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Vortical–acoustic resonance in an acoustic resonator: Strouhal number variation, destabilization and stabilization

Published online by Cambridge University Press:  26 May 2021

Xiwen Dai Open the ORCID record for Xiwen Dai [Opens in a new window]
Xiwen Dai*
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai200240, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The impact of acoustic resonance on vortical–acoustic resonance and flow instability is studied by a combined travelling–global mode analysis about a low-speed inviscid parallel shear flow in two-dimensional symmetric duct–cavity configurations. First, in a shallow-cavity case, we show that the difference between incompressible and compressible models in describing the compact feedback loop, consisting of the Kelvin–Helmholtz (KH) instability wave and the Rayleigh–Powell–Rossiter (RPR) feedback, is small and the global mode frequency follows the Strouhal law. Using the compact case as a baseline for comparison, the influence of an acoustic resonator (AR) on the $\textrm {KH}+\textrm {RPR}$ feedback loop is then examined. In this deep-cavity case, phenomena such as frequency deviation from the Strouhal law, global mode switching, global mode destabilization and stabilization, caused by a trapped or a heavily damped acoustic resonant mode, are observed. We show that those phenomena can be explained by the local–global relation of the feedback loop and the dual-feedback view: the coexistence of RPR and AR feedbacks. The Strouhal number variation is due to the phase difference of the unstable vortical wave between the upstream and downstream cavity edges being changed by the additional AR feedback. It is found that the switching is not a vortical but an acoustic effect. The destabilization and stabilization, near and far from an acoustic resonance, are respectively understood as the result of the total feedback at the upstream edge being strengthened and weakened by the AR feedback.

JFM classification

Acoustics: Aeroacoustics Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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