Sloshing and slamming oscillations in a collapsible channel flow
We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure distribution. The flow is driven by a fixed pressure d...
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Published in | Journal of fluid mechanics Vol. 662; pp. 288 - 319 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
10.11.2010
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Subjects | |
Online Access | Get full text |
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Summary: | We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T. Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes increasingly contribute to the global instability, and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilizing. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the flexible membrane is drawn close to the opposite rigid wall before recovering rapidly. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics. |
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Bibliography: | PII:S0022112010003277 istex:F0B949642A44497C5BC92DD2FD5E40147D907D98 ark:/67375/6GQ-VTV92X2L-V ArticleID:00327 |
ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/S0022112010003277 |