Experimental and numerical studies on the wake behavior of a horizontal axis wind turbine

J. Wind Eng. Ind. Aerodyn. 128 (2014) 54–65

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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Experimental and numerical studies on the wake behavior of a horizontal axis wind turbine Ali M. Abdelsalam a, K. Boopathi b, S. Gomathinayagam b, S.S. Hari Krishnan Kumar c, Velraj Ramalingam a,n a

Institute for Energy Studies, Anna University, Chennai 600025, India Centre for Wind Energy Technology C-WET, MNRE, Chennai 600100, India c AU-FRG Institute for CAD/CAM, Anna University, Chennai 600025, India b

art ic l e i nf o

a b s t r a c t

Article history: Received 4 December 2013 Received in revised form 5 March 2014 Accepted 6 March 2014

The wake characteristics of a horizontal axis wind turbine have been investigated, both experimentally and numerically. The computational numerical solution was carried out for the full rotor model, using a Navier–Stokes solver, employing the k–ε model appropriately modified for the atmospheric flows. The experiments were conducted at a 2 MW wind turbine for the measurements of upstream wind speed profiles, using SOund Detection and Ranging (SODAR), and wake wind speed profiles using Light Detection and Ranging (LIDAR), at varying distances between 2 and 7 times the rotor diameters downstream of the wind turbine. The evaluation of the computational model is made by comparing the predicted and measured velocities at the prescribed downstream locations at different upstream wind speeds. The present numerical setup employing the k–ε model and the fully mesh resolved rotor shows good agreement with the measurements. The model is used to find the relation between the wind speed and the wake recovery. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Wind turbine wake CFD Sodar Lidar k–ε model

1. Introduction The wake modeling of wind turbines has been a major issue of ongoing research, and a very challenging problem in the technical planning of wind projects, especially in last few decades, to maximize the energy production and to ensure the structural integrity of the wind turbines. Despite intense effort, and the progress made by many researchers around the world, in the possibility of generalizing the turbulence models used to predict the wake behavior under different conditions, a general solution has still not been found. As the rotational motion is induced by the turbine blades and the atmospheric stability is also expected to have a significant impact on the flow structure, the study of wind turbine wakes is a complicated problem, and depends on a large number of parameters. Therefore, it is one of the most important issues, that requires a detailed and in-depth study for prediction, as well as measurement of the horizontal axis wind turbine wakes. The ability to predict the spatial distribution of the mean wind speed deficit is essential, to optimize the design of wind farms. The spatial distribution of the turbulence intensity generated in the wake

n

Corresponding author. Tel.: þ 91 9962537765; fax: þ 91 44 22351991. E-mail address: [email protected] (V. Ramalingam).

http://dx.doi.org/10.1016/j.jweia.2014.03.002 0167-6105/& 2014 Elsevier Ltd. All rights reserved.

is very important in the determination of the fatigue loads on the subsequent wind turbines located downstream. In order to verify the CFD results, the actual measurements are needed on large wind turbines. The wind speeds are measured at fixed distances from the wind turbine at the wind farm, over a long duration, using the meteorological masts (Barthelmie et al., 1996; Frandsen et al., 1996), but the disadvantages are, that the location of the measurements is fixed, so the wake distance is fixed, and the data are only available up to the hub height, and are rarely made above that height. The hub heights rise to around 100 m at present, and the huge wind turbines pose a difficulty in the wake measurement, using the meteorological mast. This limitation led to the widespread use of two remote sensing instruments, Sodar and Lidar, in the wind energy industry. Steven and Eamon (2011) compared the data measured by Sodar and Lidar instruments, with that measured by an instrumented mast, in a semi-complex terrain. Their regression analyses provided a good correlation between the remote sensing data and the mast data. Sodar instrument was used by Barthelmie et al. (2012), to determine the magnitude and vertical extent of the wake. The Sodar measured the wake wind speed profiles at different distances downstream of the wind turbine, and the freestream wind profiles were obtained, by the same device, by shutting down the turbine. The vertical profiles reported by them showed that the Sodar data compared well with the mast data. A ZephIR Lidar was installed

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in the rotating spinner of a large wind turbine, to investigate the approaching wind fields (Mikkelsen et al., 2010). They aimed to use the measured data as input to the wind turbines yaw and pitch control systems. In recent years, more advanced Computational Fluid Dynamics (CFD) models are available, solving the three-dimensional (3-D) Navier–Stokes equations for the wake modeling. In these models, a wind turbine rotor can be represented by the actuator disk (Larsen et al., 2008) or actuator line approach (Troldborg et al., 2010). These models are capable of predicting the flow field behind the turbine, without using any initial near-wake data to start their calculations with. However, there is still a gap between the results of these CFD models and the actual data, and hence, a better use of the CFD is possible by providing more accurate representation of the physical problem including the boundary conditions, turbulence, and rotor modeling for modeling wakes, for better wind farm and turbine design, and for more load calculations and control strategies. Atmospheric, blade-generated, and wake shear-generated turbulence are the three major contributors to the turbulence generated in the wake downstream of wind turbines. Using the eddy viscosity turbulence modeling, good predictions of the mean and turbulent flow fields depend on reasonable descriptions of the turbulent scales inside the flow. The standard k–ε model proposed by Launder and Spalding (1974), is the commonly-used isotropic two-equation turbulence model. This model, with standard model constants, has been employed for a large number of turbulent flow problems. Crespo et al. (1985) have proposed values for the model constants appropriate for the neutral atmospheric boundary layers. Since the dissipation rate equation is highly empirical, enhancement in the model performance is achieved by modifying the dissipation rate equation (Hanjalic and Launder, 1980). Chen and Kim (1987) have proposed a general approach, that was tested for a wide variety of turbulent flow problems, and yielded much better results than the standard k–ε model. The numerical calculations using the standard k–ε model significantly underpredict the near-wake velocity deficit, compared with the measurements, especially in neutral atmospheric conditions (El Kasmi and Masson, 2008). These observations were made on the basis of the results obtained by the full 3-D Navier–Stokes model, and the rotor disk was simulated as a momentum sink in the Navier–Stokes equations through the actuator force. In order to improve the predictions, El Kasmi and Masson suggested a modification for the dissipation turbulence term in the ε equation, and used the model constants of Crespo et al. (1985). They impute the wake deficit underestimation to the rapid changes of turbulent kinetic energy production and dissipation rates close to the rotor leading to non-equilibrium turbulence. They have added an extra term to the dissipation rate equation, first suggested by Chen and Kim (1987), to represent the rate of energy transfer from large scale turbulence to small scale turbulence more effectively. A detailed survey on wind turbine wakes can be found in Crespo et al. (1999), Vermeer et al. (2003), and Sørensen (2011). Overall, it is not possible to establish any of the wake models as having a superior performance individually with respect to the measurements. Abelsalam and Velraj (2014) compared the results of the full rotor approach using the standard k–ε turbulence model with the results of the actuator disk approach using the standard k–ε turbulence model and two modified k–ε models used by the earlier researchers. They concluded that the full rotor model showed good agreement with the available experimental data, in comparison with the improvement achieved by the actuator disc approach using modified versions of the k–ε model. It is understood from the literature that, there is little documentation available for the large scale wake measurements, especially in the near-wake regions for which very few datasets are available. Hence, in the present work, an experiment was conducted at a

55

2 MW wind turbine to provide additional data for the near and far wake regions. These datasets were also used to validate the CFD modeling and analysis performed to predict the wind turbine wakes at various wind speeds and to examine the performance of the k–ε model appropriately modified for the atmospheric flows, using the direct rotor modeling. Both Sodar and Lidar were used to measure the wind speed profiles in the upstream, and in the wake of a wind turbine respectively.

2. Experimental details The measurement campaign was conducted on the three bladed 2 MW Kenersys wind turbine located at Kayathar, Tirunelveli, Tamil Nadu state, India. Two measuring instruments were used in the present work: (1) a Triton Sodar was used to measure the inflow wind speed profiles, and (2) a ZephIR 300 Lidar was used to measure the wake at different downstream locations. The layout depicting the top view of the wind turbine and the location of the two measuring devices is shown in Fig. 1. The wind turbine, which has been operating since 2009 and located in a flat terrain, is yawed mostly toward the west (prevailing wind direction). The hub height is 80 m and the rotor diameter is 82 m. The period between 23rd July and 10th August was chosen for the experiment to avoid periods of rains and very low wind speeds. Further, to measure the wakes, wind speeds also have to be above the turbine cut-in wind speeds of 4 m/s, making the chosen time period more attractive. A histogram with the percentage occurrence of the mean hub height upstream wind velocity is presented in Fig. 2 (a). It shows that during most periods of measurements, the site is characterized by a high wind, with typical velocities between 9 and 12 m/s. Regarding the wind direction, the one with the highest incidence is 2651 from the north as shown in Fig. 2(b). A high occurrence of turbulence intensity between 8% and 10 % is observed, as shown in Fig. 2(c). 2.1. Sodar measurements The Sodar employed was the Second Wind's Tritons Sonic Wind Profiler, which is an ultramodern device designed for use in wind energy applications. The Sodar was installed at 2D upstream the wind turbine. No echo problems were encountered in the data records. The Triton was programmed to measure the wind parameters at 16 levels, in-between 38 m and 200 m above the ground. The Sodar was set to record the wind speed, wind direction, turbulence, and vertical wind speed continuously, and the average measurements of every 10 min were considered for the analysis.

N

Sodar Upstream wind

Turbine

Lidar

2D Taking different locations downstream of the turbine

Fig. 1. Layout of the 2 MW wind turbine at Kayathar, India, with the location of Sodar and Lidar measuring instruments.

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30

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% Occurence

% Occurence

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% Occurence

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I% Fig. 2. Histograms of the Sodar data recorded at a height of 80 m during the period of measurements July–August 2012 with a sampling time of 10 min: (a) mean wind velocity, (b) mean wind direction, and (c) streamwise turbulence intensity.

20

20 y = 0.9918 x - 0.1207 R2 = 0.965

16 Lidar U65 (m/s)

Sodar U65 (m/s)

16 12 8 4 0

y = 1.0145 x - 0.0547 R2 = 0.9912

12 8 4

0

4

8 12 Mast U65 (m/s)

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20

0

0

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8 12 Mast U65 (m/s)

16

20

Fig. 3. Observed variation and linear regression fit at a height of 65 m for (a) Sodar versus sonic anemometer; (b) Lidar versus sonic anemometer.

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The turbulent viscosity ðμt Þ is evaluated using the turbulence models explained in the next section.

2.2. Lidar measurements ZephIR 300 Lidar manufactured by QinetiQ (UK), and supplied by Natural Power was used for the study. It provides remote wind measurements across 10 user-defined heights up to 300 m. It measures 50 data points every second across a full 360-degree scan, providing a high sample rate advantageous in complex and fast changing air flows. The maximum number of erroneous data removed in the Lidar measurements was 2 points out of 50 in 10 minute's average, and for most of the cases it was zero one. In the present study, Lidar was programmed to measure at 10 levels from 40 m to 135 m above the ground level. The wind speed profiles are determined for a yaw error less than 7 41. Data with more than 741 deviation from the main wind direction are excluded from the results. 2.3. Accuracy of measurements To ensure the accuracy of the measurements, a comparison of the relative accuracies of wind speeds derived from both the Sodar and Lidar with wind speeds measured by the calibrated mast-mounted sonic anemometer (tower-based sonic anemometry) has been made. The comparison is based on the data that has been carried out at a tower height level of 65 m, located at the wind turbine testing station, Kayathar, Tirunelveli, India. Data were collected using 10-min averages for a total of 15 days. The results of the comparison between the Sodar, Lidar and tower measurements are displayed in the time series and scatter diagrams shown in Fig. 3. The figures show a very good correlation between the data obtained from the Sodar, and Lidar with those of the mast-mounted sonic anemometer.

3. Numerical model

3.2. Turbulence modeling The standard k–ε model proposed by Launder and Spalding (1974) appropriately modified for the atmospheric flows (Crespo et al., 1985) is considered in the analysis, to evaluate its suitability when using the direct modeling of the turbine rotor. This model has been chosen for the closure of the Reynolds averaged turbulent flow equations, mainly because of its wide use and because of the availability of the k and ε properties of the atmospheric boundary layer meteorological data. In the standard k–ε model, the transport equation for the turbulent kinetic energy k is written as 
  ∂ku ∂ μ ∂k þ P t  ρε ρ j¼ μþ t ð4Þ ∂xj ∂xj sk ∂xj where P t is the production of the turbulence kinetic energy,
 ∂ui ∂uj ∂ui þ P t ¼ μt ∂xj ∂xi ∂xj The dissipation rate ε equation is given by 
  ∂εu ∂ μ ∂ε ε ε2 þ C 1ε P t  ρC 2ε ρ j¼ μþ t ∂xj ∂xj sk ∂xj k k

ð6Þ

The turbulent (eddy) viscosity is computed according to

μt ¼ ρC μ

k

2

ð7Þ

ε

The constants for the k–ε model modified for the atmospheric flow conditions are

sk ¼ 1; sε ¼ 1:3; C 1ε ¼ 1:176; C 2ε ¼ 1:92; C μ ¼ 0:033; κ ¼ 0:42 ð8Þ

3.1. Governing equations The flow under consideration is governed by the incompressible steady 3-D Navier–Stokes equations. For the present work, the conservation equations for the continuity and Reynolds Averaged Navier– Stokes equations, employing the Boussinesq (1897) approximation using the concept of turbulent viscosity μt , can be written as ∂uj ¼0 ∂xj

ρ

ð5Þ

ð1Þ

∂ui uj ∂pn ∂τij ¼ þ ∂xj ∂xi ∂xj

ð2Þ

where ρ is the air density, u is the velocity vector (u, v, and w), pn ¼ p þ 2=3ρk (p is the static pressure and k is the turbulent kinetic energy, and the term 2=3ρk is absorbed into the pressure term following standard practice), and the Reynolds tensor τ ij is given by
 ∂ui ∂uj τij ¼ μe þ ð3Þ ∂xj ∂xi where effective viscosity ðμe Þ ¼ μ þ μt

2D

u (z)

3.3. Computational domain and modeling The computational domain considered in the CFD analysis is shown in Fig. 4. The wind turbine rotor is located 2D downstream of the inlet boundary (D is the rotor diameter), and the point of rotation is considered as the origin point. The rotor, which rotates at 17 rpm, has a diameter of 82 m located at a hub height of 80 m, and the blades airfoils are of the NREL S-series. The maximum chord is 3.25 m at 7 m blade length. The blade is twisted 10.751 at the maximum chord and 41 at a distance of 41.25 m from the hub center. The domain considered for the analysis is 4D in the spanwise direction, and 25D in the downstream region in which the wake will be expanded. The width of the domain used by Ameur et al. (2011) and Zahle et al. (2009) is less than the 4D spanwise width that is used in the simulation. However, they have applied a symmetrical boundary condition, which gives acceptance for the boundary conditions used in the present simulation. The literature suggests that the blockage ratios below about 6–7.5%

25 D

4D

Inlet 4D

Rotor z

Outlet

x Fig. 4. Schematic representation of the computational domain. (a) Front view and (b) side view.

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have a negligible effect on the flow, for any obstructing bodies (Howell et al., 2010). In the case of the wind turbine, as a notable amount of the frontal swept area would actually be occupied by the flow, Howell et al., (2010) considered 16.7% as a blockage ratio. However, in the present simulation, to achieve better results, a blockage ratio of 4.9% is considered. The computational domain was meshed using ANSYS ICEM with an unstructured 3-D mesh, to carry out the wind turbine fluid flow simulation. The grid criteria used for the present study is the same as that used by Abelsalam and Velraj (2014), and the mesh elements adopted for the computational model are shown in Fig. 5. The surface mesh element sizes are controlled to obtain fine mesh elements close to the blades, and the hub, as shown in Fig. 5(a). In order to resolve the strong gradients in the vicinity of the wind turbine rotor, a high concentration of grid points was distributed in the region around and downstream of the rotor, to account for the wake expansion. The surface meshes were created with fine triangles and the grid consisting of layers of prism elements was used near the surface, and tetrahedral elements were used farther away from the surface. The mesh grows in size outward from the rotor surface to the extended domains. The total number of grid points used for the computations is 5.7 millions. The y þ value was found to be about 50–150, and it is in the accepted range for the wall function approach used in the computations.

3.4. Boundary conditions and solution methodology The inlet boundary is a plane located upstream of the wind turbine, as shown in Fig. 4. In this plane, the Sodar data were used to provide the wind speed and turbulence intensity profiles. In the present study, the measurements are not filtered for non-neutral data. A logarithmic wind speed profile is used to describe the change of wind speed with height and is calculated from the wind speed measurements provided by Sodar, as shown in the following equation:
 un z uðzÞ ¼ ln ð9Þ z0 κ where κ is the von Karman constant (equal to 0.42), z is the vertical distance, z0 is an aerodynamic roughness length with a value of 0.03 m that corresponds to the site topology which is a pffiffiffiffiffiffiffiffiffiffi flat terrain, un is the friction velocity, un ¼ τ0 =ρ and τ0 is the surface shear stress. The values of un are calculated depending on the wind speed considered for each case, according to Eq. (9). Fig. 6 shows a comparison between the data obtained from the Sodar measurements and the logarithmic profiles considered for the analysis. The dissipation rate profile at the inlet is found, assuming equilibrium with the production and dissipation of turbulent kinetic energy, from

εðzÞ ¼

u3n κz

The turbulent kinetic energy at the inlet is given by qffiffiffiffiffiffi k ¼ Cu2n = C μ

Fig. 5. The computational mesh. (a) The computational mesh around the rotor and (b) the computational mesh of sectional plane across the blade.

ð10Þ

ð11Þ

where C μ is the model constant. The constant C is introduced to account the turbulence intensity at the inlet. Though these specified boundary conditions are not in equilibrium, they do not affect the solution, as discussed below. The velocity, turbulent kinetic energy, and dissipation rate profiles are implemented in the inlet, by the user defined function UDF, using the former equations. The outlet boundary is a plane located downstream of the wind turbine, at the outlet of the computational domain. In this plane, the static pressure is considered to have a zero value relative to the atmospheric pressure. The ground effect is taken into account by considering the bottom surface as the wall boundary condition. In order to overcome the limitations of the standard rough-wall functions, the boundary condition of Parente et al. (2011) has been implemented at the ground, to specify the velocity, turbulent kinetic energy, and turbulent dissipation rate consistently with the inlet profiles and the turbulence model. The side walls are treated as symmetry boundary conditions, which is to consider the flux of all quantities across this area as zero (∂=∂yðu; w; p; k; εÞ ¼ 0) and zero transverse velocity (v). The wind turbine operates at a rotational speed of 17 rpm. A rotating reference frame was used for the region around the rotor, and a fixed reference frame was used for the rest of the computational domain. At the top boundary, the velocity and the turbulent quantities were set as the same values as those derived from the inlet profiles. Figs. 7 and 8 are presented in order to prove the sustainability of the vertical profiles of the mean wind speed and turbulent kinetic energy with the above considerations accounted in the present work. The vertical profiles of the mean wind speed and turbulent kinetic energy are compared for the extreme values of the constant C used in Eq. (11) of the present investigation (C ¼0.7 and C ¼1.1). The profiles are normalized to the ref value which prevails at the hub height at the inlet. All the figures are drawn for a constant reference velocity of 8 m/s. Figs. 7 and 8 show very

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u (m/s) Fig. 6. Upstream wind speed profiles for U¼ 8, 9, 10, 11, 12, 13, and 14 m/s prevailing at the hub height: Sodar data (symbols), and logarithmic profile, Eq. (9) (solid line).

good consistency of the mean wind speed and the turbulent kinetic energy with the profiles at the inlet. The two extreme values of the constant C show nearly similar results.

Further, simulation trials were also carried out, not presented in the paper, for a computational domain with an upstream length of 10D, to establish more confidence about the flow sustainability.

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3

3

C

C x/D = -2 (inlet)

x/D = -2 (inlet)

-1.5 -1.25 -1

2

-1.5 -1.25 -1

2

z/H

z/H

1

1

0

0 0.2

0.6

1

0.2

1.4

0.6

1

u/U

1.4

u/U

Fig. 7. Vertical profiles of the normalized wind speed at different locations upstream the rotor: (a) C¼ 0.7 and (b) C¼ 1.1.

3

3

C

C x/D = -2 (inlet)

x/D = -2 (inlet)

-1.5 -1.25 -1

2

-1.5 -1.25 -1

2

z/H

z/H 1

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0

0 0.2

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k/kref

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1

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k/kref

Fig. 8. Vertical profiles of the normalized turbulent kinetic energy at different locations upstream the rotor: (a) C ¼0.7 and, (b) C¼ 1.1.

The sustainability of the velocity and the turbulent kinetic energy inlet profiles has been checked. The velocity and the turbulent kinetic energy inlet profiles only deviates less than 1% and 2% respectively across the height of the rotor up to 1D upstream the turbine. However, deviation is higher at the region of 1D upstream the turbine, as the profiles are already affected by the rotor. Hence it is construed that the flow sustainability is accounted in the present work and the non-equilibrium inlet conditions do not change the solution significantly. The complete set of fluid equations consists of the continuity equation, the three momentum equations for the transport of velocity, and the transport equations for k and ε. These equations are solved by employing the commercial multi-purpose CFD solver ANSYS FLUENT 14.0, in the 3-D mode. It uses a control-volumebased technique, for converting the governing equations into algebraic equations, which are to be solved numerically. The solution algorithm adopted is SIMPLE, and the first order upwind scheme is used for all dependent properties. It is mentioned by Ameur et al. (2011) that a scheme of a higher order would have been advisable to reduce the size of the grid, but the use of such a

scheme has led to convergence problems. The results were extracted from the computational domain along different sections downstream of the wind turbine rotor.

4. Results and discussion 4.1. Comparison of the simulated and the measured wake wind speed profiles The results of the computational analysis performed on the three-bladed Kenersys 2 MW wind turbine, operating at a rotational speed of 17 rpm with a rotor diameter of 82 m located at a hub height of 80 m, are compared with the measured wake wind speed profiles, and presented in this section. Since the temperature measurements are not available in the present work, the thermal stability has not been included. Consequently, the CFD computations assumed neutral atmospheric boundary conditions, in which thermal effects are less significant and the heat flux is close to zero. However, in order to ensure that the experimental

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8–14 m/s, with an interval of 1 m/s respectively, measured by Sodar, prevailing at the hub height. The results are compared with the Lidar measurements for selected downwind locations (x/D ¼2, 3, 5, 6, and 7). The prediction gives reasonable agreement with the data measured near the hub height. However, there is an underprediction of the velocity deficit in the lower part of the wind turbine. This may be due to the tower effect, which is not considered in the present study. Also, the larger extension of the wake profiles observed for the experimental data reflects the wake meandering and unsteadiness effects that are not considered in the CFD simulation. The slight deviation observed at the hub

data used for the comparison, approximately represents the neutral measurements considered for the CFD simulation, the experimental data was chosen only for the cases in which the actual data measured upstream by the Sodar matches well with the profiles provided by the logarithmic law of the neutral atmosphere of the present site topology. This can be an approximate guide when selecting the data to be compared with the CFD results. The vertical profiles of the normalized streamwise mean velocity are presented in Fig. 9. Fig. 9(a)–(g) shows the comparison of the results that correspond to the inflow wind speeds of

2.0 x=2D

x=3D

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x=2D

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0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2

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x=3D

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0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2 0.3 0.6 0.9 1.2

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x=3D

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u/U Fig. 9. Comparison of vertical profiles of the streamwise velocity (m/s): Lidar measurements (symbols), prediction (solid line), and undisturbed inlet wind profile (dashed line) at different inlet wind speeds U and turbulence intensities I ¼ su =U prevailing at the hub height. (a) U ¼8 m/s, I¼ 10%, (b) U¼ 9 m/s, I ¼8%, (c) U¼ 10 m/s, I¼ 8%, (d) U¼ 11 m/s, I¼ 10%, (e) U ¼12 m/s, I ¼9%, (f) U¼ 13 m/s, I¼ 9% and (g) U¼ 14 m/s, I¼ 8%.

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height at the first location may be due to the absence of the nacelle in the computations which is expected to increase the thrust in the flow and reduce the velocity. It is worth mentioning also that, part of the deviation may be due to yaw errors that will affect the accuracy of the measurements. It is clearly observed from the measurements and the computational results that, the turbine extracts momentum from the incoming wind, and produces a region of reduced velocity (wake) in the downstream region of the turbine. The reduction in the velocity (deficit) with respect to the upstream flow is largest near the turbine, and it reduces as the wake proceeds downstream, mixing with the surrounding air. It is also observed from both the numerical and experimental results that, the wind still has high

2.0

x=2D

x=5D

x=3D

deficit velocity values up to the last measured location, x/D ¼7 from the turbine position. Due to the non-uniform (logarithmic) wind speed profile of the upstream flow, a non-axisymmetric distribution of the wind speed profile is observed, that results in a non-axisymmetric mean shear in the wake. In particular, as also reported by Chamorro and PortéAgel (2009), the strongest shear is found at the top level of the turbine at the upper tip. This result contrasts with the axisymmetry of the turbulence statistics reported by previous studies, in the case of wakes of turbines placed in free-stream flows (e.g., Medici and Alfredsson, 2006; Troldborg et al., 2007), and it demonstrates the substantial influence of the incoming flow on the dynamics of the wind-turbine wakes.

2.0

x=7D

x=6D

1.5

x=2D

x=5D

x=3D

x=6D

x=7D

z/H

z/H

1.5

1.0

1.0

0.5

0.5

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

I

2.0

x=2D

I

x=5D

x=3D

2.0

x=7D

x=6D

1.5

x=2D

x=5D

x=3D

x=6D

x=7D

z/H

z/H

1.5

1.0

1.0

0.5

0.5 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

I

2.0

x=2D

I

x=5D

x=3D

2.0

x=7D

x=6D

1.5

x=2D

x=5D

x=3D

x=6D

x=7D

z/H

z/H

1.5

1.0

1.0

0.5

0.5

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

I

I

2.0

x=2D

x=5D

x=3D

x=6D

x=7D

z/H

1.5 1.0 0.5

0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

I Fig. 10. Comparison of vertical profiles of the streamwise turbulence intensity: Lidar measurements (symbols), prediction (solid line), at different inlet wind speeds U and turbulence intensities I ¼ su =U prevailing at the hub height. (a) U¼ 8 m/s, I¼ 10%, (b) U ¼9 m/s, I ¼8%, (c) U¼ 10 m/s, I ¼8%, (d) U¼ 11 m/s, I ¼10%, (e) U¼ 12 m/s, I¼ 9%, (f) U¼ 13 m/s, I¼ 9% and (g) U¼ 14 m/s, I¼ 8%.

A.M. Abdelsalam et al. / J. Wind Eng. Ind. Aerodyn. 128 (2014) 54–65

1

0.8

0.6

CT

Fig. 10 presents the vertical profiles of the predicted and measured turbulence intensities I; defined as the ratio of the standard deviation of the wind velocity in the average wind direction and the average wind velocity. The turbulence intensity is commonly used as a measure of the accumulation of fatigue loads which affect the wind turbine placed downstream within a wind farm. At the upper part of the wake, as the velocity gradient is positive and larger, the predicted turbulence intensity shows a maximum near the top-tip level and large growth of the turbulence intensity is predicted in the region from 5 to 7D downstream of the wind turbine. At the lower edge of the wake, the velocity gradient is negative and consequently a decrease in the turbulence intensity is observed. However, the predictions show much lower levels in the inner region of the wake. The comparison between the predicted and measured values is quite large especially in the near wake region. It is worth mentioning that, though wind speed measurements offer high accuracy when compared with those of the sonic anemometer, turbulence cannot be measured with an adequate accuracy through Lidar instruments. Also, Sathe et al (2011) showed that quite large errors existed in the values of the turbulence intensity measured by Lidar. They reported that the errors are up to 90% for the vertical velocity variance, whereas they are up to 70% for the horizontal velocity variance, and hence Lidar cannot be used to measure turbulence precisely.

63

0.4

0.2

0

0

5

10

15

20

25

U (m/s) Fig. 12. The thrust coefficient of the wind turbine at different wind speeds: characteristic curve (solid line), and predicted (dashed line).

0.6 4.2. Velocity deficit

0.5 0.4

Md

Fig. 11 shows the fractional deficit in velocity ðU d Þ at various downstream locations. It is defined as the ratio of ðuin  uw Þ=uin , where uin and uw are the area weighted average velocities across the rotor area at the inlet, and at a particular downstream wake location respectively. It is seen from the figure that, the percentage recovery in the velocity achieved for the various inflow wind speeds converges, as the distance in the downstream direction increases, and the recovery in velocity is slow in the far wake at all the inflow wind speeds. The deficit in the velocity is high for the low inflow wind speed values, and it decreases at high wind speeds. This is consistent with the higher thrust coefficients produced at low wind speeds, as shown in Fig. 12, where the results of the thrust coefficient obtained from the CFD analysis are compared with the characteristic curve provided by the manufacturer. Since the thrust coefficient is not the measured value at the

0.3 0.2

U=8 m/s U=10 m/s U=12 m/s U=14 m/s

0.1 0

0

5

10

15

20

25

x/D Fig. 13. The fractional deficit in the momentum flux at various downstream locations.

0.35 0.3

location where the other measurements are done, the difference could be due to the site topology and other variation in the inlet conditions. Further a small percentage error may also occur due to the errors involved in the CFD simulation.

% Ud

0.25 0.2

4.3. Momentum deficit

0.15 0.1

U=8 m/s U=10 m/s

0.05 0

U=12 m/s U=14 m/s 0

5

10

15

20

25

x/D Fig. 11. The fractional deficit in velocity at various downstream locations.

In order to provide more valuable and useful representation related to the wake downstream of the wind turbine, the fractional momentum deficit is shown in Fig. 13. Assuming that the pressure components are negligible, the momentum flux at the free stream across the rotor area A is given by integration over the area as Z M in ¼ ρ u2 dA ð12Þ A

where u is the local freestream wind speed.The momentum flux at the downstream locations considering the same rotor area A is

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0.7

wind turbine. These experimental data are useful for evaluating the performance of the turbulence models in predicting the wind turbine wakes, and help to provide a basis for the modifications in the models. The wake prediction made, using the Navier–Stokes solver, and employing the k–ε model appropriately modified for the atmospheric flows using the fully mesh resolved rotor, was compared with the experimental measurements. There is a good agreement between the flow velocity evaluated from the CFD analysis and the experimental results measured downstream of the wind turbine. However, there is a considerable deviation in the turbulence intensity since the turbulence cannot be measured with adequate accuracy through Lidar as reported in the literature. Further, it is observed from the wake analysis that, the momentum and power loss increase as the wind speed decreases. The high value of the thrust coefficient associated with low wind speeds, results in a higher reduction in the momentum. The power is proportional to the cube of the wind speed, and hence, an appreciable reduction in power is seen due to the velocity deficit, and its magnitude is higher at lower wind speeds.

0.6 0.5

Pl

0.4 0.3 0.2

U=8 m/s U=10 m/s

0.1 0

U=12 m/s U=14 m/s

0

5

10

15

20

25

x/D Fig. 14. The fractional power loss at various downstream locations.

given by Z M w ¼ ρ u2w dA A

Acknowledgments

ð13Þ

where uw is the local wind speed in the wake. The fractional wake momentum deficit is evaluated as M d ¼ ðM in  M w Þ=M in , where M in and M w are the momentums across an equivalent rotor area at the inlet, and at a particular downstream wake location, respectively. A comparison of the momentum deficit at different freestream wind speeds indicates that, the ratio of momentum loss due to the wake, increases as the wind speed decreases, and the maximum loss is around 2D downstream the turbine. The high value of the thrust coefficient associated with the low speeds, results in a higher reduction in momentum. The turbine characteristics are more important in the near wake region that cause a noticeable difference in the momentum deficit between low and high wind speeds in that region. As the flow goes through the far wake region, the momentum recovers and the influence of the inlet velocity decreases, and the difference in momentum also decreases. 4.4. Power deficit Fig. 14 shows the power loss due to the presence of the wake downstream of the wind turbine. Similar to the above, the fractional power loss due to the velocity deficit in the wake is defined as P l ¼ ðP in P w Þ=P in , where P in and P w are the wind powers available from an equivalent rotor area at the inlet, and at particular downstream wake locations respectively. The power is proportional to the cube of wind speed, and as a consequence, an appreciable reduction in power is seen due to the velocity deficit, which accounts for more than 60% up to 5D downstream locations, at a wind speed of 8 m/s. More than 30% of the loss in power is still incurred, even at 20D downstream for all wind speeds considered in the analysis.

5. Conclusion In the present work, field experiments were carried out for wind turbine wake measurements. The freestream wind speed profiles were available from the Sodar measurements, and the wake wind speed profiles were measured, using a Lidar at a 2 MW

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