Eigensolutions for liners in uniform mean flow ducts

Abstract

The problem of sound attenuation in a rectangular acoustically lined duct containing uniform mean flow is investigated analytically by means of the generalized Wiener-Hopf technique. For lined sections of finite axial extent uniqueness of the solution is enforced by imposing edge conditions at the liner interfaces. Several possible edge conditions are considered, including the Kutta condition. The corresponding solutions differ by eigensolutions and it is demonstrated that solution methods, like the mode matching and singularity method, imply differing edge conditions. The power attenuation as well as the SPL traces appear to be rather insensitive to the imposed edge conditions but striking differences are observed for the reflection coefficient.