
[Sponsors] 
October 1, 2013, 13:53 
Implementating the Wilcox 2006 turbulence model

#1 
New Member
Ben Graves
Join Date: Dec 2012
Posts: 18
Rep Power: 5 
Hi everyone,
I am trying to implement the Wilcox 2006 turbulence model into openFOAM, and have gotten a little stuck. I have been able to code up everything except the closure coefficient chi_omega. The equation determines the coefficient Beta. The equation for chi_omega can be seen in the attached image. I know that the Omega_ij term is the skew symmetric matrix, what I am not sure of is how to code in Omega_jk and S_ki. I would really appreciate any insight that can be provided. Thanks for your help in advance Ben Graves 

October 2, 2013, 11:13 

#2 
New Member
Matt Laurita
Join Date: Jan 2012
Location: New York
Posts: 8
Rep Power: 6 
If you take a look at the Tensor class (actually TensorI.H) there are global functions for calculating symmetric and skewsymmetric parts of a matrix. In this case, if you start with the gradient of the velocity, grad(U), then symm(grad(U)) gives you S and skew(grad(U)) gives you Omega. You'll probably also have to make use of the inner product and mag() functions here as well to get to Chi_omega.
MJL 

October 2, 2013, 13:58 

#3 
New Member
Ben Graves
Join Date: Dec 2012
Posts: 18
Rep Power: 5 
Hi Matt,
Thanks for the reply! I know how to get Omega_ij and S_ij, what I wanted to know was how to get Omega_jk and S_ki. Basically my question is how do I specify the different index. Thanks, Ben 

October 3, 2013, 03:59 

#4 
New Member
Join Date: Nov 2012
Posts: 13
Rep Power: 6 
Hi Ben,
S_ij is the same as S_ki, both are a component of the tensor S. When calculating chi_omega, you should use i,j,k = 1, 2, 3 to construct each term and then add them up (in total there will be 27 terms, due to Einstein convention of repeated indices). You should have some basic knowledge of tensor. 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
SimpleFoam case with SpalartAllmaras turbulence model implemented  nedved  OpenFOAM Running, Solving & CFD  2  November 30, 2014 23:43 
An error has occurred in cfx5solve:  volo87  CFX  5  June 14, 2013 17:44 
turbulence model for Refrigerator  cicatrix  Main CFD Forum  0  October 3, 2012 01:47 
Low Reynolds kepsilon model  YJZ  ANSYS  1  August 20, 2010 13:57 
KOmega Turbulence model from wwwopenFOAMWikinet  philippose  OpenFOAM Running, Solving & CFD  30  August 4, 2010 10:26 