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A separated-flow model for collapsible-tube oscillations

Published online by Cambridge University Press:  20 April 2006

Claudio Cancelli  and
T. J. Pedley
Claudio Cancelli
Affiliation:
Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino. Italy
T. J. Pedley
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England
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Abstract

A new model is presented to describe flow in segments of collapsible tube mounted between two rigid tubes and surrounded by a pressurized container. The new features of the model are the inclusion of (a) longitudinal wall tension and (b) energy loss in the separated flow downstream of the time-dependent constriction in a collapsing tube, in a manner which is consistent with the one-dimensional equations of motion. As well as accurately simulating steady-state collapse, the model predicts self-excited oscillations whose amplitude is large enough to be observable only if the flow in the collapsible tube becomes supercritical somewhere (fluid speed exceeding long-wave propagation speed). The dynamics of the oscillations is dominated by longitudinal movement of the point of flow separation, in response to the adverse pressure gradient associated with waves propagating backwards and forwards between the (moving) narrowest point of the constriction and the tube outlet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 157 , August 1985 , pp. 375 - 404
Copyright
© 1985 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. & Pedley T. J.1982 A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39–50.Google Scholar
Bertram, C. D. & Pedley T. J.1983 Steady and unsteady separation in an approximately two-dimensional indented channel. J. Fluid Mech. 130, 315–345.Google Scholar
Bonis M.1979 Écoulement visqueux permanent dans un tube collabable elliptique. Thèse de Doctorat d’État, Université de Technologie de Compiègne.
Bonis, M. & Ribreau C.1978 Étude de quelques propriétés de l’écoulement dans une conduite collabable. La Houille Blanche 3, 4, 165–173.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. & Chiocchia G.1979 On the onset of self-excited oscillations in a collapsible tube flow with sonic index values less than one: mathematical model and numerical results Atti d. Acc. Naz. dei Lincei, Memorie Sc. Fisiche, sez. I, 15, 317–352.Google Scholar
Conrad W. A.1969 Pressure—flow relationships in collapsible tubes IEEE Trans. Bio-med. Engng BME-16, 284–295.Google Scholar
Conrad W. A., Cohen, M. L. & McQueen D. M.1978 Note on the oscillations of collapsible tubes. Med. Biol. Engng & Comput. 16, 211–214.Google Scholar
Conrad W. A., McQueen, D. M. & Yellin E. L.1980 Steady pressure flow relations in compressed arteries: possible origin of Korotkoff sounds. Med. Biol Engng & Comput. 18, 419–426.Google Scholar
Dawson, S. V. & Elliott E. A.1977 Wave-speed limitation on expiratory flow - a unifying concept. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 43, 498–515.Google Scholar
Flaherty J. E., Keller, J. B. & Rubinow S. I.1972 Post-buckling behaviour of elastic tubes and rings with opposite sides in contact. SIAM J. Appl. Maths 23, 446–455.Google Scholar
Griffiths D. J.1977 Oscillations in the outflow from a collapsible tube. Med. Biol. Engng & Comput. 15, 357–362.Google Scholar
Kamm, R. D. & Shapiro, A. H. 1979 Unsteady flow in a collapsible tube subjected to external pressure or body forces. J. Fluid Mech. 95, 1–78.Google Scholar
Katz A. I., Chen, Y. & Moreno A. H.1969 Flow through a collapsible tube. Biophys. J. 9, 1261–1279.Google Scholar
Kececioglu, I., McClurken, M. E., Kamm, R. D. & Shapiro, A. H. 1981 Steady, supercritical flow in collapsible tubes. Part I. Experimental observations. J. Fluid Mech. 109, 367–389.Google Scholar
Lambert, R. K. & Wilson T. A.1972 Flow limitation in a collapsible tube. J. Appl. Physiol. 33, 150–153.Google Scholar
Lyon C. K., Scott J. B., Anderson, D. K. & Wang C. Y.1981 Flow through collapsible tubes at high Reynolds numbers. Circulation Res. 49, 988–996.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
Pedley T. J.1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
Reyn J. W.1974 On the mechanism of self-excited oscillations in the flow through collapsible tubes. Delft Progr. Rep., Ser. F 1, 51–67.Google Scholar
Roache P. J.1972 Computational Fluid Dynamics. Albuquerque, NM: Hermosa.
Rouse, H. (ed.) 1950 Engineering Hydraulics. Wiley.
Schlichting H.1968 Boundary Layer Theory (6th edn). McGraw-Hill.
Schoendorfer, D. W. & Shapiro A. H.1977 The collapsible tube as a prosthetic vocal source. Proc. San Diego Biomed. Symp. 16, 349–356.Google Scholar
Shapiro A. H.1977a Physiologic and medical aspects of flow in collapsible tubes. Proc. 6th Canadian Congr. Appl. Mech., pp. 883–906.Google Scholar
Shapiro A. H.1977b Steady flow in collapsible tubes. Trans. ASME K: J. Biomech. Engng 99, 126–147.Google Scholar
Shimizu, M. & Tanida Y.1983 On the mechanism of Korotkoff sound generation at diastole. J. Fluid Mech. 127, 315–339.Google Scholar
Ur, A. & Gordon M.1970 Origin of Korotkoff sounds. Am. J. Physiol. 218, 524–529.Google Scholar
Wild R., Pedley, T. J. & Riley D. S.1977 Viscous flow in collapsible tubes of slowly varying elliptical cross-section. J. Fluid Mech. 81, 273–294.Google Scholar