# Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes

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## Abstract

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## 1. Introduction

- We propose a novel wind turbine layout approach incorporating small wind turbines into wind farm units while focusing on large wind turbines. This approach considers the mutual interactions between large and small wind turbines in a combined arrangement.
- Regarding sensor placement, an equal number of measurement points were evenly distributed at three heights: the upper blade tip, hub center, and lower blade tip. The impact of small wind turbines at various heights was analyzed from multiple perspectives, contributing to a better understanding of the vertical wake distribution within the wind farm.
- This study employed a comprehensive multi-parameter analysis for the data collected in the experiment. It considered wind speed and included factors such as turbulence integral scale and power spectral density. The study quantified the contribution of vortex motion to wake turbulence energy, providing a more detailed description of wake characteristics. This approach facilitates a comprehensive understanding of the wake evolution process.

## 2. Experimental Setup

#### 2.1. Introduction of Experimental Equipment

#### 2.2. Experimental Inlet Air Condition and Working Condition Setting

_{0}and C

_{3}, were selected, due to their clear patterns.

#### 2.3. Uncertainty Analysis of Experimental Data

_{T}), turbulence integral length (Λ), and assessing their uncertainties [41].

_{T}, and Λ at the rated wind speed were calculated using the following formulas for the corresponding Tip–Speed Ratio (TSR = 5.7), ensuring that they were each less than or equal to 1.0%, 0.7%, and 3.1%, as follows:

## 3. Results and Discussion

#### 3.1. Horizontal Direction

#### 3.1.1. Characteristics of the Spreading Wake

#### 3.1.2. Characteristics of the Turbulent Intensity Distribution in the Wake Field

_{w}is the probability condition of the top wake, D is the wind turbine diameter, v is the mean wind speed, and σ is the standard deviation of the wind speed. I

_{T}is the turbulence intensity of the free flow; I

_{T,W}is the turbulence intensity of the wake effect; and m is the Waller contrast index of the material of the structural member under consideration. The generation of flow turbulence by the wind turbine wake shear layer, ambient boundary layer turbulence, and blade tip vortex shedding from the wind turbine blades are all related phenomena.

_{0}condition (as shown in Figure 5b,c,f), the introduction of small wind turbines results in a substantial increase in turbulence intensity in the peripheral inflow to the wind turbine rotor region. The increase is approximately 35% of the incoming turbulence intensity. This suggests that the wind turbine rotor tips may experience more significant dynamic loading, consequently increasing the fluctuation in torque at the turbine input.

#### 3.1.3. Turbulence Integration Scale

#### 3.1.4. Effect of Small Wind Turbines on Wind Speed at Different Heights

_{hub}= 0.4, Z/Z

_{hub}= 1, and Z/Z

_{hub}= 1.6). In Figure 8, the vertical coordinates represent the relative positions of the wind turbine in the spreading direction, while the horizontal coordinates represent the average axial velocities, with the dashed line indicating the position of the tip of the wind turbine impeller of the large wind turbine.

#### 3.1.5. Power Spectrum Density

#### 3.2. Vertical Direction

#### 3.2.1. Vertical Wake Characteristics

#### 3.2.2. Analysis of Working Conditions

_{0}and C

_{3}, were studied to investigate the wake recovery under these two scenarios. The analysis focused on the wind profiles and turbulence intensity to understand the wake recovery in these conditions.

_{0}scenario, in the overlapping region, the C

_{3}scenario experiences a velocity deficit of approximately 20% due to the combined tip effects of the large and small wind turbines. However, as the measurement point moves beyond the upper tip height of the small wind turbines, wind speed gradually recovers. Under the C

_{3}scenario, there is an overall increase in wind speed of approximately 5%. Therefore, adding small wind turbines in the downstream direction is more favorable for enhancing wind speed.

#### 3.2.3. Turbulence Intensity

_{3}scenario to the C

_{0}scenario, in the wind turbine wake region, the impact of the small wind turbines results in an approximate 10% increase in turbulence intensity in the immediate wake region behind the small wind turbines (Figure 13a). In the measurement point between the small wind turbines (Figure 13b), turbulence intensity increases somewhat, with approximately 7% enhancement. Therefore, the adding of small wind turbines in the wind farm positively enhances turbulence intensity.

#### 3.2.4. Vertical Power Spectrum Analysis

## 4. Conclusions

- (1)
- Introducing a small wind turbine downstream of the giant wind turbine significantly reduces wake velocity, with a wind speed deficit of approximately 22%. This effect varies at different heights, with the impact of the small wind turbine becoming more pronounced from the upper to lower positions of the giant wind turbine blades.
- (2)
- After work is conducted on the wind turbine rotor, the incoming wind causes structural damage to its flow. The extent of this damage is less pronounced in the far wake region, but the addition of the small wind turbine has a notable impact on the turbulence integral scale in the far wake. Under the C
_{3}condition, the turbulence critical scale increases by 2% compared to the C_{0}condition. - (3)
- In the vertical direction, the influence of the operation of the small wind turbine on the wind speed deficit increases gradually from the near wake region to the far wake region, reaching a wind speed deficit of approximately 20% at the 7D position. Simultaneously, a positive impact is observed on the outer region of the small wind turbine rotor, particularly under the C
_{3}condition, where the wind speed at this position increases by 3%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

D | large wind turbine wheel diameter D (mm) |

d | diameter of small wind turbine wheel d (mm) |

h | small wind turbine hub height h (mm) |

I_{u} | turbulence intensity |

Λ | turbulent integral length |

V_{hub} | hub height inflow wind speed (m/s) |

Z_{hub} | hub height of large wind turbines |

τ | time interval |

V | average flow velocity |

u | instantaneous wind speed |

T | turbulent integration time |

I_{T} | free-flow turbulence intensity |

I_{T,W} | turbulent intensity of wake effect |

m | waller’s Comparison Index |

N | number of wind turbines |

P_{w} | probability conditions |

X_{i} | distance from wind turbine |

σ | standard deviation |

C_{0} | All three rows of small wind turbines are not running |

C_{1} | Small wind turbines in 3D position operating |

C_{2} | Small wind turbines running in 3D and 5D positions |

C_{3} | Small wind turbines running in 3D, 5D, and 7D positions |

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**Figure 1.**(

**a**) Photographs of the entrance to the experimental section of the wind tunnel and the model wind turbine; (

**b**) schematic diagram of the experimental wind turbine and the arrangement of measurement points, where the point (x, y) = (0, 0) is the origin of the coordinate system.

**Figure 3.**Time domain wind speed distribution in the wake area for different working conditions. (

**a**–

**c**), (

**d**–

**f**), and (

**g**–

**i**) denote the time-domain wind speeds at positions 3, 5, and 7D for the three working conditions of C

_{1}, C

_{2}, and C

_{3}, respectively.

**Figure 4.**Wind speed deficit under different working conditions. (

**a**–

**d**) indicate the four working conditions C

_{0}–C

_{3}, respectively.

**Figure 5.**Time domain distribution of horizontal turbulence intensity. (

**a**–

**c**), (

**d**–

**f**), and (

**g**–

**i**) denote the turbulence intensity in the time domain at positions 3, 5, and 7D for C

_{1}, C

_{2}, and C

_{3}, respectively.

**Figure 9.**Power spectrum density at different height positions of large wind turbines, (

**a**–

**c**) are upper blade tip heights, (

**d**–

**f**) are hub center heights, and (

**g**–

**i**) are lower blade tip height positions.

**Figure 13.**Power spectrum analysis at hub center position: (

**a**,

**b**) are the operating conditions without small wind turbines; (

**c**,

**d**) are the operating conditions with three rows of small wind turbines.

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

Large wind turbine wheel diameter D (mm) | 1000 |

Large wind turbine hub height Z_{hub} (mm) | 1200 |

Diameter of small wind turbine wheel d (mm) | 340 |

Small wind turbine hub height h (mm) | 300 |

Inlet wind speed (m/s) | 7 |

Working Condition | Code | Small Wind Turbine Position |
---|---|---|

Case0 | C_{0} | All three rows of small wind turbines are not running |

Case1 | C_{1} | Small wind turbines in 3D position operating |

Case2 | C_{2} | Small wind turbines running in 3D and 5D positions |

Case3 | C_{3} | Small wind turbines running in 3D, 5D and 7D position |

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## Share and Cite

**MDPI and ACS Style**

Zhang, L.; Feng, Z.; Zhao, Y.; Xu, X.; Feng, J.; Ren, H.; Zhang, B.; Tian, W.
Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes. *J. Mar. Sci. Eng.* **2024**, *12*, 434.
https://doi.org/10.3390/jmse12030434

**AMA Style**

Zhang L, Feng Z, Zhao Y, Xu X, Feng J, Ren H, Zhang B, Tian W.
Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes. *Journal of Marine Science and Engineering*. 2024; 12(3):434.
https://doi.org/10.3390/jmse12030434

**Chicago/Turabian Style**

Zhang, Lidong, Zhengcong Feng, Yuze Zhao, Xiandong Xu, Jiangzhe Feng, Huaihui Ren, Bo Zhang, and Wenxin Tian.
2024. "Experimental Study of Wake Evolution under Vertical Staggered Arrangement of Wind Turbines of Different Sizes" *Journal of Marine Science and Engineering* 12, no. 3: 434.
https://doi.org/10.3390/jmse12030434