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additional terms for production in k-omega turbulence model

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Old   September 16, 2012, 17:50
Default additional terms for production in k-omega turbulence model
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Hi guys,

i was just wondering whether anyone could shed some light on the following: i have been studying up on the formulation of the general RANS turbulence models, and have noticed that in the standard k-epsilon, the production term for k has:

P = 2\nu_t S_{ij} \cdot S_{ij}


S_{ij} is the mean strain tensor ...

In most of the intro CFD texts, it is pointed out that, for incompressible flow, div U = 0 and so, when calculating the Reynolds stresses, an additional term -2/3\rho k \delta_{ij} is incorporated to ensure the turbulence effects resulting from the normal Reynolds stresses are accounted for.

However, when you look at the production term in k-omega, there is an additional term included:

P = \left(2\nu_t S_{ij} \cdot S_{ij} - 2/3 \rho k \frac{\partial{U_i}}{\partial{x_j}} \delta_{ij}\right)

Could anybody explain why the additional term, which seems to be related to the normal Reynolds stresses is present in k-omega explicitly, when I would have thought this was already implied / incorporated in the strain tensor as in k-epsilon???

many thanks in advance!
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