Effects of wing shape, aspect ratio and deviation angle on aerodynamic performance of flapping wings in hover

Abstract

This numerical study is focused on assessing the effect on the aerodynamic hovering performance of wing shapes defined by the radius of the first moment of the wing area (r1¯) and aspect ratio (AR). In addition, the effect of introducing a deviation angle in the kinematics is examined. The performance of r1¯=0.43, 0.53, and 0.63 wings with AR of 1.5, 2.96, 4.5, and 6.0 is investigated at Reynolds numbers (Re) = 12, 400, and 13 500. The performance trends of the wing shapes have been observed to be independent of Re for both 2-angle and 3-angle kinematics. This is because high suction pressures associated with the leading-edge vortex are predominantly spread in the distal (away from the wing root) and leeward regions (towards the trailing-edge) of high flapping velocities for all the cases. While the deviation angle is detrimental to the production of lift and power economy (PE, defined as the ratio of the mean lift coefficient to the mean aerodynamic power coefficient) at Re = 12 due to strong viscous effects, it improves PE at Re = 400 and 13 500. A high instantaneous angle of attack at the stroke reversal results in high lift peak for 3-angle kinematics but its effect at Re = 400 and 13 500 is attenuated by strong vortical structures on the underside of the wing. Maximum PE is achieved at AR = 2.96, as a low AR wing does not produce enough lift and high AR wings consume more aerodynamic power. Although the lift is maximized using high r1¯ and AR wings, our results show that low r1¯ and high AR wings are best for maximizing PE for a given lift in insects.