Re: Turbulence Models
the problem with LBM and turbulence are the mathematics of LBM itself. The 2nd order spatial accuracy corresponding to a finite-difference scheme leads to dispersive errors at low viscosities. To suppress those dispersive errors (which also exhibit tremendous amounts of energy) we apply Navier-Stokes related turbulence models, like the Smagorinsky model, which simply increases the effective viscosity and, thus, suppresses those dispersive oscillations.
As long as you are employing an under resolved mesh at a given Reynolds number, I would suggest you use one of the Smagorinsky models or the Approximate Deconvolution Method.
If you are really considered into direct turbulence simulation I suggest a well resolved setup with a BGK approach -> which is at the hydrodynamic limit actually the solution of the Navier-Stokes equations.
I already simulated the turbulent channel flow at high Reynolds numbers and I would be happy to help you with the turbulent pipe flow and the respective forcing and mesh resolution needed for this simulation.