Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite hardwalled or lined circular duct carrying compressible, sheared mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasiparallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. A number of test cases that demonstrate the flexibility of the program are included. Convergence of the transmission coefficients and the acoustic pressure profiles with in increasing number of modes is illustrated. I. Introduction T HE trend toward the use of high-bypass turbojet engines has decreased jet noise and resulted in noise emissions from the inlet nacelles being responsible for an increasing proportion of community annoyance. Consequently, effective control measures are required to reduce the inlet noise to acceptable levels. The use of choked inlets has long been recognized as an effective means of reducing upstream noise propagation,1'2 although such inlets require careful design to prevent excessive loss in compressor performance. Hence, a promising approach to the reduction of inlet noise is the use of a high-subsonic Mach number inlet, or partially choked inlet, in conjunction with an acoustic duct liner. However, the physical mechanisms responsible for the noise reduction in high-subsonic Mach number inlets are not completely understood, and techniques for the theoretical analysis of sound propagation through regions of near-sonic mean flow are still in the development stage. Two major problems must be overcome in the development of such a model: 1) the mathematical techniques for the calculation of sound propagation in ducts are well developed for parallel ducts but are not fully developed for ducts of varying cross section that carry mean flows with strong axial and transverse gradients, and 2) linear acoustic equations are inadequate to describe acoustic propagation in regions of near-sonic mean flows. In the investigation reported herein, the first of these two problems was addressed, and a wave-envelope technique based on the method of variation of parameters was developed. This procedure can be used as the basis for the examination of the second aspect of the problem—the development of nonlinear models for the near-sonic region. Several analytical as well as numerical techniques have been developed for the analysis of wave propagation in uniform and nonuniform ducts. Surveys of these techniques were made