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Aerodynamics of wind turbine wakes in flat and complex terrains
Renewable Energy 85 (2016) 454e463
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Aerodynamics of wind turbine wakes in flat and complex terrains B. Subramanian*, N. Chokani, R.S. Abhari Laboratory for Energy Conversion, Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2014 Received in revised form 5 May 2015 Accepted 24 June 2015 Available online xxx
The wake evolution measured downstream of multi-megawatt wind turbines located in flat and complex terrains are described here. These high-resolution measurements at full-scale Reynolds number conditions are made with an instrumented drone that is equipped with a suite of sensors and detail the characteristics of the mean flow and turbulent kinetic energy in the evolving wake. Reynolds decomposition yields the nature of turbulent fluctuations in surface layer, and this decomposition is used to detail the turbulence statistics, degree of anisotropy and friction velocity. These measurements are shown to be suited for the further development of three-dimensional wake models that are currently under intensive development. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Experimental Drone Wake Wind Turbulence
1. Introduction The expansion of wind energy across Europe is mainly driven by the European Union's 2020 target of generating 20% of its energy from renewable sources [1]. As the wind energy market matures, flat sites with good winds are becoming increasingly scarce, thus sites in complex terrain with moderate winds are increasingly of interest. Such sites, which were previously considered suboptimal for investment, have gained prominence in recent years [2]. However, wind resource assessment in complex terrain is challenging, due to limited field measurement data and due to the difficulty in the accurate modelling of flow in complex terrain [3,4]; thus there are higher uncertainties in wind resource estimates in complex terrain compared to flat terrain [2]. These higher uncertainties often result in a mismatch between the predicted annual energy yield and the actual annual energy yield e which consequently result in larger risk in the development of wind farm projects. Furthermore the loads on wind turbines located in complex terrain are higher due to higher wind shear and increased levels of turbulence, thus resulting in a reduced lifetime of wind turbine components [5]. Micrositing of wind turbines in complex terrain is further complicated by the fact that the flow downstream of a wind turbine is highly unsteady and three-dimensional. This highlights the need to understand the flow behaviour in two important
* Corresponding author. E-mail address: [email protected] (B. Subramanian). http://dx.doi.org/10.1016/j.renene.2015.06.060 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
areas e one is the behaviour of atmospheric boundary layer close to ground in complex terrain and the second is the wind turbine wake behavior in different terrains including its interactions with other downstream turbines. In recent years, wake evolution in flat and complex terrains has been a topic of focus that requires improved modelling for optimised wind farm layouts [6,7]. Thus there have been efforts directed to the development of both semi-empirical wake models [8e11] and more complete field models ([12] and [13]) to predict the evolution of wakes in wind farms located in different terrain conditions. As wind farms in both complex terrain and flat terrain operate inside the turbulent atmospheric boundary layer, an understanding of the nature and structure of turbulence in the different terrains is needed. As there are several discrepancies between predictions and measurements, there continues to be a need for full-scale measurements in order to validate and calibrate the prediction methods [14]. While wind tunnel and water tunnel tests provide an environment to conduct detailed parametric studies under carefully controlled conditions, their Reynolds number is at least one order of magnitude smaller than in full-scale conditions, this may be a concern regarding the widespread applicability of sub-scale experiments. Indeed the scale of the Reynolds number is relevant in physical process such as turbulent mixing, the entrainment of kinetic energy, the evolution and breakdown of tip vortices, etc, all of which are features of wakes in wind farms. The present work extends the authors prior work [15,16] with detailed measurements of the wake up to six diameters in flat and complex terrains. Thus the primary objective of this work is to detail and distinguish the
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Nomenclature
455
su0 ; sv0 ; sw0 standard deviation of velocity fluctuations density t integral time scale L integral length scale l tip speed ratio
r D f, F P, P0 u2 , V Vf V0 X Y Z ZHH pv u, v, w
rotor diameter frequency static pressure wind speed in Earth's frame of reference FRAP air speed SCADA 10-min average wind speed longitudinal axis (along rotor axis) lateral axis vertical axis hub height vortex pitch unfiltered velocity components, u along streamwise and w is in vertical direction 0 0 0 u ; v ; w resolved stochastic fluctuations u; v; w mean velocity components u* friction velocity t0 time
vortex structure and mixing properties of wakes in flat and complex terrains. The structure of the paper is as follows. In the next section, the wind farms and instrumented drone are described. The results are then presented and discussed in detail. The paper finally concludes with a summary of the key observations.
2. Description of measurement sites The drone based wind measurements are carried out at the Mont Crosin wind farm in Switzerland, which is located in complex terrain at an average elevation of 1250 m AGL. Fig. 1 shows the layout of wind turbines at the Mont Crosin wind farm on an aerial imagery from Google map, a digital elevation map and a land cover map. The locations of the wind turbines are shown by circle symbols; the turbine at which measurements are made is shown as a filled white circle, whereas the other turbines are shown as filled black circles. This wind farm is located in complex terrain, with patches of dense, tall coniferous forest surrounding the wind farm. During the measurements, the predominant wind direction observed at the Mont Crosin wind farm was from North-East and the wind direction changed overall by no more than 10 , with wind speeds in the range of 5e9 m/s. Thus the turbine at which measurements were made was not in the wake of any other turbine. The turbine at which measurements are made is a 2 MW Vestas V90 wind turbine. The rotor diameter is 90 m and hub height is 95 m AGL, with cut-in and cut-out wind speeds of 4 m/s and 25 m/s respectively. The location of this wind turbine is indicated with a white dot at center in Fig. 1. The wind turbine has an automatic yaw control system, which aligns the rotor into the incoming wind direction. The wind farm operator provided access to the turbine's 10-min average SCADA data, which were used for comparison to supplement the drone based wind measurements. The second wind farm is the Altenbruch II wind farm in northern Germany. The wind farm is located in flat terrain at a distance of 5 km from the North Sea coast, Fig. 2. The locations of the nine wind turbines in the wind farm are shown by the circle symbols in Fig. 2; the turbine at which measurements are made, shown as a filled white circle, is a Vestas V90 with a rated power 3.0 MW and a hub height of 105 m AGL. The other turbines are shown as filled black circles. During the measurements at the
Abbreviations AGL above ground level DA Degree of anisotropy FRAP Fast response aerodynamic probe GPS global positioning system GUM guide to uncertainty in measurements HH hub height IMU inertial measurement unit MW megawatt Pdf probability density function SCADA supervisory control and data acquisition STFT short-time Fourier transform TKE turbulent kinetic energy
Altenbruch II wind farm, the predominant wind direction was from South-West and the wind direction changed overall by no more than 8 , with average wind speeds of 8 m/s. In addition to the measurements at the two above wind farms, freestream measurements at two other wind farms are also reported here. The first of these is FreudenbergeBeiersdorf wind farm in Brandenburg, Germany that is in a flat terrain and surrounded by patches of dense tall coniferous trees. The second of these wind farms is at Collonges, Switzerland. The Collonges wind farm is in a valley, that extends approximately northwest-southwest, and has hills on its sides rising up to 2500 m AGL. Thus this second site is in complex terrain. Table 1 summarises the characteristics of these two wind farms.
3. Drone measurement system The unsteady, three-dimensional flow field around the wind turbine is measured using drones instrumented with a sevensensor fast response aerodynamic probe. The drones are detailed elsewhere [15,16] but some salient characteristics are summarised in Table 2. The seven-sensor fast response aerodynamic probe that is used for wind measurements is described in detail by Mansour et al. [17]. The sensing elements of the probe are miniaturised silicon piezo-resistive chips, which are encapsulated into a 20 mm hemispherical probe head, and are installed on a cylindrical shaft to give an overall probe length of 70 mm. The probe's measurement chain consists of the sensing elements, power supply units, signal conditioners, a 14-channel 24 bit analog-to-digital converter (sampling at upto 500 Hz) and an on-board flash card for data storage. The aerodynamic calibration of the probe was carried out in a fully automated free-jet facility at ETH Zurich [18], and yields less than 0.1% relative error in angles and dynamic pressure. The drone's on-board autopilot system, which is based on Paparazzi [19], is used for fully autonomous flight. Other components in the hardware suite include an absolute pressure sensor (with resolution of ±1.2 Pa), an ambient temperature sensor (with a resolution of 0.01 C), humidity sensor (with accuracy of 1.8%), IMU (with angular accuracy of 2%), a GPS (with position accuracy of 3 m) and a magnetometer (with an accuracy of 1 ). The hardware suite transmits data in real-time through an on-board modem, and the data is logged on a ground-based computer. At a cruise speed of
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Fig. 1. Layout of the wind turbines at Mont Crosin wind farm (complex terrain) are shown on the aerial imagery from Google map (top), digital elevation map (middle) and land cover map (bottom). The circle symbols show the locations of the wind turbines.
20 m/s, the uncertainty in the airspeed measured by the FRAP probe is less than 0.05 m/s. The overall uncertainty of wind speed measurements in Earth's frame of reference obtained from GUM analysis is 0.7 m/s. The approach for computation of wind speed in Earth's frame of reference and the trajectories for measuring in both the near- and far-wake are discussed elsewhere [16,20]. The coordinate system employed here has the wind turbine at the origin (0, 0) facing the upstream wind that flows from the negative X/D axis towards the positive X/D axis. The wake evolves along the positive X/D axis and the Z-axis is used to represent the vertical height above ground level at the base of wind turbine tower. The drone takes about 10 min to scan one azimuthal measurement plane. The term ‘wind speed’ is used to denote the total wind speed in Earth frame of reference.
Fig. 2. Layout of the wind turbines at Altenbruch II wind farm (flat terrain) are shown on the aerial imagery from Google map (top), digital elevation map (middle) and land cover map (bottom). The circle symbols show the locations of the wind turbines.
4. Methodology The unsteady measurements of wind velocity along the drone's trajectory are separated into mean and fluctuating parts using Reynolds decomposition. In the three spatial directions the decompositions are 0
u¼ uþ u 0 v¼ vþ v 0 w¼ wþ w
(1)
where, the velocity components u, v and w are defined along the coordinate axes X, Y, and Z, with the X-axis oriented in the main
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Table 1 Summary characteristics of the Freudenberg-Beiersdorf, Germany and Collonges, Switzerland wind farms. Wind farm
Wind turbine
Diameter (m)
Hub height (m)
Terrain
Ground elevation (m)
Freudenberg-Beiersdorf Collonges
V80 E70
80 70
100 100
Flat Complex
95 448
Table 2 Summary characteristics of drone. Drone
Take-off mass (g)
Wing span (mm)
Endurance (minutes)
Funjet windFlyer
900 2700
795 2300
30 120
wind direction. By definition, u0 ¼ v0 ¼ w0 ¼ 0. As the wind velocity is non-stationary, an ensemble average is computed with an averaging time of t0 ¼ 0.2 s in all cases to separate the mean and fluctuating parts. The fluctuating parts are obtained directly from the wind velocity measured in the drone's frame of reference assuming that the drone's inertial response time is larger than t0 ¼ 0.2 s. In the wake of a wind turbine, the turbulent fluctuations contain both periodic (deterministic) and stochastic parts. The turbulent kinetic energy (TKE) along the drone's trajectory is then computed from the sum of square of the fluctuating parts,
TKE ¼
1 02 u þ v02 þ w02 2
(2)
Alternatively, the turbulent kinetic energy can also be computed from short time Fourier Transform (STFT) as reported earlier [15,16]; both approaches yield the same TKE. In order to quantify the departure from isotropy, the degree of anisotropy (DA) is evaluated as [21]. 0
DA ¼
2u 2 02
0
v þ w2
(3)
5. Results 5.1. Wake evolution in complex terrain versus flat terrain The streamwise evolution of the wake in complex terrain upto four diameters downstream is shown in Fig. 3a in terms of wind speed and turbulent kinetic energy. The measurements are made at hub height in a horizontal plane at the Mt. Crosin wind farm, which is in complex terrain. In comparison, the streamwise evolution of the wake in the flat terrain of the Altenbruch II wind farm is shown in Fig. 3b. The measurements are made in a vertical plane up to six diameters downstream. During measurements in complex terrain, the SCADA reported wind speed, V0, was 7.2 m/s and the corresponding wind direction was 45 (North-East). In flat terrain case, the SCADA recorded a wind speed of 8 m/s and a wind direction of 238 (South-West). In complex terrain, the turbulent kinetic energy (Fig. 3a) in the near-wake, X/D < 2, shows the evolution of the tip vortex that is identified in the high turbulent kinetic energy regions that are shed from the wind turbine blade tip. For X/D < 1, the tip vortices are convected downstream close to a span of Y/D ¼ 0.68 parallel to the direction of upstream wind. At X/D ¼ 1, the tip vortices start to migrate spanwise, that is along the direction of the negative Y/D axis, due to the wake's expansion to reach Y/D ¼ 0.75 at X/D ¼ 1.5. In the near-wake, the wind speed, shown in Fig. 3a, shows the presence of a thin shear layer that separates the low energy flow
within the wake boundary and the high energy flow outside the wake. Downstream of X/D ¼ 2, mixing starts within the wake and is manifested by the penetration of high energy flow from the wake's boundary into the relatively low energy flow within wake. This mixing and re-energisation is also seen in the measured wind speeds, as relatively high speed flow from outside the wake penetrates into the low speed wake downstream of X/D ¼ 2. The mixing of the flow affects the entire wake region downstream of X/ D ¼ 2.7. In flat terrain (Fig. 3b), the wind speed and turbulent kinetic energy evolution shows similar characteristic behaviour [16]. The streamwise extent of the near-wake in complex terrain is approximately X/D ¼ 2. This extent is one-diameter shorter than the extent of the near-wake observed in flat terrain in Fig. 3b, where the near wake extends to X/D ¼ 3. The streamwise evolution of wake is quantified in terms of the area-averaged wind speed and turbulent kinetic energy as shown in Fig. 3c. The area-averages are derived from the flow properties in the planes that are shown in Fig. 3a and b. In the near wake, the area-averaged wind speed is 50e60% of the reference wind speed in both flat and complex terrains. In both terrains, the areaaveraged wind speed initially decreases in the near-wake, but then increases in the far wake. In complex terrain the wind speed increases at the rate of 10% per diameter to reach 64% at X/D ¼ 3.75. In flat terrain the area-averaged wind speed is 60% of the reference wind speed in the near-wake up to X/D ¼ 3, and then the wind speed starts to recover at a rate of 10% per diameter distance downstream up to X/D ¼ 5.5 where the wind speed is 80% of the reference wind speed. Thus, the streamwise extent of the near wake is shorter in complex terrain than in flat terrain by one diameter. The area-averaged turbulent kinetic energy also decreases as the wake evolves in both terrains; in complex terrain the area-averaged turbulent kinetic energy is 0.075 m2/s2 in the nearwake (X/D < 2). The area-averaged turbulent kinetic energy increases from 0.07 m2/s2 at X/D ¼ 2 to 0.18 m2/s2 at X/D ¼ 2.7; over this range, 2 < X/D < 2.7, a recovery in wind speed is also seen. The area-averaged turbulent kinetic energy then increases to reach 0.1 m2/s2 at X/D ¼ 3.7. In the complex terrain of Mt. Crosin wind farm, the ensemble-averaged freestream turbulent kinetic energy measured at hub height is 0.04 m2/s2. Thus, at the end of near wake, the turbulent kinetic energy is about two times higher than in freestream. The area-averaged turbulent kinetic energy at X/ D ¼ 3.75 in the far wake is still two-and-half times larger than the turbulent kinetic energy measured in the freestream. In flat terrain the area-averaged turbulent kinetic energy also decreases as the wake evolves. There is initially a decrease in the near-wake to 0.075 m2/s2 at 2.8D, followed by increase to 0.12 m2/s2 at X/D ¼ 3.7. The region between X/D ¼ 3 and X/D ¼ 5.5 is where enhanced flow mixing occurs and this is the reason for the increase in wind speed, and the increase/decrease that is observed in the area-averaged turbulent kinetic energy. Further downstream at X/D ¼ 6, the area-averaged turbulent kinetic energy is again 0.075 m2/s2. As the velocity and pressure fields can be measured with high resolution using the FRAP probe, Fig. 4a, the streamwise evolution of tip vortices in the flat terrain of Altenbruch II wind farm and complex terrain of Mt. Crosin wind farm are compared in terms of the air speed and static pressure. The measurements in flat terrain are made at a spanwise position of Y/D ¼ 0 and at a height of
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Fig. 3. (a) Measurements of turbulent kinetic energy and wind speed at hub height in a horizontal plane downstream of a wind turbine at Mt. Crosin wind farm, (b) Measurements of turbulent kinetic energy and wind speed at hub height in a vertical plane downstream of a wind turbine at Altenbruch II wind farm, (c) Streamwise evolution of spatiallyaveraged wind speed and spatially-averaged turbulent kinetic energy in wake in flat and complex terrains.
(Z e ZHH)/D ¼ 0.5, and the measurements in complex terrain are made at a spanwise position of Y/D ¼ 0.6 and at a height of (Z e ZHH)/D ¼ 0. The tip vortices can be identified from the sharp drops in air speed and/or pressure. In the flat terrain case, three consecutive tip vortices are captured; where as in the complex terrain two consecutive tip vortices are captured. A meaningful parameter used to examine the tip vortices is the so-called vortex pitch, pv , which describes the axial distance that a vortex is transported during one blade revolution. As the vortex pitch per blade is three times the separation distance of consecutive vortices in Fig. 4a, the measurements can be used to validate Wood's [22] empirical formulation.
pv z
1 þ u2 2l
(4)
As seen in Fig. 4b, Wood's formulation over predicts the vortex pitch by 33% in flat terrain, and under predicts the vortex pitch by 23% in complex terrains. Thus the formulation cannot be considered to universal applicability. The distribution of turbulent kinetic energy in two vertical planes in complex terrain is shown in Fig. 5. The first plane is upstream at X/D ¼ 1.5 and the second plane is downstream at X/ D ¼ 0.5. The measurements are accomplished by flying the drone alternatively upstream and downstream at altitudes ranging
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Fig. 5. Measurements in complex terrain of (a) Turbulent kinetic energy upstream of turbine at X/D ¼ 1.5, (b) Turbulent kinetic energy in near-wake at X/D ¼ 0.5, (c) Yaw angle in near-wake at X/D ¼ 0.5.
Fig. 4. (a) Streamwise profiles of static pressure and air speed in flat terrain at Y/D ¼ 0, (Z e ZHH)/D ¼ 0.5 and in complex terrain at Y/D ¼ 0.6, (Z e ZHH)/D ¼ 0. (b) Comparison of measured and predicted vortex pitches in flat and complex terrains.
from 0.45<(Z e ZHH)/D < 0.5. During this measurement, the SCADA 10-min average wind speed was 6.5 m/s with wind from East to West direction. The turbulent kinetic energy upstream at X/ D ¼ 1.5 (Fig. 5a) shows the characteristics of turbulent flow upstream of the wind turbine in complex terrain. The area-averaged turbulent kinetic energy in the upstream plane is 0.03 m2/s2. Downstream at X/D ¼ 0.5 (Fig. 5b) high turbulent kinetic energy regions that are associated with the tip vortices are seen. The perimeter of the rotor tip is shown as a white circle. These vortical structures originate from blade tips and convected downstream. The variations in the turbulent kinetic energy in wake is nearly symmetrical about a vertical axis located at Y/D ¼ 0.1 indicating that there is a yaw misalignment between the wind turbine and the main wind direction. The annular-shaped region of high turbulent kinetic energy in Fig. 5b indicates the radial extent of the wake at X/ D ¼ 0.5. In the near wake, regions of low turbulent kinetic energy characterize the freestream outside the wake and within the wake. The distribution of the yaw angle downstream at X/D ¼ 0.5 is shown in Fig. 5c. The yaw angle shows that the high turbulent kinetic energy regions identified in Fig. 5b are surrounded by pairs of positive and negative yaw angle zones; these pairs confirm that the previously identified regions of high turbulent kinetic energy are vortical structures. The mirror image of diametrically opposite yaw angle pairs indicates that the vortical structures are rotating in opposite directions.
The distribution of turbulent kinetic energy in two vertical planes in complex terrain, one located in upstream at X/D ¼ 1 and the other located in downstream at X/D ¼ 1, is shown in Fig. 6. The SCADA 10-min average wind speed during this measurement was 7 m/s and the wind direction was 77. For this wind direction, there is another Vestas V90 wind turbine located seven diameters upstream, at X/D ¼ 7, of the turbine located at X/D ¼ 0. Thus, the upstream measurement plane located at X/D ¼ 1 is six diameters downstream of the wind turbine located at X/D ¼ 7. Fig. 6a shows the turbulent nature of wake flow seen by a wind turbine rotor located six diameters downstream of another wind turbine in complex terrain. At X/D ¼ 1, the wake flow is completely mixed out with no distinct signatures of upstream wind turbine. The area average turbulent kinetic energy at X/D ¼ 1 is 0.07 m2/s2, which is more than two times greater than the area averaged upstream turbulent kinetic energy discussed in Fig. 5a. Downstream at X/ D ¼ 1 (Fig. 6b) high turbulent kinetic energy regions that are associated with vortical structures are seen. The perimeter of the rotor tip is shown as a white circle. This distribution of turbulent kinetic energy also confirms that mixing has already started within the wake on one side (for Y/D > 0) and there is no symmetry in the distribution of turbulent kinetic energy at X/D ¼ 1. It can also be seen in Fig. 6b that some tip vortices have strayed out of the wake shear layer into the freestream.
6. Comparison of turbulence structure in flat and complex terrains Fig. 7 compares the turbulence structure at hub height upstream and in the wake of a turbine in complex terrain. In the wake the
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Fig. 6. Measurements in complex terrain of (a) Turbulent kinetic energy contour upstream at X/D ¼ 1, (b) Turbulent kinetic energy in near-wake at X/D ¼ 1.
measurements are made at hub height from X/D ¼ 1.5 to X/D ¼ 4.5. On the left side of Fig. 7 are scatter plots of spanwise velocity fluctuations versus the streamwise velocity fluctuations. On the right side are shown the probability distribution functions of the three fluctuating velocity components. For these measurements, the SCADA 10-min average wind speed was 7 m/s from the NorthEast direction. As seen in Fig. 7, the distribution of turbulence in the freestream and in the wake are anisotropic, with a degree of anisotropy of 0.5 that indicates the presence of secondary flow structures in the freestream and in the wake. The scatter plots in Fig. 7 show that in complex terrain, in the wake the turbulence structure is more isotropic than in the freestream. The vortical structures that are seen in Fig. 3a manifest themselves as the relatively large magnitude spanwise and streamwise fluctuations that are seen outside the cores in the scatter plot of the wake. However sizes of the core are similar in the freestream and wake. The probability distribution functions in the freestream and wake have normal distributions. The maximum probability density function of the streamwise fluctuating velocity, u0 , in the freestream is 0.06 and reduces in the wake to 0.055. However in contrast the maximum probability density function of the spanwise fluctuating velocity, v0, increases from 0.045 in the freestream to 0.055 in the wake. The probability density function of vertical fluctuating velocity, w’, is quite similar in the freestream and wake. The statistical parameters derived from probability density functions are summarized in Table 3. The turbulence structures at hub height in flat terrain are shown in Fig. 8. The measurements at the Altenbruch II wind farm are made in the freestream and in the wake (X/D ¼ 2.0e5.0), and are presented in terms of scatter plots (on the left side) and probability density functions (on the right side). For these measurements, the SCADA 10-min average wind speed was 8 m/s from the South-West
direction. In the freestream the degree of anisotropy is 4.3 that indicates an absence of secondary flow structures. In comparison, in complex terrain, Fig. 7a, the degree of anisotropy is 0.5 in the freestream. In the wake in flat terrain, Fig. 8b, the degree of anisotropy is 0.9, indicating that the turbulence structure is more isotropic in the wake compared to the freestream. The presence of strong vortical structures in the wake is indicated by the presence of large magnitude fluctuations in both the streamwise, u0 , and spanwise, v0, velocity fluctuations outside the core distribution. It can also be seen that the core of scatter plot is ten times larger in the wake (Fig. 8b) compared to the freestream (Fig. 8a). In the freestream, the probability density functions of spanwise fluctuating velocity, v0, and vertical fluctuating velocity, w0, are uni-modal normal distributions with maxima of 0.5 for the spanwise fluctuations and 0.3 for the vertical velocity fluctuations centered on a zero wind speed. However, the probability density function of the streamwise velocity, u0 , has a bi-modal normal distribution with a maximum of 0.18 that is centered on a wind speed fluctuation of 0.1 m/s. The probability density functions have a normal distribution in the wake, Fig. 8b, and are quite similar to the probability density functions that are measured in complex terrain, Fig. 7b. The statistical parameters derived from Fig. 8 are summarised in Table 4. The streamwise variations of the degree of anisotropy in complex and flat terrains are compared in Fig. 9. The measurements are made along a drone trajectory passing through the wake center line at hub height at the Mt. Crosin and Altenbruch II wind farms respectively. In both complex and flat terrains, the degree of anisotropy increases in the near wake and decreases in the far wake. In flat terrain, the degree of anisotropy increases from 1 at X/ D ¼ 1.25 to reach a maximum of 1.7 at X/D ¼ 3.2. As discussed above in relation to Fig. 3, in flat terrain, X/D ¼ 3 indicates the streamwise extent of the near wake region, thus the degree of anisotropy can be a useful parameter to identify the extent of near wake region. Further downstream for X/D > 3.2, the degree of anisotropy decreases due to mixing and flow re-energisation, and the degree of anisotropy is 0.75 at X/D ¼ 5.75. In complex terrain, the degree of anisotropy in the near wake at X/D ¼ 1.25 is 0.5. The degree of anisotropy increases to 1.15 at X/D ¼ 2.2. As discussed above the streamwise extent of the near wake in complex terrain is X/D ¼ 2. Downstream of X/D ¼ 2.2, the degree of anisotropy decreases to 0.3 at X/D ¼ 4.75. Overall it is observed that in the near- and far-wake regions the degree of anisotropy in flat terrain is higher than in complex terrain. 7. Friction velocity The characteristic velocity scale of the friction velocity (u* ) is derived from freestream measurements made during the landings of the drones at the wind farms in flat and complex terrains. Even though the friction velocity decreases with height, the friction velocity is nearly constant in the surface-layer for a neutrally stratified atmospheric boundary layer as turbulence is mechanically generated by wind shear. From local similarity hypothesis, the velocity scaling is given as [23].
u* ¼
0
02
0
02
uw þ vw
14 (5)
As the temperature and relative humidity sensors on the drone enable the atmospheric conditions to be determined, the friction velocity derived from landings in neutrally stable atmospheric conditions are summarised in Table 5. In complex terrain the friction velocity ranges from 0.23 to 0.4. Where in flat terrain, the friction velocity ranges from 0.03 to 0.11. The streamwise variations
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Fig. 7. Scatter plot (left) and probability density function, pdf, (right) of hub height velocity fluctuations in complex terrain, (a) Freestream, (b) Wake.
Table 3 Statistical parameters derived from the probability density functions measured in complex terrain. In the wake measurements are obtained over X/D ¼ 1.5e4.5. (m/s)2 0
0
uv ðsu0 Þ2 ðsv0 Þ2 ðsw0 Þ2
Freestream
Wake
1 102 4 102 8.4 102 7.3 102
7 103 8.4 102 12.3 102 8.4 102
of the friction velocity measured in horizontal flight at a height of 70 m AGL in the freestream of complex and flat terrain are shown in Fig. 10. In complex terrain, the mean friction velocity is 0.23 m/s and in flat terrain the mean friction velocity is 0.03 m/s. The measured turbulent fluctuations normalised by the friction velocity in the surface layer are summarised in Table 6. Also shown in Table 6 are the commonly used values that are presented in the open literature for the streamwise fluctuations [24] and the spanwise and vertical fluctuations [25]. In flat terrain, the streamwise turbulence is dominant and in complex terrain the turbulence is more isotropic. The normalized autocorrelation of the airspeed (Vf ) measured at hub height yields the integral time scale (tÞ [26,27]. Thus using the measured airspeed of the drone, the integral length scale can then be determined from L ¼ Vf t: As the turbulent flow field is convected at the wind speed relative to the Earth, the calculated integral length and time scales are corrected using the wind speed measured relative to Earth's frame of reference. The corrected
integral length and time scales measured at hub height in flat and complex terrains are summarised in Table 7. In the complex terrain of the Mt. Crosin wind farm, the integral length and time scales in the freestream are 43 m and 6 s respectively. While the integral time scale in the complex terrain is unchanged, the length scale in the wake, 19 m, is half that in the freestream. In the flat terrain at the Altenbruch II wind farm, the integral time scale measured in the freestream is 15 s and the corresponding integral length scale is 119 m. In the wake, the integral time scale is 6 s and the corresponding integral length scale is 20 m. 8. Conclusion A comprehensive series of drone-based measurements at a multi-megawatt wind turbine located in flat and complex terrains details the near- and far-wake evolution. The instrumented drone allows high spatial and temporal resolution measurements of the highly three-dimensional flow structures and its interactions in a wind turbine's wake. In complex terrain, the near-wake extends up to two rotor diameters and is 35% shorter than in flat terrain. In this region, tip vortices that can be distinguished from their elevated levels of turbulent kinetic energy are clearly identifiable. The tip vortices evolve just below the shear layer that separates the high speed exterior flow from the relatively low speed flow within the near wake. Further downstream of X/D ¼ 2, the wake flow is reenergised by the penetration of high-energy flow from outside wake boundary into the relatively low energy flow inside the wake. By X/D ¼ 2.7, the elevated turbulent kinetic energy flow has penetrated to the centre of the wake, and the turbulent kinetic
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Fig. 8. Scatter plot (left) and probability density function, pdf, (right) of hub height velocity fluctuations in flat terrain, (a) Freestream, (b) Wake.
Table 4 Statistical parameters derived from probability density functions measured in flat terrain. In the wake measurements are made over X/D ¼ 2.0e5.0. (m/s)2 0
0
uv ðsu0 Þ2 ðsv0 Þ2 ðsw0 Þ2
Table 5 Measured friction velocity derived from drone landings upstream of wind turbines in complex and flat terrains.
Freestream
Wake
Terrain
Friction velocity, u* (m/s)
2 104 2.5 103 4 104 9 104
9 104 5.3 102 6.76 102 6.25 102
Complex terrain (Mt. Crosin wind farm) Complex terrain (Collonges wind farm) Flat terrain (Altenbruch II wind farm) Flat terrain (Freudenberg-Beiersdorf wind farm)
0.23 0.4 0.03 0.11
energy is more than three orders of magnitude larger than that upstream. In flat terrain, the wake evolution shows similar behaviour. Reynolds decomposition yields the structure of turbulence in surface layer. These field measurements in different terrains helps to improve our knowledge of wake flows around a wind
turbine, and are well suited to advance the development of threedimensional wake models that are integrated into ReynoldsAveraged NaviereStokes solver. These advanced wake models shall allow the wind flow and turbine wake to be simulated simultaneously, and thus allow for the optimised micrositing and the improved operation of wind turbines.
Fig. 9. Degree of anisotropy (DA) along the wake center line at hub height as a function of downstream distance in flat and complex terrains.
Fig. 10. Friction velocity variation along the drone trajectory in flat and complex terrains at 70 m AGL.
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Table 6 Measured turbulent fluctuations in the surface layer under neutral atmospheric conditions in flat and complex terrains. The measurements are compared to literature [24,25]. Components of turbulence in surface layer
u0 2 =u2* v02 =u2* w02 =u2*
Freestream
Open literature [24,25]
Flat terrain
Complex terrain
5.1 1.1 1.6
1 2 1.8
6 2 1.7
Table 7 Integral time scale and integral length scale measured in complex and flat terrains.
Complex terrain, freestream Complex terrain, wake Flat terrain, freestream Flat terrain, wake
Integral time scale, t (s)
Integral length scale,L (m)
6 5 15 6
43 19 119 20
Acknowledgments The authors gratefully acknowledge the support of Michel Mansour, Flori Alickaj, Gulru Kocer and Leo Gruber of ETH Zurich. The authors also thank PNE Wind and BKW FMB Energie AG for providing access to their wind farms. References [1] European Commission 2020 Climate and Energy Package. [2] S. Krohn, P. Morthorst, S. Awerbuch, The Economics of Wind Energy, European Wind Energy Association, 2009. n, J. Sanz, J. Van Beeck, Sensitivity analysis on turbulence models for [3] D. Cabezo the ABL in complex terrain, in: Proceedings of the European Wind Energy Conference, Milan (Italy), 2007. [4] R. Cattin, B. Schaffner, S. Kunz, Validation of CFD wind resource modeling in highly complex terrain, in: European Wind Energy Conference and Exhibition, Athens (Greece), 2006. [5] F. Bingol, Complex Terrain and Wind Lidars, Doctoral Thesis, Riso-phd-52, 2009. [6] E.S. Politis, J. Prospathopoulos, D. Cabezon, K.S. Hansen, P.K. Chaviaropoulos, R.J. Barthelmie, Modeling wake effects in large wind farms in complex terrain: the problem, the methods and the issues, Wind Energy 15 (2012) 161e182. [7] R.J. Barthelmie, O. Rathmann, S.T. Frandsen, K. Hansen, E.S. Politis, n, W. Schlez, J. Phillips, A. Neubert, J. Prospathopoulos, K. Rados, D. Cabezo J.G. Schepers, S.P. van der Pijl, Modelling and measurements of wakes in large wind farms, J. Phys. Conf. Ser. 75 (2007), http://dx.doi.org/10.1088/17426596/75/1/012049. [8] N.O. Jensen, A Note on Wind Generator Interaction, Technical Report M-2411, Risø, National Laboratory, Denmark, 1983. [9] J.F. Ainslie, Calculating the flowfield in the wake of wind turbines, J. Wind Eng. Indus. Aerodynamics 27 (1988) 213e224. [10] A. Crespo, J. Hern andez, S. Frandsen, Survey of modelling methods for WIND turbine wakes and wind farms, Wind Energy 2 (1999) 1e24. [11] C. Kress, S. Barber, N. Chokani, R.S. Abhari, A new kinematic model for improved modeling of wakes, in: German Wind Energy Conference DEWEK, Bremen, Germany, 2012. [12] J.N. Sorensen, A. Myken, Unsteady actuator disc model for horizontal axis wind turbines, J. Wind Eng. Indus. Aerodynamics 39 (1992) 139e149.
[13] S. Jafari, N. Chokani, R.S. Abhari, Simulation of wake interactions in wind farms using an immersed wind turbine model, ASME J. Turbomach. 136 (2014) 061018 1e7. [14] R.J. Barthelmie, K. Hansen, S.T. Frandsen, O. Rathmann, J.G. Schepers, W. Schlez, J. Phillips, K. Rados, A. Zervos, E.S. Politis, P.K. Chaviaropoulos, Modelling and measuring flow and wind turbine wakes in large wind farms offshore, Wind Energy 12 (2009) 431e444. [15] B. Subramanian, N. Chokani, R. S. Abhari, “Experimental investigation of threedimensional flow structure of a multi-MW wind turbine in complex terrain,” accepted for publication at ASME J. Sol. Energy Eng.. [16] B. Subramanian, N. Chokani, R.S. Abhari, Experimental analysis of wakes in a utility scale wind farm, J. Wind Eng. Indus. Aerodynamics 138 (2015) 61e68. [17] M. Mansour, G. Kocer, C. Lenherr, N. Chokani, R.S. Abhari, Full scale wind turbine flow field measurements using a 7-sensor fast response probe, ASME J. Eng. Gas Turbines Power 133 (2011) 081601 1e8. € ppel, C. Roduner, G. Gyarmathy, On the development [18] K. Kupferschmied, P. Ko and application of the fast-response aerodynamic probe system in turbomachinesdPart 1: the measurement system, ASME J. Turbomach. 122 (2000) 505e516. [19] M. Mueller, A. Drouin, Paparazzidthe free autopilot. Build your own UAV, in: 24th Chaos Communication Congress, Berliner Congress Center, Dec. 27e30, 2007. [20] G. Kocer, M. Mansour, N. Chokani, R.S. Abhari, M. Muller, Full-scale wind turbine near-wake measurements using an instrumented uninhabited aerial vehicle, ASME J. Sol. Energy Eng. 133 (2011) 041011 1e8. [21] L. Porecca, M. Hollenstein, A.I. Kalfas, R.S. Abhari, Turbulence measurements and analysis in a multistage axial turbine, J. Propuls. Power 23 (2007) 227e234. [22] D.H. Wood, Simple equations for helical vortex wakes, J. Aircr. 31 (1994) 994e995. [23] Y. Shao, H.M. Hacker, Local similarity relationships in a horizontally inhomogeneous boundary layer, Bound. Layer Metrol. 52 (1990) 17e40. [24] R.B. Stull, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, 1988. ISBN 9022727694. [25] S.E. Gryning, A.A.M. Holtslag, S.J. Irwin, B. Sivertsen, Applied dispersion modelling based on meteorological scaling parameters, Atmos. Environ. 21 (1) (1987) 79e89. [26] J.C. Kaimal, J.J. Finnigan, Atmospheric Boundary Layer Flows e Their Structure and Measurement, University Press, Oxford, 1994. [27] P.K. Kundu, I.M. Cohen, Fluid Mechanics, second ed., Academic Press, New York, 2002.
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Aerodynamics of wind turbine wakes in flat and complex terrains B. Subramanian*, N. Chokani, R.S. Abhari Laboratory for Energy Conversion, Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2014 Received in revised form 5 May 2015 Accepted 24 June 2015 Available online xxx
The wake evolution measured downstream of multi-megawatt wind turbines located in flat and complex terrains are described here. These high-resolution measurements at full-scale Reynolds number conditions are made with an instrumented drone that is equipped with a suite of sensors and detail the characteristics of the mean flow and turbulent kinetic energy in the evolving wake. Reynolds decomposition yields the nature of turbulent fluctuations in surface layer, and this decomposition is used to detail the turbulence statistics, degree of anisotropy and friction velocity. These measurements are shown to be suited for the further development of three-dimensional wake models that are currently under intensive development. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Experimental Drone Wake Wind Turbulence
1. Introduction The expansion of wind energy across Europe is mainly driven by the European Union's 2020 target of generating 20% of its energy from renewable sources [1]. As the wind energy market matures, flat sites with good winds are becoming increasingly scarce, thus sites in complex terrain with moderate winds are increasingly of interest. Such sites, which were previously considered suboptimal for investment, have gained prominence in recent years [2]. However, wind resource assessment in complex terrain is challenging, due to limited field measurement data and due to the difficulty in the accurate modelling of flow in complex terrain [3,4]; thus there are higher uncertainties in wind resource estimates in complex terrain compared to flat terrain [2]. These higher uncertainties often result in a mismatch between the predicted annual energy yield and the actual annual energy yield e which consequently result in larger risk in the development of wind farm projects. Furthermore the loads on wind turbines located in complex terrain are higher due to higher wind shear and increased levels of turbulence, thus resulting in a reduced lifetime of wind turbine components [5]. Micrositing of wind turbines in complex terrain is further complicated by the fact that the flow downstream of a wind turbine is highly unsteady and three-dimensional. This highlights the need to understand the flow behaviour in two important
* Corresponding author. E-mail address: [email protected] (B. Subramanian). http://dx.doi.org/10.1016/j.renene.2015.06.060 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
areas e one is the behaviour of atmospheric boundary layer close to ground in complex terrain and the second is the wind turbine wake behavior in different terrains including its interactions with other downstream turbines. In recent years, wake evolution in flat and complex terrains has been a topic of focus that requires improved modelling for optimised wind farm layouts [6,7]. Thus there have been efforts directed to the development of both semi-empirical wake models [8e11] and more complete field models ([12] and [13]) to predict the evolution of wakes in wind farms located in different terrain conditions. As wind farms in both complex terrain and flat terrain operate inside the turbulent atmospheric boundary layer, an understanding of the nature and structure of turbulence in the different terrains is needed. As there are several discrepancies between predictions and measurements, there continues to be a need for full-scale measurements in order to validate and calibrate the prediction methods [14]. While wind tunnel and water tunnel tests provide an environment to conduct detailed parametric studies under carefully controlled conditions, their Reynolds number is at least one order of magnitude smaller than in full-scale conditions, this may be a concern regarding the widespread applicability of sub-scale experiments. Indeed the scale of the Reynolds number is relevant in physical process such as turbulent mixing, the entrainment of kinetic energy, the evolution and breakdown of tip vortices, etc, all of which are features of wakes in wind farms. The present work extends the authors prior work [15,16] with detailed measurements of the wake up to six diameters in flat and complex terrains. Thus the primary objective of this work is to detail and distinguish the
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Nomenclature
455
su0 ; sv0 ; sw0 standard deviation of velocity fluctuations density t integral time scale L integral length scale l tip speed ratio
r D f, F P, P0 u2 , V Vf V0 X Y Z ZHH pv u, v, w
rotor diameter frequency static pressure wind speed in Earth's frame of reference FRAP air speed SCADA 10-min average wind speed longitudinal axis (along rotor axis) lateral axis vertical axis hub height vortex pitch unfiltered velocity components, u along streamwise and w is in vertical direction 0 0 0 u ; v ; w resolved stochastic fluctuations u; v; w mean velocity components u* friction velocity t0 time
vortex structure and mixing properties of wakes in flat and complex terrains. The structure of the paper is as follows. In the next section, the wind farms and instrumented drone are described. The results are then presented and discussed in detail. The paper finally concludes with a summary of the key observations.
2. Description of measurement sites The drone based wind measurements are carried out at the Mont Crosin wind farm in Switzerland, which is located in complex terrain at an average elevation of 1250 m AGL. Fig. 1 shows the layout of wind turbines at the Mont Crosin wind farm on an aerial imagery from Google map, a digital elevation map and a land cover map. The locations of the wind turbines are shown by circle symbols; the turbine at which measurements are made is shown as a filled white circle, whereas the other turbines are shown as filled black circles. This wind farm is located in complex terrain, with patches of dense, tall coniferous forest surrounding the wind farm. During the measurements, the predominant wind direction observed at the Mont Crosin wind farm was from North-East and the wind direction changed overall by no more than 10 , with wind speeds in the range of 5e9 m/s. Thus the turbine at which measurements were made was not in the wake of any other turbine. The turbine at which measurements are made is a 2 MW Vestas V90 wind turbine. The rotor diameter is 90 m and hub height is 95 m AGL, with cut-in and cut-out wind speeds of 4 m/s and 25 m/s respectively. The location of this wind turbine is indicated with a white dot at center in Fig. 1. The wind turbine has an automatic yaw control system, which aligns the rotor into the incoming wind direction. The wind farm operator provided access to the turbine's 10-min average SCADA data, which were used for comparison to supplement the drone based wind measurements. The second wind farm is the Altenbruch II wind farm in northern Germany. The wind farm is located in flat terrain at a distance of 5 km from the North Sea coast, Fig. 2. The locations of the nine wind turbines in the wind farm are shown by the circle symbols in Fig. 2; the turbine at which measurements are made, shown as a filled white circle, is a Vestas V90 with a rated power 3.0 MW and a hub height of 105 m AGL. The other turbines are shown as filled black circles. During the measurements at the
Abbreviations AGL above ground level DA Degree of anisotropy FRAP Fast response aerodynamic probe GPS global positioning system GUM guide to uncertainty in measurements HH hub height IMU inertial measurement unit MW megawatt Pdf probability density function SCADA supervisory control and data acquisition STFT short-time Fourier transform TKE turbulent kinetic energy
Altenbruch II wind farm, the predominant wind direction was from South-West and the wind direction changed overall by no more than 8 , with average wind speeds of 8 m/s. In addition to the measurements at the two above wind farms, freestream measurements at two other wind farms are also reported here. The first of these is FreudenbergeBeiersdorf wind farm in Brandenburg, Germany that is in a flat terrain and surrounded by patches of dense tall coniferous trees. The second of these wind farms is at Collonges, Switzerland. The Collonges wind farm is in a valley, that extends approximately northwest-southwest, and has hills on its sides rising up to 2500 m AGL. Thus this second site is in complex terrain. Table 1 summarises the characteristics of these two wind farms.
3. Drone measurement system The unsteady, three-dimensional flow field around the wind turbine is measured using drones instrumented with a sevensensor fast response aerodynamic probe. The drones are detailed elsewhere [15,16] but some salient characteristics are summarised in Table 2. The seven-sensor fast response aerodynamic probe that is used for wind measurements is described in detail by Mansour et al. [17]. The sensing elements of the probe are miniaturised silicon piezo-resistive chips, which are encapsulated into a 20 mm hemispherical probe head, and are installed on a cylindrical shaft to give an overall probe length of 70 mm. The probe's measurement chain consists of the sensing elements, power supply units, signal conditioners, a 14-channel 24 bit analog-to-digital converter (sampling at upto 500 Hz) and an on-board flash card for data storage. The aerodynamic calibration of the probe was carried out in a fully automated free-jet facility at ETH Zurich [18], and yields less than 0.1% relative error in angles and dynamic pressure. The drone's on-board autopilot system, which is based on Paparazzi [19], is used for fully autonomous flight. Other components in the hardware suite include an absolute pressure sensor (with resolution of ±1.2 Pa), an ambient temperature sensor (with a resolution of 0.01 C), humidity sensor (with accuracy of 1.8%), IMU (with angular accuracy of 2%), a GPS (with position accuracy of 3 m) and a magnetometer (with an accuracy of 1 ). The hardware suite transmits data in real-time through an on-board modem, and the data is logged on a ground-based computer. At a cruise speed of
456
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Fig. 1. Layout of the wind turbines at Mont Crosin wind farm (complex terrain) are shown on the aerial imagery from Google map (top), digital elevation map (middle) and land cover map (bottom). The circle symbols show the locations of the wind turbines.
20 m/s, the uncertainty in the airspeed measured by the FRAP probe is less than 0.05 m/s. The overall uncertainty of wind speed measurements in Earth's frame of reference obtained from GUM analysis is 0.7 m/s. The approach for computation of wind speed in Earth's frame of reference and the trajectories for measuring in both the near- and far-wake are discussed elsewhere [16,20]. The coordinate system employed here has the wind turbine at the origin (0, 0) facing the upstream wind that flows from the negative X/D axis towards the positive X/D axis. The wake evolves along the positive X/D axis and the Z-axis is used to represent the vertical height above ground level at the base of wind turbine tower. The drone takes about 10 min to scan one azimuthal measurement plane. The term ‘wind speed’ is used to denote the total wind speed in Earth frame of reference.
Fig. 2. Layout of the wind turbines at Altenbruch II wind farm (flat terrain) are shown on the aerial imagery from Google map (top), digital elevation map (middle) and land cover map (bottom). The circle symbols show the locations of the wind turbines.
4. Methodology The unsteady measurements of wind velocity along the drone's trajectory are separated into mean and fluctuating parts using Reynolds decomposition. In the three spatial directions the decompositions are 0
u¼ uþ u 0 v¼ vþ v 0 w¼ wþ w
(1)
where, the velocity components u, v and w are defined along the coordinate axes X, Y, and Z, with the X-axis oriented in the main
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Table 1 Summary characteristics of the Freudenberg-Beiersdorf, Germany and Collonges, Switzerland wind farms. Wind farm
Wind turbine
Diameter (m)
Hub height (m)
Terrain
Ground elevation (m)
Freudenberg-Beiersdorf Collonges
V80 E70
80 70
100 100
Flat Complex
95 448
Table 2 Summary characteristics of drone. Drone
Take-off mass (g)
Wing span (mm)
Endurance (minutes)
Funjet windFlyer
900 2700
795 2300
30 120
wind direction. By definition, u0 ¼ v0 ¼ w0 ¼ 0. As the wind velocity is non-stationary, an ensemble average is computed with an averaging time of t0 ¼ 0.2 s in all cases to separate the mean and fluctuating parts. The fluctuating parts are obtained directly from the wind velocity measured in the drone's frame of reference assuming that the drone's inertial response time is larger than t0 ¼ 0.2 s. In the wake of a wind turbine, the turbulent fluctuations contain both periodic (deterministic) and stochastic parts. The turbulent kinetic energy (TKE) along the drone's trajectory is then computed from the sum of square of the fluctuating parts,
TKE ¼
1 02 u þ v02 þ w02 2
(2)
Alternatively, the turbulent kinetic energy can also be computed from short time Fourier Transform (STFT) as reported earlier [15,16]; both approaches yield the same TKE. In order to quantify the departure from isotropy, the degree of anisotropy (DA) is evaluated as [21]. 0
DA ¼
2u 2 02
0
v þ w2
(3)
5. Results 5.1. Wake evolution in complex terrain versus flat terrain The streamwise evolution of the wake in complex terrain upto four diameters downstream is shown in Fig. 3a in terms of wind speed and turbulent kinetic energy. The measurements are made at hub height in a horizontal plane at the Mt. Crosin wind farm, which is in complex terrain. In comparison, the streamwise evolution of the wake in the flat terrain of the Altenbruch II wind farm is shown in Fig. 3b. The measurements are made in a vertical plane up to six diameters downstream. During measurements in complex terrain, the SCADA reported wind speed, V0, was 7.2 m/s and the corresponding wind direction was 45 (North-East). In flat terrain case, the SCADA recorded a wind speed of 8 m/s and a wind direction of 238 (South-West). In complex terrain, the turbulent kinetic energy (Fig. 3a) in the near-wake, X/D < 2, shows the evolution of the tip vortex that is identified in the high turbulent kinetic energy regions that are shed from the wind turbine blade tip. For X/D < 1, the tip vortices are convected downstream close to a span of Y/D ¼ 0.68 parallel to the direction of upstream wind. At X/D ¼ 1, the tip vortices start to migrate spanwise, that is along the direction of the negative Y/D axis, due to the wake's expansion to reach Y/D ¼ 0.75 at X/D ¼ 1.5. In the near-wake, the wind speed, shown in Fig. 3a, shows the presence of a thin shear layer that separates the low energy flow
within the wake boundary and the high energy flow outside the wake. Downstream of X/D ¼ 2, mixing starts within the wake and is manifested by the penetration of high energy flow from the wake's boundary into the relatively low energy flow within wake. This mixing and re-energisation is also seen in the measured wind speeds, as relatively high speed flow from outside the wake penetrates into the low speed wake downstream of X/D ¼ 2. The mixing of the flow affects the entire wake region downstream of X/ D ¼ 2.7. In flat terrain (Fig. 3b), the wind speed and turbulent kinetic energy evolution shows similar characteristic behaviour [16]. The streamwise extent of the near-wake in complex terrain is approximately X/D ¼ 2. This extent is one-diameter shorter than the extent of the near-wake observed in flat terrain in Fig. 3b, where the near wake extends to X/D ¼ 3. The streamwise evolution of wake is quantified in terms of the area-averaged wind speed and turbulent kinetic energy as shown in Fig. 3c. The area-averages are derived from the flow properties in the planes that are shown in Fig. 3a and b. In the near wake, the area-averaged wind speed is 50e60% of the reference wind speed in both flat and complex terrains. In both terrains, the areaaveraged wind speed initially decreases in the near-wake, but then increases in the far wake. In complex terrain the wind speed increases at the rate of 10% per diameter to reach 64% at X/D ¼ 3.75. In flat terrain the area-averaged wind speed is 60% of the reference wind speed in the near-wake up to X/D ¼ 3, and then the wind speed starts to recover at a rate of 10% per diameter distance downstream up to X/D ¼ 5.5 where the wind speed is 80% of the reference wind speed. Thus, the streamwise extent of the near wake is shorter in complex terrain than in flat terrain by one diameter. The area-averaged turbulent kinetic energy also decreases as the wake evolves in both terrains; in complex terrain the area-averaged turbulent kinetic energy is 0.075 m2/s2 in the nearwake (X/D < 2). The area-averaged turbulent kinetic energy increases from 0.07 m2/s2 at X/D ¼ 2 to 0.18 m2/s2 at X/D ¼ 2.7; over this range, 2 < X/D < 2.7, a recovery in wind speed is also seen. The area-averaged turbulent kinetic energy then increases to reach 0.1 m2/s2 at X/D ¼ 3.7. In the complex terrain of Mt. Crosin wind farm, the ensemble-averaged freestream turbulent kinetic energy measured at hub height is 0.04 m2/s2. Thus, at the end of near wake, the turbulent kinetic energy is about two times higher than in freestream. The area-averaged turbulent kinetic energy at X/ D ¼ 3.75 in the far wake is still two-and-half times larger than the turbulent kinetic energy measured in the freestream. In flat terrain the area-averaged turbulent kinetic energy also decreases as the wake evolves. There is initially a decrease in the near-wake to 0.075 m2/s2 at 2.8D, followed by increase to 0.12 m2/s2 at X/D ¼ 3.7. The region between X/D ¼ 3 and X/D ¼ 5.5 is where enhanced flow mixing occurs and this is the reason for the increase in wind speed, and the increase/decrease that is observed in the area-averaged turbulent kinetic energy. Further downstream at X/D ¼ 6, the area-averaged turbulent kinetic energy is again 0.075 m2/s2. As the velocity and pressure fields can be measured with high resolution using the FRAP probe, Fig. 4a, the streamwise evolution of tip vortices in the flat terrain of Altenbruch II wind farm and complex terrain of Mt. Crosin wind farm are compared in terms of the air speed and static pressure. The measurements in flat terrain are made at a spanwise position of Y/D ¼ 0 and at a height of
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Fig. 3. (a) Measurements of turbulent kinetic energy and wind speed at hub height in a horizontal plane downstream of a wind turbine at Mt. Crosin wind farm, (b) Measurements of turbulent kinetic energy and wind speed at hub height in a vertical plane downstream of a wind turbine at Altenbruch II wind farm, (c) Streamwise evolution of spatiallyaveraged wind speed and spatially-averaged turbulent kinetic energy in wake in flat and complex terrains.
(Z e ZHH)/D ¼ 0.5, and the measurements in complex terrain are made at a spanwise position of Y/D ¼ 0.6 and at a height of (Z e ZHH)/D ¼ 0. The tip vortices can be identified from the sharp drops in air speed and/or pressure. In the flat terrain case, three consecutive tip vortices are captured; where as in the complex terrain two consecutive tip vortices are captured. A meaningful parameter used to examine the tip vortices is the so-called vortex pitch, pv , which describes the axial distance that a vortex is transported during one blade revolution. As the vortex pitch per blade is three times the separation distance of consecutive vortices in Fig. 4a, the measurements can be used to validate Wood's [22] empirical formulation.
pv z
1 þ u2 2l
(4)
As seen in Fig. 4b, Wood's formulation over predicts the vortex pitch by 33% in flat terrain, and under predicts the vortex pitch by 23% in complex terrains. Thus the formulation cannot be considered to universal applicability. The distribution of turbulent kinetic energy in two vertical planes in complex terrain is shown in Fig. 5. The first plane is upstream at X/D ¼ 1.5 and the second plane is downstream at X/ D ¼ 0.5. The measurements are accomplished by flying the drone alternatively upstream and downstream at altitudes ranging
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Fig. 5. Measurements in complex terrain of (a) Turbulent kinetic energy upstream of turbine at X/D ¼ 1.5, (b) Turbulent kinetic energy in near-wake at X/D ¼ 0.5, (c) Yaw angle in near-wake at X/D ¼ 0.5.
Fig. 4. (a) Streamwise profiles of static pressure and air speed in flat terrain at Y/D ¼ 0, (Z e ZHH)/D ¼ 0.5 and in complex terrain at Y/D ¼ 0.6, (Z e ZHH)/D ¼ 0. (b) Comparison of measured and predicted vortex pitches in flat and complex terrains.
from 0.45<(Z e ZHH)/D < 0.5. During this measurement, the SCADA 10-min average wind speed was 6.5 m/s with wind from East to West direction. The turbulent kinetic energy upstream at X/ D ¼ 1.5 (Fig. 5a) shows the characteristics of turbulent flow upstream of the wind turbine in complex terrain. The area-averaged turbulent kinetic energy in the upstream plane is 0.03 m2/s2. Downstream at X/D ¼ 0.5 (Fig. 5b) high turbulent kinetic energy regions that are associated with the tip vortices are seen. The perimeter of the rotor tip is shown as a white circle. These vortical structures originate from blade tips and convected downstream. The variations in the turbulent kinetic energy in wake is nearly symmetrical about a vertical axis located at Y/D ¼ 0.1 indicating that there is a yaw misalignment between the wind turbine and the main wind direction. The annular-shaped region of high turbulent kinetic energy in Fig. 5b indicates the radial extent of the wake at X/ D ¼ 0.5. In the near wake, regions of low turbulent kinetic energy characterize the freestream outside the wake and within the wake. The distribution of the yaw angle downstream at X/D ¼ 0.5 is shown in Fig. 5c. The yaw angle shows that the high turbulent kinetic energy regions identified in Fig. 5b are surrounded by pairs of positive and negative yaw angle zones; these pairs confirm that the previously identified regions of high turbulent kinetic energy are vortical structures. The mirror image of diametrically opposite yaw angle pairs indicates that the vortical structures are rotating in opposite directions.
The distribution of turbulent kinetic energy in two vertical planes in complex terrain, one located in upstream at X/D ¼ 1 and the other located in downstream at X/D ¼ 1, is shown in Fig. 6. The SCADA 10-min average wind speed during this measurement was 7 m/s and the wind direction was 77. For this wind direction, there is another Vestas V90 wind turbine located seven diameters upstream, at X/D ¼ 7, of the turbine located at X/D ¼ 0. Thus, the upstream measurement plane located at X/D ¼ 1 is six diameters downstream of the wind turbine located at X/D ¼ 7. Fig. 6a shows the turbulent nature of wake flow seen by a wind turbine rotor located six diameters downstream of another wind turbine in complex terrain. At X/D ¼ 1, the wake flow is completely mixed out with no distinct signatures of upstream wind turbine. The area average turbulent kinetic energy at X/D ¼ 1 is 0.07 m2/s2, which is more than two times greater than the area averaged upstream turbulent kinetic energy discussed in Fig. 5a. Downstream at X/ D ¼ 1 (Fig. 6b) high turbulent kinetic energy regions that are associated with vortical structures are seen. The perimeter of the rotor tip is shown as a white circle. This distribution of turbulent kinetic energy also confirms that mixing has already started within the wake on one side (for Y/D > 0) and there is no symmetry in the distribution of turbulent kinetic energy at X/D ¼ 1. It can also be seen in Fig. 6b that some tip vortices have strayed out of the wake shear layer into the freestream.
6. Comparison of turbulence structure in flat and complex terrains Fig. 7 compares the turbulence structure at hub height upstream and in the wake of a turbine in complex terrain. In the wake the
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Fig. 6. Measurements in complex terrain of (a) Turbulent kinetic energy contour upstream at X/D ¼ 1, (b) Turbulent kinetic energy in near-wake at X/D ¼ 1.
measurements are made at hub height from X/D ¼ 1.5 to X/D ¼ 4.5. On the left side of Fig. 7 are scatter plots of spanwise velocity fluctuations versus the streamwise velocity fluctuations. On the right side are shown the probability distribution functions of the three fluctuating velocity components. For these measurements, the SCADA 10-min average wind speed was 7 m/s from the NorthEast direction. As seen in Fig. 7, the distribution of turbulence in the freestream and in the wake are anisotropic, with a degree of anisotropy of 0.5 that indicates the presence of secondary flow structures in the freestream and in the wake. The scatter plots in Fig. 7 show that in complex terrain, in the wake the turbulence structure is more isotropic than in the freestream. The vortical structures that are seen in Fig. 3a manifest themselves as the relatively large magnitude spanwise and streamwise fluctuations that are seen outside the cores in the scatter plot of the wake. However sizes of the core are similar in the freestream and wake. The probability distribution functions in the freestream and wake have normal distributions. The maximum probability density function of the streamwise fluctuating velocity, u0 , in the freestream is 0.06 and reduces in the wake to 0.055. However in contrast the maximum probability density function of the spanwise fluctuating velocity, v0, increases from 0.045 in the freestream to 0.055 in the wake. The probability density function of vertical fluctuating velocity, w’, is quite similar in the freestream and wake. The statistical parameters derived from probability density functions are summarized in Table 3. The turbulence structures at hub height in flat terrain are shown in Fig. 8. The measurements at the Altenbruch II wind farm are made in the freestream and in the wake (X/D ¼ 2.0e5.0), and are presented in terms of scatter plots (on the left side) and probability density functions (on the right side). For these measurements, the SCADA 10-min average wind speed was 8 m/s from the South-West
direction. In the freestream the degree of anisotropy is 4.3 that indicates an absence of secondary flow structures. In comparison, in complex terrain, Fig. 7a, the degree of anisotropy is 0.5 in the freestream. In the wake in flat terrain, Fig. 8b, the degree of anisotropy is 0.9, indicating that the turbulence structure is more isotropic in the wake compared to the freestream. The presence of strong vortical structures in the wake is indicated by the presence of large magnitude fluctuations in both the streamwise, u0 , and spanwise, v0, velocity fluctuations outside the core distribution. It can also be seen that the core of scatter plot is ten times larger in the wake (Fig. 8b) compared to the freestream (Fig. 8a). In the freestream, the probability density functions of spanwise fluctuating velocity, v0, and vertical fluctuating velocity, w0, are uni-modal normal distributions with maxima of 0.5 for the spanwise fluctuations and 0.3 for the vertical velocity fluctuations centered on a zero wind speed. However, the probability density function of the streamwise velocity, u0 , has a bi-modal normal distribution with a maximum of 0.18 that is centered on a wind speed fluctuation of 0.1 m/s. The probability density functions have a normal distribution in the wake, Fig. 8b, and are quite similar to the probability density functions that are measured in complex terrain, Fig. 7b. The statistical parameters derived from Fig. 8 are summarised in Table 4. The streamwise variations of the degree of anisotropy in complex and flat terrains are compared in Fig. 9. The measurements are made along a drone trajectory passing through the wake center line at hub height at the Mt. Crosin and Altenbruch II wind farms respectively. In both complex and flat terrains, the degree of anisotropy increases in the near wake and decreases in the far wake. In flat terrain, the degree of anisotropy increases from 1 at X/ D ¼ 1.25 to reach a maximum of 1.7 at X/D ¼ 3.2. As discussed above in relation to Fig. 3, in flat terrain, X/D ¼ 3 indicates the streamwise extent of the near wake region, thus the degree of anisotropy can be a useful parameter to identify the extent of near wake region. Further downstream for X/D > 3.2, the degree of anisotropy decreases due to mixing and flow re-energisation, and the degree of anisotropy is 0.75 at X/D ¼ 5.75. In complex terrain, the degree of anisotropy in the near wake at X/D ¼ 1.25 is 0.5. The degree of anisotropy increases to 1.15 at X/D ¼ 2.2. As discussed above the streamwise extent of the near wake in complex terrain is X/D ¼ 2. Downstream of X/D ¼ 2.2, the degree of anisotropy decreases to 0.3 at X/D ¼ 4.75. Overall it is observed that in the near- and far-wake regions the degree of anisotropy in flat terrain is higher than in complex terrain. 7. Friction velocity The characteristic velocity scale of the friction velocity (u* ) is derived from freestream measurements made during the landings of the drones at the wind farms in flat and complex terrains. Even though the friction velocity decreases with height, the friction velocity is nearly constant in the surface-layer for a neutrally stratified atmospheric boundary layer as turbulence is mechanically generated by wind shear. From local similarity hypothesis, the velocity scaling is given as [23].
u* ¼
0
02
0
02
uw þ vw
14 (5)
As the temperature and relative humidity sensors on the drone enable the atmospheric conditions to be determined, the friction velocity derived from landings in neutrally stable atmospheric conditions are summarised in Table 5. In complex terrain the friction velocity ranges from 0.23 to 0.4. Where in flat terrain, the friction velocity ranges from 0.03 to 0.11. The streamwise variations
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Fig. 7. Scatter plot (left) and probability density function, pdf, (right) of hub height velocity fluctuations in complex terrain, (a) Freestream, (b) Wake.
Table 3 Statistical parameters derived from the probability density functions measured in complex terrain. In the wake measurements are obtained over X/D ¼ 1.5e4.5. (m/s)2 0
0
uv ðsu0 Þ2 ðsv0 Þ2 ðsw0 Þ2
Freestream
Wake
1 102 4 102 8.4 102 7.3 102
7 103 8.4 102 12.3 102 8.4 102
of the friction velocity measured in horizontal flight at a height of 70 m AGL in the freestream of complex and flat terrain are shown in Fig. 10. In complex terrain, the mean friction velocity is 0.23 m/s and in flat terrain the mean friction velocity is 0.03 m/s. The measured turbulent fluctuations normalised by the friction velocity in the surface layer are summarised in Table 6. Also shown in Table 6 are the commonly used values that are presented in the open literature for the streamwise fluctuations [24] and the spanwise and vertical fluctuations [25]. In flat terrain, the streamwise turbulence is dominant and in complex terrain the turbulence is more isotropic. The normalized autocorrelation of the airspeed (Vf ) measured at hub height yields the integral time scale (tÞ [26,27]. Thus using the measured airspeed of the drone, the integral length scale can then be determined from L ¼ Vf t: As the turbulent flow field is convected at the wind speed relative to the Earth, the calculated integral length and time scales are corrected using the wind speed measured relative to Earth's frame of reference. The corrected
integral length and time scales measured at hub height in flat and complex terrains are summarised in Table 7. In the complex terrain of the Mt. Crosin wind farm, the integral length and time scales in the freestream are 43 m and 6 s respectively. While the integral time scale in the complex terrain is unchanged, the length scale in the wake, 19 m, is half that in the freestream. In the flat terrain at the Altenbruch II wind farm, the integral time scale measured in the freestream is 15 s and the corresponding integral length scale is 119 m. In the wake, the integral time scale is 6 s and the corresponding integral length scale is 20 m. 8. Conclusion A comprehensive series of drone-based measurements at a multi-megawatt wind turbine located in flat and complex terrains details the near- and far-wake evolution. The instrumented drone allows high spatial and temporal resolution measurements of the highly three-dimensional flow structures and its interactions in a wind turbine's wake. In complex terrain, the near-wake extends up to two rotor diameters and is 35% shorter than in flat terrain. In this region, tip vortices that can be distinguished from their elevated levels of turbulent kinetic energy are clearly identifiable. The tip vortices evolve just below the shear layer that separates the high speed exterior flow from the relatively low speed flow within the near wake. Further downstream of X/D ¼ 2, the wake flow is reenergised by the penetration of high-energy flow from outside wake boundary into the relatively low energy flow inside the wake. By X/D ¼ 2.7, the elevated turbulent kinetic energy flow has penetrated to the centre of the wake, and the turbulent kinetic
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Fig. 8. Scatter plot (left) and probability density function, pdf, (right) of hub height velocity fluctuations in flat terrain, (a) Freestream, (b) Wake.
Table 4 Statistical parameters derived from probability density functions measured in flat terrain. In the wake measurements are made over X/D ¼ 2.0e5.0. (m/s)2 0
0
uv ðsu0 Þ2 ðsv0 Þ2 ðsw0 Þ2
Table 5 Measured friction velocity derived from drone landings upstream of wind turbines in complex and flat terrains.
Freestream
Wake
Terrain
Friction velocity, u* (m/s)
2 104 2.5 103 4 104 9 104
9 104 5.3 102 6.76 102 6.25 102
Complex terrain (Mt. Crosin wind farm) Complex terrain (Collonges wind farm) Flat terrain (Altenbruch II wind farm) Flat terrain (Freudenberg-Beiersdorf wind farm)
0.23 0.4 0.03 0.11
energy is more than three orders of magnitude larger than that upstream. In flat terrain, the wake evolution shows similar behaviour. Reynolds decomposition yields the structure of turbulence in surface layer. These field measurements in different terrains helps to improve our knowledge of wake flows around a wind
turbine, and are well suited to advance the development of threedimensional wake models that are integrated into ReynoldsAveraged NaviereStokes solver. These advanced wake models shall allow the wind flow and turbine wake to be simulated simultaneously, and thus allow for the optimised micrositing and the improved operation of wind turbines.
Fig. 9. Degree of anisotropy (DA) along the wake center line at hub height as a function of downstream distance in flat and complex terrains.
Fig. 10. Friction velocity variation along the drone trajectory in flat and complex terrains at 70 m AGL.
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Table 6 Measured turbulent fluctuations in the surface layer under neutral atmospheric conditions in flat and complex terrains. The measurements are compared to literature [24,25]. Components of turbulence in surface layer
u0 2 =u2* v02 =u2* w02 =u2*
Freestream
Open literature [24,25]
Flat terrain
Complex terrain
5.1 1.1 1.6
1 2 1.8
6 2 1.7
Table 7 Integral time scale and integral length scale measured in complex and flat terrains.
Complex terrain, freestream Complex terrain, wake Flat terrain, freestream Flat terrain, wake
Integral time scale, t (s)
Integral length scale,L (m)
6 5 15 6
43 19 119 20
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