# Design of Breakwaters to Minimize Greenwater Loading on Bow Structures of Fixed Vessels

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Simulation Model without the Breakwaters

#### 2.2. Design of Breakwaters

_{B}is the height of the breakwater.

_{W}of whalebacks or turtle decks shall be determined, as illustrated in Figure 4.

#### 2.2.1. Windshield Breakwater

#### 2.2.2. Horizontal Grillage Breakwater

#### 2.2.3. Perforated Breakwater

#### 2.3. Numerical Modelling

^{−6}is used for volume fraction parameters. Direct Numerical Simulation (DNS) is performed to solve the Navier–Stokes equations in 3D keeping the mesh size around the model surface near to the Kolmogorov microscale. Inside the VoF model, the “open channel flow” and “open channel wave boundary conditions” sub-models are used to define the simulation inlet, outlet and atmosphere following the experimental setup in [19]. The tracking of the interface between the phases (p, the primary phase (air); q, the secondary phase (water)) is accomplished by the solution of a continuity equation. The equation has the following form for the qth phase [24] (ANSYS Fluent Tutorial Section 16.3.2):

^{3}and 998.2 kg/m

^{3}, respectively. The boundary condition for the atmosphere was established at the pressure outlet to allow open channel flow. Inlet and outlet conditions were set as open channel flow with a depth of 3500 mm. The Third Order Stokes wave theory was applied to achieve the wave steepness of 0.06, as shown in Table 1. With reference to Table 1, the wave height and wavelength were taken as 0.225 m and 3.75 m, respectively. A hybrid initialization was then chosen to be computed from the inlet boundary condition. Based on visual convergence studies, twenty iterations per time step were deemed sufficient to achieve reasonably good residuals (1 × 10

^{−6}). As this simulation of wave studies requires comparison studies with a short period, the time step size (s) was set at 0.001 to analyse the results.

## 3. Results and Discussions

#### 3.1. Validation of the Numerical Model

#### 3.2. Influence of Various Breakwaters on Greenwater Effects

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol | Description | Units |

$\mathsf{\lambda}$ | Wavelength | m |

${A}_{W\text{}}$ | Wave amplitude | m |

${\mathrm{H}}_{\mathrm{W}}$ | Wave height | m |

k | Wave steepness | - |

D | Depth of model | m |

f | Freeboard of the model | m |

L | Length of the model | m |

B | Breadth of the model | m |

Bt | Breadth of the towing tank | m |

d | Depth of water | mm |

tp | Thickness of plate | mm |

hp | Height of plate | mm |

$\theta $ | Confronting angle | degree |

$\gamma $ | Inclination angle | degree |

H | Height of breakwater | mm |

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**Figure 1.**Simulation domain [19]: (

**a**) entire domain, including wavemaker. Side view, followed by the top view; (

**b**) box-shaped fixed ship model (as marked by dashed circles in (

**a**)) with a vertical plate acting as deck structure at the bow region (all dimensions in m).

**Figure 6.**Front view of horizontal grillage breakwater (half of the length about the symmetry plane).

**Figure 8.**Box ship model developed for this study: (

**a**) no breakwaters; (

**b**) windshield breakwater; (

**c**) horizontal grillage breakwater; (

**d**) perforated breakwater.

**Figure 9.**Sketch of the simulation domain (not to scale): (

**a**) 3D view of symmetric domain; (

**b**) side view of the entire domain; (

**c**) closeup view of the box ship model with various dimensions.

**Figure 10.**Meshing of the simulation domain: (

**a**) 2D sectional view of the domain; (

**b**) 3D view of the intermediate denser mesh region; (

**c**) 2D sectional view of the core denser mesh region (the box ship with flat plate and breakwater).

**Figure 11.**Arrangement of pressure measurement points for performance analysis of various breakwater designs.

**Figure 14.**Comparisons of greenwater behaviours on the deck at various time instants: experiment (

**column 1**) and CFD (

**column 2**) from [19] vs. present simulation (

**column 3**) results.

**Figure 15.**Impact of breakwaters on dynamic greenwater pressure variation at “PP2” on the vertical deck plate (Aw = 0.1125 m, λ = 3.75 m).

**Figure 16.**Impact of breakwaters on dynamic greenwater pressure variation at “PP3” on the vertical deck plate (Aw = 0.1125 m, λ = 3.75 m).

$k$$(\frac{{\mathbf{H}}_{\mathbf{W}}}{\mathsf{\lambda}})$ | ${\mathit{A}}_{\mathit{W}}\left(\mathbf{m}\right)$ | ||
---|---|---|---|

$\mathsf{\lambda}=2.25\mathbf{m}$ | $\mathsf{\lambda}=3\mathbf{m}$ | $\mathsf{\lambda}=3.75\mathbf{m}$ | |

0.04 | 0.045 | 0.06 | 0.075 |

0.05 | 0.05625 | 0.075 | 0.09375 |

0.06 | 0.0675 | 0.09 | 0.1125 |

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**MDPI and ACS Style**

An, L.J.; Hannan, M.A.
Design of Breakwaters to Minimize Greenwater Loading on Bow Structures of Fixed Vessels. *Fluids* **2021**, *6*, 212.
https://doi.org/10.3390/fluids6060212

**AMA Style**

An LJ, Hannan MA.
Design of Breakwaters to Minimize Greenwater Loading on Bow Structures of Fixed Vessels. *Fluids*. 2021; 6(6):212.
https://doi.org/10.3390/fluids6060212

**Chicago/Turabian Style**

An, Lim Jun, and Mohammed Abdul Hannan.
2021. "Design of Breakwaters to Minimize Greenwater Loading on Bow Structures of Fixed Vessels" *Fluids* 6, no. 6: 212.
https://doi.org/10.3390/fluids6060212