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Numerical Analysis of High Aspect Ratio Flexible Wings in Flapping Motion
Author(s): A. Shahzad, M. N. Mumtaz Qadri, Shakeel Ahmad
Keywords: Flapping wings, Wing shape, Aspect ratio, Fluid-Structure Interaction, Micro Air Vehicle
This research focuses in 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 r1, which are 0.43, 0.53 and 0.63, where low (resp. high) value of r1 corresponds to less (resp. more) span-wise area distribution towards the wingtip. The leading edges of flexible wings are modeled as rigid and the wings, therefore, predominantly deform in the chord-wise direction. Flexible wings are categorized as flexible FX2 and more flexible MFX2 for brevity. Flexibility is defined by the effective stiffness of 1.32 and 0.58 for flexible and more flexible wings, respectively, at a mass ratio of 4.0 representative of hawk-moth. 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 lift coefficient for a given shape decreases as flexibility increases. This decrease in the lift with flexibility is pronounced for r1= 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 r1 (= 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 r1 (= 0.63) wing.