Numerical Simulation of Hypersonic Boundary-Layer Instability in a Real Gas with Two-Dimensional Surface Roughness

Experimental and numerical results have shown that two-dimensional surface roughness can stabilize a hypersonic boundary layer dominated by second-mode instability. It is sought to understand how this physical phenomenon extends from an airflow under a perfect gas assumption to that of a real gas. To these ends, a new high-order shock-fitting method that includes thermochemical nonequilibrium and a cut-cell method to handle complex geometries unsuitable for structured body-fitted grids is presented. The new method is designed specifically for direct numerical simulation of hypersonic boundarylayer transition in a hypersonic real-gas flow with arbitrary shaped surface roughness. The new method is validated and shown to perform comparably to a high-order method with a body-fitted grid. For a Mach 10 flow over a flat plate with a real-gas model, a two-dimensional roughness element was found to stabilize the second mode when placed downstream of the synchronization location which is consistent with previous research for perfect-gas flows. For a Mach 15 flow over a flat plate, a two-dimensional surface roughness element stabilizes the second-mode instability more effectively in a real gas than in a perfect gas.