Time-domain asymptotics. II Application to propeller acoustics

Abstract

The method of time-domain asymptotics of double integrals described in paper I (this Issue) is applied to the thickness noise of a simple sector-shaped propeller blade with supersonic tip speed and no axial motion. The structure of the pressure field is determined by topological changes in the retarded blade shape, corresponding to the presence of stationary points of a certain phase function. The overall pressure waveform takes the form of a series of short bursts of high pressure fluctuation, each burst corresponding to the crossing of a stationary point by the retarded blade shape. Asymptotic formulae are derived, using the asymptotic régime of small chord length; the complete near-field structure is considered, with detailed calculations of the acoustic field near the various transition surfaces in observer space. The results are illustrated throughout with waveform graphs and contour plots for a blade with quadratic chord section.