The increase in emissions associated with aviation requires deeper research into novel sensing and flow-control strategies to obtain improved aerodynamic performances. In this context, data-driven methods are suitable for exploring new approaches to control the flow and develop more efficient strategies. Deep artificial neural networks (ANNs) used together with reinforcement learning, i.e., deep reinforcement learning (DRL), are receiving more attention due to their capabilities of controlling complex problems in multiple areas. In particular, these techniques have been recently used to solve problems related to flow control. In this work, an ANN trained through a DRL agent, coupled with the numerical solver Alya, is used to perform active flow control. The Tensorforce library was used to apply DRL to the simulated flow. Two-dimensional simulations of the flow around a cylinder were conducted and an active control based on two jets located on the walls of the cylinder was considered. By gathering information from the flow surrounding the cylinder, the ANN agent is able to learn through proximal policy optimization (PPO) effective control strategies for the jets, leading to a significant drag reduction. Furthermore, the agent needs to account for the coupled effects of the friction- and pressure-drag components, as well as the interaction between the two boundary layers on both sides of the cylinder and the wake. In the present work, a Reynolds number range beyond those previously considered was studied and compared with results obtained using classical flow-control methods. Significantly different forms of nature in the control strategies were identified by the DRL as the Reynolds number Re increased. On the one hand, for Re & LE;1000, the classical control strategy based on an opposition control relative to the wake oscillation was obtained. On the other hand, for Re=2000, the new strategy consisted of energization of the boundary layers and the separation area, which modulated the flow separation and reduced the drag in a fashion similar to that of the drag crisis, through a high-frequency actuation. A cross-application of agents was performed for a flow at Re=2000, obtaining similar results in terms of the drag reduction with the agents trained at Re=1000 and 2000. The fact that two different strategies yielded the same performance made us question whether this Reynolds number regime (Re=2000) belongs to a transition towards a nature-different flow, which would only admits a high-frequency actuation strategy to obtain the drag reduction. At the same time, this finding allows for the application of ANNs trained at lower Reynolds numbers, but are comparable in nature, saving computational resources.

Designing active-flow-control (AFC) strategies for three-dimensional (3D) bluff bodies is a challenging task with critical industrial implications. In this study we explore the potential of discovering novel control strategies for drag reduction using deep reinforcement learning. We introduce a high-dimensional AFC setup on a 3D cylinder, considering Reynolds numbers (ReD) from 100 to 400, which is a range including the transition to 3D wake instabilities. The setup involves multiple zero-net-mass-flux jets positioned on the top and bottom surfaces, aligned into two slots. The method relies on coupling the computational-fluid-dynamics solver with a multi-agent reinforcement-learning (MARL) framework based on the proximal-policy-optimization algorithm. MARL offers several advantages: it exploits local invariance, adaptable control across geometries, facilitates transfer learning and cross-application of agents, and results in a significant training speedup. For instance, our results demonstrate 21% drag reduction for ReD=300, outperforming classical periodic control, which yields up to 6% reduction. To the authors' knowledge, the present MARL-based framework represents the first time where training is conducted in 3D cylinders. This breakthrough paves the way for conducting AFC on progressively more complex turbulent-flow configurations.

This study presents novel active-flow-control (AFC) strategies aimed at achieving drag reduction for a three-dimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of (Re_D=3900). The cylinder in this subcritical flow regime has been extensively studied in the literature and is considered a classic case of turbulent flow arising from a bluff body. The strategies presented are explored through the use of deep reinforcement learning. The cylinder is equipped with 10 independent zero-net-mass-flux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computational-fluid-dynamics solver and a multi-agent reinforcement-learning (MARL) framework using the proximal-policy-optimization algorithm. Thanks to the acceleration in training facilitated by exploiting the local invariants with MARL, a drag reduction of (8\%) was achieved, with a mass cost efficiency two orders of magnitude lower than those of the existing classical controls in the literature. This development represents a significant advancement in active flow control, particularly in turbulent regimes critical to industrial applications.