# navier stokes

Discussion in 'Software' started by Morgig, Oct 28, 2005.

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### MorgigJunior Member

My CFD is a little rusty but I’m trying to find out the limitations of Navier Stokes equations.

It is my understanding that it is best suited to steady state flow and can only truly calculate this situation. An algorithm to estimate turbulent flow is then added, this taking different forms depending on the software being used.

At the moment I am particularly interested in wind effects; can this code model wind gusts effectively?

How do results compare to wind tunnel results?

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### marshmatSenior Member

My understanding of this model (which I must admit is VERY limited) is that it initially assumes laminar flow, and any turbulence is calculated separately and then computed into the final result as a fairly rough estimate. Whether you could use it to model a wind gust is questionable, I think; if your shape tends to encourage laminar flow already it may work, but anything with sharp or steep transitions will probably give it a hard time if you try to compute a short, strong burst of wind. Again, this is just a guess based on what little I know of the model. The Navier-Stokes code, as I recall, is very good for comparing differences between two related shapes, but is not too good at computing absolute values of the various parameters.

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### redcoopersMember

Assuming you're working with something like winds gusting over a sail, I would say that you should only consider wind-tunnel testing and forget about CFD. Steady-state flows can be handled to some extent, but transient flows in 3D are labor, time, and CPU intensive. Furthermore, if you do get CFD results, you'll need to correlate these with a few benchmark wind-tunnel experiments.

Just as a quick N-S refresher, the equations start with a Cauchy's equation of motion which is simply a glorifed balance of momentum inside a material volume:
D/Dt( rho u ) = del · sigma + f

The D/Dt is a material derivative, u is velocity, sigma is the stress tensor (and is symmetric to preserve angular momentum), and f are body forces. One of the biggest problems with the navier-stokes equations is how to handle the material derivative.

Most N-S codes use an Eulerian fixed-type grid in which you get a really nasty "convective term." Because of this convective term and for the need to constantly regrid, 3d transient flow problems are very time-consuming.

There is a rediscovered form of the N-S equations which utilizes lagrangian coordinates, or, a moving grid. Think instead of boxes of fluid which have fluid moving through them, we now have particles of fluid which move. The problem with this is that the calculations between the particles is a true nightmare. I've done this in 2D, but have not continued the development of a 3d form.

For both type of coordinate systems, simply getting transient 3d results without adding in a turbulence model is an achievement. Anyway, use experimental testing. It's much better suited to what you need.
-Jon

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