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.     

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.     

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.     

沿海滩涂风力机近尾流风速分布特性研究

为获得风力机近尾流风速在垂直方向和水平方向的变化规律,提出一种测量风力机近尾流区风速的实测方法。针对某沿海滩涂风电场,采用2台搭载风速仪的无人机对近尾流区进行测量。结果表明：垂直方向,尾流和来流风速比值在1.0D~2.5D处（D为风轮直径）随着高度的增加呈先减小后增大的趋势,在轮毂中轴线处存在最小值0.53~0.68;风速比值沿轮毂中轴线呈非对称分布。0.5D处风速比值分别在上下风轮处存在2个极小值0.56和0.50。水平方向,风速比值在1.0D~3.0D处沿径向距离从左向右呈先减小后增大的趋势,在轮毂中轴线处存在最小值（0.54~0.78）;风速比值沿轮毂中轴线呈对称分布,随着风轮下游距离的增加呈扩张趋势。最后给出用于A类风场风力机下游尾流风速剖面的预测公式。     

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.     

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.     

Effects of inflow turbulence intensity and turbine arrangements on the power generation efficiency of large wind farms

In this study, we conduct a series of large‐eddy simulations (LESs) to study the impact of different incoming turbulent boundary layer flows over large wind farms, with a particular focus on the overall efficiency of electricity production and the evolution of the turbine wake structure. Five representative turbine placements in the large wind farm are considered, including an aligned layout and four staggered layouts with lateral or vertical offset arrangements. Four incoming flow conditions are used and arranged from the LESs of the ABL flow over homogeneous flat surfaces with four different aerodynamic roughness lengths (i.e., z0 = 0.5, 0.1, 0.01, and 0.0001 m), where the hub‐height turbulence intensity levels are about 11.1%, 8.9%, 6.8%, and 4.9%, respectively. The simulation results indicate that an enhancement in the inflow turbulence level can effectively increase the power generation efficiency in the large wind farms, with about 23.3% increment on the overall farm power production and up to about 32.0% increment on the downstream turbine power production. Under the same inflow condition, the change of the turbine‐array layouts can increase power outputs within the first 10 turbine rows, which has a maximum increment of about 26.5% under the inflow condition with low turbulence. By comparison, the increase of the inflow turbulence intensity facilitates faster wake recovery that raises the power generation efficiency of large wind farms than the adjustment of the turbine placing layouts.     

A numerical study of tilt‐based wake steering using a hybrid free‐wake method

This study investigates the potential of using tilt‐based wake steering to alleviate wake shielding problems experienced by downwind turbines. Numerical simulations of turbine wakes have been conducted using a hybrid free‐wake analysis combining vortex lattice method (VLM) and an innovative free‐wake model called constant circulation contour method (CCCM). Simulation results indicate tilting a horizontal axis wind turbine's shaft upward causes its wake to ascend, carrying energy‐depleted air upward and pumping more energetic replacement air into downstream turbines, thereby having the potential to recover downstream turbine power generation. Wake cross section vorticity and velocity distributions reveal that the wake upward transport is caused by the formation of near‐wake streamwise vorticity components, and furthermore, the wake velocity deficit is weakened because of the skewed wake structure. Beyond the single turbine wake simulation, an inline two‐turbine case is performed as an assessment of the wake steering influence on the two‐turbine system and as an exploratory work of simulating turbine‐wake interactions using the hybrid free‐wake model. Individual and total turbine powers are calculated. A comparison between different tilting angles suggests turbine power enhancement may be achieved by tilting the upstream turbine and steering its wakes away from the downstream turbine.     

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.     

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.     

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.     

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.     

Simulation comparison of wake mitigation control strategies for a two‐turbine case

Wind turbines arranged in a wind plant impact each other through their wakes. Wind plant control is an active research field that attempts to improve wind plant performance by coordinating control of individual turbines to take into account these turbine–wake interactions. In this paper, high‐fidelity simulations of a two‐turbine fully waked scenario are used to investigate several wake mitigation strategies, including modification of yaw and tilt angles of an upstream turbine to induce wake skew, as well as repositioning of the downstream turbine. The simulation results are compared through change relative to a baseline operation in terms of overall power capture and loading on the upstream and downstream turbine. Results demonstrated improved power production for all methods. Analysis of control options, including individual pitch control, shows potential to minimize the increase of, or even reduce, turbine loads.Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

A wind‐tunnel study of the wake development behind wind turbines over sinusoidal hills

In the present work, the wake development behind small‐scale wind turbines is studied when introducing local topography variations consisting of a series of sinusoidal hills. Additionally, wind‐tunnel tests with homogeneous and sheared turbulent inflows were performed to understand how shear and ambient turbulence influence the results. The scale of the wind‐turbine models was about 1000 times smaller than full‐size turbines, suggesting that the present results should only be qualitatively extrapolated to real‐field scenarios. Wind‐tunnel measurements were made by means of stereoscopic particle image velocimetry to characterize the flow velocity in planes perpendicular to the flow direction. Over flat terrain, the wind‐turbine wake was seen to slowly approach the ground while it propagated downstream. When introducing hilly terrain, the downward wake deflection was enhanced in response to flow variations induced by the hills, and the turbulent kinetic energy content in the wake increased because of the speed‐up seen over the hills. The combined wake observed behind 2 streamwise aligned turbines was more diffused and when introducing hills, it was more prone to deflect towards the ground compared to the wake behind an isolated turbine. Since wake interactions are common at sites with multiple turbines, this suggested that it is important to consider the local hill‐induced velocity variations when onshore wind farms are analysed. Differences in the flow fields were seen when introducing either homogeneous or sheared turbulent inflow conditions, emphasizing the importance of accounting for the prevailing turbulence conditions at a given wind‐farm site to accurately capture the downstream wake development.     

Optimization of turbine design in wind farms with multiple hub heights,using exact analytic gradients and structural constraints

Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9% reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2%. Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.     

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).     

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.     

An experimental study on the effects of winglets on the tip vortex interaction in the near wake of a model wind turbine

An experimental study of the near wake up to four rotor diameters behind a model wind turbine rotor with two different wing tip configurations is performed. A straight‐cut wing tip and a downstream‐facing winglet shape are compared on the same two‐bladed rotor operated at its design tip speed ratio. Phase‐averaged measurements of the velocity vector are synchronized with the rotor position, visualizing the downstream location of tip vortex interaction for the two blade tip configurations. The mean streamwise velocity is found not to be strongly affected by the presence of winglet tip extensions, suggesting an insignificant effect of winglets on the time‐averaged inflow conditions of a possible downstream wind turbine. An analysis of the phase‐averaged vorticity, however, reveals a significantly earlier tip vortex interaction and breakup for the wingletted rotor. In contradistinction, the tip vortices formed behind the reference configuration are assessed to be more stable and start merging into larger turbulent structures significantly further downstream. These results indicate that an optimized winglet design can not only contribute to a higher energy extraction in a rotor's tip region but also can positively affect the wake's mean kinetic energy recovery by stimulating a faster tip vortex interaction.