# Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

#### 2.1. Actuator Line Model

#### 2.2. Rotating Beam Solver

_{0}, N

_{1}are the component of centrifugal force in 0 direction and 1 direction.

#### 2.3. New Elastic Actuator Line Model

#### 2.4. Computational Wind Turbine Model

## 3. Verification and Analysis

#### 3.1. Mesh Independence and Uncertainty Analysis

_{p}and thrust coefficient C

_{t}as below:

_{p}and C

_{t}can be achieved. They are 0.129% D and 0.126% D, where D is the reference data from the NREL technical report [8]. Because both of them are less than 1% D, that proves the results are credible. Through the verification above, the level 2 actuator point number will be adopted, and it will obtain reliable results.

#### 3.2. Comparison of the Power and the Thrust

#### 3.3. Comparison of the Tip Displacement

## 4. Aeroelastic Performance Analysis

#### 4.1. Influence on Aerodynamic Performance

#### 4.2. Wake Flows Analysis

## 5. Conclusions and Discussions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Relationship between actuator point number and aerodynamic coefficient, (

**a**) power coefficient, and (

**b**) thrust coefficient.

**Figure 9.**Comparison of different cases results in 8 m/s: (

**a**) power; and (

**b**) thrust Case 1: Elastic Actuator Line Model (present study); Case 2: NREL’s FAST code; Case 3: Horizontal Axis Wind turbine simulation Code 2nd generation results; Case 4: research by Li et al. [17]; Case 5: research by Jeong et al. [30]; Case 6: research by Ponta et al. [31]; Case 7: research by Yu et al. [32,33]; Case 8: research by Ma et al. [13].

**Figure 10.**Comparison of different cases results in 11.4 m/s: (

**a**) power; and (

**b**) thrust Case 1: Elastic Actuator Line Model (present study); Case 2: NREL’s FAST code; Case 3: Horizontal Axis Wind turbine simulation Code 2nd generation results; Case4: research by Li et al. [17]; Case 5: research by Jeong et al. [30]; Case 6: research by Ponta et al. [31]; Case 7: research by Yu et al. [32,33]; Case 8: research by Ma et al. [13].

**Figure 11.**Comparisons of the aerodynamic performance results between elastic actuator line model (EALM) and NREL’s FAST code at different wind speeds: (

**a**) thrust; and (

**b**) power.

**Figure 12.**Comparison of different cases tip displacement results in 8 m/s: (

**a**) 0 direction; and (

**b**) 1 direction Case 1: Elastic Actuator Line Model (present study); Case 2: NREL’s FAST code; Case 3: research by Li et al. [17]; Case 4: research by Yu et al. [32,33]; Case 5: research by Ma et al. [13].

**Figure 14.**Comparison of the tip displacement results between elastic actuator line model (EALM) and NREL’s FAST code at different wind speeds: (

**a**) in 0 direction; and (

**b**) in 1 direction.

**Figure 15.**Comparison of azimuthal variations of blade tip deformations between elastic actuator line model (EALM) and NREL’s FAST code at 8 m/s: (

**a**) in 0 direction; and (

**b**) in 1 direction.

**Figure 16.**Comparison of azimuthal variations of blade tip deformations between elastic actuator line model (EALM) and NREL’s FAST code at 11.4 m/s: (

**a**) in 0 direction; and (

**b**) in 1 direction.

**Figure 17.**Comparisons of the aerodynamic performance results between traditional actuator line model (ALM) and elastic actuator line model (EALM) at 8 m/s: (

**a**) power; and (

**b**) thrust.

**Figure 18.**Comparisons of the aerodynamic performance results between traditional actuator line model (ALM) and elastic actuator line model (EALM) at 11.4 m/s: (

**a**) power; and (

**b**) thrust.

**Figure 21.**The abbreviated sketches of blade deflection: (

**a**) front side view; (

**b**) left side view; (

**c**) vertical side view; and (

**d**) southwest isometric side view.

**Figure 22.**Comparison of downstream wind turbine aerodynamic performance results between Table 8. m/s: (

**a**) power; and (

**b**) thrust.

**Figure 23.**Stabilization of forces on downstream wind turbine blades: (

**a**) normal force; and (

**b**) tangential force.

**Figure 24.**The wake structure development of double wind turbine aligned: (

**a**) initial status without disturb; (

**b**) developing status; and (

**c**) interference status.

**Figure 25.**The wake velocity field development of double wind turbine aligned: (

**a**) initial status without disturb; (

**b**) developing status; and (

**c**) interference status.

**Table 1.**Properties of NREL 5 MW baseline wind turbine (NREL: National Renewable Energy Laboratory).

Properties | Content |
---|---|

Rotor orientation | Upwind |

Rotor configuration | Three blades |

Rotor diameter | 126 m |

Hub diameter | 3 m |

Hub height | 90 m |

Shaft tilt angle | 5° |

Rotor mass | 110,000 kg |

Rated power | 5 MW |

Rated wind speed | 11.4 m/s |

Rated rotor speed | 12.1 rpm |

Grid Level | Number of Cell | Size of Wake Region Cell (m) | C_{p} | C_{t} |
---|---|---|---|---|

1 | 0.38 M | 2.5 | 0.4678 | 0.8665 |

2 | 0.75 M | 2.0 | 0.4642 | 0.8599 |

3 | 2.90 M | 1.5 | 0.4634 | 0.8584 |

4 | 5.96 M | 1.0 | 0.4627 | 0.8572 |

Level | Actuator Point Number | C_{p} | C_{t} |
---|---|---|---|

1 | 54 | 0.4650 | 0.8608 |

2 | 72 | 0.4634 | 0.8584 |

3 | 90 | 0.4632 | 0.8580 |

**Table 4.**Comparison of the computational cost between actuator line method (ALM) and computational fluid dynamics (CFD) method.

Method | Software | Number of Cell | Simulated Time | Power |
---|---|---|---|---|

ALM | OpenFOAM | 1.49 M | 9.2 h | 5.036 MW |

CFD | Star CCM+ | 5.01 M | 82.0 h | 5.050 MW |

**Table 5.**Detailed information about the solved method on the aerodynamic performance and the structural responses in different cases.

Case Number | Aerodynamic Method | Elastic Dynamics Method | Studying Contents |
---|---|---|---|

1 | ALM | Rotating beam solver | Variation in wake flow |

2 | BEM | Modal approach | Blade response and aerodynamics |

3 | BEM | MBD | Blade response and aerodynamics |

4 | CFD | MBD | Influence of wind turbulence |

5 | BEM | Geometric nonlinearity beam model | Optimal yaw and pitch angle |

6 | BEM | Dynamic rotor deformation model | Rotor structure deformation |

7 | CFD | FEM-based CSD beam solver | Yaw and wind shear |

8 | ALM | Finite-element beam method | Wake behavior |

Case Number | 8 m/s | 11.4 m/s | ||
---|---|---|---|---|

Power (MW) | Thrust (kN) | Power (MW) | Thrust (kN) | |

1 | 1.891 | 432 | 5.024 | 772 |

2 | 1.856 | 466 | 5.000 | 817 |

3 | 1.928 | 391 | No data | No data |

4 | 1.865 | 389 | 5.407 | 759 |

5 | 2.242 | 410 | 5.249 | 645 |

6 | 1.817 | 340 | 5.130 | 659 |

7 | 2.000 | 362 | 5.334 | 671 |

8 | 1.924 | 384 | 5.350 | 663 |

**Table 7.**Comparisons of the power and the thrust relative error between elastic actuator line model (EALM) and NREL’s FAST code at different wind speeds.

Wind Speed (m/s) | Power (MW) | Error | Thrust (kN) | Error |
---|---|---|---|---|

5.0 | 0.4355 | 2.828% | 222.6153 | 15.965% |

6.0 | 0.8194 | 7.080% | 287.8339 | 13.253% |

7.0 | 1.2986 | 6.099% | 356.5589 | 10.233% |

8.0 | 1.8906 | 3.856% | 432.3593 | 7.543% |

9.0 | 2.6880 | 3.564% | 546.8937 | 5.374% |

10.0 | 3.6799 | 3.405% | 674.6184 | 2.392% |

11.4 | 5.0241 | 0.482% | 772.1718 | 3.948% |

Case Number | 8 m/s | 11.4 m/s | ||
---|---|---|---|---|

Out of Plane Tip Displacement (m) | In Plane Tip Displacement (m) | Out of Plane Tip Displacement (m) | In Plane Tip Displacement (m) | |

1 | 3.159 | −0.418 | 5.560 | −0.762 |

2 | 3.220 | −0.350 | 5.550 | −0.592 |

3 | 3.592 | −0.345 | 6.379 | −0.579 |

4 | 2.958 | No data | 4.851 | −0.624 |

5 | 3.675 | −0.298 | 6.212 | −0.584 |

**Table 9.**Comparison of the tip displacement relative errors between elastic actuator line model (EALM) and NREL’s FAST code at different wind speeds.

Wind Speed (m/s) | Out of Plane Tip Displacement (m) | Error | In Plane Tip Displacement (m) | Error |
---|---|---|---|---|

5.0 | 1.8092 | 5.340% | −0.2215 | −10.536% |

6.0 | 2.2194 | 2.598% | −0.2793 | −8.828% |

7.0 | 2.6592 | 0.345% | −0.3437 | −3.692% |

8.0 | 3.1594 | 2.090% | −0.4177 | −4.895% |

9.0 | 3.9490 | 0.596% | −0.5247 | −14.135% |

10.0 | 4.8308 | 2.069% | −0.6441 | −20.776% |

11.4 | 5.5591 | 2.545% | −0.7616 | −3.225% |

**Table 10.**Comparison of blade tip displacement Pearson simplified correlation coefficient between elastic actuator line model (EALM) and NREL’s FAST code.

Wind Speed (m/s) | Direction | R |
---|---|---|

8.0 | 0 | 99.18% |

1 | 99.91% | |

11.4 | 0 | 99.40% |

1 | 99.97% |

**Table 11.**Comparisons of mean output power with Jha et al. [34].

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yu, Z.; Hu, Z.; Zheng, X.; Ma, Q.; Hao, H.
Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model. *Water* **2020**, *12*, 1233.
https://doi.org/10.3390/w12051233

**AMA Style**

Yu Z, Hu Z, Zheng X, Ma Q, Hao H.
Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model. *Water*. 2020; 12(5):1233.
https://doi.org/10.3390/w12051233

**Chicago/Turabian Style**

Yu, Ziying, Zhenhong Hu, Xing Zheng, Qingwei Ma, and Hongbin Hao.
2020. "Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model" *Water* 12, no. 5: 1233.
https://doi.org/10.3390/w12051233