Predicting Dynamic Stall Hysteresis by Keeping Track of Time

Dynamic stall is an unsteady phenomenon that dominates aerodynamic forces on wind turbines and negatively impacts the performance and robustness of the turbines. Dynamic stall causes lift hysteresis loops due to significant delays in flow separation and reattachment with respect to the static lift response. The Goman-Khrabrov (GK) model is a nonlinear state-space model, which is shown to accurately reproduce dynamic lift hysteresis when the time coefficients are empirically tuned. In the present study, a modified version of the GK model is proposed by introducing physically derived times scales over empirical terms. By reinstating the time constants based on dominant flow physics attributed to stall delay and recovery, the empiricism of the GK model is removed. As a result of the removed empiricism, we can determine the unsteady position of the separation point and the degree of flow attachment over an airfoil without curve fitting to any time-averaged measurements. The modified model is validated by experimental data in terms of accuracy and generalisability for arbitrary dynamic stall oscillations. The new model captures the hysteresis effects inherent to dynamic stall for various pitching amplitudes and reduced frequencies as accurate as GK model.