Effect of twist angle on the performance of Savonius ...

Renewable Energy 89 (2016) 231e244

Contents lists available at ScienceDirect

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

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

a b s t r a c t

Article history: Received 28 January 2015 Received in revised form 30 October 2015 Accepted 6 December 2015 Available online xxx

This study aimed to understand the performance and shape characteristics of a helical Savonius wind turbine at various helical angles. The power coefficient (Cp) at different tip speed ratios (TSRs) and torque coefficient (CT) at different azimuths for helical blade angles of 0 , 45 , 90 , and 135 were observed under 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 flow 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 coefficient (Cp,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 Cp,max occurred at the twist angle of 45 , whereas it decreased by 25.5% at 90 and 135 . Regarding the CT values at various azimuths, the results showed that the peak-to-peak values in the profiles for 90 and 135 were less than those for 0 and 45 . © 2015 Elsevier Ltd. All rights reserved.

Keywords: Numerical study Savonius wind turbine Helical blade Maximum power coefficient Q-criterion

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 significant 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 capacity of wind energy in particular has increased compared to other 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

* Corresponding author. E-mail address: [email protected] (H.-C. Lim). http://dx.doi.org/10.1016/j.renene.2015.12.012 0960-1481/© 2015 Elsevier Ltd. All rights reserved.

manufactured, repaired, and maintained. Moreover, no tail or yaw device for the wind direction is necessary, because the rotor blade is installed vertically to the ground. Furthermore, VAWTs can generate power even at relatively low wind speeds compared to HAWTs, and they are also easy to install [2]. VAWTs can be classified into two groups: the Darrieus and Savonius types. A Darrieus turbine 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 optimization of a VAWT based on an evolvement in the field of experimental study and numerical analysis [10]. and [11] numerically studied the influence of the overlap ratio of a Savonius wind rotor. The results showed that 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 influences 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

232

J.-H. Lee et al. / Renewable Energy 89 (2016) 231e244

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

wind turbine at a 90 twist angle. They reported that the performance 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 twobladed rotor generated better power coefficients than the threebladed design. Furthermore, they attempted to optimize the blade shape using evolutionary algorithms [15]. numerically studied the influences of the number of blades, overlap ratio, twist angle, and aspect ratio on the power coefficient [16]. conducted an experiment using a helical blade in a wind tunnel. Their results indicated that an increase in the twist angle enhanced the performance at low speeds. 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 specific 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 coefficient [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 definite 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 parameters clearly shows that there is a lack of clear analysis results that would indicate the effects of the helical angle on the performance of a VAWT. These previous studies encouraged us to develop and optimise the Savonius wind turbine with different helical angles by means of an experiment and numerical calculation. Therefore, the primary objective of this study was to investigate the variation in the power coefficient and flow patterns of a wind turbine at different helical angles based on a constant projection area, which is the area of the wind rotor actually 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 flow. 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. Definitions 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. 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).


233

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

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 define the wind turbine performance and evaluate the interactive flow characteristics between the fluid flow and rotational blades, it is generally important to express the performance using well-known non-dimensional parameters. These parameters Cp, CT, and TSR were used. In particular, Cp is a coefficient used to present the wind rotor performance. The Reynolds number based on the configuration of the wind turbine is expressed as

rV∞ H Re ¼ 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 for the experiment and simulation, respectively. In addition, in order to define the power and torque coefficients (Cp and CT, respectively), the dynamic effects of the rotational wind turbine need to be considered; therefore, the hydraulic diameter Dh of the Savonius turbine is used to form an appropriate projection area A.

Dh ¼

2ðD HÞ DþH

where D is the diameter of the Savonius turbine. TSR is defined as the ratio of the blade tip linear speed to the undisturbed flow 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 2pRn ¼ V∞ 60V∞

Average area

f¼0 f¼45 f¼90 f¼135

0.296 0.297 0.297 0.297

m2 m2 m2 m2

Maximum area 0.392 0.386 0.366 0.335

m2 m2 m2 m2

Minimum area 0.136 0.183 0.229 0.268

m2 m2 m2 m2

(3)

The power coefficient ’Cp’ is the ratio of the power produced by the wind rotor to the power available at a specific wind speed. The power coefficient can be calculated using Eqn (4), where T represents the torque [N,m], r is the air density [kg,m3], and A is the area covered by the rotor [m2].

Table 1 Average, maximum, and minimum projection areas at different twist angles. Twist angle

(2)

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

234


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

Cp ¼

Tu 3 0:5rAV∞

(4)

The torque coefficient ’CT’ 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.

CT ¼

T 2 0:5rARV∞

(5)

2.2. Design of helical Savonius blade shape As shown in Figs. 1 and 2, a variety of parameters are used to design 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 defined as the ratio of the height (H) to the diameter (D) of the blade, as shown in Eqn (6). In order to find the influence of the aspect ratio, this study considered the effective ’a0 as one of the primary parameters, which may increase the rotor performance efficiency, as reported in previous papers (see Refs. [13,19]).

H a¼ D

(6)

and lower end-plates of the blades. In order to properly join all the blades and stabilize the flow 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 increases, 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 figures in this table indicate that the difference between 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

’b0 ,

Equation (7) represents overlap ratio 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 ratio between blades using particle image velocimetry (PIV). The parameter ’e’ is used to define 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 coefficient reach their maximums and decrease (see Refs. [38,39]). Hence, overlap ratio b is one of the design parameters used to increase the performance of Savonius rotor blades. Some papers have already been published on this subject (see Ref. [10,11,13]). Therefore, the effect of the overlap ratio was not considered in this study.

b¼

e D

(7)

The twist angle is defined as the twist angle between the upper

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


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 motor was used to keep the wind speed constant. The maximum wind speed was limited to 23 m/s with the turbulence intensity less than 1% (see Ref. [17]). One of authors previously 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 flow was analysed using a torque meter (TRD50KC) 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 the torque meter to the computer was acquired by means of in-house code, which was coded using the ’Labview’ platform data acquisition software. The output power of the helical Savonius wind turbine 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 Cp 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.

Vc 1 ¼ V 1 m CS

235

reconnects with the external domain so that the wind flows are readjusted and repeatedly renewed. Therefore, after creating this unsteady condition, it is finally stabilized. The final values depend on the number of iterations (i.e. 50 iterations in our study) and then become converged. In addition, the data began to be saved after five rotations of the turbine rotor to ensure flow stabilization. The data began to be saved after five rotations of the turbine rotor to ensure flow stabilization. 3.1. Governing equation The turbulence model employed in this paper requires an unsteady Reynolds average NaviereStokes (URANS) analysis. In this case, the governing equations under a Newtonian fluid condition required two equations: the continuity equation expressed in Eqn (9) and momentum equation expressed in Eqn (10).

vui ¼0 vxi

(9)

vui v 1 vp v þ ui uj ¼ þ vxj r vxi vxj vt

3. Numerical analysis In this study, the numerical simulations were coaxially performed using ANSYS Fluent, which is a commercial computational fluid dynamics (CFD) solver. This software calculates the complicated flow structure based on the finite 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 flow 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 flow around the wind turbine, it is important to set an appropriate iteration time at each step during the rotation of the blade. As the subdomain is rotated in each step, it

vui u0i u0j vxj

! (10)

where ui and u0i are the mean and fluctuating 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 fluid, and t is the time. The Reynolds stress u0i u0j 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 turbulence kinetic energy (k) is also described in Eqn (11). The turbulence dissipation rate (ε) is given by Eqn (12).

r

Dk v ¼ Dt vxj

ak meff

vk vxj

(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, Vc is the correction velocity, and m represents the coefficient of wall, which had a value of one. In our study, the values of S/C and Vc/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.

n

Dk v ¼ r Dt vxj

vε aε meff vxj

!

!

þ Gk rε

(11)

ε ε2 þ C1ε Gk C2ε r Rε k k

(12)

where ak and aε are the turbulent Prandtl numbers for k and ε. In addition, meff and Gk are the dispersion coefficient and the generation of turbulence kinetic energy due to the mean velocity gradients, respectively. In these equations, C1ε and C2ε are constants having values of 1.42 and 1.68, respectively. In addition, the term Rε is used to improve the accuracy for rapidly strained flows (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.

236


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 first-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 cellbased scheme. (See Ref. [28]). The time step we used in the calculation was 5.89104 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 maintained 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 variables should get closer and 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 flows 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 fixed 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 flow 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 tur02 02 bulent kinetic energy (k), k is defined as 12 u0i u0j ¼ 12 ðu02 x þ uy þ uz Þ ¼ 3 u02 and the axial stresses are assumed to be approximately 0.7 in 2 our study. Therefore, the turbulent kinetic energy (k) and turbulent dissipation rate (ε) are defined as a unit. The wall boundary condition 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 flow close to the blades determining the fine subdomain in the downstream approximately 4D, which

Fig. 8. Mesh generation and distribution around VAWT.


237

simulation results at different twist angles (f) ranging from 0 to 135 . Because of the blockage effect, Cp,max was reduced to 38.2% in the experiments and numerical simulations. Compared to 0 and 45 , Cp appeared relatively low at twist angles of 90 and 135 . Cp,max was found to be between TSR values of 0.5 and 0.65 for all of the twist angles. In addition, the Cp values were not present below a TSR of 0.4 in the experiment, which was due to the high mechanical friction between the main axle of the Savonius turbine and the mechanical powder brake. The difference between the Cp,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 efficient at the 45 twist angle from both the experiments and numerical analysis, with a Cp of 0.13 at a TSR of 0.54, whereas the twist angle with the lowest value of Cp was 135 , with a Cp 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 confidence 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 the measuring instruments. To evaluate the precision error, the standard deviation of the sample records was calculated for the surface pressure. The total error, with 95% confidence, is depicted as a form of error bar. (see Fig. 9) As shown in the figure, the maximum error of uncertainty reaches approximately 5% at most. 4.2. Temporal variation of torque coefficient at different azimuths

Fig. 9. Power coefficient variations against TSR.

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 Cp 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, CT was examined at various azimuths under the condition that the blade was being rotated. Furthermore, we also investigated how the air flow changed at different azimuths for the Savonius wind turbine. 4.1. Power coefficients 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 Cp plot for both the experimental and numerical

Fig. 10 shows the torque coefficient (CT) values at different azimuths. When the azimuth was varied, CT 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 CT decreased as the twist angle increased. At a twist angle of 135 , the phase difference was the least. In the experiment, the torque sensor actually 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 measurement. Therefore, during each measurement, we waited to obtain a stable condition that yielded a reliable rpm and 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 CT values occurred in the azimuth angle ranges of 60 -150 and 240 -330 at twist angles of 0 , 45 , and 135 , 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 CT at TSR ¼ 0.88. Fig. 11 shows CT values with a TSR of 0.6 at different azimuths. Interestingly, in Fig. 11(a) and (b), the CT of blade 1 tends to increase and decrease within the range of 225 -270 . However, this phenomenon was not observed in the case of blades with twist angles of 90 and 135 . It seems that the twist angle caused the internal

238


Fig. 10. Torque coefficient variations against TSR.

flow to circulate effectively. In addition, with twist angles of 0 and 45 , the internal flow 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 coefficient did not appear because of the twist angle. In addition, with an increase in the twist angle, the


239

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

convex surface side always faced the on-coming wind, which reduced the torque coefficient. From this observation, it can also be

implied that the generated torque would remain consistent as the twist angle increased.

240


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

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 defined as the flow regions with a positive second invariant of the velocity (see Refs. [29e31]). The value for the Q-criterion coefficient 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 figure, 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-flow pattern at an azimuth angle of 90 . Looking at the streamlines shown in Fig. 13 and velocity vector field in Fig. 14, it can be seen that the air moves towards the concave surface, and the flow separates at the inner and outer regions. 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 slowly moves 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. 13. Streamline and speed magnitude contours at different Azimuths.


241

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

occur in the direction indicated by the arrow. Fig. 15 shows the blade surface pressure (Cpr) and velocity vector fields at twist angles of 0 and 135 at an azimuth angle of 45 . Fig. 15(a) shows the vector field around the blade. In the figure, the wind 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 fields 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 flow on the suction side of the blade (i.e. convex surface). By contrast, for the case having the lowest performance, the pressure side maintains high pressure, whereas the

suction side has little effect on the pressure-driven flow. 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 experiences 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 coefficient 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 figure 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 angle changes, 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. 15. Surface pressure (Cpr) and velocity field at twist angles of 45 and 135 with an azimuth angle of 45 . In the figure, the wind directions are toward the page.

242


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

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


243

Fig. 18. Sectional averaged pressure distribution around the blades with different twist angles.

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 suction pressure would be high close to the end plate). However, this effect seems to be 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).

4) The maximum CT 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 flow, 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

5. Concluding remarks This study investigated the performance and shape characteristics of a helical Savonius wind turbine at various twist angles. The power coefficient (Cp) values at different TSRs and torque coefficient (CT) 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 key conclusions are summarized as follows. 1) The simulation results successfully verified the experiment results at a range of TSRs and maximum power coefficient (Cp,max) values as the Savonius wind turbine blade twist angle was varied. 2) The maximum Cp 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 coefficient (Cp) became lower than that at 0 , but the maximum Cp appeared to be similar. 3) When the twist angle was greater than 90 , it was found that the torque coefficients stabilized and remained constant.

This work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 20124010203230, 20114010203080). In addition, this research was supported by Basic Science Research 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). References [1] Renewable Energy Policy Network for the 21st century, Renewable 2013 Global Status Report, 2013. [2] M. Islam, D.S.K. Ting, A. Fartaj, Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines, Renew. Sust. Energ. Rev. 12 (4) (2008) 1087e1109. [3] E. Sandra, Evaluation of different turbine concepts for wind power, Renew.

244


Sust. Energ. Rev. 12 (5) (2008) 1419e1434. [4] S.H. Yoon, H.C. Lim, D.K. Kim, Study of several design parameter on multi blade vertical axis wind turbine, Int. J. Precis. Eng. Man. 14 (5) (2013) 831e837. [5] Y. Chen, Y. Lim, Numerical investigation of vortex dynamics in an H-rotor vertical axis wind turbine, Eng. Appl. Comput. Fluid Mech. (2015) 1e12. [6] H. Beri, Y. Yao, Double multiple stream tube model and numerical analysis of vertical axis wind turbine, Energy Power Eng. 3 (2011) 262e270. [7] Y.T. Lee, H.C. Lim, Numerical study of the aerodynamics performance of a 500W Darrieus-type vertical axis wind turbine, Renew. energy 83 (2015) 407e415. [8] S. Roy, U. Saha, Review on the numerical investigations into the design and development of Savonius wind rotors, Renew. Sustain. Energy Rev. 24 (2013) 73e83. [9] N.K. Sarama, A. Biswas, R.D. Misra, Experimental and computational evaluation of Savonius hydrokinetic turbine for low velocity condition with comparison to Savonius wind turbine at the same input power, Energy Convers. Manag. 83 (2014) 88e98. [10] N. Fujisawa, On the torque mechanism of Savonius rotors, J. Wind. Eng. Ind. Aero. 40 (1992) 277e292. [11] J.V. Akwa, G. Alves da Silva Junior, A.P. Petry, Discussion on the verification of the overlap ratio influence on performance coefficients of a Savonius wind rotor using computational fluid dynamics, Renew. Energy 38 (1) (2012) 141e149. [12] M.A. Kamoji, S.B. Kedare, S.V. Prabhu, Experimental investigations on single stage, two stage and three stage conventional Savonius rotor, Int. J. Energ. Res. 32 (2008) 887e895. [13] M.A. Kamoji, S.B. Kedare, S.V. Prabhu, Performance tests on helical Savonius rotors, Renew. Energy 34 (2009) 521e529. [14] M.H. Mohamed, G. Janiga, G. Pap, D. Thevenin, Optimization of Savonius turbines using an obstacle shielding the returning blade, Renewble Energy 35 (2010) 2618e2626. [15] Z. Zhao, T. Zheng, X. Xu, W. Liu, G. Hu, Research on the Improvement of the Performance of Savonius Rotor Based on Numerical Study, in: SUPERGEN ’09. Int. Conference, 2009, pp. 1e6. [16] U.K. Saha, M.J. Rajkumar, On the performance analysis of Savonius rotor with twisted blades, Renew. Energy 31 (2006) 1776e1788. [17] K.C. Kim, S.K. Kim, S.Y. Yoon, PIV measurements of the flow and turbulent characteristics of a round jet in crossflow, J. Vis. 3 (2000) 157e164. [18] N. Fujisawa, F. Gotoh, Visualization study of the flow in and around a Savonius rotor, Exp. Fluid 12 (1992) 407e412. [19] H.B. Yang, Wind Tunnel Study on the Performance Characteristics of Savonius Wind Turbine [Master thesis], Pusan National University, 2013.

[20] U.K. Saha, S. Thotla, D. Maity, Optimum design configuration of Savonius rotor through wind tunnel experiment, J. Wind. Eng. Ind. Aero. 96 (2008) 1359e1375. [21] A.J. Alexander, Wind tunnel tests on a Savonius rotor, J. Wind. Eng. Ind. Aero. 3 (4) (1978) 343e351. [22] I. Ross, A. Altman, Wind tunnel blockage corrections: review and application to Savonius vertical-axis wind turbines, J. Wind. Eng. Ind. Aero. 99 (2011) 523e538. [23] M. Takao, H. Kuma, T. Maeda, Y. Kamada, M. Oki, A. Minoda, As straight bladed vertical axis wind turbine with a directed guide vane row effect of guide vane geometry on the performance, J. Therm. Sci. 18 (1) (2009) 54e57. [24] J. Yao, J. Wang, W. Yuan, H. Wang, L. Cao, Analysis on the influence of turbulence model changes to aerodynamic performance of vertical axis wind turbine, Procedia Eng. 31 (2012) 274e281. [25] H.W. Coleman, Experimentation and Uncertainty Analysis for Engineers, Wiley, New York, 1989. [26] A. Escue, J. Cui, Comparison of turbulence models in simulating swirling pipe flows, Appl. Math. Model. 34 (10) (2010) 2840e2849. [27] R. Howell, N. Qin, J. Edwards, N. Durrani, Wind tunnel and numerical study of a small vertical axis wind turbine, Renew. Energy 35 (2010) 412e422. [28] A. Gerasimov, Modeling Turbulent Flows with FLUENT, ANSYS, Europe, 2006. [29] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flow, Comput. Method Appl. M. 3 (2) (1974) 269e289. [30] P. Chakraborty, S. Balachadar, R.J. Adrian, Kinematics of local vortex identification criteria, J. Vis. 10 (2) (2007) 137e140. [31] C.R. Hunt, A.A. Wary, P. Moin, Eddies, streams, and convergence zones in turbulent flows, Stud. Turbul. Using Numer. Simul. Databases (1988) 193e208. [32] B.K. Debnath, A. Biswas, R. Gupta, Computational fluid dynamics of a combined three-bucket Savonius and three-bladed Darrieus rotor at various overlap conditions, J Renew. Sustain. Energy 1 (2009) 033110. [33] N. Halsey, Modeling the Twisted Savonius Wind Turbine Geometrically and Simplifying its Construction, Oregon Episcopal School, 2011. [34] B. Deb, R. Gupta, R.D. Misra, Performance Analysis of a Helical Savonius Rotor without Shaft at 45 Twist Angle Using CFD, vol. 7, 2013, pp. 126e133. [35] L. Duffett, J. Perry, B. Stockwood, J. Wiseman, Design and evaluation of twisted Savonius wind turbine, Vert. wind energy Eng. (2009) 1e33. [38] S. Roy, U. Saha, Review on the numerical investigations into the design and development of Savonius wind rotors, Renew. Sustain. Energy Rev. 24 (2013) 73e83. [39] O.B. Yaakob, K.B. Tawi, D.T.S. Sunato, Computer simulation studies on the effect over lap ratio for Savonius type vertical axis marine current turbine, Int. J. Eng. Trans. A Basics 23 (2010) 79e88.