Non-dimensional k-w
 

Hi all. I am trying to implement Wilcox's two equation k-w turbulence model, and am having a hard time with the non-dimensionalization of 'w'. What is the appropriate non-d parameter:

(1) w_inf = U_inf/L-inf

(2) w_inf = (U_inf)**2/L-inf

(3) w_inf = sqrt(U_inf**3 /(Nu_inf * L-inf))

Depending on the parameter used, the Reynolds number term appears in front of the Dissipation term. What is the physics behind determining which parameter to use? Is it a problem-based choice? My test cases would involve supersonic external flows.

Thanks for all your input.

Correction
 

Oops! The second parameter should have been

(2) w_inf = U_inf/Nu_inf

which gives the correct dimensions of 1/time for w.

Thanks!

Re: Non-dimensional k-w
 

If you already have a k-eps model implemented, look at its non-d parameters. First of all, w=eps/k, so the non-dimensionalized form of k and eps will give you the appropriate form of w.

Sylvain