A new form of the elliptic relaxation equation to account for wall effects in RANS modeling

Different methods for improving the behavior in the logarithmic layer of the elliptic relaxation equation, which enable the extension of Reynolds stress models or eddy viscosity models down to the wall, are tested in a channel flow at Reτ=590 and compared with direct numerical simulation (DNS) data. First, a priori tests are performed in order to confirm the improvement predicted by the theory, either with the Rotta+IP (isotropization of production) model or the Speziale–Sarkar–Gatski (SSG) model as the source term of the elliptic relaxation equation. The best form of the model is then used for full simulations, in Durbin second moment closure or in the frame of the v2¯−f model. It is shown that the results can be significantly improved, in particular by using a formulation based on the refinement of the modeling of the two-point correlations involved in the redistribution term.

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