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Unsteady flow in a collapsible tube subjected to external pressure or body forces

Published online by Cambridge University Press:  19 April 2006

Roger D. Kamm  and
Ascher H. Shapiro
Roger D. Kamm
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA. 02139
Ascher H. Shapiro
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA. 02139
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Abstract

Flows in thin-walled, collapsible tubes are of fundamental importance to various physiologic phenomena and clinical devices.

A one-dimensional, unsteady theory is developed for flows generated either by externally applied pressures or by body forces. Part 1 deals with small-amplitude, linearized flows, part 2 with large amplitude, nonlinear flows. Experimental results for a tube collapsing under external pressure are given in part 3, together with theoretical interpretations and comparative results of numerical simulations.

Several new and unanticipated phenomena are revealed. These are in part associated with the highly nonlinear ‘equation of state’ (transmural pressure versus area) for a partially collapsed tube, and in part with whether the flow speed is sub- or supercritical relative to the speed of area waves. For instance, a flow produced by a spatially uniform external pressure applied to a limited region becomes choked at a flow-limiting throat at which point the fluid speed reaches the local wave speed. This throat forms at the edge of the pressurized region. The critical velocity can be exceeded with the application of certain types of spatially graded external pressures.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 1 , 14 November 1979 , pp. 1 - 78
Copyright
© 1979 Cambridge University Press

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