Unsteady tube flow over an expansion

Unsteady flow in a circular conduit with a smooth expansion is studied in detail by numerical integration of the equation of motion in the axisymmetric approximation. The values of governing parameters are chosen to be relevant to medical problems, and the geometry corresponds to a scenario of post-surgical conditions. The flow determined by an oscillatory volume is characterized by a sequence of vortex rings moving in the expanded part of the tube. The development of wall shear stress is governed by the separated translating vorticity which induces an evolving band of large intensity for about a complete oscillation cycle. This influences the dynamics of unsteady separation whose space-time development has revealed features of some generality which have been classified. The time variation of the pressure jump is dominated by inertial effects. The dependence of the details of the flow on the dimensionless parameters has been investigated systematically. The results obtained here have been compared with experimental and numerical studies of similar problems, similarities have been pointed out and differences discussed. Finally, the relevance of these results to physiological applications has been quantified by simulating the flow induced by a pulsatile flow rate.