Sloshing and slamming oscillations in 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 an external pressure distribution. The flow is driven by a fixed pressure drop al...
| Main Authors: | , , , |
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| Format: | Article |
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Cambridge University Press
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1234/ |
| _version_ | 1848790566274334720 |
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| author | Stewart, Peter S. Heil, Matthias Waters, Sarah L. Jensen, Oliver E. |
| author_facet | Stewart, Peter S. Heil, Matthias Waters, Sarah L. Jensen, Oliver E. |
| author_sort | Stewart, Peter S. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 an 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 contribute increasingly to the global instability and we demonstrate
a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic
slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. 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. |
| first_indexed | 2025-11-14T18:14:39Z |
| format | Article |
| id | nottingham-1234 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:39Z |
| publishDate | 2010 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12342020-05-04T20:25:56Z https://eprints.nottingham.ac.uk/1234/ Sloshing and slamming oscillations in collapsible channel flow Stewart, Peter S. Heil, Matthias Waters, Sarah L. Jensen, Oliver E. 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 an 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 contribute increasingly to the global instability and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. 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. Cambridge University Press 2010 Article NonPeerReviewed Stewart, Peter S., Heil, Matthias, Waters, Sarah L. and Jensen, Oliver E. (2010) Sloshing and slamming oscillations in collapsible channel flow. Journal of Fluid Mechanics, 662 . pp. 288-319. ISSN 0022-1120 (Submitted) http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7913929 doi:10.1017/S0022112010003277 doi:10.1017/S0022112010003277 |
| spellingShingle | Stewart, Peter S. Heil, Matthias Waters, Sarah L. Jensen, Oliver E. Sloshing and slamming oscillations in collapsible channel flow |
| title | Sloshing and slamming oscillations in collapsible channel flow |
| title_full | Sloshing and slamming oscillations in collapsible channel flow |
| title_fullStr | Sloshing and slamming oscillations in collapsible channel flow |
| title_full_unstemmed | Sloshing and slamming oscillations in collapsible channel flow |
| title_short | Sloshing and slamming oscillations in collapsible channel flow |
| title_sort | sloshing and slamming oscillations in collapsible channel flow |
| url | https://eprints.nottingham.ac.uk/1234/ https://eprints.nottingham.ac.uk/1234/ https://eprints.nottingham.ac.uk/1234/ |