Effect of Archimedes number on the dynamics of free-falling perforated disks

Abstract

The dynamics of perforated disks falling freely in a large expanse of viscous fluid at rest is investigated numerically. This complex fluid–structure interaction is solved via large eddy simulation. This numerical algorithm is verified and validated with available experimental results. The influence of Archimedes number expressing the ratio between the gravity-buoyancy and viscosity effects is discussed thoroughly, including kinematics and dynamics. Two critical Archimedes numbers are identified, Arcr1≈450 and Arcr2≈950, respectively. At these two critical Archimedes numbers, both kinematic and dynamic variables change trends. In this paper, we focus on the statistics of free-falling perforated disks. With the Archimedes number Ar increasing, the average angle of attack ⟨AoA⟩ and descent velocity ⟨Uz⟩ decrease gradually, and they arrive at a fixed value finally (here, ⟨·⟩ represents a time-average result); On the contrary, the other kinetic variables change violently when Ar is around 900, for example, terminal velocity ⟨Ut⟩. Additionally, phase differences of kinematic and dynamic variables are analyzed. A constant phase difference between the nutation angle θ and normal force FN is identified, about 66°, which is independent of Ar. Vortex structures are visualized using Q-criterion, and triangular vortex is omnipresent around holes. During the descent, a helical vortex always attaches to the perforated disk outer edge. With Ar increasing, complex vortex interaction appears, for example, merging and stretching. Some unusual behaviors in the numerical results are analyzed from the perspective of wake dynamics.