SOUND GENERATED BY TURBULENCE AND DISCRETE VORTICES INTERACTING WITH A PERFORATED ELASTIC PLATE IN LOW-MACH-NUMBER FLOW

An analytical model is developed of the production of sound by turbule nce and discrete vortex structures in low-Mach-number flow over single or multiple apertures in a thin elastic plate. The aperture dimension is comparable to or larger than the length scale of the unsteady flow , and in the undisturbed state an aperture is spanned by a vortex shee t. This sheet is assumed to be linearly disturbed from its planar form by the hydrodynamic pressure field of the flow. The strength of the r adiation is dependent on the generalized Rayleigh conductivity K-R(k,o mega), which defines the volume flux through an aperture when a pressu re disturbance of frequency omega and wavenumber k in the plane of the plate is applied to the vortex sheet. Detailed results are given for rectangular apertures of large aspect ratio, whose conductivity is kno wn in closed form, and application made to determine the sound produce d when a line vortex is swept over an isolated aperture in a rigid or elastic plate. The problem of noise generation by boundary-layer flow over a thin, perforated elastic plate is investigated for large apertu res, where the aperture diameter exceeds the boundary-layer displaceme nt thickness. The predicted sound power produced by turbulent wall pre ssures whose length scales are smaller than the streamwise dimension o f the apertures is shown to be significantly larger than traditional e stimates that ignore the shear layer. Numerical results are given for a rigid perforated plate, and for a perforated steel plate in water.