SAFEDOR International Benchmark Study on Numerical...

National Technical University of Athens

School of Naval Architecture and Marine Engineering

SHIP DESIGN LABORATORY

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

SAFEDOR International Benchmark Study on Numerical Simulation Methods for the Prediction of

Parametric Rolling of Ships in Wave

Dimitris Spanos Apostolos Papanikolaou

NTUA-SDL Report

Revision 1.0, June 30, 2009

of 60

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

Summary The report summarizes the results of the SAFEDOR international benchmark study on the performance of computer codes for the prediction of parametric rolling of ships in waves. Benchmark codes have been reviewed on a comparative way with respect to a series of specified numerical tests and in comparison to available and newly generated model experimental data in order to conclude on the present state of their performance. The study was organized within approved activities of the EU funded project SAFEDOR (Design, Operation and Regulation for Safety, Contract No. FP6-IP-516278); the study was announced in July 2008 and completed in February 2009. Thirteen institutes from all over the world participated in the study, which was coordinated by NTUA-SDL.

The study assessed first the overall performance level of the benchmarked simulation codes, which proved to be in the average low in view of the large spread in the performance of individual methods and prediction failures in some specific tests. However, taking into account a quantitatively satisfactory sample of the best performing methods it is concluded that the present state of the art in the field of numerical simulation of parametric roll is satisfactory, with the best performing twice as good as the mean overall.

Disclaimer and Copyright

The information contained in this report is subject to change without notice and should not be construed as a commitment by the authors.

Due acknowledgement must always be made of the use of information and material contained in, or derived from, this report.

All rights reserved.

of 60

Contents

1 General.................................................................................................................................. 4 2 Participation........................................................................................................................... 6 3 The Benchmark Study........................................................................................................... 8

Objectives .............................................................................................................................. 8 Study Approach ..................................................................................................................... 8 Overall Performance of Numerical Simulation....................................................................... 9 Benchmark Tests................................................................................................................. 11

4 The Study Data ................................................................................................................... 13 Experimental Data ............................................................................................................... 13

5 The Subject Ship ................................................................................................................. 14 6 Ship Hydrostatics ................................................................................................................ 15 7 The Numerical Simulation Methods..................................................................................... 16 8 Decay Tests ........................................................................................................................ 19 9 Numerical Simulation Results.............................................................................................. 21

Typical Roll Motions............................................................................................................. 23 10 Roll Amplitude Predictions................................................................................................... 24

Performance of Methods ..................................................................................................... 26 11 Roll Resonance Prediction .................................................................................................. 29

Sensitivity of Results............................................................................................................ 30 Impact of Benchmark Tests ................................................................................................. 32

12 Conclusions......................................................................................................................... 34 13 Website ............................................................................................................................... 35 14 References .......................................................................................................................... 36 Appendix I Benchmark Tests ................................................................................................... 39 Appendix II Hydrostatics........................................................................................................... 40 Appendix III Study Waves ........................................................................................................ 43 Appendix IV Typical Simulated Roll Motion.............................................................................. 45 Appendix V Full Set of Numerical Simulations ......................................................................... 49 Appendix VI Revisions of Numerical Simulations....................................................................... 60

of 60

1 General

The prediction of the parametric roll phenomenon and its impact on ship’s intact stability and safety has attracted in the last decade great scientific interest, as documented in a series of scientific publications and presentations at relevant international conferences and workshops. The subject has gained, also, significant practical importance and the interest of national and international regulatory authorities (IMO, class societies), because of the risk for the inception of large ship roll motions, shift or loss of cargo and eventually ship capsize.

Numerical simulation methods of varying complexity are nowadays routinely employed for the prediction of ship motions in waves and they are often also applied to the prediction of parametric roll phenomena. As the employed methods are of varying complexity and capabilities, their accuracy in predicting parametric rolling is accordingly of mixed quality.

In the past, the Specialists Committee of ITTC on Extreme Motions and Capsizing has conducted a benchmark study on the performance of numerical methods for the prediction of various modes of roll motion and capsizing of intact ships in waves, including the parametric roll phenomenon, [1]. The results of this study showed a quite unsatisfactory state of affairs and this may be attributed, besides the limitations of that benchmarked methods, to the complexity of the subject, when considering the various capsize modes and the inherent uncertainty, even in the experimental benchmark data, when considering free running models in modelled seaways.

The present study has been setup with the aim to review the currently available numerical simulation codes for the prediction of the parametric rolling and to assess the current level of efficiency on the basis of a benchmarking under more controlled benchmark conditions, namely considering semi-captive tests, in which the model speed and heading to the waves is fixed. In this way, the inherent capability of the benchmark simulation methods in predicting the roll motions in waves can be assessed.

Semi-captive model tests have shown acceptable agreement with free running model tests [37], however free running tests are suggested in order to take into account the full effect of speed variation in waves. The simulation tools were herein evaluated for the specific restrained conditions, for which parametric roll resonance occurs. Restrained conditions provide controllable conditions, ideal for benchmarking purpose. However this is achieved in loss of some effects like the speed variation in waves.

Qualified institutes from both inside and outside SAFEDOR that have been established as developers of relevant simulation methods and computer programs were invited to demonstrate the performance of their codes on the prediction of parametric rolling. These institutes have independently developed codes, have published relevant results in the past, thus their participation in this benchmark study suggests that they well represent the current state of art in the field.

of 60

The study comprised the simulation of the motions of a containership in longitudinal waves, known from earlier ITTC studies. For the present benchmark, a test matrix with varying operational conditions was designed; in particular, care was taken to consider both conditions for which the occurrence of parametric roll resonance was very likely, but also conditions for which due to the change of specific operational parameters the parametric roll phenomenon did not appear. Noting that the comparative experimental data were not known beforehand to the study participants, it can be concluded that the present benchmark assessment was based on a solid foundation and allowed an assessment of the genuine capabilities of benchmarked codes.

The study was announced to potential participants in mid July 2008. An initial group of sixteen participants was formed by mid September 2008, when the first study data were circulated to the participants; they referred to a first series of tests for which relevant experimental data were available to the study coordinator from a series of tests carried out within the HYDRALAB II, EU research project [3]; the benchmark study specifications were finalized on the basis of a second series of tests in early October 2008; these tests were carried out within SAFEDOR, EU research project [4]. According to the set initial plan, the participants had to submit their simulation results by mid December 2008, which was later shifted to January 04, 2009.

Not deviating from the experience of past benchmarks, part of the initially submitted results suffered from trivial errors and incompliance to study requirements. Upon submission of the results, the study coordinator checked this and relevant partners were requested to cure their submissions by repeating simulations, as necessary. At the end, a set of numerical simulations in full compliance to the study specifications was collected and analysed. The reported status includes results received by the coordinator until February 5, 2009. It is noted that until that date the comparative experimental data considered in the study were not communicated to the study participants.

Eventually thirteen (13) independent participants (CHALMERS, COPPE, DINMA, DTU, GL, HUT, IST, KTH, NMRI, NTUA, OU, SOTON and SSRC) submitted simulation results, which are presented and assessed in the next sections.

The benchmark study was organized in the framework of SAFEDOR research project and was coordinated by National Technical University of Athens (NTUA).

of 60

2 Participation

Qualified institutes that have been established as independent developers of relevant simulation computer programs were invited for participation to the benchmark. The benchmark study was open and announced initially to thirty six (36) institutes, while they were requested to further communicate the announcement to any other potentially interested institute. Eventually thirteen (13) institutes, as listed in the next Table 1, participated by contributing with numerical simulations, which produced with their own programs.

Each participant has employed one simulation method, with exception of GL who has used two different simulation methods and submitted two sets of results correspondingly. Hence, totally fourteen (14) simulation methods could be reviewed.

According to the benchmark plan the identity of the simulation results is treated anonymously as the main interest of the study is the assessment of the current overall performance of the various software tools and not of individuals in order to avoid any commercial implications. Hence, in the next sections the results are presented with coded names 01-14, which do NOT correspond to the list of Table 1.

The study was coordinated by Prof. Apostolos Papanikolaou.

Table 1 Participants: List of participants to the study Institute Research Group Country

CHALM Chalmers University of Technology

Shipping and Marine Technology

Dr. Martin Schreuder Sweden

COPPE LabOceano/COPPE

Federal University of Rio de Janeiro

Prof. Marcelo Neves

Dr. Claudio Rodríguez

Brazil

DINMA University of Trieste Prof. Alberto Francescutto

Dr. Gabriele Bulian

Italy

DTU Technical University of Denmark

Department of Mechanical Engineering

Prof. Jorgen Jensen

Dr. Jelena Vidic-Perunovic

Denmark

GL Germanischer Lloyd

Department Fluid Dynamics

Dr. Vladimir Shigunov

Mr. Ricardo Pereira

Germany

HUT Helsinki University of Technology

Applied Mechanics Department, Marine Technology

Prof. Jerzy Matusiak Finland

IST Instituto Superior Tecnico

Technical University of Lisbon

Prof. Carlos Guedes Soares

Dr. Sergio Ribeiro e Silva

Portugal

of 60

KTH KTH Centre for Naval Architecture

Royal Institute of Technology

Seaware AB

Dr. Anders Rosen

Mr.Erik Ovegard

Mr. Mikael Palmquist

Sweden

NMRI National Maritime Research Institute

Ship Structural Standards Research Group

Dr. Yoshitaka Ogawa Japan

NTUA National Technical University of Athens

Ship Design Laboratory

Prof. Apostolos Papanikolaou

Dr. Dimitris Spanos

Greece

OU Osaka University

Dept. of Naval Architecture and Ocean Engineering

Prof. N. Umeda

Mr. Jiang Lu

Japan

SOTON University of Southampton

School of Engineering Sciences

Prof. Pandelis Temarel

Dr. Tamer Ahmed

United Kingdom

SSRC The Ship Stability Research Centre

Dept. of Naval Architecture and Marine Engineering

Universities of Glasgow and Strathclyde

Prof. Dracos Vassalos

Dr. Joonyun Kang

United Kingdom

A map of the geographical origin of the participants shown in Figure 1 demonstrates a concentration of interest in Europe and particularly in North Europe, with five participants being also partners of the SAFEDOR research project.

Although most contributions to this study have been received from Europe, whereas two were from Japan and one from Brazil, it is believed, considering also the overall scientific activities in the field, that the collected results well represent the international state of the art in the field.

Figure 1 Participants: Geographical origin of participants

of 60

3 The Benchmark Study

Objectives

The objectives set for the current study were:

° To record numerical simulation methods currently employed for the prediction of the parametric rolling of ship in waves, and

° To assess the current level of accuracy and efficiency of the relevant numerical prediction methods by comparison with available experimental data.

Study Approach

The following approach has been applied in this study.

° After the announcement of the study, potential participants expressed their interest to participate within a period of two months. After the list of participants was finalized, the study data, the benchmark tests and other details were circulated by the coordinator.

° The benchmark tests, comprising a series of loading and sailing conditions for a containership and the detailed study specification, had been selected and compiled by the study coordinator.

° Each participant simulated for the specified benchmark tests (within a period of three months) and submitted to coordinator the simulation results for review.

° Initially the submitted simulations were verified with respect to their compliance with the study specifications before accepting them for further consideration in the study. All simulations that were identified deviating from the specifications were repeated by the participants (see Appendix VI). So, the final set of submitted results was in full compliance with the requirements of the study.

° The simulations were reviewed by the coordinator comparatively as well as against the corresponding model experiments to conclude on the accuracy and efficiency of the methods. The findings and results of the study are reported in the present.

of 60

The adopted benchmark approach is shown schematically in Figure 2.

NUMERICAL SIMULATION

Method 1

Method 2

…

Method

Specified Benchmark

Tests

Tank Data

Simulation Data

Comparisons

TANK TESTS

Performance of Numerical Simulation

Verification of Test

Conditions

Figure 2 Benchmark approach for performance assessment

Overall Performance of Numerical Simulation

The benchmark aims at the assessment of the overall performance of the numerical simulations and not of the individual methods. This is also enabled by the anonymous treatment of the simulation predictions.

The overall performance of the benchmarked numerical simulations is herein defined as the averaged performance of the individual methods.

Suppose the set of benchmark conditions are represented by a vector cr , and yi is a

characteristic response of the i-th simulation method to the specified conditions. The response may be any characteristic outcome of the numerical simulation, like the correlation coefficient to the experimental data, or the standard deviation, etc.

( )cfy iir

=

Then the overall numerical simulation response y is the weighted average of the total N individual methods.

∑=

=N

iii yw

Ny

1

1

of 60

Where the weight function w represents the number k of simulated benchmark tests by each method, namely,

∑=

= N

jj

ii

kw

1

k .

For each individual method the correlation coefficient and standard deviation to the experimental data is calculated

Correlation coefficient ( )X

XXCovrσσΧ

=,

Where Cov is the covariance function and σ the standard deviation of the two sets

{ nixX i ,...,1, == } the numerical simulations

{ nixX i ,...,1, == } the experimental data for the n benchmark tests

Standard deviation ( )

( )1

ˆˆ1

2

−

−=∑=

n

xxn

imi

σ

Where iii xxx −=ˆ and the mean value mx̂

The success rate (discussed in Section 11) for the prediction of the roll amplification is evaluated as

Success rate ∑=

=n

iiq

nP

1

1

Where the function qi is defined as ( )( )( )( )⎩

⎨⎧

<≥

=0x-xx-xfor 00x-xx-xfor 1

,cri,cri

,cri,criiq and formulates the

successful prediction of the roll amplification xi in comparison to the experimental data ix and a reference roll amplitude x,cr (as defined in Section 11).

of 60

Benchmark Tests

The benchmark containership (of section 5) has been studied for a series of twenty two (22) conditions, defined by variation of

− Ship loading condition − Ship speed − Wave heading − Wave height − Wave periods

The parameters considered for the definitions of the tests were: Ship Loading condition GM = 1.00 and 1.38 m Ship forward speed Fn = 0.0, 0.04, 0.08 and 0.12 Wave heading Stern (0 deg), head-oblique (160 deg), Head (180 deg) Wave heights H = 0.0, 3.6, 5.0, 5.7 and 6.0 m Wave periods T = 8.0, 10.6, 12.1 sec Waves regular (1 harmonic), group (3 harmonics), irregular

(spectrum), (see Appendix III)

The full test matrix is presented in next Table 2 (and Table 9 of Appendix I).

In setting up the benchmark tests, due attention was devoted to include variations for most possible parameters involved in the problem and that affect the sensitivity of the simulation methods. The general strategy of this benchmark was to set-up a test program with least uncertainties with respect to the environmental and ship sailing conditions. Hence, the ship was assumed restrained (semi-captive) to move in 3 degrees of freedom (heave, roll and pitch), thus minimizing any uncertainties in speed and course keeping. Also, the majority of the tests were defined for deterministic waves, namely simple harmonic waves and tri-chromatic wave groups; also, two tests were considering irregular waves of a specific spectral representation.

Benchmark tests have been designed in such a way that the parametric resonance phenomenon could occur; however, in some tests the ship does not experience roll resonance while in others a clear resonance occurs. Thus, the prime focus of the study was the predictability of the roll resonance occurrence and furthermore, but of secondary importance, the magnitude of the roll motion under resonance.

of 60

Table 2 Benchmark Tests: Benchmark test matrix TEST GM

(m) HEADING

(deg) Fn H1 (Hs)

(m) T1 (Tp) (sec)

H2(m)

T2(sec)

H3(m)

T3(sec)

Description

T01 1.38 - 0.00 - - - - - - Roll decay (in calm water)

T02 » 180 0.08 3.6 10.63 - - - - Regular (1 harmonic)

T03 » » » 5.7 » - - - - »

T04 » » 0.12 3.6 » - - - - »

T05 » » » 5.7 » - - - - »

T06 » » » 2.4 » 2.4 9.66 2.4 11.55 Group (3 harmonics)

T07 » » » 4.0 » 1.0 » 1.0 » »

T08 » » » 5.0 » - - - - Irregular (JONSWAP spectrum, γ=3.3)

T09 » 160 » 3.6 » - - - - Regular (1 harmonic)

T10 » » » 5.7 » - - - - »




T14 » » » 6.0 » - - - - »

T15 » » 0.04 3.6 » - - - - »

T16 » » » 6.0 » - - - - »


T18 » » 0.08 » » » » » » »



T21 » » 0.12 5.0 » - - - - »

T22 » » 0.08 4.0 » 1.0 10.77 1.0 13.47 Group (3 harmonics)

of 60

4 The Study Data

The data of this study comprise the ship hull definition (see section 5), the ship loading conditions and a set of two measurements of a decay test in calm water, namely for roll and pitch. No other data were provided to the study participants.

Hence, genuine prediction conditions have been established as there was not any other information known to participants in advance regarding the behaviour of the investigated ship. Insofar, the collected set of predictions was assumed unbiased and an adequate sample for the evaluation of the prediction capabilities of the numerical simulation.

Experimental Data

A set of experimental data has been used as the basis for the evaluation of the numerical simulations. These data have been selected from two recent series of ship model experiments. The first set resulted from the collaborative research of NTUA and GL, and the experiments carried out at CEHIPAR (El Pardo, Spain) within HYDRALAB II EU project [3], and the second set from model tests carried out by NTUA at INSEAN (Rome, Italy) within SAFEDOR EU project [4].

The experimental measurements regard a containership, known before from relevant ITTC studies [1], [2], which, however, has been herein investigated in semi-captive conditions, namely restrained in surge, sway and yaw, but moving in heave, roll and pitch, while it was towed at constant speed and course against the waves.

This type of semi-captive tests can be considered ideal for the benchmarking of numerical simulation methods, as the uncertainties related to the speed and course keeping are suppressed.

of 60

5 The Subject Ship

The present benchmark study refers to the containership ITTC-A1, which has been tested before in free running tests in Japan, as reported in [1], [2]. The ship hull and particulars were provided to the study coordinator by Prof. Naoya Umeda (Osaka University).

The ship main dimensions and particulars are listed in Table 3 below. The hull geometry was available in IGES format and digital offsets.

Table 3 Studied Ship: Principal Particulars

Items Ship length : Lpp 150.0 m breadth : BB 27.2 m depth : D 13.5 m draught at FP : Tf 8.5 m mean draught : T 8.5 m draught at AP : Ta 8.5 m block coefficient : Cb 0.667 prismatic coefficient : Cp 0.678 water plane coefficient : Cw 0.787 wetted surface area : S 5065 m2

The two ship loading conditions investigated were:

Tests 01 ÷ 11 GM = 1.38 m

ixx = 10.33 m

iyy = 37.5 m

Tests 12 ÷ 22 GM = 1.00 m

ixx = 10.33 m

iyy = 38.2 m

of 60

6 Ship Hydrostatics

Before dealing with the containership motion in waves, the basic hydrostatics have been reviewed to ensure that the simulation methods have employed comparable ship models and their prediction corresponds to the ship specified by the study.

The hydrostatics as computed by the simulation methods are summarized in Figure 16 up to Figure 21 of Appendix II.

All simulation methods (Figure 16) considered practically identical displacement curves, with only a small deviation for method 14. Convergent results were also observed for the computed GM (Figure 17) with a scatter of computations limited to ± 5 cm (or ±2.5%).

Regarding the numerically computed GZ curves of Figure 3 (and Figure 18 to Figure 21 in Appendix II), it can be observed that all methods converge for heel angles up to 20-25 degrees, and at least for the condition of free trim which better corresponds to the simulation conditions. This is also reflected with the drawn scatter line which represents the maximum difference of GZ at each heel angle. Because the roll response is limited below 25 degrees for the most benchmark tests (as presented in the next sections) the observed differences for larger heel angles are affecting only a limited number of tests.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40

Heel (deg)

GZ

(m)

P01P02P03P05P06P08P11P12scatter

KG = 9.50 mfree trim

Figure 3 Hydrostatics: GZ curve for KG = 9.50 and free to trim condition

Since the deck submergence occurs for a heeling angle around 20 degrees, these differences are probable related to the applied geometrical models for the upper part (deck) of the hull. It is noted that the modelling and assumptions of the upper part of the

of 60

ship appears troublesome (forecastle and poop deck, hatch covers) and it cannot be confirmed that all participants have applied the same definitions to it.

The apparent convergent hydrostatic computations indicate that practically all simulation codes have defined comparable ship hulls.

7 The Numerical Simulation Methods

Table 4 provides a list of background references to the applied simulation methods in the present study. Relevant references have been selected by the study participants themselves.

Table 4 Simulation methods: Background references to the employed simulation method Institute Participants References

CHALM Schreuder M. [5]COPPE Neves M. and Rodriguez C. [6], [7]DINMA Francescutto A. and Bulian G. [8] Note (1) DTU Jensen J. and Vidic-Perunovic J. [9], [10], [13] Note (1) GL Pereira R. and Shigunov V. [11], [12], [13], [14], [15], [16], [17] Note (2) HUT Matusiak J. [18], [19], [20], [21], [22]IST Soares C. and Silva S. KTH Rosen A., Ovegard E., Palmquist M. [23]NMRI Ogawa Y. [24], [25]NTUA Papanikolaou A. and Spanos D. [26], [27], [28]OU Umeda N. and Lu J. [29]SOTON Temarel P. and Ahmed T. [30], [31]SSRC Vassalos D. and Kang J. [32], [33], [34] Notes (1) New method not yet published

(2) Two simulation methods applied

of 60

Table 5 summarizes the basic features of the simulation methods. All benchmarked simulation methods are non-linear time domain methods. The ship basic hydrodynamics are determined by potential theory approaches for all methods, whereas there are differences with respect to the inclusion of 3D effects (3D panel or strip theory methods).

Table 5 Outline of numerical simulation methods and practice

Feature

→ Method ↓

Program

d.o.f.

Motions (d.o.f.)

Basic Hydrodynamic Coefficients

Roll Inertia Roll Damping Roll Restoring

Waves Initial Roll angle (deg)

Initial Roll veloc. (deg/s)

01 6 3 Linear strip

decay Quadratic n-l all 1.0 0.0

02 3 Strip spec. Linear Linear all 0.1 0.0

03 6 3 Linear 3D decay Quadratic n-l all 1.0 0.0

04 3 3 Linear Strip spec. Cubic n-l all 0.0 0.1

05 6 3 Linear 3D spec. Linear n-l all 0.0 0.1

06 6 3 Non-linear Strip decay Linear n-l all 0.0 0.0

07 3 3 Linear 3D spec. Linear + quadratic

n-l all 2.0 0.0

08 1 1 (roll)

Linear Strip decay Cubic n-l Not oblique 1.0 0.0

09 6 5 (surge-roll)

Linear Strip decay Cubic n-l all 2.0 0.0

10 6 4 (3 + sway)

Non-linear Strip decay Cubic n-l all 2.0 0.0

11 6 6 Linear Strip decay Quadratic n-l only harmonic

2.0 0.0

12 (2.5) 1 (roll)

Linear 3D spec. n-l n-l only harmonic

0.5 0.0

13 6 5 (3+surge,y

aw)

Linear Strip spec. Linear n-l only harmonic

0.0 0.0

14 2 1 (roll)

Linear Strip 0.4B Linear n-l only head harmonic

0.6 0.0

Comments

6: full six d.o.f. 3: heave, roll, pitch 1: roll

3: heave, roll, pitch

Potential theory Spec.: As specified in study data Decay: Determined from roll decay test

n-l: Non-linear

n-l: Non-linear

at t = 0 at t = 0

While the benchmark tests were defined for ship motion in 3 degrees of freedom (roll, heave and pitch), several methods simulated partly a different number of d.o.f. (less or more, as noted in column 2 of Table 5), which is considered either sufficient by the participants or it is a practical constraint of the employed methods.

of 60

In half of the simulations the ship roll inertia properties have been tuned to the given roll decay data (in study data). These methods are noted as “decay” in the 5th column of Table 5 and are distinguished from the “spec” methods, which calculated the roll inertia properties from the ship loading conditions as specified by the study, and without taking a direct reference to the information from the decay tests.

With respect to the estimation of roll damping a variety of models have been employed, namely linear and non-linear (quadratic or cubic) models. The parameters of these models have been eventually determined on the basis of the roll decay data; one method (07) has been based only on semi-empirical model.

The last two columns of Table 5 present the initial conditions applied at the beginning of each simulation run (t=0). A perturbation in roll angle or velocity has been applied to excite, or shorten the time of development, of the roll resonance.

of 60

8 Decay Tests

Two roll decay tests (Test01 and Test12) in calm water were simulated; they were used for the verification of the ship loading conditions as assumed in the numerical simulation as well as the damping models applied.

Both Figure 4 and Figure 5 present the simulated roll decay for Test 01. Two groups of simulations can be identified, namely those of Figure 4 where the experimental data have been used to determine the ship hydrodynamic inertia properties; and those of Figure 5, which seem to have not tuned the hydrodynamic inertia assumptions of the simulation with the given decay information.

TEST 01

-15

-10

-5

0

5

10

15

0 50 100 150 200 250 300

Time (sec)

Rol

l (de

g)

P00P01P03P04P06P08P09P10P11

Figure 4 Decay Tests: Simulation methods for which the ship properties were determined on

the basis of the experimental data (GM = 1.38 m; P00: experimental data)

TEST 01

-15

-10

-5

0

5

10

15

0 50 100 150 200 250 300

Time (sec)

Rol

l (de

g)

P00P02P05P07P12P13

Figure 5 Decay Tests: Simulation methods which were not tuned with the decay experimental

data (GM = 1.38 m; P00: experimental data)

of 60

The decay Test 12 (GM = 1.00m) differs from the Test 01 by the GM (Test 01: GM = 1.38m). The effect of GM on the linear roll period, resulting from comparisons between these two decay tests, is shown in Figure 6. For all the methods an increase of period of about 3.5 sec can be observed (as expected), which is similar to that of the model experiments (shown as method 0), with the only exception that of method 02, for which a remarkable higher increase of 5.7 sec has been recorded.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Method

Rol

l Dec

ay P

erio

d (s

ec)

GM = 1.38 mGM = 1.00 mdifference

Figure 6 Decay Tests: Simulated effect of GM on linear roll period (0: experimental)

Table 6 summarizes the effect of GM on the roll damping in a qualitatively scale. While the increase of the roll period by the decrease of GM could be demonstrated by all methods, the calculated effect on the roll damping was divergent. For example, method 13 demonstrates a moderate reduction of roll damping, when the GM increased, to the contrary, methods 02 and 08 demonstrate a high increase of damping.

Table 6 Decay Tests: GM effect on roll damping Method Simulation

tuned to Exp. Data

Effect of GM on Roll Damping

01 + Moderate 02 + High 03 + Moderate 04 + Weak 05 0 - 06 - Weak 07 - Weak 08 + High 09 0 - 10 - Weak 11 0 - 12 + Moderate 13 - Moderate

Illustrations 1) + Increase of decay coef.

- Decrease 0 Unchanged

2) Weak < 10 % of decay coef. Moderate < 25 % High > 25 %

of 60

9 Numerical Simulation Results

A total of 261 numerical simulations in compliance with the benchmark were submitted to this study, namely 239 simulations for the ship moving in waves and 22 simulations for the ship rolling in calm water (decay tests). After their verification with respect to the study requirements they formed the sample which was considered for the following statistical analysis and performance assessment. The full set of simulations per method is summarized in Table 7. A list of undertaken revisions in the course of the study by the participants is presented in Table 10 of Appendix VI.

Table 7 Simulated Tests: Analytical (row: methods, columns: tests, (x): simulated, (-): not simulated)

T 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 TTLP01 x x x x x x x x x x x x x x x x x x x x x x 22P02 x x x x x x x x x x x x x x x x x x x x x x 22P03 x x x x x x x x x x x x x x x x x x x x x x 22P04 x x x x x x x x x x x x x x x x x x x x x x 22P05 x x x x x x x x x x x x x x x x x x x x x x 22P06 x x x x x x x x x x x x x x x x x x x x x x 22P07 x x x x x x x x x x x x x x x x x x x x x x 22P08 x x x x x x x x - - - x x x x x x x x x x x 19P09 x x x x x - x - x x x x x - x x x - x x x x 18P10 x x x x x - x - x x x x x - x x x - x x x x 18P11 x x x x x - - - x x - x x x x x - - - x x - 14P12 x x x x x - - - x x - x x x x x - - - x x - 14P13 x x x x x - - - x x - x x x x x - - - x x - 14P14 - x x x x x x x - - - - - - - - - - - x x x 10TTL 13 14 14 14 14 9 11 9 12 12 9 13 13 11 13 13 10 8 10 14 14 11 261

The full list of the benchmark tests has been conducted by seven (7) methods (namely methods 01 to 07). The other methods have simulated only part of the tests, as illustrated in Table 8. Table 8 Simulated Tests: Limitation of simulation methods

Method Simulated Tests Limitations P01 All - P02 All - P03 All - P04 All - P05 All - P06 All - P07 All - P08 Longitudinal waves Oblique waves (β = 160o) P09 Most tests - P10 Most tests - P11 Regular waves Non-regular waves P12 Regular waves Non-regular waves P13 Regular waves Non-regular waves P14 Regular head waves (β = 180o) Non-regular waves and

Stern waves (β = 180o)

of 60

In particular, method 08 was not applied to the non-longitudinal (oblique) waves tests (heading 160 deg).

Methods 09 and 10 have not submitted results for some tests for which the prediction results were sensitive to the small variations of parameters.

Methods 11, 12, 13 and 14 are limited to harmonic waves only, so they could not simulate group or irregular wave scenarios. Additionally method 14 could not deal with stern waves.

Regardless the limited submitted results of some benchmark methods for specific tests, the sum total of 239 submitted numerical simulations for the roll motion of the study ship in waves is considered an adequate sample for a reliable statistical analysis and assessment of the overall performance of the benchmarked methods.

of 60

Typical Roll Motions

Typical roll responses as simulated by the methods are summarized in Figure 26 to Figure 34 of Appendix IV.

The below Figure 7 (identical to Figure 28 in Appendix IV) is the most typical simulated roll response, where after some transient period the steady response is fully developed and the ship rolls with some constant roll amplitude.

-20

-15

-10

-5

0

5

10

15

20

0 100 200 300 400 500 600 700 800 900

Time (sec)

Roll (de

g)

Stationary response

Figure 7 Typical Simulated Roll: Resonance in regular wave and stationary rolling

The mean roll amplitude of the stationary response is used subsequently for the quantification of the performance of the benchmarked methods in terms of the predictability of the roll motion magnitude, which is the mean value of successive amplitudes, as illustrated in Figure 8.

Mean Roll Amplitude ∑=

=N

iiM A

NA

1

1

-20

-15

-10

-5

0

5

10

15

20

800 850 900 950 1000

Time (sec)

Roll (de

g)

Ai

Ai+1

Ai+2

Figure 8 Roll motion: Successive roll amplitudes

of 60

10 Roll Amplitude Predictions

The mean roll amplitude (and its standard deviation) in the fully developed motion of the ship in waves (as defined above) has been herein used as a first roll performance indicator of the study phenomenon.

In stationary conditions, like that shown in Figure 7, the mean roll amplitude has been calculated. In cases in which a stationary roll could not be clearly distinguished then the full simulation record was taken into account.

Figure 9 summarizes the full set of simulation results for all the methods and tests collectively. Each method is shown with a different symbol, while corresponding tank measurements are labelled as 00.

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22

TEST

Mea

n R

oll A

mpl

. (de

g)

010203040506070809101112131400

Figure 9 Simulations: Estimated Mean roll amplitude (01-14: Methods, 00: Experimental)

The results on the x-axis (zero roll amplitude) correspond to the stable simulation runs, namely no roll amplification. Where more than one symbol is present, they are drawn overlapped in the diagram.

Any result exceeding the range of 35 degrees has been truncated to 35 deg and it is shown on the top of the diagram. Most of them resulted to capsize of the ship and only few of them resulted to larger roll amplitude, without capsize (like Figure 32 Appendix IV).

of 60

Tests 01 and 12 are the two decay tests and no roll amplitude is shown for them.

Figure 9, which enables an overview of the outcome of the present benchmark; the scatter between the alternative simulation methods is evident and for most benchmark tests a considerable spread can be observed, ranging from zero roll amplitude and up to capsize, which are contradictive predictions.

Regardless the particular performance of each individual method, this diagram is representative of the overall level for the predictability of the roll amplitude in conditions close to parametric resonance. Considering the scatter of predictions, which is large for all tested cases, it may be concluded that the inherent demands of some particular benchmark tests, which may be considered difficult to simulate, are a secondary issue for the overall assessment.

The comparative results of the roll amplitude for all the tests in waves are presented in details in Figure 35 up to Figure 54 of Appendix V. As an example, Test 07 is here presented in Figure 10. There, the simulated mean roll amplitude is shown with the vertical bars, and its variation, as detected in the considered stationary conditions, is shown with the vertical error bars of width equal to the standard deviation. The corresponding experimental data are shown as method 00. When there are no simulation data available from a method, then this method does not appears on the x-axis, like methods 11 to 13 are missed here. This is to distinguish from the methods that have predicted zero roll amplitude, like the method 01, for this test.

TEST 07

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 14

Method

Mea

n R

oll A

mpl

. (de

g)

Figure 10 Test 07 (group head waves, 00: experimental data)

of 60

Performance of Methods

Since the capabilities of the numerical methods at an aggregate level appear low (Figure 9), the individual performance of each method, or groups of methods, is necessary to be reviewed separately in order to better explain the above obtained picture.

The experimental data are used as the reference basis; two statistical quantities, namely those of the standard deviation σ of the mean roll amplitude and the correlation coefficient r are explored for each method. The standard deviation is a quantitative measure for the prediction performance and the correlation coefficient a more qualitative one. Both combined can provide a clear picture for the performance of each method as well as for the overall performance.

The overall (regardless of method) measured performance for all the tests, which correspond to Figure 9, was

Overall

Deviation of the mean roll amplitude: σ = 10.5 deg

Correlation coefficient: r = 0.37

The important Figure 11 below presents the corresponding quantities for each method together with the obtained overall values. The circle symbols correspond to the methods and the yellow triangle to the overall-aggregate performance. The full circles present the methods that have simulated the full set of benchmark tests (methods 01 to 07) and the open circles those that have simulated only part of the tests set (methods 08 – 14). The diagram is complemented with two more limits, namely the green square on the top left corner, which represents the ideal simulation performance (zero deviation and absolute correlation), and the orange circle at the bottom, which represents the zero level1 of this study (pure lack of predictability).

In this diagram, the three discrete points (ideal performance, overall-aggregate and zero level performance) are connected with a dashed line to facilitate the presentation. This path represents the progress, when starting for the pure lack of predictability towards the ultimate limit of entirely successful simulation of the parametric rolling by the numerical simulation.

The diagram shows that half of the simulation methods performed rather well and are well above the average, while the rest half is below the average point. A group of four (4) methods in the region of (r=0.7, σ=5.0) can be easily distinguished as the herein best performing methods. Also, one method of high correlation, but of large deviation (10 deg), can be observed at the top part of the diagram. 1 Zero level is assumed when the probability of roll resonance occurrence equals 0.5 and the non-zero roll amplitude is evenly distributed between 0 and 35 degrees.

of 60

10.5, 0.37

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20

Stand. Deviation of Mean Roll Amplitude (deg)

Cor

rela

tion

coef

f. of

Mea

n R

oll A

mpl

.

Methods (full)

Methods (partial)

Overall

Ideal

Zero

connecting line

Meth d o

σ 01 02 03 04 05 06 07 08 09 10 11 12 13 14

12.6 15.7 9.4 6.4 5.7 8.9 10.7 10.4 6.5 6.5 9.3 9.0 10.1 9.5 r 0.31 0.28 0.50 0.68 0.75 0.25 0.33 0.39 0.58 0.56 0.51 0.16 0.11 0.77

Figure 11 Performance: Correlation coefficient r and standard deviation σ of the simulated mean roll amplitude, compared to the experimental measurements

While the aggregate level has been recorded as low, when focusing on the group of the best performing methods then the performance rises significantly to

Best Performing

Deviation in mean roll amplitude: σ = 6.4 deg

Correlation coefficient: r = 0.64

These values are almost twice as good as for the overall level, and can be suggested as representative for the current state of art.

So, the benchmarked simulation codes can be grouped in two categories, those of higher performance and the less mature ones, and, care for this basic distinction should be given, when referring to the performance, namely when referring to the performance of the best performing methods, or the overall performance of the various methods in the field.

of 60

Figure 12 presents the simulations of the four best performing methods together with the experimental data (full diamond symbols). Apparently the simulations are now quite convergent to the experimental data. They are systematically close to the experimental data; however there are tests, like 11 and 14, where also these methods fail (as further discussed in section 11).

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22

TEST

Mea

n R

oll A

mpl

. (de

g)

Figure 12 Simulations: Mean roll amplitude as estimated from the best performing (four)

methods

of 60

11 Roll Resonance Prediction

In the previous section the numerical predictions have been reviewed with respect to the ship roll amplitude in the stationary roll motion stage. In the present section we focus on the prediction of the resonance occurrence under the tested conditions and regardless of the predicted magnitude of roll amplitude. Namely, the severity of the rolling is herein omitted and the concern is the efficiency of the methods to detect the roll resonance in waves, which is of practical importance.

Figure 13 summarizes the successful detections per method as well as the overall performance. A success event is recognized when experimental data and simulation results coincide with respect to the occurrence or not of the roll resonance. For the occurrence of roll resonance, a critical roll amplitude has been introduced, namely when the mean roll amplitude is bounded by that critical value it is assumed that no resonance occurs while when it is over that value then resonance is assumed to have encountered (as formulated in section 3). For example, when assuming a critical roll equal to 1 deg, then any simulation test that resulted to a mean roll amplitude of less than 1 deg is interpreted as a test with no roll resonance, whereas if higher than 1 deg then it is a test where roll resonance occurred.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.5 1 1.5 2 2.5

Roll,cr (deg)

Suce

ss R

ate

in p

redi

ctio

n of

roll

ampl

ifica

tion

Overall1234567891011121314

Mean overall = 0.62

Figure 13 Performance: Percentage of successful detection of roll resonance

Critical values of up to 2 degrees have been explored. The overall mean performance in Figure 13 and partially the individual methods, show a weak dependence on the

of 60

definition of the critical roll, which enables to conclude without considering the effect of that parameter.

The overall mean percentage of success detections, is shown with black line-symbols as function of the assumed critical roll amplitude and is

P = 0.62 (overall)

Similar to the analysis of results in the previous section (Figure 11), two groups of methods with different performance can be here also clearly recognized (Figure 13). Eight (8) methods are better than the overall average and the other six (6) below. So, it is verified that the prediction of the roll resonance phenomenon is better captured by the simulation methods, whereas, as could be expected, the prediction of the magnitude of roll amplitude is of higher difficulty. It is noted that compared to the shown performance of Figure 11, the group of the four (4) best performing methods there, is part of the herein best performing group too.

Limiting the analysis to the best performing methods in Figure 13, it can be concluded that the percentage of success prediction ranges between 65-90%. The mean value of this range is the characteristic success percentage of a best performing simulation method, hence

P = 0.78 (best performing)

Interpreting the above result it can be said on the basis of the present benchmark (which covered a variety of possible operational scenarios) that a state of the art simulation method is able to predict the parametric roll phenomenon in practically 8 out of 10 cases, which may be considered satisfactory for the risk-based assessment of ship’s operation.

Sensitivity of Results

The sensitivity of the above measured predictability of the numerical methods has been further investigated with respect to the basic properties of the obtained sample of predictions, namely whether the accuracy of the obtained results was in some dependence on specific test conditions or basic features of the employed simulation models.

Specifically, it was found that the predictability indicators seem independent of the experimental data set, namely tests 2-11 (GM = 1.38 m) and 13-22 (GM = 1.00 m), which have been conducted by two different model basins for the same ship.

Furthermore, with respect to the tested wave scenarios, both regular and non-regular (group and irregular) wave scenarios, the prediction capabilities do not significantly change (regular waves P=0.61, non-regular P=0.65).

of 60

A remarkable dependence was found to be related to the hydrodynamic methods employed, namely the use of a quasi 2D strip or a 3D panel method for the evaluation of the ship’s basic hydrodynamics. The four methods that have applied 3D hydrodynamic codes, have shown an average predictability of P=0.74, whereas the strip methods an average of P=0.57. It is noted that three of the benchmarked 3D methods are also part of the best performing methods (in Figure 13), with exception that of method 12.

Another remarkable dependence of the results was that of tuning the hydrodynamic roll inertia with the experimental decay data in the simulation procedures. It is evident that the prediction capability of the methods, which have determined the ship inertia properties on the basis of provided decay tests, was P=0.65, which is by 20% higher than the P=0.54 of the methods that have not fully exploited the information from the decay data.

The correlation of the predictability on the roll damping models is also noted. The performance average of the methods that have applied linear roll damping is P=0.50, which is improved to P=0.65 for the methods that have applied a non-linear roll damping. This statistical result is here noted, although it could be also attributed to other side effects, as the non-linearity of the roll damping is expected to mainly affect the roll amplitude and to a lesser degree the resonance occurrence itself.

of 60

Impact of Benchmark Tests

The assessed performance of numerical simulation methods is more analyzed aiming at identifying the possible impact of the severity of each benchmark test on the final results, thus getting some further insight for the possible causes of the recorded performance in some specific tests.

The success rate of all methods together for each of the benchmark tests is presented in Figure 14. According to this diagram, the simulation methods seem to achieve the highest performance of P=0.90 in the quite different kind of tests 07, 16 and 17, which correspond to group-head waves (test 07), regular-stern waves (test 16) and group-stern waves (test 17). The lowest performance is identified for the tests 03, 11 and 14, which correspond to regular-head wave (test 03), group-bow waves (test 11) and regular-stern waves (test 14).

Obviously the basic test parameters were not enough to explain some general performance advantage or weakness of the simulation methods. For example Tests 14 and 16 are of similar wave conditions, however with extreme opposite performance.

Aggregate Success Rate for Prediction of Roll Amplification

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22

Test

Succ

ess

Rat

e

Decay Tests 1, 12

Figure 14 Performance Analysis: Success rate for each benchmark tests

Some interesting information could be detected when examined the particular conditions of Test 03, which is similar to Test 02 with the only difference the larger wave height, and where a significant decrease of predictability occurs. According to the tank data the roll amplitude considerably decreases for the larger wave height whereas most simulation methods could not reproduce a similar trend (ref. [36] for detailed discussion of this nonlinear behaviour).

of 60

Test 14 differs from Test 13 in wave amplitude too. This case is similar to the previous cases (Test 03), however for stern waves. The tank data show here independence on the wave amplitude. However, most of numerical simulations predict a strong dependence on the wave height.

On the basis of these results, the lower performance of the numerical simulations methods (Test 03 and 14) seems to be related to the non-linear large amplitude wave effects, whereas the worst performance shown for Test 11 remains a matter of demanding test conditions, resulting from the oblique heading (160 deg) of the exciting non-regular (tri-chromatic group) wave.

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0 2 4 6 8 10 12 14 16 18 20 22 24

Omitting Test No

Succ

ess

Rat

e

OVERALLmean=0.62dev.=0.01

BESTmean=0.78dev.=0.02

Figure 15 Performance Analysis: Impact of benchmark tests on success rate

Finally, the impact of each benchmark test on the predictions can be observed in Figure 15. There the success rate has been evaluated on the basis of 19 benchmark tests (instead of 20), each time omitting one test (note that Tests 01 and 12 are decay tests). Both the overall and the best rate are herein plotted, and a standard deviation 1% and 2% respectively results.

of 60

12 Conclusions

The conducted SAFEDOR benchmark study on the performance of computer simulation software tools for the prediction of parametric rolling of ships in waves has been successfully completed. The very good international participation from both inside and outside SAFEDOR (thirteen participants) enabled the assessment of representative results and reliable conclusions about the current state of the art in the study field.

The comprehensive sample of analyzed numerical simulations and the large variety of reviewed methods led to convergent findings that can be considered with confidence. The study assessed the current overall efficiency as well as the individual performance of the codes which is of interest to code developers.

The overall efficiency of the benchmarked codes appears low, which is the consequence of the wide spread of individual codes’ performance, ranging from very low performance and up to those of high.

Nevertheless a group of leading simulation methods could be detected, which enables to assess with confidence the current capabilities in the field. In terms of a quantitative assessment of the present best methods, the mean probability to successfully detect the parametric roll resonance was estimated to be 0.78, while the predictions for the magnitude of roll amplitude seem to deviate on average 6.4 deg. The corresponding figures for the overall benchmarked methods are 0.62 and 10.5 deg respectively, as summarized in the table below.

P

Predictability of roll resonance σ (deg)

Deviation in mean roll amplitude Best Perform 0.78 6.4

Overall 0.62 10.5

of 60

13 Website

The SAFEDOR benchmark activities and results are sited on the webpage:

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

This page has been developed under the NTUA-SDL website; it is maintained by the study coordinator and is used for up and downloading of documents and as a tool for communication with all study participants and other interested scientists.

of 60

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

14 References [1]. ITTC, The Specialist Committee on Stability in Waves, Final Report and

Recommendations to the 24th ITTC, Proceedings of the 24th ITTC, Vol. II, pp.369-407, 2005

[2]. Umeda, N., A. Munif and H. Hashimoto, Numerical Prediction of Extreme Motions and Capsizing for Intact Ships in Following/ Quartering Seas, Proceedings of the 4th Osaka Colloquium on Seakeeping Performance of Ships, Osaka, Oct., 2000, pp.368-373.

[3]. HYDRALAB III, Ship Model Tests in Parametric Roll in Natural Seas, 2007. FP6 EC Integrated Infrastructure Initiative HYDRALAB III, Access to major experimental ship hydrodynamics and ice engineering facilities, NTUA-GL-CEHIPAR project.

[4]. SAFEDOR, Ship model Tests on Parametric Rolling in Waves, 2008. Research project SAFEDOR (Design, Operation and Regulation for Safety), SP.7.3.9, of the FP6 Sustainable Surface Transport Programme.

[5]. Schreuder, 2005, “Time Simulation of the Behaviour of Damaged Ships in Waves” Department of Shipping and Marine Technology, Chalmers, Göteborg, Sweden

[6]. Neves, M.A.S. and Rodríguez, C., “On unstable ship motions resulting from strong non-linear coupling”. Ocean Engineering, Vol. 33, pp. 1853-1883, 2006.

[7]. Rodríguez, C.A.,Holden, C., Perez, T., Drummen, I., Neves, M.A.S., Fossen, T.I., “Validation of a container ship model for parametric rolling”. 10th International Ship Stability Workshop, Hamburg, Germany, 2007.

[8]. Bulian, G., Francescutto, A., "SAFEDOR benchmark on parametric roll - Brief description of the simulation methodology employed in the code SHIXDOF under development at DINMA", Internal Technical Report, Department DINMA, University of Trieste, Trieste, Italy, 2008.

[9]. Vidic-Perunovic, J. and Jensen, J.J. Ship Roll Response due to the Hull Instantaneous Volumetric Changes in Head Sea. Recently submitted to Ocean Engineering.

[10]. Jensen, J.J. “Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)”, J. Marine Science and Technology, 2007, Vol. 12 (4), pp 191-202.

[11]. Söding, H. (1982) Leckstabilität im Seegang. Report No. 429, Institut für Schiffbau, Hamburg

[12]. Petey, F. (1986) Forces and moments due to fluid motions in tanks and damaged compartments, Proceedings, 3rd Int. Conf. on Stability of Ships and Ocean Vehicles STAB’86, Gdansk

[13]. Petey, F. Ermiitlung der Kentersicherheit lecker Schiffe im Seegang aus Bewegungssimulationen, Report Nr. 487, Institut für Schiffbau, University of Hamburg, November 1988

of 60

[14]. Böttcher, H. (1986) Ship motion simulation in a seaway using detailed hydrodynamic force coefficients, Proceedings, 3rd Int. Conf. on Stability of Ships and Ocean Vehicles STAB’86, Gdansk

[15]. Pereira, R. (1988) Simulation nichtlinearer Seegangslasten, Schiffstechnik 35(4) 173-193

[16]. Brunswig, J; Pereira, R. and Kim, D. Validation of Parametric Roll Motion Prediction for a Modern Containership Design, Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles, STAB 2006, Rio de Janeiro

[17]. Pereira, R. Numerical Simulation of Capsizing in Severe Seas, Proceedings of the 8th International Conference on Stability of Ships and Ocean Vehicles, STAB 2003, Madrid

[18]. Matusiak, J. Two-stage approach to determination of non-linear motions of ship in waves. 4th Osaka Collouqium on Seakeeping Performance of Ships, Osaka, Japan, 17-21st October, 2000

[19]. Matusiak, J. Parametric roll resonance of the conical buoy in regular waves, presented at the 7th International Conference on Stability of Ships and Ocean Vehicles, Launceston, Tasmania, 31 January - 4 February 2000

[20]. Matusiak, Jerzy; On the effects of wave amplitude, damping and initial conditions on the parametric roll resonance. Proceedings of the 8th International Conference on Stability of Ships and Ocean Vehicles, Madrid, Spain, September 2003, pp. 341-348.

[21]. Matusiak, Jerzy; On certain types of ship response disclosed by the two-stage approach to ship dynamics. ACME, Archives of Civil and Mechanical Engineering, 2007. Vol. VII, nro 4, 151-166

[22]. Matusiak, Jerzy Importance of memory effect for capsizing prediction. 5th International workshop University of Trieste 12. - 13. September 2001. Universitá di Trieste 2001, 6.3.1 (6 pages).

[23]. Hua J., Palmquist M., A Description of SMS – A Computer Code for Ship Motion Simulation, KTH Naval, Architecture, TRITA‐FKT, Report 9502, ISSN 1103‐470X, Stockholm, Sweden, 1995.

[24]. Ogawa, Y. et. al. (2005): “The effect of a bow flare shape on the water impact pressure”, International Journal of Offshore and Polar Engineering (IJOPE), Vol.16, No.2, 2005.

[25]. Ogawa, Y. (2007): “An examination for the numerical simulation of parametric roll in head and bow seas”, Proceedings of the 9th International Ship Stability Workshop, Hamburg, pp. 4.2.1-4.2.8.

[26]. Spanos, D. and Papanikolaou A. (2006), Numerical Simulation of Parametric Roll in Head Seas, Proc. of the 9th Inter. Conf. on Stability of Ships and Ocean Vehicles, Rio de Janeiro, Brazil, 2006.

[27]. Spanos, D., (2002). Time Domain Simulation of Motion and Flooding of Damaged Ships in Waves, Doctoral Thesis, Ship Design Laboratory, National Technical University of Athens

[28]. Papanikolaou, A., (1989). NEWDRIFT V.6: The six DOF three-dimensional diffraction theory program of NTUA-SDL for the calculation of motions and loads of arbitrarily shaped

of 60

3D bodies in regular waves, Internal Report, National Technical University of Athens, NTUA-SDL

[29]. Hashimoto, H., N. Umeda and G. Sakamoto: Head-Sea Parametric Rolling of a Car Carrier, Proceedings of the 9th International Ship Stability Workshop, Hamburg, Aug. 2007, pp. 3.5.1-3.5.7.

[30]. Ahmed, T.M., Ballard, E.J., Hudson, D.A. and Temarel, P., 2006, Prediction of Parametric Roll Resonance in Longitudinal Regular Waves Using a Non-linear Method, Proceedings of the 9th International Conference on Stability of Ships and Ocean Vehicles STAB’06, Rio de Janeiro, Brazil, 1, pp. 89-97.

[31]. Ahmed, T.M., Ballard, E.J., Hudson, D.A. and Temarel, P., 2008, A Non-linear Numerical Method for the Simulation of Parametric Roll Resonance in Regular Waves, Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008, Estoril, Portugal.

[32]. Chan, H.S., A Three-Dimensional Technique for Predicting First- and Second-Order Hydrodynamic Forces on a Marine Vehicle Advancing in Waves, Ph.D. Thesis, University of Glasgow. 1990.

[33]. Ballard, E.J., Hudson, D.A., Price, W.G. and Temarel, P., Time Domain Simulation of Symmetric Ship Motions in Waves, Transactions of RINA, Vol. 145, pp. 161-180. 2003.

[34]. Kang, J., Time Domain Mathematical Model for Manoeuvring Simulation in a Wave, PhD Thesis, Universities of Glasgow and Strathclyde, to be published in 2009.

[35]. Hua J., Palmquist M., A Description of SMS – A Computer Code for Ship Motion Simulation, KTH Naval, Architecture, TRITA‐FKT, Report 9502, ISSN 1103‐470X, Stockholm, Sweden, 1995.

[36]. Spanos, D., Papanikolaou, A., On the Decay and Disappearance of Parametric Roll of Ships in Steep Head Waves, Proc. 10th Int. Conference on Stability of Ships and Ocean Vehicles, St Petersburg, Russia, June 2009.

[37]. ITTC, The Specialist Committee on Stability in Waves, Final Report and Recommendations to the 25th ITTC, Proceedings of the 25th ITTC, 2008.

of 60

Appendix I Benchmark Tests

Table 9 Benchmark Tests: Benchmark test matrix TEST GM

(m) HEADING

(deg) Fn H1 (Hs)

(m) T1 (Tp) (sec)

H2(m)

T2(sec)

H3(m)

T3(sec)

Description



T03 » » » 5.7 » - - - - »

T04 » » 0.12 3.6 » - - - - »

T05 » » » 5.7 » - - - - »


T07 » » » 4.0 » 1.0 » 1.0 » »


T09 » 160 » 3.6 » - - - - Regular (1 harmonic)

T10 » » » 5.7 » - - - - »




T14 » » » 6.0 » - - - - »

T15 » » 0.04 3.6 » - - - - »

T16 » » » 6.0 » - - - - »


T18 » » 0.08 » » » » » » »



T21 » » 0.12 5.0 » - - - - »

T22 » » 0.08 4.0 » 1.0 10.77 1.0 13.47 Group (3 harmonics)

Where:

Heading 180 deg head waves 0 deg following (stern) waves Fn Froude number H1 Wave height (2 x wave amplitude) of the 1st wave harmonic H2 Wave height of the 2nd wave harmonic (for group waves only) H3 » 3rd » » T1 Wave period of the 1st wave harmonic T2 » 2nd wave harmonic (for group waves only) T3 » 3rd » » Hs Significant wave height Tp Spectral peak period

of 60

Appendix II Hydrostatics

10000

12000

14000

16000

18000

20000

22000

24000

26000

28000

30000

4 5 6 7 8 9 10 11

Draught (m)

Dis

pl. V

olum

e (m

3)

P01P02P03P04P05P06P07P08P11P12P13P14

3.5%

Figure 16 Hydrostatics: Displacement volume

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

9.0 9.5 10.0 10.5 11.0

KG (m)

GM

(m)

P01P02P03P04P05P08P11P12

10 cm

Figure 17 Hydrostatics: GM for the two loading conditions

of 60

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40

Heel (deg)

GZ

(m)

P01P02P03P05P06P08P11P12scatter


Figure 18 Hydrostatics: GZ curve for KG = 9.50 and free to trim condition

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40

Heel (deg)

GZ

(m)

P01P02P03P05P06P11P12P13P14scatter

KG = 9.50 mfixed trim = 0

Figure 19 Hydrostatics: GZ curve for KG = 9.50 and fixed trim condition

of 60

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30 35 40

Heel (deg)

GZ

(m)

P01P02P03P04P05P06P07P08P11P12scatter


Figure 20 Hydrostatics: GZ curve for KG = 10.50 m and free to trim condition

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30 35 40

Heel (deg)

GZ

(m)

P01P02P03P04P05P06P07P11P12P13P14scatter

KG = 10.50 mfixed trim = 0

Figure 21 Hydrostatics: GZ curve for KG = 10.50 m and fixed trim condition

of 60

Appendix III Study Waves

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200 250 300

Time (sec)

Enc. W

ave (m

)

Figure 22 Typical Tested Waves: Regular wave

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200 250 300

Time (sec)

Enc. W

ave (m

)

Figure 23 Typical Tested Waves: Group wave (low modulation)

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200 250 300

Time (sec)

Enc. W

ave (m

)

Figure 24 Typical Tested Waves: Group wave (high modulation)

of 60

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200 250 300

Time (sec)

Enc. W

ave (m

)

Figure 25 Typical Tested Waves: Irregular wave (narrow band)

of 60

Appendix IV Typical Simulated Roll Motion

Frequent were roll responses like that of Figure 26 and Figure 27, where the ship remains stable throughout the simulation record. In Figure 26 there is some small perturbation at the start of the simulation which gradually vanishes, whereas in Figure 27 there is not any kind of initial perturbation.

In Figure 29 to Figure 31 a gradual increase of the irregular character of rolling due to group or irregular wave excitation is evident.

For some limited tests, very large roll amplitudes were detected, at fully developed responses, like that of Figure 32.

Finally, typical capsize simulations are shown in Figure 33 and Figure 34 for head and stern waves respectively.

of 60

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 100 200 300 400 500 600

Time (sec)

Roll (de

g)

Figure 26 Typical Simulated Roll: No resonance with initial perturbation

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 100 200 300 400 500 600

Time (sec)

Roll (de

g)

Figure 27 Typical Simulated Roll: No resonance without initial perturbation

-20

-15

-10

-5

0

5

10

15

20

0 100 200 300 400 500 600 700 800 900

Time (sec)

Roll (de

g)

Figure 28 Typical Simulated Roll: Resonance in regular wave and stationary rolling

of 60

-30

-20

-10

0

10

20

30

0 200 400 600 800 1000

Time (sec)

Roll (de

g)

Figure 29 Typical Simulated Roll: Resonance in group waves and stationary rolling

-30

-20

-10

0

10

20

30

0 200 400 600 800 1000

Time (sec)

Roll (de

g)

Figure 30 Typical Simulated Roll: Resonance in group waves and stationary rolling

-40

-30

-20

-10

0

10

20

30

40

0 500 1000 1500 2000

Time (sec)

Roll (de

g)

Figure 31 Typical Simulated Roll: Resonance in irregular waves

of 60

-60

-40

-20

0

20

40

60

0 200 400 600 800 1000 1200 1400 1600 1800

Time (sec)

Roll (de

g)

Figure 32 Typical Simulated Roll: Resonance in regular wave and large amplitude stationary rolling

-60

-40

-20

0

20

40

60

0 100 200 300 400 500 600

Time (sec)

Roll (de

g)

Figure 33 Typical Simulated Roll: Resonance in regular head wave and capsize

-60

-40

-20

0

20

40

60

0 100 200 300 400 500 600

Time (sec)

Roll (de

g)

Figure 34 Typical Simulated Roll: Resonance in regular following wave and capsize

of 60

Appendix V Full Set of Numerical Simulations

− The reference numbers for the methods do NOT correspond to the participants − The diagrams present the mean roll amplitude plus a range equal to (+/-) rms of the roll

amplitude

of 60

TEST 02

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)

Figure 35 Test 02 (Regular wave, β = 180 deg, H = 3.6 m, Fn = 0.08, GM = 1.38 m)

TEST 03

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 04

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 05

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 06

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 14

Method

Mea

n R

oll A

mpl

. (de

g)

Figure 39 Test 06 (Group wave, β = 180 deg, Hs = 3.8 m, Fn = 0.12, GM = 1.38 m)

TEST 07

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 14

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 08

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 14

Method

Mea

n R

oll A

mpl

. (de

g)

Figure 41 Test 08 (Irregular wave, β = 180 deg, Hs = 5.0 m, Fn = 0.12, GM = 1.38 m)

TEST 09

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 09 10 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 10

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 09 10 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 11

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 09 10

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 13

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 14

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 15

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 16

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 17

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 18

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 19

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10

Method

Mea

n R

oll A

mpl

. (de

g)

Figure 51 Test 19 (Irregular wave, β = 0 deg, Hs = 5.0 m, Fn = 0.08, GM = 1.00 m)

TEST 20

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

TEST 21

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14

Method

Mea

n R

oll A

mpl

. (de

g)


TEST 22

0

5

10

15

20

25

30

35

00 01 02 03 04 05 06 07 08 09 10 14

Method

Mea

n R

oll A

mpl

. (de

g)


of 60

Appendix VI Revisions of Numerical Simulations Table 10 List of Revisions Participant Original

Submission Revision 1 Revision 2

Date Date Tests Date Tests

CHALM Dec.23 - - - -

COPPE Jan.5 Jan.23 2 Feb.2 all

DINMA Dec.18 Jan.14 2 - -

DTU Jan.8 Jan.14 1 - -

GL Jan.8 - - - -

HUT Jan.5 Jan.13 1 - -

IST Jan.12 Jan.16 1 - -

KTH Jan.15 - - - -

NMRI Jan.20 Jan.26 3 Jan.27 all

NTUA Jan.4 - - - -

OU Jan.5 - - Jan.26 all

SOTON Dec.28 - - - -

SSRC Jan.5 - - - -

Notes Revision 1: revisions to comply with the study requirements

Revision 2: revisions when fatal errors detected by participants

of 60

SAFEDOR International Benchmark Study on Numerical...

Documents

Transcript of SAFEDOR International Benchmark Study on Numerical...