# Preliminary Study on an Integrated System Composed of a Floating Offshore Wind Turbine and an Octagonal Fishing Cage

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structural Model

#### 2.1. Frame Structure of Fishing Cage

^{3}.

^{3}, is used in heave plates for ballast, which is added from the bottom of heave plates upwards until the mass requirement is met. The material of the fishing cage is selected as steel with an effective density of 8,500 kg/m

^{3}. The masses of the frame structure, girders and ballast are 8,264,815, 1,304,543 and 27,449,312 kg, respectively. The center of mass of the whole fishing cage is located at about 34 m below the still water level. Table 2 summarizes the structural properties of the undisplaced cage.

#### 2.2. Net System

_{n}is calculated by [5,17]:

_{w}is the diameter of twine, l

_{w}is the length of twine.

_{w}= 0.4 m is introduced, with an assumed twine length l

_{w}= 4.8 m, to obtain the same solidity ratio based on Equation (1).

#### 2.3. Mooring Line System

^{6}kN and a catalogue breaking strength of 2 × 10

^{4}kN [19]. Note that the length of 880 m is determined after some study on the mooring system of the DeepCWind semisubmersible platform at the same water depth [20]. All hydrodynamic coefficients are determined according to the chain’s nominal diameter. The drag and the added mass coefficients are assumed based on DNVOS-E301 [21]. Table 3 and Table 4 list the configurations and properties of the mooring line system, respectively. Figure 5 shows the mooring line system configuration.

#### 2.4. Wind Turbine System

^{3}, which is meant to be an increase above steel’s typical value of 7850 kg/m

^{3}, to consider paint, bolts, welds and flanges that are not included in the tower thickness data [15]. The tower radius and thickness are assumed to be linearly tapered from the tower base to the tower top.

## 3. Dynamics Modeling

#### 3.1. Aerodynamics and Structural Dynamics

**W**is the absolute wind speed,

**c**is the chord length of a blade element, $\phi $ is the inflow angle and

**r**is the local radius of a blade element.

#### 3.2. Mooring Line Dynamics

_{j}is the length of an unstretched line between the anchor and the jth node, and D

_{e}represents the local segment diameter of one line. Each line is treated as a chain of Morison elements subjected to various external forces. According to Ref. [32], the motion equation of each line element is defined as:

**T**and

**V**are the tension force and shear force vectors of the first element node, respectively; $R$ is the position vector of the first element node; S

_{e}is the length of an unstretched element;

**w**and

**F**

_{h}represent the weight and hydrodynamic load vectors per unit element length, respectively; m

_{e}is the mass per unit length;

**M**is the bending moment vector of the first element node; and

**q**is the distributed moment load per unit length.

**P**

_{bot}and

**P**

_{top}are the position vectors of attachment points, and L is the length of the unstretched line.

#### 3.3. Hydrodynamics of Aquaculture Cage

#### 3.3.1. Hydrodynamics of Cage Support Structures

#### 3.3.2. Net Hydrodynamics

_{D}, was estimated using the following equation:

_{n}is the net solidity ratio, θ is the angle between the inflow direction and the net normal.

_{D}= 0.2 is determined according to the selected solidity ratio, which is applied for the equivalent nets at both the side and bottom. Note that the possible influence of biofouling on the drag coefficient is neglected in this work, which requires more accurate biofouling hydrodynamic characteristics. This issue needs to be solved by performing experiments in the future.

## 4. Control System

_{drivetrain}is the drivetrain inertia cast to the low-speed shaft; N

_{gear}is the gearbox ratio; Ω

_{0}is the rated rotor rotational speed; P

_{0}is the rated mechanical power; ∂P/∂θ is the sensitivity of aerodynamic power to the rotor collective blade pitch angle; K

_{P}, K

_{I}and K

_{D}are the blade pitch controller proportional, integral and derivative gains, respectively; $\dot{\phi}=\Delta \mathsf{\Omega}$ is the rotor speed error.

_{φ}

_{n}and damping ratio ζ

_{φ}:

## 5. Results and Discussions

#### 5.1. Free Decay Test

#### 5.2. Uniform Wind with Regular and Irregular Waves Test

#### 5.3. Turbulent Wind and Irregular Wave Test

#### 5.3.1. Time Domain Analysis

#### 5.3.2. Frequency Domain Analysis

#### 5.4. Influence of Mooring Line Length

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of the integrated system of a floating offshore wind turbine and a fishing cage.

**Figure 3.**View of the fishing cage with key dimensions (without nets). (

**a**) ISO view; (

**b**) Top view; (

**c**) Side view.

**Figure 9.**Relationship between generator torque and generator speed for the baseline control system.

**Figure 11.**Time histories of cage motions under the uniform wind with regular waves. (

**a**) Translational motion. (

**b**) Rotational motion.

**Figure 12.**Time histories of cage motions under the uniform wind with irregular waves. (

**a**) Translational motion. (

**b**) Rotational motion.

**Figure 13.**Time histories of pitch angles and power output of the wind turbine under the uniform wind with irregular wave.

**Figure 15.**Time histories of responses of the cage and wind turbine under condition 3. (

**a**) Cage responses. (

**b**) Wind turbine responses.

**Figure 16.**Time histories of responses of the cage and wind turbine under condition 4. (

**a**) Cage responses. (

**b**) Wind turbine responses.

**Figure 17.**Statistical properties of the cage and wind turbine responses. (

**a**) Cage responses. (

**b**) Wind turbine responses.

**Figure 18.**Smoothed spectra of the cage and wind turbine responses under condition 3. (

**a**) Cage responses. (

**b**) Wind turbine responses.

**Figure 19.**Comparison of time histories of the fishing cage and wind turbine responses for three mooring line lengths under case 3. (

**a**) Cage responses. (

**b**) Wind turbine responses.

**Figure 21.**Comparison of upwind line tension at fairlead for three line lengths. (

**a**) Time histories. (

**b**) Statistics.

Property | Value |
---|---|

Total draft | 41 m |

Elevation of central column above the still water level | 10 m |

Elevation of outside columns above the still water level | 10 m |

Distance from central column centerline to outside column centerline | 50 m |

Height of central and outside columns | 45 m |

Height of heave plates | 6 m |

Diameter of each outside column with a heave plate | 12 m |

Diameter of each outside column without a heave plate | 6 m |

Diameter of heave plates | 24 m |

Diameter of central column | 6.5 m |

Diameter of bracings | 1.6 m |

Thickness of each outside column with a heave plate | 0.06 m |

Thickness of each outside column without a heave plate | 0.03 m |

Thickness of heave plates | 0.06 m |

Thickness of central column | 0.03 |

Thickness of bracings | 0.0175 m |

Property | Value |
---|---|

Frame structure, bracing, ballast mass | 8.265 × 10^{6}, 1.305 × 10^{6}, 2.745 × 10^{8} kg |

Center of mass location below the still water level, including ballast and bracings | −34.07 m |

Pitch inertia about the center of mass, including ballast and without bracings | 4.1867 × 10^{11} kg m^{2} |

Roll inertia about the center of mass, including ballast and without bracings | 4.1867 × 10^{10} kg m^{2} |

Yaw inertia about the center of mass, including ballast and without bracings | 7.5657 × 10^{10} kg m^{2} |

Configuration | Value |
---|---|

Number of mooring lines | 4 |

Angle between adjacent lines | 90° |

Water depth | 200 m |

Depth from fairlead to still water level | 35 m |

Radius from anchors to cage centerline | 891.6 m |

Radius from fairleads to cage centerline | 62 m |

Unstretched mooring line length | 880 m |

Property | Value |
---|---|

Chain type | Studless grade 4 |

Nominal diameter | 0.153 m |

Unit mass in water | 447 kg/m |

Axial stiffness | 2.1 × 10^{6} kN |

Catalogue breaking strength | 2 × 10^{4} kN |

Transversal drag coefficient | 2.4 |

Longitudinal drag coefficient | 1.15 |

Added mass coefficient | 1 |

Property | Parameter |
---|---|

Rating power | 5 MW |

Rotor orientation, Configuration | Upwind, Three Blades |

Control | Variable Speed, Collective Pitch |

Drivetrain | High Speed, Multiple-Stage Gearbox |

Rotor, Hub diameter | 126 m, 3 m |

Hub height | 90 m |

Cut-In, Rated, Cut-Out wind speed | 3, 11.4, 25 m/s |

Cut-in, Rated rotor speed | 6.9 rpm, 12.1 rpm |

Rated tip speed | 80 m/s |

Overhang, Shaft tilt, Precone | 5 m, 5°, 2.5° |

Rotor, Nacelle mass | 110,000 kg, 240,000 kg |

Property | Parameter |
---|---|

Elevation to tower base above still water level | 10 m |

Elevation to tower top above still water level | 87.6 |

Overall tower mass | 249,718 kg |

Center of mass location above still water level | 43.4 m |

Structural damping ration | 1% |

DOF | Natural Frequency (Hz) |
---|---|

Surge | 0.00667 |

Sway | 0.00667 |

Heave | 0.05111 |

Pitch | 0.05778 |

Roll | 0.05778 |

Yaw | 0.00778 |

Case | Mean Wind Speed (m/s) | Significant Wave Height (m) | Wave Peak Period (s) | Turbulence Intensity (%) | State |
---|---|---|---|---|---|

1 | 8 | 2 | 10.3 | 17 | Operating |

2 | 11.4 | 2.5 | 10.2 | 15 | Operatng |

3 | 18 | 4.1 | 10.5 | 13 | Operatng |

4 | 40 | 15.6 | 14.5 | 11 | Parked |

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## Share and Cite

**MDPI and ACS Style**

Zhang, C.; Xu, J.; Shan, J.; Liu, A.; Cui, M.; Liu, H.; Guan, C.; Xie, S.
Preliminary Study on an Integrated System Composed of a Floating Offshore Wind Turbine and an Octagonal Fishing Cage. *J. Mar. Sci. Eng.* **2022**, *10*, 1526.
https://doi.org/10.3390/jmse10101526

**AMA Style**

Zhang C, Xu J, Shan J, Liu A, Cui M, Liu H, Guan C, Xie S.
Preliminary Study on an Integrated System Composed of a Floating Offshore Wind Turbine and an Octagonal Fishing Cage. *Journal of Marine Science and Engineering*. 2022; 10(10):1526.
https://doi.org/10.3390/jmse10101526

**Chicago/Turabian Style**

Zhang, Chenglin, Jincheng Xu, Jianjun Shan, Andong Liu, Mingchao Cui, Huang Liu, Chongwu Guan, and Shuangyi Xie.
2022. "Preliminary Study on an Integrated System Composed of a Floating Offshore Wind Turbine and an Octagonal Fishing Cage" *Journal of Marine Science and Engineering* 10, no. 10: 1526.
https://doi.org/10.3390/jmse10101526