# Hydrodynamic Response of a Combined Wind–Wave Marine Energy Structure

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background Used for the Development of the Numerical Mode

#### 2.1. Potential Flow Theory

#### 2.2. Viscous Load Modeling

#### 2.2.1. Morison Equation (Cylinders of the Semisubmersible Platform)

_{d}represents the drag force coefficient. In the paper, C

_{d}= 1.2 is selected due to H/d ≤ 0.2 and d/L ≥ 0.2; H, d and L represent wave height, water depth and wave length, respectively; μ, D, and $\rho $ are the incoming flow velocity, structure diameter and fluid density, respectively; and f

_{d}represents drag force on a unit height of the structure.

#### 2.2.2. Heave Mode Viscous Load Effects on the WEC

_{33}, m

_{33}and K

_{33}represent the mass, added mass at heave natural frequency and hydrostatic stiffness coefficient of the WEC in the heave direction and their values are 540.982 t, 422.3 t and 1515.4 kN/m, respectively; F

^{viscous}, D

^{critical}and η are the viscous force, the critical damping and damping coefficient based on the viscous effects of the heave mode of the WEC. Based on the reference [24], a damping coefficient of 6–10% in heave direction is recommended using experimental study for different cylindrical semisubmersible platforms. Therefore, 8% of damping coefficient for WEC in heave direction is used in our simulation.

#### 2.3. Equation of Motion of the Combined Structure

_{ij}is the restoring coefficient matrix; ${f}^{wind}(t)$ and ${f}^{wave}(t)$ represent wind loads on the rotor and wave forces, respectively; ${f}_{1}^{viscous}(t)$ is the viscous force based on Morison equation applied on the semisubmersible and ${f}_{2}^{viscous}(t)$ is the viscous load applied on the WEC (Equation (21)); ${f}^{interface}(t)$ is the interface forces between the semisubmersible platform and the WEC including horizontal contact forces and vertical friction forces; and ${F}^{PTO}$ represents the PTO force.

## 3. Characteristics of the Combined Structure

#### 3.1. Design Parameters of the 5-MW Semisubmersible Wind Turbine and of the WEC

#### 3.2. Power-Take-Off (PTO) System

_{PTO}) and linear springs (K

_{PTO}) and is modeled with the use of corresponding fender features in ANSYS/AQWA (Figure 2).

_{PTO}and K

_{PTO}are the linear damping stiffness coefficient and the linear spring stiffness coefficient, respectively.

## 4. Results and Discussion

#### 4.1. Model Parameters Best Selection

#### 4.1.1. Preliminary Determination of Structural Design Parameters of the WEC

_{h}and G represent the PTO produced power, horizontal contact force and WEC weight, respectively, and α and β are related to the cost and safety of the WEC. With the comparison of different parameters with various groups (α = 0.4, β = 0.6; α = 0.3, β = 0.7; α = 0.2, β = 0.8), it is found that the best selection will be achieved when the outer diameter is 16 m. In this paper, we assume that cost reduction (related to β) is more important and the safety is less important (related to α) for the combined structure. Therefore, α = 0.3, β = 0.7 is assumed in this study.

#### 4.1.2. Determination of Rational B_{PTO} and K_{PTO} Parameters

_{PTO}= 2000 kNs/m, K

_{PTO}= 100 N/m was arbitrary selected) on the PTO produced power has been investigated under regular waves with wave height 2 m. The values of produced power are shown in Figure 5. It indicates that there is a maximum produced power when the wave period is around 9 s because the WEC was designed to have a natural period in heave around 7–2 s.

_{PTO}and K

_{PTO}parameters can significantly affect the dynamic responses of the combined structure. To illustrate mutual effects of linear damping and stiffness coefficients on the PTO produced power of the WEC, different B

_{PTO}and K

_{PTO}values are simulated with wave height 2 m and wave period 9 s. The results of produced power are shown in Figure 6; it can be seen that the value of produced power will be the largest when the B

_{PTO}coefficient is 1500 kNs/m with an invariable K

_{PTO}. The value of produced power increases when the B

_{PTO}is smaller than 1500 kNs/m, while the values will decrease when the B

_{PTO}is larger than 1500 kNs/m. Moreover, for same B

_{PTO}values, produced power decreases as K

_{PTO}increases, which is more significant when its value is over 1000 N/m. Therefore, a best B

_{PTO}coefficient of 1500 kNs/m and a K

_{PTO}coefficient of 1 N/s are selected for the rest of the paper, respectively.

#### 4.2. Viscous Effects on the Heave Motion of the WEC

#### 4.3. The Hydrodynamic Coupling Effect on the Combined Structure

#### 4.4. Dynamic Responses of the Combined Structure under Different Type Environmental Conditions

#### 4.4.1. Regular Waves

#### 4.4.2. Irregular Wave and Wind Conditions

_{s}= 2 m, T

_{p}= 9 s) and LC2 (H

_{s}= 2 m, T

_{p}= 9 s and U

_{wind}= 17 m/s) are presented in Figure 15 and Figure 16, respectively. Figure 15 shows that the semisubmersible surge and pitch motions have big differences due to wind loads. However, the values of the relative heave, PTO damping force and PTO produced power have slight differences.

#### 4.5. Dynamic Responses of the Combined Structure in Extreme Sea Conditions

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Connection detail between the column of semisubmersible and the wave energy converter (WEC).

**Figure 7.**Comparison of responses of the WEC with and without viscous effects: (

**a**) relative heave; (

**b**) radiation force; (

**c**) damping force; (

**d**) produced power.

**Figure 8.**Comparison of diffraction forces and radiation forces of the combined structure between considering and without considering hydrodynamic coupling: (

**a**) diffraction forces for semisubmersible; (

**b**) radiation forces for semisubmersible; (

**c**) diffraction forces for WEC; (

**d**) radiation forces for WEC.

**Figure 9.**Comparison of responses of the combined structure between considering and without considering hydrodynamic coupling cases under different wave periods (H = 2 m): (

**a**) WEC surge; (

**b**) relative heave; (

**c**) WEC pitch; (

**d**) produced power; (

**e**) damping force.

**Figure 10.**Time series of different responses of the combined structure under regular waves H = 2 m and T = 9 s: (

**a**) relative heave velocity; (

**b**) damping force; (

**c**) produced power.

**Figure 11.**Responses of the combined structure under different wave periods with H = 2 m: (

**a**) platform surge; (

**b**) WEC heave; (

**c**) power take-off (PTO) force; (

**d**) capture with ratio.

**Figure 12.**Responses of the combined structure under different wave heights T = 9 s: (

**a**) semisubmersible surge, relative heave and semisubmersible pitch; (

**b**) horizontal contact force, damping force and produced power.

**Figure 15.**Comparisons of the time series of the responses for LC1 and LC2 of: (

**a**) semisubmersible surge; (

**b**) relative heave; (

**c**) semisubmersible pitch; (

**d**) damping force; (

**e**) produced power.

**Figure 16.**Comparisons of the PSD of the motion and dynamic responses for LC1 and LC2: (

**a**) semisubmersible surge; (

**b**) relative heave; (

**c**) semisubmersible pitch; (

**d**) horizontal contact force; (

**e**) damping force; (

**f**) produced power; (

**g**) mooring line 1 tension; (

**h**) mooring line 2 tension.

**Figure 17.**Statistical values of the responses for LC3: (

**a**) statistic of information for semisubmersible surge, relative heave and pitch; (

**b**) statistic of information for semisubmersible wave force, WEC wave force, horizontal contact force, damping force, produced power, mooring line 1 tension and mooring line 2 tension.

**Figure 18.**Power spectral density (PSD) of motion and dynamic responses for LC3: (

**a**) semisubmersible surge; (

**b**) relative heave; (

**c**) semisubmersible pitch; (

**d**) horizontal contact force; (

**e**) damping force; (

**f**) produced power; (

**g**) mooring line 1 tension; (

**h**) mooring line 2 tension.

**Figure 20.**Statistical values of the responses for the extreme sea state LC4: (

**a**) statistic of information for semisubmersible surge, heave and pitch; (

**b**) statistic of information for wave force of the combined structure, horizontal contact force, vertical contact force, mooring line 1 tension and mooring line 2 tension.

**Figure 21.**PSD of motion responses for the extreme sea state LC4: (

**a**) surge; (

**b**) heave; (

**c**) pitch; (

**d**) mooring line 1 tension; (

**e**) mooring line 2 tension.

Parameters | Values | |
---|---|---|

Wind turbine (NREL 5 MW) | Rotor-Nacelle-Assembly | 350 t |

Hub height | 90 m | |

Tower mass | 347.46 t | |

semisubmersible platform | Semisubmersible mass | 9738 t |

Diameter of the central column | 6.5 m | |

Diameter of the three side columns | 6.5 m | |

Operating draft | 30 m | |

Water displacement | 10,298 m^{3} | |

Water depth | 200 m | |

WEC device | Outer/Inner diameter | 16 m/8 m |

Height/Draft | 8 m/3.5 m | |

Mass | 463.5 t | |

Water displacement | 452.2 m^{3} | |

Center of mass | (0, 0, −1 m) |

Sea States | Wave Type | Wave Height H_{s} (m) | Wave Period T_{p} (s) | Wind Speed U_{wind} (m/s) |
---|---|---|---|---|

LC 1 | Irregular | 2.0 | 9 | 0 |

LC 2 | Irregular | 2.0 | 9 | 17 |

LC 3 | Irregular | 3.0 | 10 | 24 |

LC 4 | Irregular | 8.6 | 15 | 31.2 |

Surge | Heave | Pitch |
---|---|---|

0.07545 | 0.2543 | 0.2108 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Zhang, L.; Michailides, C.; Wan, L.; Shi, W.
Hydrodynamic Response of a Combined Wind–Wave Marine Energy Structure. *J. Mar. Sci. Eng.* **2020**, *8*, 253.
https://doi.org/10.3390/jmse8040253

**AMA Style**

Wang Y, Zhang L, Michailides C, Wan L, Shi W.
Hydrodynamic Response of a Combined Wind–Wave Marine Energy Structure. *Journal of Marine Science and Engineering*. 2020; 8(4):253.
https://doi.org/10.3390/jmse8040253

**Chicago/Turabian Style**

Wang, Yapo, Lixian Zhang, Constantine Michailides, Ling Wan, and Wei Shi.
2020. "Hydrodynamic Response of a Combined Wind–Wave Marine Energy Structure" *Journal of Marine Science and Engineering* 8, no. 4: 253.
https://doi.org/10.3390/jmse8040253