the 24th ittc benchmark study on numerical prediction of...

NATIONAL TECHNICAL UNIVERSITY OF ATHENS School of Naval Architecture and Marine Engineering

Division of Ship Design and Maritime Transport Ship Design Laboratory

The 24th ITTC Benchmark Study on

Numerical Prediction of Damage Ship Stability in Waves

PROGRESS REPORT

Issued for comments to: 24th ITTC Specialists Committee on Stability in Waves

Prepared by: Professor Apostolos Papanikolaou and Dr. Dimitris Spanos

November 2004

Progress Report on The 24th ITTC Benchmark Study on Numerical Prediction of Damage Ship Stability in Waves

Contents 1 Introduction ..............................................................................................................................3

2 Participants ...............................................................................................................................4

3 The Benchmark Specification ..................................................................................................5

4 The Study Website ...................................................................................................................5

5 The Benchmark Tests...............................................................................................................6

6 The Ship Models ......................................................................................................................8

6.1 Passenger/Ro-Ro (PRR01) model........................................................................................8

6.2 Tanker (TNK) model............................................................................................................8

6.3 Passenger/Ro-Ro (PRR02) model........................................................................................9

7 The Numerical Methods.........................................................................................................10

8 Numerical Results ..................................................................................................................12

9 Analysis of Results.................................................................................................................13

9.1 Testing of the PRR01 model ..............................................................................................14

9.2 Testing of the TNK model .................................................................................................18

10 Concluding Remarks ..........................................................................................................21

11 The Study Coordinator .......................................................................................................22

12 References ..........................................................................................................................23

Appendix A: Investigated Ship Models ...................................................................................24

. Passenger/Ro-Ro (PRR01) Model .......................................................................25

. Tanker (TNK) Model ...........................................................................................28

. Passenger/Ro-Ro (PRR02) Model .......................................................................30

Appendix B: Numerical Results for PRR01 Model.................................................................32

Appendix C: Numerical Results for TNK Model ....................................................................37

Appendix D: Analysis of Results.............................................................................................42

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1 Introduction In December 2001 the first benchmark study on numerical methods for the prediction of capsize of damaged ships in sea waves was completed, coordinated by the 23rd ITTC Specialist Committee on the Prediction of Extreme Motions & Capsizing [1], [2]. There were five (5) independent participants in this study each employing different and independently developed computer simulation code. The five participants were: Marine Research Institute (MARIN), Ship Design Laboratory of National Technical University of Athens (NTUA-SDL), Osaka University, Flensburger Schiffbau Gesellschaft (FSG) and The Ship Stability Research Center of Universities of Glasgow and Strathclyde (SSRC). This benchmark study is believed to have represented at the time of its conduct the state of the art in the field. That study ascertained that at the current state of knowledge theoretical numerical prediction methods could greatly contribute to a pre-assessment of the survivability of damaged ships in waves. However, considering the relatively low number of the benchmark participants and the complicated nature of the set benchmark study problem it was suggested to extend and refine the study in the future with the aim to attract more benchmark study participants and to resolve to the extent feasible several open questions identified in the study. The 24th ITTC Specialists Committee on Stability in Waves has initiated the extension of the benchmark study in early 2004 and the study is expected to be completed at the end of year 2004. The basic objective of this work is to update the state of the art in the field of numerical methods for the prediction of motion and capsize of damaged ships in waves. There were five institutes expressing their interest for participation in the present study, listed in Table 1. The number of participants was below the initial expectations of the Committee, however, considering the fact that this number was at least equal to that of the previous study as well as the refreshment of the group of participants by two new institutes (IST and KRISO) it was finally decided that this is sufficient for the conduct the planned study. According to the specified benchmark procedure the different numerical methods are compared to each other for a selected number of test cases, while the overall efficiency of the investigated methods is assessed by comparison of the numerical results with relevant experimental data. The benchmark study consists of two phases. In the first one, the numerical methods are tested with respect to the simulation of ship’s motion in calm water for a selected set of free transient roll motion and flooding conditions. In the second phase, test cases for damaged ship’s behavior in irregular waves are considered. Following the completion of the three of the four tests series comprising the first phase of this benchmark, the study results are presented in this report with the aim to update the ITTC Specialists Committee and to enable an early assessment of the study.

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2 Participants

Institute Acronym Country

Instituto Superior Tecnico IST Portugal

Korea Research Institute of Ships and Ocean Engineering

KRISO Korea

Maritime Research Institute Netherlands MARIN The Netherlands

National Technical University of Athens-Ship Design Laboratory

NTUA-SDL Greece

The Ship Stability Research Centre, Universities of Glasgow and Strathclyde

SSRC United Kingdom

Table 1 Participants of the 24th ITTC Damage Stability Benchmark Study

Note:

In the following tables, charts and graphs of results the identity of the participating institutions is coded (anonymous, Participant 1 to 5). It has been ensured that there is no direct correspondence to the list of participants in Table 1.

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3 The Benchmark Specification Specification of the benchmark tests and other guidelines for the preparation and submission of results were released by Study Coordinator on April 7, 2004, [3]. • Each participant should confirm his interest for participation to the Study Coordinator by

May 15, 2004. Participants could opt to take part in test series A and B, C and D (separately), or in the entire test programme.

• The results should be submitted to the Study Coordinator within the following deadlines:

− Test series A and B by July 15, 2004.

− Test series C by September 15, 2004.

− Test series D by October 15, 2004.

Test series A, B and C have been completed according to the schedule. The last Test series D is still in progress as a delay has been occur due to some missing experimental study data. It is noted that KRISO managed recently (22.10.2004) to submit numerical results for the three Tests A, B and C.

4 The Study Website All the activities of the benchmark study are documented in the dedicated website: www.naval.ntua.gr/~sdl/ITTC/ittc.htm The models’ hull form, the experimental data, and other study data were provided to the participants through the site. Specific areas of the websites are protected with a password and can be visited only by authorized participants. The numerical results were uploaded to the website and participants could review and comment on them, providing feedback to the others and the study coordinator.

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http://www.naval.ntua.gr/~sdl/ITTC/ittc.htm


5 The Benchmark Tests Considering the complicated character of the numerical methods addressing the motion of damaged ships in waves and the prediction of ship’s stability in extreme conditions the present study has been set up to provide comparative information for the fundamental properties of the methods and to enable their assessment individually as well as a whole. The selected tests are derived by consideration of the fundamental phenomena taking place in the motion of the damaged ship and the corresponding numerical modelling applied by the methods. The basic components recognized for such a physical system, expressed as forces, are the inertia (mass and hydrodynamic), the restoring, the damping-dissipation and the wave induced forces. The flooding process through a damage opening and the floodwater effects on the ship motions are two extra components that characterize the entire problem. The various numerical methods apply to these components a specific modelling to be assessed in the framework of the benchmark study. The present benchmark testing is divided in two major phases that of Phase A and Phase B. In Phase A, the wave induced forces have been excluded and the ship models are tested in calm water, whereas in the Phase B, the models are investigated in the presence of waves too. The Phase A consists of four (4) test series referred to with the coded names Test A, Test B, Test C and Test D. These tests are all referring to the free roll motion of ship models in calm water and they are defined as follows: Test A Free roll motion of an intact passenger/Ro-Ro model, coded as PRR01, for two

different KG values. In this testing the flooding process and floodwater effects are suppressed. The change in restoring is considered by the change of KG. The first value KG = 12.000 m corresponds to the Test A1 whereas the second KG=13.456 m to Test A2.

Test B Free roll motion of the passenger/Ro-Ro model PRR01 in damaged condition and the

same two KG values as Test A. The specified damage opening is continuously open during the test and at the start of the test the damaged compartment is already fully flooded. The flooding process and floodwater dynamics are present in this test.

Test C Free roll motion of a tanker model, coded as TNK, in partially flooded conditions. The

model has one rectangular compartment amidships partially flooded with constant amount of water inside, which corresponds to a compartment breadth to water fill depth ratios equal to 31.8, 7.9 and 2.0. This test excludes the flooding process effects as the trapped water is inside the tank and no damage opening is present. In this way the ship to floodwater interaction can be investigated without interference with the flooding process. The test focuses on the floodwater dynamics and effects on ship motion.

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Test D Free roll motion of a second Passenger/Ro-Ro ferry, coded as PRR02, in transient

flooding. The intact model starts from equilibrium position. Then a specific damage opening is released and the water ingress is initiated. After that the model freely oscillates under the effects of transient flooding. In this test the flooding process is of prime interest while the progressive flooding is investigated by varying the dimensions of a cross flooding duct to control the flooding rate of damaged compartments.

PHASE A Testing in Calm Water

(free roll decay)

PHASE B Testing in Waves

A PRR01 intact A1 KG = 12.200 m

A2 KG = 13.456 m

The flooding process and floodwater effects are suppressed. The change in restoring is considered.

B PRR01 damaged B1 KG = 12.200 m

B2 KG = 13.456 m

The flooding process and floodwater effects are present. The change in restoring is considered. Test B with respect to Test A provides a change of hull integrity

C TNK C1 d = 0.00 m

C2 d = 1.00 m

C3 d = 4.00 m

partially filled

C4 d = 16.00 m

The flooding process is suppressed. The change in floodwater is considered.

D PRR02 transient flooding

D1 1-frame crossduct area



The flooding process is dominant. The progressive flooding is considered.

(planned for the 25th ITTC Committee’s activtities)

Table 2 Overview of Benchmark Tests

In all test cases, the study mainly focuses on the simulation of roll motion. However the motion in other degrees of freedom is also considered in the study. It is noted that the experimental data corresponding to each benchmark test were available beforehand to all study participants to enable equal benchmarking conditions for all participants.

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6 The Ship Models Three ship models will be used in the numerical tests. They are: − one Passenger/Ro-Ro ferry, hereafter coded as (PRR01), − one Tanker, hereafter coded as (TNK01), and − one Passenger/Ro-Ro ferry, hereafter coded as (PRR02) Each model studied in certain series of tests as follows: − The (PRR01) model studied only in the tests series A and B. − The (TNK01) model studied only in the tests series C. − The (PRR02) model will be studied only in the tests series D. The next sections present in more details the three ship models

6.1 Passenger/Ro-Ro (PRR01) model

The passenger/Ro-Ro ferry PRR01 investigated in the Test A and Test B is the model also investigated in the previous benchmark study [1], [2]. This model has been tested in systematic model experiments within the EU funded research project NEREUS [3], and these experimental data were made available to the study coordinator by Danish Maritime Institute (DMI-FORCE, Denmark). The model particulars and geometrical details are presented in Appendix A. The main dimensions of the ferry are given in Table 4, and the body plan is depicted in Figure 7. In damage condition the ship has two adjacent compartments flooded amidships and the car spaces are also damaged as shown in Figure 7. In the damaged compartments below the deck there are three intact spaces as shown in Figure 8. These three intact spaces are arranged non-symmetrically with respect to the centre plane, with the result the ship to obtain a heeling angle in the final damage condition. The damage opening is according to SOLAS 90 specification (3% L + 3.00 m), which extends unlimited vertically upwards. Bilge keels were also applied to the model.

6.2 Tanker (TNK) model

The tanker model TNK, investigated in Test C, is equipped with a rectangular tank amidships, representing a flooded compartment. The geometrical details are presented in Appendix A. The main dimensions of the model are shown in Table 5, the body plan in Figure 9 and the arrangement of the flooded tank is described in Figure 10. The TNK model has been tested in free roll motion having the compartment partially filled with constant water, and the corresponding experimental data used were those published in [5]. The experimental data have been digitized by the study coordinator from the relevant published diagram. It is noted that only the crests and the zero crossing values have been digitized.

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The partially flooded compartment is rectangular (82.50 m x 31.76 m) located amidships. Compartment is positioned at 5.20 m above keel line.

The model was kept in position by means of a soft-spring mooring arrangement. Two springs were used at each model end working on a plane parallel to still water plane.

6.3 Passenger/Ro-Ro (PRR02) model

The second passenger/Ro-Ro (PRR02) model to be investigated in the benchmark study in Test D is also presented in Appendix A. The main dimensions of the ferry are given in Table 6, and the body plan is depicted in Figure 11. The model is damaged amidships having damaged the engine room, the generator room, the double bottom below these two compartments as well as a storage room above the generator room. Cargo space was also damaged as the damage opening was extended vertically upwards. In the double bottom there is cross duct, see Figure 12 where the damage scenario is illustrated, which enables the cross flooding of the double bottom. The transient and progressive flooding in calm water of the model has been model tested within E.C. project HARDER [6] and the experimental data and test particulars were made available1 to the study by Maritime Research Institute Netherlands (MARIN). The model was constructed in a scale 1:38.25, with an intact draught of 6.40 m and a slide door was used to release the damage opening during tests and simulate the damage opening.

The tests were carried out for the worst SOLAS damage case. All tests were started in intact condition and a damage opening of V-shape was created by opening the slide door vertically upwards and revealing the damage. Damage length was according to SOLAS guidance.

No rudder and no propeller were fitted to the model whereas bilge keels were fitted. A duck tail was prepared as well. Cross-duct area was varied taking three different values of 1, 2 and 3 frames width correspondingly. During calm water tests soft springs were used to prevent model to drift away. Springs were mounted at two model’s ends and work on the lateral plane.

1 At the time of completion of this report some experimental set-up data referring to the internal arrangements of the engine room and bilge keels were pending.

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7 The Numerical Methods The mathematical models for the simulation of the motion of the damaged ship in waves, employed within the present benchmark study, are presented in the following in a unified way. In particular, the methods are decomposed into their fundamental properties and their specific modelling applied to each part of the study. All simulation methods are characterized by the particular modelling and treatment they apply to the equations of motion, namely the inertia, the restoring and the damping terms, as well as the ship to wave interaction, the modelling of the floodwater effects on the ship motion and the flooding process itself. All participating methods are non-linear time domain simulation methods considering the ship as a rigid body inertia system and accounting for non-linearities of large amplitude motion and floodwater effects. The six degrees of freedom are considered for the ship motion, by exception of method P4 where surge and yaw are omitted. The restoring forces are related to the hydrostatic term of water forces, and are calculated by direct integration of hydrostatic pressure over the instantaneous wetted surface. The ship hydrodynamics, namely the ship to wave interaction forces and radiation forces, are approached by potential theory, applying either strip theory or 3D panel methods. In particular, method P3 employs a 3D panel method, whereas all the others quasi 2D strip theory approaches. The radiation forces are calculated in the frequency domain and are transferred to the time domain by use of retardation functions. The diffraction forces in the time domain are taken by superposition of wave harmonic components calculated in frequency domain. The part of wave excitation corresponding to the undisturbed wave Froude-Krylov forces is calculated by direct integration of the wave dynamic pressure over the instantaneous wetted surface. Viscous effects, which are particularly significant for the roll motion simulation, are treated in a semi-empirical way. All methods make use of linear or higher order models for the total viscous damping on the basis of empirically evaluated coefficients form relevant experimental data. A finer approach is also applied in some case by decomposing the total damping into various components, like friction, eddy, bilge keels and other appendages damping, according to [7], [8]. The flooding process is uniformly approached by the use of hydraulic models. Pending the possible implementation of advanced CFD methods, the basic Bernoulli equation modified by semi-empirical coefficients proved to be satisfactory for the modelling of the water ingress/egress through a damage opening. The same approach is also applied to the progressive flooding, namely the flow between ship compartments through open doors and ducts or other internal openings.

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The floodwater motion, and its interaction with the ship, is approached by omitting internal wave effects and assuming the internal free surface always plane. The instantaneous orientation of the free surface is part of the numerical solution. This approach is applied by participants P1 and P3. The floodwater modelling is further simplified by assuming the internal free surface of water always horizontal, an approach that is adopted by participants P2, P4 and P5. Participant P4 applies also shallow water modelling to the internal water motion in case of the rectangular tank in Test C. Further background information on the numerical methods can be found in [9], [10], [11], [12]. The next Table 3 summarizes the basic attributes of the numerical methods as they have been applied in the present benchmark study.

Numerical Method P1 P2 P3 P4 P5 Ship motion degrees of freedom 6 6 6 4 6 hydrostatic forces by direct integration x x x x x strip theory x x x x 3D panel method x incident wave forces by direct integration x x x x x Memory effects x x x x x semi-empirical roll viscous x x x x roll viscous analysis in components x floodwater with horizontal free surface x x x floodwater with moving free surface x x Internal motion by shallow water equations

x

flooding by simple hydraulic model x x x x x

Table 3 The basic attributes of the applied numerical methods in benchmark study

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8 Numerical Results The numerical results of the roll decay tests of Test A, Test B and Test C were time series of the model motion. The submitted results by participants are presented in Appendix B for the model PRR01, namely Test A and B. The results for the TNK model are collected in Appendix C. For each motion the numerical results of all the participants are presented in comparative way. For the roll motion the experimental data are also plotted together. Four (4) diagrams are presented for each test, namely the sway, the heave, the roll and the pitch motion of the models. The results for Test D are still pending.

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9 Analysis of Results In this paragraph the numerical results are analyzed and discussed. The comparison of results mainly concerns two main quantities, the natural period and the decay rate. The natural period is a characteristic parameter which in principle reflects the appropriate modelling of the restoring and inertia terms by the numerical methods. The effects of floodwater on the natural period are considered. The decay rate of the free oscillating models reflects the ability of the methods to capture all those phenomena dealing with the energy dissipation, from roll viscous to sloshing effects. The decay rate is measured through the measurable quantity of the logarithmic decrement which is defined as log( Ao / Ai ) where Ai is the i-th roll amplitude and Ao the initial. The above two measurable quantities, together with the direct comparison of the results with corresponding experimental data are enough to provide a comprehensive insight into some fundamental properties of the complicated methods under investigation. The analysis and comments of results focuses on the roll motion of the models.

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9.1 Testing of the PRR01 model

Time Series

In Figure 13 to Figure 16 the numerical results for the Test series A and B are presented. In the roll diagrams for each test the results of all the participants together with corresponding experimental data are plotted.

1. Figure 13 corresponds to the intact condition of the PRR01 model and for the lower KG = 12.200 m. Except for the P2 method, the numerical methods demonstrate a satisfactory behaviour with respect to the experimental values. For this case the experimental data, which were available to the participants beforehand as study data, have been apparently exploited to obtain some initial information for the model’s inertia properties and the roll damping in the numerical simulation. Considering this aspect the very fine behaviour of the numerical results is understandable.

2. Method P2 has applied a direct prediction of the roll viscous damping by predefined semi-empirical coefficients without exploiting the present experimental damping values. Therefore, the underestimation of the damping could be explained.

3. In the change of the hull condition to damage and the shift of KG, namely Test B2, the numerical methods cannot capture anymore satisfactorily the behaviour of the model, as shown in the Figure 16, and quite uncorrelated time series result.

In Figure 21 and Figure 22 the time series of the roll motion for the intact and the damage condition for the two values of KG, are presented, namely one diagram for each method.

4. The general observation taken from these diagrams is that the damping increases in the damaged condition, when compared to the intact case. Also an increase of the natural period is noted. This behaviour is clearly an effect of the floodwater on the model.

5. In qualitative terms the experimental behaviour is well approached by method P3. Method P2 shows highly uncorrelated behaviour for this experiment. The performance of method P5 in these tests is considered also quite satisfactory.

Natural Periods

The natural period was measured as the mean period of the roll oscillation. As shown in Figure 23 the mean roll period was established as the converging value of the periods over the successive oscillations. The natural periods for all the tests of the PRR01 model are summarized in Figure 1. In this diagram there are two groups of lines. The lower corresponding to the KG=12.200 m whereas the second one to the higher value of KG=13.456 m. The end points of each line correspond to the natural periods for the intact and damaged conditions respectively. The following comments are made on this diagram.

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1. There is a perfect coincidence between the experimental and the numerical results for the

intact condition and lower KG value (lower left end). Presumably this is due to the calibration of the methods with respect to the available experimental data. This point could be considered as a start point for the numerical prediction.

2. With the increase of the KG (from 12.000 to 13.456 m) and consequently with the decrease of GM, the natural period increases. The perfect coincidence between the experimental and the numerical results of methods P1 and P5 is noted and might be attributed to the reasons stated under 1.

3. With the change of the hull integrity from intact to damaged and for the case of KG=12.200 m, a quite satisfactory behaviour of all numerical methods can be observed, demonstrating similar qualitative behaviour as the experimental results.

4. When a shift of the centre of gravity in the damaged condition was imposed, however, none of the methods could demonstrate a satisfactory behaviour. This is particularly interesting for the methods P1 and P5 which had shown an almost perfect behaviour for the intact condition.

5. The method P2 seems to be highly affected by the change of hull condition from intact to damage.

6. Considering the scatter of the overall results for the case of the damage condition and the higher KG value (upper right end), it becomes evident how the methods are affected by the change of the hull condition from intact to damage and the shift of the KG value.

TESTS A & B

INTACT vs DAMAGED MODEL PRR01

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Model condition

Nat

ural

Per

iod

[sec

]

P1P2P3P4P5EXP

Intact damaged

Tests A1 & B1KG=12.200 m

Tests A2 & B2KG=13.456 m

Figure 1 Natural periods for the PRR01 model

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Decay Rate

In Figure 24 the logarithmic decays of the four tests of PRR01 are presented. The following remarks pertain to these diagrams.

1. Except for the method P2, the decay rate is quite satisfactory for the other methods, for the Test A1, the intact model with the lower KG value. The P2 method, as discussed above, has applied a direct prediction of the roll damping by semi-empirical coefficients without exploiting any information from the experimental data in hand.

2. For the intact cases, the P1 method demonstrates decay rates quite close to the experimental. However in the presence of the damage the decay is substantially underestimated.

3. The method P3 demonstrated an overall good correlation to the experimental decay. The method is sensitive to the damage condition likewise the experimental values.

4. The methods P4 and P5 show similar behaviour with low sensitivity with respect to the change of conditions from intact to damage.

In the next Figure 2 and Figure 3 the logarithmic decrement for the first oscillation of the roll motion for the two studied KG values of PRR01 is presented. The first oscillation is of major significance and determines greatly the subsequent behaviour of the model.

5. In both diagrams it is observed that only the P3 method demonstrates comparable sensitivity to the experimental data with the change of the hull condition from intact to damage.

6. The method P1 demonstrates opposite behaviour compared to the experimental values for both cases.

7. The methods P4 and P5 show low sensitivity.

8. Method P2 seems non sensitive for the first KG case whereas dramatically dependent on the damage for the second KG case.

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TEST A1 & B1MODEL PRR01, KG = 12.200 m

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Model condition

Loga

rithm

ic D

ecrim

ent

P1P2P3P4P5EXP

Intact damaged

Figure 2 Logarithmic Decrement in the first oscillation for the PRR01 model (KG = 12.200 m)

TEST A2 & B2MODEL PRR01, KG = 13.456 m

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Model condition

Loga

rithm

ic D

ecrim

ent

P1P2P3P4P5EXP

Intact damaged

Figure 3 Logarithmic Decrement in the first oscillation for the PRR01 model (KG = 13.456 m)

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9.2 Testing of the TNK model

Time Series

In Figure 17 to Figure 20 the numerical results for the Test series C1 to C4 respectively are presented. In the roll diagrams for each test the results of all the participants together with the corresponding experimental data are plotted.

1. Figure 17 corresponds to the intact condition of the TNK model, namely without any water in the flooded compartment. All methods demonstrate a very fine behaviour with respect to the experimental values. A slight discrepancy of method P2 after the second oscillation is considered secondary. The intact condition for the TNK model, similar to the previous PRR01 model, has been used by the participants to transfer information from the experimental data to the numerical simulation method with respect to the inertia properties of the model. From this point of view the perfect behaviour of the numerical results can be explained.

2. The overall results become rather uncorrelated in the presence of floodwater in the tank compartment. In particular, for the intermediate water fill depth, Figure 19, significant discrepancies occur even after the first oscillation.

3. The complicated behaviour of the partially flooded model (particularly for the filling depth of 4.00m) seems well captured by two methods, namely that of P3 and P4.

In the diagrams of Figure 25 the roll response of the TNK model for varying water fill depth are presented for each method.

4. From these diagrams it is evident that the P3 and P4 methods capture the effects of the presence of floodwater likewise the experimental values.

5. The other three methods P1, P2 and P5 do not show qualitatively an equal good correspondence to the experimental values.

Natural Periods

The natural period for the TNK model for varying amount of internal water is presented in Figure 4. The data of this diagram correspond to the converging period depicted in Figure 26. In this diagram there are four points for each line, each corresponding to the different water fill depth. The following remarks are made with respect to this diagram.

1. For the natural period of the intact case a remarkable coincidence between experimental and numerical results is observed. Presumably this is due to reasons of calibration of the methods to the experimental data.

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2. The natural period substantially increases for the intermediate fill depth (where ‘sloshing effects’ are evident), whereas for the other depths the period is close to the intact case. This complicated behaviour is captured by the two methods P3 and P4. The other three methods do not succeed to capture well the floodwater dynamics and the resulting effects.

3. The methods P3 and P4 apply different modelling to the floodwater dynamics (see Table 3). However they both manage to well address the floodwater effects on the model roll motion.

4. The scatter of results for each fill depth indicates the overall performance of the benchmarked methods in the modelling of the floodwater effects.

TEST CPARTIALLY FLOODED MODEL TNK

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Water fill depth

Nat

ural

Per

iod

[sec

]

P1P2P3P4P5EXP

0.0 m 1.0 m 16.0 m4.0 m

r = ∞

r = 31.8

r = 7.9

r = 2.0

r = (tank breadth) / (water fill depth)

Figure 4 Natural periods for the TNK model

Decay Rate

The decay rate of the four tests is calculated and presented in the diagrams of Figure 27. These diagrams show the changes in roll decay rate in the presence of floodwater in the tank. The floodwater is the dominant term in the decay rate. The following remarks are made with respect to these diagrams.

1. For the intact case, no floodwater in the tank, the decay rate of the numerical methods is quite close to the experimental data. This implies the efficiency of the applied modelling for the roll viscous damping, properly representing the physical behaviour of the model. The roll viscous damping is the dominant term of the decay in this test.

2. In the presence of floodwater the decay rate substantially alters due to the floodwater effects on the model motion. The increase of the decay rate, particularly for the intermediate fill depths, is well captured by the methods P3 and P4.

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3. For the higher water fill depth the floodwater effects seem to be decreased, as the behaviour between this condition and the intact one are very close, and in this case the correlation to the experimental data has been very good.

In the next Figure 5 the logarithmic decrement for the first oscillation of the roll motion is presented. The first oscillation is of major significance and determines greatly the behaviour of the model.

4. Quite satisfactory correlation between the method P3 and the experimental results is observed.

5. Also satisfactory are considered the results for the method P4. The method shows a slight underestimation of the decay rate for the lower water fill depth. For the other water quantities the method follows the behaviour of the experiments.

6. The three methods P1, P2 and P5 demonstrate similar behaviour. They are not sensitive to the floodwater changes and the good correlation to the experimental results is confined to the cases of intact and deep fill where the floodwater effects are anyway small.

TEST C

PARTIALLY FLOODED MODEL TNK

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Water fill depth

Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP

0.0 m 1.0 m 16.0 m4.0 m

r = ∞ r = 31.8 r = 7.9 r = 2.0

r = (tank breadth) / (water fill depth)

Figure 5 Logarithmic Decrement in the first oscillation for the TNK model

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10 Concluding Remarks

1. The reviewed results of Phase A of the 24th ITTC damage stability benchmark study provide a first insight into the present status of the fundamental properties of numerical methods for the simulation of motion of the damaged ships. The various advantages and weaknesses of the participating method have been addressed enabling an overall assessment of the current status.

2. In this part of the benchmark the methods were investigated for free ship roll motion in calm water and their sensitivity in various conditions was addressed. The floodwater effects on the roll motion were a particular subject of interest. In the final stage of this study it remains to assess the modelling of the flooding process and the progressive flooding. In planned phase B of this study, then within the framework of the 25th ITTC, a critical review of the methods in the presence of waves is planned. This will complement a previous similar study conducted in the framework of the 23rd ITTC [1], [2].

3. The detailed analysis of the present results identified several discrepancies between the numerical methods and the corresponding experimental data. However, the significance of these findings with respect to the efficiency of the methods in the prediction of critical seastates with respect to the stability of the ships remains to be assessed.

4. It was shown that the benchmark methods highly depend on experimental data as to the prediction of roll viscous damping. Only one benchmark method attempted the prediction of viscous effects in direct way, by employing predefined semi-empirical coefficients according to methods from the literature and own database data, however with quite poor results. This calls for additional research both in terms of systematic experimental studies, as well as of advanced CFD numerical techniques, that should eventually lead to a satisfactory prediction of viscous roll damping.

5. Two out the five investigated methods demonstrated a quite satisfactory capability in capturing the floodwater dynamic effects on ship’s motion. It is remarkable that these two methods apply different modelling for the floodwater dynamics, but finally lead to qualitatively the same overall results.

/ 49


The Study Coordinator ITTC Damage Stability Benchmark Study Coordinator:

Professor Apostolos D. Papanikolaou Director, Ship Design Laboratory Division of Ship Design & Maritime Transport School of Naval Arch. & Marine Engineering National Technical University of Athens 9, Heroon Polytechniou 15 773 Zografou - Athens GREECE Tel.: 0030 210 772 14 16/ 14 09/ 14 07 FAX: 0030 210 772 14 08 e-mail: [email protected] URL: http://www.naval.ntua.gr/sdl

ITTC Damage Stability Benchmark Study Secretary: Dr. Dimitris Spanos Researcher, Ship Design Laboratory Division of Ship Design & Maritime Transport School of Naval Arch. & Marine Engineering National Technical University of Athens 9, Heroon Polytechniou 15 773 Zografou - Athens GREECE Tel.: 0030 210 772 14 07 FAX: 0030 210 772 14 08 e-mail: [email protected] URL: http://www.naval.ntua.gr/sdl

/ 49

mailto:[email protected]

http://www.naval.ntua.gr/sdl

mailto:[email protected]

http://www.naval.ntua.gr/sdl


References [1]. The Specialist Committee on Prediction of Extreme Ship Motions and Capsize, Proceedings

of the 23rd ITTC, Vol. II, pp 619-657, Venice, 2002.

[2]. Papanikolaou A., (2001). Benchmark Study on the Capsizing of a Damaged Ro-Ro Ship in Waves. Final Report to 23rd ITTC Specialist Committee for the prediction of Extreme Ship Motions and Capsizing.

[3]. Papanikolaou A., (2004). ITTC Damage Stability Benchmark Study, Guidelines of Numerical Tests. 24th ITTC Benchmark Study on Numerical Prediction of Damaged Ship in Waves.

[4]. NEREUS E.C. project, (2000). First Principles Design for Damage Resistance against Capsize. DG XII-BRITE, 2000-2003.

[5]. De Kat J., (2000). Dynamics of a Ship with Partially Flooded Compartment. Contemporary Ideas on Ship Stability, Elsevier, pp 249-263.

[6]. HARDER E.C. project, (2000). “Harmonization of Rules and Design Rational”. DG XII-BRITE, 2000-2003.

[7]. Ikeda U., et al. (1978), A Prediction Method for Ship Roll Damping, Department of Naval Architecture, University of Osaka Prefecture, December.

[8]. Himeno Y., (1981). Prediction of Ship Roll Damping -State of the Art. Dept. of Naval Architecture, Report No 239, The University of Michigan, Ann Arbour, MI, September.

[9]. Spanos D., (2002). Numerical Simulation of Flooded Ship Motions in Seaways and Investigation of the Behavior of Passenger/Ro-Ro ferries. Dr. Eng. Thesis, National Technical University of Athens, School of Naval Architecture and Marine Engineering.

[10]. Santos T.A., Guedes Soares C. (2003). Investigation into the Effects of Shallow Water on Deck on Ship Motions. Proceedings of the 8th International Conference on the Stability of Ships and Ocean Vehicles (STAB’03), Madrid, Spain.

[11]. Jasionowski, A., (2001). An Integrated Approach to Ship Survivability Assessment, PhD thesis, University of Strathclyde, Department of Ship and Marine Technology, Glasgow.

[12]. Letizia, L., (1997). Damage Survivability of Passenger Ro-Ro Vessels Subjected to Progressive Flooding in a Random Sea, PhD Thesis, University of Strathclyde, Glasgow.

/ 49


Appendix A: Investigated Ship Models

/ 49


. Passenger/Ro-Ro (PRR01) Model2

Length Lpp (m) 170.00Beam, B (m) 27.80Draft, T (m) 6.25Displacement (tons) 17269Car deck (m) 9.00Model scale 1:40

Table 4 Main particulars of PRR01

BODY PLAN

0

2

4

6

8

10

12

14

16

-15 -10 -5 0 5 10 15

Figure 6 Body plan of PRR01 model

The digital data of the body plan were part of the benchmark data and they were provided by he study coordinator to the participants upon confirmation of their participation.

2 The experimental data were provided to the ITTC damage stability benchmark study by DMI-FORCE. Their contribution to this study is appreciated.

/ 49


Figure 7 Damage Scenario of PRR01 model

The damage length was according to SOLAS guidance (3% L + 3.00 m), and the damage is located on ship’s port side.

/ 49


Figure 8 The three intact spaces in the damaged compartments of PRR01

/ 49


. Tanker (TNK) Model3

Length Lpp (m) 310.20 Beam, B (m) 47.20 Draft, T (m) 16.00 Depth, D (m) 26.07 Displaced weight (tf) 202600 Center of gravity above baseline, KG (m) 10.00 Metacentric height, GM (m) 9.50 Natural roll period – intact (s) 10 Model scale 1:82.5 Length of compartment, Lc (m) 82.50 Width of compartment, Bc (m) 31.76 Compartment’s height above baseline 5.20

Table 5 Main particulars of TNK model

3 The experimental data were reproduced from Jan de Kat [5].

/ 49


Figure 9 Body plan of TNK model

The next plan illustrates the arrangement of the ship model and of the partially flooded compartment.

Figure 10 General arrangement of TNK model

/ 49


. Passenger/Ro-Ro (PRR02) Model4

Length Lpp (m) 174.800 Beam, B (m) 25.000 Draft, T (m) 6.40 Car deck (m) 9.10

Center of gravity above baseline, KG (m) 12.300 Model scale 1:38.25

Table 6 Main particulars of PRR02 model

0

2500

5000

7500

10000

12500

15000

17500

20000

-12500 -10000 -7500 -5000 -2500 0 2500 5000 7500 10000 12500

Figure 11 Body plan of PRR02 model

The digital data of the body plan were part of the benchmark study data and they were provided to the participants upon confirmation of their participation.

4 The experimental data were provided to the ITTC damage stability benchmark study by MARIN. Its contribution to this study is appreciated.

/ 49


Figure 12 Damage scenario of PRR02 model

/ 49


Appendix B: Numerical Results for PRR01 Model

/ 49


TEST A1INTACT MODEL PRR01, KG = 12.200 m

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Sway

[m]

P1P2P3P4P5

TEST A1

INTACT MODEL PRR01, KG = 12.200 m

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Hea

ve [m

]

P1P2P3P4P5

TEST A1


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

P1P2P3P4P5EXP

TEST A1


-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Pitc

h [d

eg]

P1P2P3P4P5

Figure 13 Times series of results for Test A1

/ 49



-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Sway

[m]

P1P2P3P4P5

TEST A2


-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Hea

ve [m

]

P1P2P3P4P5

TEST A2


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

P1P2P3P4P5EXP

TEST A2


-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Pitc

h [d

eg]

P1P2P3P4P5

Figure 14 Times series of results for Test A2

/ 49


TEST B1DAMAGED MODEL PRR01, KG = 12.200 m

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Sway

[m]

P1P2P3P4P5

TEST B1

DAMAGED MODEL PRR01, KG = 12.200 m

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Hea

ve [m

]

P1P2P3P4P5

TEST B1


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

P1P2P3P4P5EXP

TEST B1


-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Pitc

h [d

eg]

P1P2P3P4P5

Figure 15 Times series of results for Test B1

/ 49



-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Sway

[m]

P1P2P3P4P5

TEST B2


-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Hea

ve [m

]

P1P2P3P4P5

TEST B2


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

P1P2P3P4P5EXP

TEST B2


-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Pitc

h [d

eg]

P1P2P3P4P5

Figure 16 Times series of results for Test B2

/ 49


Appendix C: Numerical Results for TNK Model

/ 49


TEST C10.00 m water depth (intact)

-0.09

-0.07

-0.05

-0.03

-0.01

0.01

0.03

0 1 2 3 4 5

Time [sec]

Sway

[m]

6

P1P2P3P4P5

TEST C1

0.00 m water depth (intact)

-0.03

-0.02

-0.02

-0.01

-0.01

0.00

0.01

0 1 2 3 4 5

Time [sec]

Hea

ve [m

]

6

P1

P2

P3

P4

P5

TEST C1


-6

-4

-2

0

2

4

6

0 1 2 3 4 5

Time [sec]

Rol

l [de

g]

6

P1P2P3P4P5EXP

TEST C1


-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 1 2 3 4 5

Time [sec]

Pitc

h [d

eg]

6

P1P2P3P4P5

Figure 17 Times series of results for Test C1

/ 49


TEST C21.00 m water depth (breadth / depth = 31.8)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 1 2 3 4 5

Time [sec]

Sway

[m]

6

P1P2P3P4P5

TEST C2

1.00 m water depth (breadth / depth = 31.8)

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 1 2 3 4 5

Time [sec]

Hea

ve [m

]

6

P1P2P3P4P5

TEST C2


-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5

Time [sec]

Rol

l [de

g]

6

P1P2P3P4P5EXP

TEST C2


-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 1 2 3 4 5

Time [sec]

Pitc

h [d

eg]

6

P1P2P3P4P5


/ 49



-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0 1 2 3 4 5

Time [sec]

Sway

[m]

6

P1P2P3p4P5

TEST C3


-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0 1 2 3 4 5

Time [sec]

Hea

ve [m

]

6

P1P2P3P4P5

TEST C3


-6

-4

-2

0

2

4

6

0 1 2 3 4 5 6

Time [sec]

Rol

l [de

g]

EXPP1P2P3P4P5

TEST C3


-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 1 2 3 4 5Time [sec]

Pitc

h [d

eg]

6

P1

P2

P3

P4


/ 49



-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 1 2 3 4 5

Time [sec]

Sway

[m]

6

P1P2P3P4P5

TEST C4


-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0 1 2 3 4 5

Time [sec]

Hea

ve [m

]

6

P1P2P3P4P5

TEST C4


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5

Time [sec]

Rol

l [de

g]

6

P1P2P3P4P5EXP

TEST C4


-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5

Time [sec]

Pitc

h [d

eg]

6

P1P2P3P4P5


/ 49


Appendix D: Analysis of Results

/ 49


EXPERIMENTAL : TEST A1 & B1INTACT vs DAMAGED MODEL PRR01, KG = 12.200 m

-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged

NUMERICAL P3 : TEST A1 & B1INTACT vs DAMAGED MODEL PRR01, KG = 12.200 m

-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged

NUMERICAL P1 : TEST A1 & B1

INTACT vs DAMAGED MODEL PRR01, KG = 12.200 m

-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged



-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged

Figure 21 Comparison of roll motion between intact and damage condition (KG = 12.000 m) for PRR01 model

/ 49


EXPERIMENTAL : TEST A2 & B2INTACT vs DAMAGED MODEL PRR01, KG = 13.456 m

-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged



-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged



-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged


-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10

Time [sec]

Rol

l [de

g]

Intact

Damaged

Figure 22 Comparison of roll motion between intact and damage condition (KG = 13.456 m) for PRR01 model

/ 49



0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9 10

Number of oscillations

Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP


1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP

Figure 23 Roll mean periods in Tests A and B for PRR01 model

/ 49



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP

Figure 24 Logarithmic decrement in Tests A (intact) and B (damaged) for PRR01 model

/ 49


TEST C - EXPERIMENTAL

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m

TEST C - NUMERICAL P3

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m


-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Time [sec]

Rol

l / (i

nitia

l Rol

l)

0.00 m1.00 m4.00 m16.00 m

Figure 25 Comparison of roll motion in Test C for TNK model in different water fill depths

/ 49



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP

TEST C2


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Mea

n Pe

riod

[sec

]

P1P2P3P4P5EXP

Figure 26 Roll mean periods in Test C for TNK model

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10


Loga

rithm

ic D

ecre

men

t

P1P2P3P4P5EXP

Figure 27 Logarithmic decrement in Test C for TNK model

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the 24th ittc benchmark study on numerical prediction of...

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