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The effect of inner blade position on the performance of the Savonius rotor
Sustainable Energy Technologies and Assessments 36 (2019) 100534
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Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta
The effect of inner blade position on the performance of the Savonius rotor Mohanad Al-Ghriybah
a,c,⁎
a
b
, Mohd Fadhli Zulkafli , Djamal Hissein Didane , Sofian Mohd
T
a
a
Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia Department of Energy and Thermofluid Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia c Department of Renewable Energy Engineering, Faculty of Engineering, Al-Isra University, Amman, Jordan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Savonius Inner blade Inner blade position VAWT Wind energy
In this study, the effect of the inner blade position on the performance of the Savonius rotor has been investigated numerically to determine the best position of the inner blade. Five values of inner blade angles are adopted (180°, 160°, 140°, 120°, and 100°). Two-dimensional simulation is performed for the conventional rotor, rotor with the inner blade tip parallel with rotor tip, and rotor with the inner blade parallel with rotor root keeping the main rotor diameter constant in each case. The simulation has been achieved using the k-ε/realizable turbulence model with the assist of the ANSYS-Fluent solver. The torque coefficient (Ct) and power coefficient (Cp) are estimated as a function of tip speed ratio (TSR) for each case. Finally, the total pressure, velocity, and streamlines are obtained and analyzed. The numerical results demonstrated the maximum Cp to be 0.1885 at TSR equal to 0.5 when the inner blade is placed parallel with rotor tip with inner blade angle of 120°. Moreover, results found that the maximum Ct is 0.407 at TSR = 0.4 for the rotor with 180° inner blade. Furthermore, the peak value of the torque found to be generated at the azimuth position of (θ = 105°).
Introduction Extracting the kinetic energy of the wind has been implemented by many countries through building new wind turbine farms, which creates many job opportunities and promotes a clean source of energy [1]. According to the global wind report-annual market update [2], the total cumulative capacity was around 539 GW with an annual growth of 10.64% in 2017. Large-scale horizontal axis wind turbines (HAWTs) have the ability to generate more than 6 MW of electric power and have the ability to extract a large amount of the available energy in the wind. In contrast, vertical axis wind turbines (VAWTs) are more used in smallscale energy production. However, VAWTs offer some advantages over HAWTs which are worthy to be considered [3]. The main feature of VAWTs is that the system of the turbine is independent of the wind direction, consequently, no need for any mechanism for directing the blades of the rotor [4]. Moreover, VAWTs are commonly used near the ground, thus the generator can be placed at the ground level which will reduce both cost and time of the maintenance. The geometry of the VAWT is small, simple in construction and less in components which it can be fabricated by mass production extrusion [5–7]. These features have put VAWTs under exploration and investigation by many researchers.
Savonius wind rotor is one of the main types of VAWTs, and it mainly depends on the drag force. Despite the fact that the Savonius rotor suffers from low efficiency, it has advantages over all other types of turbines such as self-starting capability and lower cost of construction [8–10]. As shown in Fig. 1, the conventional Savonius rotor typically consists of two blades. The Savonius rotor has many applications such as windbreakers, street lighting system, ventilation, and electricity generation [11,12]. Experimental and simulation studies have been conducted on the Savonius rotor aiming to enhance its performance. This has been accomplished by modifying the design parameters of the rotor like overlap ratio (the ratio between the overlap distance and the rotor diameter), aspect ratio (the ratio between the height and the width of the rotor), and blade profiles. The effect of the aspect ratio was studied by various researchers [13–15]. Kamoji et al. [15] studied the influence of the aspect ratio and they concluded that 0.7 aspect ratio enhances the coefficient of power (Cp ). Modi et al. [14] found that the aspect ratio value of 0.77 appears to lead to the best performance for the Savonius rotor. Roy and Saha [13] experimentally found that an optimum aspect ratio of 0.8 gives the higher performance. However, the maximum allowed value of the aspect ratio has not specified yet. This is because such parameter requires more analysis related to the
⁎ Corresponding author at: Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia. E-mail address: [email protected] (M. Al-Ghriybah).
https://doi.org/10.1016/j.seta.2019.100534 Received 24 April 2019; Received in revised form 17 August 2019; Accepted 5 September 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.
Sustainable Energy Technologies and Assessments 36 (2019) 100534
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modeling of the Savonius rotor configurations. The unstructured quadrilateral-grids are created around the numerical model. The numerical domain consisting of two sub-domains is divided by a sliding interface: circular moving domain with a diameter of 1.1D and it is placed at the centre of the numerical domain, and a stationary square domain with a size of 10D × 10D. Resolving boundary layer around the rotors’ wall is important to ensure near rotors’ wall flow is accurate, hence finer grid elements are needed near the wall. For this reason, “inflation meshing” technique is applied on the rotors’ wall. The first layer thickness is set to be 0.05 mm. The thickness of the first layer from the rotor is estimated using the following equation [33]:
y+=
ρut y μ
(1)
wherein y + is a non-dimensional parameter, ut represents the friction velocity, ρ is the density of the air (1.225 kg/m3), μ is the dynamic viscosity (N s/m2), and y is the distance of the first cell from rotors wall. ut can be can be defined in the following way:
Fig. 1. Conventional Savonius rotor.
ut =
mechanical design (fatigue forces and the stresses) along the rotor height. The influence of the overlap ratio has also been studied by many researchers. In an experimental investigation, Mahmoud et al. [16] have found the mechanical power to drop with the increase of overlap ratio. In a numerical investigation, Akwa et al. [17] demonstrated the optimum value of the overlap ratio to be 15%. Worasinchai and Suwannakij [18] experimentally studied the effect of overlap ratio on a three-bladed rotor and they found that the performance of the rotor with null overlap performed the best. The effect of number of buckets and stages have been done in previous studies [16,19–25]. These studies reported that by increasing the number of stages or number of buckets; the performance of the turbine is decreased. On the other hand, blade profiles were modified and optimized by a host of investigators [26–32]. An improvement in the range between (15%–45%) in terms of Cp compared to the conventional rotor was achieved. Thus, over the decades, various rotor configurations have been designed in order to enhance the performance of the Savonius wind turbine. However, the performance parameters for these studies have been different. Throughout the literature, several power enhancement research on the Savonius wind turbine were carried by modifying the main design parameters such as number of blades and aspect ratio, however, until now there is no study has been carried out on the effect of the inner blades and their positions on the performance of the Savonius wind rotor. In view of this, the main objective of this study is to examine numerically the influence of the inner blade with different positions on the performance of the conventional Savonius wind rotor. The addition of such inner blades on the conventional rotor is expected to enhance the generated power from the rotor by capturing more energy from the wind without changes the space requirements or effect the simplicity of the conventional rotor.
τω ρ
(2)
wherein τω represents the wall shear stress, and it can be defined as following:
∂u τω = μ ⎛ ⎞ ⎝ ∂y ⎠ y = 0 ⎜
⎟
(3)
Twenty-five inflation layers are applied to the rotor boundary with 1.1 growth ratio as shown in Fig. 5. Boundary conditions The left side of the squared stationary domain is assigned as velocity inlet (U = 9 m/s) with 5% turbulent intensity. The opposite wall of the inlet is assigned as pressure outlet. Top and bottom walls are assigned as stationary walls. No-slip condition is applied to the blade walls (Fig. 6). A sliding interface is created between the circular region and the squared region. The rotation of the circular moving region is given with respect to TSR (the ratio between the rotor speed and wind speed), with four values (0.4, 0.5, 0.6, and 0.7). Turbulence model As reported in the previous studies, the k-ε/realizable model has found to be greatly enhanced compared to the standard K-epsilon model [35]. The first enhancement was the addition of an alternative formulation for the turbulent viscosity. Secondly, the derivation of the dissipation rate (ε ) transport equation was from an exact equation for the transport of the mean-square vorticity fluctuation [36]. This model has the ability to predict the values of wall friction coefficient more accurately than all the other models [37,38]. The main features of this model include enhanced performance inflow with recirculation and strong pressure gradient. The transport equation fork and ε in the model are given as [39,40].
Geometrical details of the model and meshing
μ ∂k ⎤ ∂ ∂ ∂ ⎡⎛ (ρk ) + (ρkuj ) = μ + t⎞ + Gk + Gb − ρε − YM + Sk ⎥ ∂t ∂x j ∂x j ⎢ σ k ⎠ ∂x j ⎦ ⎣⎝
Fig. 2 illustrates the dimensions of the conventional rotor and the rotor with inner blades. Figs. 3 and 4 show the modified configuration of the Savonius rotor with different positions and angles of the inner blade where the tip of the inner blade is parallel with rotor tip in Configuration 1 and parallel with rotor root in Configuration 2. The main blade diameter is set to be (D = 0.442 m), the inner blade diameter is kept constant for all tested rotors (di = 0.144 m), shaft diameter is set to be (O = 0.03 m), the thickness of all blades is fixed (t = 0.002 m), and end plates diameter is set to (De = 1.1D). Inner blade angles are taken as 100°, 120°, 140°, and 160°. In the present study, the AutoCAD 2013 software is utilized for
⎜
⎟
(4)
∂ ∂ (ρε ) + (ρεuj ) ∂t ∂x j =
μ ∂ε ⎤ ε2 ε ∂ ⎡⎛ μ + t⎞ + ρC1 Sε − ρC2 + C1ε C3 Gb + Sε ⎢ ⎥ ∂x j ⎣ ⎝ σε ⎠ ∂x j ⎦ k + vε k ⎜
⎟
(5) where μt is the eddy viscosity, (σk , σε ) are diffusion constants of the 2
Sustainable Energy Technologies and Assessments 36 (2019) 100534
M. Al-Ghriybah, et al.
Fig. 2. (a) Conventional Savonius rotor, (b) rotor with inner blades.
model, and C1 = max ⎡0.43, ⎣
η ⎤, η + 5⎦
k
η = Sε, S =
wherein R is the rotor radius. For Cp values in the numerical analysis the following subsequent equation can be used:
2Sij Sij .
Solver set up
Cp = Ct × TSR The time step size for the simulation is evaluated on the basis of one degree of rotation per step rotation of the turbine with respect to the TSR (at TSR = 0.7 the time step is 0.0006122504 s). The numerical simulation is performed 10 completed rotations of the turbine. The maximum iteration per time step is set to be 20. Absolute criteria are used to monitor the convergence of the solution with a value of 10-5. Pressure-based transition simulation is used in the general setting of the Fluent solver. Pressure and velocity coupling are created using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The spatial discretization of the conservative equations is treated with 2nd order upwind scheme.
Results and discussion Grid-independent test The grid-independent test has been conducted by adopting the grids 32,000, 89,000, and 150,000. The average Cp of the grids is shown in table 1. It has noticed that Cp for 89,000 and 150,000 are almost equal and the numerical results is not affected by the high number of grid elements, hence, grid with 89,000 elements is adopted for all the simulations. To determine the size of the time step, the following equation can be used [34]:
Definitions of main parameters The power coefficient (Cp) of a Savonius wind turbine can be expressed as follows [41]:
Cp =
Power of the turbine T×ω = Avilable power in the wind 0.5ρAU 3
Δt|1° =
(6)
T 0.5ρAU 2R
1 ω (rps ) × 360
(9)
Validation of the numerical method
wherein T is the generated torque (N.m), ω is the angular velocity, and A is the rotor projected area (A = HD), where H is the height of the rotor. Another parameter that will be utilized in this paper is the torque coefficient (Ct), which is defined, as below:
Ct =
(8)
In this section, the simulation results by the k-ε/realizable turbulence model are compared with the experimental data obtained by Hayashi et al. [42]. The simulation is carried out on the conventional Savonius rotor at TSR = 0.6, 0.7, 0.8. Fig. 7 illustrates the comparison between the numerical simulation and the experimental data by Hayashi et al. [42]. It is noticed from the figure that the k-ε/realizable turbulence model predicts well the Cp of the Savonius rotor with an
(7)
Fig. 3. Configuration 1 (inner blade tip is parallel with rotor tip) with blade angles (a) 100° (b) 120° (c) 140° (d) 160°. 3
Sustainable Energy Technologies and Assessments 36 (2019) 100534
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Fig. 4. Configuration 2 (inner blade is parallel with rotor root) with blade angles (a) 100° (b) 120° (c) 140° (d) 160°. Table 1 Average Cp various number of cells. Number of cells
AverageCp
32,000 89,000 150,000
0.153 0.16033 0.16040
Fig. 7. Numerical simulation validation.
Fig. 5. Mesh generation for the computational domain.
overall error of less than 7%. Cp comparison Two-dimensional unsteady numerical simulation is conducted on various Savonius rotor configurations including the conventional rotor. Power coefficient (Cp) is evaluated and discussed with respect to TSR for all proposed configurations. Figs. 8 and 9 illustrate the Cp
Fig. 6. Boundary conditions of the numerical domain. Fig. 8. Cp for the conventional rotor and Configuration 1 with different angles at various TSR. 4
Sustainable Energy Technologies and Assessments 36 (2019) 100534
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Fig. 11. Ct for the conventional rotor and Configuration 1 with different angles at various TSR.
Fig. 9. Cp for the conventional rotor and Configuration 2 with different angles at various TSR.
comparison between the conventional rotor and (Configuration 1 and Configuration 2), respectively, with various blade angles. It can be clearly seen from Fig. 8 that the peak Cp for Configuration 1 is found to be 0.1885 at TSR equal to 0.5 when the angle of blade was 120°; whereas at the same TSR, the Cp is observed to be 0.1597 for the conventional rotor and 0.154, 0.153, 0.1506, and 0.147 for the rotors with inner blade angle of 180°, 160°, 100°, and 140°, respectively. Moreover, it can be observed that rotors with inner blades of 120° and 140° angles are performed better than the conventional rotor at TSRs = 0.6 and 0.7. It also can be seen from Fig. 9 that the peak value of Cp for Configuration 2 is found to be around 0.183 at TSR = 0.5 for inner blades with an angle of 120°. Moreover, the rotor with inner blades of 120° angle performed better than the conventional rotor at TSRs = 0.5, 0.6, and 0.7. The Cp comparison between Configuration 1 and 2 is indicated in Fig. 10. It was observed from the figure that Configuration 1 with inner blade angles of 160° and 120° is performed better at most of TSR values.
Fig. 12. Ct for the conventional rotor and Configuration 2 with different angles at various TSR.
Fig. 10. Cp comparison between Configuration 1 and 2. 5
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overcome most of the negative torque compared with the conventional rotor. Velocity contours The velocity contours of four rotors (conventional, with 180° inner blade, Configurations 1 and 2 with 120° inner blade) are illustrated in Fig. 15. The 6th rotation of the rotors is selected for higher accuracy. Angles of rotation (105°, 190°, and 360°) are adopted to analyze the behaviour of velocity contours. Under the effect of the incoming air, the rotor starts spinning which will force the wind around the blades to move in a circular pattern. This circular movement around the rotor reduces the effect of the incoming air velocity on the returning blade which will reduce the resistance between the blade surface and the incoming air. The formation of wake regions on the concave part of the returning blade of the conventional rotor and rotor with 180° inner blade is found to be larger than both Configurations 1 and 2. Moreover, there is a region on the convex part of the returning blade for Configurations 1 and 2 has smaller velocity, indicating its lower negative drag as compared to the other configurations. The maximum velocity region is found to be at the tip of the rotors. Configurations 1 and 2 are found to be lesser in terms of maximum velocity region. Additionally, the overlapping flow is found to be more prominent in Configuration 1 than the other configurations.
Fig. 13. Instantaneous torque as a function of θ for Configuration 1 with different inner blade angles at TSR = 0.7.
In contrast, Configuration 2 performed better when the inner blade angle was 140° at TSRs = 0.4 and 0.5.
Ct comparison
Pressure contours
Torque coefficient (Ct) is evaluated and analyzed with respect to TSR for the conventional, Configuration 1 and Configuration 2 rotors. Figs. 11 and 12 show the Ct comparison between all the proposed configurations with various blade angles. It can be observed from both figures that the maximum value of Ct is 0.407 at the lowest considered value of TSR = 0.4 for the configuration with 180° inner blade. On the other hand, Ct values for the rotor with 120° inner blade (for both configuration) were the highest at TSRs = 0.5, 0.6 and 0.7. Moreover, the generated torque for both configurations with 160°, 140°, and 100° inner blade was less than the conventional rotor expect the rotor with 140° from Configuration 1 at TSRs = 0.6 and 0.7. It is also noticed that ω of the proposed rotors decrease with the application of load and hence, the variation of Ct decrease with the increase of TSR values. The instantaneous torque versus the azimuth position of the blade (θ) is plotted during a complete cycle from θ = 0° to θ = 360° and showed in Figs. 13 and 14 for both configurations at TSR = 0.7. The angular position where the maximum torque is generated remains essentially unmodified for all tested rotors. It can be clearly seen from the figures that the peak value of the torque is generated at the azimuth position of (θ = 105°). In contrast, the lowest torque is generated when the rotor was in apposition of (θ = 188°). Furthermore, it can be observed that the rotors with inner blades of 120° for both configurations
Pressure contours of the selected rotors in Section “Ct comparison” are shown in Fig. 16. The trend of pressure distribution for all tested rotors are almost the same, but the suction area and the magnitude of pressure for the configurations with inner blades are more extensive than the conventional Savonius rotor. Consequently, in the rotor with a 120° inner blade, the pressure difference causes additional force, and in results, an increase in Cp values occurs. The incoming airflow impacts the convex side of the returning blade and gives up its momentum to the other part of the blade, which in result raises the pressure. As the air moves along the upper side of the blade surface, the pressure goes down in that region. The flowing air with lower energy then hits the advancing blade of the rotor, which lightly raises the pressure on the concave side. The low-pressure region is found to be greater in the conventional and 180° inner blade rotors than the Configurations 1 and 2 with 120° inner blades. Moreover, the high-pressure region appears on the convex side of the returning blade and its lesser for Configurations 1 and 2 as compared to the other configurations, and as a result, the generating torque is much higher in the Configurations1 and 2. Streamlines The flow field around the selected rotors in sec 3.4 is analyzed by the streamlines. The streamlines of the selected rotors are shown in Fig. 17 at TSR = 0.7, as the vortices can be clearly seen in the vicinity of the rotor. Vortices are noted to be around the lower tip and concave side of the returning blade. In Fig. 17(c) and (d) and at θ = 105°, it can be seen the high generated vortices behind the returning blade compared to the low generated vortex in the conventional rotor (a) from Fig. 17. These vortices give more evidence that the pressure difference for the new Configurations 1 and 2 is higher than the other configurations, whereby decrease the effect of the incoming air on the returning blade which leads to decrease the resistance between the surface of the returning blade and the moving wind. The presented numerical method used to simulate the different geometries of the Savonius rotor had two limitations:
• The study uses the 2-D simulation without considering the 3-D ef-
Fig. 14. Instantaneous torque as a function of θ for Configuration 2 with different inner blade angles at TSR = 0.7.
fects such as wake effects. Although it’s generally agreed that 2D simulations can’t predict the wake effect as strong as 3D simulations,
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Fig. 15. Velocity contours of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) Configuration 1 with 120° inner blade, (d) Configuration 2 with 120° inner blade.
•
are 180°, 160°, 140°, 120°, and 100°, were adopted for both configurations. The numerical simulation was done using the k-ε/realizable turbulence model. There was a considerable enhancement in the conventional rotor performance including torque coefficient (Ct) and power coefficient (Cp) when using the inner blades. Moreover, the simulation results showed that the optimum inner blade angle is 120°. It has the highest Cp of 0.1885 at TSR = 0.5 for Configuration 1, and 0.183 at TSR = 0.5 for Configuration 2. Additionally, Configuration 1 performed better than Configuration 2 at most TSRs. The static torque was found to be positive at most of the rotor angles, for both configurations with 120° inner blade. Moreover, the maximum value of Ct was found to be 0.407 at the lowest considered value of TSR = 0.4 for the rotor with 180° inner blade. On the other hand, Ct values for the rotor with 120° inner blade (for both configuration) were found to be the highest at TSRs = 0.5, 0.6 and 0.7. Finally, it was found that inner
previous studies have shown that 2D simulation for Savonius rotor gives acceptable results. The effect of the blockage ratio (the ratio between swept area and the cross-sectional area of the wind tunnel) is neglected due to the large domain which reduces the effect of the boundaries on the output power of the turbine.
Conclusion This study aimed to investigate the performance of the Savonius wind rotor with additional inner blades in various angles and positions. Two different configurations, which are rotor with the inner blade tip parallel with rotor tip (Configuration 1) and rotor with inner blade parallel with rotor root (Configuration 2), were investigated numerically at different TSR values. Five different inner blade angles, which
Fig. 16. Pressure contours of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) configuration 1 with 120° inner blade, (d) configuration 2 with 120° inner blade. 7
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Fig. 17. Streamlines of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) Configuration 1 with 120° inner blade, (d) Configuration 2 with 120° inner blade.
blade with angles of (180°, 160°, 140°, and 100°) led to decreased values of Cp.
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Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta
The effect of inner blade position on the performance of the Savonius rotor Mohanad Al-Ghriybah
a,c,⁎
a
b
, Mohd Fadhli Zulkafli , Djamal Hissein Didane , Sofian Mohd
T
a
a
Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia Department of Energy and Thermofluid Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia c Department of Renewable Energy Engineering, Faculty of Engineering, Al-Isra University, Amman, Jordan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Savonius Inner blade Inner blade position VAWT Wind energy
In this study, the effect of the inner blade position on the performance of the Savonius rotor has been investigated numerically to determine the best position of the inner blade. Five values of inner blade angles are adopted (180°, 160°, 140°, 120°, and 100°). Two-dimensional simulation is performed for the conventional rotor, rotor with the inner blade tip parallel with rotor tip, and rotor with the inner blade parallel with rotor root keeping the main rotor diameter constant in each case. The simulation has been achieved using the k-ε/realizable turbulence model with the assist of the ANSYS-Fluent solver. The torque coefficient (Ct) and power coefficient (Cp) are estimated as a function of tip speed ratio (TSR) for each case. Finally, the total pressure, velocity, and streamlines are obtained and analyzed. The numerical results demonstrated the maximum Cp to be 0.1885 at TSR equal to 0.5 when the inner blade is placed parallel with rotor tip with inner blade angle of 120°. Moreover, results found that the maximum Ct is 0.407 at TSR = 0.4 for the rotor with 180° inner blade. Furthermore, the peak value of the torque found to be generated at the azimuth position of (θ = 105°).
Introduction Extracting the kinetic energy of the wind has been implemented by many countries through building new wind turbine farms, which creates many job opportunities and promotes a clean source of energy [1]. According to the global wind report-annual market update [2], the total cumulative capacity was around 539 GW with an annual growth of 10.64% in 2017. Large-scale horizontal axis wind turbines (HAWTs) have the ability to generate more than 6 MW of electric power and have the ability to extract a large amount of the available energy in the wind. In contrast, vertical axis wind turbines (VAWTs) are more used in smallscale energy production. However, VAWTs offer some advantages over HAWTs which are worthy to be considered [3]. The main feature of VAWTs is that the system of the turbine is independent of the wind direction, consequently, no need for any mechanism for directing the blades of the rotor [4]. Moreover, VAWTs are commonly used near the ground, thus the generator can be placed at the ground level which will reduce both cost and time of the maintenance. The geometry of the VAWT is small, simple in construction and less in components which it can be fabricated by mass production extrusion [5–7]. These features have put VAWTs under exploration and investigation by many researchers.
Savonius wind rotor is one of the main types of VAWTs, and it mainly depends on the drag force. Despite the fact that the Savonius rotor suffers from low efficiency, it has advantages over all other types of turbines such as self-starting capability and lower cost of construction [8–10]. As shown in Fig. 1, the conventional Savonius rotor typically consists of two blades. The Savonius rotor has many applications such as windbreakers, street lighting system, ventilation, and electricity generation [11,12]. Experimental and simulation studies have been conducted on the Savonius rotor aiming to enhance its performance. This has been accomplished by modifying the design parameters of the rotor like overlap ratio (the ratio between the overlap distance and the rotor diameter), aspect ratio (the ratio between the height and the width of the rotor), and blade profiles. The effect of the aspect ratio was studied by various researchers [13–15]. Kamoji et al. [15] studied the influence of the aspect ratio and they concluded that 0.7 aspect ratio enhances the coefficient of power (Cp ). Modi et al. [14] found that the aspect ratio value of 0.77 appears to lead to the best performance for the Savonius rotor. Roy and Saha [13] experimentally found that an optimum aspect ratio of 0.8 gives the higher performance. However, the maximum allowed value of the aspect ratio has not specified yet. This is because such parameter requires more analysis related to the
⁎ Corresponding author at: Department of Aeronautical Engineering, Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Johor, Malaysia. E-mail address: [email protected] (M. Al-Ghriybah).
https://doi.org/10.1016/j.seta.2019.100534 Received 24 April 2019; Received in revised form 17 August 2019; Accepted 5 September 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.
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modeling of the Savonius rotor configurations. The unstructured quadrilateral-grids are created around the numerical model. The numerical domain consisting of two sub-domains is divided by a sliding interface: circular moving domain with a diameter of 1.1D and it is placed at the centre of the numerical domain, and a stationary square domain with a size of 10D × 10D. Resolving boundary layer around the rotors’ wall is important to ensure near rotors’ wall flow is accurate, hence finer grid elements are needed near the wall. For this reason, “inflation meshing” technique is applied on the rotors’ wall. The first layer thickness is set to be 0.05 mm. The thickness of the first layer from the rotor is estimated using the following equation [33]:
y+=
ρut y μ
(1)
wherein y + is a non-dimensional parameter, ut represents the friction velocity, ρ is the density of the air (1.225 kg/m3), μ is the dynamic viscosity (N s/m2), and y is the distance of the first cell from rotors wall. ut can be can be defined in the following way:
Fig. 1. Conventional Savonius rotor.
ut =
mechanical design (fatigue forces and the stresses) along the rotor height. The influence of the overlap ratio has also been studied by many researchers. In an experimental investigation, Mahmoud et al. [16] have found the mechanical power to drop with the increase of overlap ratio. In a numerical investigation, Akwa et al. [17] demonstrated the optimum value of the overlap ratio to be 15%. Worasinchai and Suwannakij [18] experimentally studied the effect of overlap ratio on a three-bladed rotor and they found that the performance of the rotor with null overlap performed the best. The effect of number of buckets and stages have been done in previous studies [16,19–25]. These studies reported that by increasing the number of stages or number of buckets; the performance of the turbine is decreased. On the other hand, blade profiles were modified and optimized by a host of investigators [26–32]. An improvement in the range between (15%–45%) in terms of Cp compared to the conventional rotor was achieved. Thus, over the decades, various rotor configurations have been designed in order to enhance the performance of the Savonius wind turbine. However, the performance parameters for these studies have been different. Throughout the literature, several power enhancement research on the Savonius wind turbine were carried by modifying the main design parameters such as number of blades and aspect ratio, however, until now there is no study has been carried out on the effect of the inner blades and their positions on the performance of the Savonius wind rotor. In view of this, the main objective of this study is to examine numerically the influence of the inner blade with different positions on the performance of the conventional Savonius wind rotor. The addition of such inner blades on the conventional rotor is expected to enhance the generated power from the rotor by capturing more energy from the wind without changes the space requirements or effect the simplicity of the conventional rotor.
τω ρ
(2)
wherein τω represents the wall shear stress, and it can be defined as following:
∂u τω = μ ⎛ ⎞ ⎝ ∂y ⎠ y = 0 ⎜
⎟
(3)
Twenty-five inflation layers are applied to the rotor boundary with 1.1 growth ratio as shown in Fig. 5. Boundary conditions The left side of the squared stationary domain is assigned as velocity inlet (U = 9 m/s) with 5% turbulent intensity. The opposite wall of the inlet is assigned as pressure outlet. Top and bottom walls are assigned as stationary walls. No-slip condition is applied to the blade walls (Fig. 6). A sliding interface is created between the circular region and the squared region. The rotation of the circular moving region is given with respect to TSR (the ratio between the rotor speed and wind speed), with four values (0.4, 0.5, 0.6, and 0.7). Turbulence model As reported in the previous studies, the k-ε/realizable model has found to be greatly enhanced compared to the standard K-epsilon model [35]. The first enhancement was the addition of an alternative formulation for the turbulent viscosity. Secondly, the derivation of the dissipation rate (ε ) transport equation was from an exact equation for the transport of the mean-square vorticity fluctuation [36]. This model has the ability to predict the values of wall friction coefficient more accurately than all the other models [37,38]. The main features of this model include enhanced performance inflow with recirculation and strong pressure gradient. The transport equation fork and ε in the model are given as [39,40].
Geometrical details of the model and meshing
μ ∂k ⎤ ∂ ∂ ∂ ⎡⎛ (ρk ) + (ρkuj ) = μ + t⎞ + Gk + Gb − ρε − YM + Sk ⎥ ∂t ∂x j ∂x j ⎢ σ k ⎠ ∂x j ⎦ ⎣⎝
Fig. 2 illustrates the dimensions of the conventional rotor and the rotor with inner blades. Figs. 3 and 4 show the modified configuration of the Savonius rotor with different positions and angles of the inner blade where the tip of the inner blade is parallel with rotor tip in Configuration 1 and parallel with rotor root in Configuration 2. The main blade diameter is set to be (D = 0.442 m), the inner blade diameter is kept constant for all tested rotors (di = 0.144 m), shaft diameter is set to be (O = 0.03 m), the thickness of all blades is fixed (t = 0.002 m), and end plates diameter is set to (De = 1.1D). Inner blade angles are taken as 100°, 120°, 140°, and 160°. In the present study, the AutoCAD 2013 software is utilized for
⎜
⎟
(4)
∂ ∂ (ρε ) + (ρεuj ) ∂t ∂x j =
μ ∂ε ⎤ ε2 ε ∂ ⎡⎛ μ + t⎞ + ρC1 Sε − ρC2 + C1ε C3 Gb + Sε ⎢ ⎥ ∂x j ⎣ ⎝ σε ⎠ ∂x j ⎦ k + vε k ⎜
⎟
(5) where μt is the eddy viscosity, (σk , σε ) are diffusion constants of the 2
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Fig. 2. (a) Conventional Savonius rotor, (b) rotor with inner blades.
model, and C1 = max ⎡0.43, ⎣
η ⎤, η + 5⎦
k
η = Sε, S =
wherein R is the rotor radius. For Cp values in the numerical analysis the following subsequent equation can be used:
2Sij Sij .
Solver set up
Cp = Ct × TSR The time step size for the simulation is evaluated on the basis of one degree of rotation per step rotation of the turbine with respect to the TSR (at TSR = 0.7 the time step is 0.0006122504 s). The numerical simulation is performed 10 completed rotations of the turbine. The maximum iteration per time step is set to be 20. Absolute criteria are used to monitor the convergence of the solution with a value of 10-5. Pressure-based transition simulation is used in the general setting of the Fluent solver. Pressure and velocity coupling are created using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The spatial discretization of the conservative equations is treated with 2nd order upwind scheme.
Results and discussion Grid-independent test The grid-independent test has been conducted by adopting the grids 32,000, 89,000, and 150,000. The average Cp of the grids is shown in table 1. It has noticed that Cp for 89,000 and 150,000 are almost equal and the numerical results is not affected by the high number of grid elements, hence, grid with 89,000 elements is adopted for all the simulations. To determine the size of the time step, the following equation can be used [34]:
Definitions of main parameters The power coefficient (Cp) of a Savonius wind turbine can be expressed as follows [41]:
Cp =
Power of the turbine T×ω = Avilable power in the wind 0.5ρAU 3
Δt|1° =
(6)
T 0.5ρAU 2R
1 ω (rps ) × 360
(9)
Validation of the numerical method
wherein T is the generated torque (N.m), ω is the angular velocity, and A is the rotor projected area (A = HD), where H is the height of the rotor. Another parameter that will be utilized in this paper is the torque coefficient (Ct), which is defined, as below:
Ct =
(8)
In this section, the simulation results by the k-ε/realizable turbulence model are compared with the experimental data obtained by Hayashi et al. [42]. The simulation is carried out on the conventional Savonius rotor at TSR = 0.6, 0.7, 0.8. Fig. 7 illustrates the comparison between the numerical simulation and the experimental data by Hayashi et al. [42]. It is noticed from the figure that the k-ε/realizable turbulence model predicts well the Cp of the Savonius rotor with an
(7)
Fig. 3. Configuration 1 (inner blade tip is parallel with rotor tip) with blade angles (a) 100° (b) 120° (c) 140° (d) 160°. 3
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Fig. 4. Configuration 2 (inner blade is parallel with rotor root) with blade angles (a) 100° (b) 120° (c) 140° (d) 160°. Table 1 Average Cp various number of cells. Number of cells
AverageCp
32,000 89,000 150,000
0.153 0.16033 0.16040
Fig. 7. Numerical simulation validation.
Fig. 5. Mesh generation for the computational domain.
overall error of less than 7%. Cp comparison Two-dimensional unsteady numerical simulation is conducted on various Savonius rotor configurations including the conventional rotor. Power coefficient (Cp) is evaluated and discussed with respect to TSR for all proposed configurations. Figs. 8 and 9 illustrate the Cp
Fig. 6. Boundary conditions of the numerical domain. Fig. 8. Cp for the conventional rotor and Configuration 1 with different angles at various TSR. 4
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Fig. 11. Ct for the conventional rotor and Configuration 1 with different angles at various TSR.
Fig. 9. Cp for the conventional rotor and Configuration 2 with different angles at various TSR.
comparison between the conventional rotor and (Configuration 1 and Configuration 2), respectively, with various blade angles. It can be clearly seen from Fig. 8 that the peak Cp for Configuration 1 is found to be 0.1885 at TSR equal to 0.5 when the angle of blade was 120°; whereas at the same TSR, the Cp is observed to be 0.1597 for the conventional rotor and 0.154, 0.153, 0.1506, and 0.147 for the rotors with inner blade angle of 180°, 160°, 100°, and 140°, respectively. Moreover, it can be observed that rotors with inner blades of 120° and 140° angles are performed better than the conventional rotor at TSRs = 0.6 and 0.7. It also can be seen from Fig. 9 that the peak value of Cp for Configuration 2 is found to be around 0.183 at TSR = 0.5 for inner blades with an angle of 120°. Moreover, the rotor with inner blades of 120° angle performed better than the conventional rotor at TSRs = 0.5, 0.6, and 0.7. The Cp comparison between Configuration 1 and 2 is indicated in Fig. 10. It was observed from the figure that Configuration 1 with inner blade angles of 160° and 120° is performed better at most of TSR values.
Fig. 12. Ct for the conventional rotor and Configuration 2 with different angles at various TSR.
Fig. 10. Cp comparison between Configuration 1 and 2. 5
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overcome most of the negative torque compared with the conventional rotor. Velocity contours The velocity contours of four rotors (conventional, with 180° inner blade, Configurations 1 and 2 with 120° inner blade) are illustrated in Fig. 15. The 6th rotation of the rotors is selected for higher accuracy. Angles of rotation (105°, 190°, and 360°) are adopted to analyze the behaviour of velocity contours. Under the effect of the incoming air, the rotor starts spinning which will force the wind around the blades to move in a circular pattern. This circular movement around the rotor reduces the effect of the incoming air velocity on the returning blade which will reduce the resistance between the blade surface and the incoming air. The formation of wake regions on the concave part of the returning blade of the conventional rotor and rotor with 180° inner blade is found to be larger than both Configurations 1 and 2. Moreover, there is a region on the convex part of the returning blade for Configurations 1 and 2 has smaller velocity, indicating its lower negative drag as compared to the other configurations. The maximum velocity region is found to be at the tip of the rotors. Configurations 1 and 2 are found to be lesser in terms of maximum velocity region. Additionally, the overlapping flow is found to be more prominent in Configuration 1 than the other configurations.
Fig. 13. Instantaneous torque as a function of θ for Configuration 1 with different inner blade angles at TSR = 0.7.
In contrast, Configuration 2 performed better when the inner blade angle was 140° at TSRs = 0.4 and 0.5.
Ct comparison
Pressure contours
Torque coefficient (Ct) is evaluated and analyzed with respect to TSR for the conventional, Configuration 1 and Configuration 2 rotors. Figs. 11 and 12 show the Ct comparison between all the proposed configurations with various blade angles. It can be observed from both figures that the maximum value of Ct is 0.407 at the lowest considered value of TSR = 0.4 for the configuration with 180° inner blade. On the other hand, Ct values for the rotor with 120° inner blade (for both configuration) were the highest at TSRs = 0.5, 0.6 and 0.7. Moreover, the generated torque for both configurations with 160°, 140°, and 100° inner blade was less than the conventional rotor expect the rotor with 140° from Configuration 1 at TSRs = 0.6 and 0.7. It is also noticed that ω of the proposed rotors decrease with the application of load and hence, the variation of Ct decrease with the increase of TSR values. The instantaneous torque versus the azimuth position of the blade (θ) is plotted during a complete cycle from θ = 0° to θ = 360° and showed in Figs. 13 and 14 for both configurations at TSR = 0.7. The angular position where the maximum torque is generated remains essentially unmodified for all tested rotors. It can be clearly seen from the figures that the peak value of the torque is generated at the azimuth position of (θ = 105°). In contrast, the lowest torque is generated when the rotor was in apposition of (θ = 188°). Furthermore, it can be observed that the rotors with inner blades of 120° for both configurations
Pressure contours of the selected rotors in Section “Ct comparison” are shown in Fig. 16. The trend of pressure distribution for all tested rotors are almost the same, but the suction area and the magnitude of pressure for the configurations with inner blades are more extensive than the conventional Savonius rotor. Consequently, in the rotor with a 120° inner blade, the pressure difference causes additional force, and in results, an increase in Cp values occurs. The incoming airflow impacts the convex side of the returning blade and gives up its momentum to the other part of the blade, which in result raises the pressure. As the air moves along the upper side of the blade surface, the pressure goes down in that region. The flowing air with lower energy then hits the advancing blade of the rotor, which lightly raises the pressure on the concave side. The low-pressure region is found to be greater in the conventional and 180° inner blade rotors than the Configurations 1 and 2 with 120° inner blades. Moreover, the high-pressure region appears on the convex side of the returning blade and its lesser for Configurations 1 and 2 as compared to the other configurations, and as a result, the generating torque is much higher in the Configurations1 and 2. Streamlines The flow field around the selected rotors in sec 3.4 is analyzed by the streamlines. The streamlines of the selected rotors are shown in Fig. 17 at TSR = 0.7, as the vortices can be clearly seen in the vicinity of the rotor. Vortices are noted to be around the lower tip and concave side of the returning blade. In Fig. 17(c) and (d) and at θ = 105°, it can be seen the high generated vortices behind the returning blade compared to the low generated vortex in the conventional rotor (a) from Fig. 17. These vortices give more evidence that the pressure difference for the new Configurations 1 and 2 is higher than the other configurations, whereby decrease the effect of the incoming air on the returning blade which leads to decrease the resistance between the surface of the returning blade and the moving wind. The presented numerical method used to simulate the different geometries of the Savonius rotor had two limitations:
• The study uses the 2-D simulation without considering the 3-D ef-
Fig. 14. Instantaneous torque as a function of θ for Configuration 2 with different inner blade angles at TSR = 0.7.
fects such as wake effects. Although it’s generally agreed that 2D simulations can’t predict the wake effect as strong as 3D simulations,
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Fig. 15. Velocity contours of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) Configuration 1 with 120° inner blade, (d) Configuration 2 with 120° inner blade.
•
are 180°, 160°, 140°, 120°, and 100°, were adopted for both configurations. The numerical simulation was done using the k-ε/realizable turbulence model. There was a considerable enhancement in the conventional rotor performance including torque coefficient (Ct) and power coefficient (Cp) when using the inner blades. Moreover, the simulation results showed that the optimum inner blade angle is 120°. It has the highest Cp of 0.1885 at TSR = 0.5 for Configuration 1, and 0.183 at TSR = 0.5 for Configuration 2. Additionally, Configuration 1 performed better than Configuration 2 at most TSRs. The static torque was found to be positive at most of the rotor angles, for both configurations with 120° inner blade. Moreover, the maximum value of Ct was found to be 0.407 at the lowest considered value of TSR = 0.4 for the rotor with 180° inner blade. On the other hand, Ct values for the rotor with 120° inner blade (for both configuration) were found to be the highest at TSRs = 0.5, 0.6 and 0.7. Finally, it was found that inner
previous studies have shown that 2D simulation for Savonius rotor gives acceptable results. The effect of the blockage ratio (the ratio between swept area and the cross-sectional area of the wind tunnel) is neglected due to the large domain which reduces the effect of the boundaries on the output power of the turbine.
Conclusion This study aimed to investigate the performance of the Savonius wind rotor with additional inner blades in various angles and positions. Two different configurations, which are rotor with the inner blade tip parallel with rotor tip (Configuration 1) and rotor with inner blade parallel with rotor root (Configuration 2), were investigated numerically at different TSR values. Five different inner blade angles, which
Fig. 16. Pressure contours of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) configuration 1 with 120° inner blade, (d) configuration 2 with 120° inner blade. 7
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Fig. 17. Streamlines of various rotor configurations at TSR = 0.7: (a) conventional rotor, (b) rotor with 180° inner blade, (c) Configuration 1 with 120° inner blade, (d) Configuration 2 with 120° inner blade.
blade with angles of (180°, 160°, 140°, and 100°) led to decreased values of Cp.
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