Chaotic vortex induced rotation of an elliptical cylinder

TL;DR

This study investigates the chaotic and stable oscillations of an elliptical cylinder induced by vortex shedding, using numerical simulations to analyze the effects of torsional spring stiffness on flow-induced rotations.

Contribution

It introduces a numerical analysis of vortex-induced oscillations of an elliptical cylinder with a torsional spring, revealing multiple dynamic regimes including chaos and stability.

Findings

Chaotic oscillations occur at Re=200 without spring.

Three dynamic branches identified with varying spring stiffness.

Stable limit cycles observed when vortices synchronize or oscillations are small.

Abstract

Non-linear oscillations of an elliptical cylinder, that can rotate about an axis that passes through its symmetry axle due to a torsional spring and hydrodynamic torque produced by the flow of a Newtonian fluid, were analysed in terms of a single parameter that compares vortex shedding frequency with the torsional spring's natural frequency. The governing equations for the flow coupled with a rigid body with one degree of freedom, were solved numerically using the Lattice Boltzmann Method (LBM). The Reynolds number used was $Re=200$ which, in absence of torsional spring, produces chaotic oscillations of the elliptical cylinder. When the torsional spring is included, we identified three branches separated by transition regions when stiffness of the restorative torque change, as in the case of vortex induced vibrations (VIV's). However in this case, several regions presenting chaotic dynamics were identified. Two regions with stable limit cycles were found when both torques synchronized and when stiffness of the torsional spring is big enough so that the ellipse's oscillation is small.