Dynamic pitching of an elastic rectangular wing in hovering motion

Abstract

In order to study the role of the passive deformation in the aerodynamics of insect wings, we computationally model the three-dimensional fluid-structure interaction of an elastic rectangular wing at a low aspect ratio during hovering flight. The code couples a viscous incompressible flow solver based on the immersedboundary method and a nonlinear finite-element solver for thin-walled structures. During a flapping stroke, the wing surface is dominated by non-uniform chordwise deformations. The effects of the wing stiffness, mass ratio, phase angle of active pitching, and Reynolds number are investigated. The results show that both the phase and the rate of passive pitching due to the wing flexibility can significantly modify the aerodynamics of the wing. The dynamic pitching depends not only on the specified kinematics at the wing root and the stiffness of the wing, but also sensitively on the mass ratio, which represents the relative importance of the wing inertia and aerodynamic forces in the wing deformation. We use the ratio between the flapping frequency, ω, and natural frequency of the wing, ω n , as the nondimensional stiffness. In general, when ω/ω n 0.3, the deformation significantly enhances the lift and also improves the lift efficiency despite a disadvantageous camber. In particular, when the inertial pitching torque is assisted by an aerodynamic torque of comparable magnitude, the lift efficiency can be markedly improved.

Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil

“…This observation is consistent with the finding in [34]. We also noted that in a recent study [52] on the role of flexibility in the hovering performance of a rectangular flapping wing, the maximum lift and efficiency (lift-to-power ratio) were also achieved at a forcing frequency much lower than the resonance point (around x ¼ 0:25-0:35).…”

“…It is interesting to note that a similar trend has also been reported in some studies of the flexibility effect on hovering performance of flapping foils or wings [19,52]. In these works, the maximum lift production was achieved at a moderate flexibility.…”

Three-dimensional flow and lift characteristics of a hovering ruby-throated hummingbird

“…A fixed, non-uniform, single-block Cartesian grid is employed to discretize the domain (figure 2a). The rectangular domain is 20 Â 20 Â 18 cm The numerical method has been previously validated for flapping-wing simulations against both experimental and simulation data in Dai et al [20], where a fruit fly model and an impulsively started plate were studied. To further validate the model in this work, we compare the flow field with that obtained from the PIV experiment by Warrick et al [10].…”

A fast Chebyshev method for simulating flexible-wing propulsion

“…Recently, great theoretical, experimental, and computational efforts have been directed towards advancing our understanding of flexible-wing propulsion [33,2,4,84,88,79,19,57,89,72]. These studies have demonstrated that flexibility can drastically improve propulsive performance, especially when a wing or fin is driven near resonance [51,50,21,54,69].…”