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, hard-walled 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. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two-dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case.

The 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, thereby reducing the computational time and the roundoff error encountered in purely numerical techniques. A computer program has been developed based on this theory. The mean-flow model consists of a one-dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows.