On High-Frequency Sound Generated by Gust-Aerofoil Interaction in Shear Flow
A theoretical model is constructed to predict the far-field sound generated by high-frequency gust–aerofoil interaction in steady parallel shear flow, including the effects of aerofoil thickness. Our approach is to use asymptotic analysis of the Euler equations linearised about steady parallel shear flow, in the limits of high frequency and small, but non-zero, aerofoil thickness and Mach number. The analysis splits the flow into various regions around the aerofoil; local inner regions around the leading and the trailing edges where sound is generated and scattered; a surface transition region accounting for the curvature of the aerofoil; a wake transition region downstream of the aerofoil; and an outer region through which the sound propagates to the observer. Solutions are constructed in all regions, and matched using the principle of matched asymptotic expansions to yield the first two terms in the expansion of both the amplitude and the phase of the far-field pressure. Result are computed for the particular case of scattering of a gust by a symmetric Joukowski aerofoil placed in symmetric Gaussian parallel shear flow. The introduction of mean shear is shown to have a significant effect on the far-field directivity and on the total radiated power.