Numerical study of hypersonic boundary-layer transition delay through second-mode absorption

Numerical time-domain impedance boundary conditions are developed within a high-order spectral difference flow solver. They are designed to accurately replicate the acoustic response of ultrasonically-absorbent coatings over a broad spectral range. The coupling of this class of high-fidelity wall boundary conditions with high-order numerical methods has enabled their use in aero-acoustics applications. This solver is used to perform direct numerical simulations (DNS) of a hypersonic boundary layer and analyze the stabilizing effects of acoustically absorbent materials on the laminar-to-turbulent transition. The damping effectiveness of such complex porous coating on key frequencies of interest is investigated, as well as its effect on the mean flow. It is found that the second-mode instability, which dominates the high-Mach number flow regime, is strongly suppressed at the expense of higher far-field noise radiation. The solutions obtained by means of DNS are also found to compare favorably with linearized stability theory.