# On the Performance of a Modified Triple Stack Blade Savonius Wind Turbine as a Function of Geometrical Parameters

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## Abstract

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## 1. Introduction

## 2. Problem Description

## 3. Numerical Method

**C section**in Figure 2) includes the rotor and its surrounding space, which has a constant rotational speed proportional to the inlet wind velocity and the velocity of the blade tip. The second set (see

**B section**in Figure 2) has no rotational speed and its grid depends strongly on the

**C section**. The third set (see

**A section**in Figure 2) also has no rotational speed and only has an inlet wind velocity.

## 4. Governing Equations

#### 4.1. Continuity

#### 4.2. Momentum

_{t}is the turbulent viscosity. To calculate the turbulence viscosity for turbulent models such as k-ɛ, two additional equations must be solved. These two equations show how to calculate the turbulent kinetic energy, k, and turbulent dissipation rate, ɛ.

## 5. Results and Discussion

#### 5.1. Grid Independence and Validation Analyses

_{Wind}= 5 m/s for different angles of attack in the laboratory are shown and compared with the presented numerical results in Figure 5.

#### 5.2. Impact of Adding Secondary Blades to the Main Blades

#### 5.3. Impact of the Distance between the Main and Secondary Blades

_{Wind}= 3, 4, 5, and 6 m/s (Figure 12). The addition of a blade within the turbine rotor increases the area under the output torque diagram, and consequently, produced power (torque). This performance improvement was achieved at all four studied wind velocities. At V

_{Wind}= 3 m/s and an angle of zero degrees, the output torque improved by about 66%. At a 30-degree angle, the output torque improves by about 70%. At 60 degrees, the torque decreases by about 47%. At a 90-degree angle with the added blade, the torque increases from 0.001 to 0.0462. At a wind velocity of V

_{Wind}= 4 m/s and an angle of zero degrees, the torque rises from about 0.0048 to 0.055. Output torque improvement percentages of 29%, 5.0%, and 320% are obtained at an angle of 30 degrees, 60 degrees, and 90 degrees, respectively. At a wind velocity of V

_{Wind}= 5 m/s and an angle of zero degrees, the output torque increased from about 0.009 to 0.088, and at an angle of 30 degrees, an improvement of about 33% was achieved. However, at a 60-degree angle, the values vary, and with the secondary blade, the output torque decreases by almost 125%. For a 90-degree angle, nearly 550 percent improvement was achieved. Additional torque increased by about ten times at a wind velocity of V

_{Wind}= 6 m/s and an angle of zero degrees. At an angle of 30 degrees, the output torque improved by about 17%. The result was reversed at an angle of 60 degrees, and the torque was reduced by about 71%. At a 90-degree angle, about 98% improvement was seen in the output torque.

#### 5.4. Impact of Adding Secondary Blades with Slots in the Centerline of the Main Blades

_{Wind}= 3, 4, 5, and 6 m/s. Furthermore, the produced torque versus various models and wind velocities are depicted in Figure 13. Accordingly, it can be seen that among the range of the considered wind velocities V

_{Wind}= 3–6 m/s, the maximum produced torque of case V

_{Wind}= 6 m/s is the highest in all studied cases and the lowest one belongs to V

_{Wind}= 3 m/s. Contours of velocity magnitude and pressure for two different cases including with and without slots and various angles of attack at V

_{Wind}= 5 m/s, h = 6 mm, and d = 16 mm are illustrated in Figure 14.

#### 5.5. Impact of the Angular Position (β) of the Secondary Blades and Slots

_{Wind}= 3 m/s, as the slots and secondary blade angular position (β) increase from 50 to 130 degrees (160% growth), the maximum and minimum produced torques belong to cases β = 130 degrees (at α = 90 degrees) and β = 90 degrees (at α = 90 degrees), respectively. In addition, at V

_{wind}= 3 m/s, the maximum produced torque in the case β = 130 degrees is 42.11 and 107.7% more than the maximum produced torques in cases β = 110 and 70 degrees, respectively. Furthermore, according to Figure 18b, at V

_{wind}= 4 m/s, by increasing the secondary blade’s angular position by 160% from β = 50 degrees, the cases β = 130 degrees (at α = 90 degrees) and β = 90 degrees (at α = 30 degrees) show the highest and lowest produced torques, respectively. At V

_{wind}= 4 m/s, the maximum produced torque in case β = 130 degrees is 350 and 260% more than the maximum produced torques in cases β = 110 and 70 degrees, respectively (Figure 18b). In addition, at V

_{wind}= 5 m/s, 160% growth in the slots and secondary blade’s angular position (β = 50 to 130 degrees) cause the cases β = 130 degrees (at α = 0 degree) and β = 90 degrees (at α = 90 degrees) to present maximum and minimum produced torques, respectively. Moreover, at V

_{wind}= 5 m/s, the maximum produced torque in the case β = 130 degrees is 86.67 and 600% more than the maximum produced torques in cases β = 70 and 110 degrees, respectively (Figure 18c). In addition, at V

_{wind}= 6 m/s, 160% growth in the secondary blade’s angular position (β = 50 to 130 degrees) causes the cases β = 130 degrees (at α = 90 degrees) and β = 90 degrees (at α = 90 degrees) to present maximum and minimum produced torques, respectively, Moreover, at V

_{wind}= 6 m/s, the maximum produced torque in the case β = 130 degrees is 525% more than the maximum produced torques in the case β = 70 degrees and the difference between cases β = 70 and 110 degrees is very minor (Figure 18d).

#### 5.6. Impact of the Secondary Blade’s Profile (Secondary Blade’s Radius (R))

_{Wind}= 3 m/s, as the secondary blade’s radius increases from R = 25 to 43 mm (72% growth), the maximum and minimum produced torques belong to cases R = 43 mm (at α = 0 degree) and R = 25 mm (at α = 90 degrees), respectively. Moreover, at V

_{Wind}= 3 m/s, the maximum produced torque of case R = 43 mm is 1863 and 137.3% more than the maximum produced torques at R = 25 and 34 mm, respectively. Furthermore, according to Figure 21b, at V

_{wind}= 4 m/s, increasing the secondary blade’s radius by 72% from the cases R = 43 mm (at α = 90 degrees) and R = 25 mm (at α = 30 degrees) show the highest and lowest produced torques, respectively. Thus, at V

_{Wind}= 4 m/s, the maximum produced torque in case R = 43 mm is 416.6 and 23.17% more than the maximum produced torques in cases R = 25 and 34 mm, respectively (Figure 21b). Furthermore, at V

_{Wind}= 5 m/s, 72% growth in the secondary blade’s radius (R = 25 to 43 mm) causes the cases R = 43 mm (at α = 0 degree) and R = 25 mm (at α = 60 degrees) to present maximum and minimum produced torques, respectively, Moreover, at V

_{Wind}= 5 m/s, the maximum produced torque of case R = 43 mm is 384.61 and 45% more than the maximum produced torques of cases R = 25 and 34 mm, respectively (Figure 21c). Furthermore, at V

_{Wind}= 6 m/s, 72% growth in the secondary blade’s radius (R = 25 to 43 mm) causes the cases R = 43 mm (at α = 0 degree) and R = 25 mm (at α = 60 degrees) to present maximum and minimum produced torques, respectively, Moreover, at V

_{Wind}= 6 m/s, the maximum produced torque in case R = 43 mm is 384.61 and 45% more than the maximum produced torques of cases R = 25 and 34 mm, respectively (Figure 21d).

## 6. Conclusions and Future Scope

- A 50 mm-diameter simple triple-blade Savonius turbine with a wind velocity of 5 m/s was tested at various wind velocities of 3, 4, and 6 m/s. The results show that as the wind velocity increases, the output torque improves.
- For a wind velocity of 5 m/s, the maximum output torque, unlike the simple triple-blade Savonius rotor obtained at 30 and 60 degrees, was obtained at zero and 90 degrees. Furthermore, the results showed that the best performance of the turbine was achieved when the secondary blade was located at a distance of 6 mm.
- The output torque curve and the numerical results show that the area below the output torque diagram increased and turbine performance was enhanced despite the secondary blade. For example, at a velocity of 5 m/s and an angle of zero degrees, the output torque increased from about 0.009 to 0.088 Nm, and at an angle of 30 degrees, an improvement of about 33% was achieved. However, at 60 degrees, the values are different, and despite the secondary blade, the output torque decreases by nearly 125%. For a 90-degree angle, about 550% improvement was achieved.
- Due to the best position and the distance between the main and the auxiliary blade, which is equal to 6 mm, the effects of a slot on the main blade with different values of d = 4, 8, 12, and 16 mm to varying velocities of 3 to 6 m/s were investigated. The results showed that with increasing the width of the slot on the main blade from d = 4 mm to 16 mm, the output torque also increased. However, this increase has a positive effect only at a 90-degree angle.
- The best output torque curve is related to the effect of creating a slot on the main blade with a slot width of 16 mm and at different wind velocities of 3 to 6 m/s; a simple triple-blade Savonius rotor and a triple-blade Savonius rotor with the secondary blade were compared at four angles. The results showed that by creating a slot on the main blade, the surface below the output torque diagram is not improved, and creating a slot on the main blade reduces the performance of the turbine rotor.
- The output torque at the angle β = 130 degrees is higher than other angles. After that, the maximum torque is obtained at angles of β = 110 degrees, β = 70 degrees, and β = 50 degrees, respectively.
- By increasing the radius of the additional blade from R = 25 mm to 43 mm, the torque is improved, and the area below the output torque curve is increased.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**3D schematic of investigated models of modified triple-blade Savonius wind turbines including (

**a**) simple triple-blade Savonius wind turbine, (

**b**) triple-blade Savonius wind turbine with the secondary blades, (

**c**) triple-blade Savonius wind turbine with secondary blades and slots, and (

**d**) computational domains (2D) with geometrical parameters.

**Figure 5.**Results of the validation analysis and comparison between the present numerical results and experimental results of Ali’s work [21] at V

_{Wind}= 5 m/s; (

**a**) static torque coefficient value and (

**b**) torque value.

**Figure 7.**The velocity contours and velocity vector of the simple triple-blade rotor at wind velocity of 5 m/s for (

**a**) α = 0 degrees, (

**b**) α = 30 degrees, (

**c**) α = 60 degrees, and (

**d**) α = 90 degrees.

**Figure 8.**The produced torque versus various angles of attack for the case with secondary blades at h = 6 mm.

**Figure 9.**Contours of velocity magnitude and pressure for two different cases and various angles of attack at V = 5 m/s and h = 6 mm.

**Figure 10.**Influence of the slot between the main and additional (secondary) blades (h) on the produced torque at a constant wind velocity of 5 m/s.

**Figure 11.**Contours of velocity magnitude and pressure for various models at V = 5 m/s and α = 90 degrees.

**Figure 12.**The produced torque versus different angles of attack for the cases with and without secondary blades at (

**a**) V

_{Wind}= 3 m/s, (

**b**) V

_{Wind}= 4 m/s, (

**c**) V

_{Wind}= 5 m/s, and (

**d**) V

_{Wind}= 6 m/s; h = 6 mm.

**Figure 13.**The produced torque versus different angle of attack for various cases at (

**a**) V = 3 m/s, (

**b**) V = 4 m/s, (

**c**) V = 5 m/s, and (

**d**) V = 6 m/s; h = 6 mm and d = 16 mm.

**Figure 14.**Contours of velocity magnitude and pressure for two different cases including with and without slots and various angles of attack at V = 5 m/s, h = 6 mm, and d = 16 mm.

**Figure 15.**The produced torque versus different angles of attack and wind velocities for (

**a**) d = 4 mm, (

**b**) d = 8 mm, (

**c**) d = 12 mm, and (

**d**) d = 16 mm at h = 6 mm.

**Figure 16.**Torque curve: The effect of slot’s width on the output torque of Savinus turbine equipped with secondary blades and slots on the main blades; (

**a**) V

_{Wind}= 3 m/s, (

**b**) V

_{Wind}= 4 m/s, (

**c**) V

_{Wind}= 5 m/s, and (

**d**) V

_{Wind}= 6 m/s.

**Figure 17.**Studied geometry of the computational domain with various profiles of the secondary blade (angular position) at h = 6 mm and d = 4 mm.

**Figure 18.**The produced torque versus different angles of attack for various secondary blade angular positions at (

**a**) V = 3 m/s, (

**b**) V = 4 m/s, (

**c**) V = 5 m/s, and (

**d**) V = 6 m/s; h = 6 mm, and d = 4 mm.

**Figure 19.**Contours of velocity magnitude and pressure for two different angular positions of the secondary blades and slots and various angles of attack at V = 5 m/s, h = 6 mm, and d = 4 mm.

**Figure 20.**Studied geometry of the computational domain with various profiles of the secondary blades at β = 90 degrees, h = 6 mm, and d = 4 mm.

**Figure 21.**The produced torque versus different angles of attack for various secondary blade radiuses (R) at (

**a**) V = 3 m/s, (

**b**) V = 4 m/s, (

**c**) V = 5 m/s, and (

**d**) V = 6 m/s; h = 6 mm and d = 4 mm.

**Figure 22.**Contours of velocity magnitude and pressure for two different secondary blade’s radiuses and various angles of attack at V = 5 m/s, h = 6 mm, and d = 4 mm.

Parameters | Value | |
---|---|---|

Length of the computational domain | L | 1700 mm |

Width of the computational domain | W | 1000 mm |

Inlet velocity of the wind | V | 3-4-5-6 m/s |

The rotation angle of blades | α | 0-30-60-90 degrees |

Angular velocity | $\mathsf{\omega}$ | 16-32-44-52 rad/s |

Diameter of rotating area | ${\mathrm{D}}_{\mathrm{o}}$ | 210 mm |

The outer diameter of the main blades | D | 100 mm |

The outer radius of the main blades | R | 50 mm |

The outer radius of secondary blades | r | 25 mm |

Thickness of blades | t | 1 mm |

Distance between the two blades | h | 6-12-18-24 mm |

Width of the slot | d | 4-8-12-16 mm |

**Table 2.**The torque values and static torque coefficient values of the experimental work [21] and the present study.

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## Share and Cite

**MDPI and ACS Style**

Norouztabar, R.; Mousavi Ajarostaghi, S.S.; Mousavi, S.S.; Nejat, P.; Rahimian Koloor, S.S.; Eldessouki, M.
On the Performance of a Modified Triple Stack Blade Savonius Wind Turbine as a Function of Geometrical Parameters. *Sustainability* **2022**, *14*, 9816.
https://doi.org/10.3390/su14169816

**AMA Style**

Norouztabar R, Mousavi Ajarostaghi SS, Mousavi SS, Nejat P, Rahimian Koloor SS, Eldessouki M.
On the Performance of a Modified Triple Stack Blade Savonius Wind Turbine as a Function of Geometrical Parameters. *Sustainability*. 2022; 14(16):9816.
https://doi.org/10.3390/su14169816

**Chicago/Turabian Style**

Norouztabar, Reza, Seyed Soheil Mousavi Ajarostaghi, Seyed Sina Mousavi, Payam Nejat, Seyed Saeid Rahimian Koloor, and Mohamed Eldessouki.
2022. "On the Performance of a Modified Triple Stack Blade Savonius Wind Turbine as a Function of Geometrical Parameters" *Sustainability* 14, no. 16: 9816.
https://doi.org/10.3390/su14169816