energies

Article Wake Effect of a Horizontal Axis Wind Turbine on the Performance of a Downstream Turbine

Haojun Tang 1,* , Kit-Ming Lam 2, Kei-Man Shum 3 and Yongle Li 1

1 Department of Bridge Engineering, Southwest Jiaotong University, Chengdu 610031, China; [email protected] 2 Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China; [email protected] 3 CLP Power Wind/Wave Tunnel Facility, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China; [email protected] * Correspondence: [email protected]; Tel.: +86-1590-2835-715



Received: 13 May 2019; Accepted: 19 June 2019; Published: 21 June 2019


Abstract: This paper presents wind tunnel tests on the wake characteristics of a three-blade horizontal axis wind turbine and the wake effect on the performance of a downstream turbine. For a single turbine model, the performance was determined and this was followed by measurement of the wind characteristics including velocities, turbulence intensities, and correlation in the wake flow field. Subsequently, taking two horizontal axis wind turbines in a tandem arrangement into account, their performance was tested and the aerodynamic mechanism was discussed. The results showed that the upstream turbine with blades set at a small pitch angle provided smaller disturbance to the flow, but as the blade turned faster, larger changes in the velocity and the turbulence intensity occurred in its wake due to the more frequent disturbance of the wind turbine. The correlation of wake velocities in the turbine swept area also obviously decreased from the free-stream situation. For the downstream turbine, the output power loss largely depended on the wake characteristics of the upstream turbine, which was closely related to lower wind velocities or higher turbulence intensities. The decrease in correlation of the streamwise velocity within the blade swept area is accompanied by the increased correlation of the tangential velocity, which may be beneficial to the downstream turbine’s performance.

Keywords: wind turbines; wind tunnel test; turbine wake; tandem arrangement

1. Introduction In the modern era, environmental pollution, climate change, as well as the energy crisis are big challenges for the whole of mankind. Wind energy, as a renewable and clean energy, is one of the most profitable energy sources and has attracted great attention. There are basically two types of wind turbines according to their hub direction, namely, the horizontal axis wind turbine (HAWT) and the vertical axis wind turbine (VAWT). The three-blade horizontal axis turbine, which has a relatively large efficiency, has been widely implemented and the principle of its performance is briefly introduced here. There have been numerous wind tunnel tests, numerical simulations, and field experiments related to research on HAWTs and many remarkable achievements have been made. The power coefficient is a key index to describe turbine performance and is closely related to the tip speed ratio (TSR). The TSR represents the rotational speed of the turbine to the wind velocity and is affected by the aerodynamic shape of the blades, such as the pitch angle. Many researchers have been trying to optimize the shape of the blade and improve the power coefficient of the HAWT in different ways. Through wind tunnel tests, Xie et al. [1] studied the performance of a pitch-regulated

Energies 2019, 12, 2395; doi:10.3390/en12122395 www.mdpi.com/journal/energies Energies 2019, 12, 2395 2 of 18 three-blade wind turbine model with a small size. Apart from the ability to adjust the power coefficient, the innovative blade design was also capable of adjusting the blade operating TSR in the range between 2.94 and 6.45 for the unfolded blade and between 1.07 and 2.55 for the 40◦ folded angle. Xie et al. [2] investigated the aerodynamic performance of an umbrella-type wind turbine using experimental and theoretical methods and showed that the power coefficient and TSR of this turbine drop significantly when its blades are folded. Sutrisno et al. [3] tested a small-scale wind turbine with a designed TSR of 3.65 and considered two types of blades, with one having a backward swept at the tip and the other a helicopter-head tip. The tested results were further used to estimate the power generation of a real-scale turbine. With computational fluid dynamics (CFD) simulations, Lee et al. [4] studied the aerodynamic performance of a wind turbine with two different blades. One blade design was based on the blade element momentum theory and its maximum power coefficient was 0.469 at a TSR of 5.61. The other design was a non-twisted type with an unchanged chord length, and the maximum power coefficient of this type was 0.3 at TSR 5.08. Lin et al. [5] studied a 150 kW wind turbine and found the maximum power coefficient at 0.42, which was achieved with a blade at a 5◦ pitch angle and a TSR of 3.6. With field experiments, Li et al. [6] studied a 30 kW wind turbine with a rotor diameter of 10.0 m and a hub height of 13.4 m, and the maximum power coefficient was 0.35 at a TSR of 7.5. Howard and Guala [7] studied the effects of turbulent flow conditions on the performance of a 2.5 MW wind turbine with an optimal TSR of approximately 8.5, and the blockage effect on the mean wind speed profile of the incoming flow was found. Although wind tunnel testing can provide an effective and reliable way to predict the performance of a wind turbine, reduced-scale turbine models have to be used due to the limited sizes of wind tunnels. There is inevitably a large difference in the Reynolds numbers between the real-sized turbine and the model turbine. This Reynolds number effect may affect the scaling of experimental results from the model scale to the full scale. The Reynolds number is usually expressed as Re = Uc/υ, where U is the incident wind velocity; c is the chord length of the airfoil; and υ is the kinematic viscosity. Chamorro et al. [8] suggested that stronger Reynolds number dependence occurs in the near wake region, while the main flow statistics become independent of Reynolds number starting from Re 9.3 104. Park et al. [9] showed that the power coefficient of a wind turbine is very sensitive to ≈ × the change in the model scale, but the thrust coefficient is not. Ge et al. [10] selected six airfoils and found they all exhibited better performance at a higher Reynolds number. Li et al. [11] studied the Reynolds number effect on four thick airfoils at two different wind tunnels and found that increasing Re makes the separation point move towards the leading edge. Tarhan and Yilmaz [12] investigated the Reynolds number effect on the lift, drag, and lift/drag coefficients of 14 small wind turbine airfoils with both wind tunnel tests and numerical simulations. Meanwhile, the Reynolds number effect on VAWTs has also received much attention [13,14]. With the increase in rotor size, the difference in the Reynolds numbers between the real-sized turbine and the model turbine becomes more obvious and its effect could not be omitted. Using multiple turbines in a wind field is a major trend used to generate more energy due to the limited land resources. However, downstream turbines usually have to operate in the wake of upstream turbines, which leads to tremendous power losses. The wake effect loss must be taken into account when calculating the efficiency of large offshore wind farms [15], and the average power loss due to the wind turbine wake is on the order of 10% to 20% of the total power output [16]. Meanwhile, small changes in wind direction, i.e., yaw angle, have strong impacts on the total power output [17]. Therefore, it is of great importance to understand the wake characteristics of a turbine and the wake effect on the performance of a downstream turbine to arrange them reasonably and efficiently. Apparently, the wake characteristics of an upstream turbine are closely related to its own TSR, and so is the performance of a downstream turbine. Medici and Alfredsson [18] suggested that the near wakes produced by wind turbines with similar TSRs show very similar characteristics. Hu et al. [19] investigated the evolution of vortices in the near wake of a turbine and the structure of the turbulent flow field. The TSR of the turbine model varied from 0 to 4.5, and the largest velocity Energies 2019, 12, 2395 3 of 18 deficit in the wake flow was observed at a TSR of approximately 3. Zhang et al. [20] showed that the near-wake region is characterized by high three-dimensionality, turbulence heterogeneity, and strong flow rotation. Bastankhah and Porté-Agel [21] predicted the wake characteristics of a yawed wind turbine, and the velocity measurement indicated that the wake velocity deficit becomes smaller and the wake deflection increases with the increase in yaw angle. Qian et al. [22] also showed that yaw misalignment has significant influence on the performance of a turbine as well as its wake. Chu and Chiang [23] studied the turbulent effect on wake characteristics and power production of a wind turbine and found that the power loss could be larger than 50%. On the other hand, researchers have been trying to improve the performance of the downstream turbine. Adaramola and Krogstad [24] found that the loss in the maximum power coefficient of the downstream turbine is mainly between 20% and 45%. When the upstream turbine is operated in a yawed inflow condition, the total power output from two wind turbines in a tandem arrangement is increased by about 12%. Considering the effect of a yaw angle as well, Bastankhah and Porté-Agel [25] studied the interaction of a turbulent boundary layer with a wind turbine operating under different TSRs. Talavera and Shu [26] found that the maximum power coefficient of a single turbine could significantly increase from 0.125 under laminar inflow to 0.345 under turbulent inflow. A similar phenomenon was observed for two turbines in a tandem arrangement. While the aforementioned studies have improved our understanding of the performance and wake characteristics of three-blade horizontal axis turbines, the mechanism of how a turbine’s wake affects the performance of another turbine has not yet been fully explored. In addition to a reduction of the wind velocities in the wake, other possible turbulence effects influencing the performance of the downstream turbine are seldom studied. For instance, the possibly altered spatial correlation of wind speeds in the turbine wake would affect the instantaneously available kinetic energy for the downstream turbine. Hence, in this study, wind tunnel tests were carried out to determine the wake characteristics of a three-blade HAWT. In particular, wind velocities, turbulence intensities, and spatial correlation coefficients in the wake with different TSRs were measured and analyzed. The instantaneous flow field behind the turbine was obtained by particle image velocimetry (PIV). The second part of the study focused on the effects of these characteristics on the performance of another downstream turbine.

2. Wind Tunnel Experiments

2.1. Experimetal Setup Wind tunnel tests were conducted at the CLP Power Wind/Wave Tunnel Facility at the Hong Kong University of Science and Technology. The high-speed test section, which has a cross-section of 3 m wide by 2 m high and a fetch of approximately 28 m, was selected. The horizontal axis wind turbine (HAWT) models used in the experiments were acquired from Horizon Educational. The wind turbine consisted of three blades at 120◦ from each other. The width of the blade chord was 30 mm and the blade profile was designed based on NASA aeronautics, with more details available from the website: www.horizoneducational.com or the authors. The root pitch angle of the blade could be adjusted within a range from 0◦ to 45◦. The diameter of the rotor plane D was 360 mm, so the turbine blade swept area was about 0.102 m2. The corresponding blockage ratio of the blade swept area to the cross-sectional area of the tunnel was less than 2%. The length of the turbine nacelle was 160 mm and the distance from the hub axis to the tunnel ground was 285 mm. A small electric generator was installed inside the nacelle. According to the direction of incoming flow, the axial, lateral, and vertical directions were defined as x-, y-, and z-axes, respectively, as shown in Figure1, and the hub center was set as the origin of the coordinate system. The wake characteristics of the HAWT model were measured using cobra probes (Turbulent Flow Instrumentation Pty. Ltd., Tallangatta, Australia) and a PIV system. The cobra probe is a multi-hole pressure probe which can measure the three components of turbulent velocity. The sampling frequency Energies 2019, 12, 2395 4 of 18 was set to 2000 Hz to resolve turbulent fluctuations of wind velocities in the wind tunnel. For PIV Energies 2019, 12, x FOR PEER REVIEW 4 of 18 measurement, a thin laser sheet was generated from a double-cavity Q-switched Nd:YAG laser (Nano 50–100,wind Litron, tunnel. Rugby, For PIV UK). measurement, The laser sheet a thin illuminated laser sheet the centralwas generated vertical from (x-z) planea double-cavity of the turbine wake,Q-switched in which theNd:YAG fluid velocities laser (Nano were 50–100, marked Litron, with fineRugby, seeding UK). particlesThe laser in sheet an oil illuminated mist generated the by a high-volumecentral vertical liquid ( seedingx-z) plane generator of the turbine (10F03, wake, Dantec in which Dynamics, the fluid Skovlunde, velocities were Denmark). marked Double-framewith fine flow imagesseeding wereparticles captured in an oil by mist a high-speed generated by CMOS a high-volume camera (SpeedSense, liquid seeding Dantec generator Dynamics, (10F03, Dantec Skovlunde, Denmark)Dynamics, which Skovlunde, had a high Denmark). sensitivity Double-frame for the weak flow scattered images were light captured signals. by The a high-speed time interval CMOS between the doublecamera laser(SpeedSense, pulses wasDantec set Dynamics, to 0.2 ms Skovlunde, to fix the initial Denmark) and which final positionshad a high of sensitivity seeding particlesfor the in weak scattered light signals. The time interval between the double laser pulses was set to 0.2 ms to a double image. Wake characteristics were computed from the double images using the adaptive fix the initial and final positions of seeding particles in a double image. Wake characteristics were cross-correlationcomputed from PIV the algorithm double images [27,28 using]. the adaptive cross-correlation PIV algorithm [27,28].

(a) (b)

FigureFigure 1. Wind 1. Wind tunnel tunnel tests: tests: (a ()a) a a single single windwind turbine; turbine; (b (b) two) two wind wind turbines turbines in operation. in operation.

2.2. Performance2.2. Performance of a of Single a Single HAWT HAWT WindWind is the is movementthe movement of air of mass.air ma Afterss. After passing passing through through a winda wind turbine, turbine, the the velocity velocity willwill drop, and thedrop, power and the captured power captured by the turbine by the turbine can be can expressed be expressed as as 1 𝜋   𝑃=𝐶 ×1 𝜌 π 𝐷2 𝑈3 (1) P = Cp 2ρ 4D U (1) × 2 air 4 0 where 𝐶 is the power coefficient of the turbine; 𝜌 is the air density; 𝐷 is the rotor diameter; whereandCp 𝑈is the is undisturbed power coeffi windcient velocity of the turbine;at the sameρair heightis the of air the density; hub axis.D is the rotor diameter; and U0 is undisturbedIn the wind wind velocity tunnel attests, the the same output height voltage of the was hub measured axis. to calculate the power generation, Inand the thereby wind tunnel𝐶 was tests,obtained the by output Equation voltage (1). was𝐶 describes measured the to turbine calculate performance the power and generation, is closely and related to the TSR determined by Equation (2) and the pitch angle of blade. thereby Cp was obtained by Equation (1). Cp describes the turbine performance and is closely related to the TSR determined by Equation (2) and the pitch𝜋𝐷𝑛 angle of blade. 𝜆= (2) 60 ∙ 𝑈 πDn where n is the revolution per minute (RPM)λ of= the wind turbine. For a variable-pitch wind turbine, (2) 60 U starting and parking can be easily achieved by adjust· ing0 the pitch angle, and it can also be used to wherestabilizen is the the revolution output power per ab minuteove the (RPM) rated wind of the speed. wind turbine. For a variable-pitch wind turbine, The effect of the root pitch angle 𝛽 on the TSR 𝜆 was first studied. The incoming flow was starting and parking can be easily achieved by adjusting the pitch angle, and it can also be used to kept unchanged with 𝑈 at 4.4 m/s and a turbulence intensity of approximately 5% at the height of stabilize the output power above the rated wind speed. hub axis. Different root pitch angles ranging between 0° and 45° were considered, and the RPM of Thethe wind effect turbine of the was root measured pitch angle by aβ digitalon the laser TSR taλchometer.was first The studied. results are The listed incoming in Table flow 1. When was kept unchanged𝛽 is small, with theU0 bladeat 4.4 causes m/s and less a turbulencedisturbance intensityto the incoming of approximately flow, thus it 5% rotates at the faster. height With of hub an axis. Differentincrease root in pitch 𝛽, the angles flow resistance ranging betweento the blade 0◦ andincreases 45◦ were so 𝜆 considered, decreases, leading and theto a RPM reduction of the of wind turbinethe waspower measured coefficient. by However, a digital laserthe relationship tachometer. between The results 𝜆 and are 𝛽 listed is not ina linear Table trend,1. When and β𝜆is is small, the blademore causessensitive less to the disturbance change of to𝛽 the when incoming it is between flow, 7.5° thus and it 22.5° rotates (see faster. Figure With 2). an increase in β, the flow resistance to the blade increases so λ decreases, leading to a reduction of the power coefficient. Table 1. Relationship between the tip speed ration (TSR) and root pitch angle. However, the relationship between λ and β is not a linear trend, and λ is more sensitive to the change Root Pitch Angle β (°) of β when itItems is between 7.5◦ and 22.5◦ (see Figure2). 0 7.5 15 22.5 30 45 Subsequently, the root pitch angles of 7.5◦, 15◦, and 22.5◦ were selected for further testing, where RPM 880 810 585 420 316 220 the wind velocity U0 varied between 2 m/s and 10 m/s. For a more convenient comparison, the power coefficients of the wind turbine with different root pitch angles and different wind velocities Energies 2019, 12, 2395 5 of 18 are normalized by the maximum value. Figure2 shows the relationship among RPM, λ, and the normalized power coefficient Cp0 . For a fixed blade angle, both the RPM and the TSR of the wind Energies 2019, 12, x FOR PEER REVIEW 5 of 18 turbine increase with increasing wind velocity. The RPM of the wind turbine increases with a TSR at a faster rateTSR when 𝜆 the TSR is 3.8 larger than3.5 its optimum2.5 value. With 1.8 the increase 1.4 in λ, the1.0 normalized power coeSubsequently,fficient Cp0 first the increases root pitch rapidly angles toof reach 7.5°, 15°, a peak and value 22.5° atwere an optimumselected for value, further beyond testing, which Cp0 decreaseswhere the gradually wind velocity with 𝑈 the varied RPM. between 2 m/s and 10 m/s. For a more convenient comparison, the power coefficients of the wind turbine with different root pitch angles and different wind velocities areTable normalized 1. Relationship by the betweenmaximum the value. tip speed Figure ration 2 shows (TSR) the and relationship root pitch angle. among RPM, 𝜆, and the normalized power coefficient 𝐶. For a fixed blade angle, both the RPM and the TSR of the Root Pitch Angle β ( ) wind turbine increaseItems with increasing wind velocity. The RPM of◦ the wind turbine increases with a TSR at a faster rate when the 0TSR is larger 7.5 than 15 its optimum 22.5 value. 30 With 45the increase in 𝜆, the normalized power coefficientRPM 880𝐶 first increases 810 rapidly 585 to 420reach a peak 316 value 220 at an optimum value, beyond which 𝐶 TSR decreasesλ gradually3.8 with 3.5 the RPM. 2.5 1.8 1.4 1.0

0 2000 U 2000 β = 0°∼45° (U = 4.4m/s) 0 g in β = 22.5° (U = 2∼10m/s) s 0 a e β ° ( ∼ ) r = 15.0 U 0 = 2 10m/s c 1500 in 1500 β ° ( ∼ ) = 7.5 U 0 = 2 10m/s

1000 0° 1000 7.5° RPM RPM

β sing increa 15° 500 22.5° 500 30° 45°

0 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.2 0.4 0.6 0.8 1.0 λ Normalized C' Tip speed ratio p (a) (b)

FigureFigure 2. Wind 2. Wind turbine turbine performance. performance. ( a(a)) relationshiprelationship between between RPM RPM and and 𝜆; (λb;() relationshipb) relationship between between RPM and 𝐶 RPM and Cp0 3. Wake3. Wake Characteristics Characteristics of aof Single a Single HAWT HAWT In this section, three root-pitch angles were used in the wind tunnel tests, i.e., 7.5°, 15°, and In this section, three root-pitch angles were used in the wind tunnel tests, i.e., 7.5◦, 15◦, and 22.5◦ among22.5° which among the turbinewhich the performance turbine performance changed significantly. changed significantly. The wind The velocity wind of velocity the incoming of the flow incoming flow (𝑈 ) was fixed at 4.4 m/s, and the corresponding TSRs of the wind turbine with the (U ) was fixed at 4.4 m /s, and the corresponding TSRs of the wind turbine with the three root-pitch 0 three root-pitch angles were 3.5, 2.5, and 1.8, respectively. It should be noted that the Reynolds anglesnumber were 3.5, for 2.5,the andturbines 1.8, respectively.in the experiments It should was be8.8 noted× 103, thatwhich the was Reynolds much smaller number than for those the turbines in in the experiments was 8.8 103, which was much smaller than those in most commercial wind most commercial wind tunnel× installations. Even though the Reynolds number effect should be tunnelsignificant, installations. as discussed Even though in Section the 1, Reynolds the primary number wake echaracteristicsffect should bebehind significant, the turbine asdiscussed may be in Sectionreproduced1, the primary with less wake inaccuracy characteristics at relatively behind low the Reynolds turbine numbers may be [18,20]. reproduced with less inaccuracy at relatively low Reynolds numbers [18,20]. 3.1. Wake Recovery 3.1. WakeThree-component Recovery flow velocities in the wake of the turbine were measured by a cobra probe, Three-componentwhich could resolve flowthe turbulent velocities part in of the the wake velocity of thesignals. turbine For wereeach measurement measured by position, a cobra the probe, whichvelocity could was resolve measured the turbulent at a rate of part 2000 of Hz the for velocity a sampling signals. time of For 60 eachs. The measurement characteristic time position, scale the of the flow past the turbine (𝐷/𝑈 ) was about 0.08 s, so that the sampling time was sufficient to velocity was measured at a rate of 2000 Hz for a sampling time of 60 s. The characteristic time scale of obtain statistically stable measurements. The measurement was taken within a region from 0.5 D to D U the flow12 D past in the the horizontal turbine (direction/ 0) was (x-direction, about 0.08 as shown s, so that in Figure the sampling 1) and from time the was tunnel su ffifloorcient level to to obtain statistically1.5 D in stable the vertical measurements. direction ( Thez-direction). measurement The streamwise was taken velocity within averaged a region over from the 0.5 samplingD to 12 D in the horizontaltime at a point direction in the (turbinex-direction, wake aswas shown named in 𝑈 Figure. Along1) the and hub from axis, the the tunnel change floor in the level ratio to of 1.5 𝑈 D in the verticalto 𝑈 is direction shown in (z Figure-direction). 3a. At The the streamwiseaxial stations velocity of X/D = averaged 2, 4, 6, 8, and over 10, the the sampling change in time the atratio a point in theof turbine 𝑈 to wake𝑈 along was the named z-directionUx. Along is shown the hub in axis,Figure the 3a change as well. in theThe ratio streamwise of Ux to Uturbulence0 is shown in 𝑢 Figurevelocity3a. At the was axial computed stations offromX /theD = standard2, 4, 6, 8,deviation and 10, of the the change turbulent in thepart ratio of the of streamwiseUx to U0 along the z-direction is shown in Figure3a as well. The streamwise turbulence velocity ux0 was computed

Energies 2019, 12, 2395 6 of 18 from the standard deviation of the turbulent part of the streamwise velocity signal, from which the Energies 2019, 12, x FOR PEER REVIEW 6 of 18 streamwise turbulence intensity Ix was calculated by Equation (3), shown in Figure3b.

velocity signal, from which the streamwise turbulences intensity 𝐼 was calculated by Equation (3), Z T shown in Figure 3b. 1 2 Ix = ux0/U ux0 = (Ux(t) Ux) dt (3) 0 N − 0 𝐼 =𝑢 /𝑈 𝑢 = (𝑈 (𝑡) − 𝑈 )𝑑𝑡 (3) where T is the measurement time; N is the total number of a sample at a certain measurement position; where T is the measurement time; N is the total number of a sample at a certain measurement and Ux(t) is the instantaneous streamwise velocity at a certain time. position; and 𝑈(𝑡) is the instantaneous streamwise velocity at a certain time.

1.6 X / D = 2 X / D = 4 X / D = 6 X / D = 8 X / D = 10 1.2 Y / D = 0 Y / D = 0 Y / D = 0 Y / D = 0 Y / D = 0 Z varies Z varies Z varies Z varies Z varies 0.8

0.4 D / /

Z 0.0

-0.4

-0.8 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 U / U U / U U / U U / U Ux / U0 x 0 x 0 x 0 x 0

1.0

0.8

0.6 0 U / x 0.4 U

λ = 3.5 X varies 0.2 λ = 2.5 Y / D = 0 λ = 1.8 Z / D = 0 0.0 0123456789101112 X / D (a) 1.6 X / D = 2 X / D = 4 X / D = 6 X / D = 8 X / D = 10 1.2 Y / D = 0 Y / D = 0 Y / D = 0 Y / D = 0 Y / D = 0 Z varies Z varies Z varies Z varies Z varies 0.8 D 0.4 / / Z 0.0

-0.4

-0.8 0102001020010200102001020

Ix (%) Ix (%) Ix (%) Ix (%) Ix (%)

20

λ = 3.5 X varies 15 λ = 2.5 Y / D = 0 λ = 1.8 Z / D = 0

10 (%) x I

5

0 0123456789101112 X / D (b)

Figure 3. Wake characteristics of the turbine with larger TSRs: (a) streamwise velocity ratio; ( b) streamwise turbulence intensity. Energies 2019, 12, 2395 7 of 18

The results in Figure3 show that, after passing through the turbine, the velocity of incoming flow decreased but the turbulence intensity increased. A small pitch angle produced smaller disturbances to the flow, but the blade turned faster, leading to larger changes in the wind velocities and turbulence intensities in the wake due to the more frequent disturbances of the wind turbine. As a result, the decreasing range of wake velocities and the increasing range of turbulence intensities were both the largest for the TSR of λ = 3.5, which was obtained with β = 7.5◦. At this situation, the wind velocity in the wake decreased first and then recovered slowly with the increase in X/D. The turbulence intensity showed an increasing trend when X/D was less than 4, and then it decreased. It is important to note that even when the downstream distance increased to X/D = 12, the wake velocity Ux/U0 only recovered to 0.83 and the turbulence intensity was still obviously larger than that of the incoming flow. At the smaller TSRs of 2.5 and 1.8, the variations of the wind velocity and the turbulence intensity with X/D show monotonically increasing and decreasing trends, respectively. The rotation of the blades became slower with the increase in β to 15◦ and 22.5◦. Therefore, the turbine absorbed less energy from winds and exerted smaller effects on its wake. Wind velocities and turbulence intensities in the wake were less affected, and they recovered faster as well, as compared to the case for β = 7.5◦. At the position of X/D = 12, the wind velocity was slightly smaller than that of the incoming flow and the turbulence intensity was slightly larger. In the transverse vertical (y-z) plane, the wake effect generated by the wind turbine within its swept area is obvious from Figure3. The wake e ffect on the wind velocity was the greatest around the hub axis, while the wake effect on the turbulent intensity was obvious near the blade tip, especially for the upper side. Both the effects decreased progressively when going radially outwards. With the increase in X/D, the decreasing range of the wind velocity and the increasing range of the turbulent intensity became small, but the flow field affected by the wind turbine became broader due to the growth of the wake width. Compared with the region above the hub axis, the wake below the turbine hub had smaller velocities with larger turbulent intensity due to the presence of the ground. The mean flow field of the turbine wake on the central x-z plane (y = 0) through the turbine hub was also measured by PIV. Considering the fact that the measurement area of the PIV camera was only 390 mm in length and 255 mm in height, the root pitch angle was set as 45◦ because the wake of the turbine with this lower TSR could recover faster. The results are shown in Figure4. In Figure4, the PIV measurement was made at four measurement areas and the measurement data were combined to obtain the flow field in an investigation region covering an axial distance from 0D to 1.8D along X direction and a vertical distance from 0.7D to 0.6D along z-direction. Figure4a − shows the contour map of Ux/U0 and Figure4b shows the contour map of Ix. Compared to the results with larger TSRs (see Figure3), the wake fields of the turbine with the smaller TSR show similar features in that the Ux/U0 decreases behind the turbine hub and is accompanied by increased Ix but with a shorter distance for wake recovery. In Figure4a, the contour lines indicate that the largest wake velocity deficit originated from the turbine nacelle and the region of velocity deficit extended farthest around the hub axis. In the region above the hub axis, the separation among adjacent contour lines increased with the increase in distance from the hub. However, the recovery rate became smaller as the wake recovered and the velocity increased. In the region below the hub axis, the velocity deficit was more significant due to the ground roughness and the disruption of the supporting pole. In Figure4b, Ix was relatively large behind the turbine hub but it recovered quite fast. In addition, large turbulence intensities were also observed on going nearer to the ground surface. Very large values of Ix were found in a region behind the supporting pole, but there appeared to be some PIV measurement errors here due to the poor lighting problem. Energies 2019, 12, 2395 8 of 18 Energies 2019, 12, x FOR PEER REVIEW 8 of 18

(a) (b)

(c) (d)

FigureFigure 4.4. Wake fieldsfields ofof thethe turbineturbine withwith aa smallersmaller TSR:TSR: ((aa)) streamwisestreamwise velocityvelocity ratio;ratio; ((bb)) streamwisestreamwise turbulenceturbulence intensity;intensity; ((cc)) verticalvertical velocityvelocity ratio;ratio; ((dd)) normalizednormalized turbulentturbulent kinetickinetic energy.energy.

FigureFigure4 4cc shows shows the the contour contour map map of ofU z𝑈/U/𝑈0 where whereUz is𝑈 the is meanthe mean vertical vertical velocity. velocity. Compared Compared with thewith streamwise the streamwise velocities, velocities, the Uz were the very𝑈 were small very implying small that implying the air flowthat remainedthe air flow approximately remained horizontalapproximately in the horizontal turbine wake. in the There turbine was wake. no obvious There patternwas no inobvious the contour pattern map, in butthe incontour most ofmap, the studybut in area,mostU ofz was the negative,study area, i.e., 𝑈 downwards, was negative, but near i.e., todownwards, the ground surfacebut near it to was the positive. ground Within surface the it zonewas positive. just behind Within the turbine the zone and just beneath behind the the hub turbine axis, the and downward beneath verticalthe hub velocity axis, the was downward relatively large,vertical which velocity was was also relatively the zone wherelarge, thewhich streamwise was also velocitythe zone deficit where was the alsostreamwise the largest. velocity deficit was alsoFigure the4d largest. shows the contour map of the normalized turbulent kinetic energy which was obtained  2 2 2 from the planar PIV data as 0.5 ux + uz and then normalized by U , where uz is the vertical Figure 4d shows the contour× map0 of0 the normalized turbulent kinetic0 energy0 which was u turbulentobtained from velocity. the planar Although PIV not data shown, as 0.5 the × 𝑢 contour +𝑢 map ofandz then0 had normalized a similar distribution by 𝑈 , where pattern 𝑢 asis u , but of slightly smaller values. It can be seen in Figure4d that high turbulent energy was found thex0 vertical turbulent velocity. Although not shown, the contour map of 𝑢 had a similar behind the supporting pole and near the ground, while the region behind the turbine hub had lower distribution pattern as 𝑢 , but of slightly smaller values. It can be seen in Figure 4d that high energy.turbulent This energy may bewas due found to the behind more streamlined the supporting flow overpole theand turbine near the hub. ground, while the region behind the turbine hub had lower energy. This may be due to the more streamlined flow over the 3.2. Wake Correlation turbine hub. One focus of this paper was to understand the change in spatial correlation of the fluctuating wind speeds3.2. Wake in theCorrelation turbine wake and whether this would affect the performance of the downstream turbine. For thisOne purpose, focus of two this cobra paper probes was to were understand used for measuringthe change the in windspatial velocities correlation simultaneously of the fluctuating at two p positionswind speeds in the in the wake. turbine One wake was placedand whether at a fixed this position, would affect that the is,the performance reference positionof the downstream, and the y z m otherturbine. was For moved this along purpose,- or tw-direction,o cobra thatprobes is, the were measurement used for position measuring. The the sampling wind velocities time was alsosimultaneously set to 60 s with at two a sampling positions frequency in the wake. of 2000 One Hz. was Two placed sets of at correlation a fixed position, measurements that is, were the reference position p, and the other was moved along y- or z-direction, that is, the measurement position m. The sampling time was also set to 60 s with a sampling frequency of 2000 Hz. Two sets of correlation measurements were made, with the reference position was placed at a position downstream of the hub axis or the blade tip, as shown in Figure 5. The correlation coefficient with respect to the two positions was calculated by:

Energies 2019, 12, 2395 9 of 18 made, with the reference position was placed at a position downstream of the hub axis or the blade tip, asEnergies shown 2019 in, 12 Figure, x FOR5 .PEER The REVIEW correlation coe fficient with respect to the two positions was calculated9 of by: 18

Cov(m, p) ρ = 𝐶𝑜𝑣(𝑚, 𝑝) (4) 𝜌= σ σ (4) m𝜎p𝜎 wherewhereρ 𝜌ranging ranging from from1 to−1 1 to is the1 is correlation the correlation coefficient coefficient between between time histories time ofhistories the two fluctuatingof the two − windfluctuating velocities wind at velocities positions mat andpositionsp; σm mand andσp pare; 𝜎 the and standard 𝜎 are deviations the standard of the deviations two histories; of the andtwo Covhistories;(m, p) andis their 𝐶𝑜𝑣(𝑚, co-variance 𝑝) is their during co-variance the sampling during time the of sampling 60 s. time of 60 s.

Z Z m X X m Y Y p (for hub axis) p (for blade tip)

reference position measurement position Wind Wind

Figure 5. Schematic diagram for reference positions. Figure 5. Schematic diagram for reference positions. Taking the hub axis as the reference position first (y = 0, z = 0), Figure6 shows the correlation coefficientTakingρ between the hub theaxis streamwise as the reference velocity position at the wake first centre(y = 0, andz = 0), the Figure streamwise 6 shows velocity the correlation at a radial positioncoefficient along 𝜌 betweeny- and z-directions, the streamwise respectively. velocity Measurementsat the wake centre were and made the at streamwise different values velocity of X at/D a rangingradial position from 0 along to 10. y- It and can bez-directions, seen from respectively. Figure6 that Measuremen the variationsts ofwereρ along made theat different two directions values showof X/D similar ranging trends. from The 0 to turbine 10. It can captures be seen energy from from Figure the 6 incoming that the flowvariations and disturbs of 𝜌 along it, changing the two thedirections spatial correlationshow similar of trends. velocity The fluctuations turbine captures in the wake energy flow. from The the correlation incoming coe flowfficient and atdisturbsX/D = it,0 reflectschanging the the characteristics spatial correlation of undisturbed of velocity incoming fluctuat flowions and in the this wake baseline flow. curve The is correlation shown in allcoefficient parts of Figureat X/D6 =for 0 reflects comparison. the characteristics of undisturbed incoming flow and this baseline curve is shown in allIn parts the centralof Figure zone 6 for of thecomparison. blade swept area, the correlation coefficient decreases largely from the free fieldIn the value central at X /zoneD = 0. of This the mayblade be swept due to area, the impedancethe correlation of the coefficient turbine nacelle decreases to the largely wind flow.from Thethe free decreased field value spatial at X velocity/D = 0. correlationThis may be recovered due to the at impedanc slightly die ffoferent the turbine rates among nacelle the to ditheff erentwind TSRs,flow. especiallyThe decreased when spatialX was velocity not larger correlation than 4D. recovered The faster at the slightly rotation, different the more rates the among decreased the correlationdifferent TSRs, coeffi especiallycient recovers, when and X thiswas maynot larger be caused than by 4D the. The hub faster vortex the rotating rotation, with the the more turbine the anddecreased increasing correlation the velocity coefficient correlation. recovers, With and the this increase may be in causedZ/D, the by correlation the hub vortex coeffi rotatingcients of with the threethe turbine cases were and close increasing to one another, the velocity and the correlation. effect from theWith turbine the rotationincrease speedin Z/ reversedD, the correlation when Z/D wascoefficients higher thanof the a criticalthree cases value were marked close as theto one reverse another, point and in Figurethe effect6a. This from means the turbine that at rotation a large radialspeed separation, reversed when a faster Z/D turbine was higher rotational than speed a critical causes value a larger marked decrease as the in reverse the correlation point in coeFigurefficient. 6a. ThisThis maymeans be attributedthat at a tolarge the strongerradial separation, impedance a offaster the turbineturbine blades rotational at higher speed rotational causes a speeds. larger Thisdecrease critical in radialthe correlation separation coeffi to thecient. hub axisThis moves may outwardsbe attributed with to the the increase stronger in X impedance. More concretely, of the theturbine separation blades was at observedhigher rotational at Z/D = 0.23speeds. when ThisX was critical equal radial to 2D separationwhile Z/D =to0.60 the when hub Xaxisincreased moves tooutwards 8D. The with correlation the increase characteristics in X. More were concretely, still affected the separation to some degrees was observed at X/D = at10. Z/ However,D = 0.23 when it is expectedX was equal that to at a2D su whilefficiently Z/D far = 0.60 downstream when X increased distance from to 8D the. The wind correlation turbine, thecharacteristics wake effect were will eventuallystill affected die to down some and degrees the correlation at X/D coe= ffi10.cients However, will return it is to expected those of thethat undisturbed at a sufficiently incoming far flow.downstream In addition, distance a faster from turbine the wind rotational turbine, speed the leads wake to strongereffect will tip eventually vortices with die more down correlated and the characteristics,correlation coefficients but these will vortices return would to those diffuse of outwardsthe undisturbed and have incoming less influence flow. onIn addition, the inner zonea faster of theturbine blade rotational swept area. speed leads to stronger tip vortices with more correlated characteristics, but these vortices would diffuse outwards and have less influence on the inner zone of the blade swept area.

Energies 2019, 12, 2395 10 of 18 Energies 2019, 12, x FOR PEER REVIEW 10 of 18

1.0 X = 0D X = 2D X = 4D X = 6D X = 8D X = 10D Y = 0D Y = 0D Y = 0D Y = 0D Y = 0D Y = 0D (No turbine) λ = 3.5 λ = 2.5 0.5 Reverse Reverse Reverse Reverse λ = 1.8 point point point point D / Z Hub axis 0.0 (reference)

-0.5 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 ρ ρ ρ ρ ρ ρ

(a) 1.2 X = 0D X = 2D X = 4D X = 6D X = 8D X = 10D Z = 0D Z = 0D Z = 0D Z = 0D Z = 0D Z = 0D 0.9 (No turbine) λ = 3.5 λ = 2.5 λ = 1.8 0.6 D / / Y 0.3

Hub axis 0.0 (reference) 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 ρ ρ ρ ρ ρ ρ

(b)

FigureFigure 6. Correlation 6. Correlation coe coefficientsfficients for for hub hub axis: axis: ((aa)) along the the zz-direction;-direction; (b) ( balong) along the they-direction.y-direction.

For aFor more a directmore comparison,direct comparison, the total the correlation total corre coelationfficient coefficient representing representing the spatial the correlationspatial of a circularcorrelation area of to a circular its center, area i.e., to its the center, reference i.e., the position referencep, isposition defined p, asis defined as / 𝜌∙𝑟𝑑𝐴 𝜌̅ =R D/2 R 2π (5) 𝐴ρ rdA ρ = 0 0 · (5) where 𝜌 is the correlation coefficient Abetween theA reference position 𝑝 and a point related to a very small area 𝑑𝐴 around it; 𝐴 is equal to 𝜋𝐷/4 as the blade swept area is selected, as shown in where ρ is the correlation coefficient between the reference position p and a point related to a very Figure 7. Here, the total correlation coefficient 𝜌̅ is approximated by the average of the correlation 2 smallcoefficients area dA around at a number it; A is of equal measurem to πDent/ points,4 as the say, blade points swept 1, 2, area3, and is 4, selected, along four as radial shown lines in Figure(see 7. Here,Figure the total 7). correlationVelocity fluctuations coefficient at ρpointsA is approximated 1, 2, and 3 were by measured the average in the of the wind correlation tunnel tests coe andfficients at a numbertheir correlation of measurement coefficients points, to the say,center points are sh 1,own 2, 3, in and Figure 4, along 6, while four the radial value lines at point (see 4 Figure was 7).

Velocityassumed fluctuations to be same at points as that 1, at 2, point and 2. 3 wereThe approximate measured intotal the correlation wind tunnel coefficients tests and 𝜌̅ their within correlation the coeffibladecients swept to the area center at different are shown streamwise in Figure locations6, while were the computed value at pointand are 4 waslisted assumed in Table 2. to It be can same be seen that the 𝜌̅ of the undisturbed incoming flow was 0.232 at X/D = 0. After passing through as that at point 2. The approximate total correlation coefficients ρA within the blade swept area at the wind turbine, 𝜌̅ decreased significantly. The decrease in 𝜌̅ ranged from 70.8% to 75.6% for 𝜆 different streamwise locations were computed and are listed in Table2. It can be seen that the ρA of the = 1.8, 2.5 and 3.5 at X/D = 2. With the recovery of the wake characteristics along the x-direction, 𝜌̅ undisturbed incoming flow was 0.232 at X/D = 0. After passing through the wind turbine, ρ decreased increased gradually. However, the decrease in 𝜌̅ remained a high value at X/D = 10, withA an significantly. The decrease in ρ ranged from 70.8% to 75.6% for λ = 1.8, 2.5 and 3.5 at X/D = 2. average value of approximatelyA 41.3%. With the recovery of the wake characteristics along the x-direction, ρA increased gradually. However, the decrease in ρA remained a high value at X/D = 10, with an average value of approximately 41.3%.

Energies 2019, 12, 2395 11 of 18 Energies 2019, 12, x FOR PEER REVIEW 11 of 18

Z

D

1 dA X

10D 8D r Y 6D 4 4D 2 2D O

Wind 3

FigureFigure 7. Schematic 7. Schematic diagram diagram for definition for definition of the of total the correlation total correlation coefficient. coefficient.

Table 2. Total correlation coefficients within the blade swept area Table 2. Total correlation coefficients within the blade swept area ¯ TotalTotal Correlation Correlation Coe ffiCoefficientcient ρ 𝝆 𝝀 λ A 𝑨 XX= =0 0DXD = 2DXX = 2D = 4DXX = 4D = 6DXX = 6D= 8DXX = 8D= 10D X = 10D 3.5 0.0676 0.1159 0.1051 0.1438 0.1598 3.5 0.2320.232 0.0676 0.1159 0.1051 0.1438 0.1598 2.52.5 (no 0.0567 0.0567 0.06250.0625 0.09870.0987 0.1042 0.1042 0.1049 0.1049 (no turbine) 1.81.8 turbine) 0.0600 0.0600 0.05150.0515 0.07510.0751 0.1254 0.1254 0.1442 0.1442 AverageAverage 0.0614 0.0614 0.07660.0766 0.09300.0930 0.1245 0.1245 0.1363 0.1363

In the other set of correlation measurements, the reference position p was located at one side In the other set of correlation measurements, the reference position p was located at one side location downstream of the blade tip (Y = −0.5D, Z = 0, see Figure 5), while the other position m was location downstream of the blade tip (Y = 0.5D, Z = 0, see Figure5), while the other position m placed at different locations along the− same horizontal line from one side to the other side of the was placed at different locations along the same horizontal line from one side to the other side of blade tip. Measurements were made at different values of X/D ranging from 0 to 4 within which the the blade tip. Measurements were made at different values of X/D ranging from 0 to 4 within which changes in wake characteristics were more significant. As shown in Figure 8, the correlation curves the changes in wake characteristics were more significant. As shown in Figure8, the correlation in all cases dropped almost monotonically with the increasing separation between the two points. curves in all cases dropped almost monotonically with the increasing separation between the two In the turbine wake, the correlation coefficients became lower than that in the freestream flow, points. In the turbine wake, the correlation coefficients became lower than that in the freestream flow, especially at small separation distances. Near the turbine (X/D = 1), it was observed that the faster especially at small separation distances. Near the turbine (X/D = 1), it was observed that the faster the the turbine rotation, the smaller the correlation coefficient became, as explained above. With the turbine rotation, the smaller the correlation coefficient became, as explained above. With the increase increase in X/D, this phenomenon gradually disappears. Among the three cases, the decreasing in X/D, this phenomenon gradually disappears. Among the three cases, the decreasing range of the range of the correlation coefficient was the maximum for 𝜆 = 3.5, while the recovery for this case correlation coefficient was the maximum for λ = 3.5, while the recovery for this case was also the was also the fastest. In addition, at the other side of the reference position, small negative fastest. In addition, at the other side of the reference position, small negative correlation coefficients correlation coefficients may occur (e.g., X = 3, 4D and Y = 0.1~0.5D). The negative correlation may occur (e.g., X = 3, 4D and Y = 0.1~0.5D). The negative correlation implies that wind velocity implies that wind velocity fluctuations at the two positions were out of phase, and this may be due fluctuations at the two positions were out of phase, and this may be due to the three-blade geometry to the three-blade geometry and the strong tip vortex when the turbine rotational speed was large and the strong tip vortex when the turbine rotational speed was large enough. enough.

Energies 2019, 12, 2395 12 of 18 Energies 2019, 12, x FOR PEER REVIEW 12 of 18

0.6 p Blade tip 0.4 X = 0D X = 1D X = 2D X = 3D X = 4D Z = 0D Z = 0D Z = 0D Z = 0D Z = 0D (No turbine) λ = 3.5 0.2 λ = 2.5

λ = 1.8 the other side of

D 0.0

/ Hub axis p Y

-0.2

-0.4

Blade tip (reference) -0.6 of side same the 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 ρ ρ ρ ρ ρ

FigureFigure 8. 8.Correlation Correlation coe coefficientsfficients for for blade blade tip tip along along the they-direction. y-direction. 4. Wake Effects on a Downstream HAWT 4. Wake Effects on a Downstream HAWT After understanding the performance and the wake characteristics of a single HAWT, two HAWTs After understanding the performance and the wake characteristics of a single HAWT, two in a tandem arrangement (see Figure1b) were taken as examples to study how the wake of a turbine HAWTs in a tandem arrangement (see Figure 1b) were taken as examples to study how the wake of affects the performance of another. The two HAWTs had the same parameters, as shown in Section 2.1. a turbine affects the performance of another. The two HAWTs had the same parameters, as shown The location of the upstream turbine was fixed at x = 0, while the downstream turbine was located at in Section 2.1. The location of the upstream turbine was fixed at x = 0, while the downstream turbine different downstream locations so as to achieve varying separation distance L. Their root pitch angles was located at different downstream locations so as to achieve varying separation distance L. Their were named βup and β , respectively. Three root pitch angles, i.e., 7.5 , 15 , and 22.5 , were used in root pitch angles weredown named 𝛽 and 𝛽 , respectively. Three root◦ pitch◦ angles,◦ i.e., 7.5°, 15°, the wind tunnel tests. and 22.5°, were used in the wind tunnel tests. βdown was first set equal to βup. Compared with the output power of a single turbine with the 𝛽 was first set equal to 𝛽 . Compared with the output power of a single turbine with the same pitch angle, the percentage change in power generation ∆P of both the two turbines are shown in same pitch angle, the percentage change in power generation ∆𝑃 of both the two turbines are Figure9 (see solid points connected by dashed lines). Due to the aerodynamic interference between shown in Figure 9 (see solid points connected by dashed lines). Due to the aerodynamic the two turbines in tandem arrangement, their output powers both decreased when compared with a interference between the two turbines in tandem arrangement, their output powers both decreased single isolated turbine, especially for the downstream turbine. The aerodynamic interference became when compared with a single isolated turbine, especially for the downstream turbine. The weaker with the increase in L/D, so the output powers recovered gradually. No matter how fast the aerodynamic interference became weaker with the increase in L/D, so the output powers recovered downstream turbine rotates, the effect on the performance of the upstream one is limited, for its output gradually. No matter how fast the downstream turbine rotates, the effect on the performance of the power loss is very small and can almost be ignored when L/D is larger than 2. For the downstream upstream one is limited, for its output power loss is very small and can almost be ignored when turbine, however, the output power may drop a lot as it is located in the wake of the upstream one. L/D is larger than 2. For the downstream turbine, however, the output power may drop a lot as it is Apparently, this power loss largely depends on βup. The faster the rotational speed of the upstream located in the wake of the upstream one. Apparently, this power loss largely depends on 𝛽. The turbine is, the smaller the output power of the downstream turbine becomes. For βup = 7.5◦, the output faster the rotational speed of the upstream turbine is, the smaller the output power of the power loss of the downstream turbine exceeded 60% when L/D was 1 or 2, and was still up to about downstream turbine becomes. For 𝛽 = 7.5°, the output power loss of the downstream turbine 20% even when L/D increased to 12. With the increasing βup, the rotational speed of the upstream turbineexceeded decreased, 60% when so itsL/D wake was had1 or less2, and adverse was still eff ectsup to on about the downstream 20% even when turbine’s L/D increased performance. to 12. With the increasing 𝛽, the rotational speed of the upstream turbine decreased, so its wake had For βup = 22.5◦, the range of the output power loss of the downstream turbine decreased to about 10% less adverse effects on the downstream turbine’s performance. For 𝛽 = 22.5°, the range of the and remained stable within the range of L/D from 1 to 10. βdown was then changed to the other two output power loss of the downstream turbine decreased to about 10% and remained stable within values not equal to βup. The resulting changes in ∆P for these two cases are also shown in Figure9 the range of L/D from 1 to 10. 𝛽 was then changed to the other two values not equal to 𝛽 . The in the form of an “error” bar. Onceβup was fixed, ∆P of the downstream turbine at a given location resulting changes in ∆𝑃 for these two cases are also shown in Figure 9 in the form of an “error” bar. fluctuated within a small range with the change in its own pitch angle, i.e., βdown. OnceIn 𝛽 summary, was fixed, the downstream∆𝑃 of the downstream turbine’s performanceturbine at a given was mainly location determined fluctuated within by the a wake small characteristicsrange with the of change the upstream in its own one, pitch which angle, were i.e., associated𝛽. with its pitch angle, while adjusting the pitchIn summary, angle of the the downstream downstream wind turbine’s turbine performance itself could notwas help mainly much determined to mitigate by the the loss wake in powercharacteristics generation. of the upstream one, which were associated with its pitch angle, while adjusting the pitch angle of the downstream wind turbine itself could not help much to mitigate the loss in power generation.

Energies 2019, 12, 2395 13 of 18 Energies 2019, 12, x FOR PEER REVIEW 13 of 18

0

-1 Downstream turbine -2 Upstream turbine (%)

P β = β 7.5° 15.0° 22.5°

Δ up down -3 Wind β increases decreases L down -4 ° ° β ≠ β 15.0 15.0 up down 22.5° 7.5° -5 123456789101112 L / D (a) 0 -10 -20 Downstream turbine Upstream turbine -30

(%) -40 P β β Δ = ° ° ° Wind 7.5 15.0 22.5 up down L -50 β down increases decreases -60 β ≠ β 15.0° 15.0° up down 22.5° 7.5° -70 123456789101112 L / D (b)

Figure 9. Variation ranges of output powe powerr at didifferentfferent gap spacing: ( a) the upstream wind turbine; ((b)) thethe downstreamdownstream windwind turbine.turbine.

As discussed in Section3 3,, aa turbineturbine capturescaptures energyenergy fromfrom thethe incomingincoming flowflow andand thethe rotatingrotating turbine blades generate a turbulentturbulent wake behindbehind thethe turbineturbine withwith lowerlower windwind velocities,velocities, smallersmaller correlation, andand larger larger turbulence turbulence intensities, intensities, as compared as compared to the undisturbedto the undisturbed incoming incoming flow. However, flow. theHowever, question the remains question as remains to how theseas to factorshow these affect factors the downstream affect the downstream turbine performance, turbine performance, and which oneand iswhich the major one is factor the major governing factor thegovern downstreaming the downstream turbine performance? turbine performance? To addressaddress thisthis question,question, thethe upstreamupstream andand thethe downstreamdownstream turbines with the same root pitch angle of 7.57.5°◦ were taken as examples,examples, and thethe percentagepercentage changeschanges in powerpower generationgeneration (∆∆𝑃P) of thethe downstream turbineturbine atat didifferentfferent separation separationL /LD/Dare are listed listed in in Table Table3. The3. The turbulent turbulent wake wake generated generated by theby upstreamthe upstream wind wind turbine turbine was mainly was mainly described described in terms in of terms the mean of the wind mean velocity, wind the velocity, turbulence the intensity,turbulence and intensity, the total and correlation the total correlation coefficient. coef Theficient. three parametersThe three parameters were averaged were overaveraged the blade over sweptthe blade area, swept and theirarea, diandfferences their differences with the corresponding with the corresponding parameters parameters in the undistributed in the undistributed flow were computedflow were andcomputed are listed and in Tableare listed3 as ∆inU ,Table∆Ix, and3 as∆ ρ∆𝑈A,, respectively.∆𝐼̅ , and ∆𝜌 To̅ , studyrespectively. their eff Toects study separately, their theeffects performance separately, of athe single performance wind turbine of a was single tested wind under turbine the flow was conditions tested under simulating the flow the conditions turbulent wakesimulating characteristics the turbulent based wake on the characteristics parameter values based inon Table the parameter3. values in Table 3. The single turbine was fixedfixed at the same position as that in SectionSection3 3,, butbut thethe inflowinflow conditioncondition was changed.changed. To To test the effect effect due to thethe reducedreduced windwind velocitiesvelocities approachingapproaching thethe downstreamdownstream turbine in thethe two-turbinetwo-turbine situation, uniform incomingincoming flowflow was simulated in the wind tunnel with = wind speed reduced from U𝑈0 =4.44.4 m m/s/s inin thethe earlierearlier tests.tests. The decrease in windwind velocityvelocity is given in thethe thirdthird columncolumn of ∆∆𝑈U in in TableTable3 .3. The The output output turbine turbine power power was was then then tested, tested, andand thethe resultingresulting percentage changeschanges are are shown shown by ∆byP 1∆𝑃in Table in Table3. To test3. To the etestffect the of increasedeffect of turbulenceincreased turbulence intensities, turbulentintensities, incoming turbulent flow incoming was simulated flow was in simula the windted in tunnel, the wind which tunnel, was achieved which was by addingachieved floor by adding floor roughness elements in the wind tunnel, as shown in Figure 10. The increase in turbulence intensity is given in the fifth column in Table 3. The output power was tested, and the

Energies 2019, 12, 2395 14 of 18 roughness elements in the wind tunnel, as shown in Figure 10. The increase in turbulence intensity is givenEnergies in 2019 the, fifth12, x FOR column PEER REVIEW in Table 3. The output power was tested, and the resulting percentage14 of 18 changes are shown by ∆P2 in Table3. To analyze the e ffect of altered spatial velocity correlation, which, resulting percentage changes are shown by ∆𝑃 in Table 3. To analyze the effect of altered spatial however,velocity is di correlation,fficult to test which, separately, however, the is corresponding difficult to test percentage separately, powerthe corresponding change ∆P 3percentagewas estimated by ∆P ∆P1 ∆P2.∆𝑃 In summary, ∆P1 and ∆𝑃∆P2 represent − ∆𝑃 −∆𝑃 the output power∆𝑃 losses∆𝑃 directly measured at power− change− was estimated by . In summary, and represent the correspondingoutput power mean losses wind directly velocities measured and turbulenceat corresponding intensities, mean whilewind ∆velocitiesP3 indirectly and turbulence represents the effectintensities, of the wake while correlation. ∆𝑃 indirectly represents the effect of the wake correlation.

(a) (b) (c)

FigureFigure 10. Di10.ff Differenterent incoming incoming flow flow conditions: conditions: ( a)) uniform; uniform; (b ()b turbulent;) turbulent; (c) (morec) more turbulent. turbulent.

TableTable 3. Variation3. Variation ranges ranges of of output output powerpower at at different different flow flow conditions. conditions.

TwoTwo HAWTs: HAWTs: A Single HAWT: Tested Estimated Tested Estimated 𝑳/𝑫 ∆𝑷 (%) ∆𝑼 (%) ∆𝑷𝟏 (%) ∆𝑰𝒙 (%) ∆𝑷𝟐 (%) ∆𝝆𝑨 (%) ∆𝑷𝟑 (%) ¯ ¯ L/D ∆P (%) ∆P (%) ∆P (%) ¯ ∆P (%) 2 −62.2 −58∆U (%) −100.01 ∆+29Ix (%) 2 - ∆ρA−71(%) 3 - 4 −43.3 −43 −86.8 +25 - −50 - 2 62.2 58 100.0 +29 - 71 - 6 −31.9− −31− −69.2− +17 −1.4 −−55 +38.7 4 43.3 43 86.8 +25 - 50 - − − − − 8 6 −25.331.9 −24 31 −54.569.2 +13+17 1.4 - −5538 +38.7- − − − − − 10 8 −23.125.3 −19 24 −43.654.5 +11+13 −4.9 - −3831 -+25.4 − − − − 10 23.1 19 43.6 +11 4.9 31 +25.4 Table 3 suggests− that −either a lower− wind velocity or a −higher turbulence− intensity in the incoming flow leads to smaller power generation. For the downstream turbine among two turbines Tablein tandem,3 suggests the changes that either in wind a lower velocity wind and velocity turbulence or a intensity higher turbulenceare brought intensity about by inthe the wake incoming of

flow leadsthe upstream to smaller turbine. power The generation. decrease in power For the generation downstream in ∆𝑃 turbine, caused among by the twolower turbines wind velocity, in tandem, the changesis obviously in wind larger velocity than that and in turbulence ∆𝑃, caused intensity by the higher are brought turbulence about intensity. by the Higher wake of turbulence the upstream turbine.intensities The decrease are expected in power to make generation the rotational in ∆ speedP1, caused of the turbine by the less lower stable, wind but velocity, this effect is on obviously the power generation is relatively small. Compared with the higher turbulence intensity, the reduced larger than that in ∆P2, caused by the higher turbulence intensity. Higher turbulence intensities are expectedmean to wind make velocity the rotational is a much speed more of dominant the turbine factor less leading stable, to but the this power effect loss on of the the power downstream generation wind turbine. Particularly, the single wind turbine under uniform inflow with the simulated is relatively small. Compared with the higher turbulence intensity, the reduced mean wind velocity is velocity corresponding to the case of ∆𝑈 = −58% could not even start to rotate, so ∆𝑃 was given a a much more dominant factor leading to the power loss of the downstream wind turbine. Particularly, value of −100%. One possible reason for this phenomenon is that the rotation of a turbine is more the singlesensitive wind to turbinethe flow undercharacteristics uniform near inflow the withtip th thean that simulated near the velocity hub. The corresponding wake generated to by the the case of ∆U = 58% could not even start to rotate, so ∆P was given a value of 100%. One possible reason for upstream− turbine is non-uniform, so that the outer1 ring close to blade tip− has higher velocities than this phenomenonthe inner ring isclose that to the hub. rotation Although of a∆𝑃 turbine and ∆𝑃 is moreare obtained sensitive under to the the flow same characteristics mean wind speed near the tip thanwithin that the near blade the swept hub. area, The wakethe rotational generated speed by of the the upstream turbine in turbine the two-turbine is non-uniform, test was higher so that the outerthan ring the close single to bladeturbine tip case has due higher to the velocities non-unif thanorm wake the inner flow, ringand closehence, to the hub. decrease Although in power∆P1 and ∆P aregeneration obtained was under lower. the On same the mean other windhand, speedthe phen withinomenon the bladealso indicates swept area,that the effects rotational of wake speed of the turbinemay be in beneficial the two-turbine to rotating test the was turbine, higher especial than thely at single relatively turbine low case wind due speeds. to the This non-uniform viewpoint wake can also be verified by other cases. As the decrease in power generation due to the ∆𝑃 and ∆𝑃 flow, and hence, the decrease in power generation was lower. On the other hand, the phenomenon also was much greater than that in ∆𝑃, there may be some beneficial factors in having the turbine being indicates that the effects of wake may be beneficial to rotating the turbine, especially at relatively low located in the turbulent wake of an upstream one. wind speeds. This viewpoint can also be verified by other cases. As the decrease in power generation Energies 2019, 12, 2395 15 of 18

dueEnergies to the 2019∆,P 121, andx FOR∆ PEERP2 was REVIEW much greater than that in ∆P, there may be some beneficial factors15 of 18 in having the turbine being located in the turbulent wake of an upstream one. TheThe wake wake correlation correlation appears appears toto bebe aa beneficialbeneficial factor governing governing the the performance performance of ofthe the wind wind turbine.turbine. According According toto thethe valuesvalues amongamong ∆∆𝑃P,, ∆∆𝑃P1,, and and ∆𝑃∆P,2 ,it it is is estimated estimated that that ∆𝑃∆P has3 has a positive a positive value.value. In In other other words, words, the the changechange inin wakewake correlationcorrelation may may be be favorable favorable to to the the performance performance of ofthe the downstream turbine. The previous section mainly focuses on the change in 𝜌̅ which represents downstream turbine. The previous section mainly focuses on the change in ρA which represents the correlationthe correlation of the of streamwise the streamwise velocities velocities within within the the blade blade swept swept areaarea toto its center. center. This This correlation correlation decreases obviously in the wake, but relatively, the decrease in 𝜌̅ may imply the increase in decreases obviously in the wake, but relatively, the decrease in ρA may imply the increase in correlation atcorrelation other directions at other such directions as the tangentialsuch as the andtangential radial and velocities. radial velocities. As discussed As discussed in Section in 3Section, owing 3, to owing to the three-blade geometry and the strong tip vortices, anti-correlation could be observed the three-blade geometry and the strong tip vortices, anti-correlation could be observed between the between the two opposite sides of the blade swept area, which acts to decrease 𝜌̅ . To better two opposite sides of the blade swept area, which acts to decrease ρ . To better illustrate this, the illustrate this, the wake characteristics in the single turbine with differentA 𝛽 (see Section 3) were wake characteristics in the single turbine with different β (see Section3) were focused again, and the focused again, and the time-averaged mean tangential velocities along the radial lines from the hub time-averaged mean tangential velocities along the radial lines from the hub axis to the top, right, axis to the top, right, bottom, and left of the blade swept area are shown in Figure 11. The values of bottom,the mean and tangential left of the velocity blade sweptaveraged area over are the shown four inpaths Figure and 11the. Thecorresponding values of thedirections mean tangentialare also velocitygiven in averaged the figure. over the four paths and the corresponding directions are also given in the figure.

Black lines: X/D = 0 (approaching flow) Red lines: X/D = 2 Blue lines: X/D = 4 Yellow lines: X/D = 6

0.54 m/s 0.54 m/s 0.54 m/s 0.42 m/s 0.75 m/s 0.70 m/s 0.45 m/s 0.94 m/s 0.65 m/s 0.41 m/s 0.92 m/s 0.64 m/s 0.22 m/s 0.22 m/s 0.26 m/s 0.08 m/s 0.21 m/s 0.26 m/s 0.08 m/s 0.17 m/s 0.19 m/s 0.08

0.15 m/s 0.13 m/s 0.01 m/s 0.35 m/s 0.15 m/s 0.11 m/s 0.01 m/s 0.71 m/s 0.15 m/s 0.14 m/s 0.01 m/s 0.30 m/s 0.29 m/s 0.47 m/s 0.22 m/s 0.01 m/s 0.31 m/s 0.21 m/s 0.49 m/s 0.49 m/s 0.49 m/s

Flow direction Flow direction Flow direction

(a) (b) (c)

Figure 11. Mean tangential velocities in the turbine wake: (a) 𝛽 = 7.5 ; (b) 𝛽 = 15 ; (c) 𝛽 = 22.5 Figure 11. Mean tangential velocities in the turbine wake: (a) β = 7.5° ◦;(b) β = 15° ◦;(c) β = 22.5°.◦.

TheThe approaching approaching flow flow at atX /XD/D= 0= in0 in the the wind wind tunnel tunnel did did not not go go perfectly perfectly in in the the axial axial direction direction and thereand were there inevitably were inevitably some velocitysome velocity values values in the in other the other two directions.two directions. As measured As measured with with the cobrathe probe,cobra the probe, values the ofvalues the mean of the tangentialmean tangential velocities velocities averaged averaged over over the topthe pathtop path and and the the bottom bottom path werepath 0.54 were m/ s0.54 and m/s 0.49 and m /0.49s with m/s the with same the direction,same direction, i.e., rightward. i.e., rightward. Similarly, Similarly, the valuesthe values of the of the mean tangentialmean tangential velocities velocities averaged averaged over the over left paththe left and path the and right the path right were path 0.15 were m /0.15s and m/s 0.08 and m 0.08/s with m/s the samewith direction the same as direction well, i.e., as downward. well, i.e., downward. In this situation, In this situation, if a turbine if a isturbine placed, is theplaced, incoming the incoming flow will haveflow opposite will have eff oppositeects on a effects blade whenon a blade it passes when through it passes the through top and the bottom top and positions, bottom positions, or the left or and the left and right positions. right positions. When the incoming flow is disturbed by an upstream wind turbine, however, the tangential When the incoming flow is disturbed by an upstream wind turbine, however, the tangential velocities along the four paths obviously change. Due to the fluid rotation in the turbine wake, the velocities along the four paths obviously change. Due to the fluid rotation in the turbine wake, the tangential velocities at one side, such as the top and the right paths, could be increased from the tangential velocities at one side, such as the top and the right paths, could be increased from the undisturbed case, while the values at the other side, such as the bottom and the left paths, could be undisturbeddecreased. About case, while the hub the axis, values the atvelocity the other differ side,s between such as the the top bottom and the and bottom the left paths paths, to form could a be decreased.clockwise Abouteffect, theand hub so axis,do the the right velocity and ditheff ersleft betweenpaths. This the difference top and the was bottom affected paths by to𝛽 formand a clockwisedecreased eff ect,with and the so increase do the rightin X/ andD. Thus, the left the paths. rotation This of di thefference downstream was affected wind by turbineβ and decreasedwill be withenhanced the increase due to in theX/D sustained. Thus, the clockwise rotation effect of the th downstreamat the aerodynamic wind turbine forces willacting be on enhanced the three due toblades the sustained are now clockwisemore in phase. effect In thatsummary, the aerodynamic the decrease forcesin 𝜌̅ was acting accompanied on the three with blades the increase are now morein correlation in phase. Inof summary,the tangential the decreasevelocities in withinρA was the accompanied blade area, withwhich the was increase favorable in correlation to the downstream turbine’s performance. However, the effect from this wake correlation was expected to

Energies 2019, 12, 2395 16 of 18 of the tangential velocities within the blade area, which was favorable to the downstream turbine’s performance. However, the effect from this wake correlation was expected to be much weaker than that due to the reduced wind velocities. The values of ∆P3 in Table3 are far from realistic.

5. Conclusions In this study, the wake characteristics of a three-blade horizontal axis wind turbine model at different TSRs were measured and analyzed. The effect of the turbine wake on the performance of a downstream turbine was also studied using wind tunnel tests. The main conclusions of this study are summarized as follows:

(1) At a fixed velocity of incoming flow, the rotational speed of the wind turbine decreased with the increase in blade pitch angle, especially when the pitch angle was between 7.5◦ and 22.5◦. This led to a reduction of the power coefficient. With the increase in velocity of incoming flow, the rotational speed of the wind turbine increased stably but the power coefficient first increased to a peak value and then decreased again. (2) After passing through the wind turbine, the velocity of incoming flow decreased but the turbulence intensity increased significantly. These wake effects were strong within the blade swept area and decreased progressively from the hub center to the blade tip. A small pitch angle provided smaller disturbance to the flow, but the blades turned faster, leading to larger changes in the wind velocity and turbulence intensity due to the more frequent passage of the turbine blades. Compared with the region above the hub axis, the wake characteristics below the hub axis were more difficult to recover due to the presence of the ground surface and disruption of the flow from the supporting pole. (3) The turbine captured energy from the incoming flow and disturbed it, changing the correlation of the wake flow. Around the hub axis, the wake correlation decreased significantly from the freestream case, but this effect could be slightly weakened by the rotation of the turbine. The faster the rotational speed of the turbine was, the more this decreased correlation coefficient recovered. Overall, the decreased correlation within the blade swept area gradually recovered to the freestream values increased at increasing downstream locations. Moreover, an anti-correlated region can be observed at the two lateral sides of the turbine blade swept area. (4) Due to the aerodynamic interference between the two turbines in the tandem arrangement, their output powers both decreased when compared with a single isolated turbine, especially for the downstream one. The interference became weaker with the increase in their separation distance, so the output powers recovered gradually. As the performance of the downstream turbine was mainly determined by the wake of the upstream one, the output power of the downstream turbine decreased with the increase in rotational speed of the upstream turbine, but was less related to its own pitch angle. In the wake of the upstream turbine, the reduced mean wind velocity was the most dominant factor in determining the loss of power generation of the downstream turbine. Although higher turbulence intensities make the rotational speed of the turbine less stable, the unfavourable effect was limited. The wake correlation was another important factor governing the performance of the downstream turbine. The decrease in the correlation of the streamwise velocity within the blade swept area was accompanied with the increased correlation of the tangential velocity, which may be favorable to the downstream turbine performance. (5) This paper mainly focused on the wake characteristics of the wind turbine whose performance was evaluated based on its power generation only, while the changes in thrust force and power quality should be further investigated. Meanwhile, the Reynolds number in the present wind tunnel experiments was much smaller than those in most commercial wind turbine installations. Although previous studies have shown that the primary wake characteristics behind a turbine can be reproduced at relatively low Reynolds numbers, the Reynolds number effect on the results should be further studied by numerical simulations or field experiments. Energies 2019, 12, 2395 17 of 18

Author Contributions: Conceptualization, K.-M.L.; methodology, H.T., K.-M.L. and Y.L.; investigation, H.T., K.-M.S. and Y.L.; formal analysis, H.T. and K.-M.S.; writing—original draft, H.T.; writing—review and editing, H.T., K.-M.L., K.-M.S. and Y.L. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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