Active Control of Laminar and Turbulent Flows Using Adjoint-Based Machine Learning

Active control of fluid dynamics in engineering applications is valuable but challenging, as traditional optimization methods struggle with the complex, high-dimensional nature of these problems. This dissertation extends and applies an adjoint-based machine learning method, the deep learning PDE augmentation method (DPM), for closed-loop active control on both laminar and turbulent flows. The end-to-end sensitivities for optimization are computed using adjoints of the governing equations without restriction on the terms that may appear in the objective function, which we construct using algorithmic differentiation applied to the flow solver. In one-dimensional Burgers' equation examples with analytic (manufactured) solutions, the DPM framework is validated, demonstrating comparable effectiveness to standard supervised learning for in-sample solutions, and superior performance for out-of-sample cases (i.e., with different analytic control functions). Additionally, the influence of optimization time intervals and neural network complexity is analyzed, providing insights that guide algorithm design and hyperparameter selection to balance control efficacy and computational cost. The DPM algorithm is then applied to three laminar flow scenarios. First, drag reduction performance and optimization costs are compared between adjoint-based controllers and deep reinforcement learning (DRL)--based controllers for two-dimensional, incompressible, confined flow over a cylinder, with control achieved via synthetic body forces along the cylinder boundary. The DPM-based controller outperforms the DRL-based controller in both computational efficiency and effectiveness. Second, DPM-based control is tested for compressible, unconfined flow over a cylinder, with the controller extrapolated to out-of-sample Reynolds numbers. A simplified, steady, offline controller is also derived from the DPM control law, achieving comparable drag reduction and vortex shedding stabilization to its adaptive counterparts. Third, a more realistic blowing/suction jet controller is developed for drag reductions with sparse sensors and actuators on the cylinder surface. Both the adaptive trained and simplified constant adjoint-based models are effective for in- and out-of-sample Reynolds numbers. Beyond laminar flows, the DPM algorithm is extrapolated to turbulent airfoil flows to enhance the lift-to-drag ratio while maintaining manageable energy expenditure. Direct numerical simulations and large eddy simulations are conducted for two-dimensional semi-infinite and three-dimensional airfoils at three angles of attack. Control actions, implemented through blowing/suction jets on the upper surface, are informed by local pressure measurements, which serve as inputs to the controller. Both 2D-trained and 3D-trained DPM controllers effectively capture flow dynamics, significantly improving aerodynamic performance.