Adjoint-ROM Based Optimal Control of the Flow with Moving Boundaries

View Video Presentation: https://doi.org/10.2514/6.2021-2894.vid The adjoint-based method has become an efficient tool for flow control problems with a huge control space, and particularly has been applied to studying the optimization of the aerodynamic performance of the flow past a pitching-flapping airfoil. In order to further reduce the size of the discretized optimality system to make the approach practical for real-time control, a Proper Orthogonal Decomposition (POD)-Garlerkin based Reduced-Order Model (ROM) would be an ideal choice as the state equation. However, the previous studies of optimal control based on POD-Galerkin ROMs are mostly restricted to a fixed fluid domain, thus the controls introduced by solid motion are not able to be studied. In this work, an adjoint-based optimal control approach is developed based on a POD-Galerkin ROMwhich is capable of solving flows with moving solid boundary. Then the adjoint optimal control is applied to two-dimensional (2D) flow cases to validate its effectiveness: the one degree-of-freedom (DoF) control on the flow past an oscillatory cylinder and the flow past a pitching elliptical airfoil; and the two DoF control on the oscillatory cylinder flow with a different solid motion. It is found that for all cases, when the cost function is set as the velocity difference between prescribed target flow and the controlled flow in the observation zone, the adjoint optimal control can minimize the cost function after only few iterations, as well as force the initial control parameter back to the target value. The results have shown the effectiveness of the present ROM-based adjoint optimal control approach. The computational cost of the method is also presented. It is found that the computational cost is significantly reduced by using the ROM-based adjoint optimal control approach when compared with optimal control using pure DNS results. In all cases tested, including the two DoF case, the computational time is reduced by over 98%, which makes near-real-time control possible.