Vortex dynamics under pulsatile flow in axisymmetric constricted tubes

Abstract

Improved understanding of how vortices develop and propagate under pulsatile flow can shed important light on the mixing and transport processes occurring in such systems, including the transition to turbulent regime. For example, the characterization of pulsatile flows in obstructed artery models serves to encourage research into flow-induced phenomena associated with changes in morphology, blood viscosity, wall elasticity and flow rate. In this work, an axisymmetric rigid model was used to study the behaviour of the flow pattern with varying degrees of constriction ($d_0$) and mean Reynolds ($\bar{Re}$) and Womersley numbers ($\alpha$). Velocity fields were obtained experimentally using Digital Particle Image Velocimetry, and generated numerically. For the acquisition of data, $\bar{Re}$ was varied from 385 to 2044, $d_0$ was 1.0 cm and 1.6 cm, and $\alpha$ was varied from 17 to 33 in the experiments and from 24 to 50 in the numerical simulations. Results for the Reynolds numbers considered showed that the flow pattern consisted of two main structures: a central jet around the tube axis and a recirculation zone adjacent to the inner wall of the tube, where vortices shed. Using the vorticity fields, the trajectory of vortices was tracked and their displacement over their lifetime calculated. The analysis led to a scaling law equation for maximum vortex displacement as a function of a dimensionless variable dependent on the system parameters Re and $\alpha$.