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-   -   RANS equation - don't understand a term (http://www.cfd-online.com/Forums/fluent/48899-rans-equation-dont-understand-term.html)

Micael Boulet July 29, 2008 20:42

RANS equation - don't understand a term
 
In the RANS equation, there is a term "-2/3*deta_ij*du_l/dx_l" in the viscous term. I did not recognize it for what I know about RANS and it is not mentioned in the nomenclature.

I have version 6.3.26 and this equation appear in the USER'S GUIDE here: "12.2.2 Reynolds (Ensemble) Averaging" and is numbered: (12.2-4).

Thanks

MicaŽl

David July 30, 2008 23:37

Re: RANS equation - don't understand a term
 
this term should be zero for incompressible fluids

Paolo Lampitella July 31, 2008 12:01

Re: RANS equation - don't understand a term
 
For a Newton Fluid the stress tensor is:

T_ij = ( - p + k dU_m/dX_m ) delta_ij + 2 mu ( S_ij - 1/3 dU_m/dX_m delta_ij )

where:

p - pressure

k - bulk viscosity (usually = 0)

mu - dynamic viscosity

dU_m/dX_m - Divergence of the velocity field

delta_ij - Kronecker's delta tensor

S_ij - symmetric part of the velocity gradient

So the term you cited exists, it's the last one.

Recognizing that

k = lambda + 2/3 mu

we get the form with which maybe you are more familiar:

T_ij = ( - p + lambda dU_m/dX_m ) delta_ij + 2 mu S_ij

the first one is more common because k >= 0 (like mu and the thermal conductivity) and this is linked with its thermodynamic meaning (non-equilibrium pressure or viscous normal stress).

Micael Boulet July 31, 2008 18:32

Re: RANS equation - don't understand a term
 
Thanks. I read further in a book on mechanics of fluids and fixed my problem (which was, in fact, a lack of knowledge).


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