Sound generated by turbulence and discrete vortices interacting with a perforated elastic plate in low-mach-number flow

Abstract

An analytical model is developed of the production of sound by turbulence 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 sheet. This sheet is assumed to be linearly disturbed from its planar form by the hydrodynamic pressure field of the flow. The strength of the radiation is dependent on the generalized Rayleigh conductivity K R (k,ω), which defines the volume flux through an aperture when a pressure disturbance of frequency ω and wavenumber κ 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 known in closed form, and application made to determine the sound produced 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 apertures, where the aperture diameter exceeds the boundary-layer displacement thickness. The predicted sound power produced by turbulent wall pressures whose length scales are smaller than the streamwise dimension of the apertures is shown to be significantly larger than traditional estimates that ignore the shear layer. Numerical results are given for a rigid perforated plate, and for a perforated steel plate in water.