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The impedance boundary condition for acoustics in swirling ducted flow

Published online by Cambridge University Press:  21 June 2018

Vianney Masson Open the ORCID record for Vianney Masson [Opens in a new window] ,
James R. Mathews Open the ORCID record for James R. Mathews [Opens in a new window] ,
Stéphane Moreau ,
Hélène Posson  and
Edward J. Brambley Open the ORCID record for Edward J. Brambley [Opens in a new window]
Vianney Masson*
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
James R. Mathews
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
Stéphane Moreau
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
Hélène Posson
Affiliation:
Acoustic Department, Airbus Commercial Aircraft, 31300 Toulouse, France
Edward J. Brambley
Affiliation:
Mathematics Institute/WMG, University of Warwick, Coventry CV4 7AL, UK
*
†Email address for correspondence: vianney.masson@usherbrooke.ca
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Abstract

The acoustics of a straight annular lined duct containing a swirling mean flow is considered. The classical Ingard–Myers impedance boundary condition is shown not to be correct for swirling flow. By considering behaviour within the thin boundary layers at the duct walls, the correct impedance boundary condition for an infinitely thin boundary layer with swirl is derived, which reduces to the Ingard–Myers condition when the swirl is set to zero. The correct boundary condition contains a spring-like term due to centrifugal acceleration at the walls, and consequently has a different sign at the inner (hub) and outer (tip) walls. Examples are given for mean flows relevant to the interstage region of aeroengines. Surface waves in swirling flows are also considered, and are shown to obey a more complicated dispersion relation than for non-swirling flows. The stability of the surface waves is also investigated, and as in the non-swirling case, one unstable surface wave per wall is found.

JFM classification

Instability: Absolute/convective instability Acoustics: Acoustics Acoustics: Aeroacoustics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 645 - 675
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Copyright
© 2018 Cambridge University Press 

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