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Turbulence within variable-size wind turbine arrays
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2014 J. Phys.: Conf. Ser. 555 012098
(http://iopscience.iop.org/1742-6596/555/1/012098)
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The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
Turbulence within variable-size wind turbine arrays
L P Chamorro, R E A Arndt and F Sotiropoulos
St. Anthony Falls Laboratory, College of Science and Engineering,
University of Minnesota
E-mail: [email protected]
Abstract. A wind tunnel experiment was performed to study turbulence processes within a
model wind turbine array of 3 by 8 model wind turbines of alternating sizes placed aligned
with the mean flow. The model wind farm was placed in a boundary layer developed over both
smooth and rough surfaces under neutrally stratified conditions. Turbulence statistics, TKE
budget terms, and the spectral structure of the turbulence generated within and above the wind
farm reveal relevant information about the processes modulating the turbulent energy transfer
from the boundary layer to the turbines. The results of the experiment suggest that
heterogeneity in turbine size within a wind farm introduce complex flow interactions not seen
in a homogeneous farm, and may have positive effects on turbulent loading on the turbines and
turbulent exchange with the atmosphere. In general, large scale motions are heavily dampened
behind the first row of turbines but a portion of such structures are generated far inside the
wind farm, and the scale of the most energetic eddy motions was relatively consistent at
different elevations. Overall, the experiment revealed the possibility that heterogeneity of wind
turbine size within wind farms have the potential to change the overall potential to harvest
energy from the wind, and alter the economics of a project.
1. Introduction
Wind farm optimization is a multidisciplinary and complex problem where turbulence plays a key
role. Several variables are involved in this problem. Among them are the turbine siting, which include
the inter-turbine separation and spatial arrangement (e.g., aligned [1], staggered [2], or other), wind
resource, local topography, turbine size, turbulence levels, distance to the grid, and access. Research
efforts are underway to reduce the total cost of energy (COE) in wind farms [e.g., 3]. Several
approaches, including genetic [4, 5, 6] and evolutionary [e.g., 7, 8] algorithms have been used to
address this (optimization) problem.
In this investigation we focus on two fundamental aspects of the problem: a) the dynamic involved
when the wind farm has turbines of various sizes, and b) the effect of surface roughness. The
dynamics involved in a wind farm with variable sized wind turbines cannot be inferred directly from
our understanding of the case with homogeneous wind turbines due to the fact that momentum
available around each turbine within a wind farm and the fatigue loads on those turbines are sensitive
to the wind farm configuration.
Understanding the mechanisms that modulate the turbulent energy fluxes from the atmospheric
boundary layer to wind turbine arrays is a necessary condition to tackle the problem of wind farm
optimization by improving the common parameterizations used in the various models (such as wake
distribution). For that reason, our study attempts to contribute toward a fundamental understanding of
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
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Published under licence by IOP Publishing Ltd
1
The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
the dynamic processes occurring in wind farms with variable rotor and hub heights, which can be used
as potential parameters to consider in the context of wind farm optimization.
2. Experimental set-up
Two sizes of miniature wind turbines, with rotor diameters of 0.128 m and 0.178 m, were placed in the
thermally stratified boundary-layer wind tunnel at the University of Minnesota’s Saint Anthony Falls
Laboratory. The model wind farm was placed in a boundary layer developed over both a smooth and a
rough surface. Two wind farm configurations, consisting of 3 rows in the spanwise direction by 8 rows
in the streamwise direction, were analyzed to better address the problem of optimization. All the
experiments were performed under the Reynolds independence regime [9] and the turbines operated at
constant tip speed ratio λ of 4.4 and 4.9 for the small and large models.
A turbulent boundary layer was developed upstream of the test section with a 40 mm picket fence
(serving as a tripping mechanism) located at the exit of the wind-tunnel contraction. Adjustments in
the wind tunnel ceiling allowed it to grow in a zero pressure gradient. The resulting boundary layer
had a well-developed surface layer with constant shear stress and a logarithmic velocity profile for the
neutral stratification regime.
The experiments were conducted in a free-stream velocity of approximately 13.5 ms-1, with a turbulent
boundary layer height of δ ≈ 0.55 m in both the rough and smooth cases. In both cases, the zero
pressure gradient boundary layer had a Reynolds number, based on the boundary layer height (δ), of
Reδ = U∞δ/ν=4.94x105. By fitting a logarithmic velocity profile to the measured average velocity in
the surface layer, a friction velocity of u* = 0.66 ms-1 and an aerodynamic surface roughness length of
z0 = 0.25 mm were found for the rough case. In the smooth case, a friction velocity of u* = 0.54 ms-1
was found, along with an aerodynamic surface roughness length of z0 = 0.002 mm.
A cross-wire anemometer was used to obtain high resolution, simultaneous measurements of both
streamwise and vertical velocity components. The probe is made of 5.0 µm tungsten wires which are
connected to an A.A. Lab Systems AN-1003 10-channel CTA/CCA system. In order to avoid bias
errors due to thermal drift in the voltage signal, temperature fluctuations were kept within ±0.2°C. The
voltage signatures were sampled from the sensor at a rate of 10kHz for a measurement period of 90s.
Calibration of the cross-wire anemometer was performed at the beginning of each experimental run,
with a post-experiment calibration carried out to confirm the validity of the calibration throughout the
experiment. The anemometer was calibrated in a customized calibration unit with a Pitot-static probe,
with the calibration performed with seven sensor inclination angles and eight flow velocities at each
position.
The rough surface was made with chains of 5mm height [10]. In both the smooth and rough cases, the
rows of turbines alternated between large and small, with the leading row consisting of the larger sized
turbines (dTL = 0.178 m). The distance between turbines was set to 8 rotor diameters (of the small
turbines dTS = 0.128 m) in the streamwise direction by 3 rotor diameters in the spanwise direction. The
bottom tip of the small turbines was set to a height of 0.62 times the turbine radius, and 0.65 in the
case of the large turbine, which is similar to that found in large-scale turbines (≥2 MW).
Measurements consisted of vertical profiles in the center of the wind-turbine array (x-z plane) at
incremental steps of one rotor diameter (with respect to the small turbine size) through the wind farm,
from two to seven rotor diameter behind each turbine. Each vertical profile included 39 elevations
ranging from z = 10mm to z = 600mm. Between z=10 to 300 mm, Δz = 10mm, between z = 320 to
400 mm, Δz = 20mm, and between z=450 to 600 mm, Δz = 50 mm. Figure 1 shows a photograph of
the set-up with rough surface and the incoming flow properties for the smooth case.
2
The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
Figure 1. Photograph of the variable size wind farm with the rough surface (left).
Incoming properties in the central plane of the heterogeneous wind farm with a
L
refers to the incoming velocity at the hub of the large
rough surface scenario. U hub
turbine
3. Turbulent flow characteristics in a heterogeneous wind farm
The normalized mean velocity distribution, U/Uhub, for the smooth surface scenario is shown in the
streamwise-vertical (x-z) plane spanning the entire length of the wind farm in Figure 3. In most cases,
a plot from only the smooth or only the rough scenario is provided, except for cases when the
difference between the two scenarios is clearly evident and of relevance. While the mean velocity in
the area above the turbines is slow to adjust, the velocity distribution behind each size of turbine,
within the area below the tip height of the rotor, appears to reach a consistent profile within the second
row of both the small and large turbines. This differs from wind farms of homogeneous size, where the
adjusted velocity profile is typically reached later, approximately within the 3rd to 5th row of turbines
[1].
Significant deviation from homogeneous wind farm turbulence distribution can be seen in the
heterogeneous case, shown in Figure 4 for the rough surface scenario. Specifically, the significant
turbulent wake from the top tip of the larger turbine is mostly avoided by the smaller turbine, leaving
the majority of the small turbine rotor in a relatively low turbulence zone. In addition, the
superposition of the wakes from upstream large and small turbines creates a more uniform turbulence
distribution over the height of the large turbine rotor than in homogeneous wind farm cases [1,2]. This
could work to prevent fatigue on the large turbines, as turbulent loading on the blades has a less
asymmetric characteristic. Figure 4 shows a reduction in near-surface turbulence levels within the
farm from the approaching boundary layer, which will be analysed and discussed at a later point from
detailed inspection of eddy frequency spectra structures in the flow.
Figure 3. Non-dimensional mean velocity distribution in the central plane of the heterogeneous
wind farm. Smooth surface scenario. Black dots represent measurement points.
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The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
Figure 4. Turbulence intensity distribution in the central plane of the heterogeneous wind farm.
Rough surface scenario.
Turbulent kinetic energy production is displayed along with dissipation for the smooth scenario in
Figure 5. These values have been non-dimensionalized with the friction velocity, u*, and the rotor
diameter of the large turbine. The values for production and dissipation are of the same order. The
highest levels of dissipation are seen at hub height behind the turbines. These values are, however,
non-symmetrical, with the areas of maximum dissipation seen slightly above the hub height. The
maximum levels of turbulence produced from each turbine, regardless of size, are seen at the top tip of
the rotor. The flow creates a negligible amount of production below the hub height and at the bottom
tip of the rotor. However, the production profiles of the two sizes of turbine are structurally different.
As shown in Figure 5, the turbulence production structures from the larger turbines extend farther
downstream than those of the smaller turbines. This effect remains even when both the downstream
distance and the production and dissipation values are normalized with the respective rotor diameters
(see more details in [11]).
Figure 5. Turbulent kinetic energy production (top) and dissipation (bottom) distributions in the
central plane of the heterogeneous wind farm. Smooth surface scenario.
The velocity measurements were used to perform a spectral analysis on the flow in order to analyse
eddy frequency and glean information on the tip vortices stability. Figure 6 shows the power spectra at
the top tip height, two rotor diameters (with respect to the smaller turbine) downstream of the first row
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The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
of large and small turbines for both the smooth and rough scenarios. As seen from comparison of the
subfigures, the addition of turbulence and surface roughness negatively impact the stability of the tip
vortices. The rough surface provides a dampening of the spike showing tip vortex frequency for both
the small and large turbines. The turbulence produced by the larger turbines makes the vortices
generated by the small turbines negligible at 2 rotor diameters downstream. Additionally, the rough
surface causes the tip vortices from the small turbine to be completely absent. The large turbine
presents a strong tip vortex signature in the power spectra at approximately the same location as the
small turbines. Like the small turbine spectra, this tip vortex spike is dampened with the addition of
surface roughness.
Figure 6. Spectra of the vertical velocity component two rotor diameters behind the large
turbine of the 1st row at the top tip height for the rough (top left) and smooth (top right) surface
cases. Similar spectra for the small turbine of the 1st row for the rough (bottom left) and smooth
(bottom right) surface scenarios.
While Figure 6 shows the spectra specifically at the top tip of the turbines, Figure 7 provides the
differential power spectra along the entire height of the measurements made throughout the farm at
certain locations downstream. This examines the flow features generated by the turbines in the central
measurement plane. These plots are determined by subtracting the incoming power spectrum from the
local power spectrum at each vertical measurement point at a given downstream point.
Figure 7 provides the spectral contribution of the turbines along various profiles far inside the wind
farm. The spectral contributions are determined by subtracting the incoming pre-multiplied spectrum
from the local one at each vertical measurement point (pre-multiplied spectral difference). It shows
that large scale motions are massively dampened at low heights behind the first large turbine. While
these large scale motions are significantly dampened after the first large turbine, the plots suggest that
the surface roughness far inside the farm recover these large eddy motions, though the recovery is not
complete in the range analysed. At all points within the farm, the distribution of the motions generated
by the turbines are qualitatively similar, with the most energetic flow features generated located
L
around the top tip of the large turbines, with sizes on the order of f × d TL / U hub
≈ 0.2. Although the
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The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
total generated motions are similar farther downstream, they are also more energetic than upstream
motions, as the generation of eddies accumulates.
Figure 7. Pre-multiplied spectra of the streamwise velocity component in the central plane
of the heterogeneous wind farm, six rotor diameters behind the 3rd row of the small (top left)
and large (top right) turbines, and six rotor diameters behind the 1st row of the small (bottom
left) and large (bottom right) turbines. Rough surface scenario.
When analysing the internal boundary layer developed above the wind farm [1], it is seen that the
motions generated are roughly the same as the flow features generated within the wind farm, with the
L
most energetic motions on the order of f × d TL / U hub
≈ 0.2 As evidenced from the downstream
L
L
= 1.75 versus the z / z tip
= 1.25 case, the development of these flow
shifted flow features in the z / z tip
features at higher elevations happens later on in the farm, consistent with the development of the
secondary boundary layer above the wind farm.
L
=1.25 reveals that the large turbines dampen the
The pre-multiplied spectral difference at z / z tip
dominant flow motions that the turbines create above the farm. The accumulated generation of
motions is higher downstream of the small turbines (denoted by thin dashed lines) than downstream of
the large turbines (denoted by thick dashed lines). Therefore, the addition of smaller turbines may
provide an advantage over a homogeneous wind farm setup, as they may enhance turbulent exchange
between the farm and the flow above it.
6
The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
Figure 8. Pre-multiplied spectra of the streamwise velocity component in the central plane
of the heterogeneous wind farm, at a height of approximately 1.25 (bottom) and 1.75 (top)
times top tip height of the large turbine. Thick dashed lines denote locations of large
turbines; thin dashed lines denote locations of small turbines. Smooth surface scenario.
The effect of surface roughness on mean velocity deficit and turbulence intensity deficit in nonnegligible, as seen in Figure 9, showing these profiles six rotor diameters behind the third row of small
turbines. Within the swept area of the turbine rotor (between the dotted lines), the rough surface
lessens the velocity deficit as compared to a smooth surface due to enhanced mixing close to the
ground induced by the higher surface roughness. However, deep within the farm, the generation of
turbulence intensity is higher in the smooth case than in the rough case, where turbulence intensity is
reduced below the hub of the turbine. This is due to the fact that the rough case has a higher
dampening of large scale motions at low elevations, which leads to a net reduction in turbulence
intensity below the hub, as the increased small scale motions do not compensate for the decreased
large scale motions.
7
The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
Figure 9. Change in streamwise velocity component (left) and turbulence intensity (right) in
the central plane of the heterogeneous wind farm, six rotor diameters behind the 3rd row of the
small turbines.
4. Summary
Wind tunnel experiments were performed with 8 alternating rows of 3 small and large turbines in
order to analyse the flow characteristics in and above a model wind farm within a boundary layer flow.
The turbines were placed 8 small rotor diameters apart in the streamwise direction, and 3 small rotor
diameters apart in the spanwise direction. Crosswire anemometry was used to measure average
velocity, turbulence intensity, kinematic shear stress, and production and dissipation of turbulent
kinetic energy. The two setups were characterized by the surface they were placed on, with a smooth
floor, and a surface that was given roughness with chains lay on the ground.
Overall results from this study suggest that an alternation between large and small turbines may have
positive effects on the turbulent loading on both sizes of turbine, and that the complex interactions
between the two sizes of turbine may increase turbulent exchange between the wind farm and the
atmosphere above.
As compared to a homogeneously sized wind farm, the addition of a different size in between rows of
turbines may cause the velocity profiles within the farm to become uniform earlier on, causing more
consistent energy output from downstream turbines.
The superposition of wakes from different sizes of turbine creates different flow conditions than would
be expected in similar homogeneous farms. Turbulent kinetic energy production is more prevalent
from the tip of larger turbines, and extends farther downstream; the turbulence profiles hitting both
sizes of turbine are different from those hitting turbines in a homogeneous farm, and the different sizes
of turbine are responsible for destruction and creation of eddy motions across a larger range of scales.
These additional interactions reveal the possibility that heterogeneity of wind turbine size within wind
farms have the potential to change the overall potential to harvest energy from the wind, and alter the
economics of a project. If there are improvements to be made with heterogeneity, then there are
additional aspects within this parameter that can be analysed and optimized, including heterogeneous
8
The Science of Making Torque from Wind 2012
Journal of Physics: Conference Series 555 (2014) 012098
IOP Publishing
doi:10.1088/1742-6596/555/1/012098
streamwise and spanwise spacing between turbines of different size, optimal differences in size, and
the appropriate staggering of spanwise rows.
Acknowledgments
Funding was provided by Department of Energy DOE (DE-EE0002980) and Xcel Energy through the
Renewable Development Fund (grant RD3-42).
5. References
[1]
Chamorro L P and Porte-Agel F 2011 Turbulent flow inside and above a wind farm: A windtunnel study. Energies. 4, 1916-1936.
[2] Chamorro L P, Arndt R E A and Sotiropoulos F 2011 Turbulence properties within a staggered
wind farm. An experimental study. Boundary-Layer Meteorol. 141, 349-367.
[3] Chowdhury S Zhang J, Messac A and Castillo L 2012 Unrestricted wind farm layout
optimization (UWFLO): Investigating key factors influencing the maximum power generation.
Renew Energy. 38 (1), 16–30.
[4] Mosetti G, Poloni C and Diviacco B 1994 Optimization of wind turbine positioning in large
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[5] Grady A, Hussaini M Y and Abdullah M M 2005 Placement of wind turbines using genetic
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[9] Chamorro L P, Arndt R E A and Sotiropoulos F 2011 Reynolds number dependence of
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[10] Chamorro L P and Porte-Agel F 2009 Wind-Tunnel Investigation of Wind-Turbine Wakes:
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[11] Chamorro L P, Tobin N, Arndt R E A and Sotiropoulos F 2014 Variable-sized wind turbines are
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