Asymptotic Theory of Flapping Wing Propulsion in Extreme Ground Effect

This study, dedicated to flapping wing propulsion in immediate proximity a wall or between closely spaced flat walls, makes use of the method matched asymptotic expansions. Its purpose is create simplified parametric model such system based on single major assumption: closeness oscillating solid wall. In case rectangular finite-aspect ratio wing, analytical expressions have been obtained for coefficients instantaneous and period-averaged thrust force as well efficiency propulsor function distance from wall, Strouhal number aspect selected cases heaving, pitching combined oscillations. It shown that some oscillation modes ground results increases efficiency, optimally (considering amplitudes phase shift contributing motions) heave–pitch oscillations allow maximize flapping-wing propulsor. Increase decrease (relative frequency oscillations) heaving invariably brings about increase ideal efficiency. An example provided non-planar extreme effect application considering ring-wing embracing circular cylinder. A rule derived recalculation characteristics near onto same operating narrow canal parallel walls. can also be applied evaluate propulsive properties co-axial cylindric surfaces.