Velocity/Pressure-Gradient Correlation Modelling for Improved Prediction of Reattachment and Relaxation

The computation of complex flows with large separation is one of the numerous instances where second-moment closures outperform two-equations models. Previous studies with the Reynolds-stress model developed by Gerolymos-Vallet [3] (GV RSM) indicate that separation is quite accurately predicted, but also that there is room for improvement in the reattachment and relaxation region. Extensive testing suggests that the modelling of the pressure terms in the Reynolds-stress transport equations has the greatest impact on the prediction of both separation and reattachment. We propose a second-moment closure including a pressure-velocity gradient model with an additional term in the basis of the slow-part redistribution tensor proposed by Lumley [7] and a closure for the pressure-diffusion tensor which model directly the divergence of the pressure-velocity correlation. The present Reynolds-stress model is validated against a shock-wave/turbulent-boundary-layer interaction on a compression ramp and compared with two second-moment closures and the linear two-equations model of Launder-Sharma [5] (LS k-epsilon).