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Flow and geometry induced scattering of high frequency acoustic duct modes

Smith, AF; Ovenden, NC; Bowles, RI; (2012) Flow and geometry induced scattering of high frequency acoustic duct modes. WAVE MOTION , 49 (1) 109 - 124. 10.1016/j.wavemoti.2011.07.006. Green and gold open access

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Abstract

Cut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood for Helmholtz numbers of order unity. Previous finite-element simulations of this phenomenon, however, appear to indicate the possibility of energy scattering into neighbouring modes at moderately large Helmholtz numbers. In this paper, such scattering phenomena are explained and predicted in slowly varying aeroengine ducts using a multiple-scales approach. It is found that, for sufficiently high frequencies, two mechanisms exist whereby energy can be scattered into neighbouring modes by an incident propagating mode. One mechanism occurs only when there is a mean flow inside the duct and induces scattering at significantly lower frequencies than the other mechanism which remains present without mean flow. A coupled system of ordinary differential equations is derived and then solved numerically for a number of example cases to obtain the corresponding transmitted and reflected amplitudes of the scattered modes as well as the overall acoustic pressure field. The theory appears to demonstrate that some exchange of energy between the acoustic and mean flow fields occurs during scattering.

Type:Article
Title:Flow and geometry induced scattering of high frequency acoustic duct modes
Open access status:An open access publication. A version is also available from UCL Discovery.
DOI:10.1016/j.wavemoti.2011.07.006
Publisher version:http://dx.doi.org/10.1016/j.wavemoti.2011.07.006
Language:English
Additional information:This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Keywords:Duct modes, Mean flow, Scattering, Standing waves
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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