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The existence of steady flow in a collapsed tube

Published online by Cambridge University Press:  26 April 2006

O. E. Jensen  and
T. J. Pedley
O. E. Jensen
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

Self-excited oscillations arise during flow through a pressurized segment of collapsible tube, for a range of values of the time-independent controlling pressures. They come about either because there is an (unstable) steady flow corresponding to these pressures, or because no steady flow exists. We investigate the existence of steady flow in a one-dimensional collapsible-tube model, which takes account of both longitudinal tension and jet energy loss E downstream of the narrowest point. For a given tube, the governing parameters are flow-rate Q, and transmural pressure P at the downstream end of the collapsible segment. If E = 0, there exists a range of (Q, P)-values for which no solutions exist; when E ≠ 0 a solution is always found. For the case E ≠ 0, predictions are made of pressure drop along the collapsible tube; these solutions are compared with experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 339 - 374
Copyright
© 1989 Cambridge University Press

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