# Hydrodynamic Analysis of a Novel Modular Floating Structure System Integrated with Floating Artificial Reefs and Wave Energy Converters

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Conceptual Design of the MFS System

- (a)
- The fixed connector (marked as f) is applied to the C3 and the C4: there is no relative movement in any direction between two adjacent modules.
- (b)
- The hinge connector (marked as h) is applied to the C2 and the C5: there is only relative pitch between two adjacent modules.
- (c)
- The hinge connector with an additional linear rotational damper (marked as H, worked as a WEC’s PTO) is applied to the C1 and the C6: There is only relative pitch between two adjacent modules, and the pitch velocity can be adjusted by the damper.

#### 2.2. Hydrodynamic Model

_{I}is the incident potential of the wave without disturbance by the floating body. ϕ

_{D}is the diffraction potential generated after the wave passes through the floating body. i (i = 1~7) denotes the number of the i-th module. j (j = 1~6) denotes the j-th modal of six degrees of freedom (6-DOF). ${u}_{i}^{j}$ denotes the complex amplitude of the i-th module in the j-th modal. ${u}_{i}^{j}$ denotes the complex amplitude of the i-th module in the j-th modal (6-DOF). ${\varphi}_{i}^{j}$ denotes the potential induced by a unit amplitude motion of the i-th module only, meanwhile other modules are regarded as fixed.

_{i,}

_{Wave}is the wave exciting force induced by scattering potential (ϕ

_{I}and ϕ

_{D}), and the radiation force is induced by the interaction radiation potential of multi-body. A

_{ij}and B

_{ij}denote added mass and radiation damping, respectively.

#### 2.3. Theoretical Basis

_{i}, C

_{i}and K

_{i}are the mass matrix, radiation damping (with certain artificial damping commonly used to compensate for viscous fluid effects), and the hydrostatic restoring matrix, respectively. X

_{i}(6-DOF) denotes the generalized displacement vector of the i-th module. F

_{i,Wave}, F

_{i,Con}, F

_{i,T}

_{lp}and F

_{i,Fender}denote the matrix of the generalized wave force, the connector force, the tension matrix of tension legs and the impact force matrix of the fender, respectively.

_{ij}denotes a topology matrix. The value of φ

_{ij}is 1 when the i-th module is connected to the j-th module, otherwise the value of φ

_{ij}is 0. K

_{cij}and δ(X

_{i}, X

_{j}) denote the connection stiffness matrix and the relative motion matrix between the i-th module and the j-th module, respectively.

_{i}denotes the elastic modulus. A

_{i}denotes the sectional area of the tension leg of the i-th module. ε

_{ij}denotes the strain of the j-th tension leg of the i-th module.

_{i,Fender}can be written as:

_{fij}(1.0 × 10

^{7}N/m) is the bottom fender linear stiffness coefficient between the i-th module and the adjacent j-th module. δx(X

_{i}, X

_{j}) is the relative bottom surge motion between the i-th module and the adjacent j-th module. If the negative relative bottom surge motion δx(X

_{i}, X

_{j}) is smaller than the module’s gap (3 m), the two adjacent modules will impact on the bottom. Then, the contact force of the bottom fender will be monitored.

#### 2.4. Estimation of the Wave Energy Output

_{Bpto}and K

_{p}denote the bending moment and the linear pitch damping, respectively.

## 3. Numerical Results

#### 3.1. Damping Effect on Wave Power Generation Performance

^{8}Nms/rad, after that, it began to gradually decrease. However, the average output power of the back-wave WEC2 was much smaller (only about 5 kW) and almost unchanged. Therefore, the optimal damping for WECs is suggested as 3 × 10

^{8}Nms/rad from the view of the largest wave energy power production, and this damping coefficient was applied for the following research.

#### 3.2. Effect of the Incident Wave Angle

#### 3.3. Effect of the Wave Period

#### 3.4. Effect of the Module Quantity

#### 3.5. Extreme Sea Conditions

## 4. Conclusions

- (1)
- The outermost floating artificial reefs with WECs showed good capacity of wave attenuation and energy conversion. The main hydrodynamic responses of the MFS system were sensitive to both the incident wave angle and the wave period. Larger incident wave angles tended to lead to the increase in both motion responses and connector forces, due to less shielding effect from the outermost artificial reef. The motion responses of the MFS system were more sensitive to long wave periods than short wave periods. In addition, the optimal PTO damping and the corresponding optimal wave period of the WEC for the MFS system were about 3 × 10
^{8}Nms/rad and 6 s, respectively. That was mainly due to the relationship between the structure dimension and the wavelength. - (2)
- More modules can provide a better shielding effect for the central module, so that the MFS system can be of better stability with expansion. The extreme connector loads did not seem significantly sensitive to the increase in the module quantity, which provided feasibility for the expansion of the MFS system with more modules. In addition, more inner modules were beneficial for improving the performance of the WECs to some degree.
- (3)
- A survival strategy of the MFS system with inner hinge connectors was proposed for reducing extreme connector loads, especially for the bending moment (My) and the shear force (Fz). The extreme connector Fz and My could be efficiently reduced by about 50 and 95%, respectively. Both the heave and the pitch responses of the MFS system were limited well, due to the good performance of the tension legs. The security of the MFS system under typical extreme sea conditions was verified.

## 5. Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

DOF | Degree of freedom |

Fx | Horizontal force of connector |

Fz | Shear force of connector |

H | Wave height |

JONSWAP | Joint North Sea Wave Project |

Kp | Damping coefficient |

MFS | Modular floating structure |

My | Pitch bending moment of connector |

PTO | Power take-off |

T | Wave period |

TLP | Tension-leg platform |

WEC | Wave energy converter |

VLFS | Very large floating structure |

θ | Incident wave angle |

## References

- Strain, E.M.A.; Alexander, K.A.; Kienker, S.; Morris, R.; Jarvis, R.; Coleman, R.; Bollard, B.; Firth, L.B.; Knights, A.M.; Grabowski, J.H.; et al. Urban blue: A global analysis of the factors shaping people’s perceptions of the marine environment and ecological engineering in harbours. Sci. Total Environ.
**2019**, 658, 1293–1305. [Google Scholar] [CrossRef] - Wang, C.M.; Watanabe, E.; Utsunomiya, T. Very Large Floating Structures; Taylor and Francis: Abingdon, UK, 2014. [Google Scholar]
- Flikkema, M.; Waals, O. Space@ Sea the floating solution. Front. Mar. Sci.
**2019**, 6, 553. [Google Scholar] [CrossRef] - Koekoek, M. Connecting Modular Floating Structures; Gemeente: Rotterdam, The Netherlands, 2010. [Google Scholar]
- Drummen, I.; Olbert, G. Conceptual design of a modular floating multi-purpose island. Front. Mar. Sci.
**2021**, 8, 615222. [Google Scholar] [CrossRef] - Souravlias, D.; Dafnomilis, I.; Ley, J.; Assbrock, G.; Duinkerken, M.B.; Negenborn, R.R.; Schott, D.L. Design framework for a modular floating container terminal. Front. Mar. Sci.
**2020**, 7, 545637. [Google Scholar] [CrossRef] - Dai, J.; Zhang, C.; Lim, H.V.; Ang, K.K.; Qian, X.; Wong, J.L.H.; Tan, S.T.; Wang, C.L. Design and construction of floating modular photovoltaic system for water reservoirs. Energy
**2020**, 191, 116549. [Google Scholar] [CrossRef] - Tseranidis, S.; Theodoridis, L.; Loukogeorgaki, E.; Angelides, D. Investigation of the condition and the behavior of a modular floating structure by harnessing monitoring data. Mar. Struct.
**2016**, 50, 224–242. [Google Scholar] [CrossRef] - Ren, N.; Wu, H.; Ma, Z.; Ou, J. Hydrodynamic analysis of a novel modular floating structure system with central tension-leg platforms. Ships Offshore Struc.
**2020**, 15, 1011–1022. [Google Scholar] [CrossRef] - Loukogeorgaki, E.; Lentsiou, E.N.; Aksel, M.; Yagci, O. Experimental investigation of the hydroelastic and the structural response of a moored pontoon-type modular floating breakwater with flexible connectors. Coast. Eng.
**2017**, 121, 240–254. [Google Scholar] [CrossRef] - Jiang, C.; El Moctar, O.; Schellin, T.E. Hydrodynamic Sensitivity of Moored and Articulated Multibody Offshore Structures in Waves. J. Mar. Sci. Eng.
**2021**, 9, 1028. [Google Scholar] [CrossRef] - Michailides, C.; Loukogeorgaki, E.; Angelides, D.C. Response analysis and optimum configuration of a modular floating structure with flexible connectors. Appl. Ocean Res.
**2013**, 43, 112–130. [Google Scholar] [CrossRef] - Jiang, D.; Tan, K.H.; Dai, J.; Ang, K.K.; Nguyen, H.P. Behavior of concrete modular multi-purpose floating structures. Ocean Eng.
**2021**, 229, 108971. [Google Scholar] [CrossRef] - Liang, N.-K.; Huang, J.-S.; Li, C.-F. A study of spar buoy floating breakwater. Ocean Eng.
**2004**, 31, 43–60. [Google Scholar] [CrossRef] - Ng, A.; Ölçer, A. A new human comfort model onboard a vessel based on Sugeno type fuzzy inference system. Ocean Eng.
**2012**, 55, 116–124. [Google Scholar] [CrossRef] - Wang, G.; Drimer, N.; Goldfeld, Y. Modular floating structures (MFS) for offshore dwelling a hydrodynamic analysis in the frequency domain. Ocean Eng.
**2020**, 216, 107996. [Google Scholar] [CrossRef] - Nguyen, H.; Wang, C.; Tay, Z.; Luong, V. Wave energy converter and large floating platform integration: A review. Ocean Eng.
**2020**, 213, 107768. [Google Scholar] [CrossRef] - Li, L.; Ruzzo, C.; Collu, M.; Gao, Y.; Failla, G.; Arena, F. Analysis of the coupled dynamic response of an offshore floating multi-purpose platform for the Blue Economy. Ocean Eng.
**2020**, 217, 107943. [Google Scholar] [CrossRef] - Cheng, Y.; Xi, C.; Dai, S.; Ji, C.; Cocard, M.; Yuan, Z.; Incecik, A. Performance characteristics and parametric analysis of a novel multi-purpose platform combining a moonpool-type floating breakwater and an array of wave energy converters. Appl. Energy
**2021**, 292, 116888. [Google Scholar] [CrossRef] - Wang, Y.; Shi, W.; Michailides, C.; Wan, L.; Kim, H.; Li, X. WEC shape effect on the motion response and power performance of a combined wind-wave energy converter. Ocean Eng.
**2022**, 250, 111038. [Google Scholar] [CrossRef] - Ren, N.; Zhang, C.; Magee, A.R.; Hellan, Ø.; Dai, J.; Ang, K.K. Hydrodynamic analysis of a modular multi-purpose floating structure system with different outermost connector types. Ocean Eng.
**2019**, 176, 158–168. [Google Scholar] [CrossRef] - Nguyen, H.; Wang, C.; Flocard, F.; Pedroso, D. Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment. Appl. Ocean Res.
**2019**, 84, 302–316. [Google Scholar] [CrossRef] - Cheng, Y.; Xi, C.; Dai, S.; Ji, C.; Collu, M.; Li, M.; Yuan, Z.; Incecik, A. Wave energy extraction and hydroelastic response reduction of modular floating breakwaters as array wave energy converters integrated into a very large floating structure. Appl. Energy
**2022**, 306, 117953. [Google Scholar] [CrossRef] - Liang, M.; Xu, S.; Wang, X.; Ding, A. Experimental evaluation of a mooring system simplification methodology for reducing mooring lines in a VLFS model testing at a moderate water depth. Ocean Eng.
**2021**, 219, 107912. [Google Scholar] [CrossRef] - Ren, Y.; Venugopal, V.; Shi, W. Dynamic analysis of a multi-column TLP floating offshore wind turbine with tendon failure scenarios. Ocean Eng.
**2022**, 245, 110472. [Google Scholar] [CrossRef] - Shi, Q.; Zhang, H.; Xu, D.; Qi, E.; Tian, C.; Ding, J.; Wu, Y.; Lu, Y.; Li, Z. Experimental validation of network modeling method on a three-modular floating platform model. Coast. Eng.
**2018**, 137, 92–102. [Google Scholar] [CrossRef] - Ding, J.; Geng, Y.; Xu, S.; Yang, W.; Xie, Z. Experimental study on responses of an 8-module VLFS considering different encounter wave conditions. Mar. Struct.
**2021**, 78, 102959. [Google Scholar] [CrossRef] - Ren, N.; Wu, H.; Liu, K.; Zhou, D.; Ou, J. Hydrodynamic Analysis of a Modular Floating Structure with Tension-Leg Platforms and Wave Energy Converters. J. Mar. Sci. Eng.
**2021**, 9, 424. [Google Scholar] [CrossRef] - Ohkura, Y. The roles and limitations of newspapers in environmental reporting. Case study: Isahaya Bay land reclamation project issue. Mar. Pollut. Bull.
**2003**, 47, 237–245. [Google Scholar] [CrossRef] - Peduzzi, P. Sand, rarer than one thinks. Environ. Dev.
**2014**, 11, 208–218. [Google Scholar] - Lima, J.S.; Zalmon, I.R.; Love, M. Overview and trends of ecological and socioeconomic research on artificial reefs. Mar. Environ. Res.
**2019**, 145, 81–96. [Google Scholar] [CrossRef] - Wang, G.; Wan, R.; Wang, X.; Zhao, F.; Lan, X.; Cheng, H.; Tang, W.; Guan, Q. Study on the influence of cut-opening ratio, cut-opening shape, and cut-opening number on the flow field of a cubic artificial reef. Ocean Eng.
**2018**, 162, 341–352. [Google Scholar] [CrossRef] - Wang, G.; Goldfeld, Y.; Drimer, N. Expanding coastal cities–Proof of feasibility for modular floating structures (MFS). J. Clean Prod.
**2019**, 222, 520–538. [Google Scholar] [CrossRef] - Abrams, M. Building cities on the sea. Mech. Eng.
**2020**, 142, 42–47. [Google Scholar] [CrossRef] - ANSYS, Inc. Aqwa User’s Manual; ANSYS, Inc.: Canonsburg, PA, USA, 2013. [Google Scholar]
- Wang, Z.; Zhou, L.; Dong, S.; Wu, L.; Li, Z.; Mou, L.; Wang, A. Wind wave characteristics and engineering environment of the South China Sea. J. Ocean Univ. China
**2014**, 13, 893–900. [Google Scholar] [CrossRef] - Faraci, C.; Musumeci, R.E.; Marino, M.; Ruggeri, A.; Carlo, L.; Jensen, B.; Foti, E.; Barbaro, G.; Elsaßer, B. Wave- and current-dominated combined orthogonal flows over fixed rough beds. Cont. Shelf Res.
**2021**, 220, 104403. [Google Scholar] [CrossRef]

**Figure 2.**The sketch of three connector types: (

**a**) fixed connector; (

**b**) hinge connector; (

**c**) hinge connector with a pitch damper.

**Figure 4.**Effect of the Kp on WECs’ performance: (

**a**) pitch bending moment; (

**b**) pitch; (

**c**) average output power.

**Figure 5.**Comparison of main motion responses of each module under different incident wave angles: (

**a**) surge; (

**b**) sway; (

**c**) heave; (

**d**) pitch.

**Figure 6.**Comparison of main connector forces of each connector under different incident wave angles: (

**a**) horizontal force; (

**b**) vertical force; (

**c**) shear force; (

**d**) pitch bending moment.

**Figure 7.**Effects of incident wave directions on WECs’ performance: (

**a**) pitch; (

**b**) average output power.

**Figure 8.**Main motion responses of each hexagonal module versus wave periods: (

**a**) surge; (

**b**) heave; (

**c**) pitch.

**Figure 9.**Main connector forces of each connector versus wave periods: (

**a**) horizontal force; (

**b**) shear force; (

**c**) pitch bending moment.

**Figure 11.**Main motion responses of the first head-wave hexagonal module under different layouts: (

**a**) surge; (

**b**) heave.

**Figure 12.**Main loads of the first connector between adjacent hexagonal modules in head sea under different layouts: (

**a**) horizontal force; (

**b**) shear force.

**Figure 13.**WEC performance in head sea under different layouts: (

**a**) pitch bending moment of C1; (

**b**) average output power of WEC1.

Parameters | Value | Units |
---|---|---|

Hexagonal floating structure | ||

Side length; height; height of mass center | 20; 12; −5 | m |

water depth; draft | 80; 10 | m |

Mass; displacement | 6000; 10,650 | t |

Ixx = Iyy; Izz | 9.6 × 10^{8}; 1.2 × 10^{9} | kg·m^{2} |

Tension-leg dimension | D = 1.2; T = 0.04; L = 70 | m |

Steel tension leg E | 2.1 × 10^{11} | N/m^{2} |

Stiffness of fenders | 1.0 × 10^{7} | N/m |

Floating artificial reef | ||

Dimension; reef wall spacing | 15 × 20 × 11; 1 | m |

draft; height of mass center | 10; −5 | m |

Mass = displacement | 800.5 | t |

Ixx; Iyy; Izz | 1.2 × 10^{8}; 9.8 × 10^{7}; 1.0 × 10^{8} | kg·m^{2} |

Adjacent distance | 3 | m |

Porosity | 20% |

Number | Structural Layout | Connector Types |
---|---|---|

Case 1 | H-h-f-f-h-H | |

Case 2 | h-f-f-h | |

Case 3 | H-h-h-H | |

Case 4 | H-H |

Surge (m) | Heave (m) | Pitch (°) | Ft (MN) | Fx (MN) | Fz (MN) | My (MNm) | Power (kW) | |
---|---|---|---|---|---|---|---|---|

H-h-f-f-h-H | (Case 1) | |||||||

Max. | 0.936 (M2~M5) | 0.0076 (M2) | 0.015 (M2) | 14.194 (M2) | 16.000 (C2) | 5.845 (C3) | 239.696 (C4) | 607.224 (WEC1) |

Mean | 0.221 | - | 0.004 | 11.309 | 3.139 | 1.154 | 48.672 | 38.214 |

STD | 0.164 | 0.0018 | 0.0028 | 1.0967 | 2.356 | 0.830 | 34.867 | 53.957 |

H-h-h-h-h-H | (new) | |||||||

Max. | 0.937 (M2~M5) | 0.0084 (M2) | 0.016 (M3) | 14.121 (M2) | 15.538 (C2) | 2.722 (C2) | 13.433 (C1) | 608.775 (WEC1) |

Mean | 0.222 | - | 0.004 | 11.307 | 3.143 | 0.552 | 2.715 | 38.206 |

STD | 0.166 | 0.0014 | 0.0033 | 1.065 | 2.359 | 0.413 | 2.021 | 53.973 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, Y.; Ren, N.; Li, X.; Ou, J.
Hydrodynamic Analysis of a Novel Modular Floating Structure System Integrated with Floating Artificial Reefs and Wave Energy Converters. *J. Mar. Sci. Eng.* **2022**, *10*, 1091.
https://doi.org/10.3390/jmse10081091

**AMA Style**

Li Y, Ren N, Li X, Ou J.
Hydrodynamic Analysis of a Novel Modular Floating Structure System Integrated with Floating Artificial Reefs and Wave Energy Converters. *Journal of Marine Science and Engineering*. 2022; 10(8):1091.
https://doi.org/10.3390/jmse10081091

**Chicago/Turabian Style**

Li, Yanwei, Nianxin Ren, Xiang Li, and Jinping Ou.
2022. "Hydrodynamic Analysis of a Novel Modular Floating Structure System Integrated with Floating Artificial Reefs and Wave Energy Converters" *Journal of Marine Science and Engineering* 10, no. 8: 1091.
https://doi.org/10.3390/jmse10081091