The motions of a flooded ship in waves are difficult to evaluate. They are affected by complex phenomena involving ship and floodwater dynamic interactions. Several numerical methods have been proposed to estimate the dynamic behavior of a damaged ship in waves. In this article, a fast simulation tool is developed to tackle the problem, aiming at a simplified method with an acceptable accuracy of the results. A novel approach in simulating floodwater effects on ship motions is presented. The method allows modeling the floodwater motions (seen as lumped mass) out of phase from ship motions. This technique is based on the basic fluid mechanics knowledge for a liquid in a uniformly accelerated tank. The study intends to analyze the behavior of a flooded ship in regular beam waves, for compartment fillings that involve shallow and intermediate fluid depths. The nonlinear model for the roll damping moment of a ship is implemented. An attempt to model viscous effects in the floodwater dynamics is proposed and applied. Two sets of applications are carried out on two different hull models. The comparisons of the intact and of the flooded ship responses in waves are conducted and discussed.
RuponenP. Adaptive time step in simulation of progressive flooding. Ocean Eng2014; 78: 35–44.
2.
VassalosDJasionowskiA. Emergency response in ship flooding casualties. In: Proceedings of the 13th international ship stability workshop, 23–26 September 2013, pp.259–263. Brest: International Conference on Stability of Ships and Ocean Vehicles.
3.
VarelaJMRodriguesJMGuedes SoaresC. On-board decision support system for ship flooding emergency response. Procedia Comput Sci2014; 29: 1688–1700.
4.
KorkutEAtlarMIncecikA. An experimental study of global loads acting on an intact and damaged Ro-Ro ship model. Ocean Eng2005; 32(11–12): 1370–1403.
5.
LeeDHongSYLeeGJ. Theoretical and experimental study on dynamic behavior of a damaged ship in waves. Ocean Eng2007; 34(1): 21–31.
6.
LeeSYouJLeeHet al. Experimental study on the six degree-of-freedom motions of a damaged ship floating in regular waves. IEEE J Ocean Eng2015; 41: 40–49.
7.
BegovicEMortolaGIncecikAet al. Experimental assessment of intact and damaged ship motions in head, beam and quartering seas. Ocean Eng2013; 72: 209–226.
8.
AcanforaMDe LucaF. An experimental investigation into the influence of the damage openings on ship response. Appl Ocean Res2016; 58: 62–70.
9.
DomehVDKSobeyAJHudsonDA. A preliminary experimental investigation into the influence of compartment permeability on damaged ship response in waves. Appl Ocean Res2015; 52: 27–36.
10.
OgawaYOhashiK. Studies on an assessment of safety with regard to the damage stability of passenger ships. In: Proceedings of the 12th international ship stability workshop, 12–15 June 2011, pp.271–275. Washington, DC: International Conference on Stability of Ships and Ocean Vehicles.
11.
StrasserCJasionowskiAVassalosD. Calculation of the time-to-flood of a box-shaped barge by using CFD. In: Proceedings of the 10th international conference on stability of ships and ocean vehicles, 22–26 June 2009, pp.733–740. Sankt Petersburg: International Conference on Stability of Ships and Ocean Vehicles.
12.
Sadat-HosseiniHKimDHCarricaPMet al. URANS simulations for a flooded ship in calm water and regular beam waves. Ocean Eng2016; 120: 318–330.
13.
LiXZhangTZhangYet al. Numerical analysis of ship motion coupled with tank sloshing. In: Proceedings of the oceans 2014: Taipei, Taipei, Taiwan, 7–10 April 2014. New York: IEEE.
14.
KrataP. The impact of sloshing liquids on ship stability for various dimensions of partly filled tanks. TransNav: Int J Mar Navig Saf Sea Transp2013; 7(4): 481–489.
15.
KimYNamBWKimDWet al. Study on coupling effects of ship motion and sloshing. Ocean Eng2007; 34(16): 2176–2187.
16.
GaoZGaoQVassalosD. Numerical study of damaged ship flooding in beam seas. Ocean Eng2013; 61: 77–87.
17.
Sadat-HosseiniHKimD-HLeeSKet al. CFD and EFD study of damaged ship stability in calm water and regular waves. In: Proceedings of the 11th international conference on stability of ships and ocean vehicles, Athens, 23–28 September 2012.
18.
WangXAraiM. A numerical study on coupled sloshing and ship motions of a liquefied natural gas carrier in regular and irregular waves. Proc IMechE, Part M: J Engineering for the Maritime Environment2013; 229(1): 3–13.
Le TouzéDMarshAOgerGet al. SPH simulation of green water and ship flooding scenarios. J Hydrodyn2010; 22(5): 231–236.
21.
TouzéLHashimotoHGrenierNet al. Comparisons of MPS and SPH methods: forced roll test of a two-dimensional damaged car deck. In: Proceedings of the 29th international workshop on water waves and floating bodies, 30 March–2 April 2014, pp.1–4. Osaka, Japan: Department of Naval Architecture & Ocean Engineering, Osaka University.
22.
Cercos-PitaJLBulianGPérez-RojasLet al. Coupled simulation of nonlinear ship motions and a free surface tank. Ocean Eng2016; 120: 281–288.
23.
FonfachJMManderbackaTNevesMAS. Numerical sloshing simulations: comparison between Lagrangian and lumped mass models applied to two compartments with mass transfer. Ocean Eng2016; 114: 168–184.
SantosTAGuedes SoaresC. Study of damaged ship motions taking into account floodwater dynamics. J Mar Sci Technol2008; 13(3): 291–307.
27.
LorkowskiODankowskiHKluweF. An experimental study on progressive and dynamic damage stability scenarios. In: Proceedings of the ASME 2014 33rd international conference on ocean, offshore and Arctic engineering, 8–13 June 2014. OMAE2014-23388, pp.1–10. San Francisco, CA: American Society of Mechanical Engineers (ASME).
28.
GodderidgeBTurnockSRTanM. A rapid method for the simulation of sloshing using a mathematical model based on the pendulum equation. Comput Fluid2012; 57: 163–171.
29.
FriesNBehruziPArndtTet al. Modelling of fluid motion in spacecraft propellant tanks-sloshing. In: Proceedings of the space propulsion 2012 conference, 7–10 May 2012, pp.1–11. Bordeaux: AAAF - ESA - CNES.
30.
PapanikolaouAZaraphonitisGSpanosDet al. Investigation into the capsizing of damaged Ro-Ro passenger ships in waves. In: Proceedings of the 7th international conference on stability of ships and ocean vehicles, 7–11 February 2000. Launceston, TAS, Australia: International Conference on Stability of Ships and Ocean Vehicles.
31.
ManderbackaTMikkolaTRuponenPet al. Transient response of a ship to an abrupt flooding accounting for the momentum flux. J Fluid Struct2015; 57: 108–126.
32.
JasionowskiA. An integrated approach to damage ship survivability assessment. Glasgow: University of Strathclyde, 2001.
33.
PapanikolaouAZaraphonitisGSpanosD. On a 3D mathematical model of the damage stability of ships in waves. In: Proceedings of the 6th international conference on stability of ships and ocean vehicles, 22–27 September 1997, pp.81–98. Varna: International Conference on Stability of Ships and Ocean Vehicles.
34.
SeokKyuKChoHSungSet al. Study on the motions and flooding process of a damaged ship in waves. In: Proceedings of the 11th international ship stability workshop, 21–23 June 2010, pp.1–9. Wageningen: International Conference on Stability of Ships and Ocean Vehicles.
35.
SpanosDMaronAPapanikolaouA. On the motions of a flooded Ro-Ro ferry in beam seas. In: Proceedings of the 10th international conference of international maritime association of the Mediterranean (IMAM’ 2002), 13–17 May 2002. Rethymno: International Maritime Association of the Mediterranean.
36.
De KatJSpyrouKUmedaN. Dynamics of a ship with partially flooded compartment. In: VassalosDHamamotoMMolyneuxDet al. (eds) Contemporary ideas on ship stability. 2000, pp.249–263. Oxford, UK: Elsevier Science Ltd.
37.
LetiziaL. Damage survivability of passenger ships in a seaway. Glasgow: University of Strathclyde, 1996.
38.
AcanforaMCirilloA. A simulation model for ship response in flooding scenario. Proc IMechE, Part M: J Engineering for the Maritime Environment2017; 231(1): 153–164.
WhiteFM. Pressure distribution in a fluid. In: WhiteFM (ed.) Fluid mechanics, vol. 6. 4th ed.New York: McGraw-Hill Series in Mechanical Engineering, 2010.
41.
MatusiakJ. Dynamics of a rigid ship. Espoo: Aalto University Publication Series SCIENCE + TECHNOLOGY, 2013.
42.
FaltinsenOMTimokhaA. Sloshing. Cambridge: Cambridge University Press, 2014.
43.
ManderbackaTLMatusiakJERuponenP. Ship motions caused by time-varying extra mass on board. In: Proceedings of the 12th international ship stability workshop, 12–15 June 2011, pp.263–269. Washington, DC: International Conference on Stability of Ships and Ocean Vehicles.
44.
SkejicRFaltinsenOM. A unified seakeeping and maneuvering analysis of ships in regular waves. J Mar Sci Technol2008; 13(123): 371–394.
45.
FaltinsenOM. Sea loads on ships and offshore structures, vol. 1. Cambridge: Cambridge University Press, 1990.
KeuleganGH. Energy dissipation in standing waves in rectangular basins. J Fluid Mech1959; 6(1): 33–50.
48.
BulianGFrancescuttoA. Second generation intact stability criteria: on the validation of codes for direct stability assessment in the framework of an example application. Polish Marit Res2013; 20(80): 52–61.
