# Vortex dynamics under pulsatile flow in axisymmetric constricted tubes

## TL;DR

This study investigates vortex formation and movement in pulsatile flow within constricted tubes, combining experimental and numerical methods to reveal flow patterns and derive a scaling law for vortex displacement.

## Contribution

It provides new insights into vortex dynamics under pulsatile flow in constricted tubes and introduces a scaling law relating vortex displacement to flow parameters.

## Key findings

- Flow consists of a central jet and recirculation zone with vortex shedding.
- Vortex trajectories can be predicted by a derived scaling law.
- Flow patterns depend on Reynolds and Womersley numbers.

## Abstract

An improved understanding of how vortices develop and propagate under pulsatile flow can shed important light on the mixing and transport processes including the transition to turbulent regime occurring in such systems. 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 constriction degree ($d_0$), mean Reynolds number ($\bar{Re}$) and Womersley number ($\alpha$). Velocity fields were acquired 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 considered Reynolds number, 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 the maximum vortex displacement as a function of a dimensionless variable dependent on the system parameters Re and $\alpha$.