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July 29, 2008, 20:42 
RANS equation  don't understand a term

#1 
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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: (12.24). Thanks Micaël 

July 30, 2008, 23:37 
Re: RANS equation  don't understand a term

#2 
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this term should be zero for incompressible fluids


July 31, 2008, 12:01 
Re: RANS equation  don't understand a term

#3 
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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 (nonequilibrium pressure or viscous normal stress). 

July 31, 2008, 18:32 
Re: RANS equation  don't understand a term

#4 
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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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