Turbulence Modelling
 

Hi,

I am at present working on implementation of high reynold's number K-epsilion turbulence model and k-omega turbulence model.

While refering to the book by Versteeg and Malalsekra, I have the wall functions for y+ between 30 and 500, but what should be the wall function for low values of y+ say around 1.

In case of k-omega, what should be the value of omega.

Also how should be the boundary conditions be implemented in case of both.

Thanks and Regards

Apurva

Re: Turbulence Modelling
 

If you are going to use k-epsilon down to y+ = 1 you need to use a low-Re model. A good review of several classical low-Re k-epsilon models is:

Virendra C. Patel, Wolfgang Rodi, and Georg Scheuerer. Turbulence models for near-wall and low Reynolds number flows: A review. AIAA Journal, 23(9):1308-1319, 1985.

The k-omega model can be used down to y+ = 1 without any modification. Strictly speaking omega goes to infinity on the wall. However, I would recommend that you use Wilcox's sruface rougness model to set a wall omega (see Wilcox's book Turbulence Modeling for CFD). The surface rougness model sets:

omega_wall = friction_velocity * S_R / nu

where

S_R = (50/k_R+)^2 when k_R+ < 25

S_R = 100/K_R+ when k_R+ >= 25

where

k_R+ = friction_velocity * average_height_of_roughness / nu

If you set k_R+ to 5 (or lower) you will get a smooth wall.

This surface wall-model is much more stable than having omega go to infinity on the wall and it works very well also for smooth walls.

Re: Turbulence Modelling
 

Hi, There are a lot of issues for the use of k-epsilon model and I have a report which I prepared after I wrote the code for k-epsilon model. If you want I can email it to you. About using the wall functions for y+ < 11.63, we do not use the equillibrium condition where G- density * epsilon = 0 is used. Instead we do this : Calculate tau_wall = mu_eff * up/yp calculate G = tau_wall * up/yp calculate epsilon = (2 * nu * Kp) /(yp^2)

About the boundary conditions implementation, I have explained in that report of mine , if you want ...

Abhijeet Vaidya IIT - Delhi