Sloshing and slamming oscillations in collapsible channel flowTools 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) Full text not available from this repository.AbstractWe 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
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