Sound reflection by periodic acoustic metasurface in sheared grazing flows

The reflection performance of periodic acoustic metasurfaces (AMs) subjected to a grazing flow, consisting of a uniform region and a finite sheared layer, is studied. A convective generalized Snell's law (CGSL) is derived to account for the effect of uniform mean flows on the reflection of AMs. Then, an AMs design method considering the mean flow profile is proposed based on the impedance transformation method. The strategy is to form a reflected phase gradient at the interface plane between the uniform and the sheared flow regions. The reflection characteristics of two acoustic porous metasurfaces (APMs), i.e., APM1 and APM2 designed for the uniform and the sheared flows, respectively, are numerically investigated. Results show that APM1 achieves efficient anomalous reflections in uniform flows, and the diffracted orders and directions of the reflected waves are well predicted by the proposed CGSL. However, the performance of APM1 deteriorates under oblique incidences if applied to a typical sheared flow. In contrast, APM2 realizes desired wavefront manipulations under the same conditions. Finally, the CGSL is extended into a three-dimensional (3D) space and is validated numerically. This study provides a means for AMs design in flow conditions, which holds good potential in aeroacoustic noise problems.