Insect wings in flight typically deform under the combined aerodynamic force and wing inertia; whichever is dominant depends on the mass ratio defined as $m^{\ast }={\rho }_{s}h/\left({\rho }_{f}c\right)$ , where ${\rho }_{s}h$ is the surface density of the wing, ${\rho }_f$ is the density of the air, and $c$ is the characteristic length of the wing. To study the differences that the wing inertia makes in the aerodynamic performance of the deformable wing, a two-dimensional numerical study is applied to simulate the flow-structure interaction of a flapping wing during hovering flight. The wing section is modeled as an elastic plate, which may experience nonlinear deformations while flapping. The effect of the wing inertia on lift production, drag resistance, and power consumption is studied for a range of wing rigidity. It is found that both inertia-induced deformation and flow-induced deformation can enhance lift of the wing. However, the flow-induced deformation, which corresponds to the low-mass wing, produces less drag and leads to higher aerodynamic power efficiency. In addition, the wing deformation has a significant effect on the unsteady vortices around the wing. The implication of the findings on insect flight is discussed.

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.