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Final Report on ITTC Benchmark Study on The Prediction of Extreme Motions and Capsizing of a Damaged Ro-Ro Passenger Ship in Waves 1/1 December 2001

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

Ship Design Laboratory

Benchmark Study on the Capsizing of a Damaged Ro-Ro Passenger Ship in Waves

FINAL REPORT

Issued for comments to: the ITTC Specialist Committee on the Prediction of

Extreme Motions & Capsizing Prepared by: Professor Apostolos Papanikolaou, NTUA-SDL

December 2001


Contents

1. References 3

2. Introduction 4

3. Participants 5

4. Overview of Compared Data 6

5. Background of the Employed Software 7

6. The Studied Ship 9

7. GZ Curves 11

8. Free Rolling Simulation 13

9. Ship Performance in Regular Waves 16

10. Ship Performance in Irregular Waves 21

11. Survivability Boundaries 31

12. Conclusions and Recommendations 33

Appendix: Detailed Analysis of Damage Benchmark Results [12]


1. References

[1]. ITTC99, Specialist Committee on Ship Stability. Final Report and Recommendations to the 22nd ITTC. February 1999.

[2]. ITTC Specialist Committee on Prediction of Extreme Ship Motions and Capsizing. Minutes of 2nd Meeting at Launceston, Australia. 11-12 February 2000. March 2000.

[3]. Stockholm Agreement Water On Deck Model Experiments for Passenger/Ro-Ro Vessel. Final report, PSBG-RE-004-AY. University of Strathclyde - The Ship Stability Research Centre (SSRC). February 2000.

[4]. SOLAS, consolidated edition 1997. Annex 5: Resolutions of the 1995 SOLAS Conference. Model test method.

[5]. Umeda N. and Papanikolaou A. Revised Guidelines for ITTC committee on the prediction of Extreme Ship Motions and Capsizing Benchmark Tests. 10 March 2000, rev. 25 October 2000.

[6]. Papanikolaou, A., Spanos, D., Benchmark Study on the Capsizing of a Damaged Ro-Ro Passenger Ship in Waves. Draft Final report, May 2001.

[7]. ITTC Specialist Committee on Prediction of Extreme Ship Motions and Capsizing. Minutes of 4th Meeting at Glasgow. Scotland. 4 May 2001.

[8]. Vassalos D., Umeda N. and Papanikolaou A. 2nd Revised Guidelines for ITTC committee on the Prediction of Extreme Ship Motions and Capsizing Benchmark Tests. 4 June 2001.

[9]. Papanikolaou, A., Benchmark Study on the Capsizing of a Damaged Ro-Ro Passenger Ship in Waves. Revised Final report, October 2001.

[10]. Jasionowski A., Detailed Analysis of the Revised Damage Benchmark Results. University of Strathclyde - The Ship Stability Research Centre (SSRC). October 2001.

[11]. ITTC Specialist Committee on Prediction of Extreme Ship Motions and Capsizing. Minutes of 6th Meeting at Crete. Greece. 11-12 October 2001.

[12]. Jasionowski A., Vassalos D. (2001). Detailed Analysis of the Final Revised Damage Benchmark Results. University of Strathclyde - The Ship Stability Research Centre (SSRC). December 2001.


2. Introduction The present document reports on the results of a benchmark study organised by the ITTC Specialist Committee on the prediction of extreme ship motions and capsizing regarding the damaged stability performance of a Ro-Ro passenger ship [1]. The benchmark study was announced in public in March 2000, in accordance to a relevant decision of the ITTC Special Committee [2], inviting ITTC member organisations and other qualified research institutions to express their interest in participating at the launched study. Based on this call five (5) organizations were submitting numerical results for this benchmark study. The selected ship under investigation was the Ship B-2 of the damage benchmark guidelines, which is a Ro-Ro Passenger ship tested earlier in ship model tank of SU-SSRC following the Res. 14 of SOLAS 95 procedure, as reported in [3]. One damage condition was finally requested for the study that is the midship damage condition [4]. Wave conditions were set in the benchmark guidelines [5], as well as the extent of prediction of the ship performance in regular and irregular seas. In particular its was requested to investigate the intact ship performance for a number of incoming regular beam waves and the damage ship capsizing boundaries in irregular beam seas for varying KG values. As reported in the draft report [6] and discussed in [7], the initially submitted results by the benchmark study participants were not uniform and comparable in a straightforward way, partly because some of the participants did not follow exactly the set benchmark specifications and partly because some of the specified ship and environmental parameters were not unanimously interpreted, introducing significant uncertainties in the identification of the exact simulation case they were referring to. In view of this fact, the benchmark specifications were revised [8] and the participating organisations were re-invited to update their results, following the updated specifications (see also http://www.strath.ac.uk/Other/SSRC/ITTC/SCEXCAP). The five (5) participating organizations re-submitted their updated numerical results and these results have been reported in [9] and [10]. The updated damage benchmark study results were discussed at the ITTC committee meeting held in Crete [11] and it was generally accepted, that the submitted updated results of the participating organisations, that were considering the revised benchmark study specifications, significantly improved in terms of uniformity and final outcome, as compared with the available experimental data. Based on this and taking into account the comments of the ITTC committee members, it was decided to ask once more the participating benchmark study organisations to verify their submitted results and general information input and to proceed to the compilation of the final damage stability benchmark study report. This final report is herein presented. The report consists of two parts, namely the main body text, summarising the overall study results and the detailed analysis of the individually submitted damage benchmark results, along with the corresponding experimental values and ship characteristics, presented in the Appendix [12]. Despite the fact that finally only a small number of organisations were able to participate at the present benchmark study and that only one ship could be benchmark tested during the present ITTC Specialist Committee’s service period (both facts indicating a presently limited ‘critical mass’ among the ITTC member organisations related to the complexity of the studied subject), it is felt that the final outcome of the present benchmark study enabled the drawing of some important conclusions regarding the studied subject. Even if some numerical results cannot be considered satisfactory, compared to model experiments, the study clearly identified the assets and gaps in the present state of knowledge on the prediction of extreme ship motions and capsizing of damaged ships in waves and recommends the further investigation of specifically identified problem areas towards establishing a fully satisfactory state of the art in the addressed field.


3. Participants

The following five institutions participated in the ITTC ship B-2 damage stability benchmark study.

Participant/Contact Institution Country

Prof. A. Papanikolaou [email protected] Mr. D. Spanos [email protected]

University of Athens, NTUA co-ordinator of damage benchmark study Greece

Prof. D. Vassalos [email protected] Mr. A. Jasionowski [email protected]

University of Strathclyde, SSRC UK

Assoc. Prof. N. Umeda [email protected]

University of Osaka Japan

Dr J. de Kat [email protected] Mr. L. Palazzi [email protected]

Maritime Research Institute Netherlands, MARIN The Netherlands

Dr. S. Krueger [email protected] Mrs. H. Cramer [email protected]

Flensburger Schiffbau Gesellschaft, FSG Germany

Table 3.1 Participants Notes:

In the following tables, charts and graphs of results the identity of the participating institutions is coded (anonymous, Participant 1 to 5).


4. Overview of compared data

Participants

P1 P2 P3 P4 P5

GZ curves (intact/damaged) x x x x x Simulated free roll decay curves (intact) x x x x x Simulated free roll decay curves (damaged) - x x x x Simulated frequency roll response curves (intact/damaged RAOs), constant wave height x x x x x Simulated roll response curves (intact), constant wave slope (1:25) x x - x x Simulated survivability boundaries (0% capsize, 100% capsize for KG=12.892 m) x x x x x Wave, roll, heave, water on deck time series for KG=12.892 m and Hs=4.0 m, 4.25 m and 4.5 m (5 runs).

x x x x x X data available

- data not available


5. Background of Employed Software A brief outline of the background of the employed software by the various participants is given in this chapter. The reference to the fundamental characteristics of the employed software is made in order to provide a global comparative view of the employed codes. More detailed information is given in the submission reports of the participating organisations.

All the employed codes are non-linear time domain codes. The ship is considered as a rigid body and her motion is governed by non-linear rigid body dynamics. The ship is assumed moving in six degrees of freedom (DOF) for all participants, expect for the code of Participant 3 that is based on a three DOF modelling (sway, heave and roll). The employed codes use alternative approaches to calculate the radiation and wave diffraction forces, all in the framework of potential theory, as presented in Table 5.1. Table 5.1

POTENTIAL THEORY APPROACHES TO SHIP MOTIONS EMPLOYED BY PARTICIPANTS

PARTICIPANT APPROACH P1 Strip theory, 6 DOF P2 3D source panel theory, 6 DOF

P3 Newly modified strip theory, 3 DOF

P4 3D source panel theory, 6 DOF

P5 Strip theory, 6 DOF

Damping forces were modelled as shown in Table 5.2. Table 5.2

DAMPING FORCES MODELLING

PARTICIPANT MODELLING P1 Non-linear roll damping according to P. Blume

P2 Equivalent linear roll damping estimated from the available intact ship roll decay measurements

P3 Nonlinear roll damping acc. to Ikeda

P4 Adaptive linear roll damping acc. to Ikeda

P5 Nonlinear (Equivalent linear & quadratic) roll

damping based on a modified Ikeda’s approach

______


The floodwater is generally considered as independent variable masses moving inside the flooded compartments and interacting with the ship through the developed forces between them. The modelling of the internal water motion can be generally described by the modelling of the floodwater free surface condition, as shown in Table 5.3. Table 5.3

FLOODWATER FREE-SURFACE MODELLING

PARTICIPANT MODELLING P1 Plane and free movable (when period away from natural)

Glimm’s equations (when period close to natural)

P2 Plane and free movable

P3 Plane and horizontal

P4 Plane and free movable P5 Plane and horizontal

____ The water ingress/egress through the damage opening is commonly based on hydraulic models following application of Bernoulli’s dynamic pressure head equation. All participants used empirically determined coefficients to take into account the actual water ingress/egress flow though the specified damage opening.


6. The Studied Ship The general particulars of the studied Ship B-2, a passenger/Ro-Ro vessel, both in full and model scale, are given next. The model scale equals 1:40. Table 6.1

Dimension Full Scale Model Scale LOA 179,00 m 4475,0 mm LBP 170,00 m 4250,0 mm B 27,80 m 695,0 mm T 6,25 m 156,3 mm DCARDECK 9,00 m 225,0 mm Displacement (even keel) 17300 tn 270,3 kg Intact KG 12,89 m 322 mm (above BL) Intact Design GM (even keel) 2,63 m 65,8 mm The ship has been studied both in intact and damage condition. Some details of the model characteristics pertaining to the intact and damage condition are given below. - Metacentric Height (intact): GM = 65,76 mm

It is determined by the inclining experiment. - Roll Radius of Gyration, ixx/B= 0,235 (ixx= 163 mm)

The roll radius of gyration ixx has been estimated by analysis of the free roll decay measurements and provided to the participants for the intact condition. This radius refers to the ship’s structural mass radius of inertia that can be derived from the relevant decay measurements when considering the hydrodynamic added inertia. It is a characteristic constant of the model, for the specific intact loading condition..

- Intact, natural roll period, Tni = 2,056 sec This period has been determined by analysis of records of the free rolling tests in intact condition.

- Damaged, natural roll period, Tnd = 2,300 sec

This period has been determined by analysis of records of the free rolling tests in damage condition.

- Pitch Radius of Gyration, iyy/L= 0,217 (iyy = 872 mm) Radius iyy has been estimated in [3] by analysis of the free pitching experiment (in air).

- Yaw Radius of Gyration, izz/L= 0,238 (iyy = 960 mm)

Radius izz was assumed to be 10% greater than pitch radius of gyration. This increase can be justified by the fact that for models in damage experiments the mass of superstructures is usually missing, therefore the models’ lateral mass distribution is expected to be greater than the vertical one.

More detailed information for the ship as well the specification of the studied damage conditions are given in document [3] and http://www.strath.ac.uk/Other/SSRC/ITTC/SCEXCAP.


In figure 6.1 the studied damage case of the benchmark study ship is depicted, whereas in figures 7.1 and 7.2 the GZ curves in both intact and damage case are presented.

Fig. 6.1 Midship Damage Case [3]


7. GZ curves The employed numerical codes of the benchmark study participants take into account the hydrostatic properties of the vessel in an approximate form, depending on the discretisation of the ship’s geometry. Therefore, an assessment of the internally calculated GZ curves by the codes of the benchmark study participants is of importance. In the following figures 7.1 and 7.2 the intact and damage GZ curves by the benchmark study participants are shown and partly some remarkable deviations are observed. These deviations should be borne in mind when analysing the predicted ship responses by the various employed codes, as any inaccuracy in the geometry and ship hydrostatics will affect the estimated stiffness of the ship and hence her natural frequencies, as well as the ship’s restoring ability over the range of stability. In case of the intact ship conditions the observed differences are minor. However, in the damaged case, the GZ curve of Participant 3 clearly shows higher initial stiffness for the flooded ship, whereas the range of stability of ship models used by Participants 2 and 5 are noticeably lower. Note that in this case only Participants 1 and 4 properly capture the hydrostatic properties of the benchmark ship over the entire stability range.

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Fig. 7.1 GZ curve of intact ship calculated by Participants


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Fig. 7.2 GZ curve of damaged ship calculated by Participants


8. Free Rolling Simulation All benchmark study participants (P1, P2, P3, P4, P5) have provided roll decay curves for the intact ship, and four of them (P2, P3, P4, P5) also the simulated curves for the damaged condition. The results are shown in figure 8.1. Simulations of the free roll decay curve in the intact condition do not seem to have presented any difficulty to the participants, as generally fine agreement with the experiments has been achieved by all participants. However, similar attempts to simulate the free roll response in damaged condition have been less successful. Results presented by all participants show a distinctive overestimation of the roll natural frequency in flooded conditions. Therefore, three possible sources of this discrepancy may be identified:

(a) Lack of understanding of the complete hydrodynamics of the damaged ship, (b) Inaccurate representation of the floodwater dynamics and its coupling with ship

motion (c) Possible inconsistencies in the available experimental data (clarification of

experimental conditions and way of analysis of data).

As a first step in explaining this inconsistency, it appears necessary to undertake in the future a new related benchmark study for at least another ship case and to perform additional experimental verifications of the free roll tests in damage condition.


PRR1, KG=12.892m, Free roll decay, Intact condition

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Fig. 8.1 Free rolling of intact and damaged ship.


9. Ship Performance in Regular Waves The comparative results of the benchmark study participants (P1, P2, P3, P4 and P5) for the intact and damage ship’s roll response in regular beam waves, with Ø constant wave height (Hw = 1.2m, 2.0m and 2.4m) and Ø constant wave slope, namely constant wave height to wavelength ratio equal to 1/25,

are presented in the following. The purpose of this particular study was to gain insight into the partners’ non-linear motion modelling at conditions as far away as possible from the linear small amplitude motion theory. Note that that in the constant slope case this leads to quite extreme seaway excitations. 9.1 Roll Response Amplitude Operators (RAOs) for Constant Wave Height Excitation Based on the results presented in the following graphs (Fig. 9.1), the following can be concluded1: 9.1.1 Simulation of Intact Ship Roll RAO for constant Wave Height Monochromatic Wave Excitation

1. All participants have generally accomplished the simulation of the basic intact Roll RAO successfully.

2. Some differences in the predicted peak values of ship response, occurring at the natural roll frequency (more pronounced in the simulation by participant 1), are due to the insufficient modelling of roll damping, which is based on semi-empirical coefficients and approaches, that need further improvement.

9.1.2 Simulation of Damage Ship Roll RAO for constant Wave Height Monochromatic Wave Excitation

1. The simulation of the basic damage Roll RAO could not satisfactorily predicted by the participants. The reason for the deviation of the numerical results from the experiments has been already identified in the damage free roll benchmark test (see Chapter 8) and emerges even clearer in the simulations of the damage roll RAO.

2. In particular, none of the participants obtained the natural frequency of the damage ship close to the value derived experimentally. In fact, the predicted natural frequency of the damaged ship is quite inconsistent among the Participants: Participants 2, 4 and 5 predict a slight decrease of this frequency in relation to the natural frequency of the intact ship, a trend shown also in the damage experiments, but not to the extent measured at the damage experiments. Rather more, a shift between the numerically predicted curves of the above 3 participants and the experimentally determined curve can be observed. Participant 1 is predicting even an increase of the intact natural frequency, whereas the natural frequency of Participant 3 remains practically unchanged.

3. The above results suggest that the predicted hydrodynamic added moment of inertia effects by all participants apparently significantly deviate from the comparative experimental values.

4. Regarding the predicted peak values of the damaged ship roll response, practically all participants predict higher peak roll values indicating a clear underestimation of damping in damage condition and hence overestimation of the roll response. Among the participants, Participant 4 comes closer to the experimentally predicted peak values.

1 Note that experiments were performed for exciting wave height equal to 1.2m and 2.4m, whereas numerical simulations of the benchmark study participants were partly for various wave heights between and equal to 1.2 and 2.4m.


5. The experimentally measured damaged ship roll response indicates the existence of a second resonance frequency at about two times the main roll resonance frequency. This phenomenon is predicted by participants 4 and 5, however at much higher frequencies and for higher secondary resonance peak values.

6. The above conclusions call for additional research in this area and a re-assessment of the damage Roll RAO results in the future, when more experimental and numerical benchmark results are available.

PRR1, KG=12.892m, Roll RAO, Intact condition

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PRR1, KG=12.892m, Roll RAO, Damage condition

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Fig. 9.1 Intact and Damage Ship Roll Responses for constant wave height regular beam wave excitation


9.2 Roll Response Amplitude Operators (RAOs) for Constant Wave Slope Excitation The purpose of this particular study was to gain a more clear insight into the partners’ non-linear motion modelling at conditions as far away as possible from the linear small amplitude motion theory. Note that that in the present constant slope case of 1/25 this leads to extreme seaway excitations, with a significant wave height of up to 20m. The present study was restricted to only the intact ship case and no experimental data were available to cross check the numerical predictions. Only Participants 1, 2, 4 and 5 delivered results for this particular study.

PRR1, KG=12.892m, Roll RAO, Constant wave slope 1:25, Intact condition

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Fig. 9.2.1 Roll response in regular beam waves with constant wave slope over λ/L

PRR1, KG=12.892m, Roll RAO, Constant wave slope 1:25, Intact condition

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Fig. 9.2.2 Roll response in regular beam waves with constant wave slope over ω


Commenting on the above results, the following can be stated:

1. Overall results of the participants partly differ significantly. 2. Results for large wavelength ratios (small wave frequencies) appear satisfactory, with the

values of Participant 5 in between those of the others and Participants 2 and 4 remarkably close together.

3. Results for small wavelength ratios (large wave frequencies) are less satisfactory, with the values of Participants 2 and 4 in between those of the others and again remarkably close together. Note that this wave excitation region is of reduced practical interest, as it corresponds to very steep short waves that might be unrealistic in practice.

4. Predictions in the resonance region deviate substantially indicating clearly the differences of the employed semi-empirical damping models by the various participants for the extreme motion amplitude conditions. This observation was also made in the constant wave height excitation study (9.1).

Concluding, it appears necessary that a more comprehensive study should be carried out in the future to investigate the relation between the employed damping models by the benchmark study participants. Unfortunately, comparative model experimental measurements were not available to enable a more thorough evaluation of the employed numerical procedures for the intact, large amplitude and large slope motion case. The only apparent result from this comparison is that the results of the different employed numerical methods deviate partly substantially, indicating that the state of the art in the numerical modelling of a highly nonlinear ship motions problem is yet not satisfactory.


10. Ship Performance in Irregular Waves The prediction of the damaged ship performance in the specified irregular waves has been herein assessed on the basis of an analysis of the numerically simulated time series records for the exciting wave, the ship’s motion response and the amount of flooded water, as compared with relevant time series records of corresponding model experiments, the assessment of the spectral properties of the corresponding time series records, the simulation of the ship’s survival boundaries and finally the identification critical survival/capsisal wave heights. Detailed results of this study (experimental and numerically simulated time series records) are given in the Appendix. Herein only some characteristic results are commented. The following figures 10.1 to 10.12 present a sample of time series of the experimentally measured and numerically predicted wave exciting and ship responses. Two representative runs per participant, one for survival and one for capsisal case, are presented, all corresponding to a significant wave height excitation of 4.00 m. Wave elevation, heave and roll motions as well the amount of water accumulated on the car deck are shown.


Fig. 10.1 Experimental responses of damaged model B-2. Survive case.

Fig. 10.2 Experimental responses of damaged model B-2. Capsize case.


Fig. 10.3 Responses of damaged model B-2. Participant 1. Survive case.

Fig. 10.4 Responses of damaged model B-2. Participant 1. Capsize case.


A visual comparison/analysis of the numerically predicted and experimentally measured time series shows a rather unsatisfactory level of agreement between the different participants and the experiments. Indeed, none of the numerical time series match satisfactorily at least in qualitative terms the experimental values where in particular the character of the experimentally measured roll response indicates a quite distinct independence of the response components induced by the wave excitation and low-frequency response due to floodwater accumulation. Some resemblance of this character of roll can be seen in the results of Participant 1. The roll responses predicted by Participants 2 and 3 display noticeably higher amplitudes, possibly due to insufficient numerical damping models, as identified before (roll decay and free roll benchmark tests). Some similarity in roll pattern can be seen in the responses derived by Participants 4 and 5. A Fourier spectral analysis of the calculated time series records enables a better understanding of the differences between the numerical simulations and the response characteristics derived by physical model tests (Fig. 10.13). - Participant 2 missed to reproduce exactly the exciting wave spectrum characteristics and has

worked with a wave spectrum having its peak slightly shifted towards lower frequencies, closer to natural roll frequency of the ship.

- The predicted roll response spectra of Participants 1, 2, 4 and 5 indicate an underestimation of the roll damping effects as considerable response values occur near the ship’s roll natural frequencies, a phenomenon not visible in the experiments.

- Participants 2 and 3 predict considerably higher roll spectral densities, partly as a consequence of the predicted higher peak roll values and partly due to the deviation of the peak frequency of the exciting wave spectrum, assumed closed to the roll resonance frequency.

- Some additional noise in the spectrum of roll motion at frequency of about 1.0 [rad/s] can be observed for Participant 5.

- The spectrum of heave response derived by Participant 3 shows a peculiar second lower peak around 0.6 rad/s.


Fig. 10.13 Spectrum analysis of Experimental and Numerical ship responses.


11. Survivability Boundaries The reported survival/capsisal boundaries have been derived with considerably high accuracy by most of the participants. Both, the “lower” and “upper” boundaries distinguishing between sea states leading to ship survival, marginal survivability or capsizes have been predicted within a remarkable accuracy of about 0.5m in Hs, varying between participants. It must be mentioned here, that the simulation time is of importance in establishing the boundary consistently, as the longer the duration of the simulation, the lower is the boundary. This, however, has not been clearly defined as a benchmark test constraint and some variation between the participants was noticeable. The demonstrated accuracy in predicting the critical sea states seems quite satisfactory from the point of view of application of such information to practical survivability assessment procedures. In Table 11.1 an overview of relevant results is shown. The understanding in compiling this table is that the ship’s survival boundary, for the particular damage case, is identified as corresponding to conditions with none capsize event occurring for five consecutive numerical simulations corresponding to different irregular seaway realisations for specified spectral seaway conditions. On the other hand a capsize boundary is identified corresponding to conditions when all five runs lead to a capsize event. Commenting on the obtained results by the benchmark participants, it appears that numerically predicted survival boundaries are in quite satisfactory correlation with the experimental values. In particular, participants P1 and P3 overestimate the survival Hs by about 6%, P2 and P4 underestimate this boundary by about 6% while P5 underestimates this boundary by about 12.5%. Regarding the prediction of the capsisal boundary, correlation results are similar to the survival boundary curve case. Four of the participants have clearly identified the capsisal boundary, with P2 and P5 predicting capsize at Hs practically equal to the experimental value (0% deviation), whereas P1 is overestimating this limit by 6% and P4 for 12.5%. Only Participant 3 misses to predict the values capsisal boundary properly (none capsisals for specified conditions).


Experiment P1 P2 P3 P4 P5

Hs=3.50m - - - - - 0

Hs=3.75m - - 0 - 0 1

Hs=4.00m 0 0 2 0 1 3

Hs=4.25m 3 0 3 0 2 4

Hs=4.50m 5 2 5 1 3 5

Hs=4.75m - 5 - 1 3 -

Hs=5.00m - - - 2 5 -

Table 11.1 Experimentally observed and numerically simulated capsize events

per 5 seaway realisations

SURVIVE/CAPSIZE BOUNDARIES

0

1

2

3

4

5

6

Hs

[m]

ExpP1P2P3

P4P5

Fig. 11.1 Comparison of predicted survive/capsize boundaries

with model experimental values


12. Conclusions & Recommendations In concluding, it appears that the herein studied numerical procedures, representing “state of the art” numerical simulation tools of damaged ship motions in waves, lead to an overall satisfactory state of knowledge, though improvements at various methodological steps appear necessary. The basic specific conclusions and recommendations of this study are as following:

1. Intact ship motions simulations

a. Intact Ship Roll decay curves Overall fully satisfactory prediction of the experimental data by the employed numerical codes of the participants.

b. Intact Ship Roll RAOs for constant wave height regular wave excitation Overall satisfactory prediction of the experimental data by the employed numerical codes of the participants, deviations observed in the resonance region (large amplitude motions) due to the not fully satisfactory employed, semi-empirical damping models. Recommendation: to investigate systematically the validity of currently employed semi-empirical roll damping model, employed in nonlinear ship motions time domain codes, through comparison with specially designed model experiments. c. Intact Ship Roll RAOs for constant wave slope regular wave excitation Taking into account that this is an extreme benchmark test case (relatively large wave slope of 1:25 leading to extreme waves heights of up to 20 m in full scale) and in addition the fact that none experimental data were available for validation of the obtained numerical results, it is difficult to reliably assess the quality of the obtained results. On the basis of the general understanding of numerical simulation of large ship motions it appears that the obtained results are of mixed quality (with partly substantial deviations among the employed numerical codes, except for two participants), except for the large wavelengths region (small wave frequencies, which are clearly of more practical interest), where a convergence of the numerical results can be observed. The reasons for the deviations are insufficiencies of the employed damping models (as stated before, under 1b), and the severeness of the studied nonlinearities for extreme wave conditions.

2. Damage ship motions simulations

a. Damage Ship Roll decay curves Overall non-satisfactory prediction of the experimental data by the employed numerical codes of the participants. Deviations concern both the prediction of the damage roll radius of inertia as well as the roll damping. Recommendation: to repeat this type of benchmark study for another ship and to carefully specify and analyse relevant model experiment.

b. Damage Ship Roll RAOs for constant wave height regular wave excitation


Overall non satisfactory prediction of the experimental data by the employed numerical codes of the participants, both as to the prediction of the damage roll natural period (over-prediction, compared to the model experiments) as well as to the actual damage roll damping (under-prediction, compared to the model experiments). This is clearly a consequence of the failure to properly predict the experimental data of the calm water damage roll decay test. These results indicate a lack of full understanding of the damage ship hydrodynamics and especially a lack of proper modelling of the floodwater effects (ingress/egress and floodwater dynamics). Recommendation: Before generalising this important conclusion, it is necessary to repeat this particular study for further ship cases and to ensure that the comparable experimental data are properly presented for enabling the verification of possible deviations by the numerical codes. Taking into account the roll response of a damaged ship is a highly nonlinear process, it appears that comparing results on the basis of linear concepts, like the Roll Response Amplitude Operator, might not lead to reliable conclusions, therefore future benchmark tests should take account of this and properly redefine relevant numerical and experimental benchmark specifications.

3. Damage Ship - Irregular Seaway Excitation - Survival Boundaries – Critical Seastates

a. Simulated Damaged Ship Time Series Records Considerable qualitative differences in trends between experimentally and numerically derived time series of ship responses have been found. None of the predictions could match the experimental records accurately. However, taking into account the complexity of the set problem, that corresponds to a nonlinear hydrodynamic phenomenon under stochastic environmental constraints (irregular seaway excitation), this could be expected. A Fourier spectral analysis of the obtained time series records has confirmed the differences in the character of the predicted and measured responses and enabled the identification of weaknesses in the employed numerical models. It should be noted that the employed numerical codes partly missed to accurately account for the hydrostatic properties of the benchmark ship over the entire stability range (due to insufficient discretisation of the ship’s geometry at large roll angles), therefore some deviations are attributed to this insufficiency. Finally, the numerical simulation of the exact exciting irregular seaway characteristics posed an additional problem to some participants, forming an additional source of error in the predicted time series records. b. Simulated Survival/Capsisal Boundaries and Critical Seastates

Overall satisfactory to excellent prediction of the survival and capsisal boundaries, and correspondingly of the critical seastates, practically by all participants. Deviations against experimentally predicted data are no more than 0.5m in significant wave height Hs. Herein the survival boundary is more accurately predicted than the boundary for the possible capsisals. Taking into account that this type of numerical studies are an essential tool for the preliminary evaluation of the survivability of damaged ships in a seaway (see, provisions of Res. 14 of the Stockholm Agreement for the Assessment of Survivability of Ro-Ro Passenger Ships), it appears that herein a satisfactory state of the art has been achieved enabling designers to effectively address complicate practical problems related to the assessment of the damaged ship’s stability, as requested by recent enhanced safety regulations or other provisions set by the ship owner or other safety control authorities.


Final Comment Considering the relatively low number of the benchmark study participants and the complicate nature of the set benchmark study problem it is felt that the main objectives of the present study have been met, though a similar study should repeated in the future with the aim to alleviate the effects of some of the above stated weaknesses. It has been ascertained that at present state of knowledge, model experiments remain indispensable for assessing the survivability of damaged ships in waves, though theoretical-numerical prediction methods can greatly contribute to a pre-assessment of the survivability of intact and damaged ships in waves. The authors of this report like to sincerely thank all benchmark study participants for the shown interest and effort to contribute to this study, promoting the state of the art in a generally accepted highly ambitious scientific filed of great practical importance to the whole maritime community.

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