The Lift Problem in Flapping Forward Flight at Low Reynolds Numbers

Abstract

This paper discusses the relationship between lift generation and flow structures in flapping forward flight at low Reynolds numbers. The simple lift formula for a wing/body in a sufficiently large rectangular control surface is given in the framework of the general viscous flow theory, which contains the two dominant terms: the vortex lift and the lift associated with the fluid acceleration. This lift decomposition allows quantitative estimation of the contributions of identified flow structures to lift generation. The Kutta-Joukowski theorem and the classical unsteady airfoil theory are the naturally reduced cases from the simple lift formula. The validation and applications of the simple lift decomposition are presented for the flows over the flapping flat-plate airfoil, flapping rectangular morphing wing and flapping bat wing.