Abstract
The limitations of the Kutta-Joukowski (K-J) theorem in prediction of the time-averaged and instantaneous lift of an airfoil and a wing in low-Reynolds-number unsteady flows are examined. A general lift formula for a rectangular control volume is given in a very simple form in the framework of viscous flow theory, which provides a rational foundation for a direct comparison with the K-J theorem considered as a reduced case. Direct numerical simulations on the stationary and flapping flat plate and rectangular wing are conducted to assess the accuracy of both the K-J theorem and the general lift formula. In particular, the Lamb vector integral for the vortex force and the acceleration term of fluid for the unsteady inertial effect are evaluated as the main contributions to the unsteady lift generation of a flapping wing.
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