Lessons Learned from RANS Simulations of Shock-Wave/Boundary-Layer Interactions

Abstract : Usual two-equation turbulence models, based on a constant value of c(sub-mu) in the definition of the eddy viscosity, are known to fail in predicting most features of Shock-Wave/Boundary-Layer Interactions (SWBLI). In searching a simple way to improve their capabilities, it appears that three different theoretical approaches end up with simple and similar Weakly Non-Linear (WNL) corrections. Such a correction, originally proposed to ensure realizability in subsonic flows, is extended to deal with compressible flows and applied to three-dimensional supersonic SWBLI developing on three single sharp fin plate configurations. The numerical solutions are obtained by solving the full Reynolds-Averaged Navier-Stokes equations on grids up to 3.3 million cells with the linear and WNL versions of the kappa-omega turbulence model. The WNL correction allows full grid-convergence and yields much better numerical solutions, including the prediction of the pressure plateau under the lambda foot of the shock, the maximum skin-friction coefficient on the bottom plate, and the secondary separation in the strong SWBLI case. The improvement is due to halving the turbulence intensity in the vortical flow embedded within the lambda foot of the shock. The WNL correction has also a beneficial effect in transonic cases, as illustrated for a two-dimensional channel flow over a bump. Finally, its success in predicting unsteady features in the case of shock-induced oscillations in transonic flows over airfoils is underlined. In the considered 3-D supersonic, 2-D transonic steady and unsteady SWBLI, the key-point is the dependency of c(sub-mu) on the strain and vorticity invariants rather than the non-linear expansion of the shear stress.