Fluid shielding of low frequency convected sources by arbitrary jets

Abstract

A low frequency asymptotic theory is proposed for the shielding of noise by jets of arbitrary cross-section. The results of the theory provide a qualitative explanation for the appearance of the quiet and noisy planes of a slot jet. The arguments in favour of this explanation are derived from a model problem in which a pulsating mass source is convecting along the axis of an infinitely long column of fluid of arbitrary cross-section. The jet velocity is represented by a uniform velocity profile (i.e. slug flow). The method of matched asymptotic expansions is applied to derive expressions for the acoustic pressure and the radiative power of the source.The solution for the elliptic jet indicates that the radiative power in the horizontal plane (containing the major axis) is less than that in the vertical plane (containing the minor axis). This difference in power varies with source Strouhal number and jet Mach number. The effects of jet temperature are also included in the analysis. The theoretical results are in good qualitative agreement with experimental findings for slot nozzles. The theory indicates that the noise shielding offered by jets is negligible at low frequencies and low Mach numbers.