Theoretical evaluation of sound fields in circular or annular ducts with rigid or nonrigid radial splitters

Abstract

In aircraft engines, extra attenuation can be obtained by installing lined radial or circumferential splitters or both. A study of the governing wave equation and its solution in the lined radial splitter environment is presented. It is shown that the general solution can be written in the terms of modified Bessel and Neumann functions of complex fractional orders and complex arguments. This is due to the fact that the circumferential wavenumber is in general complex, noninteger, and a function of the radial coordinate. In the analysis, the circumferential wave vector is evaluated first as a function of the radial coordinate and in terms of the angular separation between the splitters and the frequency parameter; this function is then used in the radial integration, yielding the mode shapes and the corresponding complex axial wavenumbers. The model attenuations are higher for two reasons: the increased surface area of absorptive materials and the much higher cutoff frequencies of the modes. This analysis can be extended to the evaluation of sound field between blades.