A correction for Reynolds-averaged-Navier–Stokes turbulence model under the effect of shock waves in hypersonic flows

Studies on the unphysical increase of turbulent quantities for RANS simulation induced by shock waves in hypersonic flows are carried out. Numerical experiments on the hypersonic flow over a blunt body reveal that the phenomenon of unphysical increase of turbulent quantities across the detached shock wave is induced by the strain-rate-based production terms of the k- (Formula presented.) and k- (Formula presented.) SST turbulence models, which leads to the over-prediction of aerothermal prediction. While this phenomenon does not occur for Spalart–Allmaras (S–A) turbulence model because of its vorticity-based production term. In order to eliminate this unphysical phenomenon, and to maintain the accuracy of the original models for boundary layer and separation flows, a new correction method for the k- (Formula presented.) and k- (Formula presented.) SST models is proposed: by comparing the orders of magnitude between the strain-rate-based and vorticity-based production terms, the vorticity-based production term is used near the shock waves, while the original strain-rate-based production term is still used in other regions. Finally, the correction method is applied to turbulence and transition flows over blunt bodies, and the numerical results show that the correction method effectively eliminates the unphysical increase of turbulent quantities across shock waves and improves the accuracy of aerothermal and transition onset location prediction.