Flow in a two-dimensional collapsible channel with rigid inlet and outlet.

This paper examines mainly oscillatory behavior of a fluid-conveying collapsible tube using a two-dimensional flexible channel made of a pair of membranes. The equation of equilibrium of the membrane in a large deflection theory is coupled with the equations of continuity and momentum of an incompressible flow in a one-dimensional flow theory accounting for flow separation. An explicit finite difference method was used to solve the governing equations numerically. According to numerical results, the fluids in the inlet and outlet rigid channels have strong effects on the oscillation of the system. Depending on initial values for the numerical integration, there may exist both a stable static equilibrium and an oscillatory solution for the same parameter values, but only if the external pressure is sufficiently large.