Effect of particle moment of inertia on the dynamics and wakes of freely rising cylinders

We perform a numerical study on the two-dimensional motions and wakes of freely rising and falling circular cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid $m^* \equiv \rho_p/\rho_f$, and its relative moment-of-inertia $I^* \equiv {I}_p/{I}_f$. Using over 144 combinations of ${m}^*$ and $I^*$, we comprehensively map out the parameter space covering very heavy ($m^* > 10$) to very buoyant ($m^* < 0.1$) particles at fixed Galileo number (Ga = 500). The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, $St_t \approx 0.17$. $St_t$ separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical $2S$ (2-Single) vortex mode to a $2P$ (2-Pairs) mode of wake vortices. Thus, autorotation, triggered by moment of inertia reduction, can significantly enhance the translational oscillations of freely rising isotropic bodies.