Questions about 2D LES, and turbulent viscosity seems orders of magnitude too small.
 

I've spent a really long time trying to figure out why my turbulent viscosity is orders of magnitude too small. I was going to write a post about all the things I've tried but I think most of it is irrelevant. I'm using the Smagorisnky-Lilly model for 2D LES (it's for an assignment, I have to use these).

My questions:

1) For 2D LES (in fluent), should I make the domain one cell thick? I think Fluent is having issues calculating length scales. I think it assumes all cells have 1 meter of thickness in the z direction.

2) I'm unfamiliar with 3D LES, when I give my domain thickness, will I have to define a boundary condition on the 'top' and 'bottom' face? Which should I use?

3) As a criteria for LES I'm comparing the resolved to the total (resolved + modelled) kinetic energy. My equation for modelled tke is (Mu_sgs/rho*L_sgs)^2 where Mu_sgs is the turbulent viscosity, and L_sgs is the subgrid length scale. I don't have a good source for my modelled tke, does anyone know where this equation originates from?

4) My criteria failed, it said that 99.999% of my flow's TKE was resolved. I suspect the issue is that Mu_sgs is way too small as my viscosity ratio ranged from about 20-200 in most of the flow. I used a custom function to calculate Mu_sgs from the Wikipedia article on turbulence modelling. This gave me good results, the tke was now about 70% resolved which is what I was expecting. But I'm 95% sure this equation is wrong, I think it should be 1/100th of what it actually is as there is no C_s constant included. Opinions?

1) Unless it has changed recently, 2D Fluent takes 2D meshes and there is no need to talk about depth.
2) Yes, you always need boundary conditions. It depends on what you are solving... But a popular BC is the periodic BC. But the domain needs to be large enough in the 3rd direction such that the two-point correlations decays to zero so that there is no contamination of the periodic BC onto the statistics.
3) That equation is the subgrid model itself, i.e. the Smagorinsky-Lilly subgrid scale model.
4) Check to make sure your flow makes sense. If there's no turbulence and your flow is laminar, then it would make sense that everything is resolved.

I am not sure but doen't Fluent set LES only for 3D cases?
And what is your flow problem?