3D Second Moment Closure
Hello all,
Does anybody have some experience with using wall functions in 3D Reynolds Stress Turbulence modelling? If so then my question is: suppose you have a controlvolume of the stress uiuj, for simplicity take uiuj = uv (this control volume in a 3D staggered arrangement is in the XYplane and is double staggered from the scalar controlvolume.) suppose the backface of this uvcontrolvolume is a wall. How do I determine the uvstress on this backface cell by using the wall function approach. Or should I not do this but just use some interpolation scheme. If someone knows some good reference on this, then I would be gratefull to hear this. Regards. 
Re: 3D Second Moment Closure
I have not worked on this for many years but from memory I recall that there are a number of treatments for handling the Reynolds shearing stress next to the wall. If the turbulence is presumed to be in equilibrium then the value can be fixed, as the ratio uv/k is known from nearwall data on pipe/channel flow. However, a more common approach is to determine uv directly from the solution of its own balance equation in the nearwall control volume, but taking care when evaluating the velocity gradients which appear in the production term and the pressurestrain correlations, e.g. presume a logarithmic variation when determining these gradients or alternatively by extrapolating from interior velocities. A lot depends on where everything is stored in the computational stencil and whether it is a colloacted or staggered arrangement. If care is not taken then "sawtooth" velocity profiles may result. The precise details are usually given in any PhD thesis on second moment closure that has emerged from Launder's group (UMIST, UK). Unfortunately, I don't have a reference to hand but I could probably find one if no one else can help.

Re: 3D Second Moment Closure
Micheal,
Thanks for your response and advice. In fact I just went to talk with some people in the group of "Hanjalic" today and we solved the problem today. I know there are lots of ways to cope with this problem. The most straight forward is solving the uiujequation, but even then when using the wall function approach if the back (or front faces) of a living cell alligns with a wall cell then still you have to know the (wall)stresses of these faces in order to obtain the gradient in the shear stresses on these faces (these you need for the turbulent diffusion > Daly Halow Diffusion model). And yes you indeed need interior flow variables for this process. The sawtooth profile or checkerboard phenomena is taken care of since staggered arrangement is chosen for storage (in total you then have 7 seperate control volumes, 1 for scalars, 3 for velocities and 3 for shear stresses uiuj, see for instance Lien & Leschziner). In this way the strong coupling of the equation (and physics also) are preserved. Regards, Ridwan. 
Re: 3D Second Moment Closure
Yes, I agree. I think I used a diffusive link to wall for the shearstress equation, and of course, the wall shearstress is known from the log law.
I do seem to remember that the 'sawtooth' problem may still persist in some swirling flows unless care is taken with the velocity gradients. One of the papers I had in mind was something by Lien & Leschziner and another by Hogg and Leschziner, but you have solved the problem now so I won't dig out the references. 
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