Revisiting URANS Computations of the Backward-facing Step Flow Using Second Moment Closures. Influence of the Numerics

Previous studies have shown that Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations are able to reproduce the vortex shedding behind a backward-facing step. The aim of the present work is to investigate not only the quantitative predictions of the URANS methodology concerning the characteristic frequencies, but also the amplitude of the energy of the resolved eddies, by using the Elliptic Blending Reynolds Stress Model. This innovative low-Reynolds number second moment closure reproduces the non-viscous, non-local blocking effect of the wall on the Reynolds stresses, and it is compared to the standard k − ε and LRR models using wall-functions. Consistent with previous studies, in the 2D computations shown in the present article, the vortex shedding is captured with the correct Strouhal number, when second moment closures are used. To complete these previous analyses, we particularly focus here on the energy contained in the unsteady, resolved part and its dependency on the numerical method. This energy is less than 5% of the total energy and is strongly dependent on the mesh. Using a refined mesh, surprisingly, a steady solution is obtained. It is shown that this behaviour can be linked to the very small spatial oscillations at the step corner, produced by numerical dispersion, which act as perturbations that are sufficient to excite the natural mode of the shear layer, when the local Peclet number, comparing convection and diffusion effects, is high enough. This result suggests that URANS is not appropriate to quantitatively predict the amplitude of the large-scale structures developing in separated shear-layers, and that URANS results must be interpreted with care in terms of temporal variations of forces, temperatures, etc., in industrial applications using marginally fine meshes.