Renewable Energy xxx (2014) 1e10

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Renewable Energy
journal homepage: www.elsevier.com/locate/renene

Effects of end plates with various shapes and sizes on helical Savonius
wind turbines
Keum Soo Jeon a, Jun Ik Jeong b, Jae-Kyung Pan c, Ki-Wahn Ryu d, *
a
Wind Valley Co. Ltd., Suncheon 540-856, Republic of Korea
b
Euro-Korea Co. Ltd., Jeonju 561-843, Republic of Korea
c
Department of Electrical Engineering and Smart Grid Research Center, Chonbuk National University, Jeonju 561-756, Republic of Korea
d
Department of Aerospace Engineering, Chonbuk National University, Jeonju 561-756, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history: We experimentally studied the effects of end plates with various shapes and sizes on the aerodynamic
Received 14 March 2014 performance of helical Savonius wind turbines with twist angles of 180
and two semicircular buckets. To
Accepted 12 November 2014 apply the blockage correction method and investigate the effect of end plate, four different helical
Available online xxx
Savonius wind turbines were tested at a subsonic open-circuit type wind tunnel. The adapted Maskell's
blockage correction method suggested by Alexander was adopted for the wind turbine model installed in
Keywords:
a closed test section of the subsonic wind tunnel. In order to clarify the end plate effect, power and
Helical Savonius wind turbine
torque coefficients were measured with various end plate shapes and areas. The use of both upper and
Power coefficient
Static torque
lower end plates significantly increases the power coefficient by 36% compared with no end plates. We
End plate found that the Maskell's blockage correction method for straight Savonius wind turbines is applicable to
Blockage correction helical Savonius wind turbines for small blockage ratios ranging from 3 to 8.3%. It was also observed that
Subsonic wind tunnel the power coefficient increases linearly in proportion to the area of the end plate.
© 2014 Elsevier Ltd. All rights reserved.

1. Introduction The use of end plates is the simplest method to increase the
aerodynamic performance of Savonius wind turbines. Many re-
Savonius wind turbines have many advantages, including a high searchers have experimentally studied the influence of end plates
starting torque, a simple design, and an ability to operate in any in conventional Savonius wind turbines without blade twist [9e11].
wind direction, though they have low aerodynamic efficiency. Thus In particular, Ushiyama and Nagai [10] suggested optimal design
Savonius wind turbines are widely used in micro and small scale configurations for Savonius rotors with straight buckets. They car-
wind turbine applications, such as domestic and residential power ried out a parametric study of the aspect ratio, the overlap and
generation. Much work has been done studying the aerodynamic separation gap between rotor buckets, the presence or absence of
characteristics and effects of geometric design parameters in rotor end plates, and the influence of bucket stacking, but they did
Savonius wind turbines [1e3]. However, conventional (or straight) not apply blockage correction (although they conducted the ex-
Savonius wind turbines have a negative torque at certain rotation periments at an open test section about 1 m downwind from the
angles and a large torque variation. To improve the torque char- exit of the wind tunnel to avoid blockage effects).
acteristics, multi-stage, out of phase Savonius wind turbines have In the wind tunnel experiments, the end plate effects of the
been proposed, but the use of a multi-stage blade reduces the po- helical Savonius wind turbines are hard to identify whilst those of
wer coefficient [4,5]. the straight Savonius wind turbines are frequent. In particular,
At present, some researchers have proposed helical Savonius partially blocked non-circular end plates rather than circular ones
wind turbines with twist angles of 90
and 180
and have investi- are expected in the industry to decrease the cost and weight of the
gated the effects of geometric parameters such as the overlap ratio, rotor. Power performance with the various shapes of the end plate
aspect ratio and shaft interface [6e8]. Helical Savonius wind tur- then becomes one of the most contested points. Because the
bines have a positive static torque coefficient for all rotor angles and Savonius wind turbine is the typical drag type, the drag forces at the
better performance than conventional Savonius wind turbines. advancing and retreating sides generate negative and positive
torque respectively. We presume that the role of the end plate is to
* Corresponding author. Tel.: þ82 63 270 4286; fax: þ82 63 270 2472. prevent spill-over flow at both ends of the bucket, and
E-mail address: kwryu@chonbuk.ac.kr (K.-W. Ryu).

http://dx.doi.org/10.1016/j.renene.2014.11.035
0960-1481/© 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Jeon KS, et al., Effects of end plates with various shapes and sizes on helical Savonius wind turbines, Renewable
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Nomenclature P power
q dynamic pressure; rU2/2
AR aspect ratio; H/D R rotor radius
AC cross-sectional area; pR2 Re Reynolds number
AE end plate area S rotor swept area
BR blockage ratio T torque
Ct torque coefficient; T/(qSR) TS static torque
Cts static torque coefficient; TS/(qSR) U wind speed
CP power coefficient; P/(qSU) w width of wind tunnel test section
D rotor diameter r density of air
ER end plate area ratio; AE/AC l tip speed ratio; UR/U
H rotor height U angular speed
h height of wind tunnel test section

consequently increases the momentum transfer from the air (diameter  height: 150 mm  300 mm, 200 mm  400 mm,
stream. The advancing bucket can reduce the drag force related to 250 mm  500 mm, and 350 mm  700 mm) were fabricated to
the negative torque of the rotor by eliminating the end plate itself. study the influence of the blockage ratio of the wind turbine model.
In other words, partially blocked non-circular end plates applied Table 1 lists the details of the rotor diameter, rotor height, rotor
just for the retreating side bucket would be sufficient to absorb the aspect ratio, shaft diameter, and blade thickness. The blades were
momentum from the impinging air stream. This idea would fulfill made from a fiber reinforced plastic which was a composite ma-
the industry's demand. The above concept is the main background terial of a polymer matrix reinforced with glass fibers.
of this study even if it is physically valid. The helical Savonius wind turbines were designed as shown in
Therefore the aim of this study is to experimentally investigate Fig. 2. The end plates were fabricated from an acrylic plate of 5 mm
end plate effects using various shapes and sizes of end plates on the thickness. To study efficiency according to end plate shape, the
aerodynamic performance of helical Savonius wind turbines. This is diameter of the end plate was the same as the diameter of the wind
the first study to conduct such an investigation. The end plate ef- turbine. In a conventional Savonius wind turbine without a blade
fects were determined in a subsonic open-circuit type wind tunnel twist, the optimal diameter of the end plate for obtaining a
with a closed test section of 1000 mm  1500 mm. Four different maximum power coefficient is 1.1 times the turbine diameter
helical Savonius wind turbines with identical aspect ratios, twist [9,14]. The end plate area ratios, i.e., the ratio of the end plate area to
angles of 180
, and two semicircular buckets were fabricated from the cross-sectional area (AE/AC) of the turbine (diameter 250 mm)
fiber reinforced plastics. All of the bucket shapes had no separation are listed in Table 2.
gaps or overlaps between the two semicircular buckets. The The static torque coefficient Cts, the torque coefficient Ct, the
adapted Maskell's blockage correction method for the straight power coefficient Cp, and the tip speed ratio l of the turbine are
Savonius wind turbine model suggested by Alexander [12,13] was given by.
chosen and verified for the helical Savonius wind turbine model.
TS
Cts ¼ (1)
qSR
2. Experimental model and apparatus

2.1. Model of helical Savonius wind turbines T

Ct ¼ (2)
qSR
Fig. 1 shows the configuration of the helical Savonius wind
turbine with a twist angle of 180
, two semicircular buckets, and P
the main shaft without overlap or a separation gap. Four different Cp ¼ ¼ l  Ct (3)
qSU
helical Savonius wind turbines with identical aspect ratios of 2.0

Fig. 1. Schematic views of helical Savonius wind turbine without end plates.

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Table 1 Table 2
Geometric parameters of the helical Savonius wind turbines. Details of end plates on the helical Savonius wind turbine with a diameter of
250 mm.
Designation Diameter Height of Aspect Diameter Thickness
of Savonius of rotor (D) rotor (H) ratio (H/D) of shaft (d) of blade (t) W/o end End End End End
rotors [mm] [mm] [mm] [mm] plates plate #1 plate #2 plate #3 plate #4

HS #1 150 300 2 10 4 AE [mm2] 0 7990 13,510 26,220 50,670

HS #2 200 400 2 15 4 AE/AC 0 0.15 0.27 0.52 1
HS #3 250 500 2 25 4
HS #4 350 700 2 25 4

this study. The dimension of the cross section at the test section is
1000 mm  1500 mm with a maximum velocity of 20 m/s. The
UR
l¼ (4) experiments were performed at air speeds ranging from 6 m/s to
U 12 m/s. The rated torque and repeatability resolution for the
where TS is the static torque at a fixed rotational angle [N-m], T is DACELL TRD-2K digital torque detector adopted for measurements
the torque [N-m], q ¼ rU2/2 is the dynamic pressure [Pa], R is the are 19.6 Nm and 0.2% (0.0392 Nm) respectively. It is presumed that
rotor radius [m], S is the swept area [m2], P ¼ TU is the wind power the torque detector ensures reliability because the interest range of
[W], U is the free stream speed [m/s], and U is the angular speed of the measured torque (0.045e0.072 Nm) for the smallest possible
the rotor [rad/s]. size for the wind turbine case, i.e., D ¼ 150 mm, is in the tolerance
The aspect ratio AR and the end plate area ratio ER are given by range. The uncertainty of the measurement can be increased due to
the value being smaller than 1% of the rated torque. To reduce
H uncertainty, the average mean values of five data points measured
AR ¼ (5)
D within 1 min was used in this study.
The static torque was measured at fixed blade rotation angles
AE every 4
of rotation using the brake function of the servo motor. The
ER ¼ (6)
AC rotating torque was measured by changing the rotational speed of
the turbines under a steady wind speed. The rotational speed was
where H is the height of the turbine, AE is the area of the end
changed by regulating the rotational speed of the AC servo motor.
plate, and AC is the cross-sectional area of the wind turbine
perpendicular to the rotating axis, i.e. AC ¼ pR2.
The blockage ratio is the ratio between the maximum projected 3. Results and discussion
area and the cross-sectional area of the wind turbine model. The
formula of the blockage ratio, BR, is: Previous studies [9,10] investigating end plate effects for Savo-
nius wind turbines presented the test results without blockage
HD correction. In particular wind tunnel experiments using closed test
BR ¼ (7)
hw section can lead to erroneous understanding or conclusions
where h and w denote the height and width of the wind tunnel regarding aerodynamic performance and trend. Moreover, the
test section, respectively. adapted Maskell's blockage correction method suggested by Alex-
ander [12,13] was developed initially not for the helical Savonius
wind turbine but for the straight Savonius wind turbine.
2.2. Experimental apparatus To examine the effects of end plate shapes on aerodynamic
performance in more detail, verification by comparing the aero-
Fig. 3 (a) and (b) show schematic diagrams of the experimental dynamic data with the values obtained after blockage correction
apparatus and the open-circuit type subsonic wind tunnel used in would be a prerequisite. Specifically, the Maskell's blockage

Fig. 2. Views of helical Savonius rotors with various shapes and sizes of end plates.

Please cite this article in press as: Jeon KS, et al., Effects of end plates with various shapes and sizes on helical Savonius wind turbines, Renewable
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4 K.S. Jeon et al. / Renewable Energy xxx (2014) 1e10

Fig. 3. The schematic diagram of experimental apparatus and the open-circuit subsonic wind tunnel.

correction method would be applicable to helical Savonius wind were then able to check the deviations of the aerodynamic data for
turbines for verifying that deviations of the performance curves for the first and the second steps. Finally, after verifying the Maskell's
various blockage ratios decreased noticeably after blockage blockage correction method for the helical Savonius wind turbine,
correction. After confirming the reliability of the Maskell's blockage the influence of the end plate shapes and sizes on the aerodynamic
correction method for the helical Savonius wind turbine, we performances was investigated.
analyzed the influence of the end plate shapes and sizes on the
power coefficients in the next step. 3.1. Blockage correction
Therefore, we performed the following steps to advance the
wind tunnel experiments for the helical Savonius wind turbine. Testing at an open test section may also lead to blockage effects,
First, the corrected power and torque coefficients according to the and so all of the power and torque curves should be corrected using
tip speed ratio at the same wind speed were compared with non- a suitable correction method. Blockage effects typically occur in
corrected values. Second, comparison of the aerodynamic data wind tunnel tests and become more critical as the blockage ratio
such as power and torque coefficients before and after blockage increases. Therefore, an appropriate blockage correction method is
correction was carried out at a similar Reynolds number range. We imperative for all wind tunnel tests, including both closed and open

Please cite this article in press as: Jeon KS, et al., Effects of end plates with various shapes and sizes on helical Savonius wind turbines, Renewable
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 K.S. Jeon et al. / Renewable Energy xxx (2014) 1e10 5

Fig. 4. Blockage correction factors, m, according to the blockage ratios for the straight
Savonius wind turbine.

test sections. Ross and Altman presented a review paper studying

various blockage correction methods such as the wall pressure
method, Pope's method, and Maskell's methods for Savonius rotors
using their own wind tunnel test results [15]. They also found that
wake constriction is strongly influenced by rotating bluff buckets.
In this study, Maskell's correction method was used because it is
very effective for correcting the blockage effect for a blunt body
[12,15]. Alexander [13] suggested the following adapted Maskell's
blockage correction method to predict wind tunnel correction for
Savonius rotors:

UC2 1
¼ (8)
U 2 1  mðBRÞ
where UC is the corrected air speed, U is the undisturbed air
speed at the inlet of the test section, and m denotes the ratio of
wake area normal to the wind direction at the maximum frontal Fig. 5. The uncorrected power coefficient and torque coefficient when U ¼ 12 m/s for
area of the wind turbine model. The correction parameter of BR ¼ 3%, U ¼ 10 m/s for BR ¼ 5.3%, U ¼ 8 m/s for BR ¼ 8.3%, and U ¼ 6 m/s for BR ¼ 16%.
m ¼ 3.02, 2.86, 2.66, and 2.77 are used for D ¼ 150, 200, 250, and
350 mm respectively, based on the correction value in Ref. [12] and
Fig. 4. absolute value, and the locations of the maximum power coeffi-
The experiments were mainly carried out using helical Savonius cient shifted to the right toward higher tip speed ratios when the
wind turbines with D ¼ 150 mm (BR ¼ 3%), 200 mm (BR ¼ 5.3%), blockage ratio increased. Fig. 6 shows the corrected results of the
and 250 mm (BR ¼ 8.3%), keeping the aspect ratio constant at power and torque curves corresponding to Fig. 5. The power coef-
AR ¼ 2. Both the upper and lower end plates were circular, as shown ficient was decreased over the whole tip speed ratio range,
in Fig. 2(e) and Table 3. compared to the uncorrected data. It was observed that the larger
Fig. 5 shows the uncorrected power coefficients and torque the blockage ratio, the higher the reduction of the power coefficient
coefficients for the similar Reynolds number when U ¼ 12 m/s for for the similar Reynolds number. From these results, the adapted
BR ¼ 3% (Re ¼ 1.24  105), U ¼ 10 m/s for BR ¼ 5.3% Maskell's blockage correction method for straight Savonius wind
(Re ¼ 1.38  105), U ¼ 8 m/s for BR ¼ 8.3% (Re ¼ 1.38  105), and turbines suggested by Alexander yields well corrected results for
U ¼ 6 m/s for BR ¼ 16% (Re ¼ 1.44  105). For the similar Reynolds helical Savonius wind turbines in similar Reynolds number ranges.
number, we observed that the power coefficients increased in Fig. 7 (a) and (b) show the uncorrected power and torque
curves with BR ¼ 3%, 5.3%, and 8.3% at a fixed air speed of 10 m/s.
We observed that the power coefficients were markedly increased
Table 3 in absolute value, and the locations of the maximum power co-
Results of the blockage correction using the adapted Maskell's method. efficient were shifted to the right toward higher tip speed ratios
D BR U Before correction After correction Change Change when the blockage ratio is increased. This is because the wind
[mm] [%] [m/s] of Cpmax [%] of l at velocity increases due to increased flow constriction caused by a
Cpmax l at Cpmax Cpmax l at Cpmax
Cpmax [%] larger body in the test section, which increases the swept area of
150 3 10 0.0906 0.5184 0.0786 0.4943 13.2 4.6 the turbine.
200 5.3 10 0.1116 0.6074 0.0.087 0.5591 22.0 8.0 Fig. 8 shows the corrected results of the power and torque
250 8.3 10 0.1349 0.6528 0.0928 0.5762 31.2 11.7
curves corresponding to Fig. 7. The power coefficient was

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Fig. 6. The corrected power coefficient and torque coefficient when U ¼ 12 m/s for
BR ¼ 3%, U ¼ 10 m/s for BR ¼ 5.3%, U ¼ 8 m/s for BR ¼ 8.3%, and U ¼ 6 m/s for BR ¼ 16%.
Fig. 7. The uncorrected power coefficient and torque coefficient at the wind speed of
10 m/s when BR ¼ 3%, 5.3%, and 8.3%.

decreased over the whole tip speed ratio range, compared to the
uncorrected data. In particular, the corrected power curves lie the wind speed while the tip speed ratio corresponding to the
close together under the various blockage ratios, especially in the maximum power coefficient was nearly fixed.
low tip speed ratio range. Table 3 shows the results of blockage Fig. 10 shows the corrected results of the power and torque
correction using the adapted Maskell's method. The correction curves corresponding to the results shown in Fig. 9 after applying
reduces the maximum power coefficients (Cpmax) by 13.2%, 22.0%, the adapted Maskell's blockage correction method suggested by
and 31.2% for BR ¼ 3.0%, 5.3%, and 8.3%, respectively. It was Alexander [13]. The power coefficient was reduced in the whole tip
observed that the larger the blockage ratio, the higher the speed ratio range. For the small blockage ratio of 3%, the correction
reduction of the power coefficient. Leftward shifts of the tip speed decreased the maximum power coefficient by about 13%. For the
ratios corresponding to the maximum power coefficients were larger blockage ratios of 5.5% and 8.3%, the maximum power co-
also observed after correction of the blockage. All of the corrected efficients were decreased by about 22% and 31%, respectively. To
power and torque curves were shifted leftward and downward, summarize, we found that the larger the blockage ratio, the higher
compared with the uncorrected values. For fixed air speeds with the reduction in the power coefficient. The power coefficients at
various blockage ratios up to 10%, the adapted Maskell's blockage BR ¼ 3%, BR ¼ 5.3%, and BR ¼ 8.3% were similar in the low tip speed
correction method also produced well corrected results for the ratio range. The tip speed ratios corresponding to the maximum
helical Savonius wind turbine. power coefficients were also decreased after the blockage
Fig. 9 illustrates the uncorrected power and torque curves at correction.
various wind speeds when BR ¼ 3.0%, BR ¼ 5.3%, and BR ¼ 8.3%. For This study shows that the adapted Maskell's blockage correction
the small blockage ratio (BR ¼ 3%), the curves of the power co- method suggested by Alexander [13] exhibits coalescing trends for
efficients at various wind speeds ranging from 8 to 12 m/s were both the power and torque curves, and that the correction method
close together. For the large ratios (BR ¼ 5.3% and BR ¼ 8.3%), is appropriate and useful for assessing the aerodynamic perfor-
however, the power coefficients increased according to increases in mance of helical Savonius wind turbines.

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 K.S. Jeon et al. / Renewable Energy xxx (2014) 1e10 7

effect in helical Savonius wind turbines with a twist of 180
, the

power and torque coefficients were measured under different
conditions: without end plates, with lower end plate only, and with
both the upper and lower end plates for each blade. Fig. 12 shows
the measured power and torque curves for the helical Savonius
wind turbine (D ¼ 200 mm) at a fixed wind speed of 10 m/s. All of
the figures in this section show corrected results using the adapted
Maskell's blockage correction method. The use of both upper and
lower end plates significantly increased the power coefficient by
36% compared with no end plate. It was observed that the power
curves lie close together under the various end plate conditions in
the range of low tip speed.
The power and torque coefficient were measured to investigate
the influence of the end plate shape, as shown in Fig. 2. Fig. 13
shows the corrected power and torque curves under various end
plate shapes at a fixed air speed of 10 m/s. The figure shows that the
power coefficient changes significantly with variations in end plate
shape. Fig. 14 (a) and (b) show the change of the maximum power
coefficient and the tip speed ratio corresponding to the maximum
power coefficient according to the end plate area ratio (ER ¼ AE/AC).
The maximum power coefficient and the tip speed ratio corre-
sponding to the maximum power coefficient increased linearly

Fig. 8. The corrected power coefficient and torque coefficient at the wind speed of
10 m/s when BR ¼ 3%, 5.3%, and 8.3%.

3.2. Static torque

Fig. 11 shows the static torque coefficient measured at every 4

of rotation for a helical Savonius wind turbine with a diameter of
350 mm and two circular end plates, at a wind speed of 6 m/s. The
angle of the rotor is the angle between the direction perpendicular
to the chord line of the rotor and the free stream direction at the
rotor's upper plane, as shown in Fig. 11. The helical Savonius wind
turbine has a positive static torque coefficient for all rotor angles. It
was found that the static torque coefficients are nearly zero at rotor
angles around 30
and 210
, and undergo a large variation near the
maximum static torque coefficients. The maximum static torque
was detected at rotor angles of 0
and 180
.

3.3. The effects of end plates of various shapes and sizes

In Section 3.1 we verified the reliability of the Maskell's blockage

correction method for the helical Savonius wind turbine. In this
section we will analyze the influence of the end plate shapes and Fig. 9. The uncorrected power coefficient and torque coefficient at different wind
sizes on the power coefficients. In order to clarify the end plate speeds when BR ¼ 3.0%, BR ¼ 5.3%, and BR ¼ 8.3%.

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8 K.S. Jeon et al. / Renewable Energy xxx (2014) 1e10

Fig. 10. The corrected power coefficient and torque coefficient at different wind speeds
when BR ¼ 3.0%, BR ¼ 5.3%, and BR ¼ 8.3%.
Fig. 12. The power and torque coefficient of the helical Savonius wind turbines
(D ¼ 200 mm) with and without end plates at the wind speed of 10 m/s.

with the end plate area ratio. We expect that the circular end plate
at the advancing bucket deflects more air flow into the retreating
rotor which can produce more power. From these parametric
studies, we conclude that the main cause of these variations comes
from changes in the end plate area.
The end plate is able to decrease spanwise spillage which rep-
resents loss of the aerodynamic torque generated from the buckets.
Therefore, the larger the end plate area, the higher the aerodynamic
power. Based on this study, the use of circular end plates at both
ends of the rotor is the best way to increase the aerodynamic
performance of helical Savonius wind turbines.

4. Conclusion

We experimentally studied the effects of end plates on the

aerodynamic performance of helical Savonius wind turbines with a
twist angle of 180
and two semicircular buckets. In order to
investigate both the blockage correction method and the end plate
Fig. 11. The measured static torque coefficient of the helical Savonius wind turbine effect, four different helical Savonius wind turbines were tested
with a diameter of 350 mm at a wind speed of 6 m/s. using a subsonic open-circuit type wind tunnel. The adapted

Please cite this article in press as: Jeon KS, et al., Effects of end plates with various shapes and sizes on helical Savonius wind turbines, Renewable
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 K.S. Jeon et al. / Renewable Energy xxx (2014) 1e10 9

Fig. 14. The change of the maximum power coefficient and the tip speed ration cor-
responding to the maximum power coefficient as a function of the end plate area ratio
(ER ¼ AE/AC).

Acknowledgments

Fig. 13. The torque and power coefficient of the helical Savonius wind turbines This paper was supported by research funds of Chonbuk Na-
(D ¼ 250 mm) with end plates of various shapes and sizes at the wind speed of 10 m/s. tional University in 2010. This work was supported by the New and
Renewable Energy grant of the Korea Institute of Energy Technol-
ogy Evaluation and Planning (KETEP), funded by the Korean Min-
istry of Trade, Industry and Energy. This work was also supported
Maskell's blockage correction method was used for the wind tur- by a National Research Foundation of Korea (NRF) grant funded by
bine model installed in the closed test section of the wind tunnel. the Korea government (MSIP) (2010-0028509).
In this study, the adapted Maskell's blockage correction method
for straight Savonius wind turbines suggested by Alexander was
adequately verified for helical Savonius wind turbines. Further- References
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Please cite this article in press as: Jeon KS, et al., Effects of end plates with various shapes and sizes on helical Savonius wind turbines, Renewable
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