freestream conditions
 

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

Jenni

Re: freestream conditions
 

Hi,

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

Re: freestream conditions
 

Hi!

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!

QKim