Relaxing the Kutta Condition for Oscillating Foils

The Kutta condition is a well-known closure condition in potential-flow-based aerodynamic modelling, but its suitability to unsteady flows has long been questioned. The present work seeks to replace the classical kinematic condition with a dynamic process, treating the Kutta condition as an equilibrium towards which the system tends, with that approach described by an ordinary differential equation. In the companion work to this one, the new approach captured well the trends of bound circulation growth around impulsively started airfoils. Herein, we consider harmonically oscillating foils, and propose a simple modification to Theodorsen's model to better predict an airfoil's lift magnitude and phase response. Predictions are compared to CFD results, demonstrating the desired improvement over Theodorsen. For those wishing to model unsteady behaviour of real airfoils, an expanded empirical approach is proposed: in addition to determining the airfoil's lift slope at low angles of attack at the Reynolds number of interest, one must also determine the time constant of the Kutta process.