effect of twist angle on the performance of savonius wind turbine

8/19/2019 Effect of Twist Angle on the Performance of Savonius Wind Turbine

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Effect of twist angle on the performance of Savonius wind turbine

Jae-Hoon Lee, Young-Tae Lee, Hee-Chang Lim*

School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Republic of Korea

a r t i c l e i n f o

Article history:

Received 28 January 2015

Received in revised form

30 October 2015

Accepted 6 December 2015

Available online 20 December 2015

Keywords:

Numerical study

Savonius wind turbine

Helical blade

Maximum power coef cient

Q-criterion

a b s t r a c t

This study aimed to understand the performance and shape characteristics of a helical Savonius wind

turbine at various helical angles. The power coef cient (C p) at different tip speed ratios (TSRs) and torque

coef cient (C T ) at different azimuths for helical blade angles of 0

, 45

, 90

, and 135

were observedunder the conditions of a constant projection area and aspect ratio. The numerical results discussed in

this paper were obtained using an incompressible unsteady Reynolds average NaviereStokes (k-ε RNG)

model. A numerical analysis in the unsteady state was used to examine the ow characteristics in 1

steps from 0 to 360. In addition, an experiment was performed at a large-scale wind tunnel, and the

results were compared with those of the numerical analysis. Wind speed correction was also employed

because of the blockage effect between the wind turbine and wind tunnel. Our results showed that the

maximum power coef cient (C p,max) values in both cases had similar tendencies for the TSR range

considered in this study, i.e. from 0.4 to 0.8, except for the twist angle of 45 . The C p,max occurred at the

twist angle of 45, whereas it decreased by 25.5% at 90 and 135. Regarding the C T values at various

azimuths, the results showed that the peak-to-peak values in the proles for 90 and 135 were less than

those for 0 and 45.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Because of the excessive use of fossil fuels, the world is facing

serious problems related to energy depletion and environmental

pollution. To overcome these problems, many alternatives to fossil

fuels have been proposed. Among these, renewable energy has

drawn much attention because of the signicant investments in

its research and development by governments and the diverse

policies established by governments to extend it to the private

sector. According to a report published by the [1] ; the amount of

renewable energy generated is increasing yearly. In 2012, the

amount had grown by about 19% from the previous year. The ca-

pacity of wind energy in particular has increased compared toother forms of renewable energy. The annual average growth rate

of wind power capacity from 2007 to 2012 was reported to be

about 25%.

Within wind energy, horizontal axis wind turbines (HAWTs)

have attracted most of the attention during recent years. However,

vertical axis wind turbines (VAWTs) have an inherent advantage

over HAWTs. For example, in the case of VAWTs, the blade is easily

manufactured, repaired, and maintained. Moreover, no tail or yaw

devicefor thewind directionis necessary, because the rotorblade is

installed vertically to the ground. Furthermore, VAWTs can

generate power even at relatively low wind speeds compared to

HAWTs, and they arealso easy to install [2]. VAWTs can be classied

into two groups: the Darrieus and Savonius types. A Darrieus tur-

bine is a device that uses the lift force generated by an airfoil,

whereas a Savonius turbine exploits the drag force. The Savonius

wind turbine, which was invented in 1929, has an inherently

simple shape compared to other types of wind turbines. Therefore,

the cost involved in its development can be lower. Furthermore, it

produces less noise and maintains stable performance at relatively

low wind speeds (see Refs. [3,4]).Recently, a few studies have been conducted on the optimiza-

tion of a VAWT based on an evolvement in the eld of experimental

study and numerical analysis [10]. and [11] numerically studied the

inuence of the overlap ratio of a Savonius wind rotor. The results

showedthat the maximum performance appears at an overlap ratio

of 0.15. Regarding the numerical study with the steady Reynolds

average NaviereStokes (k-ε RNG) model, some recent papers

simulated the vertical axis wind turbine rotors (see [5e9,12,38]);

examined the inuences of the diameter-to-height aspect ratio of a

Savonius wind rotor and an increase in the number of stages on the

performance. They also analysed the performance of a Savonius* Corresponding author.

E-mail address: [email protected] (H.-C. Lim).

Contents lists available at ScienceDirect

Renewable Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / r e n e n e

http://dx.doi.org/10.1016/j.renene.2015.12.012

0960-1481/©

2015 Elsevier Ltd. All rights reserved.

Renewable Energy 89 (2016) 231e244

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wind turbine at a 90 twist angle. They reported that the perfor-

mance at a low aspect ratio(0.88) was better than those at 0.93 and

1.17 [13,14]. performed a numerical analysis on a Savonius turbine

with either two or three blades. The results indicated that the two-

bladed rotor generated better power coef cients than the three-

bladed design. Furthermore, they attempted to optimize the

blade shape using evolutionary algorithms [15]. numerically stud-

ied the inuences of the number of blades, overlap ratio, twist

angle, and aspect ratio on the power coef cient [16]. conducted an

experiment using a helical blade in a wind tunnel. Their results

indicated that an increase in the twist angle enhanced the perfor-

mance at lowspeeds. On the other hand, increasing the twist angles

resulted in a reduction in the net positive torque.

There has been some literature regarding the helical Savonius

wind turbines. (see Refs. [32e35]). However, have focused on their

specic cases. For instance [32]; studied the Savonius-Darrieus

turbine model combined with the k-ε turbulence model, and they

validated their numerical model through comparison with existing

results [34]. attempted to obtain performance data of a helical

Savonius turbine (45), and interestingly, they found a marginal

increase in the power coef cient [35]. conducted numerical and

experimental studies on a variety of helical Savonius turbines (45 -

720), but the software platform and test model used were not

reliable enough to support the power performance [33]. proposed a

guideline for designing an appropriate helical Savonius geometry

by utilising the calculus principles of denite integrals, which

would help to gain a basic understanding of the turbine design.

If we take into account existing studies, it is evident that many

previous researchers have focused on studying various shapes of

Savonius wind turbine. However, a closer look at the design pa-

rameters clearly shows that there is a lack of clear analysis results

that would indicate the effects of the helical angle on the perfor-

mance of a VAWT. These previous studies encouraged us to develop

and optimise the Savonius wind turbine with different helical an-

gles by means of an experiment and numerical calculation.

Therefore, the primary objective of this study was to investigate thevariation in the power coef cient and ow patterns of a wind

turbine at different helical angles based on a constant projection

area, which is the area of thewind rotoractually receiving the wind.

This paper is organized in the following manner: Section 2 outlines

the basic description of experimental and numerical methods with

various blade models. Section 3 describes the parametric analysis of

VAWTs under uniform wind ow. Section 4 explains the effect of

various blade parameters on Savonius VAWT, and Section 5 gives

the major conclusions.

2. Design of wind tunnel experiment

2.1. De nitions of wind turbine performance

Usually, it is not easy to evaluate the performance of wind rotors

with different shapes using a wind tunnel experiment. In addition,

it is time consuming to fabricate an appropriate measurement

Fig. 1. Top view of Savonius wind turbine design.

Fig. 2. Top and side view of wind rotor shapes with different twist angle (solid line: contact line on the upper endplate, dashed line: lower endplate).

J.-H. Lee et al. / Renewable Energy 89 (2016) 231e 244232


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system. In addition, because of the limited conditions implanted in

the boundary condition, a numerical simulation cannot be applied

effortlessly. Therefore, we utilized both approaches in this study,

whereas most studies have focused on and used only one. In order

to dene the wind turbine performance and evaluate the interac-

tive ow characteristics between the uid ow and rotationalblades, it is generally important to express the performance using

well-known non-dimensional parameters. These parameters C p, C T ,

and TSR were used. In particular, C p is a coef cient used to present

the wind rotor performance.

The Reynolds number based on the conguration of the wind

turbine is expressed as

Re ¼ rV ∞H

m (1)

where V ∞ and H are the velocity at the tunnel freestream and the

height of the Savonius turbine, respectively. In this study, V ∞ and H

are taken as 8 m/s and 10 m/s and 2.1 m, respectively. Therefore, the

Reynolds numbers used in this study are 1.8106 and 1.44106 forthe experiment and simulation, respectively.

In addition, in order to dene the power and torque coef cients

(C p and C T , respectively), the dynamic effects of the rotational wind

turbine need to be considered; therefore, the hydraulic diameter Dhof the Savonius turbine is used to form an appropriate projection

area A.

Dh ¼ 2ðD H Þ

D þ H (2)

where D is the diameter of the Savonius turbine.TSR is dened as the ratio of the blade tip linear speed to the

undisturbed ow speed. TSR can be expressed in Eqn (3), where R

denotes the rotor radius [m], n is the revolutions per minute [rpm],

and V ∞

is the free stream wind speed [m/s].

TSR ¼ uR

V ∞¼

2pRn

60V ∞(3)

The power coef cient ’C p’ is the ratio of the power produced by

the wind rotor to the power available at a specic wind speed. The

power coef cient can be calculated using Eqn (4), where T repre-

sents the torque [N ,m], r is the air density [kg ,m3], and A is the

area covered by the rotor [m2].

Fig. 3. Various projection areas and blade shape of different azimuths.

Table 1

Average, maximum, and minimum projection areas at different twist angles.

Twist angle Average area Maximum are a Minimum area

f¼0 0.296 m2 0.392 m2 0.136 m2

f¼45 0.297 m2 0.386 m2 0.183 m2

f¼90 0.297 m2 0.366 m2 0.229 m2

f¼135 0.297 m2 0.335 m2 0.268 m2

Fig. 4. Experimental setup used for wind tunnel test.

J.-H. Lee et al. / Renewable Energy 89 (2016) 231e 244 233


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C p ¼ T u

0:5r AV 3∞

(4)

The torque coef cient ’C T ’ can be calculated using Eqn (5). In a

case where the wind rotor lift is used to determine the rotational

force, the torque can be generated using the moment due to the lift

produced by the rotating plane of the blade. On the other hand, in

the case of a drag-type wind rotor, the torque is generated using the

moment due to the drag.

C T ¼ T

0:5r ARV 2∞

(5)

2.2. Design of helical Savonius blade shape

As shown in Figs. 1 and 2, a variety of parameters are used todesign a helical Savonius wind turbine blade. Some representative

design parameters are as follows: the aspect ratio (a), overlap ratio

(b), twist angle (f), and azimuth angle (q). The aspect ratio ’a0 is

dened as the ratio of the height (H ) to the diameter (D) of the

blade, as shown in Eqn (6). In order to nd the inuence of the

aspect ratio, this study considered the effective ’a0 as one of the

primary parameters, which may increase the rotor performance

ef ciency, as reported in previous papers (see Refs. [13,19]).

a ¼ H

D (6)

Equation (7) represents overlap ratio ’b0, where b is the ratio of

the gap between two adjacent blades (e) to the distance between

both blade ends (D) [18]. explained the effect of the overlap ratiobetween blades using particle image velocimetry (PIV). The

parameter ’e’ is used to dene a gap, and the oncoming wind blows

through the gap along a concave surface of the blade, which lets air

move through this gap and reach an opposite blade. When the

overlap ratio b increases to some extent, the torque and power

coef cient reach their maximums and decrease (see Refs. [38,39]).

Hence, overlap ratio b is one of the design parameters used to in-

crease the performance of Savonius rotor blades. Some papers have

already been published on this subject (see Ref. [10,11,13]). There-

fore, the effect of the overlap ratio was not considered in this study.

b ¼ e

D (7)

The twist angle is de

ned as the twist angle between the upper

and lower end-plates of the blades. In order to properly join all the

blades and stabilize the ow around them, the use of both upper

and lower end-plates was the best choice, as previously suggested

(see Refs. [20,21]). Regarding the aspect ratio, a was set to 1.33:1,

which was considered to be the optimum shape [19]. Overlap ratio

b was set to 0.167, and end-plates were installed. In order to

conduct an experiment and numerical analysis based on different

twist angles, we made four different models: - 0, 45, 90, and

135.

In the case of a Savonius wind rotor, the projection area would

change along a cycle of rotation when two blades are rotating.

Therefore, when the blades are rotating, a performance evaluation

needs to consider a full cycle. Depending on the twist angle, the

projection area appears to have a variety of shapes: a nut, ellipsoid,

almost circle, etc. At a twist angle of 0, the projection area has the

shape of two partly overlapping circles. As the twist angle in-

creases, however, the projection area turns into an ellipsoid shape,

as indicated in Fig. 3. Therefore, the various projection area shapes

at different twist angles were taken into consideration in this study.Note that even at different twist angles, the wind turbine was

designed to have projection areas with identical average sizes. The

maximum, minimum, and average projection areas are listed in

Table 1. The gures in this table indicate that the difference be-

tween the minimum and maximum projection areas became lower

as the twist angle increased.

2.3. Wind tunnel experiment

The experiments were carried out in a large-scale boundary

Fig. 5. Experimental setup used for wind tunnel test.

Fig. 6. Variation of velocity correction factor with S/C [21].



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layer wind tunnel at Pusan National University. The dimensions of

the wind tunnel were 2 m 2.1 m 20 m. A 185kW three-phase

variable speed DC motorwas used to keep the wind speed constant.

The maximum wind speed was limited to 23 m/s with the turbu-

lence intensity less than 1% (see Ref. [17]). One of authors previ-

ously described the experimental method in detail (see

Refs. [22,23]). Therefore, only a short introduction and brief

description of the experiment is given here. Fig. 4 shows the details

of the experimental setup employed. A pitot tube was installed 5 m

ahead of the wind turbine to measure the non-disturbed wind

speed in the upstream region. The incoming wind speed was

measured using a micro-manometer (FCO12).

The incoming wind from the wind tunnel rotated the blade and

generated rotating power. The rotational power produced as a

result of the wind ow was analysed using a torque meter (TRD-

50KC) built in a circular box placed below the turbine model. When

measuring the torque, we used a powder brake (ZKG-50YN) to

create force control power. The rotational speed (rpm) of the wind

turbine was measured using a tachometer, which was installed to

receive the signal sent by an optical sensor (ROS-5P). The torque

meter was connected to a computer through an A/D converter,

through which the voltage signal produced by the torque meter

was transmitted to the computer. The signal travelling from thetorque meter to the computer was acquired by means of in-house

code, which was coded using the ’Labview’ platform data acquisi-

tion software. The output power of the helical Savonius wind tur-

bine was calculated based on the measured values. Fig. 5 shows the

helical Savonius wind turbine model and measurement devices

used in the experiment.

2.4. Wall interference effect (blockage effect)

The C p of the wind turbine was affected by the wall (see

Refs. [21,22]). Many researchers have tried to study this effect.

Among them [21]; suggested a relation for the velocity correction

due to the blockage ratio of a Savonius wind turbine, as shown in

Eqn (8) and Fig. 6.

V c V

¼ 1

1 m S C (8)

where the blockage ratio (S /C ) is the ratio of the wind turbine

projection area (S ) and wind tunnel cross-sectional area (C ). V is the

free stream velocity, V c is the correction velocity, and m represents

the coef cient of wall, which had a value of one. In our study, the

values of S /C and V c /V were 0.092 and 1.15, respectively. After

correction, the velocity in the wind tunnel during our experiments

was increased from 10 m/s to 11.5 m/s, while the velocity in the

numerical simulations was changed from 8 m/s to 9.2 m/s.

3. Numerical analysis

In this study, the numerical simulations were coaxially per-

formed using ANSYS Fluent, which is a commercial computational

uid dynamics (CFD) solver. This software calculates the compli-

cated ow structure based on the nite volume method (FVM) of

the NaviereStokes governing equation, which is suitable for

resolving the problems associated with the interaction between the

complicated on-coming wind ow and the rotating blades. The

numerical domain and meshes were generated using ANSYS ICEM.

The number of meshes used in this study ranged from 1,200,000 to

1,500,000.

In order to calculate the ow around the wind turbine, it is

important to set an appropriate iteration time at each step during

the rotation of the blade. Asthe subdomain is rotated in each step, it

reconnects with the external domain so that the wind ows are

readjusted and repeatedly renewed. Therefore, after creating this

unsteady condition, it is nally stabilized. The nal values depend

on the number of iterations (i.e. 50 iterations in our study) and then

becomeconverged. In addition, the data began to be savedafterve

rotations of the turbine rotor to ensure ow stabilization. The data

began to be saved after ve rotations of the turbine rotor to ensure

ow stabilization.

3.1. Governing equation

The turbulence model employed in this paper requires an un-

steady Reynolds average NaviereStokes (URANS) analysis. In this

case, the governing equations under a Newtonian uid condition

required two equations: the continuity equation expressed in Eqn

(9) and momentum equation expressed in Eqn (10).

vuiv xi

¼ 0 (9)

vuiv

t

þ v

v

x juiu j ¼

1

r

v p

v

xi

þ v

v

x jn

vuiv

x j

u0iu0

j! (10)where ui and u

0i are the mean and uctuating components,

respectively, of velocity in the xi direction. In addition, p is the mean

pressure, n is the kinematic viscosity, r is the density of the uid,

and t is the time. The Reynolds stress u0iu0

j also needs to be modelled

to close the problem mathematically. (See Ref. [26] Among the

various turbulence models (e.g., standard k-u and k-ε, etc), the k-ε

RNG model was chosen to better predict the swirling effect behind

the rotating blade, particularly to enhance the accuracy of the rapid

strain and streamline curvature (see Refs. [24,26,27]. The turbu-

lence kinetic energy (k) is also described in Eqn(11). The turbulence

dissipation rate (ε) is given by Eqn (12).

r DkDt ¼ v

v x j

akmeff

v

kv x j

!þ Gk rε (11)

rDk

Dt ¼

v

v x j

aεmeff

vε

v x j

!þ C 1εGk

ε

k C 2εr

ε2

k Rε (12)

where ak and aε are the turbulent Prandtl numbers for k and ε. In

addition, meff and Gk are the dispersion coef cient and the genera-

tion of turbulence kinetic energy due to the mean velocity gradi-

ents, respectively. In these equations, C 1ε and C 2ε are constants

having values of 1.42 and 1.68, respectively. In addition, the term Rεis used to improve the accuracy for rapidly strained ows (see

Refs. [24,26,27].

A k-ε RNG turbulence model was selected for our analysis. In

Fig. 7. Overall domains of boundary and internal condition used in numerical analysis.



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order to deduce the link between the pressure and velocity in the

calculation domain, the semi-implicit method for pressure-linked

equation (SIMPLE) algorithm was used.

In order to deduce the link between the pressure and velocity in

the calculation domain, we implemented a second-order upwind

scheme (thus improving accuracy and feasibility) rather than using

a rst-order scheme. In order to convert the continuity equation

into a discrete Poisson equation for pressure, the Simple method

was applied (see Refs. [11,14,27]). The differential equations are

linearized and solved implicitly in sequence, starting with the

pressure equation (predictor stage), followed by the momentum

equations and the pressure-correction equation (corrector stage).

In order to manipulate the gradient, we used a least-squares cell-

based scheme. (See Ref. [28]).

The time step we used in the calculation was 5.89 104 sec at

TSR¼1 (i.e. 1 rotation every time step) to observe the detailed

structure of the separated wake behind the turbine blades. For a

reliable result, the calculation was continuously made to achieve

consistent torque from each blade during one cycle. In addition, in

order to provide a suitable time step, the CFL number was main-

tained at less than 10, which is a bit unsuitable, but the standard

wall function compensates for the wall treatment instead.

During each iteration, the values obtained for the variablesshould get closerand closer so that they converge. For some reason,

the solution can become unstable, so a relaxation factor refers the

value from the previous iteration to dampen the solution and cut

out steep oscillations. As a rule of thumb in this study, we simply

keep the relaxation factors at default, which is quite reasonable for

especially cold ows without combustion. In our study, we used

pressure 0.3, body force 1, momentum 0.8, turbulent kinetic energy

0.8, turbulent dissipation rate 0.8, and turbulent viscosity 1.

3.2. Boundary conditions

For appropriate analysis, the overall domain was divided into

two sub-domains: surrounding xed and inner rotating bladed

domains as shown in Fig. 7. The total number of grids was 1.0~ 1.5

million, and the grid shape is shown in Fig. 8. Fig. 8 (a) and (b) are

the main grid shapes of the rotating rotor and surrounding outer

domain, respectively. In order to link the inner and outer domains,

the interface condition was used to describe the separated wake

ow interaction with the rotating blades and surrounding region. In

addition, the sliding mesh model (SMM) was used for a (pseudo-)

rotating mesh to simulate the rotating blades. The sliding mesh

could be effectively used in a case where the mesh did not deform.

The rotational speed could be set depending on the experimental

conditions (see Refs. [11,24,27]).

In order to impose a similar condition as the wind tunnel, the

inlet boundary conditions were set as follows: velocity inlet at a

uniform velocity of 8 m/s, and the outlet atmospheric pressure

condition at 1 atm. The no-slip wall condition was applied to the

surface of the domain wall and the blade surface. In terms of tur-

bulent kinetic energy (k), k is dened as 12 u0iu0

j ¼ 12 ðu

02 x þ u

02 y þ u

02 z Þ ¼

32 u

02 and the axial stresses are assumed to be approximately 0.7 in

our study. Therefore, the turbulent kinetic energy (k) and turbulentdissipation rate (ε) are dened as a unit. The wall boundary con-

dition was applied to the side and top/bottom wall planes. The

moving wall condition was set for all the moving components such

as the helical blades, main supporting pipe, and end plates. In order

to observe the vortex formation behind the blades in detail, the

downstream size of the sub-domain was set at around 4D.

Regarding the sub-domain side, this study mainly attempts to

understand the near-vortex ow close to the blades determining

the ne subdomain in the downstream approximately 4D, which

Fig. 8. Mesh generation and distribution around VAWT.



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includes the smallest scales of the vortex. In fact, a parametric study

was also conducted for the downstream subgrid of the wind blades.

It was found that an approximately 4D to 6D subdomain in the

downstream of the blades was enough to generate small-scale

eddies. In addition, in order to maintain the vortex in the region

that is farther downstream, the midsized subdomain was also

created so that the vortex region was still maintained farther

downstream. One of the interesting facts in the result is that the

dissipation of the vortex wake behind the blades depends on the

twist angle (e.g., see Fig. 12, and the periodic regular vortex wake

appears downstream, whereas the dissipation seems faster when

the twist angle increases).

4. Results and discussion

To analyze the results, we compared the C p values with various

TSRs. In this study, the wind tunnel experiment results were

compared with those of the numerical simulations. Based on the

numerical analysis, C T was examined at various azimuths under the

condition that the blade was being rotated. Furthermore, we also

investigated how the air ow changed at different azimuths for the

Savonius wind turbine.

4.1. Power coef cients of experimental and numerical analysis

The Reynolds numbers used in this study were 1.24106 and

1.55106 depending on the averaged projection area. Fig. 9 shows

the TSR versus C p plot for both the experimental and numerical

simulation results at different twist angles (f) ranging from 0 to

135.

Because of the blockageeffect, C p,max was reduced to38.2% in the

experiments and numerical simulations. Compared to 0 and 45,

C p appeared relatively low at twist angles of 90 and 135. C p,max

was found to be between TSR values of 0.5 and 0.65 for all of the

twist angles. In addition, the C p values were not present below a

TSR of 0.4 in the experiment, which was due tothe high mechanical

friction between the main axle of the Savonius turbine and the

mechanical powder brake. The difference between the C p,max values

in the experimental and simulation results was the largest (around

0.02) at the 45 twist angle, whereas at the 135 twist angle, this

difference was found to be very small (i.e. almost negligible). The

performance of the Savonius wind turbine was observed to be the

most ef cient at the 45 twist angle from both the experiments and

numerical analysis, with a C p of 0.13 at a TSR of 0.54, whereas the

twist angle with the lowest value of C p was 135, with a C p of 0.12 at

a TSR of 0.54.

All experimental data may contain more or less uncertainty. An

uncertainty analysis was carried out for all experimental results to

assess their condence levels, following the method suggested by

Ref. [25]. The total error consists of the bias error and precision

error. The bias error can be minimized by carefully calibrating themeasuring instruments. To evaluate the precision error, the stan-

dard deviation of the sample records was calculated for the surface

pressure. The total error, with 95% condence, is depicted as a form

of error bar. (see Fig. 9) As shown in the gure, the maximum error

of uncertainty reaches approximately 5% at most.

4.2. Temporal variation of torque coef cient at different azimuths

Fig. 10 shows the torque coef cient (C T ) values at different azi-

muths. When the azimuth was varied, C T attained its highest value

of 0.34 at a twist angle of 45 and TSR of 0.45. The graphs also

indicate that the phase difference of C T decreased as the twist angle

increased. At a twist angle of 135, the phase difference was the

least.In the experiment, the torque sensoractually reads the averaged

torque values during the measurement so that the values of

different azimuth angles in real time may not be possible or

available owing to the hardware limitations of our experiment. In

addition, depending on the condition of the wind tunnel, the torque

signal sometimes becomes unstable in the early stages of mea-

surement. Therefore, during each measurement, we waited to

obtain a stable condition that yielded a reliable rpmand torque. The

averaged values were obtained after waiting for approximately

5e10 min to get reliable values in the tunnel. For the numerical

simulation, the torque variation having consistent periodic values

from each blade was averaged for each cycle.

In the result, negative C T values occurred in the azimuth angle

ranges of 60

-150

and 240

-330

at twist angles of 0

, 45

, and135, with a TSR of 0.88. Regarding this observation, which will be

explained shortly, it is inferred that a force by air is not properly

transferred to the concave surfaces of both blades. Instead, it might

affect convex surfaces. However, in a case where TSR was less than

0.45, no negative values were found. This might be because the air

resistance increased at the convex part of the blade in comparison

to the rotational power of the turbine as the rotational speed

increased. In contrast, the blades with twist angles of 135 did not

show any negative value of C T at TSR ¼ 0.88.

Fig. 11 shows C T values with a TSR of 0.6 at different azimuths.

Interestingly, in Fig. 11(a) and (b), the C T of blade 1 tends to increase

and decrease within the range of 225-270. However, this phe-

nomenon was not observed in the case of blades with twist angles

of 90

and 135

. It seems that the twist angle caused the internal

Fig. 9. Power coef cient variations against TSR.



8/14

ow to circulate effectively. In addition, with twist angles of 0 and

45, the internal ow through the central overlap hole stuck the

main axis pipe during the rotation of the blade, and then moved to

the opposite side of the blade. When the twist angle was 90 , the

instant kink of the torque coef cient did not appear because of the

twist angle. In addition, with an increase in the twist angle, the

Fig. 10. Torque coef cient variations against TSR.



9/14

convex surface side always faced the on-coming wind, which

reduced the torque coef cient. From this observation, it can also be

implied that the generated torque would remain consistent as the

twist angle increased.

Fig. 11. Torque coef cient variations of Blades 1 and 2 at different azimuths.



10/14

4.3. Flow visualization at different azimuths

Fig. 12 shows the vortex formation at a twist angle of 0 and

azimuth angle of 0, 45, 90, and 135. We used the Q-criterion

method, which can be de

ned as the

ow regions with a positivesecond invariant of the velocity (see Refs. [29e31]). The value for

the Q-criterion coef cient was set as 0.011 in this case. In the case of

the Savonius wind turbine, vortex formation was in the direction of

rotation. As shown in the gure, the symmetric vortex pairs are

separated from both sides of the blade end and propagated

downstream, yielding horseshoe-shaped vortex structures. In this

visualization scheme, it is noticeable that the vortex is a bit

complicated, but owing to the end plates they would be making

better stable wake shape.

Fig. 13 shows the case with a twist angle of 0 and a TSR of 0.6 at

different azimuths. At an azimuth angle of 0, the results show that

the air did not directly impact on the concave surface of the blade,

as shown in Figs.13(a) and 14(a). Instead, it impacted on the convex

surface of blade 2, and then hit the concave surface of blade 1.

Figs. 13(c) and 14(b) show the air-ow pattern at an azimuth angle

of 90. Looking at the streamlines shown in Fig. 13 and velocity

vector eld in Fig. 14, it can be seen that the air moves towards the

concave surface, and the

ow separates at the inner and outer re-gions. Subsequently, the air moves towards the opposite blade,

passing through a narrow space between the shaft and the blades.

At this moment, the air entering blade 1 hits the concave surface of

blade 2, which creates the rotational power for blade 2. On the

other hand, Figs. 13(b) and (d) suggest that the air moves towards

the concave part of the blade. It is also found that when the concave

surface of the blade receives the force of the air, this force is

transferred to the concave surface of the opposite blade.

In Fig.14(a), the air surrounding the shaft slowlymoves from the

concave surface of blade 2 to the concave surface of blade 1. In

contrast, Fig. 14(b) shows that the air moving from blade 2 to the

inside of blade 1 moves relatively fast. Moreover, the area marked

by the black circle in Fig. 14 is the point where the separated eddies

Fig. 12. Q-criterion distribution around Savonius wind turbine (Q-value was 0.011).

Fig. 13. Streamline and speed magnitude contours at different Azimuths.



11/14

occur in the direction indicated by the arrow.

Fig.15 shows the blade surface pressure (C pr ) and velocity vector

elds at twist angles of 0 and 135 at an azimuth angle of 45.

Fig. 15(a) shows the vector eld around the blade. In the gure, thewind directions are toward the page. It can be seen that the surface

of the blade is divided into two parts, i.e. right and left. Moreover,

the surface pressure is the same at each part. In the case of

Fig. 15(b), we can see that unlike those at a twist angle of 0, here

the directions of the velocity vectors are not only towards the left

and right but also in the upward and downward directions. In

addition, the pressure elds are different in the upper and lower

portions of the blade. Generally, the pressure has been found to

increase near the end plate. This seems to occur as a result of the

wall interference effect by the end plate.

Fig. 16 presents and compares the surface pressure distributions

for the twist angles having the highest and lowest performances.

For the azimuth angle having the highest performance, Fig. 16

shows that the pressure side of the blade (i.e. concave surface)creates a pressure-driven ow on the suction side of the blade (i.e.

convex surface). By contrast, for the case having the lowest per-

formance, the pressure side maintains high pressure, whereas the

suction side has little effect on the pressure-driven ow.

Fig. 17 shows the surface pressure distribution on the blade

surfaces with different twist angles. For a twist angle of 0 (see

Fig. 17(a)), the surface pressure close to the end plates experi-ences little change, but as the twist angle increases, the surface

pressure increases gradually at the bottom area close to the end

plate and reaches a maximum at a twist angle of 135 (see

Fig. 17(d)). In addition, in Figs. (a) and (b), it is noted that the

surface pressure coef cient at the concave surface has an almost

constant distribution, whereas it increases substantially at the

convex surface.

Fig. 18 shows the sectional averaged pressure distribution

around blades with different twist angles. For slice S1, the overall

pressure distribution is a bit higher than that of the other slices. The

implication of this gure is that in the case of twist angle 0, the

oncoming wind impacts the blade at a perpendicular angle directly

so that the surface pressure on the blade is almost consistent along

the lateral direction through the blade. However, as the twist anglechanges, the wind is in multiple directions (i.e. horizontal and

vertical) along the blade surface, and the suction pressure increases

(i.e. the colour turns brighter at high twist angles). In addition, the

Fig. 14. Snapshots of velocity vector elds at different azimuths.

Fig. 15. Surface pressure (C pr ) and velocity

eld at twist angles of 45

and 135

with an azimuth angle of 45

. In the

gure, the wind directions are toward the page.



12/14

Fig. 16. Sectional pressure distribution indicating the maximum and minimum C pr . In the gure, (a) and (c) are the case of maximum C pr and (b) and (d) the minimum C pr .

Fig. 17. Averaged surface pressure distribution for different twist angles.



13/14

stagnant pressure close to the end plates is a bit high for the blade

with a twist angle of 0 (see the slices S1 and S5. The suctionpressure would be high close to the end plate). However, this effect

seems tobe reduced for the blade with a twist angle of 135 (see the

slice S5). Considering the structural stability, this effect reduces

relatively the vertical load (vertical lift force and bending moment,

etc.) on the main rotational axis (i.e. the negative lift force increases

as the twist angle increases).

5. Concluding remarks

This study investigated the performance and shape character-

istics of a helical Savonius wind turbine at various twist angles. The

power coef cient (C p) values at different TSRs and torque coef -

cient (C T ) values at different azimuths for twist blade angles of 0

,45, 90, and 135 were observed under the condition that the

projection area and aspect ratio were constant. The keyconclusions

are summarized as follows.

1) The simulation results successfully veried the experiment re-

sults at a range of TSRs and maximum power coef cient (C p,max)

values as the Savonius wind turbine blade twist angle was

varied.

2) The maximum C p appears to be approximately 0.13 at a twist

angle of 45. However, at twist angles of 90 and 135, the value

of the power coef cient (C p) became lower than that at 0, but

the maximum C p appeared to be similar.

3) When the twist angle was greater than 90, itwasfoundthat the

torque coef

cients stabilized and remained constant.

4) The maximum C T was observed at an azimuth angle of 45 and

twist angle of 0 but varied with the azimuth and twist angles.5) Regarding the surface pressure distribution around the blade,

when the convex blade faced the ow, the surface pressure had

the maximum distribution, while the concave blade had the

minimum. While the blades were rotating, some sections had an

effective torque, and others had a relative drag force, which

retarded the blades rotation.

Acknowledgements

This work was supported by the Human Resources Develop-

ment of the Korea Institute of Energy Technology Evaluation and

Planning (KETEP) grant fundedby the Korea government Ministry

of Knowledge Economy (No. 20124010203230, 20114010203080).

In addition, this research was supported by Basic ScienceResearch Program through the National Research Foundation of

Korea(NRF) funded by the Ministry of Education, Science and

Technology(2013005347).

This research was also supported by the Fire Fighting Safety &

119 Rescue Technology Research and Development Program funded

by the Ministry of Public Safety and Security (MPSS-2015-80).

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