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Recently, wind farms consisting of clusters of closely spaced vertical-axis wind turbines (VAWTs) have attracted the interest of many people. In this study, a method using a wake model to predict the flow field and the output power of each rotor in a VAWT cluster is proposed. The method uses the information obtained by the preliminary computational fluid dynamics (CFD) targeting an isolated single two-dimensional (2D) VAWT rotor and a few layouts of the paired 2D rotors. In the method, the resultant rotor and flow conditions are determined so as to satisfy the momentum balance in the main wind direction. The pressure loss of the control volume (CV) is given by an interaction model which modifies the prepared information on a single rotor case and assumes the dependence on the inter-rotor distance and the induced velocity. The interaction model consists of four equations depending on the typical four-type layouts of selected two rotors. To obtain the appropriate circulation of each rotor, the searching range of the circulation is limited according to the distribution of other rotors around the rotor at issue. The method can predict the rotor powers in a 2D-VAWT cluster including a few rotors in an incomparably shorter time than the CFD analysis using a dynamic model. [ABSTRACT FROM AUTHOR]

This paper presents some results from a computational fluid dynamics (CFD) model of a multi-megawatt crosswind kite spinning on a circular path in a straight downwind configuration. The unsteady Reynolds averaged Navier-Stokes equations closed by the k − ω SST turbulence model are solved in the three-dimensional space using ANSYS Fluent. The flow behaviour is examined at the rotation plane, and the overall (or global) induction factor is obtained by getting the weighted average of induction factors on multiple annuli over the swept area. The wake flow behaviour is also discussed in some details using velocity and pressure contour plots. In addition to the CFD model, an analytical model for calculating the average flow velocity and radii of the annular wake downstream of the kite is developed. The model is formulated based on the widely-used Jensen's model which was developed for conventional wind turbines, and thus has a simple form. Expressions for the dimensionless wake flow velocity and wake radii are obtained by assuming self-similarity of flow velocity and linear wake expansion. Comparisons are made between numerical results from the analytical model and those from the CFD simulation. The level of agreement was found to be reasonably good. Such computational and analytical models are indispensable for kite farm layout design and optimization, where aerodynamic interactions between kites should be considered. [ABSTRACT FROM AUTHOR]

In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES) model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD), three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD) calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained. [ABSTRACT FROM AUTHOR]

• The machine learning framework achieves favorable accuracy and efficiency in the wake prediction. • ADM-R/RANS coupling model can efficiently produce big wake datasets for machine learning model. • For an aligned turbine row, power drops at the second turbine and gradually stabilizes afterwards. • Turbulence model plays an important role in accurate power prediction of wind farm. In the paper, a novel framework that employs the machine learning and CFD (computational fluid dynamics) simulation to develop new wake velocity and turbulence models with high accuracy and good efficiency is proposed to improve the turbine wake predictions. An ANN (artificial neural network) model based on the back-propagation (BP) algorithm is designed to build the underlying spatial relationship between the inflow conditions and the three-dimensional wake flows. To save the computational cost, a reduced-order turbine model ADM-R (actuator disk model with rotation), is incorporated into RANS (Reynolds-averaged Navier-Stokes equations) simulations coupled with a modified k - ε turbulence model to provide big datasets of wake flow for training, testing, and validation of the ANN model. The numerical framework of RANS/ADM-R simulations is validated by a standalone Vestas V80 2 MW wind turbine and NTNU wind tunnel test of double aligned turbines. In the ANN-based wake model, the inflow wind speed and turbulence intensity at hub height are selected as input variables, while the spatial velocity deficit and added turbulence kinetic energy (TKE) in wake field are taken as output variables. The ANN-based wake model is first deployed to a standalone turbine, and then the spatial wake characteristics and power generation of an aligned 8-turbine row as representation of Horns Rev wind farm are also validated against Large Eddy Simulations (LES) and field measurement. The results of ANN-based wake model show good agreement with the numerical simulations and measurement data, indicating that the ANN is capable of establishing the complex spatial relationship between inflow conditions and the wake flows. The machine learning techniques can remarkably improve the accuracy and efficiency of wake predictions. [ABSTRACT FROM AUTHOR]

In the design of wind energy farms, the loss of power should be seriously considered for the second wind turbine located inside the wake region of the first one. The rotation of the first wind-front rotor generates a high-vorticity wake with turbulence, and a suitable model is required in computational fluid dynamics (CFD) to predict the deficit of energy of the second turbine for the given configuration. A simplified numerical model based on the classical momentum theory is proposed in this study for multiple wind turbines, which is proposed with a couple of tuning parameters applied to Reynolds-averaged Navier-Stokes (RANS) analysis, resulting in a remarkable reduction of computational load compared with advanced methods, such as large eddy simulation (LES) where two parameters reflect on axial and rotational wake motion, simply tuned with the wind-tunnel test and its corresponding LES result. As a lumped parameter for the figure of merit, we regard the normalized efficiency on the kinetic power output of computational domain, which should be directed to maximize for the optimization of wind farms. The parameter surface is plotted in a dimensionless form versus intervals between turbines, and a simple correlation is obtained for a given hub height of 70% diameter and a fixed rotational speed tuned from the experimental data in a wide range. [ABSTRACT FROM AUTHOR]