# Seakeeping Tests of a FOWT in Wind and Waves: An Analysis of Dynamic Coupling Effects and Their Impact on the Predictions of Pitch Motion Response

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. FOWT Geometry and Mooring System

^{®}[21].

#### 2.2. Experimental Setup

^{®}optical tracking system with cameras positioned above the model in the instrumentation bridge. Four stationary infrared cameras were used to track a set of six passive markers attached to the model structure. The redundancy of cameras and markers was used to provide accuracy and reliability for the motion measurements, with residual measurement for each marker being less than 1.0 mm. The sampling frequency adopted during the measurements was 100 Hz.

#### 2.3. Wind Force Emulation Using a Software-in-the-Loop (SIL) Scheme

#### 2.4. Wind Actuator

#### 2.5. Wind Turbine Characterization

#### 2.6. Numerical Model

^{®}[25]. Hull geometry and mass/inertia matrix were pre-computed using Edtools

^{®}through parametric structure modeling [26]. In the numerical mesh, hull columns were represented by high-order surfaces with panel size 5, while the heave plates were modeled using dipole panels (zero-thickness). Figure 10 brings the panels limits adopted for the WAMIT

^{®}mesh. The mass/inertia matrix adopted for the analysis of the FOWT in even-keel configuration (no ballast shift) is presented in Equation (1) (in ton and m). As discussed in Section 3, a second numerical model was constructed, considering a heeled mesh, as presented in Figure 11, and with a similar correction of the ballast mass made in the physical model. In addition, the linearized external mooring stiffness was taken into account considering the six dof, with the stiffness matrix computed by means of the analytical formulation proposed in [27]. As shown in Section 3, the mooring system stiffness dependency on both the floater mean position and the mean attitude of the platform (trim/heel) had to be considered for a proper modeling of the motions. Finally, the viscous effects arising from both hydrodynamic and aerodynamic loads were included in an external linearized damping matrix, whose calibration will be discussed ahead.

^{®}model (further details in Section 3.2).

## 3. Results and Discussion

#### 3.1. Decay Tests

^{®}with added mass matrix obtained from WAMIT

^{®}.

^{®}model with the adjusted mooring stiffness (from 62 kN/m to 56 kN/m) predicts the physical model response quite well. In Figure 13, it is notable how the mean offset and attitude of the system change the stiffness coefficients, with the offset, being the principal reason for period changing. In turn, changes in the mooring stiffness or phase shifts of the rotor loads do not seem to explain the reduction observed for the pitch period and further investigation on this issue is needed.

#### 3.2. Responses in Waves

^{®}model.

^{®}. By modeling the structure with Morison’s elements and linearizing the quadratic drag force with the statistical linearization approach discussed in [32], a preliminary quantification of this damping coefficient was made, apparently with good results. However, this procedure still requires a thorough validation and thus these results will not be used here. Finally, following the formulation presented in Section 2.6, a proper calibration of the aerodynamic damping coefficients was made. For that, the computed value of ${B}_{Wind}=\phantom{\rule{4pt}{0ex}}84$ kN/(m/s) was considered based on the rotor dimensions and the mean wind speed of 11.6 m/s; Then, with the hub height $L=88.56$ m, the damping coupling terms for surge-pitch were defined as ${B}_{ext51}={B}_{Wind}L\phantom{\rule{4pt}{0ex}}=\phantom{\rule{4pt}{0ex}}7.3\times {10}^{3}$ kN s and ${B}_{ext55}={B}_{Wind}{L}^{2}=6.4\times {10}^{5}$ kNm s. In turn, the heave-pitch coupling was empirically defined as ${B}_{ext53}=5.1\times {10}^{3}$ kN s. Figure 18 brings the final calibration of the numerical pitch RAOs, now taking into account these external damping coefficients. Even though some discrepancies still persist for wave periods above 20 s, the predicted amplitudes are now much closer than the ones obtained with the initial version of the numerical model whose calibration was made exclusively based on no wind conditions.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Details of the Jappaku Floating Offshore Wind Turbine (FOWT): (

**a**) concept for the full scale and (

**b**) model scale (1:80).

**Figure 14.**Concomitant effects of wind and waves on the RAO at different wind velocities (without TA): (

**a**) heave and (

**b**) pitch. The dashed lines represent the experimental natural periods from Table 5.

**Figure 15.**Concomitant effects of wind and waves on the RAO with and without TA: (

**a**) ${v}_{w}=7.8$ m/s and (

**b**) ${v}_{w}=11.6$ m/s. The dashed lines represent the experimental natural periods from Table 5.

**Figure 16.**Numerical and experimental RAO for concomitant wind and waves for ${v}_{w}=11.6$ m/s (without TA): (

**a**) heave and (

**b**) pitch. The dashed lines represent the experimental natural periods from Table 5.

**Figure 18.**Final numerical model calibration versus experimental data (without TA). The dashed lines represent the experimental natural periods from Table 5.

Full Scale | Model Scale (1:80) | |
---|---|---|

Diameter of center column | 15 m | 187.5 mm |

Diameter of side columns | 9 m | 112.5 mm |

Draft | 20 m | 250 mm |

Heave plate width | 4 m | 50 mm |

Diameter of central column heave plate | 25 m | 312.5 mm |

Diameter of side columns heave plate | 19 m | 237.5 mm |

Mass | 6936 ton | 13.55 kg |

Displacement | 7351 ton | 14.35 kg |

CG (from bottom) | 14 m | 175 mm |

Full Scale | Model Scale (1:80) | |
---|---|---|

Anchors’ depth | 302.8 m | 3785 mm |

Anchors’ radius from center | 534.1 m | 6789 mm |

Fairleads’ depth | 20 m | 250 mm |

Fairleads’ radius | 30 m | 375 mm |

Bottom segment material | Chain | Chain |

Bottom segment length | 280 m | 3500 mm |

Bottom segment equivalent submerged weight | 9.21 kN/m | 1.44 N/m |

Upper segment material | Polyester | Polyester |

Upper segment length | 347.6 m | 4345 mm |

Upper segment equivalent submerged weight | 0.04 kN/m | 0.01 N/m |

Wind Velocity | Periods (s) | |||
---|---|---|---|---|

(m/s) | T1 | T3 | T5 | T5 * |

0 | 97.0 | 16.2 | 27.6 | 27.9 |

7.8 | 99.6 | 16.2 | 24.5 | - |

11.6 | 102.8 | 16.0 | 22.6 | 24.6 |

**Table 4.**Experimental results for mean surge and hull trim for different wind conditions with and without trim adjustment (TA).

Wind Velocity | Mean Surge | Mean Trim Angle | ||
---|---|---|---|---|

(m/s) | Without TA | With TA | Without TA | With TA |

0 | 0.0 m | 0.0 m | 0.0° | 5.0° |

7.8 | −5.1 m | −5.8 m | −4.2° | 0.5° |

11.6 | −10.3 m | −11.1 m | −9.2° | −3.9° |

Wind Velocity | T1 | T3 | T5 | |||
---|---|---|---|---|---|---|

(m/s) | Experimental | Numerical | Experimental | Numerical | Experimental | Numerical |

0 | 97.0 | 97.6 | 16.2 | 16.4 | 27.6 | 28.1 |

7.8 | 99.6 | 100.7 | 16.2 | 16.4 | 24.5 | 28.0 |

11.6 | 102.8 | 103.3 | 16.0 | 16.2 | 22.6 | 27.6 |

**Table 6.**Experimental results for surge, heave and pitch linear and quadratic, and linearized damping ratios for each wind condition.

T1 | T3 | T5 | |||||||
---|---|---|---|---|---|---|---|---|---|

Wind Velocity | Quadratic | Linear | Quadratic | Linear | Quadratic | Linear | |||

(m/s) | $\mathit{\zeta}(\%)$ | ${\mathit{B}}_{2}/\mathit{M}(\%)$ | ${\mathit{\zeta}}_{\mathit{l}}(\%)$ | $\mathit{\zeta}(\%)$ | ${\mathit{B}}_{2}/\mathit{M}(\%)$ | ${\mathit{\zeta}}_{\mathit{l}}(\%)$ | $\mathit{\zeta}(\%)$ | ${\mathit{B}}_{2}/\mathit{M}(\%)$ | ${\mathit{\zeta}}_{\mathit{l}}(\%)$ |

0 | 2.0 | 6.7 | 5.6 | 0.3 | 18.1 | 2.9 | 0.6 | 3.7 | 2.9 |

7.8 | 4.0 | 7.8 | 8.8 | 0.3 | 16.6 | 2.7 | 6.5 | 4.1 | 7.5 |

11.6 | 5.5 | 7.3 | 9.4 | 0.8 | 13.3 | 2.6 | 6.9 | 15.4 | 13.6 |

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**MDPI and ACS Style**

Amaral, G.A.; Mello, P.C.; do Carmo, L.H.S.; Alberto, I.F.; Malta, E.B.; Simos, A.N.; Franzini, G.R.; Suzuki, H.; Gonçalves, R.T.
Seakeeping Tests of a FOWT in Wind and Waves: An Analysis of Dynamic Coupling Effects and Their Impact on the Predictions of Pitch Motion Response. *J. Mar. Sci. Eng.* **2021**, *9*, 179.
https://doi.org/10.3390/jmse9020179

**AMA Style**

Amaral GA, Mello PC, do Carmo LHS, Alberto IF, Malta EB, Simos AN, Franzini GR, Suzuki H, Gonçalves RT.
Seakeeping Tests of a FOWT in Wind and Waves: An Analysis of Dynamic Coupling Effects and Their Impact on the Predictions of Pitch Motion Response. *Journal of Marine Science and Engineering*. 2021; 9(2):179.
https://doi.org/10.3390/jmse9020179

**Chicago/Turabian Style**

Amaral, Giovanni A., Pedro C. Mello, Lucas H. S. do Carmo, Izabela F. Alberto, Edgard B. Malta, Alexandre N. Simos, Guilherme R. Franzini, Hideyuki Suzuki, and Rodolfo T. Gonçalves.
2021. "Seakeeping Tests of a FOWT in Wind and Waves: An Analysis of Dynamic Coupling Effects and Their Impact on the Predictions of Pitch Motion Response" *Journal of Marine Science and Engineering* 9, no. 2: 179.
https://doi.org/10.3390/jmse9020179