Varying Reynolds Number of Biomimetic Flapping Wing By Changing Air Density and Wing Length

Abstract

This research investigated how the nature of a biomimetic Manduca Sexta hawkmoth inspired wing changed as a function of Reynolds number by measuring the forces produced by wings with varying characteristic lengths and tested at varying air densities. A six degree of freedom balance was used to measure forces and moments, while high speed cameras were used to measure the stroke angle of the flapping wing. A GUI was used to manipulate the voltage of the drive signal sent to the piezoelectric actuator which determined the stroke angle, Φ, of the wing. The base line 50 mm wing span was compared against wings manufactured with 55, 60, 65, and 70 mm spans, while maintaining a constant aspect ratio. Tests were conducted in a sealed vacuum chamber at air densities between 0.5% and 100% of atmospheric pressure. Increasing the wing span increased the overall weight of the wing, which reduced the 1st natural frequency; and did not result in an increase in vertical force over the baseline 50 mm wing. However; if the decrease in natural frequency corresponding to the increased wing length was counteracted by increasing the thickness of the joint material in the linkage mechanism, vertical force production did increase over the baseline wing planform. Equipped with the more robust flapping mechanism, the 55 mm wing span produced 96% more vertical force at a 26% higher flapping frequency, while the 70 mm wing span produced 188% more vertical force at a 10% lower natural frequency than the baseline wing. Negligible forces and moments were measured at vacuum conditions, where the wing was demonstrating purely inertial motion, revealing the flight forces measured in atmosphere are wholly limited to its interaction with the surrounding air. Lastly, there was clear correlation between Reynolds number and vertical force production, indicating Reynolds number is a suitable parameter to predict the expected lift production for a specific wing design. Nomenclatureβ = stroke plane angle θ = elevation angle φ = wing position angle α = angle of attack Φ = stroke angle f = flapping frequency R = wing length μ = dynamic viscosity AR = aspect ratio δ = piezo tip displacement T = transmission ratio G = passive rotation joint torsional stiffness Eh = passive rotation joint Young's modulus wh = passive rotation joint width th = passive rotation joint thickness lh = passive rotation joint length V = wingtip velocity R2 = alternate wing length L = characteristic length A = driving amplitude η = stroke bias ωn = natural frequency keq = equivalent stiffness meq = equivalent mass Tref = reference temperature q = dynamic pressure S = planform area