Optimized Flow Control based on Automatic Differentiation in Compressible Turbulent Channel Flows

This study presents an automatic differentiation (AD)-based optimization framework for flow control in compressible turbulent channel flows. We developed a fully differentiable boundary condition framework that allows for the precise calculation of gradients with respect to boundary control variables. This facilitates the efficient optimization of flow control methods. The framework's adaptability and effectiveness are demonstrated using two boundary conditions: opposition control and tunable permeable walls. Various optimization targets are evaluated, including wall friction and turbulent kinetic energy (TKE), across different time horizons. In each optimization, there were around $4\times10^4$ control variables and $3\times10^{9}$ state variables in a single episode. Results indicate that TKE-targeted opposition control achieves a more stable and significant reduction in drag, with effective suppression of turbulence throughout the channel. In contrast, strategies that focus directly on minimizing wall friction were found to be less effective, exhibiting instability and increased turbulence in the outer region. The tunable permeable walls also show potential to achieve stable drag reduction through a `flux-inducing' mechanism. This study demonstrates the advantages of AD-based optimization in complex flow control scenarios and provides physical insight into the choice of quantity of interest for improved optimization performance.