Acoustic source distribution on aerofoils and its reconstruction from far-field array measurements

Abstract

This paper is concerned with the acoustic source distribution on aerofoils interacting with a turbulent flow. The source distribution is usually taken to be equal to the pressure jump across the aerofoil, whose behaviour is well understood from classical unsteady aerofoil theory. However, much of this source does not radiate to the far-field. This paper deals with the application of Fourier methods to extract the equivalent source distribution on the aerofoil that radiates perfectly to the far-field. This paper shows that, whilst the actual pressure jump across a flat plate tends to infinity at the leading edge while dropping to zero at the trailing edge (due to the Kutta condition), the equivalent source distribution is more uniform across the aerofoil chord, which explains why the radiation spectrum and single-frequency directivity both exhibit strong oscillations due to interference from coherent sources across the chord. A method for extracting this far-field equivalent source distribution from an array of far-field measurements is proposed in this paper.