Inertial effects on the rotational dynamics of a spheroid in homogeneous isotropic turbulence

We investigate the effect of particle inertia on the rotational dynamics of a spheroidal particle in homogeneous isotropic turbulence. For particles smaller than the Kolmogorov scale, the turbulent flow is approximated as a stochastic linear velocity field, where Jeffery's equation governs the orientation dynamics under fluctuating velocity gradients. The influence of particle inertia is characterized by the Stokes number, St. Using a stochastic model, we first examine how inertia modifies the spinning and tumbling rates. We then complement this analysis with direct numerical simulations (DNS) that incorporate both translational dynamics and inertial torque on the particle. Our results show that the spinning rate decreases with increasing St, primarily due to the alignment of the particle's orientation with the local vorticity vector. In contrast, the tumbling rate exhibits a nonmonotonic dependence on St. For St< 1, the tumbling rate decreases with increasing inertia, consistent across both models. At intermediate St, DNS reveals an increase in tumbling, particularly when inertial torque is included. These findings highlight distinct regimes of rotational behavior and underscore the role of particle inertia in shaping the orientation dynamics of anisotropic particles in turbulence.