Aerodynamically Interacting Vertical-Axis Wind
Turbines: Performance Enhancement and
Ian D. Brownstein 1, Nathaniel J. Wei 1and John O. Dabiri 2,*
1Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
2Mechanical Engineering and Civil & Environmental Engineering, Stanford University, Stanford,
CA 94305, USA
Received: 14 June 2019; Accepted: 15 July 2019; Published: 16 July 2019
This study examined three-dimensional, volumetric mean velocity ﬁelds and corresponding
performance measurements for an isolated vertical-axis wind turbine (VAWT) and for co- and
counter-rotating pairs of VAWTs with varying incident wind direction and turbine spacings.
The purpose was to identify turbine conﬁgurations and ﬂow mechanisms that can improve the
power densities of VAWT arrays in wind farms. All experiments were conducted at a Reynolds
. In the paired arrays, performance enhancement was observed for both
the upstream and downstream turbines. Increases in downstream turbine performance correlate with
bluff–body accelerations around the upstream turbine, which increase the incident freestream velocity
on the downstream turbine in certain positions. Decreases in downstream turbine performance are
determined by its position in the upstream turbine’s wake. Changes in upstream turbine performance
are related to variations in the surrounding ﬂow ﬁeld due to the presence of the downstream rotor.
For the most robust array conﬁguration studied, an average 14% increase in array performance over
approximately a 50
range of wind direction was observed. Additionally, three-dimensional vortex
interactions behind pairs of VAWT were observed that can replenish momentum in the wake by
advection rather than turbulent diffusion. These effects and their implications for wind-farm design
Keywords: 3D-PTV; aerodynamics; VAWT; vortex interactions; wind energy
There is growing interest in the potential for vertical-axis wind turbine (VAWT) arrays to produce
higher footprint energy densities than traditional horizontal-axis wind turbine (HAWT) arrays [
In ﬁeld demonstrations, small VAWT arrays have achieved 24 W/m
of output at 10 m/s wind
], compared to 3 W/m
measured in state-of-the-art horizontal-axis wind farms in similar
. This VAWT array performance was achieved without optimizing for power generation,
suggesting an opportunity for even further improvement with optimization across parameters such as
incident wind direction, turbine spacing, and rotational orientation.
Prior investigations have focused on the mechanisms that result in higher power densities in
VAWT arrays [
]. Field studies have shown that wake recovery behind VAWTs can occur in
as few as 4–6 turbine diameters [
] versus 15–20
behind a HAWT [
]. The spatial extent of this
recovery can be reduced by increasing the solidity [
] or tip-speed ratio [
] of the turbine. This rapid
recovery has been hypothesized to be due to an induced mean vertical ﬂow in the wake of the turbine.
This mean-ﬂow effect has been observed in the wake of an isolated turbine [
] and in an array of
Energies 2019,12, 2724; doi:10.3390/en12142724 www.mdpi.com/journal/energies
Energies 2019,12, 2724 2 of 23
analogous rotating cylinders [
], which have been shown to have similar ﬂow features to VAWTs
]). Turbulent vertical mixing from above the array can also contribute to wake recovery,
as observed in the wake of a single turbine in wind tunnel experiments [
] as well as in turbine
arrays in both ﬁeldwork [
] and simulations [
]. This turbulence-ﬂux effect is well-documented in the
literature (e.g., [
]), while the effects of an induced mean ﬂow have not been extensively characterized.
In addition to the induced vertical ﬂow phenomena hypothesized to be responsible for the rapid
wake recovery behind VAWTs, a growing body of work has demonstrated ﬂow phenomena which
result in synergistic interactions between turbines. Numerical simulations focusing on linear arrays of
turbines perpendicular to the freestream have demonstrated that the average array performance is
higher for turbines in both co- and counter-rotating conﬁgurations than in isolation [
improvements in array performance have been observed in numerical [
], experimental [
and ﬁeld studies [
] of turbines that are angled with respect to the incident freestream. Expanding
this concept to larger arrays of turbines, experimental studies of turbine triplets [
] and numerical
simulations of larger arrays [
] have demonstrated that these effects can be compounded to form
larger arrays with higher average performance than turbines in isolation. Notably, these beneﬁcial
effects are highly sensitive to wind direction, particularly when downstream turbines operate in the
wake of upstream turbines [
]. Wake effects can be stronger than the potential enhancements, thus it is
imperative to develop a fundamental understanding of the ﬂow physics governing these competing
effects when designing an array for environments with variable wind direction.
The majority of previous ﬂow ﬁeld measurements around VAWTs have been limited to planar
]. A study by Caridi et al.
investigated the tip vortices shed by single
blades of a VAWT in three dimensions using time-resolved tomographic PIV, but the small ﬁeld
of view meant that properties of the overall ﬂow ﬁeld around the turbine were not measured.
The only three-dimensional laboratory measurements around an entire VAWT were performed by
Ryan et al. 
. This work measured the three-dimensional, volumetric velocity measurements around
a single VAWT using magnetic resonance velocimetry (MRV) at
is the mean freestream ﬂow speed,
is the rotor diameter, and
is the kinematic viscosity. Other
three-dimensional VAWT ﬂow ﬁeld investigations have been numerical studies [
]. This work has
demonstrated the three-dimensional and asymmetric nature of the ﬂow around VAWT, motivating
the use of three-dimensional measurement techniques in the present work to study the interactions
between multiple rotors.
The primary objective of this study was to characterize the aerodynamic interactions between pairs
of VAWTs through both time-averaged, three-dimensional, three-component velocity measurements
and turbine performance measurements. Speciﬁcally, this study considered three principal array design
parameters for a paired turbine array: the wind direction, the spacing between the turbines, and relative
rotational orientation of the turbines (i.e., co- or counter-rotating). To enable controlled studies of these
three parameters, other design features such as the turbine solidity, aspect ratio, and loading were held
constant. The results of this parametric study will allow aerodynamic considerations to more directly
inform the arrangement of VAWTs in wind farms for optimal power generation.
The remainder of this work is organized as follows. Section 2describes the experimental
methods used, including the procedure for measuring turbine performance and three-dimensional,
three-component velocity ﬁelds. Section 3describes the results of performance and ﬂow-ﬁeld
experiments on an isolated turbine and a turbine pair. Section 4relates the turbine performance
measurements to the measured three-dimensional ﬂow ﬁelds and discusses the implications of this
work for wind farm optimization. Section 5summarizes the contributions of this work.
Energies 2019,12, 2724 3 of 23
2. Experimental Methods
2.1. Facility and Wind Turbines
Experiments were conducted in an open-circuit, subsonic wind tunnel. The test section geometry is
sketched in Figure 1a,b. The ﬂow in this tunnel was provided by a 4
4 grid of fans
located at the tunnel inlet. The test section has a cross section measuring 2.06 m in width by 1.97 m in
height, and it is 4.88 m in length. Two commercially available VAWTs
in this facility. Each turbine comprised a 5-bladed rotor that rotated a 3-phase AC permanent magnet
generator. The 5-blade conﬁguration, although not necessarily optimal for efﬁcient power generation,
was chosen to parallel the turbines currently installed at the Field Laboratory for Optimized Wind
Energy (FLOWE) (cf. [
]). The rotors were modiﬁed to have a diameter
of 0.20 m. The blades had
a constant NACA 6415 airfoil shape with the pressure side of the airfoil oriented to the outside of the
rotor, chord length
of 0.045 m, pitch angle
, and span
of 0.31 m. This corresponds
to an aspect ratio
of 1.55 and a stationary turbine solidity
of 0.36. The total height
of each turbine, including the tower mounted below the rotor, was 0.898 m. Both turbines could
be oriented to rotate clockwise or counter-clockwise, as viewed from above, by reversing the blade
orientations. The maximum blockage ratio in this facility, based on the total frontal projected area of
both turbine rotors, was 3.1%.
) Side-view and (
) top view of the wind tunnel test section with the two turbine array
shown. In both views. the ﬁlled black rectangles represent the fan grid and the dashed black rectangles
represent the maximum extent of the particle tracking measurement domain. The red dots illustrate
the conﬁguration of the seven-camera setup above the wind tunnel. All cameras were installed at
the same height above the tunnel, and were oriented such that the turbine pair was in the center of
the frame. (
) Illustration of the two turbine array geometry and the coordinate system used in the
wind tunnel. Turbine 1
was deﬁned as the upstream turbine and is located at a ﬁxed position at
Z) = (
0, 0, 0
. Turbine 2
is the downstream turbine and could be located at angles
respect to the freestream
and turbine spacings
Both turbines could be oriented to rotate either clockwise or counter-clockwise.
The mean freestream speed
measured in the particle tracking measurement domain,
illustrated in Figure 1a,b, was 5.6
0.3 m/s, resulting in a Reynolds number based on the turbine
of approximately 7.3
. At this freestream speed, the two turbines freely rotated at
0.06 rev/s and
0.09 rev/s. This free-spinning case (i.e.,
no load) was used for all experiments and corresponds to a tip-speed ratio
for the turbines
0.04. This tip-speed ratio was deﬁned for all experiments using
the free-stream ﬂow velocity in the wind tunnel (
), which, being a far-ﬁeld measurement, is a more
reliable metric for comparisons than the ﬂow conditions immediately upstream of each turbine. This
tip-speed ratio matches the optimal tip-speed ratio for the full-scale 2-kW VAWTs at the FLOWE ﬁeld
Energies 2019,12, 2724 4 of 23
site, a result shown both in ﬁeld data and in laboratory experiments at full dynamic similarity [
low tip-speed ratios are characteristic of turbines with relatively high solidities (e.g., [
]), since the
optimal tip-speed ratio for VAWT operation decreases with increasing solidity
. The application
of the results shown in this paper to turbines with lower solidity (e.g., [
]) is discussed in more detail
in Section 4.
To study the interactions between the two turbines in different incident wind directions,
the turbines were oriented in a polar coordinate system deﬁned by the turbine center-to-center spacing
and the array angle
with respect to the freestream. The origin of this coordinate system was
located in the center of the upstream turbine rotor. This array geometry is illustrated in Figure 1c.
The upstream turbine was deﬁned as Turbine 1
and was at a ﬁxed position of 2.81 m
from the test section inlet and in the center of the tunnel width (i.e., 5.15
from the sides of the
tunnel). The downstream turbine, Turbine 2
, was positioned within
turbine spacings within 1.25
. Therefore, for all of the arrays studied, the closest blade on
the downstream turbine was always ≥1.65 Dfrom the tunnel walls.
2.2. Performance Measurements
To quantify the performance of each turbine, the voltage between each pair of the three phases
of the turbine generator was collected using a data acquisition device
. The measured
voltage was reduced using a 2:1 voltage divider to keep the signal within the range of the acquisition
device rated input. The induction generator used with the turbines was operated within its linear
regime, such that higher rotation rates produced proportionally higher induced currents and thus
proportionally higher torque [
]. Thus, the generator rotational rate was used as a surrogate for
turbine performance since it is proportional to the peak-to-peak voltage measured and the energy
extracted by the turbine. This method was shown by Brownstein et al.
to correlate with power
measurements with an
value of 0.99, and was used in these experiments to provide a lower-noise
measure of performance than the power measurements. The net aerodynamic torque generated by
the turbines was only resisted by the bearing friction. While this is not a power-producing regime,
the operation regime of net zero torque was shown by Araya and Dabiri
to be physically relevant
for studying the ﬂow around VAWTs.
Data were collected by moving the turbines into position, followed by a 90-s period for the turbine
rotational rates to reach steady state. Three 10-s time-histories of the performance measurement were
subsequently recorded at 5 kHz, with a 20-s temporal spacing between sequential measurements. Each
turbine position was measured two or more times, resulting in a minimum of six time-histories of the
performance measurement per array conﬁguration tested.
Turbine performance measurements were collected for the turbine pair in co-rotating and
counter-rotating conﬁgurations. For the co-rotating array, data were collected at turbines spacings of
, and 3
. The turbines were oriented to rotate clockwise when viewed from above.
For the counter-rotating array, data were collected only at a turbine spacing of 1.25
, because this
spacing corresponded to signiﬁcant performance enhancement due to aerodynamic interactions
between the VAWT pair. Two mirror-symmetric cases were measured with the upstream turbine being
clockwise or counter-clockwise oriented when viewed from above. Due to the geometric symmetry of
these two conﬁgurations, these cases are identical with respect to the adjusted array angle,
where χis an indicator function to designate the orientation of a turbine:
χ≡(1 clockwise rotating (CW)
−1 counter-clockwise rotating (CCW)(1)
For all experiments, data were collected in 10
. For comparison
to the paired turbine performance measurements, data were also collected with the individual turbines
Energies 2019,12, 2724 5 of 23
in the same positions as in the array, but with the other turbine removed. This allowed for normalization
of the turbine performances in the paired conﬁgurations as described by:
is the rotational rate of turbine
in a given array conﬁguration;
is the rotational
rate of turbine
at a given position without the other turbine present;
is the normalized
rotational rate of turbine
in a given array conﬁguration; and
= 1 or 2, corresponding to Turbine 1 or
2. This normalization removed the effects of small spatial variations in the incident wind speed so
that comparisons could be made between the performances of the various array conﬁgurations. This
normalization also removes potential for wall effects from the data in the cases where the downstream
turbine is closest to the wind tunnel walls.
2.3. Flow Velocity Measurements
2.3.1. Tracking Technique and Data Collection
To quantify the ﬂow ﬁeld around the turbines, three-dimensional particle tracking velocimetry
(3D-PTV) was used. Since this study sought to characterize the entire ﬂow ﬁeld around two VAWTs,
resolving dynamic-stall effects on individual blades, which are generally conﬁned to a region relatively
close to the blade surface, was not possible (cf. [
]). Since the amplitudes of the angle-of-attack
variations were high and the corresponding reduced frequency was relatively low (
given the turbine’s low tip-speed ratio, dynamic-stall effects were expected to appear as bluff–body
separation events that would not change much under the conditions explored in this study [
]. The use
of time-averaged 3D-PTV data served to emphasize general trends in ﬂow–momentum distribution
and wake geometry between different test cases over unsteady effects.
Neutrally buoyant helium ﬁlled soap bubbles (HFSB) measuring
1 mm in diameter (Sage
Action Model 5) were released at the tunnel inlet and illuminated by two ellipsoidal lights (Source
Four Jr., 575 W halogen bulb). The bubbles were recorded using seven hardware-synchronized cameras
(Adimec N-5A100) positioned above the wind tunnel. The cameras were arranged in a cross pattern
above the tunnel, as shown in Figure 1b. Their positions and the maximum extent of their mutual
ﬁeld of view, which was centered around the pair of turbines, are also depicted schematically in
the ﬁgure. The relative positions and orientations of the cameras were calibrated using the protocol
developed by Theriault et al.
. For ﬂow measurements, images were captured at a resolution
1440 pixels and at 250 Hz. Particles were identiﬁed in each image using a thresholding
technique after masking the rotor. The identiﬁed particle positions in each image plane were translated
into three-dimensional space using epipolar geometry [
]. Particles were only triangulated into
three-dimensional space when they appeared on at least three cameras. This reduced the number of
ghost particles created in the three-dimensional reconstruction [
], so that the ﬁnal velocity ﬁelds
would be free from spurious vectors. These three-dimensional positions were translated into particle
trajectories and differentiated numerically to obtain velocities using a multi-frame predictive tracking
]. Time-averaged mean velocity ﬁelds were then calculated by averaging the ﬂow in
voxels measuring (2 cm)
. This voxel size was chosen to balance the resolution in the time-averaged
velocity and vorticity ﬁelds reported in this study and the uncertainty associated with low vector
counts. For this resolution, the distribution of the number of vectors per voxel from the freestream
measurement is shown in Figure 2a. Bootstrapping methods described by Efron
were used on the
voxel with the largest number of vectors to estimate the variability in voxel time-averaged means for
which less data are collected. This was done by taking 2000 re-samplings of the data and calculating
the standard deviation of means from the re-sampled data (
). The resulting standard deviations
are plotted in Figure 2b. These ﬁgures show that a majority of voxels contained ten or more vectors,
enough to produce a stable average as indicated by
. To limit voxels that represent the inﬂuence of
Energies 2019,12, 2724 6 of 23
instantaneous ﬂuctuations, voxels containing fewer than three velocity measurements were excluded
from the ﬁnal vector ﬁelds. Vorticity ﬁelds were then calculated by numerically differentiating the
time-averaged velocity ﬁeld using a ﬁve-point stencil. The smoothing inherent in the time-averaging
procedure was sufﬁcient to resolve vortical structures upon spatial differentiation of the velocity ﬁeld,
despite the higher noise levels in the vorticity ﬁelds.
) Distribution of number of vectors per (2 cm)
voxel in the freestream measurement with
an empty test section. (
) Standard deviation of the means of
calculated from 2000 re-samplings of
) versus the number of vectors used in the re-sampling. Data are from the voxel with the
most vectors in the freestream measurement.
Using this setup, three-dimensional velocity measurements were collected for the freestream
ﬂow, a single turbine, and for turbine pairs. These data were recorded over eight- or ten-minute
measurement periods, resulting in approximately 4000–5000 turbine rotations. For the single turbine,
data were collected for both clockwise and counter-clockwise orientations. Due to the symmetry
between these experiments and the offset measurement domain, the results were combined into a
single dataset with a larger effective measurement domain. For the turbine pairs, a single turbine
spacing and array angle were studied (
) for all four combinations of rotational
conﬁgurations (i.e., clockwise co-rotating, counter-clockwise co-rotating, reverse doublet, and doublet).
According to conventions established in the wind-turbine literature (e.g., [
]), the rotational
conﬁguration is deﬁned to be a doublet when the blades between the rotors are advancing upstream
and a reverse doublet when the blades between the rotors are retreating downstream. These cases
were isolated because they lay in the
regime where signiﬁcant performance enhancement was
observed, so that the ﬂow mechanisms responsible for these enhancements could be identiﬁed.
In addition to the three-dimensional measurements, vertically aggregated (i.e., along the blade
)) two-dimensional particle trajectories were obtained for the same turbine conﬁgurations
for which three-dimensional data were collected. For these measurements, the illumination was
constrained to within
to minimize three-dimensional effects. These data were collected
with the camera centered above the turbines recording at 250 Hz for one minute. Particle trajectories
were then visualized by making a composite image such that each pixel value is the maximum value
at that pixel location measured over the recording. Because these images showed individual particle
tracks up to the edge of the swept area of the turbine, they were used to show qualitatively where the
ﬂow separated from the turbine proﬁle.
2.3.2. Characterization of Wind Tunnel
The HFSB tracers were used in this study due to their ability to provide optical ﬂow measurements
in large measurement domains in a wind tunnel [
]. In previous studies, HFSBs have been
identiﬁed as valid tracers for measuring quantitative ﬂow features as long as they are neutrally
]. In this study, the HFSB were restricted to being neutrally buoyant using a ﬁlter
Energies 2019,12, 2724 7 of 23
which removes lighter and heavier than air tracers from the ﬂow. The Stokes number, i.e., the ratio
of the particle response time to a characteristic time scale of the ﬂow (
), was calculated to
quantify how faithfully the HFSBs used in this study follow the ﬂow. The particle response time of
each bubble was calculated using the relation for a small sphere reported by Crowe et al.
0.0036 s. In this relation,
is the density of the bubble,
is the diameter of the bubble,
is the dynamic viscosity of air. Since mean ﬂow ﬁelds will be investigated in this study, the time
scale of the ﬂow is estimated as the ratio between the dominant scales in the ﬂow, i.e., the turbine
) and freestream velocity (
). This results in
0.036 s. This corresponds
to the threshold
0.1 below which Tropea et al.
noted that ﬂow tracking accuracy errors are
typically below 1%.
To characterize the wind tunnel freestream, 3D-PTV measurements were recorded with an empty
test section. Three proﬁles of the normalized streamwise velocity are plotted in Figure 3. The observed
standard deviations correspond to the turbulence intensity in the tunnel,
0.01. These proﬁles
were used to determine the maximum extent of the particle tracking domain based on where the ﬂow
was sufﬁciently uniform. Additionally, the discontinuities at the edges of the domain are caused by
relatively fewer vectors passing through the edges of the domain deﬁned by the cameras’ mutual ﬁeld
Proﬁles of the normalized streamwise velocity averaged in both time and two spatial
). Dashed lines indicate the maximum extent of the measurement domain used
in particle tracking.
3.1. Performance Adjustments in Paired Turbine Arrays
In this section, the performance characteristics of paired turbines are demonstrated. This is
followed by a more detailed investigation of the ﬂow-ﬁeld features responsible for the performance
trends identiﬁed from these experiments. An extended discussion of the results presented in these
subsections follows as Section 4.
3.1.1. Performance Dependence on Relative Turbine Orientation
The normalized performances of both turbines in co-rotating and counter-rotating arrays for the
smallest turbine spacing tested,
, are plotted in Figure 4versus
. These results demonstrate
that the performance of both turbines exhibits three distinct regimes in
, based on the location of the
downstream turbine relative to the wake of the upstream turbine.
The ﬁrst regime
, where the downstream turbine lies within the region of
reduced ﬂow speed behind the upstream turbine, is characterized by strong gradients in the normalized
performance of the downstream turbine. Thus, we call this the wake regime. The performance of
Energies 2019,12, 2724 8 of 23
the downstream turbine decays far below its isolated performance until it is completely arrested at
in both the co- and counter-rotating arrays. In contrast to the downstream
turbine, the upstream turbine performance in this regime is relatively level around its performance in
isolation. A qualitatively similar result has been shown in 2D numerical simulations using a simpliﬁed
momentum-source model to represent the turbine pair .
In the second regime
, both the upstream and downstream turbines rotate at or above
their performance in isolation. The measured enhancement is most signiﬁcant for both turbines in the
co-rotating conﬁguration. The results in this regime exhibit similar trends to 2D simulations of a pair
of co- and counter-rotating three-bladed VAWTs (
] and an array of three Savonius-type
turbines (φ∗=60◦) .
Normalized performance of (
) Turbine 1 and (
) Turbine 2 versus adjusted array angle (
for a turbine spacing of
. Error bands represent plus or minus one standard deviation from
the mean measurement.
In the third regime
, the upstream turbine performance drops below that of its
performance in isolation. In the co-rotating case, this drop is less signiﬁcant than in the counter-rotating
case. In contrast to the upstream turbine, the downstream turbine performance has a strong peak at
φ∗=−50◦in the counter-rotating case and φ∗=−80◦in the co-rotating case.
These data indicate that the orientation of each turbine plays a role in the performance of the other
turbine. Signiﬁcantly, not only does the upstream turbine orientation affect the performance of the
downstream turbine, which as been observed in previous work [
]; however, the downstream
turbine orientation also affects the performance of the upstream turbine.
Of note, the upstream and downstream turbine performance at
not identical in the co-rotating case, as would be expected on the basis of geometric similarity. This
asymmetry was attributable to the corresponding mild asymmetry in the tunnel freestream ﬂow
presented in Figure 3.
3.1.2. Performance Dependence on Turbine Spacing
The normalized performance of both turbines at four turbine spacings,
are plotted in Figure 5for the co-rotating array. As in the results presented for the
smallest turbine spacing in the previous section, the performance of both turbines is approximately
broken into the same three regimes in φ∗.
Energies 2019,12, 2724 9 of 23
Normalized performance of (
) Turbine 1 and (
) Turbine 2 versus adjusted array angle
for turbine spacings of 1.25
, and 3
in a clockwise, co-rotating array. Error bands
represent plus or minus one standard deviation from the mean measurement.
Similar to the
array cases, the wake regime
is characterized by
strong gradients in the normalized performance of the downstream turbine. Notably, the strength
of these gradients increases with increased array spacing. The effect of the wake also decays with
increased array spacing. Additionally, for all spacings, the upstream turbine performance is similar to
its performance in isolation.
In the second regime
, a broad enhancement is observed for both turbines. In this region,
the maximum enhancement occurs for the closest array spacing and decays uniformly with increased
array spacing. This decay is more rapid for the upstream turbine than the downstream turbine.
In the third regime
, downstream turbine performance enhancement is observed
in a limited range of
values, i.e., the downstream turbine quickly reaches a peak enhancement
before decaying back toward its isolated performance as
. In this regime, the maximum
peak enhancement of the downstream turbine is observed for an array spacing of
within the resolution of adjusted array angles measured
, these peak performances occur at
the same cross-stream coordinate
with a median location at
for the co-rotating cases.
This coordinate corresponds with the enhancement region observed downstream of an isolated VAWT
in Figure 6. For the upstream turbine, this regime in
is characterized by relatively level performance.
To understand how the ﬂow ﬁeld around the pair of turbines corresponds to these changes
in performance, a representative array angle of
was selected, at which varying degrees
of performance enhancement were observed for all combinations of turbine rotation directions.
An intermediate spacing of
was chosen to maximize the observed performance enhancement
while still allowing the accelerated ﬂow region between the two turbines to be fully resolved.
3.2. Flow Features of an Isolated Turbine
3.2.1. Velocity Field around an Isolated Turbine
Before paired-turbine interactions were studied, ﬂow patterns around an isolated VAWT were
recorded in the wind tunnel to serve as a baseline. A qualitative quasi-two-dimensional view of
the ﬂow around a single VAWT is depicted in Figure 7. This image shows blade span-aggregated
particle trajectories around the mid-span of a clockwise rotating turbine. Particle tracks bending
around the rotor demonstrate ﬂow acceleration around the turbine. Additionally, the slow moving
(i.e., bright) trajectories downstream of the turbine illustrate the turbulent wake behind the rotor.
The wake is slightly deﬂected as it extends downstream due to the rotation of the turbine. The cyan
dots shown on the rotor represent points at which the ﬂow visibly “detaches” from the rotor, serving
Energies 2019,12, 2724 10 of 23
as an approximate indicator of the radial extent of the wake region. This idea is developed further in
the context of the turbine pair.
A quantitative view of this ﬂow is provided in Figure 6, which shows three cross-sections of
the normalized streamwise velocity (
) around a clockwise rotating VAWT. These three views
together demonstrate the spatial extent of both the wake behind the turbine as well as the regions of
accelerated ﬂow around the turbine. In Figure 6a, it is observed that the spatial extent of the accelerated
is asymmetric. On the side of the rotor where the blades are passing downstream
0), the accelerated ﬂow region is broad and persists throughout the ﬁeld of view laterally
away from the rotor and the wake boundary. On the other side of the rotor, where the blades are
advancing upstream toward the tunnel inlet (
0), the spatial extent of the accelerated ﬂow
is limited and extends
laterally from the wake boundary and downstream of the rotor center
0). Additionally, this view quantiﬁes the observation made in Figure 7that the wake is
deﬂected. In the center of this deﬂected wake, a reverse ﬂow region, which extends from the rotor is
observed. Similar reverse ﬂow regions have been observed in previous studies of VAWTs [
In Figure 6b, it is observed that the accelerated ﬂow region surrounds the entire wake region.
Additionally, this plane highlights the deﬂection of the wake, as it is not centered on the projection of
the turbine. Figure 6c provides another view of the wake recovery and the acceleration of the ﬂow
above the rotor. A relatively fast recovery of the tower wake is also observed.
Contours of the normalized time-averaged streamwise velocity (
) around a clockwise
rotating VAWT at the planes: (
1; and (
0. The grey and black contour
1, respectively. The dashed black lines denote the projection of
the turbine on the plane. The overlaid vectors denote the in-plane velocity. Vectors are shown at 25% of
the recorded resolution for visual clarity. The direction of the VAWT rotation is denoted by the blue
arrow. The empty regions in the immediate vicinity of the turbine represent zones in which particles
were not able to be tracked in multiple camera views.
Energies 2019,12, 2724 11 of 23
Particle trajectories of neutrally buoyant HFSB tracers around a clockwise rotating VAWT.
Particle trajectories are only visualized between
0.18. The rotor projected on the image is in
an arbitrary orientation and the white circle denotes the boundaries of its rotation. The direction of the
rotor rotation is denoted by the blue arrow. The cyan dots denote the position where the trajectories
“detach” from the rotor.
3.2.2. Vortical Structures Downstream of an Isolated Turbine
Isosurfaces of the streamwise vorticity (
) around a clockwise and counter-clockwise rotating
VAWT can be seen in Figure 8. The isosurface value of
represents the vorticity expected to be
shed based on the dynamic characteristics of the turbine (cf. [
]). These structures extend from
the top and bottom of the rotors and propagate downstream. Similar structures were observed by
Ryan et al.
, who demonstrated that at a higher tip-speed ratio the strength of these structures
increases. This study adds to previous work by observing that these structures are symmetric in
their streamwise spatial extent when sufﬁciently far from any tunnel boundaries. Additionally,
the differences in Figure 8a,b demonstrate that the rotational orientation of these structures are
dependent on the rotational orientation of the turbine. While data were not collected directly adjacent
to the rotor, the sign of the vorticity in these wake structures suggests that they originate from the
vorticity imparted to the ﬂow by the spinning rotor. As this vorticity extends beyond the rotor it is bent
by the ﬂow and aligns with the direction of the freestream. This linked U-shaped vortical structure is
illustrated by the grey vortex lines and rotational arrows drawn on Figure 8.
Energies 2019,12, 2724 12 of 23
Three-dimensional isosurfaces of the time-averaged streamwise vorticity for
) clockwise and (
) counter-clockwise rotating VAWT. Positive vorticity is depicted as red
and negative vorticity as blue. The transparent cylinders represent the maximum extent of the rotor
and the turbine tower. The direction of the VAWT rotation is denoted by the grey arrows in the center
of the rotors. The grey curve represents the hypothesized connecting vortex line between the turbine
and the counter-rotating isosurfaces.
A comparison with vortical structures observed in the case of a ﬁnite wall-mounted cylinder
provides some helpful context to these results. Analogies between VAWTs and rotating cylinders
were explored by Araya et al.
and Craig et al.
, but they did not capture the full 3D ﬂow ﬁeld.
A short cylinder mounted to a wall sheds counter-rotating tip vortices from its top surface that are
directed downstream of the cylinder [
]. Although the VAWT is neither solid nor wall-mounted,
one would still expect the same kind of tip vortices to form. The velocity induced by the rotation of
the turbine on the downstream side feeds one of these vortices and interferes with the other, which
is why only one vortex line is visible in the data. Since the lower end of the VAWT is not ﬁxed to a
wall, the presence of a corresponding structure with opposite sign emanating from the underside of
the turbine is expected. Since these structures are typically thin and stretched by the freestream ﬂow
above them (e.g., [
]), it makes sense that they would not be cleanly visualized given the nature of
the 3D-PTV experiment. Lastly, the induced velocity of the rotating turbine accounts for the spanwise
shift of these structures in relation to their reported locations in the wall-mounted cylinder literature.
Figure 9show isosurfaces of the transverse vorticity (
) and vertical vorticity (
a clockwise rotating turbine. Together, the counter-rotating structures found in these vorticity
components form a single coherent ringed vortical structure, which is positioned within the wake
1). This structure is a manifestation of fast-moving ﬂuid outside the wake being
pulled inward as the wake recovers. Unlike the streamwise vorticity, the orientation of this coherent
vortical structure is insensitive to the rotational orientation of the turbine. The structure is similar to
the so-called arch vortex observed behind ﬁnite wall-mounted cylinders [
]. This structure stems
from bluff–body separation behind the cylinder, and thus its sign invariance relative to the rotation of
the VAWT is expected.
Energies 2019,12, 2724 13 of 23
Three-dimensional isosurfaces of the time-averaged (
) transverse vorticity (
) vertical vorticity (
around a clockwise rotating VAWT. Positive vorticity
is depicted as red and negative vorticity as blue. The transparent cylinders represent the maximum
extent of the rotor and the turbine tower. The blue arrows on top of the rotors denote the direction
of the turbine rotation. These structures roughly correspond to bluff–body wake structures shed by a
ﬁnite wall-mounted cylinder.
3.3. Flow Features of a Pair Turbines
3.3.1. Velocity Fields around a Pair of Turbines
Once the baseline ﬂow conditions around an isolated turbine were established, the ﬂow ﬁelds
around a pair of VAWTs could be characterized. Blade span-aggregated particle trajectories of the ﬂow
around four conﬁgurations of VAWT pairs are presented in Figure 10 in order to show schematically
the differences in ﬂow topology. It is observed in all four cases that the ﬂow between the rotors is
signiﬁcantly modiﬁed when compared to the upstream turbine in isolation (i.e., in Figure 7). In the
clockwise co-rotating case, Figure 10a, a coherent jet-like structure is formed which propagates
downstream at an
angle from the line between the rotor centers. A less prominent form of
this jet-like structure is formed for the reverse doublet and doublet arrays, Figure 10c,d. In these cases,
the deﬂection of the jet is less pronounced.
In addition to the ﬂow between the rotors being modiﬁed, the shape of the wakes behind the
individual rotors is modiﬁed by the presence of the second rotor. This can be visualized near the
rotors by the location where the particle trajectories “detach” from the rotor. While the concept of ﬂow
separation for a porous rotating body is not a precisely deﬁned concept, the points of detachment are
deﬁned here as the locations where the trajectories turn away from the rotor. In Figure 10, these points
are marked by the cyan dots for the upstream turbines and the magenta dots for the downstream
turbines. The locations of these detachments are discussed further in Section 4.1.2.
Energies 2019,12, 2724 14 of 23
Particle trajectories of neutrally buoyant HFSB tracers around four turbine pairs at a turbine
and an array angle of
. The four turbine conﬁgurations represented are:
) clockwise co-rotating; (
) counter-clockwise co-rotating; (
) reverse doublet; and (
) doublet arrays.
Particle trajectories are only visualized between
0.18. The rotor projected on the image is in
an arbitrary orientation and the white circle denotes the boundaries of its rotation. The direction of the
rotor rotation is denoted by the blue (clockwise) and red (counter-clockwise) arrows. The cyan and
magenta dots denote the position where the trajectories “detach” from the upstream and downstream
To quantify these ﬂow modiﬁcations in more detail, cross-sections of the ﬂow through the rotor
0), derived from the measured time-averaged three-dimensional ﬂow ﬁeld around
these turbine conﬁgurations, are shown in Figure 11. These contours provide a more precise method of
evaluating the ﬂow features identiﬁed in the spanwise aggregated particle trajectory views in Figure 10.
The jet-like features observed in the particle trajectory images are also observed in these contour plots.
These structures transport high momentum ﬂuid into the wake of the turbine pair. Notably, in the
reverse doublet array (Figure 11c), the ﬂow is accelerated to values of
1 between the rotors.
Additionally, it is observed that the ﬂow incoming to the rotors in the clockwise co-rotating case is
accelerated by the turbine pair before passing through the downstream turbine and a portion of the
upstream turbine. In the cases where the upstream turbine is counter-clockwise rotating, accelerated
regions are only observed toward the outer lateral edges of the array.
In addition to transport of high momentum ﬂuid through the array, Figure 11 demonstrates
signiﬁcant wake suppression or enhancement due to the turbine interactions. In all of the array
conﬁgurations measured, the wake of the upstream turbine is suppressed such that there is no
signiﬁcant reverse ﬂow region. This type of suppression is also observed for the downstream turbine
in the counter-clockwise co-rotating case (Figure 11b). For the other cases, a signiﬁcant reverse-ﬂow
region is present. In the clockwise co-rotating and doublet arrays (Figure 11a,d), this reverse-ﬂow
region is signiﬁcantly larger than it would be if the downstream turbine were operating in isolation.
The presence of the reverse-ﬂow region appears to depend primarily on the ﬂow accelerations from the
upstream turbine—namely, the acceleration of ﬂow on the side of the turbine rotating with the wind,
and the deceleration of ﬂow on the side of the turbine rotating into the wind. These properties dictate
Energies 2019,12, 2724 15 of 23
the distribution of ﬂow momentum around the rotors. This suggests that the marked performance
enhancement observed for this case is associated with the redirection of momentum in the vicinity of
Contours of the normalized time-averaged streamwise velocity (
) around: (
) counter-clockwise co-rotating; (
) reverse doublet; and (
) doublet arrays at the plane
0. The arrays have a turbine spacing of
and are at an array angle of
. The grey
and black contour levels denote
1, respectively. The dashed black lines denote
the projection of the turbine on the plane. The overlaid vectors denote the in-plane velocity. Vectors
are shown at 25% of the recorded resolution for visual clarity. The direction the individual VAWT
rotations are denoted by the blue (clockwise) and red (counter-clockwise) arrows. As in Figure 6,
the empty regions around the turbines correspond to locations where particles could not be tracked in
3.3.2. Vortical Structures Downstream of a Pair of Turbines
Isosurfaces of the streamwise vorticity (
) around the four paired turbine conﬁgurations are
shown in Figure 12. As in the single turbine cases (Figure 8), these structures primarily extend from
the top and bottom of the rotor and propagate downstream. Due to this preferential alignment and the
complex nature of these structures, the views in Figure 12 are oriented facing upstream from behind the
turbines for ease of discussion. While the streamwise vortical structures are less coherent in the paired
arrays than in the isolated turbine cases, the dominant rotational sense of the structures compared
to that of the VAWT that they propagate from is consistent with the single turbine observations.
Speciﬁcally, for the co-rotating cases, the top and bottom of the turbine pair are primarily populated
with streamwise vorticity of a single sign. In the counter-rotating cases, the turbines are shedding
streamwise vorticity with opposite rotational orientation of the neighboring turbine. These structures
interact to either pull ﬂuid into the wake of the two turbine system or repel ﬂuid outward. This is
quantiﬁed in Figure 13, which shows transects of the normalized vertical velocity (
) between the
rotors and downstream of the array. Speciﬁcally, in Figure 13c, it is noted that momentum is pulled
into the reverse doublet array wake from above and below the rotor. In contrast, Figure 13d shows
momentum is pulled out of the doublet array wake in both directions. In both cases, the sign change
in the vertical velocity occurs around the rotor center (
0). These effects have not been captured
in previous numerical or experimental work, which have generally only studied ﬂow features in two
dimensions (e.g., [4,5,8,22,23]).
Energies 2019,12, 2724 16 of 23
Three-dimensional isosurfaces of the time-averaged streamwise vorticity at the value
) clockwise co-rotating; (
) counter-clockwise co-rotating; (
) reverse doublet;
) doublet arrays. The arrays have a turbine spacing of
and are at an array angle of
. Positive vorticity is red and negative vorticity is blue. The transparent cylinders represent the
maximum extent of the rotor and the turbine tower.
Vertical transects of the normalized time-averaged vertical velocity (
downstream and laterally between the rotors (
0.57). Data are shown for: (
) counter-clockwise co-rotating; (
) reverse doublet; and (
) doublet arrays. The arrays
have a turbine spacing of
and are at an array angle of
. The dashed black lines
denote the top and bottom of the rotors in the array. The transects were smoothed using a ﬁve-point
Energies 2019,12, 2724 17 of 23
4.1. Relating Performance Variations and Flow Measurements
In this section, the results presented in the previous section are further discussed, in order to show
that performance enhancements in a pair of VAWTs are due to changes in the mean ﬂow ﬁeld around
both the upstream and downstream turbines.
4.1.1. Downstream Turbine Performance
As hypothesized by Araya et al.
and Brownstein et al.
, the ﬂow and performance
measurements in this study suggest that the performance enhancement of the downstream turbine in a
turbine pair is primarily governed by ﬂow accelerations around the upstream turbine. This has already
been shown in the previous section (cf. Figure 11), where the ﬂow accelerations from the upstream
turbine visibly affected the ﬂow ﬁeld encountered by the downstream turbine. This effect is further
demonstrated in Figure 14, which shows the normalized velocity magnitude (
) around an isolated
clockwise rotating VAWT and the normalized performance of the downstream turbine in a clockwise
co-rotating array at the same locations. A comparison of these data suggests that accelerations of the
ﬂow passing around the upstream turbine are the primary source of downstream turbine enhancement.
Relatively ﬁne features, such as the maximum performance enhancement for
occurring at a
turbine spacing of
, are replicated between these independent measurements. Furthermore,
when the downstream turbine is in the wake of the upstream turbine, the shape of the downstream
turbine performance decay
has a similar shape to the skewed wake behind an isolated
VAWT. The similar trends in these data illustrate the strong correlation between these measurements.
) Normalized time-averaged velocity magnitude (
) around an isolated clockwise
rotating VAWT at the turbine mid-span (
0) and at the same positions were the downstream
turbine is located in the adjacent ﬁgure. The single black error bar represents plus or minus one
average standard deviation of the measurements plotted. (
) (Replotted from Figure 5b) Normalized
performance of Turbine 2 versus adjusted array angle
for turbine spacings of 1.25
in a clockwise, co-rotating array. Error bands represent plus or minus one standard deviation
from the mean measurement.
4.1.2. Upstream Turbine Performance
Previous works have addressed the average array enhancement that occurs when turbines are
aligned perpendicular to the freestream
] and at other array angles [
]. In these
numerical studies, it has been observed that the performance enhancement is due to modiﬁcations in
the angle of attack on the blades caused by the inﬂuence of the adjacent rotor. These changes increase
the torque produced by the rotor blades, increasing the turbine performance.
Energies 2019,12, 2724 18 of 23
The ﬂow measurements in this study cannot be used to quantify angle of attack or incident ﬂow
speed changes on the blades of the rotors due to the lack of resolution of the data at the blade surfaces.
However, the near-rotor resolution in the spanwise aggregated particle trajectory images in Figures 7
and 10 can be used to deﬁne a surrogate for the modiﬁcations in these parameters. In the wake region
of the rotor, the ﬂow speeds are too low for signiﬁcant torque to be produced by the rotor blades.
Therefore, the range of azimuthal positions where the ﬂow is “attached” to the rotor (
) can be used as
a rough surrogate for the percentage of the rotor where useful torque is produced. In Figure 10 these
points are marked by the cyan dots for the upstream turbines and the magenta dots for the downstream
turbines. Using these measurements, the values of
for both turbines in the array can be normalized
by the range of attached azimuthal positions for the isolated turbine (
) to give a normalized
metric which can be used to approximate the changes in a rotor’s net torque production (Θnorm).
Figure 15 shows this metric plotted against the normalized performance of the turbines in the
four conﬁgurations of turbine pairs for which spanwise aggregated particle trajectory images were
taken. Of note, the error bars in
represent plus or minus 10
in the identiﬁcation of the range
of azimuthal positions where the ﬂow is attached to account any ambiguity in selecting this range.
This trend demonstrates a relationship between the percentage change in where useful torque can be
produced and the normalized performance of the turbine. Hence, the inﬂuence of the downstream
turbine on the upstream one can be conceptualized as a modiﬁcation to the azimuthal extent where
the ﬂow around the blades of the upstream turbine can produce useful torque.
Range of azimuthal positions where the ﬂow is attached to the turbine normalized by the
range in azimuthal positions for an isolated turbine (
) versus the normalized performance of
both the upstream turbines (circles) and downstream turbines (squares) (
) in four turbine pair
conﬁgurations. In all four arrays, the turbine spacing was
and the array angle was
Vertical error bands represent plus or minus one standard deviation from the mean measurement.
Horizontal error bands represent plus or minus 10
in the identiﬁcation of the range of azimuthal
positions where the ﬂow is attached.
4.2. Implications for Wind Farm Performance
The time-averaged ﬂow measurements in this report demonstrate signiﬁcant turbine interactions
in paired arrays of VAWTs. These interactions have signiﬁcant implications for both the power output
of the turbine pair and for additional downstream turbines in a larger array. In the context of a larger
array, the near-wake suppression and enhancement observed directly behind the turbines will affect the
energy available for extraction by turbines further downstream. Additionally, the streamwise vortex
interactions which occur downstream of the turbine pair can be utilized to hasten wake recovery by
exciting mean vertical ﬂow of momentum into the wake from above and below the turbines. From this
Energies 2019,12, 2724 19 of 23
perspective, the reverse-doublet conﬁguration is well suited for entraining momentum from above the
array and therefore increasing the energy available within the wake to turbines downstream of the
Because of the sensitivity of VAWT dynamics to the tip-speed ratio, it is important to consider
how the effects shown in this study may be modiﬁed at higher tip-speed ratios. The strength of
the streamwise vortical structures responsible for momentum replenishment in the wake appears to
scale proportionally with tip-speed ratio (cf. [
]). The effect is thus a consequence of the turbine’s
dynamics, and not the details of the rotor geometry. The streamwise vortices and associated induced
ﬂow accelerations identiﬁed in this study are therefore expected to be even stronger in turbines
operating at higher tip-speed ratios, such as the turbine presented by Möllerström et al. [
the lower solidity of these turbines. Lower-solidity turbines will, however, likely exhibit decreases
in the strengths of the bluff–body vortex structures shed from the individual turbines, which would
decrease these structures’ contributions to turbulent entrainment of momentum into the wake. Higher
aspect ratios would imply that the momentum replenishment of the streamwise vortices would be
conﬁned to a proportionally smaller percentage of the total wake area. The wake recovery due to the
mechanisms isolated in this study for turbines of higher aspect ratios would therefore likely be slower
than that of the turbines used in these experiments; however, the mechanisms are still expected to
be signiﬁcant factors in the replenishment of momentum into the wake. Future studies could more
quantitatively determine the precise momentum-entrainment properties of VAWT arrays as functions
of solidity, tip-speed ratio, and aspect ratio.
Other considerations related to turbine efﬁciency, sensitivity to wind direction, and fatigue loading
will also be important to consider. For example, power production will be a function of the annual
variation in the site wind magnitude and directions. To maximize power output at a site where the
wind direction is variable, an array that outputs near-maximum power over the observed range of
wind directions is needed. As shown previously in Figure 5, the performance of the co-rotating pair of
turbines exhibits the desired robust performance enhancement over large ranges of array angles. At its
peak, this case results in an average of 14% increase in array performance between 40
at the closest spacing measured. This region persists for all spacings measured, with a decreasing
average enhancement for larger turbine spacings. Therefore, the co-rotating conﬁguration would be
well-suited for wind farms based on a well-spaced unit cell layout where the wind direction is variable.
The conclusions of this work are outlined as follows: (1) Performance enhancement was measured
for both the upstream and downstream turbines in paired conﬁgurations of VAWTs. While previous
studies have observed performance enhancement for the downstream turbine, upstream turbine
enhancement was observed here for the ﬁrst time. (2) The turbine spacings and incident wind
directions which result in increased performance for the downstream turbine were demonstrated to be
spatially correlated with bluff–body accelerations around the upstream turbine. These accelerations
increase the incident freestream velocity on appropriately positioned downstream turbines. (3) For the
upstream turbine, changes in performance are related to modiﬁcations to the surrounding ﬂow ﬁeld
due to the presence of the downstream rotor. (4) Three-dimensional velocity measurements revealed
streamwise vortical structures shed by the rotors, which induce mean wake replenishment from above
and below the rotor.
The data demonstrate regions of increased performance for both the upstream and downstream
turbines, which can be used to increase the performance of VAWT arrays using a turbine pair as a unit
cell in the design. While these relations were found using a surrogate for the torque produced by the
upstream and downstream rotor, future work may seek to relate changes in performance to changes in
the induced angle of attack and resultant freestream on the upstream turbine blades. Measurements of
the induced angle of attack would be particularly useful in characterizing the effects of dynamic stall
on the ﬂow-ﬁeld properties, especially across a range of tip-speed ratios.
Energies 2019,12, 2724 20 of 23
The streamwise vortical structures identiﬁed in this study can also be incorporated in the design
of large wind farms with more optimal wake-recovery characteristics. If large arrays of VAWTs are
designed with these structures in mind, the replenishment of lost momentum in the wakes of turbines
deep within the array could be facilitated so that these turbines are able to extract more energy from
the ﬂow. These observations highlight the role of vortex dynamics in the near wakes of VAWT arrays,
and should be taken into account in the optimization of wind farms for maximum power density.
Although this study focused on modifying array parameters for a ﬁxed turbine design, it
is important to acknowledge that turbine design parameters could also affect this optimization.
The turbine solidity, tip-speed ratio, aspect ratio, Reynolds number, and loading conditions all affect
both the individual efﬁciency of the turbines in isolation and the strength of turbine interactions. Future
work will quantify these dependencies and validate the assumptions used to model the performance
of the upstream turbine.
Conceptualization, I.D.B. and J.O.D.; methodology, I.D.B. and J.O.D.; software, I.D.B.,
N.J.W. and J.O.D.; experiments, I.D.B.; data analysis, I.D.B., N.J.W., and J.O.D.; writing, I.D.B., N.J.W. and J.O.D.;
and funding acquisition, I.D.B. and J.O.D.
The authors gratefully acknowledge funding from the Gordon and Betty Moore Foundation through
Grant No. 2645 and the Stanford University TomKat Center for Energy Sustainability.
The authors would like to thank Jen Cardona for her work in setting up and characterizing
the wind tunnel and camera system used in these experiments.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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