Acoustic conservation principles and an application to plane and modal propagation in nozzles and diffusers

Abstract

Acoustic conservation principles are reviewed in some detail. The energy flow in the case of plane wave transmission across a shear discontinuity is analyzed and this problem serves as a convenient test for conservation. In this situation the energy principle developed by Blokhintsev is shown to be applicable. This principle is then used to study the propagation of plane and modal acoustic waves in nozzles and diffusers. The results obtained in an earlier work from a detailed analysis of the unsteady behavior of a supercritical nozzle are here completely retrieved. For modal propagation the duct is assumed to have a slowly varying section; conservation of acoustic energy then provides the axial distribution of pressure amplitude. An interesting cut-off property of nozzles and diffusers then is presented. It is shown that these elements have a last turning section at Mach number 0·51. A mode which passes this section cannot be turned or cut-off and will keep propagating.