Inconsistency in Launder-Sharma k-e model?
 

Hi all, actually I'm not sure if this is a real bug or not, but I have some questions about the Launder-Sharma model implementation in OpenFOAM (1.6). The literature about this model tells me that, in order to avoid a singular behavior of the sink term in the epsilon equation, the epsilon itself could be replaced with a quantity called epsilonTilda, which is equal to:

epsilonTilda=epsilon-2*nu*magSqr(grad(sqrt(k))

Well, looking at the source code, it seems like the epsilon equation is solved for epsilonTilda, and after that the "corrected" epsilon (epsilonTilda + 2*nu*...) is used as a sink term for the k-equation. However, in all other formulas or equations where epsilon is needed (in particular the turbulent eddy viscosity formula and the calculation of Ret for the damping functions), epsilonTilda is used instead...Maybe I'm missing something, but this sounds not so consistent to me as, in general, epsilon and epsilonTilda are not the same. Can anybody correct me or give some explanation for this?

Thank you all

V.

So, no one's got an answer?

Hi vkrastev,
I haven't studied the OpenFOAM implementation yet, but the original model has in fact this apparent inconsistency that you mentioned. Since the extra term is expected to be zero everywhere, except near the wall, epsilon and epsilonTilda will be almost equal, so there should be no problem in using one instead of the other.

Hi Vatavuk, and thanks for the reply. What you are saying sounds logical: the extra term is multiplied by the kinematic viscosity, which has usually a quite low value, so the term involving the gradient of the root squared turbulent kinetic energy should be very high in value to cause significant discrepancies between epsilon and epsilonTilda. So, probably away from the walls it should be practically equivalent to use one or another (as you say), whether any discrepancies near the walls should be damped out by the viscous damping function. Ok, now I think it's more clear to me, thanks once again!

V.