Dynamics of a falling plate at low Reynolds numbers

Free-falling of objects in fluids is universal in nature and engineering. The falling styles of the falling object are affected by the properties of both the object and the fluid. Based on the assumption that the final state of a free-falling object at low Reynolds numbers is stable and equivalent to that of a fixed object with incoming flow, we utilize the results for the fixed plate to interpolate and obtain the state of the falling plate. It is found that the plate would exhibit multiple stable falling solutions. The number of stable falling solutions is dependent on the location of the gravity center of the plate. The distribution of the multi-solution region is affected by both Archimedes number (Ar) and the density ratio (m*). The results of the actual fall of the plate do not always agree with those obtained by the static interpolation method due to the fact that the fall of the plate is a dynamic process. We simulate the falling behaviors of plates whose center of gravity is located in the multi-solution region for different initial release angles θ0. According to the falling behaviors of the plate, there are four regions that are observed and denoted in the multi-solution region: (1) single stable region; (2) bistable region; (3) single stable and fluttering region; and (4) bistable and fluttering region. The effects of Ar,m*, and the dimensionless moment of inertia I* of the plate on the distribution of the four regions are evaluated.