On the roles of chord-wise flexibility in a flapping wing with hovering kinematics
J. D. Eldredge and J. Toomey
J. Fluid Mech. (Under review), July 2009.
Abstract:
The aerodynamic performance of a flapping two-dimensional wing section with simplified chord-wise flexibility is studied computationally. Bending stiffness is modeled by a torsion spring on a hinge connecting two rigid components. The leading portion of the wing is prescribed with kinematics that are characteristic of biological hovering, and the aft portion responds passively. Dynamically-coupled simulations of the Navier--Stokes equations and the wing dynamics are conducted for a wide variety of spring stiffnesses and kinematic parameters. Performance is assessed by comparison of the mean lift, power consumption and lift per unit power, with those from an equivalent rigid wing. Rigid wings consistently require more power than their flexible counterparts to generate the same kinematics. From the extensive parametric study, three cases which demonstrate the detrimental and beneficial roles of wing flexion are highlighted and the relevant flow phenomena are probed. The performance is degraded in softer wings undergoing large translational excursions, caused by a premature detachment of the leading-edge vortex. Performance is also weakened in softer wings undergoing small excursions when the pitching axis is moved aft, due to differences in the trailing-edge vortex shedding relative to their rigid counterpart. However, a mildly flexible wing has consistently good performance over a wide range of phase differences between pitching and heaving -- in contrast with the relative sensitivity of a rigid wing to this parameter -- due to better accommodation of the old leading-edge vortex into the wake.