A one-dimensional unsteady separable and reattachable flow model for collapsible tube-flow analysis

Taking into account both flow separation and reattachment observed in available experimental results on flows in a quasi-two-dimensional channel, we present a one-dimensional unsteady flow model, which is applicable to a flow, in a collapsible tube. The flow model has been derived from the two-dimensional Navier-Stokes equations by introducing the concept of a dividing streamline, which divides a separated flow into a jet and a dead-water zone. We also present a criterion for the determination of a separation point. Numerical results show that the locations of the predicted separation points agree well with the experimental data. The predicted static pressure of the separated flow is almost constant downstream of the separation point and increases quickly just before the reattachment point, as observed in the experiment. Finally, using the present flow model and the separation criterion, we examine the oscillatory behavior of an unsteady flow in a symmetric channel whose walls move sinusoidally.