Numerical Simulation of Hypersonic Boundary-Layer Receptivity to Three-Dimensional Wall Perturbations

The receptivity of a hypersonic boundary layer to three-dimensional wall perturbations is investigated in this paper by numerical simulations. The work is motivated by Tumin’s [1] theoretical analysis on the receptivity of compressible boundary layers to three-dimensional wall perturbations with the help of the biorthogonal eigenfunction system. Specifically, receptivity processes of a Mach 5.92 boundary-layer flow on a flat plate, corresponding to Maslov et al.’s [2] leading-edge receptivity experiments, to small-scale stationary roughness elements are studied. Due to the fact that the steady base flow profiles are independent of span-wise coordinate, the steady base flow is simulated by solving two-dimensional compressible Navier-Stokes equations with a combination of a fifth-order shock-fitting finite difference method and a second-order TVD scheme. For receptivity simulations, small-scale roughness elements are introduced to the flat plate. The subsequent responses of the hypersonic boundary layer are simulated by solving three-dimensional Navier-Stokes equations with the fifth-order shock-fitting finite difference method. Effect of thermal boundary conditions on the receptivity process is considered by comparing the results of receptivity simulations on adiabatic and isothermal flat plates. The preliminary numerical results show that pressure perturbations are excited inside the boundary layer downstream of the roughness element. In addition, pressure perturbations have relatively large amplitudes near the Mach lines generated by the roughness element. Pressure peturbations can be enhanced by concave roughness element. Counter rotating stream-wise vortices are generated for both cases. However, it is found that roughness element on adiabatic flat plate is more efficient in flow heating and stream-wise vorticity generation. Further studies are currently under way to investigate the receptivity of the hypersonic boundary layer to various wall perturbations.