Sparse identification of nonlinear unsteady aerodynamics of the oscillating airfoil

Reduced-order models are widely used in aerospace engineering. A model for unsteady aerodynamics is desirable for designing the blades of wind turbines. Recently, sparse identification of nonlinear dynamics with control was introduced to identify the parameters of an input-output dynamical system. In this paper, two models for attached flows and one for separated flows are identified through this technique. For the unsteady lift of the attached flow, Model I is a linear model that presents the dynamic change of an unsteady lift to a static lift. Model II was built based on Model I in order to obtain a more general system with closed-loop control. It has a first-order inert element that delays the overall input of the static lift. The Model II results replicate the training data very well and give an accurate prediction of other oscillating cases with different oscillation amplitudes, reduced frequency or mean angle of attack. For the unsteady lift of the separated flow, Model III is identified as a nonlinear model, which also has a first-order inert element. This model captures the nonlinear aerodynamics of the separated flow and replicates the training cases well. In addition, the prediction of Model III has good agreement with the numerical results.