No 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.

The effect of hawkmoth-like flexibility on the aerodynamic hovering performance of wings at a Reynolds number of 400 has been assessed by conducting fluid structure interaction simulations incorporating a finite difference based immersed boundary method coupled with a finite-element based structure solver. The stiffness distribution of a hawkmoth forewing was mapped onto three wing shapes (r¯1 = 0.43, 0.53, and 0.63) defined by the radius of the first moment of wing area each with aspect ratios, AR = 1.5, 2.96, 4.5, and 6.0 using elliptic mesh generation, the Jacobi method for iterations, and the concept of the barycentric coordinate system. The results show that there is a dominant chordwise deformation at AR = 1.5, and the wings also deform in the spanwise direction and their tips deviate from the horizontal stroke plane as AR increases. At AR = 1.5, 2.96, and 4.5, flexibility increases the mean lift (up to 39%, 18%, and 17.6%, respectively) for all wing shapes. At AR = 6.0, the r1¯ = 0.53 and 0.63 flexible wings give lesser lift than the rigid equivalents because of negative lift or small positive lift during the early stroke as the vortical structures remain on the bottom surface. This is attributed to the rapid pitch-down rotation, lesser stroke angular velocity than the rigid wing, and upward motion of the wingtip, away from the horizontal stroke plane. From the design perspective, the anisotropic flexible wings (except r1¯ = 0.53 and 0.63 with AR = 6.0) can be used in micro aerial vehicles for high lift requirements, such as for a high payload. Results here show that in nature, the hawkmoth wings with r1¯ and AR of 0.43-0.44 and 2.73-2.92, respectively, appear to have a combination of the shape, AR, and flexibility that optimizes power economy.