Circular Couette Flow

rockewan

Description: Circular Couette flow in 2D (laminar). Outer wall is rotating at various speed while inner wall is stationary. Since it is simulated in 2D, there is no end effect and thus the analytical solution is know as u(r)=C1*r+C2/r as shown here: http://en.wikipedia.org/wiki/Couette_flow On the radius direction, the velocity magnitude should increase almost linearly from 0 to the outer wall speed.

The Problem: Reasonable simulation results can be obtained for coarse mesh at low rotation speeds although it is noticeable that the velocity is lower at some cells or nodes. See the comparison below:

http://i217.photobucket.com/albums/c...ityProfile.jpg

However, when I was trying to refine the mesh, it doesn't converge at all, even if the results from coarse mesh is used as start value using "Interpolate Data". The residuals decrease to certain value (usually higher than 1E-4), and then increase gradually, it will stabilize at certain value eventually. One example is shown here:

http://i217.photobucket.com/albums/c...ualProfile.jpg

Although it is meaningless to discuss the unconverged results, I did notice that the pressure profile shows periodic trend like this (unlike the circular layer profile for converged ones):

http://i217.photobucket.com/albums/c...ureProfile.jpg

I tried several different geometry that has different r/R ratio, different mesh for every geometry, different rotation speed for every mesh (all cases are still within the laminar region). This problem tends to happen for large aspect ratio with finer mesh and higher rotation speed.

I tried to decrease the under-relaxation factor, it does not help. "Interpolate Data" does not help either. I also tried to use small rotation speed first, and then gradually increase the speed. It converged well initially, however, before it reaches my desired value, it will do the same thing at certain rotation speed.

Anyway, I am running out of ideas. Any suggestion is welcome.

If you want to try this simple case yourself, here are the parameters: r=0.039m; R=0.042m; outer wall rotation speed: 50rpm; inner wall rotation speed: 0

Gambit mesh parameters: Quad "Elements" and Map "Type" is used without "Smoother" 5 Layer Mesh (in radius direction) spacing: (0.042-0.039)/5=6E-4; 10 Layer Mesh: 3E-4; 20 Layer Mesh: 1.5E-4

It converges on the 5 and 10 layer meshes, but not on the 20 Layer mesh.