# Effect of Monohull Type and Catamaran Hull Type on Ocean Waste Collection Behavior Using OpenFOAM

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Round-Bilge Monohull and Inner Flat Catamaran Model

#### 2.2. Sampling Location

#### 2.3. Computational Domain

#### 2.4. Meshing Process

#### 2.5. Validation

_{t}) and resistance coefficient (C

_{t}). The results of both parameters were close to the experimental results. The experimental Ct was 4.961 × 10

^{−3}, then the current simulation Ct was 4.555 × 10

^{−3}. The differences were below 9%. The experiment procedure was determined using the ITTC guideline. This difference in numbers occurred because the model used in this simulation was not exactly the same as the model used in the experiment. The wet surface area of the experimental model was 1.945 m

^{2}, then the wet surface area of the simulation model was 1.896 m

^{2.}There was a difference of 2.519%, because the experimental and simulation models were not totally the same. In addition, the R

_{t}and C

_{t}from the present simulation were also compared to numerical results [32,33]. The experimental Rt was 12.77 N, then the current simulation Rt was 12.02 N. The results indicate that the differences were less than 5%. Then, a comparison was also made with a Prelimina solver [34], and the difference was quite large because there must have been different characteristics between the model used in this study and Prelimina.

#### 2.6. Uncertainty Analysis

_{i}

_{.}A good alternative that applied is $ri=\sqrt{2}$, as it provides a fairly large parameter refinement ratio and at least enables prolongation of the coarse-parameter solution as an initial guess for the fine-parameter solution. The change between medium-fine ${\epsilon}_{i,21}={\widehat{S}}_{i,2}-{\widehat{S}}_{i,1}$ and coarse-medium ${\epsilon}_{i,32}={\widehat{S}}_{i,3}-{\widehat{S}}_{i,2}$ solutions are used to defined the convergence ratio ${R}_{i}={\epsilon}_{i,21}/{\epsilon}_{i,32}$, where ${\widehat{S}}_{i,1},{\widehat{S}}_{i,2},\mathrm{and}{\widehat{S}}_{i,3}$ are the solutions of fine, medium, and coarse input parameters, respectively [39,40]. The total resistance at 1 m/s will be used as the solution of each mesh.

- Monotonic convergence: 0 < R
_{i}< 1 - Oscillatory convergence: R
_{i}< 0 - Divergence: R
_{i}> 1

**GCI**estimated for the grid independence test of the total resistance over two grid solutions can be expressed as [41]:

**Fs**is defined as a safety factor and implies 95% confidence for the uncertainty estimate [37],

**Fs**= 1.25 is suggested for employment over these grids [42]. Since all

**GCI**values are below 1.5% [38], it is verified that the dependency of numerical results on the grid size has been reduced and the solution achieves the grid-independent solution.

## 3. Results

#### 3.1. Flow Characterization

#### 3.2. Dynamic Pressure

_{0}is static pressure. The pressure coefficient distribution under the hull was higher on the monohull model than on the catamaran model. The bottom wetted surface of the monohull was much larger. As a result, it will amplify the pressure acting on the surface as well as the pressure force. It is identical to a ship without a conveyor, whereas catamaran ships typically have less resistance than monohull ships [43,44]. The pressure coefficient distribution on conveyor surface was similar between both models. The high magnitude of pressure was distributed at bottom end section of the conveyor. This corresponds to the deeper part immersed in the water, which is expected to have greater pressure from incoming flow. Therefore, at this location, it is necessary to provide more structural reinforcement than the other parts.

#### 3.3. Flow Patterns

#### 3.4. Velocity Contour and Velocity Sampling in Front of Model

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Monohull model: (

**a**) front view of round bilge, (

**b**) 3D view of round bilge, and (

**c**) side view.

**Figure 2.**Catamaran model: (

**a**) front view of inner flat hull, (

**b**) 3D view of inner flat hull, (

**c**) side view.

**Figure 5.**Meshing in fluid domain with refinement levels: (

**a**) side view model, (

**b**) top view, (

**c**) front view.

**Figure 6.**The actual number of surface prism layers generated around the ship model using the snappyHexMesh tool: (

**a**) surface layers, (

**b**) yPlus.

**Figure 8.**Residual and force components evolution: (

**a**) residual iteration evolution, (

**b**) force components iteration evolution using 2,196,512 cells, (

**c**) location of velocity sampling, (

**d**) velocity convergence.

**Figure 9.**Pressure coefficient distribution (

**a**) and wave patterns (

**b**) on Delft catamaran 372 surface at Froude number 0.3.

**Figure 10.**Distribution of wave generated around round-bilge monohull 1 m/s: (

**a**) wave elevation, (

**b**) wave profile along body.

**Figure 11.**Distribution of wave generated around inner flat catamaran at 1 m/s speed: (

**a**) wave elevation, (

**b**) wave profile along body.

**Figure 17.**Pressure coefficient distribution on ship surface at 0.5 m/s: (

**a**) monohull, (

**b**) catamaran.

Parameter | Symbol | Monohull | Catamaran |
---|---|---|---|

Length overall [m] | Loa | 4.000 | 4.000 |

Length perpendicular [m] | Lpp | 3.950 | 3.950 |

Length of water line [m] | Lwl | 3.858 | 3.858 |

Maximum breadth [m] | B | 1.200 | 1.200 |

Height [m] | H | 0.600 | 0.600 |

Draft [m] | T | 0.300 | 0.300 |

Wetted surface area [m^{2}] | WSA | 6.232 | 5.723 |

Conveyor length [m] | Lc | 1.625 | 1.625 |

Conveyor angle [^{o}] | La | 20 | 20 |

Conveyor wide [m] | Lw | 0.600 | 0.600 |

Volume displacement | m^{3} | 0.90 | 0.36 |

Block coefficient | - | 0.625 | 0.25 |

Probes | X (m) | Y1 | Y2 | Y3 | Z |
---|---|---|---|---|---|

P1 | 3.5 | 0 | 0.15 | −0.15 | 0 |

P2 | 4.2 | 0 | 0.15 | −0.15 | 0 |

P3 | 4.5 | 0 | 0.15 | −0.15 | 0 |

P4 | 5.2 | 0 | 0.15 | −0.15 | 0 |

P5 | 5.5 | 0 | 0.15 | −0.15 | 0 |

Parameter | Velocity | Dynamic Pressure | α. Water | Omega | k |
---|---|---|---|---|---|

Inlet | fixedValue | fixedFluxPressure | fixedValue | fixedValue | fixedValue |

Starboard | zeroGradient | zeroGradient | variableHeightFlowRate | zeroGradient | zeroGradient |

Portside | zeroGradient | zeroGradient | zeroGradient | zeroGradient | zeroGradient |

Atmosphere | pressureInletOutletVelocity | totalPressure | inletOutlet | inletOutlet | inletOutlet |

Bottom | zeroGradient | zeroGradient | fixedValue | zeroGradient | eroGradient |

Outlet | outletPhaseMeanVelocity | zeroGradient | variableHeightFlowRate | inletOutlet | inletOutlet |

Hull | movingWallVelocity | fixedFluxPressure | zeroGradient | omegaWallFunction | qRWallFunction |

**Table 4.**Average and standard deviation of force components vs. grid density for Delft catamaran 372 at Fr = 0.3.

Grid Density | Number of Cells | Pressure | Viscous | Total | Experiment Value | % Error |
---|---|---|---|---|---|---|

Coarse | 737,304 | 5.38 | 8.22 | 13.60 | 12.77 | 6.5 |

Medium | 2,196,512 | 3.46 | 8.56 | 12.02 | 12.77 | 5.8 |

Fine | 4,400,870 | 2.62 | 11.71 | 14.33 | 12.77 | 12.2 |

Vs (m/s) | Fn | Re | R_{t} (N) | C_{t} × 10^{−3} | |
---|---|---|---|---|---|

Experiment [30,31] | 1.627 | 0.3 | 4.882 × 10^{6} | 12.77 | 4.961 |

Prelimina [34] | 1.637 | 0.3 | 4.882 × 10^{6} | 14.00 | 5.523 |

Present study | 1.627 | 0.3 | 4.882 × 10^{6} | 12.02 | 4.555 |

Percentage error with experiment (%) | - | - | - | 5.843 | 8.18 |

Percentage error with Prelimina (%) | - | - | - | 12.85 | 17.52 |

Grid | No. of Cells | ${\widehat{\mathit{S}}}_{\mathit{i},\mathit{n}}\left(\mathit{R}\mathit{T}\right)$ | ${\mathit{\epsilon}}_{\mathit{i},21}$ | ${\mathit{\epsilon}}_{\mathit{i},32}$ | ${\mathit{R}}_{\mathit{i}}$ | ${\mathit{P}}_{\mathit{i}}$ | $\mathbf{G}\mathbf{C}{\mathbf{I}}_{12}(\%)$ | $\mathbf{G}\mathbf{C}{\mathbf{I}}_{12}(\%)$ |
---|---|---|---|---|---|---|---|---|

Fine | 7,735,423 | 141.51 | 1.59 | |||||

Medium | 3,143,952 | 143.10 | 6.38 | 0.2492 | 4.009 | 0.35 | 1.41 | |

Coarse | 945,286 | 149.48 |

Grid | No. of Cells | ${\widehat{\mathit{S}}}_{\mathit{i},\mathit{n}}\left(\mathit{R}\mathit{T}\right)$ | ${\mathit{\epsilon}}_{\mathit{i},21}$ | ${\mathit{\epsilon}}_{\mathit{i},32}$ | ${\mathit{R}}_{\mathit{i}}$ | ${\mathit{P}}_{\mathit{i}}$ | $\mathbf{G}\mathbf{C}{\mathbf{I}}_{12}(\%)$ | $\mathbf{G}\mathbf{C}{\mathbf{I}}_{12}(\%)$ |
---|---|---|---|---|---|---|---|---|

Fine | 5,877,600 | 136.95 | −0.07 | |||||

Medium | 3,143,952 | 136.87 | −1.19 | 0.0623 | 8.007 | 0.0042 | 0.0042 | |

Coarse | 1,777,139 | 135.68 |

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## Share and Cite

**MDPI and ACS Style**

Sugianto, E.; Chen, J.-H.; Permadi, N.V.A.
Effect of Monohull Type and Catamaran Hull Type on Ocean Waste Collection Behavior Using OpenFOAM. *Water* **2022**, *14*, 2623.
https://doi.org/10.3390/w14172623

**AMA Style**

Sugianto E, Chen J-H, Permadi NVA.
Effect of Monohull Type and Catamaran Hull Type on Ocean Waste Collection Behavior Using OpenFOAM. *Water*. 2022; 14(17):2623.
https://doi.org/10.3390/w14172623

**Chicago/Turabian Style**

Sugianto, Erik, Jeng-Horng Chen, and Niki Veranda Agil Permadi.
2022. "Effect of Monohull Type and Catamaran Hull Type on Ocean Waste Collection Behavior Using OpenFOAM" *Water* 14, no. 17: 2623.
https://doi.org/10.3390/w14172623