4. Double-Tuned Short End-Chamber Mufflers

End-chambers are an important component of multi-pass perforated (MPP) tube mufflers which are often used in automotive exhaust systems. Constraints on the physical space available necessitate end-chambers to have a short length which does not allow the higher-order evanescent modes generated at the port-chamber interface to decay sufficiently, signifying the existence of 3-D acoustic field even at low frequencies. This chapter analyzes the transmission loss (TL) performance of such short end-chambers based on the 3-D semi-analytical formulation and presents design guidelines in terms of optimal port location to achieve a broadband attenuation performance. Flow-reversal and straight-through elliptical mufflers are considered; for both configurations, it is shown that end-inlet port offset on the major-axis and end-outlet port offset on the minor-axis, at pressure nodes of \((2,1)e\) and \((0,2)e\) modes, respectively, yield a broadband TL covering the entire frequency spectrum of interest. This optimal end port location is referred to as double-tuning of short chamber mufflers and is similar to the practise of tuning the extension lengths of inlet and outlet ports of long muffler configurations through appropriate end-corrections. Parametric studies are carried out to investigate the dramatic changes in broadband TL range as the cross-sectional shape changes from an eccentric ellipse to a circle. Furthermore, this chapter also explains the 1-D transverse plane wave model in terms of the transverse mode shapes and discusses the frequency range over which it is valid, and can be used for analyzing and double-tuning highly eccentric elliptical chambers which have an end-centered port and end-offset port located on the major-axis. Finally, short chamber configurations having an end-inlet and a side-outlet are also analyzed, and their TL graph is compared with the double-tuned end-inlet and end-outlet counterpart configuration having the same aspect-ratio. Some guidelines are suggested for the acoustic design of short end-chambers in terms of the recommendation for optimal location of inlet and outlet ports.