Abstract
Flow driven through a segment of flexible tube, supported between rigid pipes and enclosed in a pressurized chamber, is susceptible to a variety of self-excited oscillations. This paper provides a brief review of recent modelling efforts aimed at understanding some of the underlying mechanisms of instability in this system. In particular, it is shown how a family of spatially one-, two- and three-dimensional models have been used to investigate a global instability arising at high frequencies, whereby axial sloshing motions driven by transverse wall oscillations are able to sustain themselves by extracting kinetic energy from the underlying mean flow.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Pedley, T.J., Brook, B.S., Seymour, R.S.: Blood pressure and flow rate in the giraffe jugular vein. Phil. Trans. Roy. Soc. B 351, 855–866 (1996)
Heil, M., Jensen, O.E.: Flows in deformable tubes and channels - Theoretical models and biological applications. In: Carpenter, P.W., Pedley, T.J. (eds.) Flow Past Highly Compliant Boundaries and in Collapsible Tubes, IUTAM Proceedings, vol. 72. Springer (2003)
Grotberg, J.B., Jensen, O.E.: Biofluidmechanics of flexible tubes. Ann. Rev. Fluid Mech. 36, 121–147 (2004)
Knowlton, F.P., Starling, E.H.: The influence of variations in temperature and blood-pressure on the performance of the isolated mammalian heart. J. Physiol. London 44, 206–219 (1912)
Bertram, C.D., Raymond, C.J., Pedley, T.J.: Mapping of instabilities for flow through collapsed tubes of differing length. J. Fluids Struct. 4, 125–153 (1990)
Bertram, C.D., Tscherry, J.: The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes. J. Fluids Struct. 22, 1029–1045 (2006)
Pedley, T.J., Luo, X.Y.: Modelling flow and oscillations in collapsible tubes. Theor. Comput. Fluid. Dyn. 10, 277–294 (1998)
Bertram, C.D., Pedley, T.J.: A mathematical model of collapsible tube behaviour. J. Biomech. 15, 39–50 (1982)
Armitstead, J., Bertram, C.D., Jensen, O.E.: A study of the bifurcation behaviour of a model of flow through a collapsible tube. Bull. Math. Biol. 58, 611–641 (1996)
Shapiro, A.H.: Steady flow in collapsible tubes. J. Biomech. Engng. 99, 126–147 (1977)
Cancelli, C., Pedley, T.J.: A separated-flow model for collapsible-tube oscillations. J. Fluid Mech. 157, 375–404 (1985)
Hayashi, S., Hayase, T., Kawamura, H.: Numerical analysis for stability and self-excited oscillation in collapsible tube flow. J. Biomech. Engng. 120, 468–475 (1998)
Jensen, O.E., Pedley, T.J.: The existence of steady flow in a collapsed tube. J. Fluid Mech. 206, 339–374 (1989)
Jensen, O.E.: Instabilities of flow in a collapsed tube. J. Fluid Mech. 220, 623–659 (1990)
Pedley, T.J.: Longitudinal tension variation in collapsible channels: a new mechanism for the breakdown of steady flow. J. Biomech. Engng. 114, 60–67 (1992)
Guneratne, J., Pedley, T.J.: High Reynolds number steady flow in a collapsible channel. J. Fluid Mech. 569, 151–184 (2006)
Luo, X.Y., Pedley, T.J.: A numerical simulation of unsteady flow in a two-dimensional collapsible channel. J. Fluid Mech. 314, 191–225 (1996)
Luo, X.Y., Cai, Z.X., Li, W.G., Pedley, T.J.: The cascade structure of linear instability in collapsible channel flows. J. Fluid Mech. 600, 45–76 (2008)
Heil, M., Hazel, A.L., Boyle, J.: Solvers for large-displacement fluid-structure interaction problems: segregated versus monolithic approaches. Comput. Mech. 43, 91–101 (2008)
Hazel, A.L., Heil, M.: Steady finite Reynolds number flows in three-dimensional collapsible tubes. J. Fluid Mech. 486, 79–103 (2003)
Marzo, A., Luo, X.Y., Bertram, C.D.: Three-dimensional collapse and steady flow in thick-walled flexible tubes. J. Fluids Struct. 20, 817–835 (2005)
Heil, M., Boyle, J.: Recent progress in the theoretical and computational modelling of flow in 3D collapsible tubes. XXII ICTAM, Adelaide, Australia (2008)
Benjamin, T.B.: The threefold classificion of unstable disturbances in flexible surface bounding inviscid flows. J. Fluid Mech. 16, 436–450 (1963)
Landahl, M.: On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632 (1962)
Davies, C., Carpenter, P.W.: Instabilities in plane channel flow between compliant walls. J. Fluid Mech. 352, 205–243 (1997)
Stewart, P.S., Waters, S.L., Jensen, O.E.: Local and global instabilities of flow in a flexible-walled channel (2008) (submitted)
Doaré, O., de Langre, E.: The role of boundary conditions in the instability of one-dimensional systems. Eur. J. Mech. B 25, 948–959 (2006)
Jensen, O.E., Heil, M.: High-frequency self-excited oscillations in a collapsible-channel flow. J. Fluid Mech. 481, 235–268 (2003)
Heil, M., Waters, S.L.: Transverse flows in rapidly oscillating elastic cylindrical shells. J. Fluid Mech. 547, 185–214 (2006)
Heil, M., Waters, S.L.: How rapidly oscillating collapsible tubes extract energy from a viscous mean flow. J. Fluid Mech. 601, 199–227 (2008)
Whittaker, R.J., Waters, S.L., Jensen, O.E., Boyle, J., Heil, M.: The energetics of flow through a rapidly oscillating tube. Part I: general theory. Part II: application to an elliptical tube (preprint) (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 © Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Jensen, O.E. (2013). Instabilities of Flows through Deformable Tubes and Channels. In: Denier, J., Finn, M. (eds) Mechanics Down Under. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5968-8_7
Download citation
DOI: https://doi.org/10.1007/978-94-007-5968-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5967-1
Online ISBN: 978-94-007-5968-8
eBook Packages: EngineeringEngineering (R0)