# Analysis of the Wave Attenuating and Dynamic Behaviour of a Floating Breakwater Integrating a Hydro-Pneumatic Energy Storage System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{®}AQWA™ have been promising, connoting that the addition of hydro-pneumatic energy storage to a floating breakwater will not lead to a degradation in the dynamic performance or wave breaking efficiency of the floating structure.

## 1. Introduction

## 2. Current Research and Technological Status

## 3. Proposed Concept

#### 3.1. Baseline Floating Breakwater—Model A

#### 3.2. Hybrid Floating Breakwater—Model B

#### 3.2.1. The Floating Breakwater Unit

#### 3.2.2. The Energy Storage System

## 4. Methodology

^{®}AQWA™, Version 2022 R2, were carried out for validation and repeatability purposes of the software tool. Investigations to minimize the uncertainty of results were also performed. The procedures undertaken are detailed further in Section 5.

_{o}, width B

_{o}, height Z

_{o}and wall thicknesses t

_{1}, t

_{2}and t

_{3}were obtained through an iterative, design optimization exercise. The latter procedure considered the influence of dimensional changes on the hydrostatic stability and wave breaking behaviour. Extensive details of the FBW design optimization can be found in [32]. The sizing of the floater was followed by the sizing of the ESS, or more precisely, of the PCS. The details of the PCS sizing are outlined in Section 6.1. The same section also outlines the hydrostatic check that was performed through the application of Archimedes law, to ensure that the structure was still able to float freely following the integration of the ESS, in both fully discharged and fully charged states.

^{®}AQWA™, which is used for a vast range of maritime engineering applications [33]. The potential flow theory is extensively detailed in the literature, and thus, the mathematical representation is not being repeated in the present article. The theory is available in the ANSYS

^{®}AQWA™ theory manual [33] and other open literature sources [34,35].

_{drag}is the drag load, ρ is the density of the fluid (i.e., seawater), D is the characteristic dimension of the body and C

_{d}is the drag coefficient that is typically determined from the Reynolds (Re) and Keulegan–Carpenter (KC) numbers. Moreover, α is the linearization factor, u

_{rms}is the root mean square (RMS) of the transverse directional relative velocity and u

_{f}and u

_{s}are the fluid and structure velocities, respectively. For simulations incorporating Model A, the inclusion of Equation (1) was not essential due to the system being classified as a large volume structure whereby the loads induced on the floater were identified to be inertia- and/or diffraction-dominated. Conversely, for Model B, the viscous loads on the cylindrical structures became relatively significant. Consequently, line elements with a C

_{d}of 0.65 [36] were added to the PVs within the hybrid model to correct for the shortcoming of the inviscid potential flow. The quoted value of C

_{d}was derived from computations neglecting shielding effects and in accordance with Clause 6.7 of the DNVGL-RP-C205 Standard [36].

## 5. Validation and Numerical Accuracy

^{®}AQWA™ were carried out for the validation and repeatability analyses of the software against external sources. Indeed, the box-type FBW studied in a wave flume by Cui et al. [37] was replicated in ANSYS

^{®}AQWA™ to quantify the model uncertainty. Figure 3 presents the response amplitude operators (RAOs) obtained from the source [37] with superimposed results generated by AQWA™ in the time response domain. The outcomes show good agreement between the physical testing and the potential flow solver with the average model uncertainty across the three results equating to 13.2%. The highest discrepancies are observed in heave at the range of low wavelengths and in pitch. The discrepancies could be arising from the fact that some mooring characteristics, for example, the chain diameter and steel grade, are not documented in [37] and thus had to be estimated within the present study. Furthermore, the viscous effects are more prominent on the small-scale prototypes studied in the lab. Ideally, validation of AQWA™ is performed utilizing large FBW structures. However, at the time of writing, no studies of large-scale FBWs were found publicly available. Future work should thus further validate the accuracy of the potential flow solver by implementing other numerical techniques such as Computational Fluid Dynamics (CFD), as well as perform physical analyses on medium-scaled models in real waters.

^{®}AQWA™ which had already been analysed by other researchers using the same potential flow solver. Indeed, the double-row, box-type FBW investigated by Rajabi and Ghassemi [38] was selected as a reference model. A different version from that currently utilized (i.e., Version 2022 R2) was adopted by Rajabi and Ghassemi [38]. The version employed is not quoted in the manuscript [38]; however, based on the publication date, it is older than 2022 R2. To illustrate, the outcomes for the transmission coefficient ${\mathrm{K}}_{\mathrm{t}}$ are presented in Figure 4, confirming the negligible difference between the source [38] and replicated model.

_{max}of 2 m or less was found to give consistent results. As an example, Figure 5 illustrates the convergence of the surge amplitude value with decreasing grid spacing. Given the simple geometry of the FBWs, refining the mesh with elements smaller than 2 m did not increase the computational time significantly. Thus, an element size of 0.8 m with a de-featuring tolerance of 0.04 m was eventually implemented and maintained throughout the investigation. Refining the mesh further to a grid size of 0.6 m was found to improve the results by a marginal value of 3%.

^{2}. Furthermore, the percentage difference between the outputs becomes minimal (i.e., <6%). Consequently, a time increment of 0.50 s was adopted and considered as adequate in striking a balance between reliable results and computational effort.

## 6. Results and Discussion

#### 6.1. Hydrostatic Analysis

^{3}, a yield strength of 483 MPa and an ultimate tensile strength of 565 MPa [42,43].

_{t}of the floating system remains positive, thus ensuring that upon a small inclination, a righting moment is induced to return the structure to its original position. Another revelation is that, in terms of the natural periods in heave, roll and pitch, the large-scale FBWs under consideration mimic the behaviour of FPSO units, as established in Clause 2.2 of the DNVGL-RP-F205 Standard [46].

#### 6.2. Wave Attenuation Performance Analysis

#### 6.3. Hydrodynamic Time Response

#### 6.3.1. Displacements

#### 6.3.2. Accelerations

^{2}for Model A to 0.28 m/s

^{2}and 0.26 m/s

^{2}for Model B (S1) and (S2), respectively. At LC 4, the highest surge accelerations are recognized for both the baseline and the hybrid FBWs. Model A undergoes a maximum surge acceleration of 2.67 m/s

^{2}which reduces to 2.50 m/s

^{2}and 2.43 m/s

^{2}for fully discharged and fully charged Model B. Considering all LCs, up to a 15% reduction in the surge acceleration is predicted for Model B, relative to Model A. The presence of the ESS within the FBW is also expected to minimize the accelerations in heave for all test LCs. According to the plots in Figure 14, Model B experiences peak accelerations which are up to 18.8% less than the accelerations of Model A. The highest percentage decreases are noticed for the moderate wave conditions of LCs 2 and 5.

^{2}to 0.04 rad/s

^{2}. It is also worth remarking that in surge and in heave, the accelerations for Model B always decrease when the PCS changes state from fully discharged (S1) to fully charged (S2). On the contrary, an increase in the pitch acceleration is observed when the ESS shifts from fully discharged (S1) to fully charged (S2) conditions.

- Peak surge (i.e., lateral) accelerations of 0.30 g;
- Peak heave (i.e., vertical) accelerations of 0.25 g;
- RMS acceleration maxima of 0.1 g in both lateral and vertical directions.

## 7. Conclusions

- The natural periods in heave, roll and pitch of large-scale FBWs resemble the natural periods of FPSO units;
- The predicted peak lateral and peak vertical accelerations of large-scale FBWs equate to 0.30 g and 0.25 g, respectively;
- The maximum RMS accelerations in both lateral and vertical directions add up to approximately 0.10 g;
- RMS accelerations in regular wave conditions are higher than the RMS accelerations arising from irregular sea states;
- Peak accelerations in irregular wave scenarios are short-lived but are more pronounced than the maximum accelerations recorded under incident regular waves.

- The hydrostatic stability of the floating assembly is enhanced as the GM
_{t}of the hybrid system remains well above zero; - The wave breaking efficiency, $\mathsf{\eta}$ (or transmission coefficient, ${\mathrm{K}}_{\mathrm{t}}$), of the FBW is significantly improved by up to 47% for mid-range incident wave periods of 5 ≤ T ≤ 8 s, corresponding to the range of incident wave frequencies 1.26 $\ge \mathsf{\omega}\ge 0.79$ rad/s;
- The presence of the ESS is likely to contribute to lower surge and heave displacements for a wide range of sea conditions;
- Contrastingly, hybrid Model B is able to provide mitigated pitch rotation relative to Model A, in calm waters only, due to a shift in the natural frequencies of the structure;
- From a hydrodynamic and stability perspective, both Model A and Model B are able to remain intact and withstand sea states up to very rough and high conditions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Validation plots comparing the numerical outputs from AQWA™ against the experimentation outputs from [37].

**Figure 4.**Repeatability plot [38].

**Figure 7.**Variation of ${\mathrm{K}}_{\mathrm{t}}$ with incident wave period for fixed-FBW Models A and B.

**Figure 8.**Variation of ${\mathrm{K}}_{\mathrm{t}}$ with incident wave period for free-FBW Models A and B.

Parameter | Baseline Model A | Hybrid Model B | |
---|---|---|---|

HPES system (-) | No | Yes | Yes |

State of charge (-) | - | S1 | S2 |

$\mathrm{Length}\text{}\mathrm{of}\text{}\mathrm{floater}\text{\u2014}{\mathrm{L}}_{\mathrm{o}}$ (m) | 150 | 150 | 150 |

$\mathrm{Width}\text{}\mathrm{of}\text{}\mathrm{floater}\text{\u2014}{\mathrm{B}}_{\mathrm{o}}$ (m) | 18 | 18 | 18 |

$\mathrm{Height}\text{}\mathrm{of}\text{}\mathrm{floater}\text{\u2014}{\mathrm{H}}_{\mathrm{o}}$ (m) | 11.90 | 11.90 | 11.90 |

Wall thickness—t_{1} (m) | 0.30 | 0.30 | 0.30 |

Wall thickness—t_{2} (m) | 0.20 | 0.20 | 0.20 |

Wall thickness—t_{3} (m) | 1.90 | 1.90 | 1.90 |

Water-plane $\mathrm{area}\text{\u2014}{\mathrm{A}\mathrm{\prime}}_{\mathrm{w}\mathrm{p}}$ (m^{2}) | 2700 | 2700 | 2700 |

$\mathrm{Freeboard}\text{\u2014}{\mathrm{f}}_{\mathrm{b}}$ (m) | 5.72 | 5.46 | 5.04 |

$\mathrm{Floater}\text{}\mathrm{draught}\text{\u2014}{\mathrm{Z}}_{\mathrm{s},\mathrm{f}\mathrm{b}\mathrm{w}}$ (m) | 6.19 | 6.43 | 6.86 |

$\mathrm{Total}\text{}\mathrm{draught}\text{\u2014}{\mathrm{Z}}_{\mathrm{s},\mathrm{t}\mathrm{o}\mathrm{t}}$ (m) | 6.19 | 12.53 | 12.96 |

$\mathrm{Total}\text{}\mathrm{displaced}\text{}\mathrm{volume}\text{\u2014}{\mathrm{V}}_{\mathrm{s},\mathrm{t}\mathrm{o}\mathrm{t}}$ (m^{3}) | 16,700 | 19,600 | 20,700 |

$\mathrm{Total}\text{}\mathrm{mass}\text{\u2014}{\mathrm{M}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$ (t) | 17,120 | 20,050 | 21,220 |

Distance from MSL to Centre of Buoyancy (CoB)—OB (m) | 3.09 | 4.01 | 4.20 |

Distance from MSL to Centre of Gravity (CoG)—OG (m) | 3.33 | 3.47 | 4.27 |

Transverse metacentric height—GM_{t} (m) | 4.61 | 3.19 | 3.59 |

$\mathrm{Roll}\text{}\mathrm{Inertia}\text{\u2014}{\mathrm{I}}_{\mathrm{g}\mathrm{x}}$ (kg m^{2}) | 3.23 × 10^{10} | 3.33 × 10^{10} | 3.58 × 10^{10} |

$\mathrm{Pitch}\text{}\mathrm{Inertia}\text{\u2014}{\mathrm{I}}_{\mathrm{g}\mathrm{y}}$ (kg m^{2}) | 6.64 × 10^{8} | 1.32 × 10^{9} | 1.67 × 10^{9} |

$\mathrm{Yaw}\text{}\mathrm{Inertia}\text{\u2014}{\mathrm{I}}_{\mathrm{g}\mathrm{z}}$ (kg m^{2}) | 3.26 × 10^{10} | 3.29 × 10^{10} | 3.51 × 10^{10} |

$\mathrm{Natural}\text{}\mathrm{period}\text{}\mathrm{in}\text{}\mathrm{heave}\text{\u2014}{\mathrm{T}}_{\mathrm{n},33}$ (s) | 7.27 | 7.56 | 7.69 |

$\mathrm{Natural}\text{}\mathrm{period}\text{}\mathrm{in}\text{}\mathrm{roll}\text{\u2014}{\mathrm{T}}_{\mathrm{n},44}$ (s) | 7.10 | 7.20 | 7.33 |

$\mathrm{Natural}\text{}\mathrm{period}\text{}\mathrm{in}\text{}\mathrm{pitch}\text{\u2014}{\mathrm{T}}_{\mathrm{n},55}$ (s) | 6.82 | 8.38 | 8.01 |

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

$\mathrm{Total}\text{}\mathrm{energy}\text{}\mathrm{storage}\text{}\mathrm{capacity}\text{\u2014}\mathrm{E}$ (MWh) | 3.84 |

$\mathrm{Total}\text{}\mathrm{volumetric}\text{}\mathrm{capacity}\text{}\mathrm{of}\text{}\mathrm{PVB}\text{\u2014}{\mathrm{V}}_{\mathrm{p}\mathrm{v}\mathrm{b}}$ (m^{3}) | 1901 |

$\mathrm{Mass}\text{}\mathrm{of}\text{}\mathrm{pressurized}\text{}\mathrm{fluid}\text{}(\mathrm{i}.\mathrm{e}.,\text{}\mathrm{air})\text{\u2014}{\mathrm{m}}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ (t) | 181 |

$\mathrm{Operating}\text{}\mathrm{pressure}\text{}\mathrm{ratio}\text{\u2014}{\mathrm{r}}_{\mathrm{p}}$ (-) | 2.50 |

Pre-charged $\mathrm{pressure}\text{\u2014}{\mathrm{p}}_{1}$ (bar) | 80 |

$\mathrm{Peak}\text{}\mathrm{pressure}\text{\u2014}{\mathrm{p}}_{2}$ (bar) | 200 |

$\mathrm{Design}\text{}\mathrm{pressure}\text{\u2014}{\mathrm{p}}_{\mathrm{d}}$ (bar) | 220 |

**Table 3.**Structural properties for the PCS obtained from SmartPVB [40].

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

$\mathrm{Number}\text{}\mathrm{of}\text{}\mathrm{cylinders}\text{\u2014}\mathrm{N}$ (-) | 8 |

$\mathrm{Length}\text{}\mathrm{of}\text{}\mathrm{cylinders}\text{\u2014}{\mathrm{L}}_{\mathrm{p}\mathrm{v}}$ (m) | 150 |

$\mathrm{Outer}\text{}\mathrm{diameter}\text{\u2014}{\mathrm{D}}_{\mathrm{o}}$ (m) | 1.524 |

$\mathrm{Internal}\text{}\mathrm{diameter}\text{\u2014}{\mathrm{D}}_{\mathrm{i}}$ (m) | 1.423 |

$\mathrm{Total}\text{}\mathrm{wall}\text{}\mathrm{thickness}\text{\u2014}\mathrm{e}$ (m) | 0.050 |

$\mathrm{Corrosion}\text{}\mathrm{allowance}\text{\u2014}{\mathrm{e}}_{\mathrm{c}}$ (m) | 0.003 |

$\mathrm{Total}\text{}\mathrm{mass}\text{}\mathrm{of}\text{}\mathrm{steel}\text{\u2014}{\mathrm{m}}_{\mathrm{s}\mathrm{t}}$ (t) | 2304 |

$\mathrm{Additional}\text{}\mathrm{mass}\text{}\mathrm{allowance}\text{}\mathrm{per}\text{}\mathrm{PV}\text{\u2014}{\mathrm{m}}_{\mathrm{a}}$ (%) | 5 |

$\mathrm{Von}\text{}\mathrm{Mises}\text{}\mathrm{safety}\text{}\mathrm{factor}\text{\u2014}{\mathrm{f}}_{\mathrm{v}\mathrm{m}}$ (-) | 1.70 |

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

Nominal chain diameter (m) | 0.171 |

Angle with seabed (°) | 0 |

Anchoring depth (m) | 200 |

Un-stretched cable length for corner lines (x4) (m) | 1420 |

Un-stretched cable length for middle lines (x2) (m) | 1231 |

Pre-tension per cable (kN) | 4800 |

Transverse drag coefficient (-) [48] | 2.40 |

Longitudinal drag coefficient (-) [48] | 1.15 |

Safety factor under normal conditions (-) [49] | 1.67 |

Maximum allowable load under normal conditions (kN) | 15,000 |

Load Case (-) | Wave Type (-) | Wave Height H (m) | Wave Period T (s) | WMO Code (-) [50] | Sea State (-) [50] |
---|---|---|---|---|---|

1 | Regular | 7.7 | 10.5 | 7 | High |

2 | Regular | 3.1 | 7.5 | 5 | Rough |

3 | Regular | 1.5 | 5.5 | 4 | Moderate |

4 | Irregular | 4.5 | 8.5 | 6 | Very rough |

5 | Irregular | 2.2 | 6.5 | 4 | Moderate |

6 | Irregular | 1.1 | 4.5 | 3 | Slight |

**Table 6.**Peak and RMS accelerations of the FBW models in surge (i.e., lateral) and heave (i.e., vertical) directions for LC 1.

DoF | Acceleration (g) | Model A | Model B (S1) | Model B (S2) | Difference (%) |
---|---|---|---|---|---|

Surge (X) | Peak—${\ddot{\mathrm{x}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ | 0.141 | 0.135 | 0.132 | −5.451 |

RMS—${\ddot{\mathrm{x}}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ | 0.095 | 0.091 | 0.089 | −4.979 | |

Heave (Z) | Peak—${\ddot{\mathrm{z}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ | 0.170 | 0.167 | 0.167 | −1.962 |

RMS—${\ddot{\mathrm{z}}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ | 0.101 | 0.102 | 0.103 | +1.567 |

**Table 7.**Peak and RMS accelerations of the FBW models in surge (i.e., lateral) and heave (i.e., vertical) directions for LC 4.

DoF | Acceleration (g) | Model A | Model B (S1) | Model B (S2) | Difference (%) |
---|---|---|---|---|---|

Surge (X) | Peak—${\ddot{\mathrm{x}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ | 0.272 | 0.255 | 0.248 | −7.530 |

RMS—${\ddot{\mathrm{x}}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ | 0.022 | 0.021 | 0.020 | −7.584 | |

Heave (Z) | Peak—${\ddot{\mathrm{z}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ | 0.242 | 0.235 | 0.233 | −3.501 |

RMS—${\ddot{\mathrm{z}}}_{\mathrm{r}\mathrm{m}\mathrm{s}}$ | 0.025 | 0.024 | 0.024 | −3.698 |

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## Share and Cite

**MDPI and ACS Style**

Cutajar, C.; Sant, T.; Farrugia, R.N.; Buhagiar, D.
Analysis of the Wave Attenuating and Dynamic Behaviour of a Floating Breakwater Integrating a Hydro-Pneumatic Energy Storage System. *J. Mar. Sci. Eng.* **2023**, *11*, 2189.
https://doi.org/10.3390/jmse11112189

**AMA Style**

Cutajar C, Sant T, Farrugia RN, Buhagiar D.
Analysis of the Wave Attenuating and Dynamic Behaviour of a Floating Breakwater Integrating a Hydro-Pneumatic Energy Storage System. *Journal of Marine Science and Engineering*. 2023; 11(11):2189.
https://doi.org/10.3390/jmse11112189

**Chicago/Turabian Style**

Cutajar, Charise, Tonio Sant, Robert N. Farrugia, and Daniel Buhagiar.
2023. "Analysis of the Wave Attenuating and Dynamic Behaviour of a Floating Breakwater Integrating a Hydro-Pneumatic Energy Storage System" *Journal of Marine Science and Engineering* 11, no. 11: 2189.
https://doi.org/10.3390/jmse11112189