Fluid-Structure Interaction Problems:

Flow in Collapsible Tubes

The figure below shows the deformation of a thin-walled elastic tube which conveys a viscous flow (the direction of the flow is from left to right). In its undeformed state, the tube is cylindrical and the ends of the tube are held open (think of a thin-walled rubber tube, mounted on two rigid tubes). As we increase the external pressure [from (a) to (d)], the tube buckles and deforms strongly. The reduction in the tube's cross sectional area changes its flow resistance and thereby the pressure distribution in the fluid, which in turn affects the tube's deformation.

This is a classical example for a large-displacement fluid-structure interaction problem for which many applications exist in biomechanics (e.g. blood flow in veins and arteries, flow of air in the bronchial airways).

To model this problem, the wall deformation was described using geometrically non-linear shell theory, coupled to the three-dimensional steady Stokes equations (zero Reynolds number flow). The equations were discretised with Finite Element Methods and the coupled solution was achieved with a segregated solver.

Page last modified: July 25, 1997

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