An effective impedance for modelling the aeroacoustic coupling of ducts connected via apertures

Abstract

An effective impedance that models the aeroacoustic coupling between periodic arrays of ducts that communicate via apertures is derived. A lumped description of the interaction between the one-dimensional acoustics in the ducts and the transverse unsteady fluctuations in the connecting apertures is exploited in the derivation of the impedance. This configuration is of relevance for some industrial applications, for example to model the aeroacoustic coupling between cans in gas turbines equipped with can-annular combustors. The derived impedance can be used as a Bloch-type boundary condition to reduce theoretical and computational analysis on the dynamics of these arrays of ducts to a single duct. After the derivation of a general result, simpler limits of interest are discussed. For some of these limits, impedance models are available in the literature. It is shown how the effective impedance derived in this study reduces to already available models in these limits, but more generally embeds new features, including the explicit dependence of the impedance on the grazing flow Mach number and the finite extension of the apertures.