** Abstract: **

###
Hazel, A. L. & Heil, M. (2002) Steady finite-Reynolds-number flows in
three-dimensional collapsible tubes
*Journal of Fluid Mechanics* (submitted)

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A fully-coupled, finite-element method is used to investigate the
steady flow of a viscous fluid through a thin-walled elastic tube
mounted between two rigid tubes. The steady 3D Navier-Stokes equations,
which describe the fluid motion, are solved simultaneously
with the equations of geometrically-non-linear,
Kirchhoff-Love shell theory.
If the transmural (internal minus external) pressure acting on the tube
is sufficiently negative then the tube buckles
non-axisymmetrically and the subsequent large deformations
lead to a strong interaction between the fluid and solid
mechanics.

The main effect of fluid inertia on the macroscopic behaviour of the
system is due to the Bernoulli effect, which induces an
additional pressure drop when the tube buckles and its
cross-sectional area is reduced.
Thus, the tube collapses more strongly than it would
in the absence of fluid inertia.
Typical tube shapes and flow fields are presented. In strongly
collapsed tubes, at finite values of the Reynolds number, two
``jets'' develop downstream of the region of strongest
collapse and persist for considerable axial distances.
For sufficiently high values of the Reynolds number,
these ``jets'' impact upon the sidewalls and spread
azimuthally. The consequent azimuthal transport of momentum
dramatically changes the axial velocity profiles, which become
approximately ``Theta''-shaped when the flow enters the rigid
downstream pipe. Further convection of momentum from the centreline to
the edges of the tube causes the development of a ring-shaped
velocity profile before the ultimate return to the parabolic profile
far downstream.

Page last modified: September 2, 2002

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