Numerical study on the freely falling plate: Effects of density ratio and thickness-to-length ratio

A numerical study on two-dimensional (2D) rectangular plates falling freely in water is carried out in the range of 1.2 ≤ ρ_s/f ≤ 5.0 and 1/20 ≤ β ≤ 1/4, where ρ_s/f is the solid-to-water density ratio and β is the plate thickness-to-length ratio. To study this problem, the immersed boundary-lattice Boltzmann flux solver in a moving frame is applied and validated. For the numerical result, a phase diagram is constructed for fluttering, tumbling, and apparent chaotic motions of the plate parameterized using ρ_s/f and β. The evolution of vortical structures in both modes is decomposed into three typical stages of initial transient, deep gliding, and pitching-up. Various mean and instantaneous fluid properties are illustrated and analyzed. It is found that fluttering frequencies have a linear relationship with the Froude number for all cases considered. Lift forces on fluttering plates are linearly dependent on the angle of attack α at the cusp-like turning point when $α ≥π/5$⁠. Hysteresis of the lift force on fluttering plates is observed and explained whilst the drag forces are the same when $α$ has the same value. Meanwhile, the drag force in the tumbling motion may have a positive propulsive effect when the plate begins a tumbling rotation from α = π/2.