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The modified Myers boundary condition for swirling flow

Published online by Cambridge University Press:  29 May 2018

James R. Mathews Open the ORCID record for James R. Mathews [Opens in a new window] ,
Vianney Masson Open the ORCID record for Vianney Masson [Opens in a new window] ,
Stéphane Moreau  and
Hélène Posson
James R. Mathews
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1TN, UK
Vianney Masson
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
Stéphane Moreau*
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada
Hélène Posson
Affiliation:
Acoustic Department, Airbus Commercial Aircraft, 31060 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

This paper gives a modified Myers boundary condition in swirling inviscid flow, which differs from the standard Myers boundary condition by assuming a small but non-zero boundary layer thickness. The new boundary condition is derived and is shown to have the correct quadratic error behaviour with boundary layer thickness and also to agree with previous results when the swirl is set to zero. The boundary condition is initially derived for swirling flow with constant azimuthal velocity, but easily extends to radially varying swirling flow, with terms depending on the boundary layer model. The modified Myers boundary condition is then given in the time domain rather than in the frequency domain. The effect of the boundary layer profile is then considered, and shown to be small compared to the boundary layer thickness. The boundary condition is then used to analyse the eigenmodes and Green’s function in a realistic flow. Modelling the thickness of the boundary layer properly is shown to be essential in order to get accurate results.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics Boundary Layers: Boundary Layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 868 - 906
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Copyright
© 2018 Cambridge University Press 

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