Lift disturbance cancellation with rapid-flap actuation

Experimental results examining a rapidly-deflecting simple flap of a wall-to-wall NACA 0006 wing in a water tunnel at Re = 40k are presented for a survey of flap deflections designed to negate the lift-transient from an imposed plunge motion of the entire wing. The plunge, over a period ranging from eight convective times to one convective time, is regarded as a vertical disturbance, or a “gust”. The flap deflection history is initially derived from Theodorsen’s formula for unsteady flap motions, from which one obtains phase and amplitude information. The theoretical derivation makes the standard assumptions of attached flow, planar wake, and no leading edge vortices. Experimental data measurements of lift on the fore-element and the flap of the wing are examined for pure-plunge, for pure flap deflection, and for the combined airfoil plunge and flap deflection motion. The latter shows up to 87% of lift cancellation, verifying the limited, but substantial applicability of Theodorsen’s formula. Improvements over the theoretical formulation of lift cancellation are sought by constructing empirical models for both airfoil plunge and flap deflection. The empirical models for airfoil plunge and flap deflection are constructed independent of one another and their superposition is employed to approximate the total lift in combined plunge and deflection motions. It is shown that although the empirical model approach performs similar to the inviscid theory of Theodorsen’s model, the empirical model proves more effective in suppressing the leading-edge vortex induced in plunge.