# Numerical Investigation of the Savonius Vertical Axis Wind Turbine and Evaluation of the Effect of the Overlap Parameter in Both Horizontal and Vertical Directions on Its Performance

^{1}

^{2}

^{*}

## Abstract

**:**

_{m}and C

_{p}improvements are 16% and 7.5%, respectively, compared to the base with a zero overlap ratio.

## 1. Introduction

## 2. Subject Theory

^{2}, the thickness of the blade is considered to be 2 mm according to the validation work, and the diameter of the mid-shaft is 15 mm [23]. Simulations begin by examining horizontal overlap ratios. The overlaps of 0, ±0.1, ±0.25, and ±0.4 are investigated. Then, according to the results and values, the overlap ratios of ±0.05, ±0.15, and +0.2 are also studied to obtain the best possible ratio (Figure 5).

#### 2.1. Governing Equations and the Numerical Solution Method

_{k}is the turbulence kinetic energy generation due to the gradient of average velocity; G

_{b}is the turbulent kinetic energy generation due to the gradient of average buoyancy; and σ

_{k}, and σ

_{ε}are, respectively, the turbulent Prandtl number for k and ε equations. C

_{1}

_{ε}, C

_{2}

_{ε}, C

_{3}

_{ε}, and C

_{μ}are constants, and S

_{k}and S

_{ε}are source terms. Y

_{M}is the effect of changing the expansion in compressible turbulence to a total dissipation rate, which is defined as

_{1}is defined as

#### 2.2. Mesh and Boundary Layers

^{+}value on the rotor blades was always less than 2.5.

## 3. Results and Discussion

_{m}in the horizontal overlap state is 11.5%, and in the vertical overlap state, it is 16%, when compared to the base state with a zero overlap ratio. The improvement percentage in the average C

_{p}, however, is less pronounced. Its increment in the most optimized horizontal overlap state is 3.7%, and in the best vertical overlap state, it is 7.5%, when compared to the same base state.

## 4. Conclusions

_{m}in the horizontal overlap state, was 11.5%, and in the vertical overlap state, was 16%, when compared to the base state with zero overlap. Additionally, the improvement percentage in the average C

_{p}in the horizontal overlap state was 3.7%, and in the vertical overlap state, was 7.5%, when compared to the same base state.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

TSR (λ) [-] | Tip speed ratio |

VAWT | Vertical axis wind turbine |

CFD | Computational fluid dynamics |

U [m/s] | Free stream velocity |

A [m^{2}] | Rotor swept area (A = DH) |

C_{P} | Power coefficient |

C_{m} | Torque coefficient |

HOLR | Horizontal overlap ratio |

VOLR | Vertical overlap ratio |

D | Rotor diameter |

RANS | Reynolds Averaged Navier–Stokes |

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**Figure 1.**The variation curve of the rotor power coefficient (Cp) average to tip speed ratio (TSR) in different types of wind turbines [6].

**Figure 2.**Schematic diagram of the overlap ratio according to Roy and Saha [33].

**Figure 3.**Schematic diagram. The overlap ratio is defined separately for the horizontal and vertical position by transferring the guide point in the Cartesian coordinate in two dimensions.

**Figure 4.**Wind Atlas of Iran for a height of 50 m, 2016, which is used to determine the acceptable wind speed for simulations [34].

**Figure 6.**Triangular grid with 15 layers of inflation for a rotor with a horizontal overlap ratio (HOLR) of 0 and vertical overlap ratio (VOLR) of 0.

**Figure 7.**The mesh independency was investigated by changing the number of cells from 5400 to 730,000.

**Figure 9.**(

**a**) Torque and (

**b**) power coefficients obtained at different horizontal overlaps for a vertical overlap ratio (VOLR) of 0.

**Figure 10.**2D schematic of rotors with investigated vertical overlap ratios along the Y-axis for a constant horizontal overlap ratio (HOLR) of +0.15.

**Figure 11.**(

**a**) Torque and (

**b**) power coefficients obtained at different vertical overlap ratios along the Y-axis when the horizontal overlap ratio (HOLR) is +0.15.

**Figure 12.**Variations trend and relative improvement of (

**a**) torque and (

**b**) power coefficients in three states of zero overlap ratio, optimal overlap ratio in horizontal investigation, and overall optimal overlap ratio.

**Figure 13.**Velocity contours at different overlap ratios to display the gradient of velocity around the rotor for U = 9 m/s and the tip speed ratio (TSR) of 0.4.

**Table 1.**Comparison of the zero overlap ratio and optimal mode at horizontal and overall overlap ratios.

HOLR = 0 VOLR = 0 | HOLR = +0.15 VOLR = 0 | HOLR = +0.15 VOLR = −0.1 | % Increase with Regard to Horizontal Overlap Ratio Optimization | % with Regard to Overall Overlap Ratio Optimization | |
---|---|---|---|---|---|

Average C_{m} | 0.264 | 0.295 | 0.306 | 11.5 | 15.8 |

Average C_{p} | 0.128 | 0.133 | 0.138 | 3.7 | 7.5 |

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**MDPI and ACS Style**

Ebrahimpour, M.; Shafaghat, R.; Alamian, R.; Safdari Shadloo, M.
Numerical Investigation of the Savonius Vertical Axis Wind Turbine and Evaluation of the Effect of the Overlap Parameter in Both Horizontal and Vertical Directions on Its Performance. *Symmetry* **2019**, *11*, 821.
https://doi.org/10.3390/sym11060821

**AMA Style**

Ebrahimpour M, Shafaghat R, Alamian R, Safdari Shadloo M.
Numerical Investigation of the Savonius Vertical Axis Wind Turbine and Evaluation of the Effect of the Overlap Parameter in Both Horizontal and Vertical Directions on Its Performance. *Symmetry*. 2019; 11(6):821.
https://doi.org/10.3390/sym11060821

**Chicago/Turabian Style**

Ebrahimpour, Mohammad, Rouzbeh Shafaghat, Rezvan Alamian, and Mostafa Safdari Shadloo.
2019. "Numerical Investigation of the Savonius Vertical Axis Wind Turbine and Evaluation of the Effect of the Overlap Parameter in Both Horizontal and Vertical Directions on Its Performance" *Symmetry* 11, no. 6: 821.
https://doi.org/10.3390/sym11060821