Numerical Simulation and Experimental Verification of Wave Propagation in a Collapsible Tube

Propagation of solitary pressure wave through a thin-walled collapsible tube filled with a viscous incompressible fluid is calculated numerically. One-dimensional continuity equation, equation of motion including a wall friction term, and the tube law obtained experimentally are used as the basic equations. The pressure wave-forms at three locations along the collapsible tube calculated by the present method are compared with those obtained by the experiment. It is shown that the tube law obtained experimentally needs to be modified to make the slope discontinuous at an onset point of the locally two-dimensional buckling of the collapsible tube. The viscous effect is evaluated using an equivalent Womersley number a for the solitary wave. Incorporation of the wall friction term with high accuracy is necessary in the case of small a in one-dimensional flow calculation. The propagation velocity can be approximately calculated using the Moens-Korteweg velocity corresponding to a tube having circular cross-section when the disturbance velocity is small.