On the Effects of Sound in Subsonic Boundary Layer Flows

Abstract

The study of acoustic receptivity in quiet disturbance environments can be decomposed into several sub-problems. One such problem consists of determining the response of the unsteady boundary layer to acoustic forcing in the freestream. In this paper, we describe two methods to characterize the acoustic boundary layer response based on the linear stability equations. In their inviscid form, we first show how to determine the reflection coefficient. The sum of the incident and reflected waves then drives the unsteady Stokes motion within the boundary layer, for which a double-layer high Strouhal number asymptotic solution is obtained. The outer layer solution is calculated numerically whereas the inner layer solution, introduced to satisfy the no-slip condition, is determined analytically. The full linear stability equations can also be integrated numerically to directly obtain a complete disturbance profile accounting for the effects of viscosity. A comparison between these models and the linearised unsteady boundary layer equation (LUBLE) model shows good agreement at high Strouhal number, low Mach number and for downstream-travelling waves. However, for near sonic Mach numbers and for upstream-travelling waves, the LUBLE are shown to be not valid because the assumption that the acoustic wavelength is long compared to the boundary layer thickness no longer holds.