Reynolds number dependence of turbulence statistics in the wake of wind turbines

A wind tunnel experiment has been performed to quantify the Reynolds number dependence of turbulence statistics in the wake of a model wind turbine. A wind turbine was placed in a boundary layer flow developed over a smooth surface under thermally neutral conditions. Experiments considered Reynolds numbers on the basis of the turbine rotor diameter and the velocity at hub height, ranging from Re = 1.66 × 10⁴ to 1.73 × 10⁵. Results suggest that main flow statistics (mean velocity, turbulence intensity, kinematic shear stress and velocity skewness) become independent of Reynolds number starting from Re ≈ 9.3 × 10⁴. In general, stronger Reynolds number dependence was observed in the near wake region where the flow is strongly affected by the aerodynamics of the wind turbine blades. In contrast, in the far wake region, where the boundary layer flow starts to modulate the dynamics of the wake, main statistics showed weak Reynolds dependence. These results will allow us to extrapolate wind tunnel and computational fluid dynamic simulations, which often are conducted at lower Reynolds numbers, to full‐scale conditions. In particular, these findings motivates us to improve existing parameterizations for wind turbine wakes (e.g. velocity deficit, wake expansion, turbulence intensity) under neutral conditions and the predictive capabilities of atmospheric large eddy simulation models. Copyright © 2011 John Wiley & Sons, Ltd.     

LiDAR measurements for an onshore wind farm: Wake variability for different incoming wind speeds and atmospheric stability regimes

Wind measurements were performed with the UTD mobile LiDAR station for an onshore wind farm located in Texas with the aim of characterizing evolution of wind‐turbine wakes for different hub‐height wind speeds and regimes of the static atmospheric stability. The wind velocity field was measured by means of a scanning Doppler wind LiDAR, while atmospheric boundary layer and turbine parameters were monitored through a met‐tower and SCADA, respectively. The wake measurements are clustered and their ensemble statistics retrieved as functions of the hub‐height wind speed and the atmospheric stability regime, which is characterized either with the Bulk Richardson number or wind turbulence intensity at hub height. The cluster analysis of the LiDAR measurements has singled out that the turbine thrust coefficient is the main parameter driving the variability of the velocity deficit in the near wake. In contrast, atmospheric stability has negligible influence on the near‐wake velocity field, while it affects noticeably the far‐wake evolution and recovery. A secondary effect on wake‐recovery rate is observed as a function of the rotor thrust coefficient. For higher thrust coefficients, the enhanced wake‐generated turbulence fosters wake recovery. A semi‐empirical model is formulated to predict the maximum wake velocity deficit as a function of the downstream distance using the rotor thrust coefficient and the incoming turbulence intensity at hub height as input. The cluster analysis of the LiDAR measurements and the ensemble statistics calculated through the Barnes scheme have enabled to generate a valuable dataset for development and assessment of wind farm models.     

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。     

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.     

Observations of wind turbine wakes and surface roughness effects on wind flow variability

Wind data collected at nine meteorological towers at the Goodnoe Hills MOD-2 wind turbine site were analyzed to characterize the wind flow over the site both in the absence and presence of wind turbine wakes. Free-flow characteristics examined were the variability of wind speed and turbulence intensity across the site as a function of wind direction and surface roughness. The nine towers' data revealed that scattered areas of trees upwind of the site caused pronounced variations in the wind flow over the site. At two towers that were frequently downwind of an extensive grove of trees, up to 30% reductions in wind speed and a factor of 2 to 3 increase in turbulence intensity were measured. A substantial increase in the magnitude of the wind gusts, as well as a considerable decrease in the mean wind speed, was observed when a tower was downwind of the trees.Wind turbine wake characteristics analyzed included the average velocity deficits, wake turbulence, wake width, wake trajectory, vertical profile of the wake, and the stratification of wake properties as a function of the ambient wind speed and turbulence intensity. The wind turbine rotor disk spanned a height of 15 m to 107 m. The nine towers' data permitted a detailed analysis of the wake behavior at a height of 32 m at various downwind distances from 2 to 10 rotor diameters (D). The relationship between velocity deficit and downwind distance was surprisingly linear, with average maximum deficits ranging from 34% at 2 D to 7% at 10 D. Largest deficits were at low wind speeds and low turbulence intensities. Average wake widths were 2.8 D at a downwind distance of 10 D. Implications for turbine spacing are that, for a wind farm with a 10-D row separation, array losses would be significantly greater for a 2-D than a 3-D spacing because of incremental effects caused by overlapping wakes. Other interesting wake properties observed were the wake turbulence (which was greatest along the flanks of the wake). the vertical variation of deficits (which were greater below hub height than above), and the trajectory of the wake (which was essentially straight).     

Wind tunnel investigation on the effect of the turbine tower on wind turbines wake symmetry

In wind farms, the wake of the upstream turbines becomes the inflow for the downstream machines. Ideally, the turbine wake is a stable vortex system. In reality, because of factors like background turbulence, mean flow shear, and tower‐wake interaction, the wake velocity deficit is not symmetric and is displaced away from its mean position. The irregular velocity profile leads to a decreased efficiency and increased blade stress levels for the downstream turbines. The object of this work is the experimental investigation of the effect of the wind turbine tower on the symmetry and displacement of the wake velocity deficit induced by one and two in‐line model wind turbines (,D= 0.9 m). The results of the experiments, performed in the closed‐loop wind tunnel of the Norwegian University of Science and Technology in Trondheim (Norway), showed that the wake of the single turbine expanded more in the horizontal direction (side‐wall normal) than in the vertical (floor normal) direction and that the center of the wake vortex had a tendency to move toward the wind tunnel floor as it was advected downstream from the rotor. The wake of the turbine tandem showed a similar behavior, with a larger degree of non‐symmetry. The analysis of the cross‐stream velocity profiles revealed that the non‐symmetries were caused by a different cross‐stream momentum transport in the top‐tip and bottom‐tip region, induced by the turbine tower wake. In fact, when a second additional turbine tower, mirroring the original one, was installed above the turbine nacelle, the wake recovered its symmetric structure. Copyright © 2017 John Wiley & Sons, Ltd.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition

In this study, large-eddy simulations (LES) is combined with a turbine model to investigate all the terms in the budgets of mean and turbulent kinetic energy (TKE) inside and above very large wind farms. Emphasis is placed on quantifying the relative contribution of the thermal stratification in the free-atmosphere and wind-turbine spacing on the energy balance. The mean kinetic energy budget through the wind farms indicates that the magnitude of the kinetic energy entrainment form the free atmosphere into the boundary layer increases by increasing the density of the farms and decreasing the static stability in the free atmosphere, leading to larger power output from the wind farms. This entrainment is the only source of kinetic energy to balance that extracted by the turbines inside very large wind farms. In addition, it is shown that the distribution of the kinetic energy flux above the wind turbines, at top-tip level, is quite heterogeneous and its magnitude just behind the wind turbines is much larger due to the strong wind shear at that level. The simulation results also show that increasing the wind-farm density leads to an increase in the boundary-layer height, the ratio of the ageostrophic to the geostrophic velocity component inside the boundary layer, and the potential temperature near the surface. Detailed analysis of the TKE budget through the wind farms reveals also an important effect of the thermal stratification and wind turbine spacing on the magnitude and spatial distribution of the shear production, dissipation rate and transport terms. In particular, the shear production and dissipation rate have a peak at the turbine-top level, where the wind shear is largest, and their magnitude increases as the static stability in the free atmosphere and the wind-turbine spacing decrease.     

风力机三维尾流模型的提出与校核

针对大型风力机叶轮范围内风剪切效应突出以及当前工程尾流模型局限于二维空间而忽略垂直方向风速变化的问题,该文综合考虑风速和湍流强度切变效应对尾流的影响,在前期所发展的二维2D_K Jensen尾流模型的基础上,提出一种新型三维尾流模型。之后,新模型被应用于多种工况条件、多种类型的风力机尾流计算中,较为全面地验证其精度及适用性。通过与外场实测和其他高精度数值模拟的结果进行对比,表明新模型对流向、横风向和垂直向的尾流速度均具有良好的预测精度,将来可应用于大型风电场发电量评估和微观选址工作。     

Large‐eddy simulations of wind‐farm wake characteristics associated with a low‐level jet

In this study, we performed a suite of flow simulations for a 12‐wind‐turbine array with varying inflow conditions and lateral spacings, and compared the impacts of the flow on velocity deficit and wake recovery. We imposed both laminar inflow and turbulent inflows, which contain turbulence for the Ekman layer and a low‐level jet (LLJ) in the stable boundary layer. To solve the flow through the wind turbines and their wakes, we used a large‐eddy simulation technique with an actuator‐line method. We compared the time series for the velocity deficit at the first and rear columns to observe the temporal change in velocity deficit for the entire wind farm. The velocity deficit at the first column for LLJ inflow was similar to that for laminar inflow. However, the magnitude of velocity deficit at the rear columns for the case with LLJ inflow was 11.9% greater because of strong wake recovery, which was enhanced by the vertical flux of kinetic energy associated with the LLJ. To observe the spatial transition and characteristics of wake recovery, we performed statistical analyses of the velocity at different locations for both the laminar and LLJ inflows. These studies indicated that strong wake recovery was present, and a kurtosis analysis showed that the probability density function for the streamwise velocity followed a Gaussian distribution. In a quadrant analysis of the Reynolds stress, we found that the ejection and sweep motions for the LLJ inflow case were greater than those for the laminar inflow case.     

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.     

Synthetic atmospheric turbulence and wind shear in large eddy simulations of wind turbine wakes

A method of generating a synthetic ambient wind field in neutral atmosphere is described and verified for modelling the effect of wind shear and turbulence on a wind turbine wake using the flow solver EllipSys3D. The method uses distributed volume forces to represent turbulent fluctuations, superimposed on top of a mean deterministic shear layer consistent with that used in the IEC standard for wind turbine load calculations. First, the method is evaluated by running a series of large‐eddy simulations in an empty domain, where the imposed turbulence and wind shear is allowed to reach a fully developed stage in the domain. The performance of the method is verified by comparing the turbulence intensity and spectral distribution of the turbulent energy to the spectral distribution of turbulence generated by the IEC suggested Mann model. Second, the synthetic turbulence and wind shear is used as input for simulations with a wind turbine, represented by an actuator line model, to evaluate the development of turbulence in a wind turbine wake. The resulting turbulence intensity and spectral distribution, as well as the meandering of the wake, are compared to field data. Overall, the performance of the synthetic methods is found to be adequate to model atmospheric turbulence, and the wake flow results of the model are in good agreement with field data. An investigation is also carried out to estimate the wake transport velocity, used to model wake meandering in lower‐order models. The conclusion is that the appropriate transport velocity of the wake lies somewhere between the centre velocity of the wake deficit and the free stream velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Upwind preview to a horizontal axis wind turbine: a wind tunnel and field‐scale study

Data collected at the Eolos wind research facility and in the Saint Anthony Falls Laboratory atmospheric boundary layer wind tunnel are used to study the impact of turbulent inflow conditions on the performance of a horizontal axis wind turbine on flat terrain. The Eolos test facility comprises a 2.5MW Clipper Liberty C96 wind turbine, a meteorological tower and a WindCube LiDAR wind profiler. A second set of experiments was completed using particle image velocimetry upwind and in a wake of a miniature turbine in the wind tunnel to complement LiDAR measurements near the Eolos turbine. Joint statistics, most notably temporal cross‐correlations between wind velocity at different heights and turbine performance, are presented and compared at both the laboratory and field scales. The work (i) confirms that the turbine exerts a blockage effect on the mean flow and (ii) suggests a key, specific elevation, above hub height, where the incoming velocity signal is statistically most relevant to turbine operation and control. Wind tunnel measurements confirm such indication and suggest that hub height velocity measurements are optimal for wind preview and/or as input for active control strategies in aligned turbine configurations. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance and wake comparison of horizontal and vertical axis wind turbines under varying surface roughness conditions

A numerical study of both a horizontal axis wind turbine (HAWT) and a vertical axis wind turbine (VAWT) with similar size and power rating is presented. These large scale turbines have been tested when operating stand‐alone at their optimal tip speed ratio (TSR) within a neutrally stratified atmospheric boundary layer (ABL). The impact of three different surface roughness lengths on the turbine performance is studied for the both turbines. The turbines performance, the response to the variation in the surface roughness of terrain, and the most relevant phenomena involved on the resulting wake were investigated. The main goal was to evaluate the differences and similarities of these two different types of turbine when they operate under the same atmospheric flow conditions. An actuator line model (ALM) was used together with the large eddy simulation (LES) approach for predicting wake effects, and it was implemented using the open‐source computational fluid dynamics (CFD) library OpenFOAM to solve the governing equations and to compute the resulting flow fields. This model was first validated using wind tunnel measurements of power coefficients and wake of interacting HAWTs, and then employed to study the wake structure of both full scale turbines. A preliminary study test comparing the forces on a VAWT blades against measurements was also investigated. These obtained results showed a better performance and shorter wake (faster recovery) for an HAWT compared with a VAWT for the same atmospheric conditions.     

ENDOW (efficient development of offshore wind farms): modelling wake and boundary layer interactions

While experience gained through the offshore wind energy projects currently operating is valuable, a major uncertainty in estimating power production lies in the prediction of the dynamic links between the atmosphere and wind turbines in offshore regimes. The objective of the ENDOW project was to evaluate, enhance and interface wake and boundary layer models for utilization offshore. The project resulted in a significant advance in the state of the art in both wake and marine boundary layer models, leading to improved prediction of wind speed and turbulence profiles within large offshore wind farms. Use of new databases from existing offshore wind farms and detailed wake profiles collected using sodar provided a unique opportunity to undertake the first comprehensive evaluation of wake models in the offshore environment. The results of wake model performance in different wind speed, stability and roughness conditions relative to observations provided criteria for their improvement. Mesoscale model simulations were used to evaluate the impact of thermal flows, roughness and topography on offshore wind speeds. The model hierarchy developed under ENDOW forms the basis of design tools for use by wind energy developers and turbine manufacturers to optimize power output from offshore wind farms through minimized wake effects and optimal grid connections. The design tools are being built onto existing regional‐scale models and wind farm design software which was developed with EU funding and is in use currently by wind energy developers. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of tower and nacelle on the flow past a wind turbine

Large eddy simulations (LES) of the flow past a wind turbine with and without tower and nacelle have been performed at 2 tip speed ratios (TSR, ), λ=3 and 6, where the latter corresponds to design conditions. The turbine model is placed in a virtual wind tunnel to reproduce the “Blind test 1” experiment performed at the Norwegian University of Science and Technology (NTNU) closed‐loop wind tunnel. The wind turbine was modeled using the actuator line model for the rotor blades and the immersed boundary method for the tower and nacelle. The aim of the paper is to highlight the impact of tower and nacelle on the turbine wake. Therefore, a second set of simulations with the rotating blades only (neglecting the tower and nacelle) has been performed as reference. Present results are compared with the experimental measurements made at NTNU and numerical simulations available in the literature. The tower and nacelle not only produce a velocity deficit in the wake but they also affect the turbulent kinetic energy and the fluxes. The wake of the tower interacts with that generated by the turbine blades promoting the breakdown of the tip vortex and increasing the mean kinetic energy flux into the wake. When tower and nacelle are modeled in the numerical simulations, results improve significantly both in the near wake and in the far wake.     

Analytical model for predicting the performance of arbitrary size and layout wind farms

A simple engineering model for predicting wind farm performance is presented, which is applicable to wind farms of arbitrary size and turbine layout. For modeling the interaction of wind farm with the atmospheric boundary layer (ABL), the wind farm is represented as added roughness elements. The wind speed behind each turbine is calculated using a kinematic model, in which the friction velocity and the wind speed outside the turbine wake, constructed based on the wind farm‐ABL interaction model, are employed to estimate the wake expansion rate in the crosswind direction and the maximum wind speed that can be recovered within the turbine wake, respectively. Validation of the model is carried out by comparing the model predictions with the measurements from wind tunnel experiments and the Horns Rev wind farm. For all validation cases, satisfactory agreement is obtained between model predictions and experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

基于Park-Gauss模型考虑大气稳定性对布局优化的影响

基于Park模型尾流区线性膨胀假设和径向风速呈高斯分布假设,提出一种新的修正型的工程尾流模型Park-Gauss模型,采用小生境遗传算法,并考虑大气稳定性对风电场布局优化的影响。结果表明:对常风速单风向风电场微观选址布局优化结果是风力机组主要布置在垂直风向的第1排和最后1排;大气边界层稳定性对风电场微观选址布局优化影响显著,在大气边界层不稳定状态下,风电场安装机组总数最多、发电总量及风电场利用效率最高,中性状态和稳定状态依次次之。