From physical to lbm units - Power law fluid

Hi everybody,

I’m having some trouble when trying to simulate a power law fluid.

For a newtonian fluid we normally rescale the kinematic viscosity, nu_p, as follows: nu_lb = nu_p / (dx^2/dt).

For a power law fluid, the consistency index, K, has units of [Pa.s^n], where n is the power law index. Thus, knowing that
Pa . s^n = N . s^n/m^2 = kg/m^3 . m^2 /s^(2-n), I arrived to the following relation:

nu_lb = (K/rho_p) * [dt^(2-n)/dx^2]

In this case, for n >= 2 (dilatant fluid) I have enormous values of tau (relaxation factor), which get even bigger when I try to refine the lattice spacing. I read lots of papers, but the authors do not give attention to the way they pass from physical units to lbm units.

Is there anyone who has/had this same problem?

Thanks in advance!