Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

Quantification of power losses due to wind turbine wake interactions through SCADA,meteorological and wind LiDAR data

Power production of an onshore wind farm is investigated through supervisory control and data acquisition data, while the wind field is monitored through scanning light detection and ranging measurements and meteorological data acquired from a met‐tower located in proximity to the turbine array. The power production of each turbine is analysed as functions of the operating region of the power curve, wind direction and atmospheric stability. Five different methods are used to estimate the potential wind power as a function of time, enabling an estimation of power losses connected with wake interactions. The most robust method from a statistical standpoint is that based on the evaluation of a reference wind velocity at hub height and experimental mean power curves calculated for each turbine and different atmospheric stability regimes. The synergistic analysis of these various datasets shows that power losses are significant for wind velocities higher than cut‐in wind speed and lower than rated wind speed of the turbines. Furthermore, power losses are larger under stable atmospheric conditions than for convective regimes, which is a consequence of the stability‐driven variability in wake evolution. Light detection and ranging measurements confirm that wind turbine wakes recover faster under convective regimes, thus alleviating detrimental effects due to wake interactions. For the wind farm under examination, power loss due to wake shadowing effects is estimated to be about 4% and 2% of the total power production when operating under stable and convective conditions, respectively. However, cases with power losses about 60‐80% of the potential power are systematically observed for specific wind turbines and wind directions. Copyright © 2017 John Wiley & Sons, Ltd.     

On atmospheric stability in the dynamic wake meandering model

The present study investigates a new approach for capturing the effects of atmospheric stability on wind turbine wake evolution and wake meandering by using the dynamic wake meandering model. The most notable impact of atmospheric stability on the wind is the changes in length and velocity scales of the atmospheric turbulence. The length and velocity scales in the turbulence are largely responsible for the way in which wind turbine wakes meander as they convect downstream. The hypothesis of the present work is that appropriate turbulence scales can be extracted from the oncoming atmospheric turbulence spectra and applied to the dynamic wake meandering model to capture the correct wake meandering behaviour. The ambient turbulence in all stability classes is generated using the Mann turbulence model, where the effects of non‐neutral atmospheric stability are approximated by the selection of input parameters. In order to isolate the effect of atmospheric stability, simulations of neutral and unstable atmospheric boundary layers using large‐eddy simulation are performed at the same streamwise turbulence intensity level. The turbulence intensity is kept constant by calibrating the surface roughness in the computational domain. The changes in the turbulent length scales due to the various atmospheric stability states impact the wake meandering characteristics and thus the power generation by the individual turbines. The proposed method is compared with results from both large‐eddy simulation coupled with an actuator line model and field measurements, where generally good agreement is found with respect to the velocity, turbulence intensity and power predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

A stochastic wind turbine wake model based on new metrics for wake characterization

Understanding the detailed dynamics of wind turbine wakes is critical to predicting the performance and maximizing the efficiency of wind farms. This knowledge requires atmospheric data at a high spatial and temporal resolution, which are not easily obtained from direct measurements. Therefore, research is often based on numerical models, which vary in fidelity and computational cost. The simplest models produce axisymmetric wakes and are only valid beyond the near wake. Higher‐fidelity results can be obtained by solving the filtered Navier–Stokes equations at a resolution that is sufficient to resolve the relevant turbulence scales. This work addresses the gap between these two extremes by proposing a stochastic model that produces an unsteady asymmetric wake. The model is developed based on a large‐eddy simulation (LES) of an offshore wind farm. Because there are several ways of characterizing wakes, the first part of this work explores different approaches to defining global wake characteristics. From these, a model is developed that captures essential features of a LES‐generated wake at a small fraction of the cost. The synthetic wake successfully reproduces the mean characteristics of the original LES wake, including its area and stretching patterns, and statistics of the mean azimuthal radius. The mean and standard deviation of the wake width and height are also reproduced. This preliminary study focuses on reproducing the wake shape, while future work will incorporate velocity deficit and meandering, as well as different stability scenarios. Copyright © 2016 John Wiley & Sons, Ltd.     

Large eddy simulation study of the humidity variation in the shadow of a large wind farm

Numerous studies have shown that wind turbine wakes within a large wind farm bring about changes to both the dynamics and thermodynamics of the atmospheric boundary layers (ABL). Previously, we investigated the relative humidity budget within a wind farm via field measurements in the near‐wake region and large eddy simulations (LES). The effect of the compounding wakes within a large wind farm on the relative humidity was also investigated by LES. In this study, we investigate how the areas of relative humidity variation, that was observed in the near‐wake, develop downstream in the shadow region of a large wind farm. To this end, LES of a wind farm consisting of 8x6 wind turbines with periodic boundary condition in the lateral direction (inferring an infinitely wide farm) interacting with a stable ABL is carried out. Two wind farm layouts, aligned and staggered, are considered in the analysis and the results from both configurations are compared to each other. It is observed that a decrease of relative humidity underneath the hub height and an increase above the hub height build up within the wind farm, and are maintained in the downstream of the farm for long distances. The staggered farm layout is more effective in keeping a more elongated region of low relative humidity underneath the hub, when compared to the aligned layout.     

Offshore wind farm wake recovery: Airborne measurements and its representation in engineering models

We present an analysis of wind measurements from a series of airborne campaigns conducted to sample the wakes from two North Sea wind farm clusters, with the aim of determining the dependence of the downstream wind speed recovery on the atmospheric stability. The consequences of the stability dependence of wake length on the expected annual energy yield of wind farms in the North Sea are assessed by an engineering model. Wakes are found to extend for significantly longer downstream distances (>50 km) in stable conditions than in neutral and unstable conditions (  15 km). The parameters of one common engineering model are modified to reproduce the observed wake decay at downstream distances  30 km. More significant effects on the energy yield are expected for wind farms separated by distances  30 km, which is generally the case in the North Sea, but additional data would be required to validate the suggested parameter modifications within the engineering model. A case study is accordingly performed to show reductions in the farm efficiency downstream of a wind farm. These results emphasize not only the importance of understanding the impact of atmospheric stability on offshore wind farms but also the need to update the representation of wakes in current industry models to properly include wake‐induced energy losses, especially in large offshore clusters.     

Numerical investigation of wind turbine wake development in directionally sheared inflow

Turbines in wind farms are subject to complex mutual aerodynamic interactions, which in detail depend upon the characteristics of the atmospheric boundary layer. Our two objectives with this paper were to investigate the impact of directionally sheared inflow on the wake development behind a single wind turbine and to analyse the impact of the wakes on the energy yield and loading of a downstream turbine, which is exposed to partial and full wake conditions. We performed simulations with a framework based on a coupled approach of large‐eddy simulation and an actuator line representation of an aeroelastic turbine model. Our results show that directionally sheared inflow leads to a non‐symmetrical wake development, which transfers to distinct differences in the energy yield and loading of downstream turbines of equal lateral offsets in opposite direction. Therefore, the assumption of wakes being axisymmetrical could lead to notable deviations in the prediction of wake behaviour and their impact on downstream turbines for atmospheric inflow conditions, which include directional shear. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterizing power performance and wake of a wind turbine under yaw and blade pitch

Wind turbine wakes have been recognized as a key issue causing underperformance in existing wind farms. In order to improve the performance and reduce the cost of energy from wind farms, one approach is to develop innovative methods to improve the net capacity factor by reducing wake losses. The output power and characteristics of the wake of a utility‐scale wind turbine under yawed flow is studied to explore the possibility of improving the overall performance of wind farms. Preliminary observations show that the power performance of a turbine does not degrade significantly under yaw conditions up to approximately 10°. Additionally, a yawed wind turbine may be able to deflect its wake in the near‐wake region, changing the wake trajectory downwind, with the progression of the far wake being dependent on several atmospheric factors such as wind streaks. Changes in the blade pitch angle also affect the characteristics of the turbine wake and are also examined in this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Wind turbine partial wake merging description and quantification

Individual turbine location within a wind plant defines the flow characterisitcs experienced by a given turbine. Irregular turbine arrays and inflow misalignment can reduce plant efficiency by producing highly asymmetric wakes with enhanced downstream longevity. Changes in wake dynamics as a result of turbine position were quantified in a wind tunnel experiment. Scale model turbines with a rotor diameter of 20 cm and a hub height of 24 cm were placed in symmetric, asymmetric, and rotated configurations. Simultaneous hub height velocity measurements were recorded at 11 spanwise locations for three distances downstream of the turbine array under two inflow conditions. Wake interactions are described in terms of the time‐average streamwise velocity and turbulence intensity as well as the displacement, momentum, and energy thicknesses. The effects of wake merging on power generation are quantified, and the two‐point correlation is used to examine symmetry in the mean velocity between wakes. The results indicate that both asymmetric and rotated wind plant arrangements can produce long‐lasting wakes. At shallow angles, rotated configurations compound the effects of asymmetric arrangements and greatly increase downstream wake persistence.     

Atmospheric stability‐dependent infinite wind‐farm models and the wake‐decay coefficient

We extend the infinite wind‐farm boundary‐layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind‐speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind‐speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind‐speed reduction). We further adjust the wake‐decay coefficient of the Park wake model for an infinite wind farm to match the wind‐speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP‐recommended values for the wake‐decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ～ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub‐height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.     

一种新修正的风电机组尾流分析模型

基于尾流区线性膨胀、径向风速损失呈高斯分布的假设,在BP模型基础上建立一种新修正的风电机组尾流分析模型。该模型针对BP模型无法对近尾流区进行分析的问题,基于质量守恒原理求解近尾流区速度损失分布;通过大涡模拟数据拟合,对BP模型中速度损失标准差方程进行修正,提升了模型在不同地表粗糙度下的计算精度。采用大涡模拟数据对多种工程尾流模型的计算结果进行比较。结果表明,相比于Jensen、Frandsen和BP模型,该模型能更好地预测全尾流范围的径向速度分布,并且具有更高的计算精度。     

Modelling and measurements of power losses and turbulence intensity in wind turbine wakes at Middelgrunden offshore wind farm

Understanding of power losses and turbulence increase due to wind turbine wake interactions in large offshore wind farms is crucial to optimizing wind farm design. Power losses and turbulence increase due to wakes are quantified based on observations from Middelgrunden and state‐of‐the‐art models. Observed power losses due solely to wakes are approximately 10% on average. These are relatively high for a single line of wind turbines due in part to the close spacing of the wind farm. The wind farm model Wind Analysis and Application Program (WAsP) is shown to capture wake losses despite operating beyond its specifications for turbine spacing. The paper describes two methods of estimating turbulence intensity: one based on the mean and standard deviation (SD) of wind speed from the nacelle anemometer, the other from mean power output and its SD. Observations from the nacelle anemometer indicate turbulence intensity which is around 9% higher in absolute terms than those derived from the power measurements. For comparison, turbulence intensity is also derived from wind speed and SD from a meteorological mast at the same site prior to wind farm construction. Despite differences in the measurement height and period, overall agreement is better between the turbulence intensity derived from power measurements and the meteorological mast than with those derived from data from the nacelle anemometers. The turbulence in wind farm model indicates turbulence increase of the order 20% in absolute terms for flow directly along the row which is in good agreement with the observations. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions

The modelling of wind turbine wakes is investigated in this paper using a Navier–Stokes solver employing the k–ω turbulence model appropriately modified for atmospheric flows. It is common knowledge that even single‐wind turbine wake predictions with computational fluid dynamic methods underestimate the near wake deficit, directly contributing to the overestimation of the power of the downstream turbines. For a single‐wind turbine, alternative modelling enhancements under neutral and stable atmospheric conditions are tested in this paper to account for and eventually correct the turbulence overestimation that is responsible for the faster flow recovery that appears in the numerical predictions. Their effect on the power predictions is evaluated with comparison with existing wake measurements. A second issue addressed in this paper concerns multi‐wake predictions in wind farms, where the estimation of the reference wind speed that is required for the thrust calculation of a turbine located in the wake(s) of other turbines is not obvious. This is overcome by utilizing an induction factor‐based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are employed to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the case of five wind turbines in a row. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of wind turbine wake superposition models using Reynolds‐averaged Navier‐Stokes simulations

It is well accepted that the wakes created by upstream turbines significantly impact on the power production and fatigue loading of downstream turbines and that this phenomenon affects wind farm performance. Improving the understanding of wake effects and overall efficiency is critical for the optimisation of layout and operation of increasingly large wind farms. In the present work, the NREL 5‐MW reference turbine was simulated using blade element embedded Reynolds‐averaged Navier‐Stokes computations in sheared onset flow at three spatial configurations of two turbines at and above rated flow speed to evaluate the effects of wakes on turbine performance and subsequent wake development. Wake recovery downstream of the rearward turbine was enhanced due to the increased turbulence intensity in the wake, although in cases where the downstream turbine was laterally offset from the upstream turbine this resulted in relatively slower recovery. Three widely used wake superposition models were evaluated and compared with the simulated flow‐field data. It was found that when the freestream hub‐height flow speed was at the rated flow speed, the best performing wake superposition model varied depending according to the turbine array layout. However, above rated flow speed where the wake recovery distance is reduced, it was found that linear superposition of single turbine velocity deficits was the best performing model for all three spatial layouts studied.     

Investigation of terrain and wake effects on the performance of wind farms in complex terrain using numerical and experimental data

In this work, the combination effects on wind turbine performances of wakes and terrain‐driven flow are investigated. The test case is a subcluster of four turbines from a wind farm sited in southern Italy in a very complex terrain. The layout, the inter‐turbine distance and the wind rose result in a challenging performance scenery. The subcluster is analyzed, when the wind blows from the west, through computational fluid dynamics numerical simulations and experimental supervisory control and data acquisition data mining. Two wind intensity regimes and several simulation setups are employed. It is shown that the main effect of the terrain is the northward distortion of the wake of the upstream turbine. This explains the non‐trivial yawing patterns of the cluster and the fact that the wake line affects the overall performances of the subcluster less than it would do in flat terrain. It is further shown that the presence of the rest of the subcluster in operation southward deviates the wake line of the upstream turbine. The dependency on wind intensity of these directional distortions allows to estimate the relative importance of wakes and terrain‐driven flow. A bijective feedback between models and data is established and a convincing framework is constructed, for separating and assessing the effect of the terrain and of the single and multiple wake. Copyright © 2017 John Wiley & Sons, Ltd.     

Wake impacts on downstream wind turbine performance and yaw alignment

Aerodynamic wake interaction between commercial scale wind turbines can be a significant source of power losses and increased fatigue loads across a wind farm. Significant research has been dedicated to the study of wind turbine wakes and wake model development. This paper profiles influential wake regions for an onshore wind farm using 6 months of recorded SCADA (supervisory control and data acquisition) data. An average wind velocity deficit of over 30% was observed corresponding to power coefficient losses of 0.2 in the wake region. Wind speed fluctuations are also quantified for an array of turbines, inferring an increase in turbulence within the wake region. A study of yaw data within the array showed turbine nacelle misalignment under a range of downstream wake angles, indicating a characteristic of wind turbine behaviour not generally considered in wake studies. The turbines yaw independently in order to capture the increased wind speeds present due to the lateral influx of turbulent wind, contrary to many experimental and simulation methods found in the literature. Improvements are suggested for wind farm control strategies that may improve farm‐wide power output. Additionally, possible causes for wind farm wake model overestimation of wake losses are proposed.Copyright © 2012 John Wiley & Sons, Ltd.     

Large eddy simulation of dynamically controlled wind turbines in an offshore environment

Accurate modelling of transient wind turbine wakes is an important component in the siting of turbines within wind farms because of wake structures that affect downwind turbine performance and loading. Many current industry tools for modelling these effects are limited to empirically derived predictions. A technique is described for coupling transient wind modelling with an aero‐elastic simulation to dynamically model both turbine operation and wake structures. The important feature of this approach is a turbine model in a flow simulation, which actively responds to transient wind events through the inclusion of controller actions such as blade pitching and regulation of generator torque. The coupled nature of the aero‐elastic/flow simulation also allows recording of load and control data, which permits the analysis of turbine interaction in multiple turbine systems. An aero‐elastic turbine simulation code and a large eddy simulation (LES) solver using an actuator disc model were adapted for this work. Coupling of the codes was implemented with the use of a software framework to transfer data between simulations in a synchronous manner. A computationally efficient simulation was developed with the ability to model turbines exhibiting standard baseline control operating in an offshore environment. Single and multiple wind turbine instances were modelled in a transient flow domain to investigate wake structures and wake interaction effects. Blade loading data were analysed to quantify the increased fluctuating loads on downwind turbines. The results demonstrate the successful implementation of the coupled simulation and quantify the effect of the dynamic‐turbine model. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling the aerodynamics of vertical‐axis wind turbines in unsteady wind conditions

Most numerical and experimental studies of the performance of vertical‐axis wind turbines have been conducted with the rotors in steady, and thus somewhat artificial, wind conditions—with the result that turbine aerodynamics, under varying wind conditions, are still poorly understood. The vorticity transport model has been used to investigate the aerodynamic performance and wake dynamics, both in steady and unsteady wind conditions, of three different vertical‐axis wind turbines: one with a straight‐bladed configuration, another with a curved‐bladed configuration and another with a helically twisted configuration. The turbines with non‐twisted blades are shown to be somewhat less efficient than the turbine with helically twisted blades when the rotors are operated at constant rotational speed in unsteady wind conditions. In steady wind conditions, the power coefficients that are produced by both the straight‐bladed and curved‐bladed turbines vary considerably within one rotor revolution because of the continuously varying angle of attack on the blades and, thus, the inherent unsteadiness in the blade aerodynamic loading. These variations are much larger, and thus far more significant, than those that are induced by the unsteadiness in the wind conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

On the wake deflection of vertical axis wind turbines by pitched blades

Wake losses are a critical consideration in wind farm design. The ability to steer and deform wakes can result in increased wind farm power density and reduced energy costs and can be used to optimize wind farm designs. This study investigates the wake deflection of a vertical axis wind turbine (VAWT) experimentally, emphasizing the effect of different load distributions on the wake convection and mixing. A trailing vortex system responsible for the wake topology is hypothesized based on a simplified vorticity equation that describes the relationship between load distribution and its vortex generation; the proposed vorticity system and the resulting wake topology are experimentally validated in the wind tunnel via stereoscopic particle image velocimetry measurements of the flow field at several wake cross-sections. Variations in load distribution are accomplished by a set of fixed blade pitches. The experimental results not only validate the predicted vorticity system but also highlight the critical role of the streamwise vorticity component in the deflection and deformation of the wake, thus affecting the momentum and energy recoveries. The evaluation of the various loading cases demonstrates the significant effect of the wake deflection on the wind power available to a downwind turbine, even when the distance between the two turbines is only three diameters.     

Large‐eddy simulation of stable boundary layer turbulence and estimation of associated wind turbine loads

Stochastic simulation of turbulent inflow fields commonly used in wind turbine load computations is unable to account for contrasting states of atmospheric stability. Flow fields in the stable boundary layer, for instance, have characteristics such as enhanced wind speed and directional shear; these effects can influence loads on utility‐scale wind turbines. To investigate these influences, we use large‐eddy simulation (LES) to generate an extensive database of high‐resolution ( ～ 10 m), four‐dimensional turbulent flow fields. Key atmospheric conditions (e.g., geostrophic wind) and surface conditions (e.g., aerodynamic roughness length) are systematically varied to generate a diverse range of physically realizable atmospheric stabilities. We show that turbine‐scale variables (e.g., hub height wind speed, standard deviation of the longitudinal wind speed, wind speed shear, wind directional shear and Richardson number) are strongly interrelated. Thus, we strongly advocate that these variables should not be prescribed as independent degrees of freedom in any synthetic turbulent inflow generator but rather that any turbulence generation procedure should be able to bring about realistic sets of such physically realizable sets of turbine‐scale flow variables. We demonstrate the utility of our LES‐generated database in estimation of loads on a 5‐MW wind turbine model. More importantly, we identify specific turbine‐scale flow variables that are responsible for large turbine loads—e.g., wind speed shear is found to have a greater influence on out‐of‐plane blade bending moments for the turbine studied compared with its influence on other loads such as the tower‐top yaw moment and the fore‐aft tower base moment. Overall, our study suggests that LES may be effectively used to model inflow fields, to study characteristics of flow fields under various atmospheric stability conditions and to assess turbine loads for conditions that are not typically examined in design standards. Copyright © 2013 John Wiley & Sons, Ltd.