Freely falling cylinders of length to diameter ratio around one

Abstract

The paper presents numerical simulations of the free fall of homogeneous cylinders of length to diameter ratios 0.8 through 1.6 and solid to fluid density ratios ${\rho }_s/\rho$ going from 0 to 5 in transitional regimes. The results shed light on the transition from flat cylinders falling with their axis oriented vertically or oscillating about this equilibrium position to oblong cylinders keeping a horizontal or predominantly horizontal orientation. A significant bi-stability region extending as much as to an interval of $L/d$ ratios of $0.9\le L/d\le 1.35$ shortly before the onset of path instabilities has been evidenced. With the onset of path instabilities, the scenario starts to depend on the density ratio and the bi-stability domain progressively disappears. In these regimes, cylinders of length to diameter ratio 0.9 and 1 are observed to change periodically or intermittently the orientation of their axis. Cylinders of ratio $L/d=1.6$ behave qualitatively like those of ratio $L/d\ge 2$ investigated elsewhere and present subcritical effects for density ratio of 5.