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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 

September 7, 2016, 08:23 

#4  
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annn
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Quote:
if so where does the solver get the epsilon value from, since its not calculated in the turbulence model? 

November 24, 2016, 05:58 

#5 
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Riccardo
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Citing cfdonline:
"There is no strict mathematical definition of the specific turbulence dissipation, (at least none known by the author, please add one here if you know it). Instead it is most often defined implicitly using the turbulence kinetic energy, , and the turbulence dissipation, : Where is a model constant, most often set to: Please note that some models/codes instead use a different definition without the model constant: " So my question is: which is the definition used by FLUENT for defining omega? I wasn't able to find a precise answer to such a question. According to FLUENT user's guide: "which can also be thought of as the ratio of to " makes me think there is not C_mu inside the FLUENT definition...but it is not so clear after all. 

February 2, 2017, 16:10 

#6 
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Mike
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Hi, from the paper by Ferrari et al. CFD study of Savonius wint turbine: 3D model validation and parametric analysis. (Elsevier, Renewable Energy)
Omega= [C_mu^(3/4)]*[ (k^(1/2)) / L] Where C_mu= 0.09 L=0.07*HydraulicDiameter k= (3/2)*[(FlowSpeed*Turbulence Intensity)^2] This is the one I am using for my simulations. Hope this helps. 

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