Eddy viscosity ratio denominator for compressible flows
 

When plotting the eddy viscosity ratio () with a CFX Expression for a compressible aerodynamics flow should the dynamic viscosity be the freestream value (i.e. a constant) or the local vocal (i.e. varies since I have used the Sutherland's law in the air material)?

Thanks

I would consult the literature for that question.

But note that eddy viscosity turbulence models have not been developed to handle variable laminar viscosity (at least I don't know of any), so you are going beyond what turbulence models are designed for anyway. So you should expect to encounter grey areas where it is not clear how to apply it, because it was not designed to apply to this situation anyway.

I could not find an answer in the any paper, yet many papers show plots of the eddy viscosity ratio (the ANSYS SRS Best Practice Guide is one example). However, when this is plotted for a compressible airflow e.g. using the NASA Drag Prediction Workshop as a testcase where the freestream is compressible, it is reasonable to use a dynamic viscosity when evaluating the eddy viscosity ratio using the Sutherland Law, which will vary around the vehicle, rather than using a constant value (e.g. 1.7894E-5 Pa s if using the ISA sea-level as the farfield condition). This might be immaterial.

Your question is really a general fluid mechanics question, not a CFX question. Also I suspect there is not a universal answer to it - the normalising viscosity you use is what is appropriate in your case. Not a very useful answer I guess, but it means you can just do whatever seems to make sense.