Flow control optimization of a circular cylinder with control rods using deep reinforcement learning

Control rods are a classical passive strategy for suppressing vortex shedding in circular-cylinder wakes, but their effectiveness is highly sensitive to rod position and diameter. In the present study, deep reinforcement learning is coupled with direct numerical simulation based on the high-order spectral/hp element method to optimize the control-rod position and diameter according to the hydrodynamic response of the main cylinder at Reynolds numbers of 80 and 150. The results show that the control responses exhibit a clear regionalized pattern in parameter space, with four representative functional regions identified as regions I–IV. In the variable-diameter case, the learned distribution of control-rod diameters is concentrated around 0.22D, where D is the main-cylinder diameter. Region I achieves drag reduction primarily by reducing the pressure drag through incoming-flow redistribution. Region II amplifies lift fluctuations by enhancing the instantaneous imbalance between the upper and lower shear layers and strengthening wake flapping. Region III produces the largest drag because strong direct interference with the separated shear layers simultaneously enhances local blockage and deepens the rear-side pressure deficit. Region IV most effectively suppresses lift fluctuations by inhibiting shear-layer development, delaying vortex formation, and weakening vortex shedding. These results indicate that the four representative regions correspond to distinct mechanisms of shear-layer evolution, recirculation-zone reorganization, and wake dynamics. This study provides a new perspective for the parameter design and physical understanding of passive wake control of circular cylinders.