Performance investigation of a new Darrieus Vertical Axis Wind Turbine

Performance investigation of a new Darrieus Vertical Axis Wind Turbine

Journal Pre-proof Performance investigation of a new Darrieus Vertical Axis Wind Turbine S.M.H. Karimian, Abolfazl Abdolahifar PII: S0360-5442(19)322...

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Journal Pre-proof Performance investigation of a new Darrieus Vertical Axis Wind Turbine S.M.H. Karimian, Abolfazl Abdolahifar PII:

S0360-5442(19)32246-7

DOI:

https://doi.org/10.1016/j.energy.2019.116551

Reference:

EGY 116551

To appear in:

Energy

Received Date: 18 June 2019 Revised Date:

21 September 2019

Accepted Date: 13 November 2019

Please cite this article as: Karimian SMH, Abdolahifar A, Performance investigation of a new Darrieus Vertical Axis Wind Turbine, Energy (2019), doi: https://doi.org/10.1016/j.energy.2019.116551. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Performance Investigation of a New Darrieus Vertical Axis Wind Turbine S.M.H. Karimian, Abolfazl Abdolahifar* Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract In present work, a new configuration of Darrieus type Vertical Axis Wind Turbine (VAWT) is introduced, and its aerodynamic performance is examined using three-dimensional numerical simulation by the solution of Reynolds averaged Naiver-Stokes equations. In comparison to each other, straight-blade VAWTs have higher average output torque and are simpler to manufacture while helical-blade VAWTs deliver non-oscillatory and smoother torque. To include advantages of both types of Darrieus VAWTs, a new straight-blade turbine is proposed which in general performs better than helical-blade VAWT. This turbine, called three-part-blade or simply 3-PB VAWT, includes straight blades where each of them is vertically cut into three parts. The objective of this paper is to show that while the proposed turbine is simple to manufacture, its performance is better than that of helical-blade VAWT. Present simulation is validated using experimental data. Having compared performance of the proposed turbine with a helical-blade VAWT, it is shown that 3-PB VAWT produces 6.06% higher average of total torque coefficient at low Tip Speed Ratio (TSR) of 0.44, and 158.19% at high TSR of 1.77. Based on these results, it is strongly recommended to use 3-PB VAWT considering its better aerodynamic performance and low cost of production.

Keywords: Darrieus wind turbine; Helical blade; Straight blade; New design; Numerical simulation.

*

Corresponding author. Address: Dept. of Aerospace Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, P.O.Box: 15875-4413, Iran. Emails: [email protected] (S.M.H. Karimian), [email protected] (Abolfazl Abdolahifar).

1

Nomenclature Latin letters   

  

      Abbreviations CFD HAWT RANS rpm SST TSR URANS VAWT 3-PB Greek letters ε ( * +    

The swept area of turbine = 2 [m2] Average of total power coefficient during one cycle [-] Torque coefficient [-] Average of total torque coefficient during one cycle [-] Turbine height [m] Turbulent kinetic energy [J/kg] Number of data during one cycle for calculation of the deviation [-] Average of total power during one cycle =    [W] Turbine radius [m] Torque [Nm] Average of total torque during one cycle [Nm] Free stream velocity [m/s] Dimensionless wall distance [-] Computational Fluid Dynamics Horizontal Axis Wind Turbine Reynolds-averaged Navier Stokes Revolution per minute Shear-Stress Transport  Tip Speed Ratio=  !"#$ [-] %&

Unsteady Reynolds-averaged Navier Stokes Vertical Axis Wind Turbine Three-part-blade Turbulent dissipation rate [J/kg.s] Azimuth angle [°] Air density [kg/m3] Deviation of the total torque coefficient from its average [-] Specific turbulence dissipation rate [s-1] Volume-weighted average of vorticity magnitude [s-1] Angular velocity of the turbine [rad/s]

Subscripts ,-.

/ 0

Average during a cycle Total power Swept Torque

2

1. Introduction Wind energy is one of the well-known sources of renewable energy that is being used vastly in recent years [1]. There are two types of wind turbines to extract wind energy, horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). HAWTs are normally employed at large scales and are used for heavy-duty commercial purposes [2]. VAWTs are mainly installed near the ground and are categorized as low altitude wind turbines. This makes their installation cost low [3]. Focus of this paper is on VAWTs and HAWTs are not discussed here; for their comparison and advantages of VAWTs over HAWTs interested readers are referred to Refs. [3-10]. Savonius and Darrieus are two general types of VAWTs that perform based on drag and lift forces, respectively. Savonius turbines are well-known for their good self-starting and suitable performance at low Tip Speed Ratios (TSRs). At high TSRs however, they perform less efficient in comparison to Darrieus type wind turbines [5, 11]. Among VAWTs, Darrieus type wind turbines with straight or helical blades are the most common turbines used these days. Straight-blade Darrieus VAWTs are well-known for their high average of output torque and their low cost of blade production. In this case, each blade is located at its designated azimuth angle, i.e., azimuth angles of 0°, 120° and 240° in a three-blade straight turbine. Therefore at these three azimuth angles, it delivers maximum torque. Since this maximum torque is high, straight-blade turbines produce high average output torque. However, they suffer from high cyclic fluctuations of aerodynamic load. Therefore they need sophisticated and expensive electrical generators. Aerodynamic load fluctuations also impose high mechanical vibration on the turbine body,

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which reduces the lifetime of the turbine and produces extra noise [12-14]. In addition, having only three maximum torques in each cycle, straight-blade Darrieus turbines do not perform well at self-starting. In contrast to straight-blade turbines, helical-blade Darrieus VAWTs are well-known for their low fluctuations in output torque along with the least difficulty for self-starting among almost all of Darrieus VAWTs. These advantages came from the configuration of the helical blade in which each blade continuously covers wide range of azimuth angles. However, it should not be forgotten that the turbine produces lower average of output torque, and its cost of blade production is high [13, 15-19]. There are some investigations which have compared aerodynamic performance of straight-blade and helical-blade VAWTs focusing on their output torque/power and their fluctuations. For instance, Castelli et al. [20] have shown that in comparison to straight-blade turbine, power of helical-blade turbine drops significantly at TSRs of 2.6 to 4.1. Also, it can be seen that at TSR of 3.36 and azimuth angle of 92° instantaneous torque coefficient of a single straight-blade is 24.4% higher than that of a helical blade with a twist angle of 120°. As about the fluctuations, according to the results of Tjiu et al. [18], variation of the power coefficient in a cycle for their helicalblade VAWT at TSR of 5 is only 15% of their straight-blade turbine. Other researchers have compared aerodynamic distortion behind VAWTs. For instance, Salazar [21] investigated flow region behind VAWTs, using Unsteady Reynolds averaged Naiver-Stokes (URANS) simulation

with turbulence model of Shear-Stress Transport (SST) −  developed by Menter [22]. It was

shown that at the same condition, a straight-blade VAWT makes less distortion in the flow field

than that of a helical-blade VAWT. Region influenced by the straight-blade VAWT was about

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2.5 times of its rotor diameter, while for the helical-blade VAWT this was about 4.2. This in fact can be named one of the advantages of straight-blade VAWTs. There are many researchers who have worked to resolve drawbacks of straight-blade VAWTs. Here, some of those are mentioned. Hybrid turbines, designed to resolve self-starting problem of straight-blade VAWTs, include a combination of Savonius and Darrieus VAWTs [23, 24]. Although this combination improves self-starting of the turbine, Savonius part of hybrid turbine reduces the total output torque of the turbine at high TSRs. For instance, the torque coefficient of the Savonius part of Wakui et al. [25] hybrid turbine has dropped to negative values at TSRs higher than about 3.5. In their hybrid turbine Savonius part is divided into two parts (upper and lower) and are installed with azimuthangle offset of 90°. Also, investigations performed in 2019 by Behrouzi et al. [26] and MarinicKragic et al. [27] show that torque coefficient of Savonius turbines decrease to zero at TSRs about 0.7 and 1.75. In addition, papers can be found in which performance of the straight-blade VAWTs at operational mode is being improved. In 2012, Mohamed [28] numerically simulated a straightblade turbine with 20 different airfoils to maximize its output torque coefficient. In 2016, Zamani et al. [29] numerically simulated a straight-blade VAWT, with their newly designed J-shaped

blades using the turbulence model of SST − . These blades were designed to take advantage

of drag and lift forces on blades for production of torque. Although turbine performance was

improved at self-starting condition and low TSRs, due to low lift coefficient of J-shaped blades at high TSRs, total torque of this turbine was reduced for TSRs of higher than 2.25. In 2017, Wang and Zhaung [2] proposed several sinusoidal wave-serration blade profiles which in best case caused maximum enhancement in power coefficient of about 18.7% at TSR of 2. Li et al. 5

[30], in 2018, proposed a truncated-cone-shaped wind gathering device and installed it up and down of a straight-blade VAWT in order to collect more inflow and increase inflow speed. Finally, they improved self-starting performance of their turbine for about 24.2% with respect to that of the straight-blade turbine without gathering device. Note that due to installation of the gathering device, radius of the turbine and its height are generally increased. Other works also can be found in which the effect of blade pitch angle variation has been studied. Examples are the works of Lee et al. [16] and Rezaeiha et al. [31] and Lei et al. [32]. After reviewing the literature, it became clear that a Darrieus VAWT should be designed which benefits from the advantages of both straight-blade and helical-blade VAWTs. Based on this idea, authors of this paper decided to propose a Darrieus VAWT configuration which will have high average-torque, low amplitude of torque fluctuations, and low cost of turbine blade production. This turbine is formed from a straight-blade VAWT with three blades where each blade is vertically cut into three similar parts. Upper and lower parts then are rotated 30° forward and backward from their azimuth angles with respect to the middle part, respectively. This means that the azimuth angle between tips of first and third parts would be 60°. This VAWT, called three-part-blade or simply 3-PB VAWT, is in fact a straight-blade turbine which is re-designed to become conceptually similar to helical-blade VAWT. This turbine contains advantages of helical-blade VAWTs, including little fluctuation due to aerodynamic load, and those of straightblade VAWTs including high average-torque and low cost of turbine blade production. Note that according to the works of Battisti et al. [15], Li et al. [33] and Castelli et al. [34], three blades are selected to make a balance between the higher power coefficient, and lower fluctuations and installation costs.

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Numerical simulation is used to analyze performance of the proposed 3-PB VAWT. Results are compared with those of a helical-blade VAWT with the same geometrical specifications. In section 2, numerical modeling is explained, and in section 3, specifications of turbine geometry are introduced. Next, computational domain and specifications of the grid are explained in section 4. Solution independence study with respect to the size of the computational domain, grid size in static mode, and time and grid size in dynamic mode is conducted in section 5. In section 6, present simulation is validated with experimental data of Elkhoury et al. [35] on a straightblade Darrieus VAWT. Finally, performance of the proposed 3-PB and helical-blade VAWTs at the self-starting condition and operational mode are compared with each other in terms of total torque coefficient and deviation of total torque coefficient per cycle. 2. Numerical modeling and methodology Based on the literature, there are enough studies which have applied turbulence model of SST

− , in their 2D and 3D flow simulations around VAWTs to obtain acceptable results. These

include Zamani et al. [29], Salazar [21], Cheng et al. [36], and Rezaeiha et al. [31]. In addition, McLaren et al. [37] numerically studied flow field around a straight-blade VAWT at Reynolds number of 3.6E+5 using different turbulence models. They showed that among − , SST

−  and − 3 turbulence models, results obtained using SST −  model were in quite good agreement with experimental data of Sheldahl et al. [38]. Therefore turbulence model of SST −  will be used in present work.

Transient three-dimensional incompressible turbulent flows around proposed 3-PB and helicalblade wind turbines are simulated by the solution of RANS equations using turbulence model of SST − . Solution domain is discretized using finite volume method and sliding mesh

technique of ANSYS Fluent Software is applied at the interface of two moving grids. For 7

pressure and velocity coupling, a pressure-based double-precision solver with the implicit formulation is employed using SIMPLEC algorithm. Second-order discretization scheme is applied for pressure, and the second-order upwind scheme is used for momentum variables. Solution is carried out on an 8-processor, 4.00 GHz clock frequency computer. Each simulation required a total CPU time of about ten days. Residual criteria for solution convergence per each physical time step of the simulation is selected to be 1E-4 for continuity equation and and 

terms. For three velocity components, this criterion is chosen to be 1E-6. In average, 25 iterations per time step was necessary. Free stream Reynolds number calculated based on the chord length of blade is estimated to be about 1.5E+5. On turbine blades, however, it increases up to 4E+5. 3. Geometry In order to make a fair comparison, general specifications of both 3-PB and helical-blade VAWTs are set similarly and are given in table 1. Different views of two turbines are shown in figures 1 and 2. Turbines rotate in the positive direction of Z-axis. Azimuth angle is defined in the X-Y plane and is set equal to zero on the Y-axis. At each cycle, azimuth angle increases from 0° to 360° in counterclockwise direction. Note that azimuth angle of the whole turbine is determined by the azimuth angle of the middle of its first blade. Flow direction is along X-axis from azimuth angle of 90o towards that of 270o. The radius of each turbine is measured from the turbine center to the middle of its blade. Middle of each airfoil is defined as its surface center, which locates at 56.67% of chord length. As seen in figure 1, middle of the first blade of the helical turbine is at the azimuth angle of 0° and middle of the second and third blades are at the azimuth angles of 120° and 240°, 8

respectively. As about each helical blade, the first blade for instance begins from the azimuth angle of -30o and twists up to the height of H= 1.15 m where the azimuth angle is +30°. Again, middles of airfoil sections located at bottom and top of first blade, have azimuth angles of -30° and +30°, respectively. As shown in figure 2, in the 3-PB VAWT each blade is replaced by three straight blades (parts)

with same heights, i.e. each part is equal to 53. Upper and lower parts then are rotated 30°

forward and backward from their azimuth angles with respect to the middle part, respectively. Therefore, for instance middles of the three parts of first blade of 3-PB VAWT from bottom to top have azimuth angles of -30°, 0°, and +30°, respectively. Their middles also have been located

at 56, 356 and 556 in Z coordinates, respectively. For the sake of clarity note that the middle of second parts of first, second, and third blades will remain at azimuth angles of 0°,

120°, and 240° respectively. Note that starting and ending positions of the helical blade are the same as those of the 3-PB blade. This means that the lowest section of the helical blade and the lowest section of the first part of the 3-PB blade are exactly located at the same position. Accordingly, the highest section of the helical blade and the highest section of the third part of the 3-PB blade are exactly located at the same position.

Table 1. Helical-blade and 3-PB VAWTs specifications. No. 1 2 3 4 5 6

Denomination Turbine Radius R [m] Turbine height H [m] Blade chord length [m] Twist angle [°] Number of blades [-] Airfoil section

9

Value 0.99 1.15 0.3 60 3 NACA 0021

(a)

(b)

(c) Figure 1. Different views of helical-blade VAWT: (a) front view, (b) isometric view, and (c) top view.

10

(a)

(b)

(c) Figure 2. Different views of 3-PB VAWT: (a) front view, (b) isometric view, and (c) top view.

4. Computational domain and grid generation As shown in figures 3(a) and (b), solution domain is a rectangular cube with dimensions of 32R, 12R and 12R in X, Y, and Z directions, respectively, including stationary and rotating zones. Uniform air at sea level condition of the standard atmosphere with constant speed of 7 m/s along 11

the X-axis flows over the turbine. As seen in figures 3(c) and (d), turbine is located in a rotating cylinder with radius of 4 m (4.04R) and height of 7.15 m (7.22R), whose center is at the center of the cube in Y-Z plane and 8.0R from the inlet boundary. Outer surfaces of the solution domain located in the Y-Z plane are inflow and outflow boundaries. Constant free stream velocity is applied at the inflow boundary, and static pressure at sea level condition of the standard atmosphere is specified at the outflow boundary. Other outer surfaces of the solution domain located in the X-Y and X-Z planes are set as symmetry, i.e. shear stress and velocity gradient on these faces are considered to be zero [39]. No-slip condition is applied on the walls of the blades.

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(a)

(b)

(c)

(d)

Figure 3. Different views and geometrical parameters of the computational domain: (a) top view, (b) isometric view, (c) top view of the rotating zone, (d) isometric view of the rotating zone.

For the sake of clarity, top views of the generated grid at the plane of Z= 0 are presented in figure 4. The whole domain and the rotating zone are shown in figures 4(a) and (b), respectively. Unstructured grid is generated within the domain, except close to the turbine blades and over the 13

rotating zone where structured grid (prism-shaped) is generated; see figures 4(c) and (d). Note that with the structured grid at the interface of the rotating and stationary zones accurate calculation of mean flux across the two interface zones is achievable.

(a)

(c) (b)

(d)

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Figure 4. Top views of the generated grid at plane of Z= 0: (a) whole domain, (b) rotating zone, (c) structured grid at the interface of the stationary and rotating zones, (d) structured grid close to the turbine blade. 5. Solution independence study

Solution independence study is carried out regarding with respect to the size of computational domain, number of grids in static and dynamic modes, and time step. 5.1. Size of the computational domain

In order to find the proper domain in which solution becomes independent of its size, total torque produced by the aerodynamic load is chosen as the main criterion. Consider the helical-blade VAWT in its static mode where its first blade is at the azimuth angle of 0°. Flow field with the

boundary conditions defined previously is solved within four different solution domains with sizes defined in table 2. First solution domain is the smallest one. Other domains are enlarged in X, Y, and Z directions with respect to the 1st domain as indicated in the table. Error of the total

torque decreases with domain enlargement. With the 3rd and 4th domains, the error has been decreased to almost the same value of 0.18%, which provides appropriate accuracy in this study to reach solution independent of domain size. Grid generated in these domains will be discussed in section 5.3. Also note that dimensions of the domain noted in section 4 is in fact the 3rd domain introduced here. Note that definition of error used in this paper for the general parameter of Q for instance, is as 8|: − :; |⁄|:|= × 100 where :; is the previous value of Q.

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Table 2. Results of domain independence study. No. 1 2

3

4

5

Parameters Dimensions

1st domain 24R×9R×9R

2nd domain 28R×10.5R×10.5R

3rd domain* 32R×12R×12R

4th domain 40R×15R×15R

Enlargement in each direction with respect to the 1st domain (%)

-

16.7

33.33

66.67

Domain enlargement with respect to the 1st domain (%)

-

60

140

360

Turbine center distance from the inlet boundary

6R

7R

8R

10R

Total torque [Nm]

2.7909

2.7781

2.773

2.7678

-

0.46

0.18

0.18

Total torque error with respect to that of the previous domain (%) * Domain finally chosen in this study. 6

5.2. A general guide for the static and dynamic grid independence studies

Grid refinement is required to get accurate results and also results independent of the grid size. Therefore grid refinement in different regions of the solution domain has been applied. It was observed that although grid refinement in the whole domain improves results including total torque, special attention should be paid to the quality and fineness of grid around the blades to get accurate results. Therefore the maximum grid size of the first layer on the blade and its height were refined in two sequential steps. Note that maximum grid size means maximum length of the prism edges along the blade surface. At the first step, the height of first layer grids is kept constant while their maximum size is decreased in order to reach a total torque independent of the grid size. In the second step, for the right maximum grid size height of the first layer on the blades is decreased. Best grid configuration is obtained based on the maximum and average values of Y+ [40]. This strategy is applied in both static and dynamic modes. 16

5.3. Static grid independence study

In the static mode, flow field around the helical-blade VAWT with the solution domain and boundary conditions defined previously is studied while the first blade of turbine is located at the

azimuth angle of 0°. As noted above, maximum size of the first layer grids is determined from the solution of flow field with different grids defined in part (a) of table 3, including 2750000, 3950000, 5550000, and 7350000 control volumes. As seen, with 5550000 control volumes the error decreases to an acceptable level. Therefore maximum size of the first layer of grid, i.e 0.0065 m, will be used here. In the second step, to determine the right value of the first-layer height, grids with first-layer heights of 1E-4 m, 6E-5 m, and 4E-5 m are applied which results in grids with 4950000, 5550000, and 5800000 control volumes. Quality of these grids and their average Y+ are defined in part (b) of table 3. As seen, with 5550000 control volumes, the error decreases to less than 1%. Therefore specifications of the independent grid are 5550000 control volumes with 0.0065 m for the maximum size of the first layer grid and 6E-5 m for its height and average Y+ of 0.75.

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Table 3. Results of static grid independence study. a) Grid size refinement on the blades (first step) Parameters Number of control volumes 2750000 3950000 5550000* ** 1 Max. size of the first layer with the constant height of 6E-5 m [m] 0.01 0.008 0.0065 2 Total torque [Nm] 3.0567 2.873 2.773 3 Total torque error*** (%) 6.4 3.61 b) Grid height refinement on the blades (second step) No. Parameters Number of control volumes 4950000 5550000* 5800000 1 Height of the first layer with the constant max. 1E-4 6E-5 4E-5 size** of 0.0065 m [m] 2 Total torque [Nm] 2.7486 2.773 2.7834 3 Total torque error*** (%) 0.9 0.3 Max. Y+ 6.98 4.43 2.91 4 5 Average Y+ 1.24 0.75 0.5 * Grid finally chosen in static mode. ** Maximum length of the prism edges along the blade surface. *** With respect to that of the previous one. No.

7350000 0.0055 2.687 3.2

5.4. Time independence study

Before grid independence study in dynamic mode, it is necessary to choose the right time step for the chosen rotational speed. For this purpose, it is only required to specify a proper time step for one rotational speed. Then for other rotational speeds, each time step can be calculated accordingly. Using the final grid concluded for static mode, the helical-blade VAWT is analyzed at 60 rpm with four different time steps of 0.01, 0.005, 0.001, and 0.0005 sec. Since during transient solution quantities change with time, variation of the total torque during a cycle should be the main criterion. In order to compare the variation of total torque in a cycle for different cases, four errors are defined. These are errors in amplitude, azimuth angle between peaks, azimuth angle phase difference, and total-torque peak difference, which are defined in figure 5. According to the results in table 4, these errors decrease to less than 2% with the time step of 0.0005 sec. With this small error accuracy of results with the time step of 0.0005 sec will not change noticeably with respect to that of the time step of 0.001 sec. Therefore solution with the time step of 0.001 sec. will be independent of the time step in rotational speed of 60 rpm. 18

Total-torque peak difference Amplitude

Total torque

Azimuth angle between peaks

Azimuth angle phase difference

Azimuth angle

Figure 5. Schematic for the definition of four errors used to analyze transient solution.

Table 4. Results of time independence study at 60 rpm. No.

Parameters

1 Amplitude [Nm] 2 Error in amplitude** (%) 3 Azimuth angle between peaks [°] Error in azimuth angle between peaks** (%) 4 5 The azimuth angle of last peak [°] 6 Error in azimuth angle phase difference** (%) 7 Total torque of last peak [Nm] 8 Error in total-torque peak difference** (%) * Time step finally chosen for the rotational speed of 60 rpm. ** With respect to that of the previous one.

0.01 4.2062 119.26 641.24 4.6567 -

Time step [sec.] 0.005 0.001* 3.7978 3.4947 10.75 8.67 120.99 120.72 1.43 0.22 639.49 636.97 0.27 0.39 4.21 4.05 10.61 3.95

0.0005 3.4995 0.14 120.76 0 636.97 0 4.1304 1.94

Based on the time step of 0.001 sec. for the rotational speed of 60 rpm, time steps at other rotational speeds are calculated and listed in table 5.

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Table 5. Selected time steps for different rotational speeds. No. 1 2 3 4 5

rpm 30 60 75 90 120

Time step [sec.] 0.002 0.001 0.0008 0.000667 0.0005

5.5. Dynamic grid independence study

For grid study in dynamic mode, helical-blade VAWT is studied at rotational speed of 90 rpm with the time step of 0.000667 sec. Similar to the process followed for static mode, the two-step analysis performed in section 5.3 is applied here for the same grids used in that section. Again four errors defined in figure 5 are the criteria to determine the appropriate grid. According to the results shown in part (a) of table 6, all of the four errors with respect to results obtained on the grid with 5550000 control volumes become less than 2% on the grid with 7350000 control volumes. With this small error accuracy of results on grid with 7350000 control volumes will not change noticeably with respect to that of grid with 5550000 control volumes. Therefore solution on grid with 5550000 control volumes will be independent of maximum grid size in dynamic mode. Based on the same argument grid with 5550000 control volumes is selected in part (b) of table 6. Therefore specifications of the selected grid are the same grid of static mode with average Y+ of 1.22.

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Table 6. Results of dynamic grid independence study at 90 rpm. a) Grid size refinement on the blades (first step) Number of control volumes 2750000 3950000 5550000* 7350000 ** 1 Max. size of the first layer with the constant height of 6E-5 m [m] 0.01 0.008 0.0065 0.0055 2 Amplitude [Nm] 5.1771 5.5198 5.9121 6.023 3 Error in amplitude*** (%) 6.21 6.63 1.98 4 119.815 120.435 120.39 120.3 Azimuth angle between peaks [°] 5 Error in azimuth angle between peaks*** (%) 0.51 0 0 6 650.52 652.07 653.56 654.35 The azimuth angle of last peak [°] 7 Error in azimuth angle phase difference*** (%) 0.24 0.22 0.12 8 Total torque of last peak [Nm] 4.8674 5.0958 5.2721 5.3548 9 Error in total-torque peak difference*** (%) 4.48 3.34 1.54 b) Grid height refinement on the blades (second step) No. Parameters Number of control volumes 4950000 5550000* 5800000 1 Height of the first layer with the constant max. size** of 0.0065 m [m] 1E-4 6E-5 4E-5 2 Amplitude [Nm] 5.364 5.9121 5.9179 3 Error in amplitude*** (%) 9.27 0 120.18 120.39 120.28 4 Azimuth angle between peaks [°] 5 Error in azimuth angle between peaks*** (%) 0.17 0 651.27 653.56 653.54 6 The azimuth angle of last peak [°] 7 Error in azimuth angle phase difference*** (%) 0.35 0 8 Total torque of last peak [Nm] 4.6035 5.2721 5.3569 9 Error in total-torque peak difference*** (%) 12.68 1.58 Max. Y+ 6.94 4.72 3.48 10 Average Y+ 2.01 1.22 0.81 11 * Grid finally chosen for dynamic mode. ** Maximum length of the prism edges along the blade surface. *** With respect to that of the previous one. No.

Parameters

6. Validation of CFD modeling

In order to validate numerical simulation being used in present work, experimental data of helical or straight-blade VAWT with airfoil section, number of blades, and general dimensions similar to the present turbine should be used for different TSRs. Unfortunately, among available experimental data proper and complete data for the helical-blade VAWT could not be found. Instead, the work of Elkhoury et al. [35] was found in which a straight-blade VAWT defined in table 7 was studied both numerically and experimentally. In this section, their experimental data 21

at constant free-stream velocity of 8 m/s is used to validate the present numerical simulation. Elkhoury’s case is simulated on the grid concluded in section 5.5 and with the time step determined in section 5.4. Average of total power coefficient during one cycle defined by relation (1) [41] has been compared with those of experimental data in Ref. [35] for TSRs from 0.25 to 1.5.  =



15 * C  2  

(1)

Table 7. Straight-blade turbine specifications in Elkhoury et al. study [35]. No. 1 2 3 4 5

Denomination Turbine radius [m] Turbine height [m] Blade chord length [m] Number of blades [-] Airfoil section

Value 0.4 0.8 0.2 3 NACA 0021

As shown in figure 6, at TSRs between 0.25 to 0.4 and 1 to 1.2 errors of the present results with respect to the experimental data are about zero. At TSRs between 0.4 to 1 and 1.2 to 1.5, average of these errors is about 12%. Having known that comparison is made with the experimental data, one can conclude a quite good agreement between the present results and the experimental data exists.

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0.3 Present 3D Numerical Simulation Exp., Elkhoury et al [35] 0.25

CP ave

0.2

0.15

0.1

0.05

0 0

0.25

0.5

0.75 1 TSR

1.25

1.5

1.75

Figure 6. Comparison between averages of the total power coefficient of experimental data [35] and present 3D results. 7. Results and discussion

Performances of both 3-PB and helical-blade VAWTs introduced in section 3 are analyzed with boundary conditions defined in section 4, and computational domain and time steps concluded in section 5. For instance, specifications of the concluded grid are 5550000 control volumes with 0.0065 m for the maximum size of the first layer grid and 6E-5 m for its height. At constant wind speed of 7 m/s, numerical results of 3-PB turbine at self-starting and operational mode for rotational speeds of 30, 60, 75, 90 and 120 rpm (TSRs up to 1.8) are compared with those of helical-blade turbine in figures 7 and 8. Note that TSR values in figure 8 are calculated based on turbine rotational speed and constant wind speed of 7 m/s. Since actual rotational speed of wind turbine at specified wind speed is not precisely known at this stage, it is required to simulate different possible rotational speeds of the turbine for each wind speed. In present work, main results are obtained at constant wind speeds 7 m/s; then in the section of 7.7 23

other simulations are conducted at wind speed of 5 m/s for the two TSRs of 1.33 and 1.77, as well. Coefficients compared with each other in these figures include, (a) torque coefficient of a single blade, and (b) torque coefficient of the whole turbine, called total torque coefficient, which are defined by relation (2) [41]:  =



15 * D   2  

(2)

in which  is either torque of a single blade or torque of the whole turbine. Both coefficients are presented versus azimuth angle in one cycle. In order to compare performance of both turbines quantitatively, two extra parameters called average of total torque coefficient and deviation of total torque coefficient are introduced. Average of the total torque coefficient,   , is the average of  taken over one cycle. Deviation of the total torque

coefficient from its average is defined by relation (3) [42] as a statistical dimensionless parameter to analyze fluctuations of the total torque coefficient. 1 + = E (G( # −   )D ) 

(3)

IJ

Results of the average and deviation of the total torque coefficient are shown in table 8. Analysis of those results is given in the following sections. Since rotational speed during each simulation is constant, the trend of both power and torque coefficients diagrams for each rotational speed will be the same. Therefore one of them is enough to represent the performance of the turbines.

24

7.1. Self-start mode

For the analysis of the self-starting condition, steady state solutions of both turbines are studied at 12 stages where azimuth angles of first blade are at 0° to 110° (with 10° increments) at wind speed of 7 m/s. Note that this covers all situations that may occur at the self-starting condition. As shown in figure 7(a), in almost all of the stages a single blade of 3-PB VAWT which includes three parts produces a little bit less torque coefficient than that of helical-blade VAWT. This why helical-blade VAWT generates higher total torque coefficient than that of 3-PB VAWT, shown in figure 7(b). Average of total torque coefficients of each turbine calculated using data of these 12 stages for helical-blade and 3-PB VAWTs are equal to 0.0344 and 0.0249, respectively. This shows that the average of the total torque coefficient of helical-blade VAWT is 27.62% higher than that of the 3-PB turbine. Although 3-PB VAWT has not gained much in self-starting condition, it will be seen that present turbine delivers a higher average of total torque coefficient with less deviation in its operational mode.

25

Single Blade

Whole Turbine 3-PB Helical

3-PB Helical

0

0 30

30

330

60

60

300

0.04 0.02 90

0

-0.02

0.05 90

270

Ct(ν)

120

300

0.025

0

270

Ct(ν)

120

240 150

330

240 150

210

210

180

180

ν°

ν°

(a)

(b)

Figure 7. Torque coefficients of 3-PB and helical-blade VAWTs for different azimuth angles at the self-starting condition: (a) single blade, (b) whole turbine.

7.2. Operational mode

In this section, dynamic behaviors of 3-PB and helical-blade VAWTs in operational mode for rotational speeds of 30 rpm to 120 rpm and wind speed of 7 m/s are analyzed.

Torque

coefficient of a single blade and total torque coefficient of whole turbines are shown in parts (a) and (b) of figure 8. In addition, table 8 presents average and deviation of total torque coefficients. As seen in parts (a-1) and (b-1) of figure 8 results of both turbines are close to each other at the rotational speed of 30 rpm. The exciting fact is that both average and deviation of total torque coefficients are improved for 3-PB VAWT.

26

As seen in parts (a-2) and (b-2) of figure 8, at rotational speed of 60 rpm torque coefficient of a single blade of 3-PB VAWT is higher than that of helical-blade VAWT between the azimuth

angles of 35° to 130°. The same conclusion can be made about the total torque coefficient of the turbines. It can be seen that the pattern of total torque coefficient of 3-PB turbine is advanced a little bit with respect to that of helical-blade VAWT. This happens at higher rotational speeds as well. Again quite interestingly, according to table 8, 3-PB VAWT produces 19.05% higher average of the total torque coefficient and 13.83% less deviation in comparison to the helicalblade VAWT. As seen in parts (a-3, a-4, a-5) and (b-3, b-4, b-5) of figure 8, at rotational speeds of 75, 90 and 120 rpm torque coefficient of a single blade of 3-PB VAWT is either higher than or with a small difference equal to that of the helical blade. Therefore, 3-PB VAWT performs much better than helical blade in terms of total torque coefficient especially at higher TSRs, which is an excellent achievement. The superiority of 3-PB VAWT is demonstrated quantitatively in table 8 as well. As seen, averages of the total torque coefficient of 3-PB VAWT in rotational speeds of 75, 90 and 120 rpm are 60.96%, 87.6%, and 158.19% higher than that of helical-blade VAWT, respectively. Similarly, deviations of the total torque coefficient of 3-PB VAWT in these rotational speeds are 26.02%, 36.49%, and 59.48% less than that of helical-blade VAWT, respectively. It is believed that having considered ease of blade manufacturing for a 3-PB VAWT, such excellent performance demonstrates the superiority of this turbine and its novelty. 30 rpm (TSR= 0.44)

27

Single Blade 0

Whole Turbine

3-PB Helical

30

0 30

330

60

0.05 90

-0.03

0.06 90

270

Ct(ν)

120

300

0.04

0.02

0

270

Ct(ν)

120

240 150

330

60

300

0.01

3-PB Helical

240 150

210

210 180

180

ν°

ν°

(a-1)

(b-1)

60 rpm (TSR= 0.89) Single Blade

Whole Turbine 3-PB Helical

3-PB Helical

0

0 30 60

0.1 90

30

330 60

300

0.03

-0.04

0.07 90

270

Ct(ν)

120

300

0.035

0

270

Ct(ν)

120

240 150

330

240 150

210

210

180

180

(a-2)

(b-2)

ν°

ν°

75 rpm (TSR= 1.11)

28

Single Blade

Whole Turbine 3-PB Helical

3-PB Helical 0

0 30 60

0.12 90

30

330 60

300

0.035

-0.05

0.09 90

270

Ct(ν)

120

300

0.035

-0.02

270

Ct(ν)

120

240 150

330

240 150

210

210 180

180

ν°

ν°

(a-3)

(b-3)

90 rpm (TSR= 1.33) Single Blade

Whole Turbine

3-PB Helical

3-PB Helical

0 30 60

0.13 90

0

330

30 300

0.04

-0.05

60

0.11 90

270

Ct(ν)

120

240 150

330 300

0.035

-0.04

270

Ct(ν)

120

240 150

210

210 180

180

ν°

ν°

(a-4)

(b-4)

120 rpm (TSR= 1.77)

29

Single Blade

Whole Turbine

3-PB Helical

0

0 30

0.14 90

30

330

60

-0.06

0.12 90

270

Ct(ν)

120

300

0.05

-0.02

270

Ct(ν)

120

240 150

330

60

300

0.04

3-PB Helical

210

240 150

180

210 180

ν°

ν°

(a-5)

(b-5)

Figure 8. Torque coefficients of 3-PB and helical-blade VAWTs at 30 rpm to 120 rpm: (a) single blade, (b) whole turbine.

Table 8. Results of the total torque coefficient, including its average and deviation at 30 rpm to 120 rpm. No.

Parameters

TSR

rpm

Helical-blade VAWT

3-PB VAWT

Percent of change*

0.0297 0.0336 0.0333 0.0363 0.033 0.0129 0.0188 0.0246 0.0285 0.0306

0.0315 0.04 0.0536 0.0681 0.0852 0.01 0.0162 0.0182 0.0181 0.0124

6.06 19.05 60.96 87.6 158.19 -22.48 -13.83 -26.02 -36.49 -59.48

1 0.44 30 2 0.89 60 3 1.11 75   4 1.33 90 5 1.77 120 1 0.44 30 2 0.89 60 3 1.11 75 + 4 1.33 90 5 1.77 120 * With respect to the helical-blade VAWT.

30

7.3. Overall performance

All together average and deviation of the total torque coefficient for rotational speeds of 30 rpm to 120 rpm are plotted versus TSR in figure 9 at wind speed of 7 m/s. As seen, in contrast to the helical-blade VAWT, average of total torque coefficient of 3-PB VAWT significantly improves with TSR. This conclusion is in consistence with the results of Alaimo et al. [19] in which they showed that average of the total torque coefficient of straight-blade VAWT gets higher than that of helical-blade VAWT after TSR of about 0.9. In terms of the deviation of total torque coefficient, it can be seen that 3-PB VAWT performs substantially better as well; its deviation is much less than that of helical-blade VAWT in all range of TSRs. Obviously high output-torque of the 3-PB turbine is due to its straight-blade parts, and its smooth operation is due to the azimuth angle offset between those straight-blade parts. Therefore claims made in section 1 including lower torque fluctuation and higher average torque while using blades produced cheaper are proved.

0.12

0.05 3-PB Helical

3-PB Helical 0.04

0.08

σ

Ct ave

0.03

0.02 0.04 0.01

0

0 0.3

0.7

1.1 TSR

1.5

1.9

0.3

(a)

0.7

1.1 TSR

(b) 31

1.5

1.9

Figure 9. Overall performance comparison between 3-PB and helical-blade VAWTs: (a) average of the total torque coefficient, (b) deviation of the total torque coefficient. 7.4. Energy production

As about energy production, which is the goal of all wind turbines, here an average of the total power for both 3-PB and helical-blade turbines are computed and compared with each other at wind speed of 7 m/s. Values of energy production, defined by relation (4), are calculated and listed in table 9 for both turbines having worked for 3 hours per day during a week for different TSRs. K .LMN LOPQR0SO = (  )(TUL,0SO ,V ℎOQL/)

(4)

As seen 3-PB turbine produces between 6 and 150 percentages more energy with respect to that of the helical-blade turbine, which shows the superiority of the present turbine in operational mode.

Table 9. Summary of energy production for both turbines in operational mode. No.

TSR

rpm

Turbine type

 

 [Nm]

 [W]

Energy production during a week* [Wh]

1 0.44 30 3-PB 0.0315 2.13 6.69 140.49 2 Helical 0.0297 2.01 6.31 132.51 3 0.89 60 3-PB 0.04 2.71 17.03 357.63 4 Helical 0.0336 2.27 14.26 299.46 5 1.11 75 3-PB 0.0536 3.63 28.51 598.71 6 Helical 0.0333 2.25 17.67 371.07 7 1.33 90 3-PB 0.0681 4.61 43.45 912.45 8 Helical 0.0363 2.46 23.18 486.78 9 1.77 120 3-PB 0.0852 5.76 72.38 1519.98 10 Helical 0.033 2.23 28.02 588.42 * As a sample, three operational hours per day for each rotational speed is considered. ** With respect to helical-blade VAWT.

32

Percent of increase** 6.06 19.05 60.96 87.6 158.19

7.5. Torque coefficient analysis of each part of a single blade

To have more insight into physics of the flow around the 3-PB turbine blade, torque coefficients of three parts of its single blade are compared with each other at wind speed of 7 m/s and rotational speed of 120 rpm in figure 10. All results reported in this section are based on the azimuth angle of the middle part of the 3-PB turbine blade. As seen in figure 10 torque coefficients of all three parts are almost the same, only with an azimuth angle offset equal to the offset between these 3 parts of the blade, i.e. 30o each. This means that appropriate space left between three parts of each blade has caused the middle part act very similar to its upper and lower parts. In addition, the azimuth angle offset makes the torque coefficient of the 3-PB blade to be much smoother in comparison with the helical blade.

Single Blade Helical 3-PB Part 1, 3-PB 0 30

Part 2, 3-PB Part 3, 3-PB 330

60

300

0.14 90

-0.06

270

Ct(ν)

120

240 150

210 180

ν°

Figure 10. Torque coefficients at wind speed of 7 m/s and rotational speed of 120 rpm: for each part of a single blade of the 3-PB turbine, and for whole single blades of 3-PB and helical-blade VAWTs 33

7.6. Analysis of vortices According to the work of Salazar [21], a helical-blade VAWT makes more distortion in the flow field than that of straight-blade VAWT with the same geometry. It is known that in comparison to a helical blade, each blade of 3-PB has four more blade tips which lead to extra tip vortex generation. Therefore for the sake of clarity, the volume of vortices and their effect are analyzed for the present turbine in order to provide valuable insight into the flow structure. A qualitative view of vorticity generation at wind speed of 7 m/s and rotational speed of 120 rpm is demonstrated in figure 11 by vorticity magnitude Iso-surface of 65s-1 at the azimuth angle of 25°. One can see that the volume of vortices generated by 3-PB VAWT is a bit more than those of helical-blade VAWT. Although it should be noted that even with this extra vorticity generation, performance of 3-PB turbine is better than that of helical-blade turbine as concluded in section 7.3.

(a-1)

(b-1) 34

(a-2)

(b-2)

(a-3)

(b-3) -1

Figure 11. Different views of vorticity magnitude Iso surface of 65s at wind speed of 7 m/s, rotational speed of 120 rpm, and azimuth angle of 25°: (a) 3-PB, and (b) helical blade turbines.

A quantitative analysis can be made by comparison between vorticity magnitudes generated by each blade of 3-PB and helical-blade VAWTs during one cycle at this rotational speed. For this purpose, the volume-weighted average of vorticity magnitude is calculated in a volume including one blade, as shown in figure 12. The volume starts from 7° azimuth angle after the previous blade’s leading edge to 7° azimuth angle after the leading edge of the blade under consideration.

35

Radius of this volume is 1.4 m (1.41R), and its height includes the blade plus one chord from each end. As it can be seen in figure 13, 3-PB blade generates more vortices than that of the helical blade. In table of this figure, averages of the volume-weighted average of vorticity magnitude during a cycle are compared with each other. The exciting result is that although with respect to the helical-blade VAWT, a single blade of proposed 3-PB VAWT generates 16.1% more vortices during a cycle, this fact has not affected aerodynamic performance of 3-PB VAWT including higher total torque coefficient and less deviation in all of TSR values in operational mode.

(a)

(b)

Figure 12. Definition of the volume in which the volume-weighted average of vorticity magnitude is calculated for both turbine blades: (a) 3-PB, (b) helical blade.

36

Single Blade 3-PB Helical 0 30

330

60

No. 300

2 25 90

12.5

0

270

ω ave(ν)

120

Average of  [s ] Parameters

1

-1

Percent of increase with respect to the helical blade

Helical blade

3-PB

13.48

15.66

16.1

240 150

210 180

ν°

Figure 13. Volume-weighted average of vorticity magnitude produced by each blade of 3-PB and helical-blade VAWTs at 120 rpm and wind speed of 7 m/s.

7.7. Dynamic performance of the 3-PB VAWT at wind speed of 5 m/s In order to evaluate performance of the proposed turbine more precisely, its simulation for wind speed of 5 m/s at TSRs of 1.33 and 1.77 are carried out as well. According to the wind speed data in Iran, averages of annual wind speed in different cities vary approximately from 3 m/s to 10 m/s at the height of 10 m from the ground. For instance, in cities of Khaf, Binalood, Nehbandan, and Semnan wind speeds are 8.984 m/s, 6.511 m/s, 5.05 m/s and 2.73 m/s, respectively [43-46]. Therefore wind speeds of 5 m/s and 7 m/s are selected to be in the range of real speeds in the region. Results obtained at wind speed of 5 m/s are shown in parts (a) and (b) of figure 14. Similar to the results obtained at wind speed of 7 m/s (figure 8) it is clear that the proposed 3-PB wind turbine has performed better. Results of the total torque coefficients of the 3-PB turbine for both wind

37

speeds are compared with each other in table 10. As seen, these results show that at wind speed of 5 m/s performance of the 3-PB turbine is similar or even better than that obtained at wind speed of 7 m/s for same TSRs. Therefore it is believed that at the examined TSRs (up to 1.8), conclusions made in this paper are valid for a range of practical wind speeds.

TSR= 1.33 (64.17 rpm) Single Blade 0

Whole Turbine

3-PB Helical

30

0

330

60

0.13 90

3-PB Helical 30 300

0.04

-0.05

60

0.11 90

270

Ct(ν)

120

300

0.03

-0.05

270

Ct(ν)

120

240 150

330

240 150

210

210 180

180

ν°

ν°

(a-1)

(b-1)

TSR= 1.77 (85.37 rpm) Single Blade 0 30

Whole Turbine

3-PB Helical 0 330

60

0.13 90

3-PB Helical 30 300

0.04

-0.05

60

0.12 90

270

Ct(ν)

120

300

0.05

-0.02

270

Ct(ν)

120

240 150

330

240 150

210

210

180

180

(a-2)

(b-2)

ν°

ν°

38

Figure 14. Torque coefficients of 3-PB and helical-blade VAWTs at TSRs of 1.33 and 1.77 and wind speed of 5 m/s: (a) single blade, (b) whole turbine.

Table 10. Results of the total torque coefficient, including its average and deviation at TSRs of 1.33 and 1.77 and wind speeds of 5 m/s and 7 m/s. No.

Parameters

TSR

rpm

1.33 90 1 2   64.17 3 1.77 120 4 85.37 5 1.33 90 6 64.17 + 7 1.77 120 8 85.37 * With respect to the helical-blade VAWT.

Wind speed [m/s] 7 5 7 5 7 5 7 5

Helical-blade VAWT 0.0363 0.0272 0.033 0.0209 0.0285 0.0264 0.0306 0.0277

3-PB VAWT 0.0681 0.0581 0.0852 0.0746 0.0181 0.0175 0.0124 0.0106

Percent of change* 87.6 113.6 158.19 256.9 -36.49 -33.7 -59.48 -61.73

8. Conclusion Wind turbine introduced in this paper, called 3-PB VAWT, is proposed to benefit from advantages of both straight-blade and helical-blade VAWTs, including high average-torque, low amplitude of torque fluctuations and low cost of production. As was shown in this paper 3-PB VAWT has high output-torque while operating smoothly without much torque fluctuations. Obviously its high output-torque is due to its straight-blade parts, and its smooth operation is due to the azimuth angle offset between those straight-blade parts.

39

At constant wind speed of 7 m/s, at the self-starting condition and operational mode of TSRs less than and equal to 1.8, aerodynamic performance of the 3-PB and helical-blade VAWTs are examined numerically, and their results including average of the total torque coefficient and its deviation from the average per cycle were compared with each other. The following conclusions were made from the present study: 1. At TSRs from 0.8 to 1.8, the performance of the 3-PB VAWT is far better than the helical-blade VAWT. For instance, at TSRs of 0.89, 1.11, 1.33 and 1.77, the average of the total torque coefficient being produced by 3-PB VAWT during each cycle is 19.05%, 60.96%, 87.6%, and 158.19% higher than that of helical-blade VAWT, respectively. Accordingly, deviation of the total torque coefficient of 3-PB VAWT from its average during each cycle is 13.83%, 26.02%, 36.49%, and 59.48% less than that of helical-blade VAWT, respectively. 2. At TSRs less than 0.5, 3-PB and helical-blade VAWTs are close to each other in terms of the amount of average and deviation of the total torque coefficient. For instance, at the TSR of 0.44, the average of total torque coefficient produced by the 3-PB turbine is 6.06% higher than that of helical-blade VAWT. Further, the deviation of total torque coefficient of 3-PB VAWT is 22.48% less than that of helical-blade VAWT. 3. At the self-starting condition, in comparison to 3-PB VAWT, helical-blade VAWT produces 27.62% higher average of total torque coefficient at different azimuth angles; therefore, helical-blade VAWT can start with lower wind speeds. It seems that 3-PB VAWT should be improved for a better self-starting.

40

It is believed that simple production of straight blades and much better aerodynamic performance of the 3-PB VAWT in operational mode are criteria that demonstrate the superiority of the present wind turbine and completely justifies its utilization instead of the helical-blade VAWT.

References [1] Leung DY, Yang Y. Wind energy development and its environmental impact: A review. Renewable and Sustainable Energy Reviews. 2012;16(1):1031-9. [2] Wang Z, Zhuang M. Leading-edge serrations for performance improvement on a vertical-axis wind turbine at low tip-speed-ratios. Applied Energy. 2017;208:1184-97. [3] Tjiu W, Marnoto T, Mat S, Ruslan MH, Sopian K. Darrieus vertical axis wind turbine for power generation II: Challenges in HAWT and the opportunity of multi-megawatt Darrieus VAWT development. Renewable Energy. 2015;75:560-71. [4] Rezaeiha A, Montazeri H, Blocken B. Characterization of aerodynamic performance of vertical axis wind turbines: Impact of operational parameters. Energy Conversion and Management. 2018;169:45-77. [5] Ghasemian M, Ashrafi ZN, Sedaghat A. A review on computational fluid dynamic simulation techniques for Darrieus vertical axis wind turbines. Energy Conversion and Management. 2017;149:87-100. [6] Shires A. Design optimisation of an offshore vertical axis wind turbine. Proceedings of the ICE-Energy. 2013;166(EN1):7-18. [7] Howell R, Qin N, Edwards J, Durrani N. Wind tunnel and numerical study of a small vertical axis wind turbine. Renewable energy. 2010;35(2):412-22. 41

[8] Riegler H. HAWT versus VAWT: Small VAWTs find a clear niche. Refocus. 2003;4(4):446. [9] Zanforlin S, Deluca S. Effects of the Reynolds number and the tip losses on the optimal aspect ratio of straight-bladed Vertical Axis Wind Turbines. Energy. 2018;148:179-95. [10] Li Qa, Maeda T, Kamada Y, Murata J, Kawabata T, Shimizu K, et al. Wind tunnel and numerical study of a straight-bladed vertical axis wind turbine in three-dimensional analysis (Part I: For predicting aerodynamic loads and performance). Energy. 2016;106:443-52. [11] Driss Z, Mlayeh O, Driss S, Maaloul M, Abid MS. Study of the incidence angle effect on the aerodynamic structure characteristics of an incurved Savonius wind rotor placed in a wind tunnel. Energy. 2016;113:894-908. [12] Horiuchi N, Kawahito T. Torque and power limitations of variable speed wind turbines using pitch control and generator power control. Conference Torque and power limitations of variable speed wind turbines using pitch control and generator power control, vol. 1. IEEE, p. 638-43. [13] Scheurich F, Fletcher T, Brown R. The influence of blade curvature and helical blade twist on the performance of a vertical-axis wind turbine. Conference The influence of blade curvature and helical blade twist on the performance of a vertical-axis wind turbine. p. 1579. [14] Wang Z, Wang Y, Zhuang M. Improvement of the aerodynamic performance of vertical axis wind turbines with leading-edge serrations and helical blades using CFD and Taguchi method. Energy Conversion and Management. 2018;177:107-21.

42

[15] Battisti L, Brighenti A, Benini E, Castelli MR. Analysis of Different Blade Architectures on small VAWT Performance. Conference Analysis of Different Blade Architectures on small VAWT Performance, vol. 753. IOP Publishing, p. 062009. [16] Lee Y-T, Lim H-C. Numerical study of the aerodynamic performance of a 500 W Darrieustype vertical-axis wind turbine. Renewable Energy. 2015;83:407-15. [17] Erfort G, von Backström TW, Venter G. Reduction in the torque ripple of a vertical axis wind turbine through foil pitching optimization. Wind Engineering. 2019:0309524X19836711. [18] Tjiu W, Marnoto T, Mat S, Ruslan MH, Sopian K. Darrieus vertical axis wind turbine for power generation I: Assessment of Darrieus VAWT configurations. Renewable Energy. 2015;75:50-67. [19] Alaimo A, Esposito A, Messineo A, Orlando C, Tumino D. 3D CFD analysis of a vertical axis wind turbine. Energies. 2015;8(4):3013-33. [20] Castelli MR, Benini E. Effect of blade inclination angle on a Darrieus wind turbine. Journal of turbomachinery. 2012;134(3):031016. [21] Salazar AB. CFD Analysis On The Flow Field For Small Scale Helical Twisted And Straight 3-Bladed Vertical Axis Wind Turbine (VAWT). 2016. [22] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA journal. 1994;32(8):1598-605. [23] Bhuyan S, Biswas A. Investigations on self-starting and performance characteristics of simple H and hybrid H-Savonius vertical axis wind rotors. Energy Conversion and Management. 2014;87:859-67.

43

[24] MacPhee D, Beyene A. Recent advances in rotor design of vertical axis wind turbines. Wind Engineering. 2012;36(6):647-65. [25] Wakui T, Tanzawa Y, Hashizume T, Nagao T. Hybrid configuration of Darrieus and Savonius rotors for stand‐alone wind turbine‐generator systems. Electrical Engineering in Japan. 2005;150(4):13-22. [26] Behrouzi F, Nakisa M, Maimun A, Ahmed YM, Souf-Aljen AS. Performance investigation of self-adjusting blades turbine through experimental study. Energy Conversion and Management. 2019;181:178-88. [27] Marinić-Kragić I, Vučina D, Milas Z. Concept of flexible vertical-axis wind turbine with numerical simulation and shape optimization. Energy. 2019;167:841-52. [28] Mohamed M. Performance investigation of H-rotor Darrieus turbine with new airfoil shapes. Energy. 2012;47(1):522-30. [29] Zamani M, Maghrebi MJ, Varedi SR. Starting torque improvement using J-shaped straightbladed Darrieus vertical axis wind turbine by means of numerical simulation. Renewable Energy. 2016;95:109-26. [30] Li Y, Zhao S, Tagawa K, Feng F. Starting performance effect of a truncated-cone-shaped wind gathering device on small-scale straight-bladed vertical axis wind turbine. Energy Conversion and Management. 2018;167:70-80. [31] Rezaeiha A, Kalkman I, Blocken B. Effect of pitch angle on power performance and aerodynamics of a vertical axis wind turbine. Applied Energy. 2017;197:132-50. [32] Lei H, Zhou D, Lu J, Chen C, Han Z, Bao Y. The impact of pitch motion of a platform on the aerodynamic performance of a floating vertical axis wind turbine. Energy. 2017;119:369-83. 44

[33] Li Qa, Maeda T, Kamada Y, Murata J, Furukawa K, Yamamoto M. Effect of number of blades on aerodynamic forces on a straight-bladed Vertical Axis Wind Turbine. Energy. 2015;90:784-95. [34] Castelli MR, De Betta S, Benini E. Effect of blade number on a straight-bladed vertical-axis Darreius wind turbine. World Academy of Science, Engineering and Technology. 2012;61:3053011. [35] Elkhoury M, Kiwata T, Aoun E. Experimental and numerical investigation of a threedimensional vertical-axis wind turbine with variable-pitch. Journal of wind engineering and Industrial aerodynamics. 2015;139:111-23. [36] Cheng Q, Liu X, Ji HS, Kim KC, Yang B. Aerodynamic Analysis of a Helical Vertical Axis Wind Turbine. Energies. 2017;10(4):575. [37] McLaren K, Tullis S, Ziada S. Computational fluid dynamics simulation of the aerodynamics of a high solidity, small‐scale vertical axis wind turbine. Wind Energy. 2012;15(3):349-61. [38] Sheldahl RE. Comparison of field and wind tunnel Darrieus wind turbine data. Journal of Energy. 1981;5(4):254-6. [39] Hoffmann KA, Chiang ST. Computational Fluid Dynamics Volume I. Engineering Education System, Wichita, Kan, USA. 2000. [40] Vaughn M, Chen C. Error versus y+ for three turbulence models: Incompressible flow over a unit flat plate. Conference Error versus y+ for three turbulence models: Incompressible flow over a unit flat plate. p. 3968.

45

[41] Castelli MR, Englaro A, Benini E. The Darrieus wind turbine: Proposal for a new performance prediction model based on CFD. Energy. 2011;36(8):4919-34. [42] Wolf PR, Ghilani CD. Adjustment computations: statistics and least squares in surveying and GIS: Wiley-Interscience, 1997. [43] Hosseinidoost SE, Sattari A, Eskandari M, Vahidi D, Hanafizadeh P, Ahmadi P. Technoeconomy study of wind energy in Khvaf in Razavi Khorasan Province in Iran. Journal of Computational Applied Mechanics. 2016;47(1):53-66. [44] Mostafaeipour A, Sedaghat A, Ghalishooyan M, Dinpashoh Y, Mirhosseini M, Sefid M, et al. Evaluation of wind energy potential as a power generation source for electricity production in Binalood, Iran. Renewable Energy. 2013;52:222-9. [45] Saeidi D, Mirhosseini M, Sedaghat A, Mostafaeipour A. Feasibility study of wind energy potential in two provinces of Iran: North and South Khorasan. Renewable and Sustainable Energy Reviews. 2011;15(8):3558-69. [46] Mirhosseini M, Sharifi F, Sedaghat A. Assessing the wind energy potential locations in province of Semnan in Iran. Renewable and Sustainable Energy Reviews. 2011;15(1):449-59.

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Highlights •

A new low-cost Darrieus wind turbine, called three-part-blade (3-PB), is proposed.



Each 3-PB blade is similar to a helical one but includes small straight blades.



The solution of transient 3D RANS equations with SST ݇ − ߱ turbulence model is used.



Total torque of 3-PB and helical turbines are compared at various TSRs (up to 1.8).



3-PB turbine gives higher average torque with less fluctuations over helical blade.