Generalized coupled wake boundary layer model: applications and comparisons with field and LES data for two wind farms

We describe a generalization of the coupled wake boundary layer (CWBL) model for wind farms that can be used to evaluate the performance of wind farms under arbitrary wind inflow directions, whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7 , 023115 (2015)) focused on aligned or staggered wind farms. The generalized CWBL approach combines an analytical Jensen wake model with a ‘top‐down’ boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub‐height obtained using both models converges in the ‘deep‐array’ portion (fully developed region) of the wind farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here, we present detailed comparisons of model predictions with large eddy simulation results and field measurements for the Horns Rev and Nysted wind farms operating over a wide range of wind inflow directions. Our results demonstrate that two‐way coupling between the Jensen wake model, and a ‘top‐down’ model enables the generalized CWBL model to predict the ‘deep‐array’ performance of a wind farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind farms than the original CWBL model, which increases the utility of the approach for wind farm designers. Copyright © 2016 John Wiley & Sons, Ltd.     

大型风电场尾流效应的耦合求解方法

针对大型风电场尾流评估问题,考虑大气边界层垂向动量输运和风电场内流动不均匀性,提出一种基于传统尾流模型和风电场边界层模型的耦合求解方法。采用Horns Rev风电场和青海锡铁山矿区风电场群实测数据对所提出的耦合方法进行验证,结果显示该方法可较为准确的评估大型风电场的场内、场间尾流效应,对大型风电场和集群化风电场开发具有重要理论和工程应用价值。     

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.     

An actuator sector method for efficient transient wind turbine simulation

This paper investigates a new method for transient simulation of flow through a wind turbine using an actuator technique. The aim, in the context of wind turbine wake simulation, is to develop an alternative to the widely used actuator disc model with an increased resolution and range of applications, for the same or less computational expense. In this new model, the actuator sector method, forces applied to the fluid are distributed azimuthally to maintain a continuous flow solution for increased time‐step intervals compared with the actuator line method. Actuator sector results are presented in comparison with actuator disc and actuator line models initially for a non‐dimensionalized turbine in laminar onset flow. Subsequent results are presented for a turbine operating in a turbulent atmospheric boundary layer. Results show significant increases in flow fidelity compared with actuator disc model results; this includes the resolution of diametric variation in rotor loading caused by horizontal or vertical wind shear and the helical vortex system shed from the turbine blade tips. Significant reductions in computational processing time were achieved with wake velocities and turbulence statistics comparable with actuator line model results. The actuator sector method offers an improved alternative to applications employing conventional actuator disc models, with little or no additional computational cost. This technique in conjunction with a Cartesian mesh‐based parallel flow solver leads to efficient simulation of turbines in atmospheric boundary layer flows. Copyright © 2014 John Wiley & Sons, Ltd.     

基于非均匀致动盘的风力机尾流模拟分析

针对常规致动盘方法中诱导因子均匀分布，而实际叶片的诱导因子沿径向变化的问题，提出了诱导因子非均匀分布的方法来模拟风力机的尾流流场。先以常规致动盘方法进行计算，根据理论和试验数据对比验证流场参数；在此基础上由叶片翼型参数求出诱导因子，根据其沿径向非均匀分布的特点进行计算，定性分析其尾流流场的特点及发展变化过程；最后，应用该方法分析两台同轴风力机在不同间距下所受到的影响。该研究结果可为风电场微观选址提供参考。     

基于非均匀致动盘的风力机尾流模拟分析

针对常规致动盘方法中诱导因子均匀分布,而实际叶片的诱导因子沿径向变化的问题,提出了诱导因子非均匀分布的方法来模拟风力机的尾流流场。先以常规致动盘方法进行计算,根据理论和试验数据对比验证流场参数;在此基础上由叶片翼型参数求出诱导因子,根据其沿径向非均匀分布的特点进行计算,定性分析其尾流流场的特点及发展变化过程;最后,应用该方法分析两台同轴风力机在不同间距下所受到的影响。该研究结果可为风电场微观选址提供参考。     

Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.     

The flow in the induction and entrance regions of lab-scale wind farms

With the increasing demand for wind energy, it is important to be able to understand and predict the available wind resources. To that end, the present wind tunnel study addresses the flow in the induction and entrance region of wind farms through particle image velocimetry, with focus on differences between actuator disks and two-bladed rotating wind turbine models. Both staggered and aligned farm layouts are examined for three different incoming wind directions. For each layout, 69 disks or turbines are used, and the field of view ranges from 12 rotor diameters upstream of the farms to 8 diameters downstream of the first row. The results show that the induction, or blockage effect, is higher for the disks, even though the thrust (or drag) coefficient is the same. In contrast, the wake is stronger downstream of the turbines. The orientation and layout of the farm do not have a major impact on the results. Modal decomposition of the flow shows that the flow structure similarity between the disk and turbines improves downstream of the second row of wake generating objects, indicating that the substitution of wind turbines by actuator disks is more appropriate for wind farms than for the investigation of single wakes.     

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.     

Simulation and wake analysis of a single vertical axis wind turbine

Because of several design advantages and operational characteristics, particularly in offshore farms, vertical axis wind turbines (VAWTs) are being reconsidered as a complementary technology to horizontal axial turbines. However, considerable gaps remain in our understanding of VAWT performance since cross‐flow rotor configurations have been significantly less studied than axial turbines. This study examines the wakes of VAWTs and how their evolution is influenced by turbine design parameters. An actuator line model is implemented in an atmospheric boundary layer large eddy simulation code, with offline coupling to a high‐resolution blade‐scale unsteady Reynolds‐averaged Navier–Stokes model. The large eddy simulation captures the turbine‐to‐farm scale dynamics, while the unsteady Reynolds‐averaged Navier–Stokes captures the blade‐to‐turbine scale flow. The simulation results are found to be in good agreement with three existing experimental datasets. Subsequently, a parametric study of the flow over an isolated VAWT, carried out by varying solidities, height‐to‐diameter aspect ratios and tip speed ratios, is conducted. The analyses of the wake area and velocity and power deficits yield an improved understanding of the downstream evolution of VAWT wakes, which in turn enables a more informed selection of turbine designs for wind farms. Copyright © 2016 John Wiley & Sons, Ltd.     

An experimental investigation on the effect of individual turbine control on wind farm dynamics

Individual wind turbines in a wind farm typically operate to maximize their performance with no consideration of the impact of wake effects on downstream turbines. There is potential to increase power and reduce structural loads within a wind farm by properly coordinating the turbines. To effectively design and analyze coordinated wind turbine controllers requires control‐oriented turbine wake models of sufficient accuracy. This paper focuses on constructing such a model from experiments. The experiments were conducted to better understand the wake interaction and impact on voltage production in a three‐turbine array. The upstream turbine operating condition was modulated in time, and the dynamic impact on the downstream turbine was recorded through the voltage output time signal. The flow dynamics observed in the experiments were used to improve a static wake model often used in the literature for wind farm control. These experiments were performed in the atmospheric boundary layer wind tunnel at the Saint Anthony Falls Laboratory at the University of Minnesota using particle image velocimetry for flow field analysis and turbine voltage modulation to capture the physical evolution in addition to the dynamics of turbine wake interactions. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Uncertainty quantification of infinite aligned wind farm performance using non‐intrusive polynomial chaos and a distributed roughness model

Uncertainty of wind farm parameters can have a significant effect on wind farm power output. Knowledge of the uncertainty‐produced stochastic distribution of the entire wind farm power output and the corresponding uncertainty propagation mechanisms is very important for evaluating the uncertainty effects on the wind farm performance during wind farm planning stage and providing insights on improving the performance of the existing wind farms. In this work, the propagation of uncertainties from surface roughness and induction factor in infinite aligned wind farms modeled by a modified distributed roughness model is investigated using non‐intrusive polynomial chaos. Stochastic analysis of surface roughness indicates that 30% uncertainty can propagate such that there is up a 8% uncertainty in the power output of the wind farm by affecting the uncertainty in the position of the individual wind turbines in the vertical boundary layer profile and uncertainty in vertical momentum fluxes which replenish energy in the wake in large wind farms. Induction factor uncertainty of the wind turbines can also have a significant effect on power output. Not only does its uncertainty substantially affect the vertical boundary layer profile, but the uncertainty in turbine wake growth which affects how neighboring turbine wakes interact. We found that optimal power output in terms of reduction of uncertainty closely correlates with the Betz limit and is dependent on the mean induction factor. Copyright © 2016 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。     

An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms

An experimental investigation was conducted for a better understanding of the wake interferences among wind turbines sited in wind farms with different turbine layout designs. Two different types of inflows were generated in an atmospheric boundary layer wind tunnel to simulate the different incoming surface winds over typical onshore and offshore wind farms. In addition to quantifying the power outputs and dynamic wind loads acting on the model turbines, the characteristics of the wake flows inside the wind farms were also examined quantitatively. After adding turbines staggered between the first 2 rows of an aligned wind farm to increase the turbine number density in the wind farm, the added staggered turbines did not show a significant effect on the aeromechanical performance of the downstream turbines for the offshore case. However, for the onshore case, while the upstream staggered turbines have a beneficial effect on the power outputs of the downstream turbines, the fatigue loads acting on the downstream turbines were also found to increase considerably due to the wake effects induced by the upstream turbines. With the same turbine number density and same inflow characteristics, the wind turbines were found to be able to generate much more power when they are arranged in a staggered layout than those in an aligned layout. In addition, the characteristics of the dynamic wind loads acting on the wind turbines sited in the aligned layout, including the fluctuation amplitudes and power spectrum, were found to be significantly different from those with staggered layout.     

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.     

Interaction between heterogeneous thermal stratification and wakes of wind turbine arrays

The thermal heterogeneity between the land and sea might affect the wind patterns within wind farms (WF) located near seashores. This condition was modeled with a large-eddy simulation of a numerical weather prediction model (Weather Research and Forecasting) that included the wind turbine actuator disk model (ADM). The assumed condition was that the downstream surface temperature was relatively higher (unstably stratified condition) than the neutrally stratified upstream wind. Under this condition, a thermal internal boundary layer (TIBL) was developed from an area where a step-changed surface temperature was implemented. The combined effect of the wake deficit due to the WF and velocity recovery as a result of enhanced mixing under unstable stratification showed significant modulation of the wind speed at the hub height when local atmospheric stability affected the wind turbine (WT). We show that TIBL height depends on the variables to be evaluated as the threshold. A precise prediction of the TIBL height is beneficial for better estimation of power generation. A prediction model was proposed as an extension of the internal boundary layer (IBL) model for neutral stratification, and the results tracked TIBL development reasonably well. The effects of WFs on surface properties (e.g., friction velocity, heat flux, and Obukhov length) and the tendency of IBL growth were minor. A single WT wake was also assessed under several TIBL developmental stages (i.e., location) and thermal stratification conditions. The standard deviation of the wake deficit increased vertically during the development stage of the TIBL. In contrast, the coefficients in the horizontal and vertical directions were comparable when the WT was deep inside the TIBL.     

Impact of different forest densities on atmospheric boundary‐layer development and wind‐turbine wake

The aim of this work is to investigate the atmospheric boundary‐layer (ABL) flow and the wind turbine wake over forests with varying leaf area densities (LAD). The forest LAD profile used in this study is based on a real forest site, Ryningsnäs, located in Sweden. The reference turbine used to model the wake is a well‐documented 5‐MW turbine, which is implemented in the simulations using an actuator line model (ALM). All simulations are carried out with openFOAM using the Reynolds averaged Navier‐Stokes (RANS) approach. Twelve forest cases with leaf area index (LAI) ranging from 0.42 to 8.5 are considered. Results show that the mean velocity decreases with increasing LAI within the forest canopy, but increases with LAI above the hub height. Meanwhile, the turbulent kinetic energy (TKE) varies nonmonotonically with forest density. The TKE increases with forest density and reaches to its maximum at an average LAI of 1.70, afterwards, it decreases gradually as the density increases. It is also observed that the forest density has a clear role in the wake development and recovery. Comparisons between no‐forest and forest cases show that the forest characteristics help in damping the added turbulence from the turbine. As a consequence, the forest with the highest upstream turbulence has the shortest wake downstream of the turbine.     

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.     

Large‐eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS)

A large‐eddy simulation framework, dubbed as the Virtual Wind Simulator (VWiS), for simulating turbulent flow over wind turbines and wind farms in complex terrain is developed and validated. The wind turbines are parameterized using the actuator line model. The complex terrain is represented by the curvilinear immersed boundary method. The predictive capability of the present method is evaluated by simulating two available wind tunnel experimental cases: the flow over a stand‐alone turbine and an aligned wind turbine array. Systematic grid refinement studies are carried out, for both single turbine and multi‐turbine array cases, and the accuracy of the computed results is assessed through detailed comparisons with wind tunnel experiments. The model is further applied to simulate the flow over an operational utility‐scale wind farm. The inflow velocities for this case are interpolated from a mesoscale simulation using a Weather Research and Forecasting (WRF) model with and without adding synthetic turbulence to the WRF‐computed velocity fields. Improvements on power predictions are obtained when synthetic turbulence is added at the inlet. Finally the VWiS is applied to simulate a yet undeveloped wind farm at a complex terrain site where wind resource measurements have already been obtained. Good agreement with field measurements is obtained in terms of the time‐averaged streamwise velocity profiles. To demonstrate the ability of the model to simulate the interactions of terrain‐induced turbulence with wind turbines, eight hypothetical turbines are placed in this area. The computed extracted power underscores the significant effect of site‐specific topography on turbine performance. Copyright © 2014 John Wiley & Sons, Ltd.