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Self-excited oscillations in three-dimensional collapsible tubes: simulating their onset and large-amplitude oscillations

Published online by Cambridge University Press:  13 April 2010

MATTHIAS HEIL  and
JONATHAN BOYLE
MATTHIAS HEIL*
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
JONATHAN BOYLE
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
†Email address for correspondence: M.Heil@maths.man.ac.uk
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Abstract

We employ numerical simulations to explore the development of flow-induced self-excited oscillations in three-dimensional collapsible tubes which are subject to boundary conditions (flow rate prescribed at the outflow boundary) that encourage the development of high-frequency oscillations via an instability mechanism originally proposed by Jensen & Heil (J. Fluid Mech., vol. 481, 2003, p. 235). The simulations show that self-excited oscillations tend to arise preferentially from steady equilibrium configurations in which the tube is buckled non-axisymmetrically. We follow the growing oscillations into the large-amplitude regime and show that short tubes tend to approach an approximately axisymmetric equilibrium configuration in which the oscillations decay, whereas sufficiently long tubes develop sustained large-amplitude limit-cycle oscillations. The period of the oscillations and the critical Reynolds number beyond which their amplitude grows are found to be in good agreement with theoretical scaling estimates.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 405 - 426
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

‡

Present address: Research Computing Services, University of Manchester, Oxford Road, Manchester M13 9PL, UK

References

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