Active Control of Turbulent Airfoil Flows Using Adjoint-Based Deep Learning

We train active neural-network flow controllers using a deep learning PDE augmentation method to optimize lift-to-drag ratios in turbulent airfoil flows at Reynolds number [Formula: see text] and Mach number 0.4. Direct numerical simulation and large-eddy simulation are employed to model compressible, unconfined flow over two-dimensional (2D) and three-dimensional (3D) semi-infinite NACA 0012 airfoils at angles of attack [Formula: see text], 10, and 15 deg. Control actions, implemented through a blowing/suction jet at a fixed location and geometry on the upper surface, are adaptively determined by a neural network that maps local pressure measurements to optimal jet total pressure, enabling a sensor-informed control policy that responds spatially and temporally to unsteady flow conditions. The sensitivities of the flow to the neural network parameters are computed using the adjoint Navier–Stokes equations, which we construct using automatic differentiation applied to the flow solver. The trained flow controllers significantly improve the lift-to-drag ratios and reduce flow separation for both 2D and 3D airfoil flows, especially at [Formula: see text] and 10 deg. The 2D-trained models remain effective when applied out-of-sample to 3D flows, which demonstrates the robustness of the adjoint-trained control approach. The 3D-trained models capture the flow dynamics even more effectively, which leads to better energy efficiency and comparable performance for both adaptive (neural network) and offline (simplified, constant-pressure) controllers. These results underscore the effectiveness of this learning-based approach in improving aerodynamic performance.