Adding a simple production term to Reynolds-averaged Navier–Stokes turbulence models for flows over two-dimensional hills

Abstract

We consider an additional production term for the k,ε turbulence model that is activated by curvature, for turbulent flow over two-dimensional hills of varying steepness. The new term depends on the difference between the strain rate, S, and the rotation, R, which we refer to as the “SR” modification. It is compared to the standard k,ε turbulence model, the Kato–Launder model, and the re-normalization group and realizable versions of the k,ε model. The Kato–Launder model showed the best overall predictions for mean velocity, turbulent kinetic energy, and Reynolds shear stress at most locations before, on, and after the crest of the hills. The SR model was slightly less accurate but uniquely predicted the flow separation in the lee of the steeper hill and was also correctly predicted the flow re-attachment point. This study demonstrates the importance of including a curvature production term in k–ε-based models for flows over hills.