The far field of high frequency convected singularities in sheared flows, with an application to jet-noise prediction

Abstract

The purpose of the present paper is to derive expressions for the pressure fields of various high frequency convected singularities immersed in a unidirectional sheared flow. These expressions include the simultaneous effects of fluid and source convection and refraction. These results are then combined to predict the far-field directivity of cold round jets. It is found that the agreement between experiment and the present theory is quite good at a source Strouhal number of unity but that this agreement deteriorates as the source frequency is increased. Our theoretical results show the explicit form of the ‘refraction integral’ and that convective amplification for the pressure of a quadrupole is increased by a factor of (1 —M_Jcos Θ)⁻¹over the classical results, whereM_Jis the jet Mach number and Θ is the angle from the jet axis. Thus acoustic/mean-flow interaction not only implies refraction but also additional convective amplification duenotto source convection but to fluid motion.