etc.), they break down into series of steps which introduce their own sources of error (there will be error and you must account for it):

1. Idealization
2. Discretization
3. Solution

Idealization are the physical assumptions made to come to some mathematical model. Discretization is the process of breaking up that mathematical model into a series of smaller, simpler problems. Solution is the process of actually solving those smaller problems. The errors associated with each step are modeling errors, discretization errors, and numerical errors, respectively (though the latter two are often grouped together). While this wiki page won't go into these steps in detail (it's worthy of a textbook), it's important to understand where errors come from and (thus) how to mitigate/fix them.

Modeling (Idealization)

Turbulence Modeling

The extremely short answer for why turbulence modeling is necessary is that at the Reynold's numbers characteristic of FSAE aerodynamic systems, the large scale physics of the flow (skin friction, flow separation, and so on) depend on vortices and other fluid motions at exceptionally small length and time scales (this is Kolmogorov's limit). However, by the use of ensemble averaging (comparing the results of an indefinite number of near identical experiments such as 100 airfoils in 100 wind tunnels) or time averaging, the effects of these motions can be modeled using a reasonable mesh size and steady state modeling. Turbulence modeling is an exceptionally diverse and evolving field, but very generally Reynold's Averaged Navier Stokes (RANS) approaches which model the turbulence in the flow as transported and generated properties similar to mass and momentum are the most practical for engineering CFD. If I had a very large design space and I wanted to narrow it down to a few good designs, RANS would be the choice. Large Eddy Simulation (LES) uses RANS-like methods to model subgrid eddies and then more or less directly models the larger eddies in a truly 3D and transient simulation. LES is very expensive but can provide insights into the physics that RANS may not for certain problems. To dismiss LES for Formula Student out of hand would be foolish, but it is likely that the uncertainty in how the automotive geometry as constructed and how the vehicle is driven is larger than the gains made from the use of LES.

Other Physical Assumptions

External CFD for FSAE assumes incompressibility and constant gas properties; CFD for the powertrain system (whether in a conventional CFD tool like FLUENT or a dedicated tool like Ricardo WAVE) will not. CFD of course uses the continuum assumption and ignores chemical reactions unless you are doing something really crazy with the combustion modelling.

Discretization

Finite Volume is by far the most popular discretization method for fluid problems, though Finite Difference and Finite Element methods are equally applicable.

Beyond discretization method, geometric and fluid feature resolution are very important.

$y^{+}$ is important near the wall. Essentially, it is a ratio of the mesh size near the wall to the estimated viscous sublayer thickness. What you want from this is highly dependent on the CFD model in use; if you want to resolve the boundary layer in detail, then it needs to be about 1. If you are using a RANS model and are less concerned about the boundary layer, then it can be higher. Check the documentation for the CFD solver to see what they recommend, and do a mesh refinement study, reporting out $y^{+}$and the parameters of interest at each mesh size. Results are more than useless without a mesh refinement study. With one, their slightly more useful.

Solution

Description of order of accuracy considerations and convergence criteria

Solvers

ANSYS, Star CCM, OpenFOAM, SimScale (which is just cloud based OpenFOAM).

Fun Acronyms

• Colorful Fluid Dynamics
• Can't Fit the Data.
• Conspiracy Fraud Deceit

probably should have notes on meshing, model selection (suggested and why), analysis/postprocessing