Aerodynamic characteristics of hoverflies during hovering flight

The aerodynamic characteristics of model hoverflies during hovering flight are studied with a three-dimensional sharp-interface immersed boundary method. The wing is modelled as a rectangular generic wing to test the effects of an accessory flap called the alula, which is located at the wing root. Simulations are conducted in two groups: One group of simulations are conducted to determine the equilibrium kinematics of the wings with and without alula; the other group of simulations are conducted to study the effects of pitching phase differences between the wing and the alula on the performance of the wings. The forces, aerodynamic power, efficiency and vortical structures are discussed in detail. It is found that the wing without alula experiences a larger angle of attack at equilibrium. This difference requires 5% more aerodynamic power compared to the wing with alula. By performing simulations of the wing without alula, and wings with alula flapping 45° ahead, in phase with, or 45° behind the wing, we find that the wing with alula flapping in phase produces the largest lift, but that its efficiency is lowest. Vortical structure analysis shows that the vortical structures of the wing with alula flapping 45° ahead of the wing are similar to those of the wing without alula. The alula provides a stabilizing effect on the leading edge vortex for the wings with alula flapping 45° ahead or in phase.