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Nonlinear sound propagation in 2D curved ducts : a multimodal approach
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McTavish, James and Brambley, Edward J. (James) (2019) Nonlinear sound propagation in 2D curved ducts : a multimodal approach. Journal of Fluid Mechanics, 875 . pp. 411-447. doi:10.1017/jfm.2019.497 ISSN 0022-1120.
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Official URL: https://doi.org/10.1017/jfm.2019.497
Abstract
A method for studying weakly nonlinear acoustic propagation in 2D ducts of general shape - including curvature and variable width - is presented. The method is based on a local modal decomposition of the pressure and velocity in the duct. A pair of nonlinear ODEs for the modal amplitudes of the pressure and velocity modes is derived. To overcome the inherent instability of these equations, a nonlinear admittance relation between the pressure and velocity modes is presented, introducing a novel `nonlinear admittance' term. Appropriate equations for the admittance are derived which are to be solved through the duct, with a radiation condition applied at the duct exit. The pressure and velocity are subsequently found by integrating an equation involving the admittance through the duct. The method is compared, both analytically and numerically, against published results and the importance of nonlinearity is demonstrated in ducts of complex geometry. Comparisons between ducts of differing geometry are also performed to illustrate the effect of geometry on nonlinear sound propagation. A new 'nonlinear reflectance' term is introduced, providing a more complete description of acoustic reflection that also takes into account the amplitude of the incident wave.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics T Technology > TL Motor vehicles. Aeronautics. Astronautics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) |
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Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||||
Publisher: | Cambridge University Press | ||||||||||
ISSN: | 0022-1120 | ||||||||||
Official Date: | 25 September 2019 | ||||||||||
Dates: |
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Volume: | 875 | ||||||||||
Page Range: | pp. 411-447 | ||||||||||
DOI: | 10.1017/jfm.2019.497 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Fluid Mechanics http://doi.org/10.1017/jfm.2019.497 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Copyright Holders: | © 2019 Cambridge University Press | ||||||||||
Date of first compliant deposit: | 21 June 2019 | ||||||||||
Date of first compliant Open Access: | 19 January 2020 | ||||||||||
Funder: | EPSRC, Royal Society | ||||||||||
Grant number: | UF150695 | ||||||||||
RIOXX Funder/Project Grant: |
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