Machine learning has recently become a promising technique in fluid mechanics, especially for active flow control (AFC) applications. A recent work [Rabault et al., J. Fluid Mech. 865, 281–302 (2019)] has demonstrated the feasibility and effectiveness of deep reinforcement learning (DRL) in performing AFC over a circular cylinder at Re = 100, i.e., in the laminar flow regime. As a follow-up study, we investigate the same AFC problem at an intermediate Reynolds number, i.e., Re = 1000, where the weak turbulence in the flow poses great challenges to the control. The results show that the DRL agent can still find effective control strategies, but requires much more episodes in the learning. A remarkable drag reduction of around 30% is achieved, which is accompanied by elongation of the recirculation bubble and reduction of turbulent fluctuations in the cylinder wake. Furthermore, we also perform a sensitivity analysis on the learnt control strategies to explore the optimal layout of sensor network. To our best knowledge, this study is the first successful application of DRL to AFC in weakly turbulent conditions. It therefore sets a new milestone in progressing toward AFC in strong turbulent flows.

We demonstrate the use of high-fidelity computational fluid dynamics simulations in machine-learning based active flow control. More specifically, for the first time, we adopt the genetic programming (GP) to select explicit control laws, in a data-driven and unsupervised manner, for the suppression of vortex-induced vibration (VIV) of a circular cylinder in a low-Reynolds-number flow (Re = 100), using blowing/suction at fixed locations. A cost function that balances both VIV suppression and energy consumption for the control is carefully chosen according to the knowledge obtained from pure blowing/suction open-loop controls. By implementing reasonable constraints to VIV amplitude and actuation strength during the GP evolution, the GP-selected best ten control laws all point to suction-type actuation. The best control law suggests that the suction strength should be nonzero when the cylinder is at its equilibrium position and should increase nonlinearly with the cylinder’s transverse displacement. Applying this control law suppresses 94.2% of the VIV amplitude and achieves 21.4% better overall performance than the best open-loop controls. Furthermore, it is found that the GP-selected control law is robust, being effective in flows ranging from Re = 100 to 400. On the contrary, although the P-control can achieve similar performance as the GP-selected control at Re = 100, it deteriorates in higher Reynolds number flows. Although for demonstration purpose the chosen control problem is relatively simple, the training experience and insights obtained from this study can shed some light on future GP-based control of more complicated problems.

This paper studies the control of two-dimensional vortex-induced vibrations (VIVs) of a single circular cylinder at a Reynolds number of 100 using a novel windward-suction-leeward-blowing (WSLB) concept. A lattice Boltzmann method based numerical framework is adopted for this study. Both open-loop and closed-loop controls are implemented. In the open-loop control, three types of actuation arrangements, including the pure suction on the windward side of the cylinder, the pure blowing on the leeward side, and the general WSLB on both sides, are implemented and compared. It is found that the general WSLB is the most effective, whereas the pure suction is the least effective. In the closed-loop control, the proportional (P), integral (I), and proportional-integral (PI) control schemes are applied to adjust the WSLB velocities according to the flow information obtained from a sensor. The effects of four key control parameters including the proportional gain constant, the integral gain constant, the length of data history used for the feedback, and the location of the sensor are investigated. It is found that the use of only P control fails to completely suppress the VIV, the use of only I control can achieve the complete suppression, and the PI control performs the best in terms of both the control effectiveness and efficiency. In the PI control, there exists an optimal length of data history for the feedback, at which the VIV control is the most efficient. There also exist the minimum required WSLB velocities for the VIV suppression, independent of the control schemes. Moreover, it is found that the VIV control is independent of the sensor location.