A Scaling Parameter for the Thrust Generation of Flapping Flexible Wings

Thrust generation and scaling parameters for flapping flexible wings are investigated using an integrated framework of computational fluid dynamics and structural dynamics solvers. To explore the influences of the density ratio and the effective stiffness on the thrust generation, surrogate models have been generated for a flapping thin isotropic flat Zimmerman wing in still air at = 1.5×10. Time averaged thrust, bending angle, and twist show qualitatively similar behavior and increased with higher ratio between the density ratio and effective stiffness. Flexibility-induced twisting in the wing promotes the thrust generation. To further investigate the flexibility-induced thrust enhancement, plunging chordwise flexible airfoils in forward flight at = 9.0×10 in water are considered. Time averaged thrust increases with larger airfoil thickness, however the thinnest airfoil responded with degradation in performance when motion frequency becomes high. Finally, unified scaling parameters are proposed based on properly normalized governing equations and give a priori order of magnitude estimation of the time averaged thrust and the degree of fluid-structure coupling. The results show that these scaling parameters, given as combinations of the wing geometry, structural properties, and the motion amplitude and frequency, can be applied for both cases with different motion type, Reynolds number, and the fluid medium.