An Explicit Progressive Flooding Simulation Method

Transcription

1 Ships and Ocean Vehicles, September 212, Athens, Greece 1 An Explicit Progressive Flooding Simulation Method Hendrik Dankowski, Institute of Ship Design and Ship Safety, Hamburg University of Technology, dankowski@tu-harburg.de ABSTRACT Several severe ship accidents in the past were caused by the flooding of the internal compartmentation of these ships. In most cases the occurred flooding scenario is very complicated and it is not directly obvious, how a certain damage case caused the actual loss of the whole ship. To figure out the most likely scenario, it is necessary to analyze many different possible flooding paths. For more detailed accident investigations and to prevent such accidents in the future, a new numerical progressive flooding simulation method is developed. A direct approach is chosen, which computes the flux between the compartments based on the Bernoulli equation and the current pressure heads at each intermediate step. The flooding paths are modeled by using graph theory. This quasi-static approach fills the gap between dynamic seakeeping simulations and purely hydrostatic damage calculations. The developed method is validated by investigating the accident of the S.S. Heraklion occurred in In addition, the results of the simulation method are compared with model tests of a barge performed by Ruponen at the Helsinki University of Technology in 26. Key Words: Progressive Flooding; Sinking; Ship Design; S.S. Heraklion; Accident Investigation; Ship Safety 1. INTRODUCTION Several progressive flooding simulation methods for damaged ships have been developed in recent years (Vassalos et al., 1998; Papanikolaou et al., 23; Palazzi and de Kat, 24; Schreuder, 25; Ruponen, 27, to mention but a few). These simulations allow to better understand the floating behaviour of ships after damage. The method presented here focuses on the main physical effects and represents a fast, direct approach of solving the underlying mathematical model allowing to investigate several design options in a short period of time. The simulation method is implemented in the ship design environment E4, a first-principal ship design software used and developed at our institute together with partners from the german shipbuilding industry. In doing so, direct access to the whole ship data model and already implemented computational algorithms like hydrostatic evaluations is granted. 2. PHYSICAL MODEL The flooding process is mainly driven by pressure differences leading to relatively slow internal water flows. The surfaces of the water levels are expected to remain mostly horizontal. These kind of flows are quite accurate described by the Bernoulli equation. 2.1 Basic Equations The flooding of a floating object is driven by certain pressure differences at openings leading to the in- or egress of flood water. These fluxes

2 Ships and Ocean Vehicles, September 212, Athens, Greece 2 can be idealized by the incompressible, stationary, non-viscous and rotational-free Bernoulli equation given in Equation 1 formulated for a streamline connecting point a and point b: p a p b ρ g + u2 a u 2 b 2 g + z a z b ϕ ab g = dz. (1) Any dissipative effects are modeled by a semi-empirical discharge coefficient proportional to the flux velocity. If the outflow is free (left side of Figure 1), the pressure height difference is dz = p a p b ρ g + u2 a 2 g + z a z. (2) The flux through a deeply submerged opening (right side of Figure 1) is independent of the location z of the opening and given by dz = p a p b ρ g + u2 a u 2 b 2 g + z a z b. (3) 2.2 Large Openings More challenging is the determination of the flux over large openings, since the cross section area and the fluid velocity may vary over the opening. In general, the flux is given by the integral Q = u da = u(z(s)) y(s) ds, (6) A t where the velocity u is best described as a function of the earth fixed vertical direction z. The width y of the opening varies in the plane of the cross section. To model any shape of opening, it is described as a plane polygon oriented arbitrary in space. For the flux integration it is discretized in several z-stripes (see Figure 2). s s 1 y 1 y(s) y s z 1 z Figure 2 Stripe in z-direction z a p a a p b b z a p a a p b b In this case the relation between the two directions z and s is linear: z z b z b Figure 1 Small openings z p This pressure height difference dz yields a fluid velocity u = 2 g dz. (4) The integration of the velocity over the area of the opening under the assumption of a perpendicular flow direction leads to the total flux V t = Q = Q = A A u da = A u n da, u da. (5) z(s) = z + s z1 z s 1. (7) The free outflow flux of each stripe can be determined analytically by the definite integral with Q = 2 2 g [y 1 h y h s z + 2 (y 1 y ) 5 (z 1 z ) (h h 5 2 )], (8) α = p a ρ g p b ρ g + u2 a 2 g, s z = z 1 z, s 1 h 1 = z a z 1 + α, h = z a z + α. Among others Schröder and Zanke (23) showed that the flux through a rectangular weir is given to be: Q = 2 3 B 2 g h 3 2. (9)

3 Ships and Ocean Vehicles, September 212, Athens, Greece 3 This is a special of Equation 8 with a constant width B = y = y 1 of an upright cross section (s = 1), no pressure difference α = and height h = z a z together with h 1 =. This kind of flux integration can be performed in the same way for further basic opening shapes like circular holes or manholes. 2.3 Flooding System The connections between the compartments of a ship by openings are nicely modeled by directed graphs. A simple example is shown in Figure 3 describing the validation case B from Ruponen (27), which will later be investigated in more details. This graph is de- 6 R21P 1 Outside DB2 3 5 R R21S 2 DB R R R22 Figure 3 Simple subdivision graph fined by the edges representing the openings and the neighboring nodes representing the compartments. Each node is defined by an ID number and a name. The direction of the edge defines the sign of the flux through the opening. Using this kind of definition for the flooding system is a very convenient and direct way. All methods and algorithms developed in graph theory can simply be applied to flooding systems of ships. This way questions like Which neighbors belong to a certain compartment in question? can easily be answered. 2.4 Mass Balance Using a flooding graph, the total flux of one compartment is given by the sum over all openings belonging to this compartment. For example, the flux for compartment R21 (No. 5) shown in Figure 3 is given by Q 5 = Qo 3 Qo 4 Qo 5 + Qo 6 Qo 9. Integrating the flux to one compartment in the time domain gives the amount of water transported in a certain time step from one compartment to its neighbor(s): V = Q(t) dt. (1) t This transported water volume leads to new filling levels in the compartments, since the fluid volume in each compartment changes. The determination of this new filling has to be done iterative, since the compartment geometry is usually arbitrary and the filling level depending on the current waterline and fluid volume is not given analytically, especially if the ship is heeled and/or trimed. 2.5 Flux Integration The system of ordinary differential equations to be solved is of first order and nonlinear. The volume flux V to each compartment must be equal to the flux Q o through all coressponding openings, where the opening fluxes depend nonlinear on the water heights respectively the water volumes in each compartment. V (t) = Q o (t) (11) Q o (t) f(v (t)) (12) By using a simple Euler forward scheme assuming a constant flux during one time step, the compartments are decoupled, since the new flux depends only on the water heights of the last time step. dv = V (t 1) V (t ) = dt Q (t ) o (13) To better account for the nonlinearity and the coupling of the compartments, a kind of

4 Ships and Ocean Vehicles, September 212, Athens, Greece 4 weighted predictor-corrector scheme for the fluxes through the openings is applied dv = dt (ω Q (tm) o + (1 ω) Q (t ) o ), (14) while the intermediate value Q o (t m ) is the flux after the prediction step and ω is the relaxation factor. This inner iteration can be sketched as follows: - Predict opening fluxes - Propagate predicted volumes assuming a constant flux - Calculate new filling levels - Recompute opening fluxes based on these new fillings - Correct volume fluxes acc. to Equation 14 - Reset volumes and propagate again, recompute filling levels based on the corrected flux and proceed This strategy avoids efficiently the flux direction change during one time step caused by the explicit characteristic of the method. In practice, only two inner iterations (one predictor-corrector step) are sufficient to reduce the fluctuations and to significantly stabilize the whole simulation. A direction change in the flux happens, if the filling levels of two neighboring compartments are very close and the propagated volume assumed by a constant flux leads to a change of the sign of the flux. How often this overflowing happens depends on the time step and the size of the opening. Even for a very small time step, the flux only becomes zero if the extrapolated volume change leads to exactly equal filling levels of neighboring compartments in the next time step. In contrast, the weighted predictor-corrector scheme smoothes the flux by using also the flux opening values from the last time step. However, the influence of the filling level fluctuations on the integrated values like the ship motion is usually small. 2.6 Propagation of Full Compartments If one or more neighboring compartments are completely filled with water, the corresponding compartments are coupled. The following holds in that situation: - The total flux of a full compartment must be zero - The water flux from partly filled compartments must be propagated through these full compartments - The only free variable remaining is the pressure These conditions lead to a nonlinear system of equations, which must be solved to find the unknown pressure values. The system can be composed by finding a sub-graph of all connected and fully flooded compartments. As an example, consider again the flooding system illustrated in Figure 3 and the situation when the DB2 compartment is completely filled with water. In that case, the water coming from outside must be propagated through DB2 to the other compartments, while the total flux to DB2 must be zero leading to the following equation: = A 1 ρ g (z 1 z 3 ) + p 1 p 3 (15) A 2 ρ g (z 2 z 3 ) + p 2 p 3 A 3 ρ g (z 3 z 5 ) + p 3 p 5. This nonlinear equation has to be solved for the only unknown value p 3. An analytical solution may only be found for less than three openings connected to a completely filled compartment, but the resulting nonlinear system is usually not very large and can easily be solved with standard iterative algorithms like Powell s method described in Moré et al. (198). 2.7 Conditions of Openings To allow the modeling of, for example, breaking doors or windows during flooding, a

5 Ships and Ocean Vehicles, September 212, Athens, Greece 5 pressure head criterion is used for the openings. If the water column height above the opening becomes larger than this defined value, the opening breaks and stays open. This technique may also be used to introduce conditional flooding. A time dependent closure (or opening) of, for example, watertight doors are modeled by a time-dependent discharge coefficient. In the same way the leakage of doors as described in Ruponen and Routi (211) might be considered. 2.8 Air Compression In some cases, it might also be necessary to take into account trapped air, although in most cases the assumption of fully ventilated tanks is valid. But the occurrence of air pockets might especially be important for the later phases of a sinking sequence. This effect is taken into account by assuming an ideal gas and the compression to be isotherm according to Boyle s law. The air pressure of the corresponding compartment with the trapped air is increased by the reduction of air volume: p V = p 1 V 1. (16) An extension of this simple approach is to model the effect that at a certain pressure, parts of the air solutes in water. The concentration of air in water is proportional to the pressure according to Henry s Law (Henry, 183): c = m lw V w = k p. (17) The concentration c is linear proportional to the pressure p by a certain constant k. The so-called Henry constant k depends on the mixture of the gas and the temperature. This results in a nonlinear relation for the pressure increase caused by the air compression. Here the pressure increase is lower compared to the case when neglecting the solubility of air in water. The solute air slowly diffuses in the whole floodwater and may result into the occurrence of bubble flows, if the pressure decreases again in other regions. 2.9 Simulation Overview To summarize one time step of the flooding simulation, the different parts are listed in the following: 1. Check the opening pressure conditions 2. Perform pressure iteration for full tanks 3. Flux determination of remaining openings 4. Inner iteration for higher-order integration of fluxes 5. Propagation of water volumes 6. Update of filling levels and determination of full tanks 7. Optional air compression 8. Iteration of new floating equilibrium 9. Check of convergence This is repeated for each time step until either the requested simulation time is reached or a convergence criteria is fulfilled. 3. VALIDATION BY MODEL TESTS 3.1 Introduction As a first validation of the developed method a comparison with model tests of a box-shaped barge performed at the Ship Laboratory of the Helsinki University of Technology by Ruponen (26) is made. These model tests were later also used as a validation for Ruponen s simulation method presented in Ruponen (27). It is also part of the ITTC benchmark test presented in van Walree and Papanikolaou (27) and used by several other authors to validate their flooding simulation methods (Santos et al., 29; Strasser et al., 29; Corrignan and Arias, 21).

6 Ships and Ocean Vehicles, September 212, Athens, Greece 6 The comparison with one of the test cases is presented in the following, even though the two other test cases were successfully reproduced as well. The naming of the test cases is the same as in Ruponen (27). The simulated results from the new method are marked with the prefix calc D., the measured values with meas R. and the computed values by Ruponen with calc R.. R12 9 R11 DB R22 R21 DB R22 8 R21P R21 R21S DB2 3.2 Computational Setup The geometry of the barge and the openings together with the loading conditions and all other relevant model data is given in Ruponen (26), the main dimensions are summarized in Table 1. With these data, a detailed computational model of the same scale as used in the model tests has been defined including the relative large wall thicknesses of the model. The discharge coefficients for the openings are taken from Ruponen (27). Figure 4 Openings for test case B leading to a higher total amount of floodwater. In addition, the effect of the selected time step is studied for the trim motion and also shown in Figure 5. The results for larger time steps (5 and 2 seconds) deviate significantly from the measured results. If the time step is reduced below.5 seconds, the results clearly converge to the final results. This short convergence study show, that a time step of.2 seconds is an approiate choice for this test case in model scale. 2 Table 1 Main dimensions of the barge Length (oa) L OA 4. m Height H.8 m Moulded Breadth B.8 m Draft design T.5 m For the simulation a time step of.2 seconds is used (compared to.5 seconds used by Ruponen), if not mentioned otherwise. The overall simulation of 8 minutes real-time for test case B takes on an ordinary computer approximately 1 seconds for this simple model setup. trim [deg] meas. trim R. calc. trim R. dt=.5s calc. trim D. dt=.2s calc. trim D. dt=.5s calc. trim D. dt=2.s calc. trim D. dt=5.s Figure 5 Trim Motion 3.3 Test Case B This test case is a very challenging one, since it does not only includes air compression effects, but also complex down-flooding events. The setup is shown in Figure 4. The simulated trim and heave motion given in Figure 5 and 6 show a very good agreement, even though both simulated results are too small at the end compared to the measured ones. But this can be well explained by the escape of air Looking at the lower double bottom compartments, the compressed air pocket in DB1 plays an important role. The water levels are shown in Figure 7 and the overpressure (difference to ambient pressure) is given in Figure 8, together with the results for a smaller time step of.5 seconds. Again, the simulated results are both very similar. As already mentioned in Ruponen (27), an air bubble flow occurred, which allowed some air to escape, resulting in a lower overpressure in that compartment and allowing more water

7 Ships and Ocean Vehicles, September 212, Athens, Greece meas. heave R. calc. heave R. calc. heave D. 6 5 heave [mm] Figure 6 Heave Motion over pressure [Pa] meas. R. calc. R. dt=.5s calc. D. dt=.2s calc. D. dt=.5s Figure 8 Overpressure in DB water height at sensor [mm] meas. DB1 R. calc. DB1 R. calc. DB1 D. 2 meas. DB2 R. calc. DB2 R. calc. DB2 D Figure 7 Water Heights in DB1 and DB2 water height at sensor [mm] meas. R11 R. calc. R11 R. 5 calc. R11 D. meas. R21 R. calc. R21 R. calc. R21 D Figure 9 Water Heights in R11 and R21 to enter. Before these bubbles can actually be formed the air probably solutes in the water. This effect may be modelled by taken into account Henry s law, as already mentioned in subsection 2.8. Since the overall effect is quite small, this has not yet been implemented in the current simulation model, but further investigations are planed for the future. The higher oscillations in the overpressure are caused by the larger time step, but these are not reflected by the water height in that compartment. These oscillations are significantly reduced at the smaller time step of.5 seconds, as shown in the additional graph in Figure 8. The water levels in the part between double bottom and upper deck are shown in Figure 9 and 1. It can be observed, that the new simulation predicts a slightly faster rise of water, but this might simply be caused by small differences in the geometry modelling. The sensitivity of the whole system may best be observed from the water levels of the upper deck compartments shown in Figure 11. Especially in the first phase of flooding, larger differences may be observed. At the end, both simulations reach the same level and the measured values are slightly higher. The reason for that was already explained by the air compression effect. What makes this flooding case quite complicated is the fact, that especially the aft compartment R12 is flooded by an up-flooding opening from R11 but also from the front compartment R Summary of the Model Test Validation The new developed method has been successfully validated by the prescribed model tests. All relevant effects have been modelled,

8 Ships and Ocean Vehicles, September 212, Athens, Greece 8 Water height at sensor [mm] It should also be mentioned, that the simulation of model tests serves very well as a first validation case, but in reality a lot more uncertainties like the correct estimation of the discharge coefficients exist. For this reason, a real accident from the past will be examined in more detail in the following section. 5 meas. R21P R. meas. R21S R. calc. R21P R. calc. R21S R. calc. R21P D. calc. R21S D Figure 1 Water Heights in R21P and R21S 2 4. THE HERAKLION ACCIDENT The accident of the S.S. Heraklion will be reinvestigated with the described simulation method to validate the developed method and to better understand the flooding events leading to the loss of the ship. water height at sensor [mm] meas. R12 R. calc. R12 R. calc. R12 D. meas. R22 R. calc. R22 R. calc. R22 D Figure 11 Water Heights in R12 and R22 Figure 12 Photo of the S.S. Heraklion 4.1 Introduction even though the air compression treatment may require some improvement, but the overall influence is not very large. The new developed method and the one from Ruponen give very similar results. Both methods are based on the same physical assumptions, while the solution of the equations are different. The here presented method chooses a more direct, explicit approach, together with a simple higher-order approach for the flux integration. The solution of a small nonlinear system of equations is only required for fully flooded compartments. Additionally, in this new approach the compartments are only indirectly coupled in the time domain and not in between one time step, as it is the case in Ruponen, where a pressure-correction equation based system is solved in each time step. The S.S. Heraklion capsized and sank in heavy weather on the 8th of December 1966 in the Aegean Sea on its voyage from Crete to Piraeus causing the loss of over 2 people s life. The main cause of the accident has been appointed by the former investigations to be a large reefer truck on the vehicle deck, which started to move in rough sea conditions leading to the damaging of a large side door. The resulting water ingress finally resulted in the capsizing and sinking of the vessel. The main focus of this investigation is to describe the general flooding events after the side door was lost. Even though the accident occurred in heavy weather leading to large ship motions, the general rough flooding events may be described by the here presented quasi-hydrostatic flooding simulation in the time domain neglecting the dynamic components of motion.

9 Ships and Ocean Vehicles, September 212, Athens, Greece 9 The spreading of the ingressed floodwater through the internal subdivision of the ship leads to additional heel and trim moments. As the fluid shifting moments of each compartment are directly taken into account by the prescribed method, a correction of the vertical center of gravity due to free surface effects is in this case not required. 4.2 General Description of the Vessel The ship was originally built as the S.S. Leicestershire by Fairfield Shipbuilding and Engineering Company in Glasgow in It was later converted to a passenger ferry sailing on routes in the Aegean Sea. The main particulars are given in Table 2. Table 2 Main dimensions of the Heraklion Length (oa) L OA m Length (bp) L BP m Moulded Breadth B m Draft design T m 4.3 Previous Investigations The available documents from previous investigations are listed in the following: - Official Accident Report (Frangoulis, 1968) - Official Report of the Accident Investigation Board (AEENA, 1968) - Additional Accident Report (Georgiadis, 1968) - Accident Report (Wendel, 197) - Technical Drawings by the Greek naval architect A. Theodoridis Based on these available documents, the ship data model and the accident situation is reconstructed. 4.4 Final Voyage Condition The loading condition during the final voyage is thoroughly reconstructed based on the information provided in the accident reports and the capacity plan. In addition, the heeling moment due to wind and the cargo shift as described in Wendel (197) leads to a heeling angle of approximately 11.5 degrees. These additional heeling moments are modeled as a transversal shift of the center of gravity leading to a cosine shape of the heeling lever. This is assumed to be a well approximation of the wind lever. The condition of the vessel prior to flooding is summarized in Table 3. Table 3 Assumed condition prior to flooding Total Mass 7547 t Draft at A.P. T a 6.2 m Draft at F.P. T f 2.85 m Heel (pos. stbd) ϕ 11.5 deg Metacentric Height GM 1.14 m For the flooding simulation it is required to model the whole buoyancy body of the ship including all superstructures, even though these parts are not weathertight or even watertight according to the regulations. In addition, all internal and external openings, like windows and doors on the upper deck, are defined including pressure head conditions for the collapsing of some of the openings. A total number of 81 openings are defined connecting 7 compartments including the ones on the upper decks. An illustration of the computational model including all openings is shown in Figure 13. Certain special openings are marked with a red dot. These are the large side door of the vehicle deck leading to the first initial water ingress and two doors on the upper decks relevant for the later phase of flooding. 4.5 Most Likely Scenario of the Accident With the prescribed condition of the ship, a first flooding simulation is started. The interest-

10 Ships and Ocean Vehicles, September 212, Athens, Greece 1 Figure 13 Data model with openings ing first outcome is, that the flooding stops only after a few moments. This is simply caused by the fact that the water levels of the vehicle deck and the outside sea become equal. This situation is certainly not a very stable one, since one must still keep in mind that this is only a quasi-static simulation. To overcome this pseudo stable point, only a small additional heeling moment is added, represented by an increase of 11 cm of the vertical center of gravity. This critical point will be discussed in more detail in subsection 4.6 by a sensitivity analysis driven by the vertical center of gravity. The results of the flooding simulation for some significant values are shown in Figure 14 together with a selection of frames of some interesting time steps given in Figure 16. The spreading of the floodwater can be depicted from the volume fillings in percent shown in Figure 15 for some selected compartments. After 11 seconds the heeling dramatically increases for around one minute, before the upper decks are immersed providing additional buoyancy for some time. At the same time the Dining Room and the Tourist Saloon, which are located on the upper deck above the Car Deck, start to fill up with water mainly through left open side doors. Due to the forward trim, the flooding of the Tourist Saloon located in the aft of the ship is a little delayed. Volume Filling (%) heel Void 1 Engine Room Car Deck Dining Room Tourist Saloon 2nd Prom. Deck Time (sec) Figure 15 Fillings of selected Compartments Then the heeling constantly increases until 1 seconds with a small bump at around 5 seconds, which is caused by the immersion of the funnel leading to a significant down-flooding to the Engine Room also shown in Figure 15. The additional water in the lower parts of the ship stabilizes the ship shortly at that point Heel Angle (deg) heel (deg) 2*trim (deg) deplacement (%) Time (sec) Figure 14 Values over time After this long constant and relatively slow increase in heel, the ship moves from around 12 degrees up to 17 degrees in just one minute. This is explained by the immersion of the superstructures from the other side. After around 13 seconds a stationary state is started when only the displacement and the trim increase almost linear, while the heel stays constant. During this time the void spaces below the vehicle deck, represented by Void 1 in Figure 15, are flooded from inspection manholes located on the portside. At around 16 seconds (or 27 minutes) the ship vanishes from the sea surface.

11 Ships and Ocean Vehicles, September 212, Athens, Greece Sensitivity Analysis of Vehicle Deck Immersion 11 sec 17 sec As already mentioned in the last section, the first phase of the vehicle deck flooding through the damage side door may result in a pseudo-stable situation when both water levels become equal. In Figure 17 the heeling angles over time for different vertical centers of gravity (short: KG) are plotted. First, the flooding stops only after 1-2 minutes. After a critical value of 11 cm increase in the KG is exceeded, the heeling ascends again very fast. The instabil- 52 sec Heel Angle (deg) dkg= cm dkg= 5cm dkg=1cm dkg=11cm dkg=12cm dkg=15cm Time (sec) Figure 17 Heel angles of KG-Variation 125 sec ity of this situation becomes more obvious when leverarm curves are compared for the initial KG value. In Figure 18 three different curves are shown. The red and green curves are the lever sec Lever Arm (m).4.2 Figure 16 Frames of flooding simulation.2 damage no superstr. flooding Heel Angle (deg) Figure 18 Leverarm curves arm curves of the case, when the vehicle deck is assumed as a damaged compartment with the

12 Ships and Ocean Vehicles, September 212, Athens, Greece 12 lost buoyancy method. For the red curve, the upper superstructure is also included in the buoyancy body, but its influence is only important for angles greater than 4 degrees. The blue leverarm curve is computed after the flooding simulation with a fixed water mass on the vehicle deck. At this point the question arises what a leverarm curve should represent. It actually illustrates the capability of a ship to withstand additional heeling moments. This means that if flooding simulations are performed, the leverarm curve becomes also time dependent. If an additional heeling moment is taken into account in the situation of a flooded compartment connected to the outside with equal water levels, the additional heel will again lead to a floodwater ingress. But this makes it quite complicated to compute a complete leverarm curve. One proposal is to successively increase a heeling lever and to perform a flooding simulation for a specified duration until a new heeling angle is reached. This gives again a series of heeling angles together with leverarms. The interesting parameter in that case would be the time duration of one heeling lever step. The blue leverarm curve shown in Figure 18 actually represents the case when this duration is set to zero. The classical damage case leverarm calculation (represented by the other two curves) is equivalent to the case, when for each heeling angle the flooding simulation is performed until convergence, but only if the initial flooding case is already converged as well. 4.7 Summary of the Accident Investigation In general, the simulated heeling behaviour after the water ingress matches quite well with the statements of the witnesses mentioned in the previous investigations. The whole behaviour of the ship is reasonable. More advanced seakeeping simulations may provide more accurate results, but the average flooding process is well reproduced by the here presented methods. A very interesting aspect is actually the shown sensibility depending on small changes in the KG representing additional heeling moments. A time dependent calculation of leverarm curves will be an interesting challenge for further investigations. 5. CONCLUSIONS AND OUTLOOK The new developed flooding simulation method has been successfully validated by standard benchmark model tests and the reinvestigation of the Heraklion accident. This method represents a fast and robust tool for the simulation of floodwater ingress in the time domain and gives very reasonable results for the behaviour of damaged ships in still water conditions. The fast run-time of around 3 seconds for the flooding simulation of the Heraklion accident allows to study several different scenarios in a very short time. For the aspect of air compression, the solubility of air in water might be an interesting aspect to be implemented in the future. Another aspect would be to model the leakage of doors and other structures, which is probably especially important for accident investigations involving passenger ships. In addition, further investigations relating to leverarm curves in flooding simulations should be carried out. This aspect may also be interesting for the assessment of intermediate stages of damage cases for standard damage calculations according to the current SOLAS regulations. More practical accident investigations with other ship types like e.g. passenger vessels have to be carried out to further improve and validate the developed method. It may also be possible to couple the developed method with ship motion seakeeping simulation codes.

13 Ships and Ocean Vehicles, September 212, Athens, Greece REFERENCES AEENA. Official Report of the Accident Investigation Board Heraklion. Technical report, AEENA, Philippe Corrignan and Ana Arias. Flooding simulations of ITTC and SAFEDOR benchmarks test cases using CRS SHIPSURV software. In 11th International Ship Stability Workshop, 21. V. Frangoulis. Official Accident Report Heraklion. Technical report, National Technical University of Athens, S. Georgiadis. Additional Accident Report Heraklion. Technical report, unknown, William Henry. Experiments on the Quantity of Gases Absorbed by Water, at Different Temperatures, and under Different Pressures. Philosophical Transactions of the Royal Society of London, 93:29 274, 183. doi: 1.198/rstl URL org/content/93/29.short. Jorge J. Moré, Burton S. Garbow, and Kenneth E. Hillstrom. User Guide for MIN- PACK-1. Technical Report ANL-8-74, Argonne National Laboratory, Argonne, IL, USA, August 198. Lionel Palazzi and Jan de Kat. Model Experiments and Simulations of a Damaged Ship With Air Flow Taken Into Account. Marine Technology, 41:38 44, 24. A. Papanikolaou, D. Spanos, E. Boulougouris, E. Eliopoulou, and A. Alissafaki. Investigation into the Sinking of the Ro-Ro Passenger Ferry EXPRESS SAMINA. In STAB Conference, number 8 in International Conference on the Stability of Ships and Ocean Vehicles, 23. Pekka Ruponen. Model Tests for the Progressive Flooding of a Boxshaped Barge. 26. thesis, Helsinki University of Technology, 27. URL fi/diss/27/isbn / isbn pdf. Pekka Ruponen and Anna-Lea Routi. Guidelines and criteria on leakage occurrence modelling. In FLOODSTAND Project. Napa Ltd and STX Finland, 211. URL http: //floodstand.aalto.fi. T. A. Santos, P. Dupla, and C. Guedes Soares. Numerical Simulation of the Progressive Flooding of a Box-Shaped Barge. In 1th International Conference on Stability of Ships and Ocean Vehicles, 29. Martin Schreuder. Time Simulation of the Behaviour of Damaged Ships in Waves. Master thesis, Chalmers University of Technology, Göteborg, 25. Ralph Schröder and Ulrich C. E. Zanke. Technische Hydraulik: Kompendium für den Wasserbau. Springer, Berlin, 2. a. edition, May 23. ISBN Clemens Strasser, Andrzej Jasionowski, and Dracos Vassalos. Calculation of Timeto-Flood of a Box-Shaped Barge by Using CFD. In 1th International Conference on Stability of Ships and Ocean Vehicles, 29. F. van Walree and A. Papanikolaou. Benchmark study of numerical codes for the prediction of time to flood of ships: Phase I. In 9th International Ship Stability Workshop, pages 45 52, 27. D. Vassalos, L. Letizia, M. Shaw, and C. MacPherson. An Investigation On The Flooding of Damaged RO-RO Ships. In RINA Transactions doi: 1.394/rina. sbt.1998.d4. Kurt Wendel. Gutachten "Heraklion". Technical report, Institut für Schiffbau, 197. Pekka Ruponen. Progressive Flooding of a Damaged Passenger Ship. PhD