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Old   November 20, 2010, 17:13
Default question for specific dissipation rate
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Hi all,

a basic question: What is the mathematical correct definition of omega (specific dissipation rate in the k-omega)?

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 Baldwin-Lomax as div x c ?

Hope, someone has a clue...

Thnx,

kippo
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Old   November 21, 2010, 04:16
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Hamid Zoka
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Dear Kippo;
omega has a different meaning in k-omega 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 k-omega C is defined as a function of mean flow strain and rotation rates and omega itself implicitly.

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Old   November 22, 2010, 05:08
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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 Reynold-shear-stress tensor.
epsilon will occure in the equation in this way:

eij=2/rho*avg(du'i*du'j)/(dxjdxj)

the k-equation is the trace of the Rij-tensor: Meaning in the k-equation, which can be derrived by avg(u'i*Ns(ui))=0
you will get a dissipation-term 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 k-omega-SST equations. Menter transformed the epsilon in the k-epsilon to suit the omega-equation. So an additional term occurs in the transformed epsilon-equation:

+2*rho/(sigma*omega)*dk/dxj*domega/dxj

(this is the cross-diffusion modification, see manuals CFX of Fluent, or StarCD).

Where can I derive this term from the epsilon and omega-definition?

Or again, what is the correct mathematical definition of omega?

thnx a lot,

kippo
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