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Multiple states for flow through a collapsible tube with discontinuities

Published online by Cambridge University Press:  14 November 2014

A. Siviglia  and
M. Toffolon
A. Siviglia*
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, 8093 Zurich, Switzerland
M. Toffolon
Affiliation:
Department of Civil, Environmental and Mechanical Engineering, University of Trento, 38123 Trento, Italy
*
†Email address for correspondence: siviglia@vaw.baug.ethz.ch
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Abstract

We study the occurrence of the multiple steady states that flows in a collapsible tube can develop under the effect of: (i) geometrical alterations (e.g. stenosis), (ii) variations of the mechanical properties of the tube wall, or (iii) variations of the external pressure acting on the conduit. Specifically, if the approaching flow is supercritical, two steady flow states are possible in a restricted region of the parameter space: one of these flow states is wholly supercritical while the other produces an elastic jump that is located upstream of the variation. In the latter case the flow undergoes a transition through critical conditions in the modified segment of the conduit. Both states being possible, the actual state is determined by the past history of the system, and the parameter values show a hysteretic behaviour when shifting from one state to the other. First we set up the problem in a theoretical framework assuming stationary conditions, and then we analyse the dynamics numerically in a one-dimensional framework. Theoretical considerations suggest that the existence of multiple states is associated with non-uniqueness of the steady-state solution, which is confirmed by numerical simulations of the fully unsteady problem.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 105 - 122
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Copyright
© 2014 Cambridge University Press 

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