Coherent structures and turbulent model refinement in oblique shock/hypersonic turbulent boundary layer interactions

In the present study, we investigate the evolution of turbulent statistics and coherent structures in hypersonic turbulent boundary layers at the Mach number of 5 impinged by oblique shock waves generated by the wedge with the angles of $14 ° , 10 °$⁠, and $6 °$⁠, inducing strong, mild, and incipient flow separation, by exploiting direct numerical simulation databases, for the purpose of revealing the underlying flow physics that are of significance to turbulent modeling. We found that the large-scale structures are amplified within the interaction zone, manifested in the form of large-scale low- and high-speed streaks with the spanwise length scale of boundary layer thickness, and gradually decay downstream, the process of which is extremely long. The abrupt variation in the characteristic length, time, and velocity scales as well as the incompatible viscous dissipation of the mean and turbulent kinetic energy results in the incorrect predictions by the Reynolds-Averaged Navier–Stokes (RANS) equation simulations, provided the models are established based on solving the transport equations of the turbulent kinetic equation and its viscous dissipation (⁠ $k − ε$ or $k − ω$ models, for instance). To amend this issue, we propose to refine the parameters in the model as the functions of wall pressure, the flow quantities related to multiple flow features. The RANS simulations with the $k − ω$ SST model utilizing the proposed refinement improve greatly the accuracy of the skin friction, wall heat flux, and Reynolds shear stress downstream of the interaction zone, and the wall pressure distributions in hypersonic turbulence over compression ramp, suggesting its promising prospect in engineering applications.