question for specific dissipation rate
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...
omega has a different meaning in k-omega turbulence models. it can be stated as:
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.
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:
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):
meaning, epsilon is a tensor built out of the second derivation of the turbulent energy k (correct?).
the units for k~m²/s², epsilon~m²/s³
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:
(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,
if so where does the solver get the epsilon value from, since its not calculated in the turbulence model?
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