Effect of flexibility on flapping wing characteristics under forward flight

Through two-dimensional numerical simulation and by solving the unsteady incompressible Navier–Stokes (NS) equations, coupled with the structural dynamic equation for the motion of the wing, the effect of flexibility on flapping wing characteristics during forward flight is systematically studied. The flapping wing is considered as a cantilever, which performs the translational and rotational motion at its leading edge, and the other part is passively deformed by the aerodynamic force. The frequency ratio ω * and mass ratio m * are defined and used to characterize the flexibility of the flapping wing. It has been found that an optimal range of the frequency ratio exists in which the flexible wing possesses both a larger propulsive efficiency and lifting efficiency than their rigid counterpart. Also, the flexible wing with the smaller mass ratio may be of benefit to generate thrust, while the larger mass ratio may be of benefit to generate lift. In addition, a stronger leading edge vortex and reattachment vortex are observed around the appropriate flexibility wing's surface, which therefore leads to better aerodynamic characteristics.