Analysis of higher-order mode effects in the circular expansion chamber with mean flow

Abstract

The effects of higher-order acoustic modes produced by the areal discontinuities of the simple expansion chamber with mean flow on the acoustic performance are studied. The chamber is modeled as a piston-driven circular rigid tube with no losses and, by using the Fourier–Bessel expansion, a general expression of the output pressure to the given input uniform volume velocity is obtained for a whole chamber. Quantitative estimation for the transmission loss can be performed using the derived four-pole parameters, whereas the characteristics of the chamber, as a result of the interactions between the plane wave and the transverse waves, can be easily investigated with respect to the relative locations of the inlet/outlet, the chamber length, and the mean flow. The expression as a form of C in four-pole parameters is adopted to describe the chamber characteristics for computational convenience. All the parameters involved in the experimental works by Eriksson [L. J. Eriksson, J. Acoust. Soc. Am. 72, 1208–1211 (1982)] are taken in the examples. Using the derived four-pole parameters, the transmission losses for both the concentric and offset inlet/outlet configurations are predicted and compared with the experimental results. The theoretical results of the present study are in good agreement with the experiments of the authors and the previous works.