Global stability analysis of flexible channel flow with a hyperelastic wall

Herrada, M.A., Blanco-Trejo, S., Eggers, J. and Stewart, P.S. (2022) Global stability analysis of flexible channel flow with a hyperelastic wall. Journal of Fluid Mechanics, 934, A28. (doi: 10.1017/jfm.2021.1131)

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Abstract

We consider the stability of flux-driven flow through a long planar rigid channel, where a segment of one wall is replaced by a pre-tensioned hyperelastic (neo-Hookean) solid of finite thickness and subject to a uniform external pressure. We construct the steady configuration of the nonlinear system using Newton’s method with spectral collocation and high-order finite differences. In agreement with previous studies, which use an asymptotically thin wall, we show that the thick-walled system always has at least one stable steady configuration, while for large Reynolds numbers the system exhibits three co-existing steady states for a range of external pressures. Two of these steady configurations are stable to non-oscillatory perturbations, one where the flexible wall is inflated (the upper branch) and one where the flexible wall is collapsed (the lower branch), connected by an unstable intermediate branch. We test the stability of these steady configurations to oscillatory perturbations using both a global eigensolver (constructed based on an analytical domain mapping technique) and also fully nonlinear simulations. We find that both the lower and upper branches of steady solutions can become unstable to self-excited oscillations, where the oscillating wall profile has two extrema. In the absence of wall inertia, increasing wall thickness partially stabilises the onset of oscillations, but the effect remains weak until the wall thickness becomes comparable to the width of the undeformed channel. However, with finite wall inertia and a relatively thick wall, higher-frequency modes of oscillation dominate the primary global instability for large Reynolds numbers.

Item Type:Articles
Additional Information:Funding: M.A.H. and S.B.T. acknowledge funding from the Spanish Ministry of Economy, Industry and Competitiveness under Grants DPI2016-78887 and PID2019-108278RB and from the Junta de Andalucía under Grant P18-FR-3623. P.S.S. acknowledges funding from Engineering and Physical Sciences Research Council (UK) grants EP/P024270/1, EP/N014642/1 and EP/S030875/1.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Stewart, Dr Peter
Authors: Herrada, M.A., Blanco-Trejo, S., Eggers, J., and Stewart, P.S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Fluid Mechanics
Publisher:Cambridge University Press
ISSN:0022-1120
ISSN (Online):1469-7645
Published Online:18 January 2022
Copyright Holders:Copyright © The Author(s) 2022
First Published:First published in Journal of Fluid Mechanics 934: A28
Publisher Policy:Reproduced under a Creative Commons licence
Data DOI:10.5525/gla.researchdata.1113

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