Chaotic vortex-induced rotation of an elliptical cylinder

Non-linear oscillations of an elliptical cylinder, which 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 analyzed 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. The Reynolds number used was Re=200, which, in the 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 changes, as in the case of vortex-induced vibrations. 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.