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Old   June 6, 2003, 11:58
Default freestream conditions
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hi there everyone,

Does anybody know of any guidelines for choosing the freestream values of the turbulence kinetic energy (k), and the specific dissipation rate (omega) (or turbulence length scale - L) for a compressible boundary layer modelled using the k-omega model?

I plan to do a freestream sensitivity study on the compressible boundary layer but just need a ballpark figure to get me started.

thankyou y'all

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Old   June 7, 2003, 08:17
Default Re: freestream conditions
James Date
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Check in "Turbulence Modelling for CFD", by David C. Wilcox.

But I think you need to set them to reasonable small values i.e. 0.0001. It is important, however, that the calculated values don't turn negative as the solution progresses. I think this only happens with high order differencing schemes (QUICK), but don't quote me on it. I know in CFX the CCCT scheme prevents this happening.

Have a read of: "An Introduction to Computational Fluid Dynamics: The Finite Volume Method", by H.K. Versteeg, W. Malalasekera.

This book has some excellent basic information which will get you on the right track.

There is a book some where on the web by CT Shaw from Warwick University, called something like "Practical CFD modelling" which is also excellent.

Regards James
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Old   June 9, 2003, 23:38
Default Re: freestream conditions
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Upstream omega value can be estimated by assuming homogeneous/isotropic turbulence. Then, production term and diffusion term in omega eq. go away. From the simplified eq., omega can be approximated as omega_inf ~ 1/(beta*t), beta=3/40. Assuming t~ L/u_inf, omega_inf ~ 40*u_inf/(3L).

Menter came up with the similar value, omega_inf ~ O(c*u_inf / L), c=10. The more detail on inlet condition and the sensitivity of freestream omega value can be found in the following paper: author = {F. R. Menter}, title = {Influence of Freestream Values on $k$-$\omega$

Turbulence Model Prediction }, journal = {AIAA Journal}, year = {1992}, volume = {30}, number = {6}, pages = {1657-1659}, month = {August}

The values of k and omega can be limited such that they don't become negative. For example, k>k_inf and omega and omega_inf*10^-3 (AIAA paper 98-2554).

Good luck!

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