The Mach wave field radiated by supersonic turbulent shear flows

Abstract

Theoretical studies of aerodynamic noise suggest that the sound field of supersonic flows will be dominated by eddy Mach waves. Recent experimental evidence supports this view. In supersonic turbulent boundary layers, and rocket exhaust flows, turbulence occurs in regions of high mean velocity gradient. At low speed, such gradients are known to amplify the sound emitted by turbulence. This paper deals with the corresponding Mach wave problem. The exact equations of sound radiation by turbulence are rearranged in a form where the equivalent sources, derivatives of the turbulence stress tensor, are shown to be dominated by one term. That term is formed from the product of the mean velocity gradient and the rate of change of density. It seems that its resemblance to the dominant source of sound in low speed shear flows is largely fortuitous. In the Mach wave case, the theory is designed to include effects of both temperature gradients and density perturbations, and the approximations of the estimate are of a type that would not be expected to be valid away from the Mach wave condition. The basic theory is used to make an estimate of the sound radiated from supersonic boundary layers, and an approximate equation relating the radiated pressure to the surface pressure is derived. Experimental evidence is then examined to show that the equation is in excellent agreement with observation. The theory is then applied to annular shear flows of the rocket exhaust type. Again an approximate equation relating near and far field pressures is established, and the paper concludes with suggestions for experiments that could check the result.