Effect of Wing Flexibility on the Lift Force Generated by a 2D Model Insect Wing Flapping in Hover Mode

In this study, we numerically examine the effect of wing flexibility on the lift force generated by a modeled flapping wing that simulates an insect flight in hover mode. The flow field around the flapping wing is assumed to be two-dimensional (2D), and the flow equations are formulated with the notion of "immersed boundary" for easy handling of the moving-boundary problem. In the 2D framework, the wing chord is treated as an elastic filament. To account for the large deformation in the wing, the motion of the filament is modeled using a geometrically nonlinear equation for bending beams. Both sets of equations are then solved according to the fluid-structure interaction concept using appropriate numerical schemes. Time variation of lift force on the wing is calculated for different values of wing flexural rigidity. Effects of elastic deformation of the wing and interactions between the bending wing and vortical flow structure are discussed. Flexural rigidity that gives the highest average lift force on the wing is sought. This study affirms that the flexibility of wing and the vortex-pair capture phenomenon are crucial to the lift force generation in the flapping-wing mechanics.