Effect of sheared grazing mean flow on acoustic transmission in perforated pipe mufflers

Abstract

At present there are two competing numerical approaches for practical one-dimensional acoustical analyses of perforated pipe muffler components, namely, the discrete approach and the continuous approach. In a recent experiment (Journal of Sound and Vibration 265 (2003) 109) on the measurement of the elements of the transfer matrix across a perforate row with a subsonic low Mach number grazing mean flow, a discrepancy is observed between the experimental data and the prediction of a discrete approach. The present analysis shows that this discrepancy can be corrected by including an effect of the mean flow velocity profile, which is neglected in the current discrete methods as well as the distributed parameter method. Accordingly, the paper develops, for the first time, a quasi-one-dimensional theory of sound transmission in a perforated pipe carrying sheared grazing mean flow. The distinguishing features of this theory are the inclusion of the mean flow velocity in the sense of cross-sectional average and the introduction of slip flow velocity at the perforate wall. Two alternative formulations of the theory are presented. The proper formulation should necessarily be based on continuity, momentum and energy equations for one-dimensional acoustic perturbations. The simpler approximate formulation, which assumes isentropic wave propagation and neglects the energy equation, is shown to represent the proper formulation accurately for subsonic low Mach numbers. The current discrete and distributed parameter methods are reformulated on the basis of the proposed theory. Both the parallel and co-axial perforated multiple pipe elements are considered and the effect of mean flow velocity profile and slip velocity is shown by application to a straight-through resonator.