Acoustic Propagation in Partially Choked Ducts

  • Ali H. Nayfeh
Conference paper

Abstract

Sound propagation in partially choked hard- or soft-walled ducts is discussed. Techniques for its theoretical analysis are still in the development stage, because linear theory is inadequate to. describe acoustic propagation in regions of near-sonic mean flows and the ducts have varying cross sections and carry mean flows with strong axial and transverse gradients. The linear three-dimensional problem has been successfully treated using the wave envelope technique, whereas the quasi-one-dimensional continuous nonlinear problem has been successfully treated by using spectral methods or the method of matched asymptotic expansions. Efforts are underway to combine the wave envelope technique with either spectral methods or the method of matched asymptotic expansions to treat the nonlinear three-dimensional problem. The wave envelope technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. It is applicable to hard-walled as well as lined ducts, strong as well as weak transverse gradients, and strong as well as weak axial gradients. The numerical results show that converging ducts produce substantial refractions toward the duct’s center for axisymmetric waves propagating against near choked flows. Spinning modes get refracted toward an annulus away from the duct’s center. The degree of refraction and intensification at the throat of a partially choked duct decreases with increasing spinning mode number and/or real part of wall admittance. The acoustic signals become arbitrarily large as the throat Mach number approaches sonic conditions because the linear acoustic equations are singular there. The nonlinearity generates higher harmonics and an acoustic streaming, resulting in a decrease in the energy carried by the fundamental. The strength of the nonlinearity increases with increasing source, frequency, or mean flow Mach number. Beyond a given nonlinear strength, acoustic shocks form.

Keywords

Mach Number AIAA Paper Sound Propagation Acoustic Streaming Axial Variation 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Ali H. Nayfeh
    • 1
    • 2
  1. 1.Virginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Yarmouk UniversityIrbidJordan

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