# Savonius Wind Turbine Numerical Parametric Analysis Using Space-Filling Design and Gaussian Stochastic Process

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Performance of the Savonius Wind Turbine

_{m}and C

_{p}, respectively. These coefficients were obtained from the ratios between the actual parameter over the theoretical parameter. Two of the important parameters are the moment and the power coefficients [34]. The moment coefficient is quantified using Equation (1) while the power coefficient is determined using Equation (2).

^{2}, M represents the rotor moment in N-mm, ${P}_{w}$ indicates the extracted power in W, V depicts the air velocity in m/s, r shows the radius of the rotor in m, $\rho $ covers the density of air in kg/m

^{3}, and λ denotes the tip-speed ratio. Barlow et al. [35] described the model frontal area of the turbine concerning the cross-sectional area of the air domain as shown in Equation (3).

^{2}and $\u03f5$ represents the percent blockage ratio.

## 3. Methodology

#### 3.1. Computational Fluid Dynamics

#### 3.1.1. Simulation Set-Up

^{−6}was used with a maximum of 1000 iterations per simulation run. Figure 3 shows the separated cell zone of the simulation in a section view.

#### 3.1.2. Evaluation of the Simulation Mesh

#### 3.2. Design of Experiments

#### 3.3. Gaussian Stochastic Process (GaSP) Model

## 4. Results and Discussion

#### 4.1. Gaussian Stochastic Process Results

#### 4.2. Static Condition Analysis

#### 4.3. Dynamic Condition Analysis

#### 4.4. Discussion on the Comparison of the Results with Other Studies

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**The profiler plot regarding the power coefficient versus the (

**a**) diameter, (

**b**) height, (

**c**) twist angle, (

**d**) moment, and (

**e**) moment coefficient.

**Figure 10.**The relationship between the static moment coefficient of the new SWT versus its angle of attack.

**Figure 11.**The relationship between the static moment coefficient of the traditional SWT wind turbine with semi-cylindrical shape versus its angle of attack.

Mesh Sizing (Relevance Center, Relevance) | Number of Nodes | Aspect Ratio | Skewness Value | Orthogonal Quality |
---|---|---|---|---|

Coarse (−100) | 29,636 | 1.942 | 0.254 | 0.844 |

Coarse (0) | 68,709 | 1.898 | 0.245 | 0.85 |

Medium (0) | 77,040 | 1.895 | 0.243 | 0.851 |

Fine (0) | 107,690 | 1.88 | 0.24 | 0.853 |

Fine (100) | 313,822 | 1.836 | 0.221 | 0.862 |

**Table 2.**Summary of the parameters used in the sphere-packing design method adopted from Lee et al. [38].

Factors | Role | Values |
---|---|---|

Rotor Diameter (m) | Continuous | 0.29 to 0.40 |

Rotor Height (m) | Continuous | 0.16 to 0.35 |

Twist Angle (degree) | Continuous | 15 to 65 |

Parameters | θ-Values |
---|---|

Rotor Diameter | 0.93 |

Rotor Height | 7.80 × 10^{−7} |

Twist Angle Moment | 0 0 |

Moment Coefficient (C_{m}) | 0.63 |

$\mathbf{Fitted}\mathbf{Mean}\left(\mathit{\mu}\right)$ | $\mathbf{Variance}\left({\mathit{\sigma}}^{2}\right)$ | Nugget |
---|---|---|

0.296 | 0.564 | 8.11 × 10^{−8} |

No. | R′ |
---|---|

1 | 1866.17 |

2 | −2635.16 |

3 | −2803.35 |

4 | 1206.91 |

5 | 4019.12 |

6 | −2056.81 |

7 | 3222.55 |

8 | 86.46 |

9 | 2043.26 |

10 | 1946.31 |

11 | 2394.82 |

12 | −4339.64 |

13 | −1982.76 |

14 | 2257.21 |

15 | 2195.78 |

16 | 183.21 |

17 | 945.57 |

18 | 1150.75 |

19 | −1056.43 |

20 | −1425.85 |

21 | 3564.55 |

22 | −1442.13 |

23 | −420.78 |

24 | −2082.96 |

25 | −64.14 |

26 | −5626.42 |

27 | −826.45 |

28 | 1014.12 |

29 | −540.61 |

30 | −793.3 |

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**MDPI and ACS Style**

Ubando, A.T.; San, R.; Cruz, J.D.P.
Savonius Wind Turbine Numerical Parametric Analysis Using Space-Filling Design and Gaussian Stochastic Process. *Wind* **2022**, *2*, 113-128.
https://doi.org/10.3390/wind2010007

**AMA Style**

Ubando AT, San R, Cruz JDP.
Savonius Wind Turbine Numerical Parametric Analysis Using Space-Filling Design and Gaussian Stochastic Process. *Wind*. 2022; 2(1):113-128.
https://doi.org/10.3390/wind2010007

**Chicago/Turabian Style**

Ubando, Aristotle T., Rathana San, and John Deric P. Cruz.
2022. "Savonius Wind Turbine Numerical Parametric Analysis Using Space-Filling Design and Gaussian Stochastic Process" *Wind* 2, no. 1: 113-128.
https://doi.org/10.3390/wind2010007