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Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate

Fabre, David and Longobardi, Raffaele and Citro, Vincenzo and Luchini, Paolo Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate. (2020) Journal of Fluid Mechanics, 855. A11. ISSN 0022-1120

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Official URL: https://doi.org/10.1017/jfm.2019.953

Abstract

We study the unsteady flow of a viscous fluid passing through a circular aperture in aplate characterized by a non-zero thickness. We investigate this problem by solving theincompressible Linearized Navier-Stokes Equations (LNSE) around a laminar base flow,in both the forced case (allowing to characterize the coupling of the flow with acousticresonators) and the autonomous regime (allowing to identify the possibility of purelyhydrodynamical instabilities). In the forced case, we calculate the impedances and discussthe stability properties in terms of a Nyquist diagram. We show that such diagramsallow us to predict two kinds of instabilities: (i) a conditional instability linked to theoverreflexion of an acoustic wave but requiring the existence of an conveniently tunedexternal acoustic resonator, and (ii) a purely hydrodynamic instability existing even in astrictly incompressible framework. A parametric study is conducted to predict the rangeof existence of both instabilities in terms of the Reynolds number and the aspect ratio ofthe aperture. Analysing the structure of the linearly forced flow allows to show that theinstability mechanism is closely linked to the existence of a recirculation region withinthe thickness of the plate. We then investigate the autonomous regime using the classicalnormal-mode ansatz. The analysis confirms the existence of the purely hydrodynamicalinstability in accordance with the impedance-based criterion. The spatial structure ofthe unstable eigenmodes are found to be similar to the structure of the correspondingunsteady flows computed using the forced problem. Analysis of the adjoint eigenmodesand of the adjoint-based structural sensitivity confirms that the origin of the unstabilitylies in the recirculation region existing within the thickness of the plate.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Università degli Studi di Salerno - UniSa (ITALY)
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Deposited On:18 May 2021 10:03

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