Compounding Transient Airfoil Motions and the Effectiveness of Linear Superposition

Abstract

This paper investigates, for the first time, the effects of compounding transient airfoil motions and the predictive capability of the linear superposition principle in vortex dominated flows. Significant increases in the peak lift and nose-down pitching moment were observed during the second of two transient plunging motions at a poststall angle of attack. The load response of the second motion was estimated through linear superposition of the first motion response with a surprising level of accuracy. Flowfield measurements revealed this performance to coincide with a constructive merging of leading-edge vortices (LEVs). LEV merging showed sensitivity to motion timing. Breakdown of the linear superposition prediction coincided with LEV detachment and trailing-edge vortex formation, which disrupted constructive LEV merging. The amplitude of the second motion showed no discernible effect on LEV merging, and subsequently the accuracy of the linear superposition prediction. An extension to periodic motion was investigated, where linear superposition of a single sinusoidal cycle was compared with the true periodic response. This was found to capture the mean lift increase for low to moderate reduced frequencies. Lift amplitude, however, was captured with reasonable accuracy across the range of reduced frequencies and amplitudes tested.