CFD study of airflow through a disc brake installed on a wheel/tire. Photo Credit: apps.exchange.autodesk.com

For much of our design we had to do some complicated analysis on the way the water acts around our vehicle. To do this we had to do some Computational Fluid Dynamics. The complex math involved in these calculations has been briefly touched on in past posts, but this post is here to tell you how we did it. Autodesk offers a massive suite of analysis software for free to students and one of them does the analysis we need: Autodesk Simulation CFD. There are many great tutorials out there on how to do this but here are the basics we used.

Create an external volume: our device interacts with the water around it so we needed to model that.

Then we assigned materials to each component. Each part has a different density and surface finish that will affect its interactions with the water so we needed to assign these values.

Then we set the boundary conditions. These are values of pressure or velocity that remain constant or change at a prescribed rate. For ours we set our pressure far away from the device to zero gauge pressure.

Next we assigned a rotational velocity to our propulsor. This sucker moves the water so we gotta have it spinning.

Then we mesh the whole thing. The automesh feature in the program does a pretty good job. The mesh connects all of the data points; the calculations will be done at each of these points so the more of them there are the longer the analysis will take.

Then click solve and take a nap, these things can take a while to solve!

All of this analysis is right at your fingertips if you know where to look (and happen to be a student!) It’s pretty cool the things you can find out!

Water is incredibly common, all of us see it on a daily basis, we know what it looks like and how it behaves. This makes life very hard for the people working in the animation business because our day to day observations alert us when the fluid isn’t acting as we would have expected. This can detract from the movie going experience. Animators have looked to engineering for the solution.

We have known for a while that the flow of fluids can be modeled using the Navier Stokes equations, a set of second order, nonlinear, partial differential equations. Unfortunately this equation is so hard to solve that it’s solution has been named one of the Millennium Problems, 7 of the hardest problems in all of mathematics. It is essentially impossible to solve, at least analytically; that is to say that the solution of the Navier Stokes equations is impossible in the traditional “solve for x” way most people are used to.

This is where numerical techniques come in; these are ways to reduce equations to the basic +,-,*,/ operations and then solve the equations a huge number of times in order to approximate (or get closer to) a real solution. This math is still quite complicated, requiring several hours to days of processing on supercomputers to solve; but, if a few assumptions are made and the initial conditions are properly set, close enough solutions can be found.

If you want to learn a bit more about the math look into the Taylor Series. It’s the little mathematical bridge that takes the calculus normally associated with solution of the Navier Stokes equations and turns it into the simpler arithmetic utilized by CFD programs.