On the dynamic behaviors of freely falling annular disks at different Reynolds numbers

Abstract

Freely falling or rising objects in quiescent Newtonian fluid have been frequently encountered in nature or industry, such as the spreading of seeds from a tree or the movement of ores in deep sea mining. The dynamic behaviors of freely moving objects can provide a significant understanding of the evolution of the body wake and the resulting path instability. In this study, we present numerical simulations of freely falling annular disks released from quiescent water for relatively low Reynolds numbers from 10 to 500 while keeping the non-dimensional moment of inertia [Formula: see text] and inner to outer diameter ratio η constant. The falling stage experiences a variation from quasi-one-dimensional mode, steady oblique motion (SO motion), to the fully three-dimensional mode, helical motion. The stage diagram is plotted to show the variation tendency with the increment of Reynolds numbers. The detailed characteristics of the trajectories and orientation of the annular disks for different motions are analyzed. The corresponding vortical structures are presented, and an analog of the wingtip vortex is found at the outer rim of the disk for transitional and helical motion. A steady recirculation region of SO motion is observed, which is similar to that of a stationary disk but with complex multilayer structures formed by the combined effects of both the inner and outer rims. The limit streamline and pressure coefficient are investigated, demonstrating that the asymmetrical pressure distribution that exerts fluid forces and torques on the disk plays a crucial role in the dynamic response of the disk. Furthermore, combining the flow fields and fluid forces, the physical mechanism responsible for the diverse falling patterns is explored in detail.