Propulsive performance of two- and three-dimensional flapping flexible plates

Abstract

The propulsive performance of two-and three-dimensional (2D and 3D) flapping flexible plates in a fluid at rest is investigated by a finite element method for the plate motion and an immersed boundary-lattice Boltzmann method for the fluid flow. We consider a model that as the leading-edge of the plate takes a vertical oscillation, the entire plate moves freely due to the fluid-structure interaction. The effects of flexibility on the dynamics of the 2D and 3D flapping plates are investigated. It is found that a suitable flexibility is benefit for improving the propulsive performance.The results obtained in this study provide physical insight into the understanding of the dynamics of the flapping-based locomotion.

Effect of aspect ratio in free-swimming plunging flexible plates

“…Experiments with flexible oscillating plates [8][9][10][11][12][13][14][15], two-dimensional [16,17], and three-dimensional computational studies [18][19][20] have provided further insights on thrust production, cruising velocity, and efficiency in a wide parameter space. These studies indicated that fast swimming and larger thrust are related to resonance oscillations.…”

Underlying principle of efficient propulsion in flexible plunging foils

“…where F (2) is the total vertical force exerted on the filament. Lastly, the propulsive efficiency in the filament is defined as…”

“…where u u u, p, and X X X = (X (1) , X (2) ) are the fluid velocity, fluid pressure and displacement of the filament respectively; f f f and F F F are the Eulerian and Lagrangian force densities which represent the interactions between the fluid and the structure.…”

Gravity-coupled flutter and contact of a flag near a wall

“…Experimentally, the effect of gravity has been minimized by positioning a flagpole vertically and fabricating a flag from a sufficiently stiff material, which prevents three-dimensional deformation by sagging and twisting. Numerical simulations have generally excluded the gravitational term from the equation of flag motion, even for three-dimensional flag models (Yu, Wang & Shao 2012;Banerjee, Connell & Yue 2015;Tang & Lu 2015;Chen et al 2020). However, to consider the more realistic situations that occur in nature and to improve the performance of engineering applications, the flag behaviours should be comprehensively examined under gravity, because gravity dramatically changes the response of a flag subjected to a uniform flow.…”

“…Experimentally, the effect of gravity has been minimized by positioning a flagpole vertically and fabricating a flag from a sufficiently stiff material, which prevents three-dimensional deformation by sagging and twisting. Numerical simulations have generally excluded the gravitational term from the equation of flag motion, even for three-dimensional flag models (Yu, Wang & Shao 2012; Banerjee, Connell & Yue 2015; Tang & Lu 2015; Chen et al. 2020).…”