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Acoustic boundary conditions at an impedance lining in inviscid shear flow

Published online by Cambridge University Press:  04 May 2016

Doran Khamis  and
Edward James Brambley Open the ORCID record for Edward James Brambley [Opens in a new window]
Doran Khamis
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Edward James Brambley*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

The accuracy of existing impedance boundary conditions is investigated, and new impedance boundary conditions are derived, for lined ducts with inviscid shear flow. The accuracy of the Ingard–Myers boundary condition is found to be poor. Matched asymptotic expansions are used to derive a boundary condition accurate to second order in the boundary layer thickness, which shows substantially increased accuracy for thin boundary layers when compared with both the Ingard–Myers boundary condition and its recent first-order correction. Closed-form approximate boundary conditions are also derived using a single Runge–Kutta step to solve an impedance Ricatti equation, leading to a boundary condition that performs reasonably even for thicker boundary layers. Surface modes and temporal stability are also investigated.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 386 - 416
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Copyright
© 2016 Cambridge University Press 

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