An elliptic-blending-related upgrade of a near-wall Reynolds-stress model

Abstract

A new version of the near-wall Reynolds-stress $\overline{u_i{u}_j}-{\omega }^h$ model by Jakirlić and Maduta (2015), based on the pressure–strain model term derived in accordance with the elliptic-blending procedure introduced by Manceau and Hanjalić (2002), is proposed. Accordingly, a quadratic formulation modeled in terms of Reynolds-stress anisotropy tensor, as proposed by Speziale et al. (1991), that is active in the off-wall region, is blended with an appropriately specified wall-related counterpart satisfying the exact asymptotic behavior. This blending approach eliminates the necessity to express model coefficients as complex functional dependencies, allowing them instead to be specified as constants. A further modeling refinement of importance involves the use of an appropriately modified turbulent diffusion coefficient in both the Reynolds-stress and scale-supplying equations, thereby removing the need for additional, often ad hoc, source terms typically introduced to address the well-known anomaly of the back-bending of the mean dividing streamline at the reattachment point in separating flows. The computational robustness of the model is significantly enhanced by including a specific form of coupling between the velocity and Reynolds-stress fields in the RANS (Reynolds-Averaged Navier–Stokes) equations of motion. In this formulation, a small, variably designed percentage of the Reynolds stress derived from Boussinesq’s correlation is retained. The model is thoroughly validated in various attached and separated, two-dimensional and three-dimensional flow configurations over a range of Reynolds numbers. The results obtained exhibit a high level of agreement with available experimental measurements and reference data from DNS (Direct Numerical Simulation) and LES (Large-Eddy Simulation).