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Steady analysis of transcritical flows in collapsible tubes with discontinuous mechanical properties: implications for arteries and veins

Published online by Cambridge University Press:  04 November 2013

A. Siviglia  and
M. Toffolon
A. Siviglia*
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology VAW, ETH Zurich, Switzerland
M. Toffolon
Affiliation:
Department of Civil, Environmental and Mechanical Engineering, University of Trento, Italy
*
†Email address for correspondence: nunzio.siviglia@ing.unitn.it
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Abstract

We study the conditions under which discontinuous mechanical properties of a collapsible tube can induce transcritical flows, i.e. the transition through the critical state where the speed index (analogous to the Mach or the Froude numbers for compressible and free surface flows, respectively) is one. Such a critical transition may strongly modify the flow properties, cause a significant reduction in the cross-sectional area of the tube, and limit the flow. General relationships are obtained for a short segment using a one-dimensional model under steady flow conditions. Marginal curves delimiting the transcritical regions are identified in terms of the speed index and the cross-sectional area ratio. Since there are many examples of such flows in physiology and medicine, we also analyse the specific case of prosthesis (graft or stent) implantation in blood vessels. We then compute transcritical conditions for the case of stiffness and reference area variations, considering a collapsible tube characterized by physiological parameters representative of both arteries and veins. The results suggest that variations in mechanical properties may induce transcritical flow in veins but is unrealistic in arteries.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Blood flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 195 - 215
Copyright
©2013 Cambridge University Press 

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