A REVIEW ON COUNTER-ROTATING WIND TURBINES [600165]

A REVIEW ON COUNTER-ROTATING WIND TURBINES
DEVELOPMENT

OPRINA G.*, CHIHAIA R.A.*, EL-LEA THEY L.A.*, NICOLAIE S.*, B ĂBUȚANU C.A.*,
VOINA A.*
*National Institute for R&D in Electrical Engine ering ICPE-CA, Splaiul Unirii no. 313, Bucharest,
[anonimizat]

Abstract – On a dynamic energy market
characterized by the constant energy demand increase and economic as well as environmental
constraints, the study and development of efficient
conversion systems of wi nd’s energy has been
approached by a considerab le number of researchers.
Given the modern econo mic and environmental
challenges regarding the energy production and consumption, an advan ce in the research of
innovative or improved wind energy conversion
solutions has been registered . The objective of this
paper is to provide a comprehensive, but not
exhaustive overview of re search achievements in
counter-rotating wind turb ine systems development,
characterization and use. The review presents the
first theoretical results that led to the counter-
rotating wind turbines de velopment as well as the
related methods used for investigating their
performance. Valuable res ults have been found
within various studies, wh ich are carried out for
different testing syst ems and conditions.
Furthermore, there is still need of extensive studies, taking into account that the counter-rotating wind
turbines have to prove their reliability in real
operating conditions.
Keywords: wind energy, counter-rotation, wind turbine,
performance.

1. INTRODUCTION

On a dynamic energy mark et characterized by the
constant energy demand increase and economic as well
as environmental constraints, the research on finding new or improved means of renewable energy sources
conversion represents a su itable solution. The advance
recorded in recent years for the energy produced by the
conversion of renewables, esp ecially wind, is reflected in
the latest GWEC (Global Wind Energy Council) report.
Across Europe, 13.805 GW of wind power was installed in 2015 [GWEC, 2016]. Romania installed in 2015 an
additional 23 MW to the existing 2953 MW already
installed by the end of 2014. In EU countries, there are currently installed 141.6 GW, out of the total cumulative
capacity of 147.8 GW for all European countries.
Furthermore, in 2015 the installed wind power exceeded the installed hydropower, becoming the third largest source of power generation in the EU [GWEC]. The
world total of 432.883 GW of wind power is unevenly shared across the world (Fig. 1).

Fig. 1. Wind power across the world [1]

Given the modern economic and environmental
challenges regarding the energy production and
consumption, an advance in th e research of innovative or
improved wind energy conversion solutions has been
registered. Therefore, the obj ective of this paper is to
provide a comprehensive, but not exhaustive overview of research achievements in counter-rotating wind turbine
systems (CRWT) development, characterization and use.
A CRWT system consists of two rotors, one rotating
clockwise, the other one counter-clockwise and either a
unique generator adding-up the rotation of both wind rotors, or two independent electric generators, each of
them connected to a rotor. Th e wind rotors can be placed
in several positions: up-wind (in front of the generator), down-wind (in the rear of the generator) or at a certain
distance, one up-wind and one down-wind. In the various
existing studies in literature, the front rotor is called also main rotor or up-wind rotor; likewise, the rear rotor is
called secondary rotor or down-wind rotor.

2. FIRST THEORETICAL RESULTS LEADING TO CRWT DEVELOPMENT

The starting point in the research and development
of CRWT systems is represented by the results of the

theoretical research performed by Newman in 1983 [2],
who further analyzed and developed Betz’s theory, which
states that the wind turb ine rotors reduce the wind
velocity from the initial value v1 (m/s), upstream the rotor,
to v2= v1/3 (m/s), downstream the rotor. Betz introduced
the power coefficient C P, which is a dimensionless
parameter expressing a turb ine’s capacity to extract
energy from wind.

3
1 0,5=ρabs
PPCvA (1)
According to Betz’s law, a wind turbine can
theoretically capture approximately 59.3% from the
airstream’s energy. In real conditions, the power
coefficient is lower than th e theoretical value since the
aerodynamic and mechanical losses of the turbine are
considered. In equation (1), Pabs is the theoretical power
absorbed by a wind turbine, ρ – air density in kg/m3,A –
the area swept by the turbine’s rotor, perpendicular on
wind’s direction, in m2.
By applying the actuator-disc theory to a vertical
axis wind turbine, it was showed [2] that the theoretical
maximum power coefficient of a wind turbine can be increased for a very high tip speed ratio from 59% to
64% if a second rotor with the same radius is placed
downstream the first one (Fig. 2). This theoretical result led to various theoretical and experimental studies
aiming to determine the conditions that ensure more
power extraction from the wind.

Fig. 2. Stream tubes and parameters in Newman’s
theory, retrieved from [4]

Furthermore, in [3], it was theoretically
showed/demonstrated that in the case of multiple rotors
with the same radius, the ideal power coefficient can be further increased, approximately by 13% compared to the
single rotor case. The limitations of this theory were
determined by flow visualization that showed inaccurate
results beginning from a distance equal to a half of a disc
diameter. A theoretical model aimed to improve the power extraction from wind is proposed in [4], which
considers two co-axial rotors (Fig. 3), the second rotor
being smaller than the front rotor (Fig. 4) and placed
approximately in the inner bladeless region of the front
rotor. The central part of the upstream rotor (76.2% of
the rotor diameter) doesn't ex tract wind’s energy since it
has no blades. After further calculation, it was shown that
the theoretical power coefficient depends on the
induction velocities a and c. For the analyzed case, the
maximum power coefficient of 0.814 was obtained for a
= 0 and c = 0.418, meaning that the velocity doesn't
modify (does not decrease) when crossing the front rotor due to the absence of the blades. The study and development of CRWT prototypes of
500 W ÷ 50 kW [5] intensifie d starting with early 2000's.
Thus, in 2003, a 6kW prototype was tested in California
(USA) [6] over a period of 4 months, for various meteorological conditions. It was found that the system is
more efficient at low rotational speeds (16-60 rpm), the
energy extracted from wind can increase with up to 40%
compared with the single rotor case and the bending
stress over the tower is lower.

Fig. 3. Design of counter rotating horizontal axis wind
turbine system proposed in [4]

Fig. 4. Stream tubes of the rotors considered in [4],
retrieved from the presentation

3. PARAMETERS AFFECTING THE
TURBINE EFFICIENCY

The power extracted by a wind turbine from wind
depends on the geometrical parameters, aerodynamic
parameters and operating conditions. Thus, the size and
number of blades, the airfoil type, the method the rotation is transmitted to the electrical generator etc. are
parameters affecting the overall efficiency of a turbine.
The performance of a wind turbine is described by
the variation of the power coefficient C
P and the torque
coefficient Cm with the rapidity of the turbine: CP = CP
(λ) and Cm=Cm(λ).
The torque coefficient is given by:

2
1 0,5=ρmMCvA R (2)

with M [Nm] the aerodynamic torque of the rotor and R
[m] – turbine’s radius.

The tip-speed ratio of the turbine is a dimensionless
coefficient given by the ratio of linear velocity at blade’s
tip, u [m/s], to the wind velocity, V∞:

∞∞ωλ= =uR
VV (3)

with R [m] the radius of the rotor and ω [rad/s] the
rotational speed.
Considering the wind velocity V∞ as being the
velocity at the entrance of the rotor v1 and
using=ω⋅PM , it results:

=λ⋅p m CC (4)

Another dimensionless parameter on which depend
the characteristics of a wind turbine is solidity (σ); it
represents the ratio between the area of the blades, Ap,
and the area swept by the blades, A, at one spin of the
rotor:
σ= ⋅pA
A (5)

The rapid the turbine is ( λ > 4), the lower the
solidity; thus, the lift area of the blades is decreasing.
Besides the parameters above, the efficiency of a
CRWT system depends also on other parameters such as the diameter ratio of the two rotors and on which rotor
(larger or smaller) is placed in front, the distance the
rotors are placed one to each other.

4. VARIOUS METHODS FOR INVESTIGATING THE PERFORMANCE OF CRWT

The research and development of counter rotating
wind turbines focussed on the investigation of different issues, like the method the movement is transmitted
from the rotors to the electri c generator, blade type and
solidity, diameter ratio between the front and rear rotor, the distance between the two ro tors etc. Thus, one of the
issues encountered in the development of CRWT
systems is represented by the type of movement transmission, namely the generator or generators.
Several approaches are found in literature: one generator
for each rotor [7], one genera tor coupled to the rotors
through a differential planetary system in [8] and one
single permanent magnets generator, with kinematic
coupling of the rotors [9].
Most of the research reported within the literature
approached the study of CRWT systems both
theoretically (especially CFD) and experimentally,
either by performing own tests or by comparing the
theoretical results with experimental results reported in other works.
The study of counter-rotating wind turbines
optimization using blade element momentum theory (BEMT) is developed in [10]. The pitch angles, radius
ratios and rotation speeds were chosen as design values
and were used in the investigation of the power and thrust coefficients. Also , the torque balance was
considered in the design process, considering in the case
of one generator with kinematic coupling to the two
rotors that the shaft torque is the same for both front and rear rotor. This assumption is also used in [11]. By using
BEMT for the front rotor, the induction factor and
angular induction factors were determined and, consequently, the power and thrust coefficients. The
aerodynamic performance of th e rear rotor was predicted
by considering as input data the flow field developed downstream the front rotor, namely assuming that the
rear rotor is placed in the fu lly developed stream tube of
the first rotor. The study was performed for a fix distance
between the two rotors: 0.33 D, where Dis the diameter of
the front rotor. Therefore, since this assumption couldn't be proved in their study (not having exactly the
information regarding the distance associated to this fully
developed flow), the authors addressed this issue by Vortex Lattice Method (VLM). The optimization was
performed by using a genetic algorithm. A shorter length
of the front rotor than the one of the rear rotor was found. Also, for the optimized case, it was found that the power
coefficient of the front rotor is superior to the one of the
second rotor.
The free-wake vortex lattice method [12] considers
simultaneously the interaction between the two rotors by
not imposing any constraint to the inflow velocity of the rear rotor. The study is performed by considering that
the two rotors have the same radius, R, the same solidity
as a wind turbine having a single rotor and are placed at the distance d/R=0.25, 0.5, 0.75, 1. The maximum
power coefficient for zero pitch angles showed little
changes among the 4 analysed distances. Even if the
power coefficient of the front rotor increases along with
the distance, in the same ti me, the power coefficient of
the rear rotor decreases, so the overall efficiency is
almost constant. The results obtained by this study were
compared with the experiment al ones resulted from the
research performed in [13] and in [14] in order to
validate the numerical model. The theoretical reduced
axial velocity behind the front rotor showed a good agreement with the one experi mentally obtained in [13].
By comparing the axial indu ction factor for the rear
rotor obtained by VLC and by BEMT, it was found that BEMT can be applied in limited cases, since the
difference between the values increases with the
distance d.
In [15], the aerodynamic performance of the front
and rear rotors was numerically investigated aiming to
extract the maximum energy from wind, both by the
front and rear rotor. By CFD simulations, the
performance of each rotor was separately determined
and by parametric study the optimum axial distance
between them was determ ined. The CRWT system
consisting of two rotors with 3 blades each was also compared wind a single 3 bladed wind turbine. The
performed computations showed an increase of about
35% of the CRWT thrust over the single turbine thrust, namely 545N versus 350 N for 10m/s wind velocity.
The results of the CFD simulations were compared and
validated with experimental data from literature, reported in [8]. The maximum computed torque was
identified: 4770 Nm for 14 m/s wind velocity. Also, this

wind velocity is associated with the maximum power
output of 90 kW. The optimum axial distance between
the two rotors was calculated at 0.65 d, where d is the
diameter of the up-wind rotor, leading to a maximum power increase of 9.67%. A good correlation between
the CFD results and the measurements was identified.
Still, in some conditions, the predictions were slightly larger than the measured valu es. In the single rotor case,
the results of the CFD simulations were slightly lower
than the experimental values reported in [8]. In [16], there are presented theoretical investigations through
CFD methods (k- ω shear stress transport turbulence and
moving reference frame for the second rotor) compared
with experimental results reported in [8] and with own
experimental results obtained in a wind tunnel on a 1:20 scale model of the 30 kW CRWT system reported in [8].
In order to determine or predict the performance of
the CRWT systems, several studies were performed [6], [8], [17-21]. For example, using the quasi-steady strip
theory and a wake model resulted from the data obtained
by carrying out experiments on a scale model in a wind tunnel, the aerodynamic pe rformance of a 30 kW
CRWT system was predicted in [8]. The CRWT system
had two rotors, each of them with 3 blades (NACA 4415
airfoil for the front and NACA 0012 for the rear rotor),
the front rotor having a 5.5 m diameter and the rear rotor
an11 m diameter. The front rotor had a rotational speed of 150 rpm, while the rear rotor rotated at 300 rpm. A
differential planetary system connected the rotors to the
electric generator. The rotors were placed at different
distances, in the range of 0. 125…0.5 from the diameter
of the front rotor. In order to compare the results of the
proposed theoretical method to the wind tunnel data, the
analysis was performed by considering a uniform flow
field for the front rotor and no aerodynamic interference between the two rotors. The relative size and the
optimum placement of the rotors were obtained by
parametric investigation. The size of the rear rotor was considered as increasing fr om zero to the size of the
front rotor. The best performance of the 30 kW CRWT
system was identified at approximately 0.5 of the front rotor's diameter. Also, field measurements were
performed for a period of 9 and a half hour. Each of the
measured data was averaged over a period of 10 minutes [22]. A relatively good agreement of the field data and
theoretical data was obtai ned. Moreover, the CRWT
data were compared to the single rotor case and an increase of about 21% was found at a rated speed of
10.6 m/s. The total maximum power coefficient of 0.5
of the CRWT system was determined.
In [7], an increase of 43 .5% of the annual energy
that can be produced by a CRWT having two 500 kW
rotors compared with a singl e turbine of the same type,
when operating at 10 m/s wind velocity was predicted.
The numerical prediction was achieved by using the actuator line technique which combines the Navier-
Stokes solver with the technique described in [23], which
was validated with the experimental results of a 50kW Nordtank turbine. The numerical investigation was
performed in EllipSys3D code.
Using a modified blade el ement momentum theory,
the influence on the performance of CRWT system of
different parameters (pitch angles, rotating speed, and blades radii) was studied in [21], by assuming that the
rear rotor operates inside the fully developed stream tube
of the front rotor. It was found that, for a maximum
extracted power of the system , the rotors have to share
the total extracted power (not when the front rotor
extracts the maximum power from wind), the pitch of the
rear rotor has to be lower than the one of the front rotor and the rotating speed of the rear rotor is lower than the
one of the front rotor.
Based on solidity effect, a numerical investigation
of single wind rotors and of a CRWT system was
performed in [18]. The results were compared to the
experiments obtained on a 10 m diameter wind rotor. A
30% increase in the maximu m power coefficient was
found for the case of CRWT when compared to a single rotor of half solidity and 5% decrease when the single
rotor has the same solidity.
The majority of the CRWT systems reported in
literature are provided with a front rotor smaller than the
rear rotor. Despite this fact , in [24-26], the Intelligent
Wind Turbine Generator (a system having the front rotor larger than the second rotor), is presented while
being found in tandem operation. Both rotors are placed
either in front of the generator (up-wind), or after the generator (down-wind), having both inner and outer
rotational armatures.

Fig. 5. Down-wind turbine system [26]

Fig. 6. Double rotational armatures synchronous
generator [26]

The system was tested in a wind tunnel and the
influence of different parameters on the performance of
the system was analyzed. The front rotor has 2 m

diameter, and the rear rotor 1.33 m diameter. The power
of the electric synchronous generator with mobile
armatures is of 1 kW. In order to simulate the wind
velocity, the system was test ed by placing it on a vehicle
driven at different speeds, the acceleration and
deceleration periods being removed from the measured
data sets. It was determined that the system's performance varies signific antly along with the blade
setting angles as well as with the applied load.

Fig. 7. Double rotational armatures synchronous
generator [11]

Priyono et al. [27] design ed, optimized and studied
the characteristics of an Intelligent Wind Turbine (IWT) by means of BEM and CFD simulations. The optimized
IWT consists of two rotors having 3 blades each, of
NACA 6412 profiles. The diameter ratio is 1:1, each
blade with 600 mm diameter. It was shown that both
rotors are counter-rotating at low wind velocities (4-6 m/s), but for higher wind velocities, the rear rotor is
entrained by the front rotor, so it rotates in the same
direction with the first rotor. Thus, starting with the velocity of 7 m/s, the rotational speed of the rear rotor
begins to decrease. At higher wind velocities of 11.5 m/s,
the rear rotor is co-rotating with the front rotor.
A CRWT model having the rotor’s diameter of 0.8 m,
same (mirrored) blade types and independent generators
was investigated in [28], both numerically and experimentally. Each of the rotors was separately tested
in a wind tunnel and afterwards, the operation of the
counter-rotating system was tested. In order to get a correlation between the operation of the CRWT system
in a free stream and its operation in a wind tunnel, the
blockage effects in the wind tunnel were investigated using both a CFD model and measurement of the drag
coefficient. An increase of 9% of the maximum extracted
power was found in comparison to the single rotor case. The results were used to predict the dynamic behaviour
of the system for the case of a single generator coupled to
the rotors by a differential pl anetary gearing. In the case
of 0.8m diameter rotors, it was found that the front rotor
extracts 74% power while the rear rotor only 26%. Therefore, it was concluded that the diameter of the front
rotor should be smaller than th e one of the rear rotor.
In [29], a 10 kW CRWT system with horizontal axis,
same diameter for the rotors and NREL airfoils was
investigated. The diameter of the rotors for the
investigated system is 7.16 m and the distance between the two rotors is 6 m. The CFD modelling revealed that
while the power coefficient for the single rotor case is
37%, at 6 tip speed ratio (T SR), the one for the system
counter-rotation case is 39%, obtained for 5 TSR.
In [11], there was investigated a CRWT system of
1kW rated power at 10 m/s, having the front rotor
diameter of 1.23 m and the rear rotor diameter of 1.33 m as well as a single generator, with double rotational
armatures. The wind tunnel tests revealed an output
power increase in the range of 37%÷45.2% (varying with
the wind velocity) compared to the single rotor case, the
front rotor being considered as reference. The unique
generator of the system is subject to a patent request [30]
and has some advantages such as reduced size, increased
rotational speed and no losses due to movement transmission. Subsequently, the 1kW CRWT system was
tested in field conditions [31]; 3 levels of electrical loads
proportional to the wind intensity were used: 300 W for wind velocities in the range of 3 ÷ 6 m/s, 600 W for the
range of 6 ÷ 8 m/s and 900 W for the range of 8 ÷ 10 m/s.
A good agreement between the results of the field tests and the results of the wind tunnel tests was found. Still,
due to the short testing period of the system and to
weather conditions, the results can be considered as being preliminary. The CRWT system used in the
research reported in [11] an d [31] was achieved within a
research project [32].

Fig. 8. 1kW CRWT system operating in situ [31]

Given the fact that the second rotor operates inside
the wake of the first rotor, an important issue to be
considered in the design of the counter-rotating wind turbine systems is the wake aerodynamics . This issue
was investigated in severa l research works [33-38],
which studied the wake aerodynamics of the rotor and/or the tower. For example, model wind turbines of 0.9m
diameter were used in some studies: in [36] there were
performed investigations regarding wake aerodynamics on wind turbines placed at a distance of 3 and 5 rotor
diameters by measuring the axial velocity component; in
[38] there were performed experiments in a wind tunnel both for the single rotor case and for two counter-rotating
rotors case for turbines with 0.9m diameter and
investigated near and far the wake fields.
Since the counter-rotating systems require special
types of electric generators, some patents have been developed regarding the wind turbines with rotors in

counter rotation and/or the related generator [7], [9], [30].
The patent in [7] refers to a system consisting of two
separate conversion units, formed by a rotor and a
generator. The regulation of the rotational speed between the two rotors, counter-rotating independently, is
performed by a power electronic system which controls
the electric current produced by the two rotors. With the
modification of the wind velocity, the rotational speeds
are regulated at a value that optimizes the power
produced by the system (operating at maximum power coefficient). In a range of wind velocities over a
reference period, the contribution of each rotor to the
overall power produced by the system is the same. The
patent application in [30] refers to a generator having
both armatures mobile, suitable to be used both for wind and hydro counter rotating turbines.

5. COMPLEMENTARY STUDIES TO THE
CRWT RESEARCH FIELD

Lately, the promising results obtained by the
theoretical and experimental investigation of some
developed CRWT systems led to studies aiming to
analyze the benefit of the ef fects brought by a second
rotor in the case of wind power plants. This approach has its reasons mainly due to smaller turbine spacing,
especially for onshore applications but not only. An
example is represented by the research reported in [39], consisting in an experimental study for some models of
stand-alone co-rotating wind turbines and stand-alone
counter-rotating wind turbines of the same diameter and having horizontal axis. By performing tests both in
counter and co-rotation cases, for a constant wind
velocity and for a spacing of 0.7 d (with d the diameter of
the rotor) between the turbines, it was determined that the
overall power is 17% larger in the case of counter
rotation. The analysis was ma de for different spacing and
showed that better results can be obtained when the
rotors of the turbines in a wind farm are operating in
counter rotation. Thus, for spacing lower than 2 d and
counter-rotation, the second turb ine, placed in the rear of
the first one produces at least 10% more power than in
the case of co-rotation operation; for 5 d spacing this
benefit reduces to about 4%.
Since the research reported in literature is based
mainly on theoretical studies and on the investigation of
experimental models and since the positive effects
brought by the second turbine is doubtless, rules or laws for scaling up the models are necessary in order to
deploy CRWT systems in situ . Therefore, even if not
representing the main goal of this paper, there is mentioned some research [40-43] that approached the
study of some similarity parameters necessary in the
wind turbines scaling-up process and/or for predicting the turbines behaviour in different operating conditions.
In [40] are reported some results obtained during the
UpWind research project. Theoretical, technical and economic issues involved in the wind turbine's scaling
up process were approached especially in order to
determine if a superior power leads to a lower cost of the obtained energy. On the other hand, in order to
predict the behaviour and long term performance of
some offshore turbines by laboratory investigations on reduced scale models, the study of some scaling laws for
achieving 1:100 models is approached in [41]. The
laboratory tests are aimed at determining the long term
performance, especially as regards the dynamic interaction between soil and structure.

6. CONCLUSION

Several studies have been performed, focussed either on
determining the influence of a limited number of
parameters on the performance of a counter rotating wind
turbine or on a larger number of parameters.
Summarizing some of the an alyzed research on CRWT
systems, Table 1 shows few details about the type of
investigation and applied methods.

Table 1. Types of investigation and applied methods
n the study of CRWT systems
Reference Method of investigation, short details
[28] Theoretical and experimental study of CRWT
system with 0.8 m diameter rotors
[13] Experimental study in wind tunnel
[11] Experimental study in wind tunnel of 1kW
CRWT system
[12] Numerical study (free VLM) compared to
experiments from [13] and to BEMT; same
rotor diameters, different distances
d=0.25;0.5;0.75;1
[10] Theoretical study (BEMT and genetic
algorithm for optimization) of a CRWT
system with rotors placed at 0.33diameter of
the front rotor
[16] Theoretical study (CFD using k- ω coupled
with Moving Reference Frame technique)
compared to experimental results obtained on
a 1:20 scale model of the CRWT from [8] and
to experimental results reported in [8]
[8] Theoretical study compared to own field
experiments for 30 kW CRWT system
[15] Theoretical (CFD) study compared to
experimental results reported in [8]
[17] Numerical performance prediction of a
CRWT system consisting of two 500 kW
turbines
[24], [25]Experimental study of Intelligent Wind
Turbine Generator system, design of blades
and generator
[27] Design and theoretical optimization study
[6] Design of a 6kW CRWT prototype and field
tests
[21] Theoretical study using modified BEMT
[18] Numerical investigation compared to
experiments on a 10 m diameter rotor
[31] Experimental study of 1kW CRWT model –
field tests compared to wind tunnel tests
reported in [11]
[36] Theoretical and experimental study of wake
aerodynamics on wind turbines placed at a
distance of 3 and 5 rotor diameters
[38] Experimental study on wake measurements in
a wind tunnel – near and far wake field both
for single rotor and for counter-rotating rotors

Despite the valuable results found within the studies,
since the performance of the turbine system depends on
multiple parameters (such as blade type, solidity of the
two rotors, area swept by the blades, diameter ratio of the
front and rear rotor, distance between the two rotors,
movement transmission system), there is still need of
extensive studies of this type of wind kinetic energy conversion system. Also, the counter rotating wind
turbines have to prove their reliability in real operating
conditions. However, the studies performed during the last two decades, proved the a dvantages of these systems.
Thus, the additional energy converted by the second
rotor, either smaller or larger than the first one, it is
certain, even if its additional input to the overall
efficiency of the CRWT system varies from one study to another.

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