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Old   August 16, 2001, 16:36
Default 3D Second Moment Closure
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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 XY-plane and is double staggered from the scalar controlvolume.) suppose the backface of this uv-controlvolume is a wall. How do I determine the uv-stress 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.

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Old   August 17, 2001, 11:35
Default Re: 3D Second Moment Closure
Michael Malin
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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 near-wall 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 near-wall control volume, but taking care when evaluating the velocity gradients which appear in the production term and the pressure-strain 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 "saw-tooth" 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.

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Old   August 17, 2001, 13:34
Default Re: 3D Second Moment Closure
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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 uiuj-equation, 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 saw-tooth 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.


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Old   August 20, 2001, 03:55
Default Re: 3D Second Moment Closure
Michael Malin
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Yes, I agree. I think I used a diffusive link to wall for the shear-stress equation, and of course, the wall shear-stress is known from the log law.

I do seem to remember that the 'saw-tooth' 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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