# Time Domain Simulation of Damage Flooding Considering Air Compression Characteristics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Time Domain Simulation with Air Compression

#### 2.1. Air Description

#### 2.2. Flow of Compressed Air

## 3. Simulation Study

#### 3.1. Model Arrangement

#### 3.2. Numerical Set Up

#### 3.3. Simulation Results

#### 3.3.1. Effect of the Ventilation Level

#### 3.3.2. Variation of Density

^{3}. The theoretical calculation values fit the finally simulated density value of 1.20 kg/m

^{3}in the Figure 10. For other cases with better ventilation levels, the extent of compression is much smaller than the small ventilation case, and the variation processes of the corresponding density are similar. In general, the changing processes satisfy the state equation of the ideal gas. Simultaneously, the consistency between the theoretical density value and the simulated density value validates the reliability of the CFD simulation and the convergence of the calculated results in this paper.

#### 3.3.3. The Height of the Flooding Water

#### 3.3.4. Motion Responses of the Damaged Ship

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Shafiepour, R.; Waltham-Sajdak, J. Total Ship Survivability System. 2015. Available online: https://pdfs.semanticscholar.org/5521/d27816202520bc50abbbd0c993c64bfcb42b.pdf (accessed on 20 February 2019).
- Pennanen, P.; Manderbacka, T.; Ruponen, P. Implications of different alternatives for damage stability analysis in decision support. In Proceedings of the 16th International Ship Stability Workshop, Belgrade, Serbia, 5–7 June 2017. [Google Scholar]
- ITTC. The specialist committee on prediction of extreme ship motions and capsizing. In Proceedings of the 23rd International Towing Tank Conference, Venice, Italy, 8–14 September 2002. [Google Scholar]
- ITTC. Stability in Waves Committee, Final Report and Recommendation. In Proceedings of the 27rd International Towing Tank Conference, Copenhagen, Denmark, 31 August–5 September 2014. [Google Scholar]
- ITTC. Stability in Waves Committee, Final Report and Recommendation. In Proceedings of the 28rd International Towing Tank Conference, Wuxi, China, 17–23 September 2017. [Google Scholar]
- Gao, Z.; Gao, Q.; Vassalos, D. Numerical simulation of flooding of a damaged ship. Ocean Eng.
**2011**, 38, 1649–1662. [Google Scholar] [CrossRef] - Dankowski, H. A Fast and Explicit Method for Simulating Flooding and Sinkage Scenarios of Ships. Ph.D. Thesis, Technical University of Hamburg-Harburg, Hamburg, Germany, 2013. [Google Scholar]
- Gao, Z.; Vassalos, D. The dynamics of the floodwater and the damaged ship in waves. J. Hydrodyn.
**2015**, 27, 689–695. [Google Scholar] [CrossRef] [Green Version] - Sadat-Hosseini, H.; Kim, Do.; Carrica, P.M.; Rhee, S.H.; Stern, F. URANS simulations for a flooded ship in calm water and regular beam waves. Ocean Eng.
**2016**, 120, 318–330. [Google Scholar] [CrossRef] - Santos, T.A.; Guedes Soares, C. Time domain simulation of ship global loads due to progressive flooding. In Proceedings of the 1st International Conference on Marine Structures, Glasgow, UK, 12–14 March 2007; pp. 79–88. [Google Scholar]
- Manderbacka, T.; Mikkola, T.; Ruponen, P.; Matusiak, J. Transient response of a ship to an abrupt flooding accounting for the momentum flux. J. Fluid Struct.
**2015**, 57, 108–126. [Google Scholar] [CrossRef] [Green Version] - Le Touzé, D.; Marsh, A.; Oger, G.; Guilcher, P.-M.; Khaddaj-Mallat, C.; Alessandrini, B.; Ferranta, P. SPH simulation of green water and ship flooding scenarios. J. Hydrodyn.
**2010**, 22, 231–236. [Google Scholar] - Ming, F.R.; Zhang, A.M.; Cheng, H.; Sun, P.N. Numerical simulation of a damaged ship cabin flooding in transversal waves with Smoothed Particle Hydrodynamics method. Ocean Eng.
**2018**, 165, 336–352. [Google Scholar] [CrossRef] - Guo, K.; Sun, P.; Cao, X.; Xiao, H. A 3-D SPH model for simulating water flooding of a damaged floating structure. J. Hydrodyn.
**2017**, 29, 831–844. [Google Scholar] [CrossRef] - Cao, X.Y.; Ming, F.R.; Zhang, A.M. Multi-phase SPH modelling of air effect on the dynamic flooding of a damaged cabin. Comput. Fluids
**2018**, 163, 7–19. [Google Scholar] [CrossRef] - Palazzi, L.; de Kat, J.O. Model experiments and simulations of a damaged ship with air-flow taken into account. Mar. Technol.
**2004**, 41, 38–44. [Google Scholar] - Ruponen, P.; Kurvinen, P.; Saisto, I.; Harras, J. Air compression in a flooded tank of a damaged ship. Ocean Eng.
**2013**, 57, 64–71. [Google Scholar] [CrossRef] - Ruponen, P. Progressive Flooding of a Damaged Passenger Ship. Ph.D. Thesis, Helsinki University of Technology, Espoo, Finland, 2007. [Google Scholar]
- Gao, Z.; Wang, Y.; Su, Y. Numerical study of damaged ship’s compartment sinking with air compression effect. Ocean Eng.
**2018**, 147, 68–76. [Google Scholar] [CrossRef] - Lee, G.J. Dynamic orifice flow model and compartment models for flooding simulation of a damaged ship. Ocean Eng.
**2015**, 109, 635–653. [Google Scholar] [CrossRef] [Green Version] - Ruponen, P.; Pulkkinen, A.; Laaksonen, J. A method for breach assessment onboard a damaged passenger ship. Appl. Ocean Res.
**2017**, 64, 236–248. [Google Scholar] [CrossRef] - IMO. Resolution MSC.245 (83): Recommendation on a Standard Method for Evaluating Cross-Flooding Arrangements; IMO: London, UK, 2007. [Google Scholar]
- Begovic, E.; Day, A.H.; Incecik, A.; Mancini, S.; Pizzirusso, D. Roll damping assessment of intact and damaged ship by CFD and EFD methods. In Proceedings of the 12th International Conference on Stability of Ships and Ocean Vehicles, Glasgow, UK, 14–19 June 2015. [Google Scholar]
- Mancini, S.; Begovic, E.; Day, A.H.; Incecik, A. Verification and validation of numerical modelling of DTMB 5415 roll decay. Ocean Eng.
**2018**, 162, 209–223. [Google Scholar] [CrossRef] - CD-adapco STAR CCM+; Computational Dynamics-Analysis & Design Application Company Ltd.: Melville, NY, USA.
- Ubbink, O. Numerical Prediction of Two Fluid Systems with Sharp Interfaces. Ph.D. Thesis, Department of Mechanical Engineering, Imperial College of Science. Technology & Medicine, London, UK, 1997. [Google Scholar]
- Muzaferija, S.; Peric, M. Computational of Free Surface Flows Using Interface Tracking and Interface Capturing Methods”, Nonlinear Water Wave Interaction; WIT Press: Southampton, UK, 1999. [Google Scholar]

Constant Temperature | ${T}_{atm}$ | 20° |

Initial Pressure | ${P}_{atm}$ | 101,325 Pa |

Initial Density | ${\rho}_{atm}$ | 1.18 km/m^{3} |

Universal gas constant | R | 8.314 J/mol·K |

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

Length | 40 | m |

Maximum Breath | 6.0 | m |

Depth | 2.0 | m |

GM (Metacentric height) | 0.86 | m |

${\mathrm{C}}_{\mathrm{B}}$ (Block coefficient) | 0.546 | Non-dimensional |

${\mathrm{C}}_{\mathrm{P}}$ (Prismatic coefficient) | 0.601 | Non-dimensional |

${\mathrm{C}}_{\mathrm{M}}$ (Midship section coefficient) | 0.908 | Non-dimensional |

The thickness of the body hull | 10 | mm |

Center of mass | (13.44, 0, 0.77) | m |

Measuring point (Pressure Density) | (0.8, −0.2, 0.95) | m (Relative to center of mass) |

Measuring point (Flooding water) | (0.8, −0.2, −0.25) | m (Relative to center of mass) |

The size of damaged opening | 300 × 300 | mm |

Calculating Displacement | 130,000 | kg |

Moment of inertia along x-axis | 1.0 × 10^{5} | km·m^{2} |

Moment of inertia along y-axis | 1.54 × 10^{6} | km·m^{2} |

Moment of inertia along z-axis | 1.62 × 10^{6} | km·m^{2} |

Case | Ventilation Level | Ventilation Ratio (%) | State of the Air |
---|---|---|---|

1 | Closed | 0 | Trapped air |

2 | Small ventilation hole | 6 | Vented air |

3 | Big ventilation hole | 12 | Vented air |

4 | Both ventilation holes | 18 | Vented air |

5 | Full ventilation | No compressed air |

Boundary Name | Boundary Type (This Paper) | Boundary Type [23,24] | Boundary Type [25] |
---|---|---|---|

Inlet | Velocity inlet | Velocity inlet | Velocity inlet |

Outlet | Pressure outlet | Velocity inlet | Pressure outlet |

Top/Bottom | Velocity inlet | Velocity inlet | Velocity inlet |

Left/Right | Symmetry plane | Pressure outlet | Symmetry plane |

Hull | Wall with no-slip condition | Wall with no-slip condition | Wall with no-slip condition |

Convection Term | 2nd order | 2nd order | 1st order (default) |

Temporal Discretization | 2nd order | 2nd order | 1st order (default) |

Part | Size (m) | Ratio Relative to the Base Size (%) |
---|---|---|

Deck | 0.24 | 40 |

Hull | 0.15 | 25 |

Bulkhead | 0.03 | 5.0 |

Small ventilation hole | 0.009 | 1.5 |

Big ventilation hole | 0.3 | 5.0 |

Damaged opening | 0.048 | 8.0 |

Flooding area | 0.072 | 12 |

Free surface | 0.15 | 25 |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Lin, Z.; Li, P.; Dong, Y.; Liu, F.
Time Domain Simulation of Damage Flooding Considering Air Compression Characteristics. *Water* **2019**, *11*, 796.
https://doi.org/10.3390/w11040796

**AMA Style**

Zhang X, Lin Z, Li P, Dong Y, Liu F.
Time Domain Simulation of Damage Flooding Considering Air Compression Characteristics. *Water*. 2019; 11(4):796.
https://doi.org/10.3390/w11040796

**Chicago/Turabian Style**

Zhang, XinLong, Zhuang Lin, Ping Li, Yue Dong, and Fei Liu.
2019. "Time Domain Simulation of Damage Flooding Considering Air Compression Characteristics" *Water* 11, no. 4: 796.
https://doi.org/10.3390/w11040796