Lift increment scaling and its failure due to the leading-edge vortex detachment transition for a flapping wing under perturbations

A heaving and pitching wing encountering effective angle-of-attack perturbations at the Reynolds numbers of 2000 and 20 000 is numerically studied by using an immersed boundary–lattice Boltzmann method. The perturbations are introduced as an abrupt heaving or pitching motion superposed on the baseline motion. It is found that the lift increment scales with the increase in the perturbation effective angle of attack, especially during the heaving perturbation. The pitching perturbation is more likely to disrupt this scaling due to the transition of the leading-edge vortex (LEV) detachment mechanism, where the detachment mechanism of the LEV transitions from bluff-body shedding dominant to vorticity layer eruption dominant. Despite the same variation in the effective angle of attack for the heaving and pitching perturbations, vorticity layer eruption is more likely to occur under the fast pitching perturbation. When the Reynolds number is increased to 20 000, the time histories of aerodynamic force are similar to those at the Reynolds number of 2000. Moreover, the boundary layer under the LEV is more resistant to the adverse pressure gradient, leading to greater variability in vorticity layer eruption.