A Quasi-Steady Model for the Lift on a Hovering Flexible Wing

Abstract

In the analysis of flexible flapping wing, the aerodynamic outcome resulting from the combined structural dynamics and the unsteady fluid physics of the wing depends on the instantaneous angle of attack (AoA) and wing shape, which are a priori unknown. To offer a simplified and effective framework to address such challenges, we propose an analytic model to predict the unsteady lift on a hovering flexible wing. We model the fluid dynamic force with the Morison equation to estimate the instantaneous AoA, resulting from passive pitch. The corresponding unsteady lift is obtained using a quasi-steady model. Besides the imposed plunge amplitude, the model inputs are the scaling parameters accounting for the wing thickness, density, and stiffness. The structural damping coefficient is empirically determined. The predicted time histories of the passive pitch and lift can satisfactorily mimic the high fidelity aeroelastic solutions. Such analytic models of instantaneous wing deformation and lift generation improve our understanding of flexible flapping wing aerodynamics and can be used as fast yet reliable tools for design analysis.