Gust mitigation through closed-loop control. I. Trailing-edge flap response

We quantify and model the airfoil response to its pitching flap using a comprehensive experimentally acquired database at chord-based Reynolds number 1.8 x 106. This quantification relies on two proposed metrics that characterize the dynamic lift hysteresis and allow describing its evolution under different pitching conditions. The analysis reveals a saturation of the relative lift hysteresis that is independent of the angle of attack. Moreover, the hysteresis loop is shown to reach phase opposition at the same reduced frequency as when its tilt slope begins to change direction. The two-pronged characterization of the lift hysteresis is a promising approach to quantify the unsteady aerodynamic behavior beyond the reported conditions and of other immersed bodies. The modeling strategy yields one nonlinear model and a set of linear models. The models' performance is examined under a range of flow and pitching conditions. Despite their reduced accuracy compared to the nonlinear model, the linear models are chosen to be incorporated in the closed-loop control strategy that we detail in Part II of this series [Phys. Rev. Fluids 7, 024706 (2022)].