A numerical study on two-dimensional (2D) rectangular plates falling freely in water is carried out in the range of 1.2 ≤ ρs/f ≤ 5.0 and 1/20 ≤ β ≤ 1/4, where ρs/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 ρs/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 . Hysteresis of the lift force on fluttering plates is observed and explained whilst the drag forces are the same when 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.
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Research Article| October 11 2016
Numerical study on the freely falling plate: Effects of density ratio and thickness-to-length ratio
C. J. Teo ;
Y. Wang, C. Shu, C. J. Teo, L. M. Yang; Numerical study on the freely falling plate: Effects of density ratio and thickness-to-length ratio. Physics of Fluids 1 October 2016; 28 (10): 103603. https://doi.org/10.1063/1.4963242
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