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High fidelity numerical simulations are currently a key method to gain insight into flows in very large wind farms. However, these simulations are extremely costly in terms of computational resources and the progress in computational efficiency has been outrun by the growing size of wind farms and the need for simulations. The adoption of massively parallel hardware, namely graphics processing units (GPUs), by the wind energy community has begun but the numerical structure of the Navier-Stokes equations hinders an efficient use of such hardware. That is one of the reasons, the lattice Boltzmann method has gained increasing attention in recent years. By construction, this method for simulating the Navier-Stokes equations is perfectly parallelizable and well suited for massively parallel hardware. However, as with every new method, the foundation of the method is not widely known by the wind energy community and often met with doubt. This review paper collects the various methods necessary for a potential GPU-resident wind farm flow solver based on the lattice Boltzmann method. Furthermore, it discusses various aspects of the application of the lattice Boltzmann method to wind farm flows and related flow regimes. It also identifies gaps in the current literature and aims to direct future research on the lattice Boltzmann method for wind farm flows.

The use of graphics processing units (GPUs) has facilitated unprecedented performance gains for computational fluids dynamics in recent years. In many industries this has enabled the integration of large-eddy simulation (LES) in the engineering practice. Flow modelling in the wind industry though still primarily relies on models with significantly lower fidelity. This paper seeks to investigate the reasons why wind energy applications of LES are still an exception in the industrial practice. On that account, we present a survey among industry experts on the matter. The survey shows that the large runtimes and computational costs of LES are still seen as a main obstacle. However, other reasons such as a lack of expertise and user experience, the need for more validation, and lacking trust in the potential benefits of LES reveal that computational efficiency is not the only concern. Lastly, we present an exemplary simulation of a generic offshore wind farm using a GPU-resident Lattice Boltzmann LES framework. The example shows that the runtime requirements stated by a large part of the respondents can already now be fulfilled with reasonable hardware effort.

Two of the major limitations facing the adoption of large-eddy simulation (LES) to the industry today are a lack of validation against full-scale measurements and the high computational cost. The lattice Boltzmann method is an approach to conduct LES that is suitable for parallelization on graphics processing units, leading to reduction in energy-tosolution by multiple orders of magnitude compared to Navier-Stokes solvers. We validate the lattice Boltzmann solver VirtualFluids against the measurements published in the SWiFT benchmark and the results obtained with LES by the participants in the benchmark. We compare inflow, turbine response and wake quantities and show that our method yields similar results. While the other LES methods vary in the required energy by one order of magnitude, our methodology is always about one to two orders of magnitude more efficient. The benchmark allows for a comparison to a large number of models, however, the scale of the turbine is not representative of modern turbines and therefore important challenges of modern turbines, such as blade deflection, could not be validated.

The actuator line method for modeling wind turbine blades in wind farm flow simulations often offers a good compromise between accuracy and computational cost. A variety of methods have been proposed to correct the force prediction by the actuator line near the tip and root due to smearing the force in the flow domain. This article compares the two most commonly used methods (the filtered lifting line and the vortex-based smearing correction) in terms of accuracy, applicability and computational performance. Both corrections perform well for a single turbine, significantly reducing the force and power overprediction. The effect on power is larger than on thrust. Applying the corrections leads to more accurate results even at lower resolutions. The application of the corrections in an ALM simulation of a wind farm with 30 turbines reduces power by up to 10% compared to a case without correction. Different turbines in the farm are affected differently. The improvements in accuracy due to the corrections far outweigh the additional computational cost.

Thermal stratification plays an important role in wind farm flows and must therefore be included in simulations of such flows. Meanwhile, wind farms are covering larger areas, requiring very large domains and leading to exceptional computational costs for Large Eddy Simulation (LES). The lattice Boltzmann method (LBM) is a novel approach to LES of wind farm flows that is particularly efficient and suitable for massively parallel hardware, such as GPUs (graphics processing units). In this work we present a novel model for LES-LBM of stratified atmospheric boundary layers, using a so-called double distribution function approach. We develop a novel boundary condition to apply Monin-Obukhov similarity theory and implement a number of other components required for simulations of stratified boundary layers in the GPU-resident version of the open-source LBM solver VIRTUALFLUIDS. The model is validated for conventionally neutral and stably stratified boundary layers. Results agree closely with numerical references. The model is able to simulate conventionally neutral boundary layers at around realtime on a single GPU. Future work will include development of a precursor-successor method for wind farm flow simulations and improvements to the collision operator of temperature model.

Deep convolutional neural networks are a promising machine learning approach for computationally efficient predictions of flow fields. In this work we present a simple modelling framework for the prediction of the time-averaged three-dimensional flow field of wind turbine wakes. The proposed model requires the mean inflow upstream of the turbine, aerodynamic data of the turbine and the tip-speed ratio as input data. The output comprises all three mean velocity components as well as the turbulence intensity. The model is trained with the flow statistics of 900 actuator line large-eddy simulations of a single turbine in various inflow and operating conditions. The model is found to accurately predict the characteristic features of the wake flow. The overall accuracy and efficiency of the model render it as a promising approach for future wind turbine wake predictions.

The helix approach is a new individual pitch control method to mitigate wake effects of wind turbines. Its name is derived from the helical shape of the wake caused by a rotating radial force exerted by the turbine. While its potential to increase power production has been shown in previous studies, the physics of the helical wake are not well understood to date. Open questions include whether the increased momentum in the wake stems from an enhanced wake mixing or from the wake deflection. Furthermore, its application to a row of more than two turbines has not been examined before. We study this approach in depth from both an analytical and numerical perspective. We examine large-eddy simulations (LES) of the wake of a single turbine and find that the helix approach exhibits both higher entrainment and notable deflection. As for the application to a row of turbines, we show that the phase difference between two helical wakes is independent of ambient turbulence. Examination of LES of a row of three turbines shows that power gains greatly depend on the phase difference between the helices. We find a maximum increase in the total power of approximately 10 % at a phase difference of 270°. However, we do not optimise the phase difference any further. In summary, we provide a set of analytical tools for the examination of helical wakes, show why the helix approach is able to increase power production, and provide a method to extend it to a wind farm.