#
Design and Stability Analysis of an Offshore Floating Multi-Wind Turbine Platform^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Larsen Wake Loss Model

#### 2.2. CFD Model

## 3. Results and Discussion

#### 3.1. Wake Effect Analysis

_{r}distance downstream of the first row, and the 2 turbines in the second row (T3 and T4) are placed in between the first and third row in the windward direction, whereas in the crosswind direction they are placed to avoid the wake expansion with an added 20% of the rotor diameter distance between the tip of the wake and the wind turbine rotor. The hexagon configuration is similar to the pentagon except for the two turbines (T5 and T6) in the third row instead of one. The Larsen wake loss model implemented on the three configurations using MATLAB is shown in Figure 1, Figure 2 and Figure 3.

_{r}distance downstream in the wake for the square (T3) and pentagon platform (T5) configurations are depicted in Figure 6. The velocity profile for the hexagon platform is not considered because it will be similar to the square platform as the downstream wind turbines in both cases are in the direct wake. The normalized average velocity along the radial distance for the square platform wind turbine is slightly lower relative to the pentagon platform near the center, which can correspond to the fact that the downstream wind turbine (T3 and T4) for the square platform is in direct wake, whereas for the pentagon platform (T5) it is in the partial wake. However, the normalized velocities in both cases become equal between 1 and 1.5 times the diameter distance.

^{+}is less than 1, as necessary by turbulence models [43,47,48]. To obtain the grid-independent results, different levels of grid refinements were tested in ANSYS Fluent to reach y

^{+}< 1 for all the conditions of the rotor. Figure 7 presents the mesh sensitivity study results in terms of a normalized velocity profile for turbine 5 of the pentagon platform configuration. This sensitivity study showed that mesh 2 and mesh 3 have approximately similar results and were found to have a satisfactory computational speed and accuracy, valid for all the simulated operating conditions.

^{−4}. The velocity contours of the three platform configurations are shown in Figure 9, Figure 10 and Figure 11. It can be observed that there is a velocity deficit downstream of the wind turbines in all cases which corresponds to the wind turbine wake that is surrounded by the varying turbulence intensity, as shown in Figure 12.

_{r}distance downstream for the three platform configurations (T3 for square, T5 for the pentagon and hexagon) is depicted in Figure 13. The velocity profile is approximately similar for the most part in the square and hexagon platforms as the wind turbines are in the direct wake. It can also be observed that the velocity for the pentagon configuration is slightly higher than in the other two cases, which can correlate to the values from the Larsen wake loss model shown in Figure 6.

#### 3.2. Platform Configuration

#### 3.3. Hydrostatic Analysis

^{3}. The ballast requirement is fulfilled by using the seawater filled in the platform columns.

#### 3.4. Hydrodynamic Analysis

#### 3.5. Cost Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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${\mathit{\sigma}}_{\mathit{k}}$ | ${\mathit{\sigma}}_{\mathit{\omega},1}$ | ${\mathit{\sigma}}_{\mathit{\omega},2}$ | ${\mathit{\gamma}}_{2}$ | ${\mathit{\beta}}_{2}$ | ${\mathit{\beta}}^{*}$ |
---|---|---|---|---|---|

1 | 2 | 1.17 | 0.44 | 0.083 | 0.09 |

Type | Grid Features | Mesh 1 | Mesh 2 | Mesh 3 |
---|---|---|---|---|

Square | Elements | 1,021,500 | 2,122,370 | 3,982,860 |

Global growth rate | 1.2 | 1.1 | 1.05 | |

y^{+} maximum | 0.27 | 0.21 | 0.2 | |

Skewness maximum | 0.8 | 0.73 | 0.72 | |

Pentagon | Elements | 1,050,600 | 2,150,730 | 4,050,340 |

Global growth rate | 1.2 | 1.1 | 1.05 | |

y^{+} maximum | 0.27 | 0.21 | 0.2 | |

Skewness maximum | 0.8 | 0.73 | 0.72 | |

Hexagon | Elements | 1,065,000 | 2,163,740 | 4,122,610 |

Global growth rate | 1.2 | 1.1 | 1.05 | |

y^{+} maximum | 0.27 | 0.21 | 0.2 | |

Skewness maximum | 0.8 | 0.73 | 0.72 |

Larsen Wake Loss Model | CFD | ||
---|---|---|---|

Square | Maximum | 1 | 0.99 |

Minimum | 0.54 | 0.51 | |

Mean | 0.77 | 0.74 | |

Pentagon | Maximum | 1 | 0.99 |

Minimum | 0.56 | 0.58 | |

Mean | 0.79 | 0.77 | |

Hexagon | Maximum | 1 | 0.97 |

Minimum | 0.54 | 0.53 | |

Mean | 0.77 | 0.72 |

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

Power | 8 MW |

Rotor diameter | 164 m |

Hub height | 110 m |

Nominal rotor speed | 10.5 rpm |

Cut-in, rated, and cut-out wind speed | 4, 12.5, and 25 m/s |

Total wind turbine mass | 1,038,000 kg |

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

Water depth | 250 m |

Platform draft | 15 m |

Freeboard | 15 m |

Platform mass | 16,081,370 kg |

Platform roll inertia | 5.027 × 10^{11} kg.m^{2} |

Platform pitch inertia | 3.277 × 10^{11} kg.m^{2} |

Platform yaw inertia | 8.284 × 10^{11} kg.m^{2} |

Number of mooring lines | 4 |

Mooring line length | 600 m |

Parameter | X | Y | Z |
---|---|---|---|

Center of gravity above the keel | 0 m | 0 m | 15 m |

Center of buoyancy above the keel | 0 m | 0 m | 7 m |

Center of flotation above the keel | −5 m | 0 m | 15 m |

Other Properties | |||

Longitudinal metacentric height | 23.5 m | ||

Transverse metacentric height | 23.5 m | ||

Volumetric displacement | 34,620.45 m^{3} | ||

Cut waterplane area | 534 m^{2} | ||

Principal second-moment area | X: 10,433,353 m^{4} | Y: 1,955,0784 m^{4} |

Variable | Value |
---|---|

Heave (Z) | 5.36 × 10^{3} kN/m |

Roll (RX) | 3.38 × 10^{6} kN.m/° |

Pitch (RY) | 1.78 × 10^{6} kN.m/° |

Variable | Value |
---|---|

Surge | 3.2 × 10^{7} kg |

Sway | 2.3 × 10^{7} kg |

Heave | 3.6 × 10^{7} kg |

Roll | 2.2 × 10^{10} kg.m^{2} |

Pitch | 1.1 × 10^{10} kg.m^{2} |

Yaw | 2.6 × 10^{10} kg.m^{2} |

Mode | Type | Angular Frequency (rad/s) |
---|---|---|

I | Heave | 0.28 |

II | Pitch | 0.34 |

III | Roll | 0.35 |

Variable | Value |
---|---|

${P}_{R}$ | 8 MW |

${C}_{MW}$ | USD1,300,000/MW |

${M}_{P}$ | 16,081 tons |

${C}_{S}$ | USD600/ton |

${N}_{M}$ | 4 |

${L}_{M}$ | 600 m |

${m}_{l}$ | 120 kg/m |

${c}_{m}$ | USD3/kg |

${C}_{Install}$ | USD290,000/MW |

${C}_{transport}$ | USD140,000/MW |

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**MDPI and ACS Style**

Bashetty, S.; Ozcelik, S.
Design and Stability Analysis of an Offshore Floating Multi-Wind Turbine Platform. *Inventions* **2022**, *7*, 58.
https://doi.org/10.3390/inventions7030058

**AMA Style**

Bashetty S, Ozcelik S.
Design and Stability Analysis of an Offshore Floating Multi-Wind Turbine Platform. *Inventions*. 2022; 7(3):58.
https://doi.org/10.3390/inventions7030058

**Chicago/Turabian Style**

Bashetty, Srikanth, and Selahattin Ozcelik.
2022. "Design and Stability Analysis of an Offshore Floating Multi-Wind Turbine Platform" *Inventions* 7, no. 3: 58.
https://doi.org/10.3390/inventions7030058