Effect of acoustic metasurface on hypersonic-boundary-layer wave packet

Effect of the acoustic metasurface on a broadband wave packet in a Mach 6 boundary layer is studied. Direct numerical simulations (DNSs) with time-domain impedance boundary condition (TDIBC) and metasurface with microstructures are performed. It is shown that DNS with TDIBC resolves the amplitude and phase information of the wave packet satisfactorily. The minor prediction discrepancy arises from the modeling error in the acoustic impedance. The interesting finding of this paper is that the metasurface behaves as an equivalent unsteady blowing-suction model to perturb the wall-normal velocity and then passively the pressure field. Although both pressure and wall-normal velocity appear in the characteristic-wave variable, the pressure can be decoupled to be updated by the Neumann condition, as usually employed in Navier-Stokes solvers. The dominant frequency scale that enables reproducing the stabilization effect of the metasurface is found to be slightly smaller than the energetic frequency maximum of the wave packet. This observation indicates that the high-frequency unsteadiness nature of the blowing-suction behavior is indispensable, which is induced by the interaction of the metasurface and the wave packet. For the stabilization mechanism, energy analysis reveals that a dilatation-related work near the wall is significantly suppressed by the metasurface, which agrees with the wall-normal location where the wave-packet fluctuation gets attenuated.