Sound attenuation characteristics of acoustically lined curved pipes

Boundary element solutions of the Helmholtz integral equation for the sound attenuation of acoustically lined curved pipes are presented. The curved pipes are in the form of cylindrical and toroidal coordinates. The main objective of the study is a comparative analysis of sound attenuation characteristics of lined toroidal pipes. Although toroidal pipes with circular cross-section are used extensively in industrial and agricultural applications, they have been taken little attention in literature. One reason may be the impossibility of theoretical solution since wave equation is not separable in toroidal coordinates. A numerical method should be utilized in the solution; in fact, not many researchers are familiar with toroidal coordinates on the contrary of other coordinate systems, such as cylindrical coordinates. The use of toroidal coordinates and generation of a pipe in these coordinates are illustrated herein. Sound waves in the pipes are produced by the vibrating inlet surface and resulting sound pressure distribution on the interior surfaces of side walls and anechoic exit are computed. Sound transmission loss of the pipes is represented by the ratio of inlet to exit pressures, as sound attenuation spectra. The results of cylindrical and toroidal pipes with the same cross-sectional area are compared. The sound attenuation performance of lined toroidal pipes is compared in terms of bend sharpness as a measure of curvature. The comparison is extended to cover the hard-walled and lined toroidal pipes to conclude their common and/or different acoustic behaviours.