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.     

Tailoring incoming shear and turbulence profiles for lab‐scale wind turbines

An active grid is used to generate a variety of turbulent shear profiles in a wind tunnel. The vertical bars are set to flap through varying angles across the test section producing a variation in the perceived solidity, resulting in a mean shear. The horizontal bars are used in a fully random operational mode to set the background turbulence level. It is demonstrated that mean velocity profiles with approximately the same shear can be produced with different turbulence intensities and local turbulent Reynolds numbers based on the Taylor microscale, λ. Conversely, it is also demonstrated that flows can be produced with similar turbulence intensity profiles but different mean shear. It is confirmed that the length scales and dynamics, the latter being assessed through the velocity spectra and probability density functions, do not vary significantly across the investigation domain. Such flows are of particular relevance for studies investigating the effect of in‐flow conditions on obstacles where these studies wish to decouple the effects of turbulence intensity and mean shear, a feat previously unattainable in experimental facilities. Given that the power output of wind turbines is known to be a function of both mean shear and turbulence intensity, the experimental methodology presented herein is invaluable to the wind turbine model testing community who, at present, cannot exert such control authority over the in‐flow conditions.     

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.     

LiDAR‐based characterization of mid‐altitude wind conditions for airborne wind energy systems

Engineers and researchers working on the development of airborne wind energy systems (AWES) still rely on oversimplified wind speed approximations and coarsely sampled reanalysis data because of a lack of high‐resolution wind data at altitudes above 200 m. Ten‐minute average wind speed LiDAR measurements up to an altitude of 1100 m and data from nearby weather stations were investigated with regard to wind energy generation and impact on LiDAR measurements. Data were gathered by a long‐range pulsed Doppler LiDAR device installed on flat terrain. Because of the low overall carrier‐to‐noise ratio, a custom‐filtering technique was applied. Our analyses show that diurnal variation and atmospheric stability significantly affect wind conditions aloft which cause a wide range of wind speeds and a multimodal probability distribution that cannot be represented by a simple Weibull distribution fit. A better representation of the actual wind conditions can be achieved by fitting Weibull distributions separately to stable and unstable conditions. Splitting and clustering the data by simulated surface heat flux reveals substate stratification responsible for the multimodality. We classify different wind conditions based on these substates, which result in different wind energy potential. We assess optimal traction power and optimal operating altitudes statistically as well as for specific days based on a simplified AWES model. Using measured wind speed standard deviation, we estimate average turbulence intensity and show its variation with altitude and time. Selected short‐term data sets illustrate temporal changes in wind conditions and atmospheric stratification with a high temporal and vertical resolution.     

Experimental study of the effect of turbulence on horizontal axis wind turbine aerodynamics

Incident flows on wind turbines are often highly turbulent, because these devices operate in the atmospheric boundary layer and often in the wake of other wind turbines. This article presents experimental investigations of the effects of a high turbulence level on wind turbine aerodynamics. Power and thrust are measured on a horizontal axis wind turbine model in the ‘Lucien Malavard’ wind tunnel. A grid is used to generate three turbulence levels (4·4%, 9% and 12%) with integral length scale of the order of magnitude of the chord length. Experiments show little effect of turbulence on the wind turbine model power and thrust. This can be justified by analysis of the aerodynamic loads along the blade. Copyright © 2005 John Wiley & Sons, Ltd.     

Variable‐sized wind turbines are a possibility for wind farm optimization

The potential benefits associated with harnessing available momentum and reducing turbulence levels in a wind farm composed of wind turbines of alternating size are investigated through wind tunnel experiments. A variable size turbine array composed of 3 by 8 model wind turbines is placed in a boundary layer flow developed over both a smooth and rough surfaces under neutrally stratified thermal conditions. Cross‐wire anemometry is used to capture high resolution and simultaneous measurements of the streamwise and vertical velocity components at various locations along the central plane of the wind farm. A laser tachometer is employed to obtain the instantaneous angular velocity of various turbines. The results suggest that wind turbine size heterogeneity in a wind farm introduces distinctive flow interactions not possible in its homogeneous counterpart. In particular, reduced levels of turbulence around the wind turbine rotors may have positive effects on turbulent loading. The turbines also appear to perform quite uniformly along the entire wind farm, whereas surface roughness impacts the velocity recovery and the spectral content of the turbulent flow within the wind farm. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessment of turbulence intensity of local wind regimes

This paper analyses the turbulence intensity of seven different sites in the coastal region of South Africa. The study is based on 12 months, 10-minute average wind speed measurement. The turbulence intensity is calculated using mean wind speed and the standard deviation method. Some of the key results show that generalised extreme value distribution gives the best fit to the turbulence intensity in the entire sites. The annual shape parameter of the distribution ranges from 0.11 at site WM06 to 0.3 at site WM05. The scale parameter varies from 3.55 at site WM04 to 6.06 at site WM02, while the location parameters span between 7.07 at site WM04 and 10.65 at site WM01. The annual turbulence intensity varies from 9.6% at site WM04 to 15.9% at site WM03. The result also reveals that sites with higher turbulence intensity have lower wind power potential and hence are less attractive for wind power application.     

Analysis of axial‐induction‐based wind plant control using an engineering and a high‐order wind plant model

Wind turbines are typically operated to maximize their performance without considering the impact of wake effects on nearby turbines. Wind plant control concepts aim to increase overall wind plant performance by coordinating the operation of the turbines. This paper focuses on axial‐induction‐based wind plant control techniques, in which the generator torque or blade pitch degrees of freedom of the wind turbines are adjusted. The paper addresses discrepancies between a high‐order wind plant model and an engineering wind plant model. Changes in the engineering model are proposed to better capture the effects of axial‐induction‐based control shown in the high‐order model. Copyright © 2015 John Wiley & Sons, Ltd.     

A Tomo‐PIV study of the effects of freestream turbulence on stall delay of the blade of a horizontal‐axis wind turbine

Volumetric velocity fields were measured using tomographic particle image velocimetry on a model of the blade of a 5 kW horizontal‐axis wind turbine to study the effects of freestream turbulence levels (FTLs) at 0.4%, 4% and 13% on stall delay phenomenon at two different global tip speed ratios of 3 and 5 with Reynolds number (Re) ? 5000. Static pressures were measured, and results illustrated that FTL has stronger effect on the surface pressures of the static airfoil. Magnitudes of the absolute velocities within the separated flows above the static airfoil's suction surface increase significantly with higher FTL, while the changes of these velocities above the rotating blade's surface are less obvious. Radial flows from rotating blade's root to tip were also observed with strong spanwise velocity component located in the vicinities of the vortices. At the root and middle sections of the rotating blade, the flows with strong radial velocity component, w, become wider with higher FTL near to the rotating blade's leading edge when the angles of attack (AOAs) are large. At large AOAs, the strength and size of the vortices shed from the rotating blade's leading and trailing edges decrease significantly with higher FTL. However, at small AOAs, the size and coherence of the vortices near the rotating blade's trailing edge increase significantly with higher FTL. Surface streamlines of the rotating blade illustrated that at the rotating blade's root region and at large AOAs, the streamlines tend to lean toward the rotating blade's trailing edge at higher FTL. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

De‐trending of wind speed variance based on first‐order and second‐order statistical moments only

The lack of efficient methods for de‐trending of wind speed resource data may lead to erroneous wind turbine fatigue and ultimate load predictions. The present paper presents two models, which quantify the effect of an assumed linear trend on wind speed standard deviations as based on available statistical data only. The first model is a pure time series analysis approach, which quantifies the effect of non‐stationary characteristics of ensemble mean wind speeds on the estimated wind speed standard deviations as based on mean wind speed statistics only. This model is applicable to statistics of arbitrary types of time series. The second model uses the full set of information and includes thus additionally observed wind speed standard deviations to estimate the effect of ensemble mean non‐stationarities on wind speed standard deviations. This model takes advantage of a simple physical relationship between first‐order and second‐order statistical moments of wind speeds in the atmospheric boundary layer and is therefore dedicated to wind speed time series but is not applicable to time series in general. The capabilities of the proposed models are discussed by comparing model predictions with conventionally de‐trended characteristics of measured wind speeds using data where high sampled time series are available, and a traditional de‐trending procedure therefore can be applied. This analysis shows that the second model performs significantly better than the first model, and thus in turn that the model constraint, introduced by the physical link between the first and second statistical moments, proves very efficient in the present context. © 2013 The Authors. Wind Energy Published by John Wiley & Sons Ltd.     

A new turbulence model for offshore wind turbine standards

Correct turbulence intensity modeling is crucial for fatigue load estimation for wind turbine structural design. It is well known that the International Electrotechnical Commission 61400‐3 Normal Turbulence Model recommended for offshore wind turbine design is not representative of offshore wind conditions. A new model is urgently needed as offshore wind energy is rapidly developing worldwide. After evaluating the suitability of the Normal Turbulence Model at three sites in Asia, Europe and the USA, it is found that wind–wave interaction and stability correction should be taken into account in modeling the offshore turbulence intensity and wind speed relationship. Therefore, a new turbulence intensity model, which models wind–wave interaction with the Charnock equation and adjusts for the influence of atmospheric stability through empirical turbulence scaling functions for the unstable atmospheric boundary layer, was developed. The new model is physically based and is tested against observations from the three sites. It shows better performance than the Normal Turbulence Model and hence is recommended to replace the Normal Turbulence Model. For model application, only two parameters are required, which are defined herein to represent offshore sites with high, medium and low turbulence intensities. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Model of wind shear conditional on turbulence and its impact on wind turbine loads

We analyse high‐frequency wind velocity measurements from two test stations over a period of several years and at heights ranging from 60 to 200 m, with the objective to validate wind shear predictions as used in load simulations for wind turbine design. A validated wind shear model is thereby proposed for flat terrain and that can significantly decrease the uncertainty associated with fatigue load predictions for wind turbines with large rotors. An essential contribution is the conditioning of wind shear on the 90% quantile of wind turbulence, such that the appropriate magnitude of the design fatigue load is achieved. The proposed wind shear model based on the wind measurements is thereby probabilistic in definition, with shear jointly distributed with wind turbulence. A simplified model for the wind shear exponent is further derived from the full stochastic model. The fatigue loads over different turbine components are evaluated under the full wind measurements, using the developed wind shear model and with standard wind conditions prescribed in the IEC 61400‐1 ed. 3. The results display the effect of the Wöhler exponent and reveal that under moderate turbulence, the effect of wind shear is most pronounced on the blade flap loads. It is further shown that under moderate wind turbulence, the wind shear exponents may be over‐specified in the design standards, and a reduction of wind shear exponent based on the present measurements can contribute to reduced fatigue damage equivalent loads on turbine blades. Although the influence of wind shear on extreme loads was found to be negligible, the IEC 61400‐1 wind shear definition was found to result in non‐conservative estimates of the 50 year extreme blade deflection toward the tower, especially under extreme turbulence conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Effective turbulence and its implications in wind turbine fatigue assessment

The effective turbulence approximation is widely used in the wind energy industry for site‐specific fatigue assessment of wind turbines with reference to loads. It significantly reduces the amount of aero‐elastic simulations required to document structural integrity by integrating out the directional variation of turbulence. Deriving the effective turbulence involves assumptions related to load effect histories, structural dynamics, and material fatigue strength. These assumptions may lead to low accuracy of fatigue load assessments by the effective turbulence compared with full directional simulations. This paper quantifies the implications of the effective turbulence for a multimegawatt wind turbine during normal operation. Analyses based on wind measurements from almost one hundred international sites document that the effective turbulence provides accurate results compared with full sector‐wise simulations, but only when linear SN ‐curves are assumed. For a more advanced steel tower design approach using a bilinear SN ‐curve, a reduction of the cross‐sectional design parameters by almost 10% is achieved. Additional 10% reduction can be obtained if fatigue damage is estimated utilizing the wind direction information. By applying a probabilistic approach, it is shown that this reduction in the design parameter of the steel tower does not compromise the structural integrity when the current IEC 61400‐1 standard is followed. The results presented may improve decision making in site‐specific fatigue assessments of wind turbines and prevent overconservative design, which results from the use of the effective turbulence, and thereby reduce the cost of wind energy.     

Adaptive post‐processing of short‐term wind forecasts for energy applications

We present a new method of reducing the error in predicted wind speed, thus enabling better management of wind energy facilities. A numerical weather prediction model, COSMO, was used to produce 48 h forecast data every day in 2008 at horizontal resolutions of 10 and 3 km. A new adaptive statistical method was applied to the model output to improve the forecast skill. The method applied corrective weights to a set of forecasts generated using several post‐processing methods. The weights were calculated based on the recent skill of the different forecasts. The resulting forecast data were compared with observed data, and skill scores were calculated to allow comparison between different post‐processing methods. The total root mean square error performance of the composite forecast is superior to that of any of the individual methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthetic turbulence modelling for offshore wind farm engineering models using coherence aggregation

Turbulent wind fields are known to be a major driver for structural loads and power fluctuations on offshore wind turbines. At the single-turbine scale, there exist well-established design standards based on wind spectra and coherence functions calibrated from years of measurements, which are used to generate multiple 10-min wind field realisations known as synthetic turbulence boxes, themselves used as input to turbine-scale aero-hydro-servo elastic codes. These methods are however not directly applicable at farm scale. When analysing the dynamics of large offshore wind farms, measurements reveal the importance of large, low-frequency turbulent vortices for power fluctuations and hence for wind farm control and grid integration. Also, farm-scale wind fields are needed as input to farm-scale aero-servo-elastic codes for the modelling of wake dynamics, affecting structural loads. These new concerns motivate an upgrade in the original turbine-scale wind field representation: (1) spectral models need to be based on farm-scale measurements, (2) the frozen-turbulence assumption merging temporal and along-wind coherence must be lifted, (3) simplifications are needed to reduce the number of degrees of freedom as the domain becomes excessively large. This paper suggests models and algorithms for aggregated farm-wide corrrelated synthetic turbulence generation—lumping the wind field into space-averaged quantities—adapted to the aero-hydro-servo elastic modelling of large offshore wind farms. Starting from the work of Sørensen et al. in the early 2000s for grid integration purposes, methods for structural load modelling (through wake meandering and high-resolution wind field reconstruction) are introduced. Implementation and efficiency matters involving mathematical subtleties are then presented. Finally, numerical experiments are carried out to (1) verify the approach and implementation against a state-of-the-art point-based—as opposite to aggregated—synthetic turbulence generation code and (2) illustrate the benefit of turbulence aggregation for the modelling of large offshore wind farms.     

Aerodynamic loads on wind turbine nacelles under different inflow turbulence conditions

The aerodynamic loads on wind turbine nacelles for range of inflow turbulence conditions are investigated. To this end, a series of wind tunnel experiments are conducted to investigate pressure field distributions over the surface of scaled models of rectangular and ellipsoidal nacelles. It is found that the mean pressure fields on the roof of the rectangular nacelle are similar for all the inflow turbulence cases for respective yaw angles. However, when yaw angle is around 90°, the mean pressure coefficient becomes more negative close to upstream edge with increasing inflow turbulence. For the ellipsoidal nacelle, the magnitude of the mean pressure coefficient increases with decreasing inflow turbulence in the adverse pressure gradient region, although the minimum peak pressure coefficient remains unaffected by inflow turbulence. The overall effect of wind‐induced load on the nacelle surfaces is evaluated by computing force coefficients from the pressure data. It is observed that the peak force coefficients for both rectangular and ellipsoidal nacelles increase with increasing inflow turbulence. The models for the estimation of peak aerodynamic loads on the nacelle surfaces are proposed as functions of inflow turbulence and mean force coefficients and show satisfactory agreement with measurements. Finally, the loads calculated by the GL guideline are compared against the measurements. It is found that the guideline estimation is conservative for design load case (DLC) 6.1, but it underestimates the load by about 35% for DLC 6.2 when the inflow turbulence intensity is 13.2%.     

Gaussian vs non‐Gaussian turbulence: impact on wind turbine loads

From large‐eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non‐Gaussian counterpart. Time series from the two types of turbulence are then used as input to wind turbine load simulations under normal operations with the HAWC2 software package. A slight increase in the extreme loads of the tower base fore‐aft moment is observed for high wind speeds when using non‐Gaussian turbulence but is insignificant when taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non‐Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low‐pass filter that averages out the non‐Gaussian behaviour, which is mainly associated with the fastest and smallest scales. Copyright © 2016 John Wiley & Sons, Ltd.     

Atmospheric turbulence and its influence on the alternating loads on wind turbines

Analysis of measurements on atmospheric turbulence with respect to the statistics of velocity increments reveals that the statistics are not Gaussian but highly intermittent. Here, we demonstrate that the higher quantity of extreme events in atmospheric wind fields transfers to alternating loads on the airfoil and on the main shaft in the form of torque fluctuations. For this purpose, alternating loads are discussed with respect to their increment statistics. Our conjecture is that the anomalous wind statistics are responsible for load changes, which may potentially contribute to additional loads and may cause additional fatigue. Our analysis is performed on three different wind field data sets: measured fields, data generated by a standard wind field model and data generated by an alternative model based on continuous time random walks, which grasps the intermittent structure of atmospheric turbulence in a better way. Our findings suggest that fluctuations in the loads might not be reflected properly by the standard wind field models. Copyright © 2010 John Wiley & Sons, Ltd.