Two point correlations of jet noise

Abstract

A large body of careful experimental measurements of two-point broad band correlations of far-field jet noise has been carried out and was briefly reported recently by Lucio Maestrello in NASA TM X-72835. The rather sharp directional lobes and marked absence of axisymmetry were striking and motivated the present effort to bring theory to bear. The model of jet-noise generation is an approximate version of an earlier work of Ribner, based on the foundations of Lighthill. The model incorporates isotropic turbulence superimposed on a specified mean shear flow, with assumed space-time velocity correlations, but with source convection neglected. The particular vehicle is the Proudman format, and the previous work (mean-square pressure) is extended to display the two-point space-time correlations of pressure. The shape of polar plots of correlation is found to derive from two main factors: (1) the non-compactness of the source region, which allows differences in travel times to the two microphones—the dominant effect—and (2) the directivities of the constituent quadrupoles —a weak effect. The non-compactness effect causes the directional lobes in a polar plot to have pointed tips (cusps) and to be especially narrow in the plane of the jet axis. In these respects, and in the quantitative shapes of the normalized correlation curves, results of the theory show generally good agreement with Maestrello's experimental measurements.