A low-order nonlinear model of a stalled airfoil from data: Exploiting sparse regression with physical constraints

This work uses data-driven sparsity-promoting methods to obtain low-order governing equations for the wake of a stalled airfoil. Direct numerical simulation data of a NACA-0009 airfoil at an angle of attack of α = 15^◦ is utilized in this study, with actuation being performed by injecting momentum into the flow near the airfoil’s leading edge. Proper Orthogonal Decomposition (POD) is used to obtain a reduced order representation of the flow field. The Sparse Identification of Nonlinear Dynamics (SINDy) framework is then implemented to obtain low-order quadratic governing equations for the flow over the stalled airfoil. The SINDy model is constrained to preserve the energy-conserving property of the quadratic nonlinear-ity and associated triadic energy-transfer mechanisms. Low-order nonlinear models of the unsteady flow field associated with the stalled airfoil are obtained and cross-validated using off-design data. Furthermore, an output equation that predicts the lift coefficient is also identified and cross-validated. These low-order nonlinear models are expected to facilitate future developments in model-based analysis and control of separated flows.