A semi-analytical odel for erforated pipe muffles

A quasi-steady semi-analytical model is proposed to predict the grazing-bias flow in a perforated-pipe muffler at low Mach numbers for high Reynolds numbers based on the diameter of the perforation. This model allows both the prediction of the steady flow distribution through a muffler and the prediction of the acoustical response of the perforated pipe in terms of the impedance. The model is compared with experimental and numerical data from the literature. The incorporation of the influence of the flow in this impedance allows predicting the global acoustical response of the muffler by means of a Finite Element Method solution of the Helmholtz equation, neglecting other convective effects. This procedure is tested for two extreme cases. Firstly we consider a through flow muffler consisting of an expansion chamber mounted axis-symmetrically around a perforated pipe. Secondly a plug flow muffler is considered, which is the same muffler but with a plug placed halfway along the perforated pipe, forcing the flow through the pipe perforations. In both cases the model predicts the transmission loss of the muffler within 1 dB for Strouhal numbers (based on the perforation diameter and main flow velocity) of order unity. The performance of the through flow muffler is essentially that of an expansion chamber without major contribution of flow effects. In the plug flow muffler the flow does significantly enhances the muffler performance, but this is at the cost of a significant static pressure loss