Transverse plane-wave analysis of short elliptical end-chamber and expansion-chamber mufflers

Abstract

The flow-reversal end chambers are used quite often in commercial automotive mufflers. The conventional axial plane-wave theory is not able to predict their acoustic performance because of the fact that the length of the end chambers is not enough for the evanescent three-dimensional modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large expansion ratio at the inlet, the first few higher- order modes get cut on even in the low-frequency regime. This necessitates a finite element or boundary element analysis, which is cumbersome and time-consuming. Therefore, an ingenious one-dimensional method has been developed. It models plane-wave propagation in the transverse direction between the incoming pipe and the return pipe, with the lateral-end cavities being modeled as variable-area quarter-wave resonators. Making use of this novel approach, the transfer matrices have been derived for elliptical and circular cross-section mufflers, which enable these elements to be analyzed along with the rest of the muffler elements by means of the transfer matrix-based muffler program. Through a comparison with a full, three-dimensional analysis on commercial software, it is shown that the one-dimensional approach presented in this paper is able to predict the transmission loss quite accurately up to about 1000 Hz for typical automotive mufflers.