Flapping Thin Airfoil Interacting With the Ground

Abstract

The rotary wing and the flapping wing technology for the MAVs (Micro Air Vehicle) demand the studies of unsteady aerodynamic effects on the vehicles performing near the ground. In this study, a fast and robust numerical method based on the general formulae for the lift and propulsive forces, acting on a heaving-plunging airfoil, induced by a vortex sheet and its ground image, is developed and implemented. The Keldish-Lavrentiev series expansion of the Kernel function is employed to find the effect of the image vortex sheet on the airfoil. Coupled with the unsteady aerodynamics, the unsteady boundary layer equations cast in the velocity-vorticity formulation are solved numerically to predict the viscous drag on the airfoil performance under the: i) restrained condition where the mean distance to the ground remains the same, and ii) unrestrained condition for which the airfoil ascends or descends freely during its interaction with the ground. Applications of these two different