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Teta term in Menter's Momentum thickness Reynolds number equation for transition

Hi, I'm currently undertaking a task of implementing the gamma-Re transition formulation for turbulence modelling by way of a UDF in Fluent.
I've come across a problem.
There's lambda term in used for prediction of transition onset, denoted lambda underscore theta. In the formulation of this term, a parameter given by a capital theta is required. (equation 28 in Langtry & Menter, 2009, 'Correlation-based transition modelling for unstructured parallelized computations CFD')
The problem is, that in all the literature I have looked in, no correlation or formulation for this term is given.
As you would expect, this has brough my progress to a standstill.
I would be grateful if anyone could suggest where I might be able to look for an answer.
Many thanks.

 mb.pejvak June 28, 2012 20:09

it should be calculated iteratively. you should take following step:
1-guess teta (teta=0)
2-find F(lateta) and Rethetat (from form. 35-38)
3-find theta from Retheta (Retheta=ru*theta*U/mu - you can see it in Nomenclature)
4-go to step 2 and iterate until it converge.

I hope I can explain it well.

That makes it much clearer. Thanks very much.

Just one thing, to calculate theta in step three, which value for Retheta do I use? Do I make it equal to Rethetat?

 mb.pejvak June 29, 2012 12:10

I am sorry, i made a mistake. In fact, Rethetat is true in step three instead of Retheta.

But then Rethetat is calculated using thetat, whereas lambdatheta is calculated using just theta.

 mb.pejvak June 29, 2012 22:35

yes that is true, but in calculation of landa it was recommended to Theta= thatat. In fact, I have never understand why and in all paper and thesis I have read, never describe its reason.
if I complete my former reply, following steps can explain it better:

(a) guess the initial value for Thetat (=0 was recommended)
(b) calculate the Landa by setting Theta= thatat
(c) calculate the Flanda
(d) calculate the Rethetat
(e) calculate the t from the definition of Thetat =(no/U)Ret.
(f) go to step 2 and iterate until it converge.
The calculation may converge in a few iterations.

I'll try that out. Many thanks for your help.

A friend of mine is also implementing the Transition formulation of Menter for the Spalart Allmaras turbulence model based on the paper by Medida and Baeder 'Application of the Correlation based gamma-retet Transition Model to the Spalart-Allmaras Turbulence model' and has encountered a problem with the blending function.
In the paper it is specified that the blending function is used to distinguish a wall boundary layer and a free shear layer to deactivate the production term in the wall boundary layer only. However, this function depends on the dissipation rate, which is not available in the S-A model. The paper says that the blending function has been turned off manually, but does not explicitly specify how this is done.
Can anyone suggest how this is done? Any help would be greatly appreciated.

 TedBrogan November 30, 2012 20:30