How flexibility affects the wake symmetry properties of a self-propelled plunging foil

Abstract

The wake symmetry properties of a flapping-foil system are closely associated with its propulsive performance. In the present work, the effect of the foil flexibility on the wake symmetry properties of a self-propelled plunging foil is studied numerically. We compare the wakes of a flexible foil and a rigid foil at a low flapping Reynolds number of 200. The two foils are of the same dimensions, flapping frequency, leading-edge amplitude and cruising velocity but different bending rigidities. The results indicate that flexibility can either inhibit or trigger the symmetry breaking of the wake. We find that there exists a threshold value of vortex circulation above which symmetry breaking occurs. The modification of vortex circulation is found to be the pivotal factor in the influence of the foil flexibility on the wake symmetry properties. An increase in flexibility can result in a reduction in the vorticity production at the leading edge because of the decrease in the effective angle of attack, but it also enhances vorticity production at the trailing edge because of the increase in the trailing-edge flapping velocity. The competition between these two opposing effects eventually determines the strength of vortex circulation, which, in turn, governs the wake symmetry properties. Further investigation indicates that the former effect is related to the streamlined shape of the deformed foil while the latter effect is associated with structural resonance. The results of this work provide new insights into the functional role of passive flexibility in flapping-based biolocomotion.

Flow-Mediated Interactions between Two Self-Propelled Flapping Filaments in Tandem Configuration

“…This is very different from the model used in some previous works [11,12,14], where the body was held fixed in an oncoming flow. Although a single actively flapping body in self-propulsion has been studied before [17][18][19][20][21], the multibody interactions under such condition have never been considered.…”

“…The filaments are inextensible and the surrounding flow is two dimensional, incompressible, and laminar. The motions of the fluid and the filaments are governed by the Navier-Stokes equations coupled with the geometrically non-linear structural equation [20][21][22], written in a dimensionless form as Here, u, p, and X ¼ ðX ð1Þ ; X ð2Þ Þ are the fluid velocity, fluid pressure, and displacement of the filaments, respectively. f and F are the Eulerian and Lagrangian force densities which represent the interactions between the fluid and the filaments.…”

Numerical Study of Mechanisms of the Vortex Formation in the Wake of Dual-Flapping Foils

“…Zheng and Wei indicated that the deflection angle can be correlated with the effective symmetry breaking and symmetry holding phase velocities [13]. Many factors, such as the aspect ratios, the flexibility and the shape of the foil, that influence the formation of vortex wake of a flapping foil, were studied experimentally and numerically [14] [15] [16] [17]. The system of dual-flapping foils is a new style and unconventional device which has high propulsive efficiency [1].…”

Propulsion of a Plunging Flexible Airfoil using a Torsion Spring Model

“…In this regard, the effect of wing flexibility on flying performance has received some attention in the past decade [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”