Large eddy simulations of free-falling perforated disks with small inertias

The dynamics of free-falling perforated disks of porosity χ=0.2 are numerically investigated by the large eddy simulation (LES) within the range 100≤Ar≤1000 and 7×10⁻⁴≤I^∗≤2.7×10⁻³. Three falling styles are identified, namely spiral motion, spiral irregular motion and Hula-Hoop motion. A linear relationship of the Archimedes number Ar and the Reynolds number Re is observed within the intermediate Reynolds number regime. The mean values of crucial kinematic and dynamic variables are also given, and some scaling laws related to the perforated disk thickness h and diameter D are determined. For the mean descent velocity U_z, the gravitational velocity U_g is a suitable characteristic velocity scale; this is not the case for the terminal velocity U_t, which is proportional to h^{[Formula presented]}D^{[Formula presented]}. The characteristic timescale t_v for vortex shedding is proportional to D^{[Formula presented]}/h^{[Formula presented]}, which indicates thin perforated disks facilitate vortex shedding. The mean normal force F_N is proportional to h^{[Formula presented]}D^{[Formula presented]}, and irrespective of falling styles. It indicates different falling styles are related to the velocity fluctuations U(t)−U_ze_z. Vortex structures of three falling styles are provided. For spiral motion and spiral irregular motion, a vertical vortex appears inside the large-scale helical vortex. For Hula-Hoop motion, small-scale vortexes are omnipresent, and a new independent vortex is identified. The results of this paper is limited, and much work remains to be done, including the effects of the solid-to-fluid density ratio ρ and holes topology.