# Validation of a Tool for the Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Design and Modeling of Floating Structures with a Mooring System

- Configuration 1: Radiation/diffraction without a drag element.
- Configuration 2: Radiation/diffraction with drag elements in surge, heave and pitch.

#### 2.2. Experimental Setup

#### 2.2.1. Mooring System

#### 2.2.2. Environmental Conditions

## 3. Results

#### 3.1. Quasi-Static Results

#### 3.2. Decay Test

#### 3.3. Regular Sea States

#### 3.3.1. Motion Response

#### 3.3.2. Mean Drift

#### 3.3.3. Tension Response

#### 3.3.4. Influence from Wave Height

#### 3.4. Irregular Sea States

#### 3.5. Optimized Model

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Floating Power Plant. Available online: http://www.floatingpowerplant.com/ (accessed on 5 April 2017).
- LEANCON Wave Energy. Available online: http://www.leancon.com/ (accessed on 5 April 2017).
- Wave Dragon. Available online: http://www.wavedragon.net/ (accessed on 5 April 2017).
- Cruz, J. Ocean Wave Energy: Current Status and Future Perspectives; Springer: Berlin, Germany, 2008. [Google Scholar]
- Martinelli, L.; Ruol, P.; Cortellazzo, G. On mooring design of wave energy converters: The Seabreath application. Coast. Eng. Proc.
**2012**, 1. [Google Scholar] [CrossRef] - Fitzgerald, J. Position Mooring of Wave Energy Converters. Ph.D. Thesis, Chalmers Univerisity of Technology, Goteborg, Sweden, 2009. [Google Scholar]
- Thomsen, J.; Kofoed, J.; Delaney, M.; Banfield, S. Initial Assessment of Mooring Solutions for Floating Wave Energy Converters. In Proceedings of the Twenty-Sixth (2016) International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–2 July 2016; Chung, J., Muskulus, M., Kokkinis, T., Wang, A., Eds.; International Society of Offshore & Polar Engineers: Cupertino, CA, USA, 2016; Volume 1, pp. 590–596. [Google Scholar]
- Ridge, I.; Banfield, S.; Mackay, J. Nylon fibre rope moorings for wave energy converters. In Proceedings of the OCEANS 2010, Seattle, WA, USA, 20–23 September 2010; pp. 1–10. [Google Scholar]
- Fitzgerald, J.; Bergdahl, L. Considering mooring cables for offshore wave energy converters. In Proceedings of the 7th European Wave and Tidal Energy Conference, Porto, Portugal, 11–14 September 2007. [Google Scholar]
- Det Norske Veritas (DNV). Position Mooring; DNV Offshore Standard DNV-OS-E301; DNV: Høvik, Norway, 2010. [Google Scholar]
- API. Design and Analysis of Stationkeeping Systems for Floating Structures; American Petroleum Institute API-RP-2SK; API: Washington, DC, USA, 2005. [Google Scholar]
- ISO. Stationkeeping Systems for Floating Offshore Structures and Mobile Offshore Units; ISO 19901-7:2005; ISO: Geneva, Switzerland, 2013. [Google Scholar]
- Harnois, V.; Weller, S.D.; Johanning, L.; Thies, P.R.; Le Boulluec, M.; Le Roux, D.; Soule, V.; Ohana, J. Numerical model validation for mooring systems: Method and application for wave energy converters. Renew. Energy
**2015**, 75, 869–887. [Google Scholar] [CrossRef] [Green Version] - Andersen, M.T.; Wendt, F.F.; Robertson, A.N.; Jonkman, J.M.; Hall, M. Verification and Validation of Multisegmented Mooring Capabilities in FAST v8. In Proceedings of the 26th International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–2 July 2016; International Society of Offshore and Polar Engineers: Cupertino, CA, USA, 2016. [Google Scholar]
- Wendt, F.F.; Andersen, M.T.; Robertson, A.N.; Jonkman, J.M. Verification and Validation of the New Dynamic Mooring Modules Available in FAST v8. In Proceedings of the 26th International Ocean and Polar Engineering Conference, Rhodes, Greece, 26 June–2 July 2016; International Society of Offshore and Polar Engineers: Cupertino, CA, USA, 2016. [Google Scholar]
- Oberkampf, W.L.; Trucano, T.G. Verification and validation in computational fluid dynamics. Prog. Aerosp. Sci.
**2002**, 38, 209–272. [Google Scholar] [CrossRef] - Babarit, A.; Delhommeau, G. Theoretical and numerical aspects of the open source BEM solver NEMOH. In Proceedings of the 11th European Wave and Tidal Energy Conference (EWTEC2015), Nantes, France, 6–11 September 2015. [Google Scholar]
- Orcina Ltd. Orcaflex User Manual; Orcina Ltd.: Cumbria, UK, 2013. [Google Scholar]
- Thomsen, J.; Ferri, F.; Kofoed, J. Experimental testing of moorings for large floating wave energy converters. In Progress in Renewable Energies Offshore; Soares, C., Ed.; CRC Press LLC: Boca Raton, FL, USA, 2016; pp. 703–710. [Google Scholar]
- Assessment of Mooring System for Marine Energy Converters (MECs); IEC 62600-10; International Electrotechnical Commission (IEC): Geneva, Switzerland, 2014.
- DNV. Design of Floating Wind Turbine Structures; DNV Offshore Standard DNV-OS-J103; DNV: Høvik, Norway, 2013. [Google Scholar]
- Wehmeyer, C.; Ferri, F.; Andersen, M.T.; Pedersen, R.R. Hybrid Model Representation of a TLP including flexible topsides in non-linear regular waves. Energies
**2014**, 7, 5047–5064. [Google Scholar] [CrossRef] - Hall, M.; Goupee, A. Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data. Ocean Eng.
**2015**, 104, 590–603. [Google Scholar] [CrossRef] - Subrata, K.C. Handbook of Offshore Engineering; Elsevier Science: Amsterdam, The Netherlands, 2005. [Google Scholar]
- Newman, J.T. The drift force and moment on ships in waves. J. Ship Res.
**1967**, 11, 51–60. [Google Scholar] - Ecole Centrales Nantes. Available online: http://lheea.ec-nantes.fr/doku.php/emo/nemoh/start (accessed on 5 April 2017).
- Newman, J. Second-order, slowly-varying forces on vessels in irregular waves. In Proceedings of the International Symposium on the Dynamics of Marine Vehicles and Structures in Waves, London, UK, May 1974. [Google Scholar]
- DNV. Environmental Conditions and Environmental Loads; DNV Recommended Practice DNV-RP-C205; DNV: Høvik, Norway, 2014. [Google Scholar]
- AwaSys 7. Two and Three Dimensional Wave Generation. 2016. Available online: http://www.hydrosoft.civil.aau.dk/awasys/ (accessed on 5 April 2017).
- WaveLab 3. Data Acquisition and Analysis Software. Department of Civil Engineering, Aalborg University, 2016. Available online: http://www.hydrosoft.civil.aau.dk/wavelab/ (accessed on 5 April 2017).
- OptiTrack. Motion Capture Systems. NaturalPoint, Inc., 2016. Available online: https://www.optitrack.com/ (accessed on 5 April 2017).
- Ingram, D.; Smith, G.; Bittencourt-Ferreira, C.; Smith, H. Protocols for the Equitable Assessment of Marine Energy Convertes; Technical Report; University of Edinburgh: Edinburgh, UK, 2011; ISBN 978-0-9508920-2-3. [Google Scholar]
- McCombes, T.; Johnstone, C.; Holmes, B.; Myers, L.; Bahaj, A.; Heller, V.; Kofoed, J.; Finn, J.; Bittencourt, C. Assessment of Current Practice for Tank Testing of Small Marine Energy Devices; Technical Report, EquiMar Deliverable; Aalborg University: Aalborg, Denmark, 2010. [Google Scholar]
- Bridon. Wire and Fibre Rope Solutions. 2016. Available online: http://www.bridon.com/uk/ (accessed on 5 April 2017).
- Le Mehaute, B. An introduction to Hydrodynamics and Water Waves; Springer Science & Business Media: New York, NY, USA, 1976. [Google Scholar]
- Faltinsen, O. Sea Loads on Ships and Offshore Structures; Cambridge University Press: Cambridge, UK, 1993; Volume 1. [Google Scholar]
- Lee, C.H.; Newman, J.N. WAMIT User Manual; WAMIT, Inc.: Chestnut Hill, MA, USA, 2016. [Google Scholar]

**Figure 1.**Illustration of the Floating Power Plant P60 device. The red color indicates the foundation, and the blue color indicates the floaters (power take off (PTO)).

**Figure 4.**(

**a**) Side view of the laboratory model at the prototype scale (measurement in m); (

**b**) front view of the model; (

**c**) picture of the laboratory model; (

**d**) illustration of the mesh used in the BEM code; (

**e**) simplified geometry used for the estimation of drag coefficients.

**Figure 5.**(

**a**) Illustration of the considered mooring layout. The green shapes illustrate the load cells. (

**b**) Mooring line stiffness curve determined during experiments. The values are presented at full scale.

**Figure 6.**(

**a**) Time series of segment convergence analysis with a zoom on the maximum and minimum tensions; (

**b**) error of each analysis compared to the test with the maximum segment number. Note the different y-axes.

**Figure 7.**(

**a**) Diagram of the sea states simulated in the wave basin; (

**b**) the sea states plotted against the depth condition (x-axis), wave steepness (y-axis) and application areas of wave theories as defined in [35]; (

**c**) the sea states plotted against wave force regimes as defined in [24], with D being the total width of the structure and not considering the open spaces.

**Figure 8.**Quasi-static test results for experimental (Exp.) and numerical (Num.) line tension in the starboard (

**a**) and rear (

**b**) line; (

**c**) illustration of the line layout during surge motion.

**Figure 9.**(

**a**) Free surge decay test from experiments and Configurations 1 and 2 (with and without the drag element); (

**b**) determination of linear and quadratic damping coefficients using linear regression [36]; (

**c**) heave and pitch motion during the surge decay test.

**Figure 10.**Measured and calculated motion response amplitude operators (RAOs) in surge, heave and pitch.

**Figure 12.**Direct comparison of measured and calculated tension time series for a regular sea state with $H=5.1$ m and $T=8.0$ s.

**Figure 17.**(

**a**) Decay test from experiments, the model with drag elements (Configuration 2) and the optimized model with additional linear damping; (

**b**) determination of ${p}_{1}$ and ${p}_{2}$ from the experiments, Configuration 2 and the optimized model using linear regression.

**Figure 18.**Comparison of the optimized numerical model with experimental data for all regular sea states.

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

Drag coefficient, ${C}_{d}$ | 1.35 | 1.68 | 1.25 |

Drag area, ${A}_{d}$ | 0.545 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{3}$ m${}^{2}$ | 1.92 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{3}$ m${}^{2}$ | 7.63 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ m${}^{5}$ |

Parameter | Model-Scale | Full-Scale |
---|---|---|

Structure mass, m (kg) | 22.4 | $6.0\times {10}^{6}$ |

Moment of inertia, ${I}_{xx}$ (m${}^{2}$ kg) | 1.474 | $1.645\times {10}^{9}$ |

Moment of inertia, ${I}_{yy}$ (m${}^{2}$ kg) | 2.525 | $2.819\times {10}^{9}$ |

Moment of inertia, ${I}_{zz}$ (m${}^{2}$ kg) | 3.325 | $3.712\times {10}^{9}$ |

Parameter | Model-Scale | Full-Scale |
---|---|---|

Unstretched length (m) | 0.7 | 46.1 |

Nominal diameter d (m) | 0.01 | 0.6 |

Mass (kg/m) | 0.04 | 176.0 |

Number of segments n (-) | 15 | |

Segment length (m) | - | 3 |

Drag coefficients (axial/normal) (-) | 0.0/1.6 | |

Inertia coefficients (axial/normal) (-) | 0.0/1.0 |

**Table 4.**Measured and calculated natural frequency, linear and quadratic damping in surge, together with the relative error.

Parameter | Experiment | Num.: Config 1 | Num.: Config 2 |
---|---|---|---|

Value/Relative Error | Value/Relative Error | ||

Natural surge frequency, ${f}_{n}$ | 0.0305 Hz | 0.0284 Hz/6.9% | 0.0293 Hz/3.9% |

Linear damping, ${p}_{1}$ | 0.0164 s${}^{-1}$ | 0.0004 s${}^{-1}$/97.6% | 0.0004 s${}^{-1}$/97.6% |

Quadratic damping, ${p}_{2}$ | 0.0519 m${}^{-1}$ | 0.0024 m${}^{-1}$/95.4% | 0.0378 m${}^{-1}$/27.2% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Thomsen, J.B.; Ferri, F.; Kofoed, J.P.
Validation of a Tool for the Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters. *J. Mar. Sci. Eng.* **2017**, *5*, 45.
https://doi.org/10.3390/jmse5040045

**AMA Style**

Thomsen JB, Ferri F, Kofoed JP.
Validation of a Tool for the Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters. *Journal of Marine Science and Engineering*. 2017; 5(4):45.
https://doi.org/10.3390/jmse5040045

**Chicago/Turabian Style**

Thomsen, Jonas Bjerg, Francesco Ferri, and Jens Peter Kofoed.
2017. "Validation of a Tool for the Initial Dynamic Design of Mooring Systems for Large Floating Wave Energy Converters" *Journal of Marine Science and Engineering* 5, no. 4: 45.
https://doi.org/10.3390/jmse5040045