# Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion

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## Abstract

**:**

## 1. Introduction

## 2. Scaled Rotor for Unsteady Aerodynamic Experiments

- The coefficient of thrust of the model rotor must be similar to the full scale reference for a range of tip speed ratios,
- The chord must be scaled by the same geometric scale factor as the diameter of the rotor,
- The twist distribution along the non-dimensional length of the model blade must be same as full scale reference,
- The axial induction factor along the non-dimensional length of the model blade must be same as the full scale reference for a range of tip speed ratios.

#### Experimental Design of Surge Motion

## 3. Numerical Methodology

#### 3.1. CFD Model

#### 3.1.1. CFD Mesh Model

#### 3.1.2. CFD Numerical Solver

#### 3.1.3. Mesh Sensitivity Study, Static Case Simulation and Validation

#### 3.1.4. CFD Model for Unsteady Experimental Scenarios

#### 3.2. LR–AeroDyn Model for Unsteady Experimental Scenario

_{α}). To calculate the total relative wind speed (V

_{rel}) normal to the rotor disc, each blade element’s structural velocity is added to the free-stream wind velocity at the rotor disc, as shown below:

_{rotor}, is the structural velocity of the blade element normal to the disc (measured positive when pointing upwind).

#### 3.3. LR–u BEM Model for Unsteady Experimental Scenario

- An improved tip-loss model which accounts for changes in tip speed ratio and changes in loss distributions in different wake states.
- An unsteady airfoil model including a modified Beddoes-Leishman model which models the unsteady circulation using the suction surface shape-dependent time constants
- A combined unsteady airfoil and stall delay model, accounting for changes in stall delay due to changes in wind and rotational velocities in real-time.
- An extension of the Gluaert correction by Buhl to the propeller and propeller-brake wake states.
- A dynamic wake model to account for the time-lag between aerodynamic forces on the rotor and wake velocities.

_{0}is the blade-specific wind speed at the blade element including relative speed due to rotor motion, $\Omega $ is the rotor rotational speed in rad/s, r is the local blade segment radius. The flow angle, $\varphi $, is the angle between the relative velocity and the normal of the rotor plane:

_{g}is the Glauert correction for high axial induction factors and C

_{l}is the coefficient of lift computed using the Du&Selig stall-delay model [20] and the shape-specific modified Beddoes-Leishman model with the angle of attack equal to the flow angle less the blade twist [21]. W

_{x}is set to 0. At every time step, for each blade element in each blade, Equations (1) and (2) are iterated until there is no change in the induced velocity vector. When the steady-state induced velocity vector is computed, it is corrected for the dynamic wake effect using the dynamic wake model [22]. The force coefficients are then recomputed to determine the unsteady forces at each blade element. The LR-uBEM model is customized and simulated for scaled rotor model unsteady simulations as per the experimental scenarios.

## 4. Results and Discussion of Unsteady Test Cases

#### 4.1. Hydrodynamic Thrust

#### 4.1.1. TSR 8.5 Scenario

#### 4.1.2. TSR 7 Scenario

#### 4.1.3. TSR 6 Scenario

#### 4.2. Hydrodynamic Torque Comparison

#### 4.3. Evaluation of Wind Turbine Operating State

## 5. Conclusions

## 6. Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Hypothetical floating wind turbine motions [1].

**Figure 2.**Scaled rotor model airfoil shapes in comparison with reference [1].

**Figure 4.**Physical scaled rotor with a rig setup (for surge motion unsteady effects) on the carriage of the towing tank.

**Figure 10.**Mesh independent study (

**a**) 0.59 million nodes with coarse mesh (

**b**) 1.65 million nodes with medium mesh size (

**c**) 2.38 million nodes with fine mesh.

**Figure 11.**CFD computational domain (

**a**) 1/3rd rotor model is swept for 360 deg with near wake domain (

**b**) the complete near wake region mesh model inside the global model.

**Figure 13.**Static state validation curves for CFD (

**a**) Comparison of thrust co-efficient (

**b**) Comparison of torque co-efficient.

**Figure 14.**TSR 8.5 Cases: (

**a**) SFA1-Low f & lower A; (

**b**) SFA2-Low f & higher A; (

**c**) SFA3-Medium f & lower A; (

**d**) SFA4-Medium f & higher A; (

**e**) SFA5-High f & lower A; (

**f**) SFA6-High f & higher A; (

**g**) Mean trust-comparison for all TSR 8.5 cases; (

**h**) Mean trust-percentage error comparison for all TSR 8.5 cases.

**Figure 15.**TSR 7 Cases: (

**a**) SFA7-Low f & lower A; (

**b**) SFA8-Low f & higher A; (

**c**) SFA9-Medium f & lower A; (

**d**) SFA10-Medium f & higher A; (

**e**) SFA11-High f & lower A; (

**f**) SFA12-High f & higher A; (

**g**) Mean trust-comparison for all TSR 7 cases; (

**h**) Mean trust-percentage error comparison for all TSR 7 cases.

**Figure 16.**TSR 6 Cases: (

**a**) SFA13-Low f & lower A; (

**b**) SFA14-Low f & higher A; (

**c**) SFA15-Medium f & lower A; (

**d**) SFA16-Medium f & higher A; (

**e**) SFA17-High f & lower A; (

**f**) SFA18-High f & higher A; (

**g**) Mean trust-comparison for all TSR 6 cases; (

**h**) Mean trust-percentage error comparison for all TSR 6 cases.

**Figure 17.**TSR 7 Cases: (

**a**) SFA7-Low f & lower A; (

**b**) SFA8-Low f & higher A; (

**c**) SFA9-Medium f & lower A; (

**d**) SFA10-Medium f & higher A; (

**e**) SFA11-High f & lower A; (

**f**) SFA12-High f & higher A; (

**g**) Mean torque-comparison for all TSR 7 cases; (

**h**) Mean torque-percentage error comparison for all TSR 7 cases.

**Figure 18.**Axial induction factor Vs Thrust/thrust co efficient [24].

**Figure 19.**Axial induction factor of element 14–17 of the scaled rotor for the SFA10 scenario with LR-AeroDyn model simulation and corresponding point wise CFD based axial induction factor comparison at 1.25 s.

**Figure 20.**SFA10 mean rotor position at the end of 6th cycle of surge motion, velocity (

**a**) Line plot; (

**b**) contour plot showing tip vertices and compressed and elongated wake in the near wake field by CFD.

**Figure 21.**SFA10 mean rotor position at the end of 6th cycle of surge motion, near wake field velocity contour plots at 0.5 m intervals from rotor plane in the rotating domain by CFD.

Element/Node | Element Center Radius (m) | Twist (^{o}) | Element Center Chord (m) | * Cross-Sectional Profile |
---|---|---|---|---|

1 | 0.023 | 13.308 | 0.028 | Cylinder |

2 | 0.044 | 13.308 | 0.031 | Cylinder |

3 | 0.066 | 13.308 | 0.033 | Cylinder |

4 | 0.093 | 13.308 | 0.036 | DU40 (SMA3540) |

5 | 0.126 | 11.48 | 0.037 | DU35 (SMA3540) |

6 | 0.158 | 10.162 | 0.035 | DU35 (SMA3540) |

7 | 0.191 | 9.011 | 0.034 | DU30 (SMA2130) |

8 | 0.223 | 7.795 | 0.032 | DU25 (SMA2130) |

9 | 0.256 | 6.544 | 0.03 | DU25 (SMA2130) |

10 | 0.288 | 5.361 | 0.028 | DU21 (SMA2130) |

11 | 0.321 | 4.188 | 0.026 | DU21 (SMA2130) |

12 | 0.354 | 3.125 | 0.024 | NACA64 (SMA64) |

13 | 0.386 | 2.319 | 0.022 | NACA64 (SMA64) |

14 | 0.419 | 1.526 | 0.02 | NACA64 (SMA64) |

15 | 0.446 | 0.863 | 0.018 | NACA64 (SMA64) |

16 | 0.467 | 0.37 | 0.017 | NACA64 (SMA64) |

17 | 0.489 | 0.106 | 0.011 | NACA64 (SMA64) |

Tow Speed (m/s) | TSR | Rotational Speed (rad/s) |
---|---|---|

1.000 | 3.000 | 6 |

0.931 | 4.500 | 9 |

1.000 | 7.000 | 14 |

0.822 | 8.519 | 14 |

0.735 | 9.522 | 14 |

**Table 3.**Unsteady experimental test case scenarios chosen for numerical validation at the rotor rotational speed of 14 rad/sec.

TSR | Tow Speed, m/s | Surge Frequency (f), rad/s | Amplitude(A), M | Scenario Name for Reference |
---|---|---|---|---|

8.5 | 0.824 | 1.12 (0.18 Hz) | 0.0238 | SFA1 |

1.12 (0.18 Hz) | 0.1190 | SFA2 | ||

3.37 (0.54 Hz) | 0.0238 | SFA3 | ||

3.37 (0.54 Hz) | 0.1190 | SFA4 | ||

5.61 (0.89 Hz) | 0.0238 | SFA5 | ||

5.61 (0.89 Hz) | 0.0952 | SFA6 | ||

7.0 | 1.000 | 1.12 (0.18 Hz) | 0.0238 | SFA7 |

1.12 (0.18 Hz) | 0.1190 | SFA8 | ||

3.37(0.54 Hz) | 0.0238 | SFA9 | ||

3.37 (0.54 Hz) | 0.1190 | SFA10 | ||

5.61 (0.89 Hz) | 0.0238 | SFA11 | ||

5.61 (0.89 Hz) | 0.0952 | SFA12 | ||

6.0 | 1.167 | 1.12 (0.18 Hz) | 0.0238 | SFA13 |

1.12 (0.18 Hz) | 0.1190 | SFA14 | ||

3.37 (0.54 Hz) | 0.0238 | SFA15 | ||

3.37 (0.54 Hz) | 0.1190 | SFA16 | ||

5.61 (0.89 Hz) | 0.0238 | SFA17 | ||

5.61 (0.89 Hz) | 0.0714 | SFA18 |

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## Share and Cite

**MDPI and ACS Style**

Sivalingam, K.; Martin, S.; Singapore Wala, A.A.
Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion. *Energies* **2018**, *11*, 2578.
https://doi.org/10.3390/en11102578

**AMA Style**

Sivalingam K, Martin S, Singapore Wala AA.
Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion. *Energies*. 2018; 11(10):2578.
https://doi.org/10.3390/en11102578

**Chicago/Turabian Style**

Sivalingam, Krishnamoorthi, Steven Martin, and Abdulqadir Aziz Singapore Wala.
2018. "Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion" *Energies* 11, no. 10: 2578.
https://doi.org/10.3390/en11102578