On the Directivity and Spectra of Noise from Unheated and Heated Jets

Abstract

The present paper considers the transmission of sound from a source distribution inside a jet to a receiver or observer outside; the source can be represented by a combination of multipoles moving relative to the jet. The shear layer has a random shape with a plane mean position, and entrains a region of turbulence. The transmission across the plane shear layer involves: (i) scattering by the convected, irregular and unsteady interface across which occurs the transition from the jet to the ambient medium; (ii) refraction in the region of low Mach number turbulence entrained by the shear layer. If the jet Mach number does not exceed two the local turbulence can be taken as incompressible. The transmission involves: (i) a deterministic amplitude factor due to the difference in sound speed, mass density and velocity between the jet and ambient medium; (ii) a random phase shift due to the scattering of sound by the irregular interface and the convection of sound by the turbulence entrained with the shear layer. Since there is a random phase shift for the acoustic pressure, the acoustic power, which is quadratic in the acoustic pressure, involves the statistics of interference between two waves. The latter specify the spectral directivity, defined as the acoustic power radiated per unit solid angle and unit frequency band, i.e. either the spectrum received in each direction or the directivity of sound received outside the jet at each frequency. The statistics of sound scattering by irregular interfaces and convection by turbulence are subject to assumptions and constraints which affect critically the directivity and spectra. The evaluation of radiation integrals without low- or high-frequency approximations is also essential to reproduce experimental results on the noise of cold or hot jets. An accuracy of 3 dB can be expected for directivities and 6 dB for spectra, for directions not too far away from the vertical, (i.e perpendicular to the jet).