Dynamics of a collapsible tube with internal constriction

Abstract

The deformation and oscillation dynamics of a thin-walled collapsible tube carrying internal flow with and without internal constriction is studied experimentally and theoretically for a constant chamber pressure. The internal constriction of different blockage ratios is employed by attaching spherical balls of different diameters to the inner wall of the tube. The effect of the axial location of the constriction is also studied. Without any internal constriction, the tube response is observed to be steady collapsed, periodic/aperiodic oscillatory or steady distended, depending on the Reynolds number. With constriction of low blockage ratios near the inlet of the collapsible tube, the system exhibits oscillatory response; however, no aperiodic oscillations are found. With bigger constrictions, the oscillations are completely suppressed. The viscous pressure drop due to the constriction is responsible for this behavior. When the constriction is present at the middle of the tube, the downstream half of the tube is under high tension, leading to the excitation of first and second radial vibrational modes of the tube (which are different from the milking-mode oscillations), depending upon the Reynolds number and blockage ratio. The results from a lumped parameter-based theoretical model are able to capture most of the qualitative features of the tube response such as the shift of the Hopf bifurcation point and the shrinkage of the oscillatory regime.