5. Summary of Contribution and Directions for Future Work

This monograph has tabulated for the first time, the parametric zeros and the non-dimensional resonance frequencies of the higher-order transverse modes of a rigid-wall elliptical waveguide for a complete range of aspect-ratio. This is followed by an analysis of the first few mode shapes. Based on the modal summation and uniform piston-driven model, a theoretical formulation is presented for characterizing and evaluating the TL performance of reactive elliptical muffler configurations having an end-inlet and end-/side-outlet [1, 2]. The TL analysis has resulted in formulation of a set of comprehensive guidelines for designing short elliptical and circular mufflers which are used as end-chambers in a modern-day automotive exhaust system. The guidelines suggest optimal port locations which suppress the propagation of certain higher-order transverse modes, thereby yielding a flat but broadband attenuation despite a small expansion volume. More precisely, it was shown that locating the inlet and outlet ports on the major-axis and minor-axis, respectively, at appropriate pressure nodes yields a broadband attenuation for Helmholtz number \(0.5k_{0} D_{1} > 6\). Similarly, for short chambers of nearly circular cross section, a concentric end-inlet and offset end-outlet centered on the pressure node of the first radial mode yield a broadband attenuation for Helmholtz number as high as \(0.5k_{0} D_{1} \approx 7\), see Ref. [3].