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Asymptotic theory of an oscillating wing section in weak ground effect. (English) Zbl 1143.76015
Summary: This study addresses unsteady aerodynamic forces acting on a wing section oscillating in a steady incompressible (and inviscid) uniform flow in the presence of a distant flat ground. Three fundamental dimensionless parameters characterize the magnitude of those forces: the ratio δ of the wing transversal displacement to its chord, the ratio ε of the wing chord to its average distance from the ground, and the ratio k of the wing chord to the distance traveled by the flow during one oscillation period. With the first two serving as small parameters, asymptotic series of the form δf 0 (k)+δε 2 f 1 (k)+δε 2 g(k/ε)f 2 (k)+ have been constructed for the wing lift and pitching moment. In the case of heave oscillations, three-term series for the lift fits nicely the available numerical data for wide range of δ,ε and k.
MSC:
76B10Jets and cavities, cavitation, free-streamline theory, water-entry problems, etc.
76M45Asymptotic methods, singular perturbations (fluid mechanics)