Unsteady Forces on a Two-Dimensional Wing in Plunging and Pitching Motions

Abstract

Unsteady e uid dynamic forces acting on a two-dimensional wing in sinusoidal plunging and pitching motions in still water were measured. The measured e uid dynamic forces were larger than those estimated by quasi-steady analysis, where the effect of unsteady separated vortices on the e uid dynamic forces is not considered. Vortex capture is a phenomenon related to the larger e uid dynamic forces in wing motion that is similar to wing motion of real insects. By using the measured e uid dynamic forces, we identie ed combinations of plunging and pitching motions for maximum time-averaged thrust and for maximum efe ciency. Nomenclature a = dimensionless position of the rotational axis of the pitching motion b = span length of the wing immersed in water C`;Cd = lift and drag coefe cients Cn;Ct = normal and tangential force coefe cients CX;CZ = force coefe cients in X and Z directions c = chord length c = chord vector Fn; Ft = e uid dynamic forces normal and tangential to airfoil chord FX; FZ = e uid dynamic forces in X and Z directions Fx; Fz = forces in x and z directions f = frequency of both pitching and plunging motions