On the utility of nonlinear data-driven models for separation control

Flow separation can adversely impact aircraft performance by reducing lift and increasing drag. Active flow control has been proposed as a means of mitigating this performance degradation by temporarily reattaching the boundary layer. However, the placement of flow control actuators can have a significant influence on achievable performance. Prior work on optimal actuator selection for separation control has utilized linear data-driven models of the fluid dynamics, which disregards nonlinear flow interactions that could potentially be harnessed for improved control. In this work we investigate the utility of using nonlinear models to facilitate the optimal actuator selection task. We leverage a physically constraine data-driven approach called the Sparse Identification of Nonlinear Dynamics (SINDy). The SINDy model is constrained to preserve the energy-conserving property of the quadratic nonlinearity in the incompressible Navier-Stokes equations. The SINDy framework is also modified to provide output equations that predict flow-dependant parameters, such as the separation angle or lift. The model is obtained from direct numerical simulation data of two-dimensional and three-dimensional separated flows. Opportunities for optimal control analysis are also discussed.