Combining Theodorsen's and impulse theories to predict the lift of large-amplitude pitching foils

Abstract

The prediction of the unsteady aerodynamic lift experienced by a streamlined body is critical for a wide range of applications including, for instance, the control of aerial vehicles. Closed-form analytical formulations, such as Theodorsen’s lift formula for a sinusoidally pitching plate, have been found accurate for thin aerofoils at small angles of attack. In this talk, we will show that Theodorsen’s formulation can provide an accurate prediction even for non-sinusoidal large-amplitude pitching kinematics resulting in flow separation. The model fails when the interaction between the shed leading- and trailing-edge vortices provide a significant lift contribution, which is not accounted by the model. We compute this lift contribution from the measurements of the rate of change of the impulse of the vortex pair with particle image velocimetry, and we show that it accounts for the difference between the measured and predicted total lift. We also attempt with some degree of success a semi-empirical predictive model of this lift contribution to improve Theodorsen’s model prediction for highly separated flow. Overall, the results provide new insights on the accuracy of Theodorsen’s theory, and paves the way to the development of predictive models for unsteady loads in massively separated flow.