Propagation of plane waves in a variable-area duct carrying a compressible subsonic flow

Abstract

A complete numerical solution is obtained for plane wave propagation in a variable-area duct which carries a mean compressible flow. The equation solved is a matrix formulation of the equation first derived by Tsien in 1952. The solution is uniformly valid in the sense that waves of all frequencies are allowed for in the calculations. Solutions for the two extreme cases of very low frequency (compact element theory) and very high frequency (geometrical acoustics) are computed and compared with analytical predictions. Sample calculations are presented for two particular applications pertaining to aircraft engine silencing technology: the sonic inlet problem and the core noise exhaust problem. For the sonic inlet, the effect of various convergent-divergent nozzle geometries and throat Mach numbers on the acoustic power transferred to the surrounding medium is examined. For the exhaust nozzle, the effect of nozzle geometry and flow on the acoustic power output is calculated. These latter calculations represent an extension of a previous analytic solution [J. Acoust. Soc. Am. 55, 425(A) (1974)] for compact nozzles.