# CFD Calculations of Average Flow Parameters around the Rotor of a Savonius Wind Turbine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model of the Savonius Wind Turbine

#### 2.1. Description of the Rotor

#### 2.2. Benchmark

#### 2.3. Rotor Aerodynamic Performance

_{available}, available in the air stream flowing through the rotor cross-sectional area at the wind velocity ${V}_{\infty}$:

#### 2.4. Computational Domain and Boundary Conditions

#### 2.5. Solver Settings and Turbulence Model

#### 2.6. Mesh Convergence Study

#### 2.7. Validation

#### 2.8. Flow Parameters Averaging Method

## 3. Results

#### 3.1. Torque Coefficient and Forces Acting on the Rotor

#### 3.2. Averaged Flow Parameters

_{x}, parallel to the wind direction, and a component, V

_{y}, perpendicular, respectively. In contrast, Figure 12a,b shows the flow angle and the static pressure distribution around the rotor, respectively. The velocities in Figure 11 have been normalized by the undisturbed flow velocity ${V}_{\infty}$. This flow angle is defined as $tan{}^{-1}\left({V}_{y}/{V}_{x}\right)$ [48] and expressed in degrees. All results are compared for three tip speed ratios.

_{x}component of the flow velocity (Figure 11a), two characteristic decreases in this velocity can be seen. The first is for the windward part of the rotor, for azimuth in the range of 0 to 180 degrees, and the second is for the leeward part, for azimuth in the range of 180 to 360 degrees. Of course, the velocity drop in this second part of the rotor is greater compared to the velocity drop in the windward part. What is evident from these results, however, is that the velocity distribution is not significantly TSR-dependent. The average velocity for all tip speed ratios for the windward part of the rotor is 12.49 m/s and for the leeward part, it is equal to 8.79 m/s. It is worth emphasizing that with increasing tip speed ratio, average V

_{x}decrease, but these differences are negligible. The difference in average velocity V

_{x}for TSR = 0.75 and 1.25 is 0.08 m/s for the windward part and 0.48 for the leeward part. This is therefore a difference of less than one meter per second. This is a different tendency than in the case of the Darrieus wind turbine, for which the distribution of the average velocity V

_{x}depends quite significantly on the tip speed ratio [49,50]. In addition, unlike the Darrieus wind turbine, a significant increase in the average velocity V

_{x}can be seen near the azimuth of 180 degrees. In the case of the Darrieus wind turbine, for this azimuth and for optimal TSR, it can be seen that the local flow velocity V

_{x}reaches or slightly exceeds the wind velocity ${V}_{\infty}$ [50]. In contrast, in the case of the Savonius wind turbine, the local velocity V

_{x}can increase by up to 32% on average compared to the undisturbed flow velocity ${V}_{\infty}$. It is also interesting that the maximum value of this velocity is localized for the azimuth of 190–200 degrees. Thus, it appears already in the downwind part of the rotor. On the other hand, the area for which the velocity ratio ${V}_{x}/{V}_{\infty}$ is greater than one and extends in the azimuth range from 140 to 220 degrees. This local increase in the average speed V

_{x}up to the azimuth of about 200 degrees entails a decrease in the rotor torque coefficient (Figure 9), which for the azimuth of 172–200 degrees, depending on the tip speed ratio, reaches a minimum value.

_{x}velocity down to a negative value is visible, which means that locally, the flow velocity is opposite to the direction of the wind (In the leeward part of the rotor, a significant decrease in V

_{x}velocity down to a negative value is visible, which means that locally the flow velocity is opposite to the direction of the wind). This local velocity V

_{x}drop also significantly modifies the velocity component field V

_{y}(Figure 11b), and the static pressure field (Figure 12b). The minimum value of the velocity V

_{x}was obtained with an average of −0.73 m/s, which corresponds to an azimuth of 300 degrees and a maximum flow angle of 122 degrees on average (Figure 11b).

_{x}becomes more and more symmetric concerning the y = 0 coordinate. This is due to the weakening of the vortex flowing down from the lower blade.

## 4. Conclusions

- Aerodynamic performance, rotor power coefficient, directly depends on aerodynamic torque. The aerodynamic torque of the two-bladed rotor changes significantly with azimuth. The operation of the rotor at these tip speed ratios requires, of course, the use of a second additional rotor section with blades rotated 90 degrees relative to the first section;
- Each blade produces a positive torque in the azimuth range from 34–38 to 222–245 degrees, depending on the tip speed ratio. As the tip speed increases, the aerodynamic drag acting on the blade in the downstream part of the rotor increases;
- Contrary to the Darrieus rotor, in the case of the Savonius rotor, the tip speed ratio has little influence on the average speed distribution around the rotor. This applies to both the velocity component parallel to the direction of undisturbed flow and the perpendicular component. In the upwind part of the rotor, the average velocity parallel to the direction of undisturbed flow is on average 29% lower than in the downwind part;
- In the case of the Savonius wind turbine, an increase in the V
_{x}velocity can be observed locally in relation to the undisturbed flow velocity. Locally, the velocity component V_{x}may be as much as 32% higher when compared to the velocity V_{∞}. In addition, the maximum of the velocity component V_{x}is observed already in the leeward part of the rotor; - In the downwind part of the rotor, the flow is much more complex. Both the pressure and the flow angle reach their extreme values. On the other hand, the velocity component V
_{x}reaches a locally negative value. This is directly influenced by the geometry of the rotor and the aerodynamic performance of the rotor blades; - Negative static pressure is visible throughout the area on the downwind part of the rotor. This is another significant difference compared to Darrieus wind turbine rotor with high solidity and operating at low tip speed ratios [49];
- The influence of the tip speed ratio on the pressure distribution in the wake downstream behind the rotor is much larger than in the case of the pressure distribution around the rotor;
- As in the case of the distribution of velocity components around the rotor, the impact of the tip speed ratio on the velocity distributions in wake is definitely much smaller;
- Both the static pressure and the tip speed ratio are a function of the distance from the axis of the rotor;
- As the distance from the rotor axis increases, the velocity V
_{x}distribution becomes more symmetrical with respect to the y = 0 coordinate; and - Moving away from the rotor axis has a much greater effect on the pressure distribution than on the velocity distribution.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Flow parameters across the two sides of the interface zone: (

**a**) Velocity profiles; (

**b**) static pressure profiles.

**Figure 5.**2D mesh for two-bladed rotor: (

**a**) Mesh of the rotating domain; (

**b**) the zoom view on mesh details around the blade.

**Figure 6.**Comparison of CFD results with the experiment [10]: (

**a**) Torque coefficient; (

**b**) power coefficient.

**Figure 7.**Comparison of CFD results with numerical results from [12]: (

**a**) Torque coefficient; (

**b**) power coefficient.

**Figure 8.**Checkpoints for recording speeds and pressures: (

**a**) Points in the wake; (

**b**) points around the rotor.

**Figure 11.**Average flow parameters around the rotor: (

**a**) V

_{x}velocity component; (

**b**) V

_{y}velocity component.

**Figure 14.**Static pressure in the wake: (

**a**) Location x/R = 1 behind the rotor axis; (

**b**) location x/R = 2 behind the rotor axis.

**Figure 15.**Static pressure in the wake: (

**a**) Location x/R = 3 behind the rotor axis; (

**b**) location x/R = 4 behind the rotor axis.

**Figure 16.**Velocity components in the wake at TSR = 1.00 for four x/R locations: (

**a**) Velocity component V

_{x}; (

**b**) velocity component V

_{y}.

Parameter | Value |
---|---|

blade/bucket diameter, d [m] | 0.5 |

number of buckets, N | 2 |

diameter of the turbine, D [m] | 0.95 |

overlap ratio, OR | 0.1 |

sheet thickness, δ [m] | 0.0005 |

Name | TSR | Cells | ${\mathit{C}}_{\mathit{Q}}$ | ${\mathit{C}}_{\mathit{P}}$ | Err |
---|---|---|---|---|---|

Fine | 1 | 498,766 | 0.2815 | 0.2815 | - |

Medium | 1 | 388,328 | 0.2810 | 0.2810 | −0.16% |

Coarse | 1 | 277,898 | 0.2818 | 0.2818 | 0.11% |

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**MDPI and ACS Style**

Michna, J.; Rogowski, K. CFD Calculations of Average Flow Parameters around the Rotor of a Savonius Wind Turbine. *Energies* **2023**, *16*, 281.
https://doi.org/10.3390/en16010281

**AMA Style**

Michna J, Rogowski K. CFD Calculations of Average Flow Parameters around the Rotor of a Savonius Wind Turbine. *Energies*. 2023; 16(1):281.
https://doi.org/10.3390/en16010281

**Chicago/Turabian Style**

Michna, Jan, and Krzysztof Rogowski. 2023. "CFD Calculations of Average Flow Parameters around the Rotor of a Savonius Wind Turbine" *Energies* 16, no. 1: 281.
https://doi.org/10.3390/en16010281