This paper focuses on the active flow control of a computational fluid dynamics simulation over a range of Reynolds numbers using deep reinforcement learning (DRL). More precisely, the proximal policy optimization (PPO) method is used to control the mass flow rate of four synthetic jets symmetrically located on the upper and lower sides of a cylinder immersed in a two-dimensional flow domain. The learning environment supports four flow configurations with Reynolds numbers 100, 200, 300, and 400, respectively. A new smoothing interpolation function is proposed to help the PPO algorithm learn to set continuous actions, which is of great importance to effectively suppress problematic jumps in lift and allow a better convergence for the training process. It is shown that the DRL controller is able to significantly reduce the lift and drag fluctuations and actively reduce the drag by ∼5.7%, 21.6%, 32.7%, and 38.7%, at Re = 100, 200, 300, and 400, respectively. More importantly, it can also effectively reduce drag for any previously unseen value of the Reynolds number between 60 and 400. This highlights the generalization ability of deep neural networks and is an important milestone toward the development of practical applications of DRL to active flow control.

Incorporating controlled elitism and dynamic distance crowding strategies, a modified NSGA-II algorithm based on a fast and genetic non-dominated sorting algorithm is developed with the aim of obtaining a novel multi-objective optimization design algorithm for wind turbine blades. As an example, a high-performance 1.5 MW wind turbine blade, taking maximum annual energy production and minimum blade mass as the optimization objectives, was designed. A 1/16-scale model of this blade was tested in a 12 m × 16 m wind tunnel and the experimental results validated the high performance. Moreover, both the computational fluid dynamics (CFD) method and a free-vortex method (FVM) were applied to calculating the aerodynamic performance, which was consistent with the experimental data. For completeness, the CFD and FVM were used to analyze the wake structure, and good and consistent results were obtained between them.

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier–Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models.

This paper presents a new variable pitch (VP) approach to increase the peak power coefficient of the straight-bladed vertical-axis wind turbine (VAWT), by widening the azimuthal angle band of the blade with the highest aerodynamic torque, instead of increasing the highest torque. The new VP-approach provides a curve of pitch angle designed for the blade operating at the rated tip speed ratio (TSR) corresponding to the peak power coefficient of the fixed pitch (FP)-VAWT. The effects of the new approach are exploited by using the double multiple stream tubes (DMST) model and Prandtl’s mathematics to evaluate the blade tip loss. The research describes the effects from six aspects, including the lift, drag, angle of attack (AoA), resultant velocity, torque, and power output, through a comparison between VP-VAWTs and FP-VAWTs working at four TSRs: 4, 4.5, 5, and 5.5. Compared with the FP-blade, the VP-blade has a wider azimuthal zone with the maximum AoA, lift, drag, and torque in the upwind half-cycle, and yields the two new larger maximum values in the downwind half-cycle. The power distribution in the swept area of the turbine changes from an arched shape of the FP-VAWT into the rectangular shape of the VP-VAWT. The new VP-approach markedly widens the highest-performance zone of the blade in a revolution, and ultimately achieves an 18.9% growth of the peak power coefficient of the VAWT at the optimum TSR. Besides achieving this growth, the new pitching method will enhance the performance at TSRs that are higher than current optimal values, and an increase of torque is also generated.

The past few years have witnessed a renewed blossoming of data-driven turbulence models. Quantification of the concomitant modeling uncertainty, however, has mostly been omitted, and the generalization performance of the data-driven models is still facing great challenges when predicting complex flows with different flow physics not seen during training. A robust data-driven Reynolds-averaged turbulence model with uncertainty quantification and non-linear correction is proposed in this work with the Bayesian deep neural network. In this model, the Reynolds stress tensor is decomposed into linear and non-linear parts. The linear part is taken as the usual linear eddy viscosity model while the non-linear counterpart is learned by a Bayesian deep neural network. Independent tensor bases of invariants and tensors constituted by mean strain rate tensor and rotation rate tensor are embedded into the neural network to effectively consider key turbulence features in different flows. The proposed model is well validated through numerical simulations of four canonical flows that significantly deviate in geometrical configurations and/or Reynolds numbers from those in the training data. With the non-linear corrections of embedded invariants and tensors representing key features of turbulence, the proposed model not only improves the predictive capabilities of Reynolds-averaged turbulence models on the same mesh but also has better generalization performance when simulating complex turbulent flows with large scale separation. In addition, this model allows us to quantitatively demonstrate the confidence interval of the predicted flow quantities that are originated from the model itself.

Stall, a complex phenomenon related to flow separation, is difficult to be predicted accurately. The motivation of the present study is to propose an approach to improve the simulation accuracy of Reynolds Averaged Navier–Stokes equations (RANS) for wind turbines in stall. The approach is implemented in three steps in simulations of the S809 airfoil and the NREL (National Renewable Energy Laboratory) Phase VI rotor. The similarity between airfoil and rotor simulations is firstly investigated. It is found that the primary reason for the inaccuracy of rotor simulation is not the rotational effect or the 3-D effect, but the turbulence-related problem that already exists in airfoil simulation. Secondly, a coefficient of the SST turbulence model is calibrated in airfoil simulation, ensuring the onset and development of the light stall are predicted accurately. The lift of the airfoil in the light stall, which was overestimated about 30%, is reduced to a level consistent with experimental data. Thirdly, the calibrated coefficient is applied to rotor simulation. That makes the flow patterns on the blade properly simulated and the pressure distribution of the blade, as well as the torque of the rotor, are predicted more accurately. The relative error of the predicted maximum torque is reduced from 34.4% to 3.2%. Furthermore, the procedure of calibration is applied to the MEXICO (Model Experiments in Controlled Conditions) rotor, and the predicted pressure distributions over blade sections are better than the CFD (Computational Fluid Dynamics) results from the Mexnext project. In essence, the present study provides an approach for calibrating rotor simulation using airfoil experimental data, which enhances the potential of RANS in accurate simulation of the wind turbine aerodynamic performance.