Numerical analysis for stability and self-excited oscillation in collapsible tube flow

This paper describes numerical analysis of collapsible tube flow based on the one-dimensional distributed parameter model of Hayashi. In the present model the effect of flow separation at the collapsed part is replaced with simple viscous friction along the tube, so no ad-hoc modeling for flow separation in former studies is required. A stable semi-implicit numerical procedure based on the SIMPLE method is developed for the problem of flow and tube interaction. The numerical result for a characteristic self-excited oscillation agrees qualitatively with the experimental result. Nonlinear stability of the steady state dependent on the amplitude of the disturbance is numerically investigated and the result is compared with the linear stability analysis based on the former lumped parameter model. Finally, initiation of the self-excited oscillation is examined by applying the initial disturbance at the upstream end of the tube. The disturbance propagates in the downstream direction and is amplified to the self-excited oscillation.