ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 1 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

Table of Contents

3.3 Wave conditions ...... 8 1. PURPOSE ...... 2 3.4 Wind conditions ...... 8 2. NUMERICAL METHODS ...... 2 3.5 Simulations ...... 8 2.1 Accounting for the Inertia of Flood 3.6 Simulation data ...... 9 Water ...... 2 3.7 Analysis ...... 10 2.2 Additional Considerations ...... 4 3.8 Documentation of simulations ...... 10 3. PREPARATION, SIMULATIONS AND ANALYSIS ...... 5 4. VALIDATION ...... 10 3.1 Geometry ...... 5 5. REFERENCES ...... 11 3.2 Preparations ...... 7

Prepared by Approved

Specialist Committee on Stability in Waves 27th ITTC 2014 of the 27th ITTC

Date 03/2013 Date 09/2014

ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 2 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

Simulation of Capsize Behaviour of Damaged Ships in Irregular Beam Seas

relation between the ship motions and the flooding process. Ship motions depend on the 1. PURPOSE amount of flood water mass and in turn, flooding depends on the ship motions. The This procedure is for carrying out numerical whole process can be highly nonlinear, simulations on a damaged ship in beam seas to especially in case of large damage openings. predict the occurrence of capsizing. For a full Hence, nonlinear time domain simulation capsize-risk assessment a definition of capsize methods are required. is required in combination with an assessment procedure. These two items are outside the The numerical method used for simulations scope of this procedure. of a damaged ship in waves should be capable of including: The term capsizing refers to loss of buoyancy (sinking) as well as insufficient  Time varying mass, inertia terms and CoG righting arm to keep the ship under a prescribed location, heel angle. For instance, the IMO (Resolution  Large transient and large amplitude MSC 76/23) considers a RoRo ship to have motions, capsized when the instantaneous roll angle exceeds 30 deg or when the 3-minute average  Nonlinear hydrostatics, heel exceeds 20 deg. For naval ships capsize  Nonlinear wave excitation forces, definitions may be quite different.  Nonlinear hydrodynamic reaction forces, including roll damping, Generally the aim is to use computational  Nonlinear viscous reaction forces, tools that yield the most reliable results. For  Water on deck dynamics, and simulations for damaged ships however,  Flood water dynamics, including flow computational time requirements play a major between compartments and sloshing. role in selecting a suitable computational method. The large number of simulation 2.1 Accounting for the Inertia of Flood conditions (damage size and location, ship Water loading condition, sea states, etc.) and required simulation time length for determining a reliable Newton’s Second Law states that the force capsize-risk figure often prohibit the use of (moment) on a body is equal to its time rate-of- advanced methods such as CFD. change of momentum (angular momentum). For a body of constant mass (moment of inertia) 2. NUMERICAL METHODS this translates to F ma M I d dt However, for a body such as a rocket which is Simulation methods for a damaged ship in burning fuel and ejecting gas or a damaged ship waves must combine ship motion and flooding in a seaway taking on and possibly discharging dynamics. In general there exists a strong water, the analogy is not correct, but

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in fact the time-rate-of-change of mass must be where v and  are the relative velocity and taken into account. As the force must remain angular velocity of the flooding (discharging) independent of the coordinate system, a simple water relative to the vessel, respectively, with application of the rule for differentiation of the the same sign conventions on the flow velocities product of two functions is not correct—the as for vessel motions. All of the quantities contribution from the time-rate-of-change of mass term belongs on the left-hand side of the dm dt and can be determined from equation with the force. In the context of rocket analysis of the flow at the damaged opening (If propulsion, the time-rate-of-change of mass there is flow between flooded compartments, contribution is the equivalent of the thrust of the then the flow between the compartments must rocket motor, and the entire system must be be incorporated in a similar manner.) The looked at as a constant mass system. Similar evaluation of d I d t is somewhat more analogies apply to the time-rate-of-change of complex as it involves the actual shape of the moment of inertia. compartment.

If we represent the momentum of the vessel The floodwater in a fully filled compartment as p and the angular momentum as L , where is often treated as a part of the ship and treated as a solid. In rectilinear acceleration, the p m V and LI  , with m the mass of floodwater acts like a solid. In rotational the ship, V the velocity, I the moment of acceleration, the moment of inertia is smaller inertial tensor and  the angular velocity, then than that of a solid, because there is a part of Newton’s second law can be written as: water that does not rotate with the ship. Lee (2014) shows the ratio of the moment of inertia dV of floodwater and that of solids for various Fm dt shapes of compartments. (1) d MI CIIRLiquidSolid dt where I and I are the moment of When the mass and hence the moment of Liquid S o li d inertia are constant, then these equations reduce inertias of the floodwater when treated as liquid and solid respectively. to the traditional F ma form. However, in the damaged condition, the vessel’s mass and The following, Figure 1 shows the shapes of moment of inertia vary with time and the compartment treated in his study. equations of motion must be written in the above form. Rewriting equation (1) to account for the intake or discharge of floodwater as for a closed system yields:

dm dV F v m dt dt

dI d MI dt dt ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 4 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

퐴2 ℎ푏 퐼 = 휌푘 ( ) , 퐿푖푞푢푖푑 푒 휋 ℎ2 + 푏2 where A is the cross-sectional area of the tank, h is the height of the tank, b is the width of the tank, and ke is given by the following:

(휋⁄4)1⁄2 for rectangle

1⁄3 (휋⁄2√3) for hexagon 1⁄4 h/b = 0.25 h/b = 0.5 h/b = 0.75 h/b = 1.0 푘푒 = 휋 ( ) for octagon Figure 1 Various cross-section shapes of tanks 8(√2 − 1) useful for application from Lee (2014) { 1 for ellipse

The inertias of the fluid in tanks of different 2.2 Additional Considerations aspect ratios and shapes, Figure 2, become small as the aspect ratio goes to unity. The solid lines Nonlinearity is required to account for the of Figure 2 are analytical or numerical results changes in mean heel, draft and trim due to while the dashed lines are an estimation formula flooding. The principal axes of inertia may that provide accurate results. change as well due to the flood water mass.

1 Water may appear on the weather deck. Calculated Furthermore, the method of determining the Proposed Formula viscous reaction forces should be capable of 0.8 R dealing with a ship drifting in irregular beam

_

C

a

i seas.

t

r

e

n

i 0.6

f

o

t In view of the use of the instantaneous roll

n

e

m and mean heel in survivability criteria it is o 0.4

m

f recommended that unsteady wind loading be

o

o

i

t included in the excitation forces. It is noted that

a R 0.2 unsteady wind loads may also affect the Rectangle flooding process through their effect on the heel Hexagon angle. 0 Octagon Ellipse 0 0.2 0.4 0.6 0.8 1 h/b or b/h Apart from a method that includes nonlinear hydrodynamics, the effects of flooding must be Figure 2 Moment of Inertia prediction of fully accounted for. Air compressibility effects must filled liquid for various shaped tanks; be determined when the compartments are not calculated and estimated from Lee (2014) or partially ventilated. For RoRo type ships, sloshing of flood water on large, open deck The approximate formula for the moment of spaces is important. The method should be inertia of the fluid in a tank given in Lee (2004) capable of dealing with multi-compartment is: configurations connected through doors, vents ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 5 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

(down flooding) and ducts. The size of openings type simulations, i.e. performing a large number can be large and in and outflow of flood water of time domain simulations. For example, a full may have a chaotic character. capsize-risk assessment is estimated to require a simulation duration of 10,000 hours real time: 5 Several types of flooding methods can be loading conditions, 10 damage positions and /or used, varying from fast methods based on sizes, 20 sea states, 10 wave seeds and a 1 hour Bernoulli’s law to more advanced but complex simulation duration. This means that the CFD based methods, including SPH methods. simulation tool preferably is faster than real time Most times a compromise must be sought and that it must be used on multi-processor between fidelity and computational resources. hardware.

Most flooding methods are based on Another feature that may be required for Bernoulli type equations. By using a pressure simulations for damaged ships is the ability to correction method air compressibility can be include effects due to: taken into account. Such flooding methods have been shown to yield accurate results for ships  collapsing watertight doors and bulkheads, with relatively small compartments (no  leaking (watertight and non-watertight) significant sloshing) and small openings, see doors and bulkheads, Ruponen (2007).  counter flooding measures, for instance pumping ballast water in compartments, However, for RoRo vessels sloshing can be  cross flow ducts, etc. of importance. This can be approximated by using the equivalent gravity angle approach.  forward speed effects on water ingress at Better yet, shallow water equations can be used the instant the damage is created, to account for sloshing, and should yield more  flood water loads and loads in waves, for accurate results, see Cho et al (2006), at the analysing the (weakened) ship structure. expense of a computational burden. Sloshing should be taken in to account when the natural 3. PREPARATION, SIMULATIONS frequency of the water motion in a flooded 휋 AND ANALYSIS compartment 휔 = √𝑔ℎ is close to the 푛푓 푏 frequency of the ship roll motion ω: 0.7휔 ≤ 3.1 Geometry 휔푛푓 ≤ 1.25휔. Here h is the height of the water level and b is the width of the compartment. The discretisation of the hull form should be such that buoyancy and restoring forces can be Coupling the seakeeping method with CFD accurately predicted. A three-dimensional panel for flooded compartments is a logical next step. discretisation is recommended in lieu of a CFD methods are capable of dealing with highly discretisation based on sections. The calculated complex and chaotic flows as well as sloshing displacement and GZ curve should be within and air compressibility. For relatively simple 2.5% of that of well-established hydrostatics compartment configurations such methods have software. Other hydrostatic data such as water appeared recently, see Strassner et al (2009), yet plane area, block and prismatic coefficients are the computational burden seems still too high also useful checks on the geometry for application to ships with a complex discretisation. A check on geometry errors by compartment arrangement and for Monte-Carlo means of 3D surface plots is recommended. It is ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 6 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

noted that besides hydrostatics, wave excitation If no information is available for a specific ship, forces are also sensitive to the geometry the ITTC Procedure 7.5-02-07-04.2 Model discretisation and the same discretisation error Tests on Damage Stability in Waves margin as for the GZ curve can be used: 2.5%. recommends volume permeability’s as follows: This should be verified by grid refinement.  Void spaces: 100% According to IMO (MSC.76/23/Add.1), for  Passenger or accommodation spaces: 80% Ro-Ro ships the superstructure should be  Engine room: 70% included up to at least three superstructure deck  Machinery spaces: 70% heights above the bulkhead deck to include effects of reserve buoyancy, wave excitation For Ro-Ro ships, the ITTC Procedure 7.5- and down flooding openings. 02-07-04.2 Model Tests on Damage Stability in Waves recommends volume recommends using The correct mass, position of the centre of SOLAS-defined permeabilities: gravity and radii of gyration in the transverse and longitudinal directions corresponding to the  Void spaces: 98% data on the full scale ship should be used. In the  Passenger or accommodation spaces: 98% absence of more accurate knowledge, a value of  Engine room: 85% 0.35B to 0.45B for the roll radius of gyration,  Machinery spaces: 60% and 0.25LPP for both the pitch and yaw radii of gyration are generally used. The roll radius of inertia can also be estimated by: When CFD is used to determine flooding, the permeability can be accounted for by using simple shapes such as blocks or cylinders. When 1 2 0.BH.BH 40 6 22 using Bernoulli-type flooding methods, the 12 kxx permeability’s can be specified when generating 2 T. Hz05 G tank tables. Tank tables define the relation where B, d and T are the beam, depth and draft between the water level and the mass and centre of mass of the floodwater in a compartment. In of the ship respectively and HCG is the height of the centre of gravity above the water surface. practice, the permeability is usually not homogeneously distributed over the Forces due to appendages such as rudders, compartment volume, however this is generally skegs, bilge keels and fin stabilisers, affecting neglected in Bernoulli-type flooding methods. the roll motion and drift velocity should be included. For roll damping one is referred to the Another feature specific for Bernoulli-type flooding methods is the need to use discharge ITTC Procedure 7.5-02-07-04.5 on Numerical Estimation of Roll Damping. coefficients. These coefficients relate the pressure difference over an opening to the flow The internal configuration should include all velocity through that opening. Discharge compartments, vents, other openings and cross coefficients typically have a value of CD=0.60 to ducts having an effect on flooding and air 0.70 for small openings, see Ruponen (2007). compression. The location and size of damage openings is Surface and volume permeability’s of generally defined in the applied damage stability floodable spaces should be modelled correctly. criteria. The location follows from either the ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 7 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

most probable position or a worst location in and location of the centre of gravity within 2.5%. terms of flooding effects, see for instance Next, the GZ -curves for the intact and SOLAS 90 (MSC.194(80) regulation II- equilibrium damaged condition (calm water) 1/8.2.3.2). The opening width is typically 10-15% should be compared with these from hydrostatic of the ship length. The height of the opening software packages. The differences in covers two floodable decks. The shape of the should be less than 2.5% up to the point of damage opening is a simple triangle, rectangle vanishing stability. or trapezoid. More detailed information can be found in SOLAS 90 regulation II-1/8.4.1 or in Next, a zero forward speed roll decay MSC 76/23/Add.1. simulation should be performed for the intact case to check the external roll damping. Initial Other rules/criteria apply to for instance amplitudes of 15 to 25 degrees are to be used. naval vessels and high speed craft (see HSC For the equilibrium damage case with a constant code (2000)). amount of flood water (closed damage opening) During the simulations, the instantaneous a roll decay simulation can be performed as well. submergence of the opening must be determined, It is recommended to compare the derived roll accounting for ship motions and wave elevation. damping response for the intact and damaged If the vertical extent of the opening is large, a cases with those from model tests on a similar horizontal strip wise approach should be taken ship and damage cases. This is of particular to deal with local pressures and velocities. For a relevance when sloshing is expected to occur. large horizontal opening extent, variations in When no experimental data are available more pressures and velocities can be taken in account general validation data can be used, see Section by subdividing the opening in more than one 4. part. It should be realised that before and/or during roll decays with flood water present in a 3.2 Preparations multiple compartment configuration, asymmet- ric and up and down flooding can occur which Since flooding simulations in waves involve can make the resulting roll motion non-periodic a number of complex physical phenomena with and rather dependent on the initial heel angle a sometimes chaotic nature, small differences in and potentially on how long the vessel was held wave induced ship motions, damage openings, at the initial heel angle. The procedure and vents, doors, etc., affecting the flooding process, results should be documented, especially may have large effects on the final result, i.e. to differences between simulated and experimental capsize or not to capsize. Furthermore, it is roll response. difficult to distinguish between cause and effect when inspecting for instance time traces of the Generated tank tables should be visually amount of flood water in certain compartments. inspected for inconsistencies and irregularities. Therefore it is recommended to check and document a number of basic properties before For the equilibrium damage condition in performing the actual time domain simulations. calm water, the water level in fully ventilated compartments extending through the water line As a first basic check, the trim and draught should be equal to the water level outside the at calm water should match the displacement ship (sea level). For non-vented compartments, ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 8 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

the air pressure should match the hydrostatic exceeded, a series of simulations must be pressure at the opening. performed for a matrix of HW1/3 and TP combinations, selected from the wave statistics It is also recommended that a sensitivity for the area of operation. For efficiency it is analysis on discharge coefficient values and recommended to start with wave spectra at the compartment permeability be performed. expected survivability limit and to go upwards and/or downwards in wave steepness until the Furthermore, it is recommended to limit is well defined. investigate the basic drifting behaviour (velocity and heading) of the ship under influence of a The wave signal generated from the constant force, for instance a constant wind spectrum should not repeat during a simulation. loading. Drifting in regular waves can be It is recommended to use randomly spaced investigated as well (for instance for frequency bands and to use one very narrow deterministic validation), but it should be noted frequency band near the peak frequency. At that the drifting behaviour in regular waves can least 100 frequencies should be used to be markedly different from that in irregular discretise the long-crested wave spectrum. For waves. short-crested spectra 100 frequencies times 25 wave directions are recommended for 3.3 Wave conditions discretisation.

The simulations are generally carried out in 3.4 Wind conditions long-crested irregular beam waves. Simulations and model tests have shown that the flooding At zero speed (drifting), wind forces can be process in regular waves can be different than important as they have an effect on ship heading, and not representative of that in irregular waves. drifting direction and velocity and thereby on Therefore, it is recommended not to perform flooding and heel angles. The wind velocity can simulations in regular waves other than for be constant or wind gusts and direction validation purposes. No data is available on the variations can be generated from multi desirability to conduct simulations in short- directional wind velocity spectra. Wind load crested seas and this could be subject to further coefficients in six degrees of freedom can be investigation. obtained from wind tunnel experiments and CFD, or from empirical methods based on non- The simulation method should be capable of dimensional wind tunnel data. Examples are including wave spectra for the area of operation Isherwood (1972), Blendermann (1994) and or as required by rules. In absence of Fujiwara et al (1998). information on specific spectrum data, JONSWAP and ITTC (1978) spectra should be used for limited fetch and ocean waves, 3.5 Simulations respectively. A maximum characteristic wave 2 Forward speed effects at the instant that steepness of 퐻W1/3⁄(𝑔푇푝 ⁄2휋) = 0.05 is damage occurs can have an important effect on recommended as a guide. initial flooding (Herald of Free Enterprise, Estonia). However, starting the simulation with For determining the survival wave height, i.e. the condition (speed and heading) at which the the wave height at which the capsize criteria are damage is expected to occur adds more degrees ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 9 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

of freedom to the problem and the effects of an of having the damage opening at the leeward instantaneous opening or damage at forward side should be investigated. speed with another ship present (collision) can probably not be simulated adequately with the Per condition (displacement, CoG location, current state of the art. As a compromise and sea state, damage opening, etc.) at least 10 until more complete tools and more powerful simulations should be performed with a duration hardware are available, the ship can be initially sufficient for 30 minutes after reaching a steady positioned in beam seas with zero drifting state (in terms of the three minute average draft, velocity. The wave height should be slowly trim, heel angles and drift velocity) to obtain increased from zero to its nominal height extreme value statistics. In each of the 10 through the use of a ramp function. A similar simulations a different wave realisation must be ramp function can be used for the wind velocity. obtained. During this ramp-up period the ship will assume its initial drifting velocity and heading angle. 3.6 Simulation data

The damage opening may be closed initially In order to analyse the possible capsizing and then opened once the wave height has process, the following quantities should be reached its nominal value. The initial transient stored, as applicable, at a sufficient sampling heel can be simulated in this way, but it is not rate (at least 20 divided by the natural roll very representative of the actual transient when period): a collision or grounding occurs. Alternatively, the simulation can be started with the  Ship position in space. equilibrium amount of flood water on board and  Average ship draught, heel angle, drifting the corresponding equilibrium draft, trim and velocity and heading relative to the wave heel. The damage opening then opens at the start direction. of the simulation.  Ship motions (displacements, velocities and accelerations) in 6 degrees of freedom. For damage model testing of passenger ships an additional heeling moment that is likely to be  Wave elevation at the reference ship CoG present in an emergency situation can be position, the relative wave elevation at the included. This can be caused by passengers damage opening(s) and possibly at a gathering at the edge of the deck for life boat number of positions at the deck edge. launching. For RoPax ferries a heeling moment  Wind characteristics (speed, direction and resulting in a 1 degree heel angle towards the gradient profile) at the ship position. damage side is recommended by IMO-MSC  Floodwater mass and level in each 76/23/Add.1. It is noted here that heeling compartment, flow rate through openings moments may already be present due to wind. and air pressure for non-ventilated compartments. During the simulation the ship must be allowed to drift freely under influence of waves Visualisation of the ship motions in and wind. The damage opening should be facing combination with the instantaneous floodwater the incident waves since experience indicates levels and openings in the compartments is that this is generally worse than when the indispensable for analysing the simulation damage opening is at the leeward side. results. Nevertheless, for some critical cases the effect ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 10 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

3.7 Analysis simulation runs and their duration should be documented. Considering the possibly chaotic behaviour of flooding in irregular waves, the number of The report should also contain the simulation runs and their duration should be following (where applicable): documented. The level of confidence of estimated capsizing probability should be  Loading condition, damage opening and calculated by using the formula of a binomial internal arrangement. External probability distribution. A simple estimate of configuration details including the capsizing probability, pc, is a ratio of the appendages. number of capsizing events, Nc, to that of  Differences in predicted and expected different realizations, N, as follows (from ITTC hydrostatics should be reported. procedure 7.5-02-07-04.1, Model Tests on  A description of the capsizing modes Intact Stability): identified.  Ship condition information including 푁푐 푝 = GZ curves with and without flood water 푐 푁 at equilibrium condition. If p is the true capsizing probability, the  Roll decay simulation time series and confidence interval of capsizing probability can derived coefficients. be calculated by the following equation:  Wave spectrum and wave characteristics.  Initial conditions. 2  Statistical analysis of the time series of ∆푝 = √푝푐(1 − 푝푐)푧1−∝́ ⁄2 √푁 wave elevation and ship motions in 6 degrees of freedom. Here, 푧1−∝́ /2is the (1 − ∝́ ⁄2) quantile of the standard normal distribution, which can be determined from the table of normal 4. VALIDATION distributions and ∝́ is the confidence level of the predicted capsizing probability. The range of In absence of specific model test data, the error tolerance of the capsizing probability can cases described below can be used for validation finally be determined as follows: purposes.

∆푝 ∆푝 In van Walree (2007) and Ruponen (2006) 푝 − ≤ 푝 ≤ 푝 + benchmark model tests are described that can be 푐 2 푐 2 used for validation. The case considered is a with a probability of (1-ά). barge with small damage openings. Detailed experimental data are available.

3.8 Documentation of simulations In Spanos and Papanikolaou (2008) a validation study of several codes is presented The main simulation results should be based on model tests on a Ro-Ro ship. presented as capsizing probabilities in irregular seas. They should be a function of the main ship Further validation data for these two cases is characteristics and operational and presented by Corrigan (2010). environmental parameters. The number of ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 11 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

Cho et al (2009) present experimental results Isherwood R.M., “Wind resistance of merchant for a damaged cruise ship at calm water and in ships”. Transactions Royal Institution of waves. Detailed data are available at the Naval Architects, Vol. 114, pp. 327–338, Stability in Waves committee. 1972.

Macfarlane et al (2010) describe damage Lee, G. J. “Moment of Inertia of Liquid in a model tests on a destroyer with large openings. Tank”, Int. J. of Naval Architecture and Special attention is paid to the transient roll Ocean Engineering, Vol. 6, No. 1, pp. 132– immediately after the occurrence of the damage. 150, 2014.

Macfarlane, G.J, Renilson, M.R. and Turner, T., 5. REFERENCES ‘The Transient Effects of Flood Water on a Warship in Calm Water Immediately Blendermann, W., "Parameter identification of Following Damage’, Transactions RINA, wind loads on ships", Journal of Wind International Journal of Maritime Engineering and Industrial Aerodynamics, Engineering, Vol. 152, Part A4, 2010. Vol. 51, pp. 339-351, 1994. Maritime Safety Committee, publication Cho S. K., Hong, S.Y. and Kyoung, J. H. , “The MSC.194(80), International Maritime Numerical Study on the Coupled Dynamics Organisation, 2005. of Ship Motion and Flooding Water“, Proc. STAB 2006, Rio de Janeiro, pp. 599-605, Maritime Safety Committee, publication 2006. MSC.76/23/Add.1, International Maritime Organisation, 2002. Cho S. K., Sung H., Nam B., Hong, S. and Kim K. , “Experimental Study on Flooding of a Ruponen P., ”Progressive Flooding of a Cruiser in Waves“, Proc. STAB 2009, St. Damaged Passenger Ship”, Ph. D. Thesis, Petersburg, pp. 233-243, 2009. Helsinki University of Technology, 2007.

Corrigan P., “Flooding simulations of ITTC and Ruponen P., “Model tests for the Progressive Safedor benchmark test cases using CRS Flooding of a Box-Shaped Barge”, Report Shipsurv software”, Proc. 11th International M-292, Helsinki University of Technology, Ship Stability Workshop ISSW 2010, 2006. Wageningen, pp. 238-245, 2010. Spanos D.A. and Papanikolaou A., “Benchmark Fujiwara T., “Estimation of Wind Force and Study on Numerical Codes for the Prediction Moments Acting on Ships”, Journal of the of the Motions and Flooding of Damaged Society of Naval Architects of Japan, Vol. Ships in Waves”, Report SAFEDOR-R- 183, 1998. 7.3.4-2008-05-31.NTUA.rev-0, 2008.

HSC Code: International Code of Safety for Strassner C., Jasionowski A. and Vassalos D., High-Speed Craft, Published by IMO, “Calculation of Time-to-Flood of a Box London, 2000. Shaped barge by using CFD”, 10th International Conference on Stability of ITTC – Recommended 7.5-02 -07-04.4 Procedures and Guidelines Page 12 of 12 Numerical Simulation of Capsize Effective Date Revision Behaviour of Damaged Ships in 2014 01 Irregular Beam Seas

Ships and Ocean Vehicles, St. Petersburg, Progress report on benchmark testing of Russia, 2009. numerical codes for time-to-flood prediction, SLF 50/8, IMO, July 2007. Walree F. van, “Time dependent survivability of passenger ships in damaged condition”,