Steady finite-Reynolds-number flows in three-dimensional collapsible tubes

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, three-dimensional, Navier–Stokes equations 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 local 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