Numerical Analysis of High Aspect Ratio Flexible Wings in Flapping Motion

Wing geometry, kinematics and flexibility are the fundamental components which contribute towards the aerodynamics performance of micro aerial vehicles. This research focuses on determining the role of isotropic flexibility in the aerodynamic performance of high aspect ratio (AR = 6.0) wings with different shapes in hovering flight. Three shapes are chosen, defined by the radius of the first moment of wing area 𝑟̅1, which are 0.43, 0.53 and 0.63, where low (resp. high) value of 𝑟̅1 corresponds to less (resp. more) spanwise area distribution towards the wingtip. The leading edges of flexible wings are modelled as rigid and the wings, therefore, predominantly deform in the chordwise direction. Flexible wings are categorized as flexible FX2 and more flexible MFX2 for brevity. The governing equations of fluid flow are solved using a sharp interface immersed boundary method, coupled with an in-house finite element structure solver for simulations of flexible wings. The results indicate that the rigid wings produce one lift peak per stroke during the mid-stroke and its magnitude increases with an increase in 𝑟̅1 due to strong leading-edge vortex. For flexible wings, the numbers of lift peaks per stroke and their timings during a flapping cycle depend on the deformation that affects the pitch angle and pitch rotation rate of the wings. The lift coefficient for a given shape decreases as flexibility increases because the pitch angle decreases during the mid-stroke. This decrease in lift coefficient with flexibility is pronounced for 𝑟̅1= 0.63 wing (up to 66 % less lift as compared to rigid equivalent) due to pitch down rotation at the commencement of the stroke, resulting in vortical structures on the bottom surface of the wing. For more flexible wings at high AR considered in this study, a wing with low 𝑟̅1 (= 0.43) may be suitable for the wing design of micro-aerial vehicle, as in general, it has better aerodynamic performance (24.5 % more power economy and similar lift coefficient) than high 𝑟̅1 (= 0.63) wing.