Acoustic end-correction in a flow-reversal end chamber muffler: a semi-analytical approach

Abstract

This work presents a semi-analytical technique based on the Green's function and uniform-piston driven model to determine the end-correction length l in an axially long flow-reversal end chamber muffler having an end-inlet and an end-outlet. The semi-analytical procedure is based on the 3D analytical uniform piston-driven model for obtaining the impedance Z] matrix parameters and numerically evaluating the frequency f(p) at which the imaginary part of the cross-impedance parameter Z(E2E1) crosses the frequency axis at the first instance. The frequency f(p) corresponds to the low-frequency peak in the transmission loss (TL) spectrum of the axially long flow-reversal end-chamber muffler obtained a priori to its computation by considering the influence of higher order evanescent transverse modes. The effective chamber length (and thence, the end-correction length) in the low-frequency range are determined by using the expression for resonance frequency of a classical quarter-wave resonator. This method is employed to determine the end-correction in axially long elliptical cylindrical end chambers and circular cylindrical end chambers (with or without a rigid concentric circular pass-tube). The TL graph predicted by the 1D axial plane wave model (incorporating the end-correction length) is shown to be in an excellent agreement with that obtained by the 3D analytical approach and an experimental result (from literature) up to the low-frequency limit, thereby validating the semi-analytical technique. Parametric studies are conducted using the proposed semi-analytical method to investigate and qualitatively explain the effect of angular location and offset distance of the end ports and the pass-tube diameter on the end-correction length, thereby yielding important insights into the influence of transverse evanescent modes on dominant axial plane wave modes of the axially long end-chamber. Development of an empirical end-correction expression in a flow-reversal circular end-chamber with offset inlet and outlet ports is a practically useful contribution of this work.