Aerodynamic Force and Vortex Force on Flapping Wings

A recently proposed far-field aerodynamic force theory based on the concepts of vortex force and Lamb vector is here considered to investigate on the unsteady aerodynamics of flapping wings. Vortical force formulations in the incompressible flow regime are derived, for inertial or non-inertial reference frames, in a form valid for both viscous and inviscid flows. Then a mixed inertial/non-inertial formulation, originally proposed for two-dimensional viscous flows, is extended to three-dimensional and to inviscid flow regimes and used to post-process numerical solutions for a NACA0012 airfoil in pure plunging motion. Results are compared to classical linear theories by Theodorsen-Mutchler (for lift) and Garrick (for drag/thrust), then an analysis of the different terms of the far-field formula is illustrated focusing on their contribution to the thrust force exerted on the flapping wing. Furthermore, the dependence of total force and its far-field decomposition on the choice of the integration domain is also analysed.