Sound propagation in the presence of non-isothermal sheared flow refraction and metasurface impedance reflection

Sheared flow can profoundly influence the aeroacoustic performance of near-wall structures like metasurfaces on moving vehicles. In this work, a refractive generalized Snell’s law is developed by combining Snell’s law with the generalized Snell’s law to manipulate anomalous reflections in an idealized sheared flow, comprising a uniform flow region and a stationary air region with velocity and temperature gradients. Theoretical analysis and numerical simulations of planar wave reflection by metasurface impedance under non-thermal sheared flows are conducted, yielding favorable predictions of the zone of silence, as well as anomalous and total reflection behaviors. The total reflection between the shear layer and the metasurface is analyzed with the objective of confining incident wave below the shear layer. Remarkably, a specific configuration of hot-sheared flow and metasurface length can achieve total absorption over a range of incident wave angles from 0° to almost 90°. Moreover, the refractive generalized Snell’s law, extended to account for directional deflection induced by flow convection, is utilized to regulate sound beam reflection, resulting in satisfactory outcomes under sheared conditions. This study offers a theoretical framework for wave control under non-isothermal and sheared flow conditions, which cannot be resolved by the traditional generalized Snell’s law, and can be implemented in the design of metasurfaces for moving applications.