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How rapidly oscillating collapsible tubes extract energy from a viscous mean flow

  • MATTHIAS HEIL (a1) and SARAH L. WATERS (a2)
Abstract

We present a combined theoretical and computational analysis of three-dimensional unsteady finite-Reynolds-number flows in collapsible tubes whose walls perform prescribed high-frequency oscillations which resemble those typically observed in experiments with a Starling resistor. Following an analysis of the flow fields, we investigate the system's overall energy budget and establish the critical Reynolds number, Recrit, at which the wall begins to extract energy from the flow. We conjecture that Recrit corresponds to the Reynolds number beyond which collapsible tubes are capable of performing sustained self-excited oscillations. Our computations suggest a simple functional relationship between Recrit and the system parameters, and we present a scaling argument to explain this observation. Finally, we demonstrate that, within the framework of the instability mechanism analysed here, self-excited oscillations of collapsible tubes are much more likely to develop from steady-state configurations in which the tube is buckled non-axisymmetrically, rather than from axisymmetric steady states, which is in agreement with experimental observations.

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C. Bertram & J. Tscherry 2006 The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes. J. Fluids Struct. 22, 10291045.

C. D. Bertram & R. J. Castles 1999 Flow limitation in uniform thick-walled collapsible tubes. J. Fluids Struct. 13, 399418.

C. D. Bertram & C. J. Raymond 1991 Measurements of wave speed and compliance in a collapsible tube during self-excited oscillations: a test of the choking hypothesis. Med. Biol. Engng Comput. 29, 493500.

C. D. Bertram , C. J. Raymond & T. J. Pedley 1990 Mapping of instabilities for flow through collapsible tubes of differering length. J. Fluids Struct. 4, 125153.

M. Heil & O. E. Jensen 2003 Flows in deformable tubes and channels – theoretical models and biological applications. In Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries (ed. T. J. Pedley & P. W. Carpenter ), pp. 1550. Kluwer.

M. Van Dyke 1964 Perturbation Methods in Fluid Mechanics. Academic.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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