
[Sponsors] 
November 20, 2010, 17:13 
question for specific dissipation rate

#1 
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Hi all,
a basic question: What is the mathematical correct definition of omega (specific dissipation rate in the komega)? I cannot find a correct answer, anywhere. Also in Wilcox's book it is not mathematically described. Even in all books and publications I got, it is only derived by the turbulent viscosity definition. Is it according to the BaldwinLomax as div x c ? Hope, someone has a clue... Thnx, kippo 

November 21, 2010, 04:16 

#2 
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Hamid Zoka
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Dear Kippo;
omega has a different meaning in komega turbulence models. it can be stated as: Epsilon=C*Omega*K in which epsilon is eddy dissipation, K is turbulence kinetic energy and C is the model constant. although in some versions of komega C is defined as a function of mean flow strain and rotation rates and omega itself implicitly. regards 

November 22, 2010, 05:08 

#3 
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Thnx a lot,
but this is again all the time the same definition I get. What I mean is the following: To derive the equation for k, you can take the trace of the Reynoldshearstress tensor. epsilon will occure in the equation in this way: eij=2/rho*avg(du'i*du'j)/(dxjdxj) the kequation is the trace of the Rijtensor: Meaning in the kequation, which can be derrived by avg(u'i*Ns(ui))=0 you will get a dissipationterm like the following (factor 2 is not there, because trace): rho*epsilon=avg(µdu'i*du'i)/(dxjdxj) meaning, epsilon is a tensor built out of the second derivation of the turbulent energy k (correct?). the units for k~m˛/s˛, epsilon~m˛/sł If you look then to the specific dissipation rate omega, as also defined as omega=epsilon/(Cµ*k)~1/T (according to the turbulent viscosity definition), then omega should be mathematically seen a tensor built by the tensors k/epsilon. But what is then the correct mathematic definition. If you look further to the komegaSST equations. Menter transformed the epsilon in the kepsilon to suit the omegaequation. So an additional term occurs in the transformed epsilonequation: +2*rho/(sigma*omega)*dk/dxj*domega/dxj (this is the crossdiffusion modification, see manuals CFX of Fluent, or StarCD). Where can I derive this term from the epsilon and omegadefinition? Or again, what is the correct mathematical definition of omega? thnx a lot, kippo 

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