Dynamic pitching of an elastic rectangular wing in hovering motion

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 immersed-boundary 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 greatly 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, $\omega $, and natural frequency of the wing, ${\omega }_{n} $, as the non-dimensional stiffness. In general, when $\omega / {\omega }_{n} \leq 0. 3$, 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.