# FAVRE-average: Compressible or just varying density

• onestudent

#### onestudent

Hi.

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".

Favre averages apply to any situation in which density is not constant. This applies equally to both compressible flows and to flows that are incompressible but feature variable density anyway.

Thank you!

And also, the Reynolds average does not apply to the situation where the fluid in incompressible and features variable density, agree?

Do the density variations result in variations in the fluid viscosity, which is a key factor in determining the Reynolds number?

Viscosity is not dependent on density. However, the Reynolds number is dependent directly on density, so it would still change ##Re##. That said, this is all irrelevant to Favre and Reynolds averaging.

Yesterday at 11:38 PM#5
@boneh3ad , I generally find that you are accurate with all of your responses; but, I am confused by your above (#5) response because the basic formula for Re is: Re = V*D/ν where V = flow velocity; D = pipe inside diameter and v = Kinematic viscosity of the fluid.

Kinematic viscosity is the (dynamic) viscosity normalized by density.
$$\nu = \dfrac{\mu}{\rho}$$
So yes, kinematic viscosity clearly depends on density, by dynamic viscosity is usually what is meant by simply saying "viscosity". It is the one that is directly proportional to shear stress and is the more fundamental quantity.

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