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I am modelling a fluid flow that is incompressible and has variable density.

I am applying RANS turbulence models.

When deriving the equations for the mean flow when the denisity is non-constant using the Reynolds average, I do not get the same as the standard RANS-equations.

This even if I assume incompressibility.

But if I use the FAVRE-average, I get the FAVRE-equations.

My question:

Every time I read about FAVRE, it is reffered to compressible flow.

Is it not really "non-constant density", and not "compressible", that should be the condition for using FAVRE instead of Reynolds average?

I wonder if many mix up incompressibility and non-constant denisty, and say "incompressible" when they really mean "constant denisty".