# Output Power and Wake Flow Characteristics of a Wind Turbine with Swept Blades

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^{2}

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## Abstract

**:**

## 1. Introduction

^{4}orders of magnitude in the Reynolds number. In the light of the existing time-domain results, with the decline of the Reynolds number, the output aerodynamic efficiency of the rotating wind turbine also decreases [23,24,25]. In view of the current design methods, the research on wind turbine rotors in low wind speed ranges is insufficient. Therefore, this paper investigated the performance advantages of swept blades compared with straight blades by combining numerical simulation with wind tunnel test methods. Consequently, wind farms located in regions of low wind speeds can benefit from using the design of swept blades aimed at small horizontal axis wind turbines. This study is mainly conducted on the aerodynamic and wake characteristics of wind turbines with swept blades and straight blades, especially investigating the changes in wind turbines with swept blades. Finally, the conclusion from this investigation is presented. These results may provide a reference for simulations and algorithm predictions and have a guiding significance for the promotion of swept blades in wind fields with low wind speed.

## 2. Design and Numerical Calculation of Swept Blades

#### 2.1. Preliminary Swept Blade Design

_{r}is the radial distance of the blade section, r

_{s}is the radial distance of the sweep start section, R is the rotor radius, P

_{s}is the ratio of the tip offset z to the rotor radius (P

_{s}= z/R), M is the sweep mode, P

_{r}is the ratio of the radial distance of the blade section to the blade radius (P

_{r}= r

_{r}/R), and P

_{rs}is the ratio of the radial distance of the location of sweep start to the blade radius (P

_{rs}= r

_{s}/R). The strength of the sweep M defines the strength of the sweep. Increasing the value of M would reduce the sweeping strength, while decreasing the value to close to one would increase the strength of the sweep. According to the definition from Ref. [9], when M was taken as 2, it can represent the average sweep strength. Therefore, the value was also chosen as M = 2 in this study.

#### 2.2. Numerical Calculation

_{t}is the eddy viscosity coefficient, ${\overline{u}}_{\mathrm{j}}$ is the average value of fluctuating velocity in the j direction, σ

_{k}and σ

_{ω}are the Turbulent Prandtl number of two equations, Y

_{k}and Y

_{ω}are the dissipative term of two equations, G

_{k}and G

_{ω}are used to represent the turbulence generation term, and D

_{ω}is the cross-diffusion term. For more variable meanings of Equations (2) and (3), one can refer to Refs. [29,30].

_{P}between Middle and Fine was negligible. The power coefficient of the turbine can be determined using Equation (4),

_{x}, ω

_{1}, u

_{0}are the axial torque, the angular velocity of rotation, and the mean inflow velocity at hub height, respectively. Hence, it was finally determined that the number of grids in the rotation domain was 7.82 million, and the number of grids in the stationary domain was 6.14 million, so the total number of grids was 13.96 million.

_{s}/R). The last two digits define the ratio of tip offset to the rotor radius (z/R). For example, ‘f2010’ refers to the forward swept blade whose radial distance of the location of the sweep start is 20% of the rotor radius (r

_{s}/R = 0.20), and the blade tip has an offset of 10% (z/R = 0.10).

## 3. Experimental Setup

#### 3.1. Test Setup and Test Model

#### 3.2. Experimental Procedure

## 4. Results of the Wind Turbine with Swept Blades

#### 4.1. Analysis of Power Characteristics

#### 4.2. Analysis of Wake Velocity Characteristics

_{0}. It can be seen from the figures that, owing to the rotation effect of the turbine, the wake of the wind turbines with straight blades and swept blades presented the phenomenon of velocity deficit. The streamwise time-averaged velocity distribution at different sections of the wake area basically presented a symmetrical distribution along the centerline of the rotor. As the wake continued to develop downstream, the velocity distribution gradually changed to a ‘V’ shape. At 0.5D and 1D sections in the near wake region, the minimum wake velocities at the rotor center of the wind turbine with swept blades and straight blades were nearly the same. Because of the intense development of tip vortices and central vortices in the near wake region, the radial distribution of velocities at the center height of the rotor fluctuated wildly, showing a ‘W’ distribution. Moreover, because of the tip acceleration effect, the velocities at the blade tip were high, the velocity deficit in the central vortex region was prominent, and the minimum streamwise velocities only recovered to about 18.5% and 21.7% of the incoming flow. As the position moved towards the blade tip, the wake progressively recovered. Additionally, it can be clearly seen from the figures that the wake recovery of the wind turbine with swept blades was slower than the one with straight blades, and the speed deficit of the wind turbine with swept blades at the same position was severe as well. As the wake of the wind turbine recovered, at the 2D, 3D, 5D, and 8D sections, the minimum velocity at the rotor center of the wind turbine with swept blades and straight blades recovered 29.8%, 51.1%, 59.0%, 68.7%, and 33.7%, 54.4%, 61.3%, and 70.7% of the incoming wind speed, respectively. Therefore, the wake recovery of the wind turbine with swept blades was slightly slower than that with straight blades. It is important to note that although the shape of the blades only changed near the tip position, the swept blades decreased the average wake velocities in the whole wake region. Such results indicated that the flow near the tip of the swept blade has an expansion effect along the spanwise direction. This may be due to the vortices behind the rotor pulsing dramatically, and the collision probability increasing accordingly. Hence, the wake changed in other positions.

#### 4.3. Analysis of Wake Turbulence Intensity

## 5. Conclusions

_{s}/R) as variables, the swept equation was thus determined. The simulation results show that the larger the values of the tip offset and the location of the sweep start, the smaller the power coefficients and thrust coefficients of the wind turbine. In contrast to the backward swept design, the forward swept design had a more pronounced improvement in the power characteristics of the blades. The power characteristics of the wind turbine with forward swept blades whose tip offset was 10% of the radius and the sweep start location was 20% of the radius were most significantly improved.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Pressure coefficient distribution of different sections at λ = 5. (

**a**) 35% section; (

**b**) 65% section; (

**c**) 80% section; (

**d**) 95% section.

**Figure 6.**Comparison of coefficient curves for the wind turbines with straight blades and the swept blades ‘f2010’. (

**a**) C

_{P}-λ curves; (

**b**) C

_{T}-λ curves.

**Figure 7.**Photographs of the wind turbines with different blades taken inside the wind tunnel. (

**a**) Straight blade; (

**b**) swept blade; (

**c**) blade parameters.

**Figure 11.**Wind turbine power characteristic curves at different yaw angles. (

**a**) 0°; (

**b**) 10°; (

**c**) 20°; (

**d**) 30°.

**Figure 12.**Streamwise time-averaged velocity distribution at a yaw angle of 0° when λ = 4.67. (

**a**) 0.5D; (

**b**) 1D; (

**c**) 2D; (

**d**) 3D; (

**e**) 5D; (

**f**) 8D.

**Figure 13.**Lateral time-averaged velocity distribution at a yaw angle of 20° when λ = 4.1. (

**a**) 0.5D; (

**b**) 1D; (

**c**) 2D; (

**d**) 3D; (

**e**) 5D; (

**f**) 8D.

**Figure 14.**Streamwise turbulence intensity distribution at a yaw angle of 0° when λ = 4.67. (

**a**) 0.5D; (

**b**) 1D; (

**c**) 2D; (

**d**) 3D; (

**e**) 5D; (

**f**) 8D.

**Figure 15.**Streamwise turbulence intensity distribution at a yaw angle of 20° when λ = 4.1. (

**a**) 0.5D; (

**b**) 1D; (

**c**) 2D; (

**d**) 3D; (

**e**) 5D; (

**f**) 8D.

Blade No. | Sweep Direction | Sweep Starts (r_{s}/R) | Tip Offset (z/R) |
---|---|---|---|

1 | Backward | 0.2 | 0.1 |

2 | Backward | 0.2 | 0.2 |

3 | Backward | 0.4 | 0.1 |

4 | Backward | 0.4 | 0.2 |

5 | Forward | 0.2 | 0.1 |

6 | Forward | 0.2 | 0.2 |

7 | Forward | 0.4 | 0.1 |

8 | Forward | 0.4 | 0.2 |

Rotation Domain (Million) | Stationary Domain (Million) | C_{P}(%) | |
---|---|---|---|

Coarse | 427 | 614 | 18.169 |

Middle | 782 | 614 | 18.186 |

Fine | 782 | 975 | 18.198 |

**Table 3.**Changes in power coefficients and thrust coefficients of the wind turbine with swept blades.

Blade No. | Swept Blade | ΔC_{P} (%) | ΔC_{T} (%) |
---|---|---|---|

1 | b2010 | 0.497 | 0.384 |

2 | b2020 | −1.605 | −3.113 |

3 | b4010 | −0.113 | −1.998 |

4 | b4020 | −2.433 | −5.384 |

5 | f2010 | 2.167 | 2.478 |

6 | f2020 | −1.481 | −3.064 |

7 | f4010 | 0.064 | −1.605 |

8 | f4020 | −1.998 | −4.675 |

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**MDPI and ACS Style**

Huang, X.; Yang, J.; Gao, Z.; Sha, C.; Yang, H.
Output Power and Wake Flow Characteristics of a Wind Turbine with Swept Blades. *Machines* **2022**, *10*, 876.
https://doi.org/10.3390/machines10100876

**AMA Style**

Huang X, Yang J, Gao Z, Sha C, Yang H.
Output Power and Wake Flow Characteristics of a Wind Turbine with Swept Blades. *Machines*. 2022; 10(10):876.
https://doi.org/10.3390/machines10100876

**Chicago/Turabian Style**

Huang, Xiaoxi, Junwei Yang, Zhiying Gao, Chenglong Sha, and Hua Yang.
2022. "Output Power and Wake Flow Characteristics of a Wind Turbine with Swept Blades" *Machines* 10, no. 10: 876.
https://doi.org/10.3390/machines10100876