This study presents novel drag reduction active-flow-control (AFC) strategies for a three-dimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of ReD=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. This work introduces a multi-stage training approach to expand the exploration space and enhance drag reduction stabilization. By accelerating training through the exploitation of local invariants with MARL, a drag reduction of approximately 9% is achieved. The cooperative closed-loop strategy developed by the agents is sophisticated, as it utilizes a wide bandwidth of mass-flow-rate frequencies, which classical control methods are unable to match. Notably, the mass cost efficiency is demonstrated to be two orders of magnitude lower than that of classical control methods reported in the literature. These developments represent a significant advancement in active flow control in turbulent regimes, critical for industrial applications.

Purpose: Wall-modeled large eddy simulation (LES) is a practical tool for solving wall-bounded flows with less computational cost by avoiding the explicit resolution of the near-wall region. However, its use is limited in flows that have high non-equilibrium effects like separation or transition. This study aims to present a novel methodology of using high-fidelity data and machine learning (ML) techniques to capture these non-equilibrium effects. Design/methodology/approach: A precursor to this methodology has already been tested in Radhakrishnan et al. (2021) for equilibrium flows using LES of channel flow data. In the current methodology, the high-fidelity data chosen for training includes direct numerical simulation of a double diffuser that has strong non-equilibrium flow regions, and LES of a channel flow. The ultimate purpose of the model is to distinguish between equilibrium and non-equilibrium regions, and to provide the appropriate wall shear stress. The ML system used for this study is gradient-boosted regression trees. Findings: The authors show that the model can be trained to make accurate predictions for both equilibrium and non-equilibrium boundary layers. In example, the authors find that the model is very effective for corner flows and flows that involve relaminarization, while performing rather ineffectively at recirculation regions. Originality/value: Data from relaminarization regions help the model to better understand such phenomenon and to provide an appropriate boundary condition based on that. This motivates the authors to continue the research in this direction by adding more non-equilibrium phenomena to the training data to capture recirculation as well.

With the recent advances in machine learning, data-driven strategies could augment wall modeling in large eddy simulation (LES). In this work, a wall model based on gradient boosted decision trees is presented. The model is trained to learn the boundary layer of a turbulent channel flow so that it can be used to make predictions for significantly different flows where the equilibrium assumptions are valid. The methodology of building the model is presented in detail. The experiment conducted to choose the data for training is described. The trained model is tested a posteriori on a turbulent channel flow and the flow over a wall-mounted hump. The results from the tests are compared with that of an algebraic equilibrium wall model, and the performance is evaluated. The results show that the model has succeeded in learning the boundary layer, proving the effectiveness of our methodology of data-driven model development, which is extendable to complex flows.