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August 7, 2020, 04:14 |
Derivation of k-omega SST turbulence model.
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#1 |
New Member
Dustin Weaver
Join Date: Dec 2016
Posts: 4
Rep Power: 9 |
Does anyone know a detailed derivation of the k-omega SST turbulence model? I can't seem to find a fully derivation anywhere and yet a lot of people use this model quite frequently. I am having issues with going from the k-epsilon to the "transformed" k-epsilon in terms of omega.
The kinetic energy equation transformed derivation is straight forward but I'm struggling with dissipation. With the dissipation in the standard k-epsilon equation given by: (eq1) and using the ratio given by: (eq2) We now obtain (eq3) Plugging eq2 and eq3 into eq1 while putting a placeholder for epsilon constants with phi we obtain (eq4) Some reducing and rearranging... (eq5) I'm now stuck here and I believe just the last two terms are incomplete. My calculus is pretty rusty and not sure quite where to go. The transformed k-epsilon model stated by Menter,1994 is given by I've seen a lot of people just say that merely the addition of the last cross-diffusion term makes it an exact copy of the k-epsilon equation (that's what menter,1994 states as well) but I haven't seen a full derivation of this anywhere and so I'm not sure how that's the case. This being said, I feel I'm getting closer but my calculus is rusty and so any help will be greatly appreciated. |
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August 7, 2020, 07:36 |
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#2 |
Senior Member
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I suggest to give a look here
http://www.tfd.chalmers.se/~lada/pos...port_lowre.pdf and to the original references |
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August 7, 2020, 13:12 |
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#3 |
New Member
Dustin Weaver
Join Date: Dec 2016
Posts: 4
Rep Power: 9 |
This is a good reference and I'll go through this and post a reply. I already checked the original references and many others and they just say that the exact transformed k-epsilon equation merely has the addition of the cross-diffusion term. It seems that there is also a turbulent diffusion term that gets dropped out. I'm really surprised that I haven't found a full derivation when so many people use this model.
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