# Numerical Investigation of the Resistance of a Zero-Emission Full-Scale Fast Catamaran in Shallow Water

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## Abstract

**:**

## 1. Introduction

## 2. Geometry and Parameters

#### 2.1. Catamaran Geometry and Dimensions

#### 2.2. Parameters for Analysis

## 3. Methodology

#### 3.1. Computational Methods

#### 3.1.1. Flow Simulation

#### 3.1.2. Free Surface Capturing

#### 3.1.3. Dynamic Trim and Sinkage

#### 3.1.4. Coordinate System

#### 3.2. Computational Domain and Boundary Conditions

_{pp}in front of the hull and 5 L

_{pp}behind it. The lower and upper boundaries were 2.5 L

_{pp}and 1.5 L

_{pp}away from the undisturbed water level, respectively. The side boundary of the Tank Region was 2.5 L

_{pp}away from the symmetry plane of the catamaran. The velocity inlet condition was applied at the inlet, top, bottom and side boundaries. The pressure outlet condition was used for the outlet boundary. The demi-hull surface was considered as the no-slip wall. To avoid wave refection, a wave forcing method was applied to the regions near the inlet, outlet and side boundaries, as shown in Figure 2a,b. For shallow water scenarios, the size of the Tank Region remained the same as the one used for deep water cases except that the bottom surface was 2.15 m below the water level, where the slip wall boundary condition was applied. The size of the Hull Region is determined by guaranteeing there are sufficient cells (at least five cell layers) in the overlapping area between the two regions. Besides, the cell size in the overlapping area should be comparable. In the present work, the Hull Region was 0.1 L

_{pp}in front of the forward perpendicular and 0.15 L

_{pp}behind the aft perpendicular. The lower and upper boundaries were 0.05 L

_{pp}away from the waterline, and the side boundaries were 0.05 L

_{pp}away from the mid-plane of the demihull.

#### 3.3. Mesh Generation

#### 3.4. Numerical Validation and Verification

#### 3.4.1. NPL 4a02 Catamaran

#### 3.4.2. Stavanger Demonstrator

#### 3.4.3. Mesh Convergence Study for the London Demonstrator

## 4. Results and Discussion

#### 4.1. Resistance, Sinkage and Trim

#### 4.2. Wave Patterns

#### 4.3. Longitudinal Wave Cuts

_{pp}ahead of the catamaran and reaches the maximum height near the FP. In deep water, both the wave height and wave length increase as the Froude number rises, confirming the observations from Figure 14. The increase of the wave length leads to a reduction in the number of waves between FP and aft perpendicular (AP). For example, there are approximately three waves between FP and AP when $Fn$ = 0.23, while the number becomes less than one when $Fn$ increases to 0.805. It is interesting to observe that at $Fn$ = 0.575, the wave number between FP and AP is approximately unity and this Froude number corresponds to the maximum value of the pressure component of total resistance (see Figure 9a). In shallow water, the first wave crest behind the bow is always higher than that created in deep water, especially near the critical speed. The difference is considered small only when the Froude number is greater than 0.575. Moreover, no noteworthy wave troughs are generated between FP and AP in shallow water, which significantly differs from those in deep water. Furthermore, the catamaran generates higher wave crests behind the stern in deep water, while creating deeper wave troughs in shallow water.

#### 4.4. Crossflow Fields

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

b | Breadth of the demihull |

B | Breadth of the catamaran |

C_{T} | Total resistance coefficient |

C_{F} | Frictional resistance coefficient |

C_{F,ITTC} | Frictional resistance coefficient calculated according to ITTC 1957 correlation line formula |

C_{P} | Pressure resistance coefficient |

Fn | Froude number |

Fn_{H} | Depth Froude number |

g | Gravity acceleration |

H | Water depth |

L_{pp} | Length between perpendiculars |

Re | Reynolds number |

R_{T} | Total resistance |

R_{F} | Frictional resistance |

R_{P} | Pressure resistance |

s | Separation distance between the demihulls |

S_{sw} | Static wetted surface area |

S_{dw} | Dynamic wetted surface area |

T | Draught |

U | Ship speed relative to the incoming flow |

$\sigma $ | Sinkage |

$\theta $ | Trim |

AP | Aft Perpendicular |

CFD | Computational Fluid Dynamics |

FP | Forward Perpendicular |

HSVA | Hamburg Ship Model Basin |

ITTC | International Towing Tank Committee |

LCG | Longitudinal centre of gravity |

MSRC | Maritime Safety Research Centre |

VCG | Vertical centre of gravity |

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**Figure 2.**Computational meshes and domain dimensions used for deep water (

**a**,

**c**) and shallow water cases (

**b**,

**d**).

**Figure 4.**Computed y+ distribution on the demihull surface at Fn = 0.287 (

**upper**) and 0.805 (

**below**) in shallow water.

**Figure 9.**Comparison of resistances (

**a**) and motions (

**b**) of London Demonstrator in deep and shallow water (H = 2.15 m).

**Figure 10.**Total resistance coefficient (

**a**), and pressure and frictional resistance coefficients (

**b**) of the London Demonstrator in deep water.

**Figure 11.**Total resistance coefficient (

**a**), and pressure and frictional resistance coefficients (

**b**) of the London Demonstrator in shallow water.

**Figure 16.**Comparison of the longitudinal wave cuts at the catamaran symmetry plane in deep and shallow water.

**Figure 17.**Comparison of the longitudinal wave cuts at the mid-plane of the demihull in deep and shallow water.

**Figure 18.**Crossflow fields at the mid-plane of the demihull for deep (

**left**) and shallow (

**right**) water. Positive and negative velocity values mean the flow moves towards the outer and inner sides of the demihull, respectively.

Dimension | Symbol | Value |
---|---|---|

Demihull breadth | b/${L}_{pp}$ | 0.068 |

Separation | s/${L}_{pp}$ | 0.187 |

Draught | T/${L}_{pp}$ | 0.033 |

Depth/draught | H/T | 2.0 |

Vertical centre of gravity | VCG/${L}_{pp}$ | 0.012 |

Longitudinal centre of gravity | LCG/${L}_{pp}$ | 0.447 |

Dimension | Symbol | Value |
---|---|---|

Demihull breadth | b/${L}_{pp}$ | 0.096 |

Separation | s/${L}_{pp}$ | 0.200 |

Draught | T/${L}_{pp}$ | 0.064 |

Vertical centre of gravity | VCG/${L}_{pp}$ | 0.020 |

Longitudinal centre of gravity | LCG/${L}_{pp}$ | 0.436 |

Dimension | Symbol | Value |
---|---|---|

Demihull breadth | b/${L}_{pp}$ | 0.074 |

Separation | s/${L}_{pp}$ | 0.227 |

Draught | T/${L}_{pp}$ | 0.045 |

Vertical centre of gravity | VCG/${L}_{pp}$ | 0.016 |

Longitudinal centre of gravity | LCG/${L}_{pp}$ | 0.450 |

**Table 4.**Total resistance coefficient of Stavanger demonstrator obtained from model tests and CFD simulation.

Fn | ${\mathit{C}}_{\mathit{T},\mathit{C}\mathit{F}\mathit{D}}\times {10}^{3}$ | ${\mathit{C}}_{\mathit{T},\mathit{E}\mathit{x}\mathit{p}}\times {10}^{3}$ | Error |
---|---|---|---|

0.57 | 5.476 | 5.520 | −0.79% |

0.63 | 4.844 | 4.899 | −1.11% |

0.69 | 4.404 | 4.437 | −0.74% |

0.75 | 4.098 | 4.157 | −1.42% |

$\overline{\mathit{r}}$ | ${\mathit{N}}_{1}$ | ${\mathit{N}}_{2}$ | ${\mathit{N}}_{3}$ | ${\mathit{\phi}}_{1}$ | ${\mathit{\phi}}_{2}$ | ${\mathit{\phi}}_{3}$ | $\overline{\mathit{R}}$ | ${\mathit{E}}_{\mathit{a},21}$ | ${\mathit{E}}_{\mathit{e}\mathit{x}\mathit{t},21}$ | $\mathit{G}\mathit{C}{\mathit{I}}_{\mathit{f}\mathit{i}\mathit{n}\mathit{e},21}$ |
---|---|---|---|---|---|---|---|---|---|---|

1.2 | 10.35 | 5.99 | 3.47 | 2.537 | 2.557 | 2.589 | 0.607 | 0.78% | 1.22% | 1.50% |

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**MDPI and ACS Style**

Shi, G.; Priftis, A.; Xing-Kaeding, Y.; Boulougouris, E.; Papanikolaou, A.D.; Wang, H.; Symonds, G.
Numerical Investigation of the Resistance of a Zero-Emission Full-Scale Fast Catamaran in Shallow Water. *J. Mar. Sci. Eng.* **2021**, *9*, 563.
https://doi.org/10.3390/jmse9060563

**AMA Style**

Shi G, Priftis A, Xing-Kaeding Y, Boulougouris E, Papanikolaou AD, Wang H, Symonds G.
Numerical Investigation of the Resistance of a Zero-Emission Full-Scale Fast Catamaran in Shallow Water. *Journal of Marine Science and Engineering*. 2021; 9(6):563.
https://doi.org/10.3390/jmse9060563

**Chicago/Turabian Style**

Shi, Guangyu, Alexandros Priftis, Yan Xing-Kaeding, Evangelos Boulougouris, Apostolos D. Papanikolaou, Haibin Wang, and Geoff Symonds.
2021. "Numerical Investigation of the Resistance of a Zero-Emission Full-Scale Fast Catamaran in Shallow Water" *Journal of Marine Science and Engineering* 9, no. 6: 563.
https://doi.org/10.3390/jmse9060563