Aerofoil Surface Pressure Reconstruction from Far-Field Array Measurements

Abstract

This paper covers the relationship between the far-field sound radiation of an aerofoil interacting with a turbulent flow and the Spatial Fourier Transform of the dipole source strength distribution over the aerofoil surface. It is shown that each far-field microphone effectively samples the source wavenumber spectrum at a particular wavenumber associated with the observer position and the Mach number; these wavenumbers are inside the “acoustic domain” in the wavenumber space and correspond to propagating plane waves, while wavenumbers outside this domain correspond to evanescent waves and are not visible in the far-field. We briefly discuss the surface pressure properties of a flat plate aerofoil, where the flat plate response functions for supercritical and subcritical gusts are interpreted from a wavenumber-domain perspective and some examples of aerofoil surface pressure wavenumber power spectra are shown. We then propose a source estimation method from far-field measurements in a convected medium: this is based on the Inverse Spatial Fourier Transform of the sampled source wavenumber spectrum within the “acoustic domain”. Wavenumbers outside this domain are not recoverable from far-field observations; hence, the estimated source distribution contains only components that are efficient radiators of far-field sound, but is spatially bandlimited.