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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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References

Bertram, C. D. 1982 Two modes of instability in a thick-walled collapsible tube conveying a flow. J. Biomech. 15, 223–224.Google Scholar
Bertram, C. D. 1986 Unstable equilibrium behaviour in collapsible tubes. J. Biomech. 19, 61–69.Google Scholar
Bertram, C. D. 1987 The effects of wall thickness, axial strain and end proximity on the pressure-area relation of collapsible tubes. J. Biomech. 20, 863–876.Google Scholar
Bertram, C. D. & Pedley, T. J. 1982 A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39–50.Google Scholar
Bertram, C. D., Raymond, C. J. & Pedley, T. J. 1989 Mapping of instabilities during flow through collapsed tubes of differing length. J. Fluids Structures (submitted).Google Scholar
Bonis, M. & Ribreau, C. 1978 Etude de quelques propriétés de l'écoulement dans une conduite collabable La Houille Blanche 3/4, 165–173.Google Scholar
Bonis, M. & Ribreau, C. 1981 Wave speed in noncircular collapsible ducts. Trans. ASME K: J. Biomech. Engng 103, 27–31.Google Scholar
Brower, R. W. & Scholten, C. 1975 Experimental evidence on the mechanism for the instability of flow in collapsible vessels. Med. Biol. Engng 13, 839–845.Google Scholar
Cancelli, C. & Pedley, T. J. 1985 A separated-flow model for collapsible-tube oscillations. J. Fluid Mech. 157, 375–404.Google Scholar
Conrad, W. A. 1969 Pressure-flow relationships in collapsible tubes. IEEE Trans. Bio-med. Engng BME-16, 284–295.Google Scholar
McClurken, M. E., Kececioglu, I., Kamm, R. D. & Shapiro, A. H. 1981 Steady, supercritical flow in collapsible tubes. Part 2. Theoretical studies. J. Fluid Mech. 109, 391–415.Google Scholar
Oates, G. C. 1975 Fluid flow in soft-walled tubes. Part 1: Steady flow. Med. Biol. Engng 13, 773–784.Google Scholar
Reyn, J. W. 1987 Multiple solutions and flow limitation for steady flow through a collapsible tube held open at the ends. J. Fluid Mech. 174, 467–493.Google Scholar
Shapiro, A. H. 1977a Physiologic and medical aspects of flow in collapsible tubes. Proc. 6th Canadian Congr. Appl. Mech., pp. 883–906.
Shapiro, A. H. 1977b Steady flow in collapsible tubes Trans. ASME K: J. Biomech. Engng 99, 126–147.Google Scholar
Smith, F. T. & Duck, P. W. 1980 On the severe non-symmetric constriction, curving or cornering of channel flows. J. Fluid Mech. 98, 727–753.Google Scholar