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A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

Published online by Cambridge University Press:  02 August 2018

Xiwen Dai Open the ORCID record for Xiwen Dai [Opens in a new window]  and
Yves Aurégan
Xiwen Dai*
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Yves Aurégan
Affiliation:
Laboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613 Av. O Messiaen, F-72085 Le Mans CEDEX 9, France
*
†Email address for correspondence: xiwen.dai@sjtu.edu.cn
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Abstract

This paper presents a two-dimensional (2-D) cavity-by-cavity description of a convective instability near a lined wall with low dissipation due to the coupling of hydrodynamic modes with resonance of the wall. For a liner consisting of an array of deep cavities periodically placed along a duct containing a mean shear flow, the acoustic and hydrodynamic disturbances are described by the linearized Euler equations. The Bloch modes and the scattering matrix of periodic cells are used to examine the instability over the liner. The unstable Bloch mode is due to the coupling of a hydrodynamic mode in the shear flow with the cavity resonance. It is demonstrated that even when all the transverse modes are stable in the duct–cavity system, i.e. when the Kelvin–Helmholtz instability of the shear flow over the cavities does not occur, such an instability over the liner can still exist. The unstable Bloch wave, excited by the incident sound wave at the upstream part of the liner, convectively grows along the liner, and regenerates sound near the downstream edge of the liner with a sound level higher than the incident sound level. It is shown that a homogenized approach, where the wall effect is described by a homogeneous impedance, can also explain the unstable behaviour above the liner. It reveals that a small wall resistance and a small and positive reactance are two necessary conditions for such an instability.

JFM classification

Acoustics: Aeroacoustics Instability: Instability Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 126 - 145
Copyright
© 2018 Cambridge University Press 

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