CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
-   Main CFD Forum (https://www.cfd-online.com/Forums/main/)
-   -   question for specific dissipation rate (https://www.cfd-online.com/Forums/main/82237-question-specific-dissipation-rate.html)

 kippo November 20, 2010 17:13

question for specific dissipation rate

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

 Hamidzoka November 21, 2010 04:16

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.

regards

 kippo November 22, 2010 05:08

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~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:

+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

 cleoo September 7, 2016 08:23

Quote:
 Originally Posted by Hamidzoka (Post 284250) 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. regards
can this definition be used for kOmegaSST model as well?
if so where does the solver get the epsilon value from, since its not calculated in the turbulence model?

 RANSES November 24, 2016 05:58

Citing cfd-online:
"There is no strict mathematical definition of the specific turbulence dissipation, http://www.cfd-online.com/W/images/m...98d86b4602.png (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, http://www.cfd-online.com/W/images/m...21e8759df3.png, and the turbulence dissipation, http://www.cfd-online.com/W/images/m...b060f7daf5.png:
http://www.cfd-online.com/W/images/m...0b4f750897.png
Where http://www.cfd-online.com/W/images/m...fdd925d922.png is a model constant, most often set to:
http://www.cfd-online.com/W/images/m...fa783bccd8.png
Please note that some models/codes instead use a different definition without the model constant:
http://www.cfd-online.com/W/images/m...f97ee7106e.png"

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 https://www.sharcnet.ca/Software/Flu...ug/img4040.gif to https://www.sharcnet.ca/Software/Flu...ug/img4041.gif" makes me think there is not C_mu inside the FLUENT definition...but it is not so clear after all.