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Twenty-Third Symposium on Naval Hydrodynamics (2001)
Naval Studies Board (NSB)

Page
98
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Page
98
Front Matter (R1-R19)
Modern Seakeeping Computations for Ships (1-45)
Forces, Moment and Wave Pattern for Naval Combatant in Regular Head Waves (46-65)
New Green-Function Method to Predict Wave-Induced Ship Motions and Loads (66-81)
Validation of Time-Domain Prediction of Motion, Sea Load, and Hull Pressure of a Frigate in Regular Waves (82-97)
Ship Motions and Loads in Large Waves (98-111)
Prediction of Vertical-Plane Wave Loading and Ship Responses in High Seas (112-125)
Basic Studies of Water on Deck (126-142)
Second Order Waves Generated by Ship Motions (143-156)
Prediction of Nonlinear Motions of High-Speed Vessels in Oblique Waves (157-170)
Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways (171-180)
Hull Design by CAD/CFD Simulation (181-190)
Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern (191-205)
Practical CFD Applications to Design of a Wave Cancellation Multihull Ship (206-222)
Simulation of Ship Maneuvers Using Recursive Neural Networks (223-242)
Flow- and Wave-Field Optimization of Surface Combatants Using CFD-Based Optimization Methods (243-261)
Marine Propulsor Noise Investigations in the Hydroacoustic Water Tunnel 'G.T.H.' (262-283)
Propulsor Design Using Clebsch Formulation (284-300)
Unsteady Flow Quantities on Two-Dimensional Foils: Experimental and Numerical Results (301-313)
Hydrofoil Turbulent Boundary Layer Separation at High Reynolds Numbers (314-329)
Pressure Fluctuation on Finite Flat Plate Above Wing in Sinusoidal Gust (330-341)
Control of the Turbulent Wake of an Appended Streamlined Body (342-354)
Investigation of Global and Local Flow Details by a Fully Three-Dimensional Seakeeping Method (355-367)
Prediction of Wave Pressure and Loads on Actual Ships by the Enhanced Unified Theory (368-384)
Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships (385-401)
International Collaboration on Benchmark CFD Validation Data for Surface Combatant DTMB Model 5415 (402-422)
Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications (423-440)
Free Surface Viscous Flow Computation Around A Transom Stern Ship by Chimera Overlapping Scheme (441-456)
Anti-Roll Tank Simulations With A Volume of Fluid (VOF) Based Navier-Stokes Solver (457-473)
Validation of Tab Assisted Control Surface Computation (474-484)
Experimental and Numerical Investigation of the Flow Around the Appendices of a Whitbread 60 Sailing Yacht (485-492)
Propeller Wake Analysis by Means of PIV (493-510)
Experimental and Numerical Investigation of the Unsteady Flow Around a Propeller (511-526)
Simulation of Incompressible Viscous Flow Around a Ducted Propeller Using a RANS Equation Solver (527-539)
On Submerged Stagnation Points and Bow Vortices Generation (540-552)
Numerical Prediction of Scale Effects in Ship Stern Flows with Eddy-Viscosity Turbulence Models (553-568)
The Experimental and Numerical Study of Flow Structure and Water Noise Caused by Roughness of a Body (569-578)
Large-Eddy Simulations of Turbulent Wake Flows (579-598)
Instability of Partial Cavitation: A Numerical/Experimental Approach (599-615)
An Unsteady Three-Dimensional Euler Solver Coupled with a Cavitating Propeller Analysis Method (616-638)
On the Flow Structure, Tip Leakage Cavitation Inception and Associated Noise (639-653)
An Experimental Investigation of Cavitation Inception and Development of Partial Sheet Cavaties on Two-Dimensional Hydrofoils (654-669)
Modeling 3D Unsteady Sheet Cavities Using a Coupled UnRANS-BEM code (670-686)
Ship Wake Detectability in the Ocean Turbulent Environment (687-703)
An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415 (704-712)
Breaking Waves in the Ocean and Around Ships (713-745)
Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil (746-761)
The Numerical Simulation of Ship Waves Using Cartesian Grid Methods (762-779)
Radiation Loads on a Cylinder Oscillating in Pycnocline (780-791)
Wave Resistance Computations - A Comparison of Different Approaches (792-804)
Computations of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code (805-819)
Submarine Maneuverability Assessment Using Computational Fluid Dynamic Tools (820-832)
Simulation of UUV Recovery Hydrodynamics (833-847)
Reynolds-Averaged Modeling of High-Froude-Number Free Surface Jets (848-862)
On Roll Hydrodynamics of Cylinders Fitted with Bilge Keels (863-880)
Combining Accuracy and Effciency with Robustness in Ship Stern Flow Computation (882-896)
An Unstructured Multielement Solution Algorithm for Complex Geometry Hydrodynamic Simulations (897-909)
Ship Stern Flow Calculations on Overlapping Composite Grids (910-926)
Study on the Prediction of Flow Characteristics Around a Ship Hull (927-940)
Analysis of Turbulence Free-Surface Flow Around Hulls in Shallow Water Channel by a Level-Set Method (941-956)
A Design Tool for High Speed Ferries Washes (957-967)
Flow Around Ships Sailing in Shallow Water - Experimental and Numerical Results (968-982)
Ship Stability Study in the Coastal Region: New Coastal Wave Model Coupled with a Dynamic Stability Model (983-992)
Waves and Forces Caused by Oscillation of a Floating Body Determined Through a Unified Nonlinear Shallow-Water Theory (993-1005)

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Ship motions and loads in large waves Ryuji Miyake, Tsuguki Kinoshita, Hiroshi Kagemoto (The University of Tokyo, Japan) Tingyao Zhu(Research Institute, Nippon Kaiji Kyokai, Japan) ABSTRACT Comprehensive experiments regarding ship motions and loads are conducted using a large container-ship model advancing in a regular wave train. The emphasis is on the nonlinear characteristics of motions and loads in large waves. Computations are also carried out and their results are compared with the measured ones. A CFD(computational fluid dynamics) technique is used for the computation, in which the equations of motion of water particles and those of a ship are solved simultaneously under the exact boundary conditions within the context of an inviscid flow. It is found that the theoretical computation can account for the nonlinear natures of the measured motions and loads fairly well, while distinct discrepancies exist from the measured results in some cases even in a moderate sea state. 1 INTRODUCTION Facing the current keen international competitions, shipyard companies need a rational design basis that enables them to construct cost effective ships. For that purpose, the expected maximum loads on a ship in her lifetime need be predicted with good accuracy at the design stage of the ship. Recently several numerical tools that can predict the loads on a ship advancing in large waves have been appearing (e.g. King, Beck & Magee 1988, Lin & Yue 1990, Huang & Sclavounos 19984. Although some comparisons of ship motions and loads predicted by such numerical tools with experimental ones can be found sporadically, no systematic experimental studies on ship motions or loads in large waves have ever been conducted, or at least, been published. Under these circumstances, Table 2.1 The particulars of the model Length (L) (m) Breadth (B) (m) Draft (m) Displacement weight (N) Froude Number Force transducer 5.000 0.617 0.214 4000.4 _ 0.171 - ~ +P15 +P14 jP' ~ , ~ I ~ , ~ , ~ , ~ , ~ , ~ , ~ , UP P13 1 _ _ _P12_— P15 ~ P14 Pll .+ P6~P10 P8iP7{ ~h +ps P2`P4 Pl+( - l=W ~_ PlO4P9 1: |:L5lertical Bending Moment,P3 J =30deg. _~_ 'P4 Horizontal Benclin~ Moment P5 P2 P3 ~ . _ Tx=9Odeg. ~ X= 1 20deg. Fig.2.1 The container-ship model -

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ship motions Ed loads m large waves me experimentally mv stigated in c quite >! tematic maimer usmg c k Be contamer-ship model of Sm le g6h Six deg ees of motions, v rticcl es w 11 es hori ontal bending mome t Ed hyd odynamic pressures acting on She ship hull are measured es the ship is finely advancing without coy e ternal flesh ictions m c red lar wave ham The h ight of the waves is varied to 5 m, lOcm, 15 m, which may correspond to Croat 2 6m, 5 2m, 7 8m respectiv Iy in c reel see The advancing di ection of She ship Pectin to waves is varied from 180deg~ecd waves) to Odeg(followmg waves) with 30deg interval while the wavelength(~) is changed fi om )/l=0 2 to )/l=1 5 The nonlinear characteristics that appear m motions, bending moments Ed hyd odynamic pressures are discussed in detail while usmg She experimental resorts N mericcl computations based on c newly dev loped CF (computatiom~l fluid dynamics) code IT moshita Kcgemoto & Fujino 1999), which solv s th Enler's equations of motion of water particles tog ther with She equations of motion of th conespondi g ship alder exact nonlinear bo mdary conditions, are also carried out m order to examine to what extent the observed nonlinearities c m be acco mted for by the sophisticated m mericcl method 2 EXPERIMENT The experiment was conducted in c water tmk(length:SOm, width:30m, water deaths 14m) et She Univ rsity of Tokyo The co hmer-ship model used for She experime t is show in Fig2 I Ed its principal particulars are specified in Table 2 I Six deg ees of motions, v tic i es w it es hori ontal bending mome t Ed hyd odynamic pressures acting on the ship hull et 15 locations w re measured es the ship was freely advancing without coy e ternal flesh ictions m c red lar wave ham Fig2 1 also shows the locations of the IS pressme gauges Pl~PIS) attached to She ship hull for She mecsmement of hyd odynamic pie.. se. The fme part Ed th aft part of the model is com cted et its longit dmal center vie c force transducer so that the v rticcl cod the horizontal moment acting et the midship section c m be measured The si deg ees of motions were measured by opticcl-flber g os The height of She waves was varied to 5 m, lOcm, 15 m, which may correspond to Croat 2 6m, S. 2m, 7 8m re Fe m- Iy in c reel see The advancing direcrbn of the ship relative to waves was varied from 180deg heed ways) to Odbglfollovi g waves) with 30deg Interval while the wavelength(~) was chs Led from )/l=0 2 to )/l=1 5 (A/l=0 2,0 3,0 4,0 5,0 625, 0 75,0 875,1 00,1 25,1 SO) The ship speed U was kept to be U/~= 0 171 in all the experiments (Th ship speed may be low r 6 m that of c conventional container ship, but fi is was She maximum speed that could be cchiev d m the t mk used ) The height of She waves Ed She ship speed w re conholled m c q ite strict manner in such c way that if the desired 14 12 08 06 04 02 14 12 08 06 04 Heave %=180deg. -. ~~ _... ~ ..~. F... ~ ...... _... 7 ..~. ,... ~ ....~.. .j.... -..... _... .... ....----.------ -------i-------'-'m' _..._~____..,.______:...____.__....,..____.i,~.._..... _... ~ ..,. If. .~.... F..... O :. t§.~. ^ i.. i ..i.. i. .i .. 0 02 04 06 08 1 12 14 16 Heave X=120deg......-- .i.... I..... _... ~ --..~-------~-------~------~-----: I}' if 7 O ' t~-I';'.-'-i---;;-i-;-;~ 0 02 04 06 08 1 12 14 16 12 _... .. . Heave %=9Odeg. ~ I . ~ \ 0 6 _... L ~ / ~ /- L ~ Lo l ---L- 04 ~ >l-t)(~ i... ---------- ink. 02 ~ - ;~.3~ ~~ -- 3 ~ 1—~-I5 ml- O . ~ ~.i . i.. i ..i.. ]. .! .. O 02 04 06 08 1 12 14 16 Fig3 1(1) The experimental remits on heave motion amplitude(Zt)

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1 2 coos 506 04 02 . _ 4~08 ,306 04 02 35 ,25 2 05 Roll X 90deg. ..4 -} 5 ml..L . i ~ 10 m 0 _ ., ~ , ~15 m Hi '''i ------i-------'------~------1-------i---~-'/=-- _ l : ! 1 10.~1 m. / '''~------'-'''''-'--- ~' 7:; - ~ _ ^~ iJ~ 1; ;~,. 0 02 04 06 ~ I 12 14 16 4 : c) ~ Roll %=30deg. - ~ 150Ccm ..y. . A 0 02 04 06 08 1 12 14 16 Fig 3 1(2) Ibe experimental re mlts on roll motion amplitude(~) waveheight and/or She desired ship speed was not engined, the experiment was carried out again till the prescribed values of both She watch ight Ed She ship sped w me attained within allowable diffe~ences(4% for the ship speed Ed 10%~5% for the Scm~lScm waveheight) 3 RESULTS OF THE EXPERIMENT 3.1 Motion Fig 3 1(1),(2),(3) show some of She resoles on She motions of She model ship as ~ function of A l(wave length ship length) he ve ti al 9:~t. of ah the fames - Roll %=120deg. ~ A-- 12 _ Pttch %=130deg. ~ l ~ .... .. 0 8 _ .... i ~ ,~ . 8 _ ~ ....... ...... ......... Ah 0 6 _ , , , ..~, ...... 6 ~ ~ . ;^ ~ 0 4 _ 1 ,. Lit ~;;q 0 1 0 2 0 4 0 6 0 8 1 2 1 4 1 0 1 0 2 0 4 0 6 0 8 1 ~ 2 1 4 _ 6 A/L 12 l 08 Qh 06 $) o4 02 to _ Pitch %=120deg ...,..~. - i if i . L ..... I , . , j : ,;^r . ''t§'~W I' 'I ..1.. i. ,, A ~ A 12 1 1 1 0 8 06 :------------j-------j--...--...... ~ 04 1 ' ' ~ . O 2 1~------------r------i----t'-- ------- -------r------ o 1 ..,9.~i i. i. 0 02 04 06 08 1 12 14 16 A/L Fig 3 1(3) he e perime tal results on pitch motion amplihnde(O~) represent th nondimensiom3lized motion amplih de of the Fourier component that has the same fiequency as the enco mtering fiequency with th incident waves Ibe legends -5 m-, '10cm', '15 m' indicate that th correspondi g remits w re obtained m waves of 5 m, 10cm, 15 m height respectively Since at the qua titles show m the figm es me normalized by th amplitude of the incident wave(5A) or the maxim m slope of th incident waved the results for 'Scm', '10cm', 'IScm' should coincide with each other if the phenomena w re of linear ones How ver, She so-called wave-height effect is observed in some cases, particularly in heave motions in z=120deg, 90deg Ed in roll motion in z=90deg, 30deg in such ~ way that

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The re porno per mit mm d m-~s e emplit de becomes smeller es the waveheight increases The six if icmt wave-height effect observed in the roll motion in x=30deg in the long wave r ma may be eth Abated to The nonlinear viscous-damping characteristics At me k ow to be m mifested m large roll motions On th ocher h md, The amplitudes of the other motions per mit mcident-wave amplitude ineludmg those that are not show in Fig 3 I vary little in all th th ee waveheights es t pically observed in The pitch motions Fig3 1 (c)) 3.2 Pressure Fig 3 2, Fig 3 3, Fig 3 4, Fig 3 5 show The re mlts on The pressme emplit des measured et Pl, P2, PS, P14 (se Fig2 1) respectively Like m Fig 3 1, the vertical axes of the flgmes represent The nondimensiom~lized pressme amplitude of th Fourier component that has The same fiequeney es th eneo mtering frequency with The incident waves p,g in the vertical axes represent The fluid density md the gavitatiom~l acelemtion respectively As c m be seen in Fig 2 1, P I, P2, PS, P14 me located along th same horizontal level(2cm below The cc m water smfae) on the w etherside of The hull At Pl, The pressure amplitudes nommalied by the mcident-wave emplitude(~) differ sigmfic Fitly among Those obtained in th th ee waveheights, m which the pressme amplitudes per mit mcide t-wave emplit de become mallet es The waveh ight becomes Erg r These nonlinearities with respect to waveheight me also observed in the pressures measured et P2, PS, P14, e peeielly in The short-wave r mge As for th pressures et other locations, Fig3 6(1) ~Fig3 6(4) show th pressures measured m x=120deg et P7, P10, P12, P13, which me located aro md The cross section close to the midship(see Fig 2 1) Again, although The men it de is not Erg, the nonlmearities wish re pect to waveheight are clearly observed, e pecielly in the short-wave r mge She reason why The results m x=120deg me show in Fig 3 6 is that it is the case m which The nonlinear characteristics me m mffe ted ) Fig 3 7(1),(2) show example time histories of the pressmes meesmed et Pl md P10 respectively As show in Fig3 7(1), The time history of the pressure et Pl, which is located et The bow ju t below The calm water surfae(see Fig2 1), is huneated et c eertam pressure level, which may cone pond to the atmospheric pressure This is c w 11-k ow characteristic of the pressure on c ship hull near the calm water surface, which may come out of th water into th atmosphere es c Urge displacement is induced in waves his should be The mom cause of The nonlinear wave-h ight effects observed in th fiequeney characteristics of the pressure et Pl that were show m Fig 3 2(1), because The results show in the figure me those obtained by c Fourier decomposition while taki g no consideration on the possible truncation of The pressure time history ~ order to co firm this speculation, m attempt was made in which The pressure emplit des were reerurly:osd by c Fourier decomposition after sinusoidal time hi tories w He reproduced fi om the truncated ones The typical results obtained in fi is maimer me show m Fig38(1),Fig38(2) in th figm es, the re mlts obtained by c Fourier decomposition without ECHO mti g for th pressure tn:mation et th atmospheric level are show m Fig 3 8(1) while those obtained vifih The consideration on the p~essme truncation me show in Fig3 8 2) As evident in th figures, th once-seemed nonlinearities vifih respect to the waveheight tom out to be ECHO mted for m mo t part if The huneation of pressure time histories is taken into scco mt O the other h md, es is show in Fig 3 7(2), slfihongh the time history of the pressure et P10,which is located well below The calm water smfae, is never trim sted bec mse The conespondmg portion is slway be l ow the water s mfae , m spprec itb le nonlinear in still exists as w obseh d in Fig 3 6(2) Coverall, slfihongh o by 9 limited n mber of res fits are show here due to the limitation of space, th nonlinesrities with re pect to waveheight Sue psrticoh Iy m mffe ted in quartering waves ~120deg, 30deg ) m 911 locations of fihe pressure Badges 3.3 Bendflng moment Fig 3 9, Fig 3 10 show fihe results on the vertical bending moment md fihe horizontal bending moment re pectively acting at th midship section The vertical axes of the flgures represent th nondimensionsli:osd amplitude of fihe con espondmg moment 7 he amplitude show in the flgmes is that of fihe Fourier component which ht. the same frequency as the enco mtering

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35 ~25 05 35 ~25 05 35 ~25 05 35 \~ 2 2 I 5 05 1 ~ 6eml Pl %=180deg. ,,1 ~ 10 ml....l.................................... | ~l Sem | ~ : j JZ`i i i t A : i £~—d~, r~ Qr~ i i i . .~. .1. .1 1 . i i . 0 02 04 06 08 1 //L (I)z=180deg . . : Pl %=120deg ~ | ~ Seml. of ~ ...... ,{: , i~ i .... ~ i.~- ... ~ ; i 0 02 04 06 08 1 12 14 16 ~JL 2) z=120deg - Pi %=90deg. 1 - } 5 :::::::::::::: ::::::: :::::::::::::: ::::::1~1: (~\ . i i i 0 02 04 06 08 1 12 14 16 //L (3) X=90deg i ~ i ~ 5 mll ............. ~ ~` ~ I m|| ..... ~ ~''1 :::::::::~:~ :1 ....... ~ Ef.~ Pl %=30deg. | . .Q .1. .1. .i. ~ I 0 02 04 06 08 1 //L (4) 1,=30deg Fig 3 2 Ihe experimental ~esults on p~essure emplitude(P~) et P I ~ j 2 I 05 O— 0 02 i : : ~ P2 %=130deg. ~ i ~3 t 2 | | .------i------ ~15 ml ,L. + i i + i i I ,,,,,l,,,,,,l,,,,,,,l,,,~,i,,,,,,,L,,,,,,,L,.... (,,,~ 04 06 08 1 12 14 16 //L (I)z=180deg 31 2 5 1 P2 X= 1 20deg _ , ~3 ', t - ~s ml ~,SI ~ i , ~ ~: 0 02 04 06 08 1 12 14 16 ~JL (2)z=120deg j : 1 ~ P2 X 90deg. ,------,------~-1 t----- ------------------- ------------ -1 ,L. + ~; . + . i . I ~::':'~:~ 12 14 16 ~ j 2 = I 05 O — 0 02 04 06 08 1 //L (3) X=90deg | P2 x=30deg. r: 1 1 = 1 ~= 1 ~ j 2 : ~} 5 ml ~10 ml L ~ ~ | ~15 ml ,L +/ : ~ ~+ i i 12 14 16 0 02 04 06 08 1 i/L (4) 1,=30deg Fig 3 3 Ihe experimental re mits on pressme cmplitude(P~) ct P2

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~ l ls os ls - l -os o - os 2 _ 21 05 . . PS X:180deg , . -.~ 0 02 04 06 08 1 //L (I)z=180deg . . : PS X 120deg : 1~15 ml ~ ~ , . . ......... ~ . .~ 02 04 06 08 1 12 14 16 ~JL 2) z=120deg 2 - P5 x=9ode8 1~ 5 ml ~IOctr . ~ISctr ...... ~, i ''' ~' 0 02 04 06 08 1 12 14 16 //L (3) X=90deg : . . 2 PS X 30de8 ' ~ I s f~ , 1~16 ml kr , ; x - ~h~ ~, 6i~ ~Nt + . ' ~ ~ ~ ~ ~ ~ i . . i~. i ~ 05 0 0 2 0 4 0 6 0 8 1 //L (4) X=30deg Fig 3 4 Ihe experimental ~esults on p~essure amplitude(P~) at PS 0 02 2 ~ P 4 X 180de8. ~t ',1..... ~ IF +,, +,,, ~0s~ ~ o 04 06 08 1 12 14 16 //L (I)z=180deg 2 , s L ,,, X,,, 8,,, W1 | . . . ~15 ml ~ 11 -~ _ i i = t ~ ~ f:':':~=3 o 12 14 16 0 02 04 06 08 1 ~JL - ~ o l (2)z=120deg i 1 P 4 X 90deg ~ 1 ~a-9. ~f ~ + . i . ~''''~=L 12 14 16 0 02 04 06 08 1 //L (3) X=90deg . . . : P14 X 30de8 | ~ C34 . . . ~15 ml 0 02 04 06 08 1 //L (4) 1,~30deg 12 14 16 Fig 3 5 Ihe experimental re mits on pressme amplitude(P~) at P14

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19 _ g~08 ~06 04 ~2 12 g~08 ~06 04 02 12r 0 02 04 06 08 1 //L (l) p7 . . : i ~ P10 %=120deg. : ~ Sctr 0r' V ' A10 /~ ' ~15~ ~ ~ _ ~ 0 02 04 06 08 1 ~JL (2) plo ~06 04 02 19 _ l O8 04 (l OE3) (1) 7he time history of th pressure mecsured et P I (x=180deg . waveh ight=1 Scm,2/l=l 000) ............. i i ''~ 0 02 04 06 08 1 //L (3) P12 , P13 %=120deg. 1 1 Fig 36 7he experimental ~esults on p~essure cmplit des(P~) et P7, P10, P12, P13 inz=120deg ~ 25 I 5 05 O _ 6 0 02 04 06 08 1 12 14 16 //L (1) witho t th considerction on 6he pressure h mcation ~ -~' - ~ :,,,,,~f,,.,,,,,,~ ;- :,,,,,~,~ -.~.~.~i~.~.~.~;~.~.~,~i~.~.~. 0 02 04 06 08 1 12 14 16 //L (2) wi6h the com idemtion on the p~essure tn~ncation Fig 38 7he effect of 6he pressure truncation on c Fourier cmplitude

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003 _ 0 025 0 02 0 015 - i 0 005 003 _ 0 25 ~ 0 02 ;,0015 ,~, 0 01 0 005 003 _ 0 25 ~ 0 02 ;,0015 _ 0 0 1 0 005 003 _ 0 025 ~ 0 02 ;,0015 001 0 005 Ve ticai Bending Mom':nt X IdOdeg - ! ~ U! .~ i~. .],~.~.~ ~ 4. 0 02 04 06 08 1 12 14 16 ~JL (I)z=180deg Ve ticai Bff~dmg Moment ~ 5 m . X i20deg ~i5 m ' ~ 4~;Jf' i . ~ rA.i. i ,,i., i ,i.. i. , 0 02 04 06 08 1 12 14 16 //L 2) z=120deg Ve tieai Bff~d6ng M m':nt - } 5 m X 90deg . ~i5 m : . . ! ~ i . .. . .. - ~—,b ~—, o~ ',~ ~, 02 04 06 08 1 12 14 //L (3) X=90deg Ve tieai Bff~dmg Moment ~ 5 m x=30deg . ~ 10 m ~ ~ ~i5 m , }., ~ . . `. . . ,_~ - ! '! i -. —. i ..i.. ~ O 02 04 06 08 1 12 14 16 //L (4)X=30deg Fig 3 9 he e perime hi results on the verticei bending moment empiit des(MY) et th midship 0 025 0 02 B rim hi B~:ndi g Mome~ .~ 0015 ~ · 6^i ~ 0005 2~ o 02 04 06 08 1 12 14 16 jI/L o (I)z=120deg 0 025 ~ Horim hi B':ndi g M mff~ - } 5 m 0 02 ~ x=30deg , ~1 m ~001 . ~ -0005 ~1 I ~1 ,1, 1, 1. O 02 04 06 08 1 12 14 16 jI/L (2) X=30deg Fig 3 10 Ibe experimentei re mits on th hori motei bendmg moment empiit des(Mz) et the midship 350 300 250 :: 200 150 100 50 .I.. i. .~.. i. .l . i. . 12 14 16 0 02 04 06 08 1 L Fig 3 11 Ibe esymmeh icity of 6he ve ticei bendi g moment(z=120deg ) f~equeney with 6he meide t waves he noniinearities

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with re pect to waveheight are observed Maim in She short-wase r mge(A/l=0 2-0 8) m quartermg heed wavesX=l20deg ) for bodh She semi cl moment md She horizontal moment es She moment per Emit waveheight becomes smeller with th increase of the waveheight They me also observed in th horizo till mome t in She long-wave r mge in quartermg following waves (x=30deg) The nonlinearities m x=120deg may be du to the nonlinearities of the p~essmes bec use, es Greedy show, the nonlmearities of the pressures are comm only observed m x=120deg m the con espondmg short-wane r mge 0 th other h Ed, the mom c use of She nonlmearities observed m the horizontal moment m x=30deg may be th trong nonlinear ferns es of She roll motion es we observed in Fig3 1 2) Of her f m These, Although they are not show here, bodh She ve ticcl Ed the hori ontcl moments show fairly linear characteristics it is k ow that the ve ticcl moment on c container ship possesses c crest-trough c mmetricity Ed f is is redo firmed m Fig3 11, m which the sagging Ed She hogging bending moment et She midship measured fiom She moment level acting on She ship cdvancmg in c calm water are separately show lithe vertical axis is not nondimensiomdi:osd be represents She moment itself ) it is evident that the sagging m oment is larger th m the hogging moment Ed f is tendency is erJurxed sin Tic mtly es She waveheight becomes larger 4 COMPUTATION 4.1 Basic idea of the computation As for th Theoretical estimation of ship motions Ed loads m large waves, quite c few works are now bemg conducted, although the Ember of work that have been applied successfully to the computation of motions Ed loads of c practical ship advancing in large waves is till limited LAMP code developed by Lm, Yu et cl (1990) or SWAN code developed by Sckvoumos et cl (1998) account for She exact body boundary condition under She mcide t-wave su face whereas the he su face condition is linearized You She incident wave su face based on c so-called w ck-scatter hypothesis Comparisons of th se cclcoktions with experimental resuts on motions Ed loads in large waves c m also be fouled in some litemtmes LAMP code, e peciclly, has Men extensively tested in comparing She results on su h qu mtities es motions, loads, waves Ed p~essmes Lin & Yu 1994, Lin, Shin et cl 1997) Mo t of these cu rent methods mcludmg LAMP, SWAN me velocity-potenticlbased panel methods Here, on the other h Ed, w apply c CF (computatiorud fluid dynamics) for the cclcu ction of ship motions Ed loads by di ectly solving simultaneou Iy She equations of motion of water particles Ed those of She corresponding ship together with She continuity equation of the fluid while discretizmg She fluid domain into hexahed cl g ids Since most of the nonlinearities that are observed in the motions Ed loads m k ge waves c m be ctinbuted to non-viscous forces, Euler's equations me used m the present computations es th equations of motion of water particles The present method, as described clove, discreti:oss She fluid domain Ed solves fluid velocities Ed pressu es by c fmite-dffference scheme while satisfying She boundary conditions on She tree su face es well es on She body su face exactly within She context of m inviscid flow Since, when iscous effects are neglected, c panel method based on c velocity pote till theory ca n be used, the volume-dismetized CF computation may not seem c good shategy How we, She exact treatment of mo ing boundaries mob es c flee surface or c body su face m some ca ses tons out to be much easier f m the suface-discretized panel method his is particularly tea when shong nonlinearities associated with th motions in k g waves me involved Although the details of th present CF calcoktion method c m be fouled in Kmoshitc et cl (1999), c brief exphrmtion is reprodu ed here to give a rou h idea of the method 4.2 Computatiort procedure The equations of motion of water particles Ealer's equation) are det ribed with respect to a pace-fixed coordinate system (z,y,z) whereas Those of a floating body are det Ned with respect to a body-fi ed coordinate ystem (XY<) Obese two t ts of motion equations Ed the continuity equation of th fluid are solved under The exact boundary conditions on a flee su face as w 11 as on a body su face by a fmite-difference scheme The temporal derivatives are

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evaluated by c fi st-order Enleri m scheme As for fhe spaticl derivativ s, c third-order upwind-diffe~ence scheme is used for fhe convection terms while c second-order central-dffference scheme is used for the of her temms After obtcini g fhe XYZ v locities of the body md fhe mgular v locities of the body aro md fhe XYZ cxes, the locations md fhe cttitudes of the body wifh re pect to the spae-fixed coordincte ystem me updated et eah time step 02 Og 0 02 04 06 08 1 12 y[m] Fig 41 he hy rid g id ystem used for the CF compubtion (one-hcff of the v ticcl cross section of the compubtioncl domcm) 4.3 Grid system In c CF compubtion, which uses c vol me-dismetized g id sy tem, th choice of the g id sy tem is one of th crucicl pomts for fhe successful computation in fhe p~esent cclcuhtion, c hybrid g id sy tem is used m which c body-fi cd bo mdary-fltted g id system is used m the vicinity of c body wherecs c spa -flxed g id system is used cway fi om th body es show in Fig 41 he two g id sy tems are ov rlapped partially et fhe perimeter of eah g id system Alhough fhe body-fi cd g id system is fltted to the body bo mdary, it is not flt cd to fhe flee surfae as show in fhe figme, b t, imtecd, fhe fiee smfae is displaced f ough the g ids m such c way that fhe mass contimmity of fhe fluid is satisfled in the g ids located clong fhe fiee surfae 08 lt~E p (IOcm)l Heave 7=180deg _06 |~=C~(IO m) I . , o , , , , , ~f, ; , ; , . . . . 0 02 04 06 L 1 12 14 16 (1) Heave Od Pitch x=180deg DS=~` ~to6 : |t~E p (10 m)| 04 1 ~ C~ (lOcm)|.' 02 _ ,~: o 1~ ~ i.i..... 0 02 04 06 ~iL 1 12 14 16 (2) Pitch Fig 42 he comparisons of the calculated md mecsmed results on motions in h cd waves I ~ 0 02 04 Pl X=lSOdeg, ~ ~E p (10 m) ~ : : : ~ Ccl (10 m) , . . ~ ~ r -2~ : _ ; ~ . : _~ _ . t, ,~. i . i . i . i . i . i . 4 06 08 1 12 14 16 //L (1) Pl P2 x=180deg l~ t~E p (10 m) . : : : ~Ccl (10 m) h I 5 ~ ., . ~ ., i i I - t ~ . os +, ;', +, o ~ i .i . i . i . i . i . 0 02 04 06 08 1 12 14 16 //L (2)P2 Fig 4 3 he comparisons of the calculated md mecsuredremlts onpressmes inhecdwaves (contmues to th next page)

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~ ~ - ~ l s os ~ - ~15 0s 2s 2 I s I 0s 2s 2 0s !> . . . P3 %=lSOdeg. ~Exp (lOcm 2 ~ C~(10 m) . i i i .............. ~ i---,^~ ''i'''''''i'''''' i i~. O , ,~ .;. .i. .i. i i .i 0 02 04 06 08 1 //L (3) p3 _ . . P4 x=lSOdeg. -~-Exp (lOcm 2 ~ ~ C~OOcm) . ~,_, i i i i - o 0 02 04 06 08 1 ~JL (4)p4 . . . PS X=lSOdeg ~Exp (lOcm ~ Cal (10 m) i i i . ~ . .K~ 0 02 04 06 08 1 //L s) PS . . . P7 x=180deg l ~ Exp(10 m)| |~Cal (10 m) | ---------------------i--- j ; i i i i · i i i ''''~' 0 02 04 06 08 1 //L (6)P7 Fig 4 3 he comparisons of fhe cclcuhted md mecs:med~esults onp~essures mhecdwa~s (contim es to fhe next page) - 05 O— o - 05 O— o8 j ! ! ! : ' 1 I PS X=lsodeg i I~EXP (10 m)| I E ~ | ii-----~ l~---c--al-(l-o--cim)-l-] 1 i i i i i 1 ~ t------i-------i----~.=~-----i------1 1 i A - f~ —~ 1 r T^T I T I i~ 1 1 ~.. i .i . i .; . i . i . I 02 04 06 08 1 12 14 16 //L (7)P8 I P9 %=lSOdeg. i I~EXP (10 m)| r T----l ~ C~l (lOcm) l 1 - . ... I i i i i i 1 - - - ~ - f:-:-:~ 0 02 04 06 08 1 12 14 16 ~JL (8)P9 i | P10 x=180deg. |~EXP (IO m)| r I ~ C~l(lOcm)l L-----~- . . ~ . . . I i i i i i ~ -.-------.-------------.-------i ------- ----- u1 ~=: 0 02 04 06 08 1 12 14 16 //L (9)plo i | Pll x=lSOdeg |~Exp(lO m)| I ~ Cal (l O m) | t t I I t i ~ ~ ~ i i r L l l i _~ 1 i 1~ t --~------b'-i------~------i----~- ~, ~ .i . i . i . i . i . 0 02 04 06 08 1 12 14 16 //L (lo)pll Fig 4 3 he comparisons of the calculated md mecsuredremlts onpressmes inhecdwa~es (contmues to th next page)

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12 g~08 ~06 04 02 _22F - 05 _22F - 05 2 . 05 P12 x=180deg. |~EXP (IO m)| | ~ Cal(lOcm)| . . . ::::::::::::4~: ..~.i..,. i..i ., 0 02 04 06 L I (11) P12 P13 x=180deg. |~EXP (10 m)l | ~ Cal(lOcm)| .................................................... ~ ........................................................... ., . .~.~. .i. .,. i. .i . 0 02 04 06 08 1 //L (12) P13 . P14 %~180deg |~EXP (I m)| | ~ Cal (I Ocm ) | ''''''''''''''''''''''''''''''''''''''''''''i'''''''''''''' . . . i L ,, . .......... ;,,~ — .. i .~ .. ,. , , ., 0 02 04 06 08 1 //L r13)PI4 ~ ~ P15 x=180deg. |~EXP (10 m)| | ~ Cal(lOcm)| ! . . . ''''~' 0 02 04 06 d I 12 14 16 (l4) P15 Fig 4 3 he comparisons of fhe cclcuhted md mecs:med~esults onp~essures mhecdwa~s 4 i _ ~ ., . I- 25 0 5 5 p+CclP(Scm ~ - Pl %=lSOdeg. 3 tl ~Exp (10 m 5 ~ ~ Cal (10 m)] ~=.=~ 2 t|~Ccl (15 m)l75°' iii~t 5r ~=j: st ~i,; i, 0 02 04 06 L I 12 14 16 (1) Pl - 1 :: ~. ~oSt ~ O' 5— . .. . O 02 04 06 L I 12 14 16 (2) P2 Fl+ Cal (5 m) I . P7 %=180deg. 2n~Exp(lOmY----~ ~-~ rl ~ Cal (10 m)l oclSn~Exp(lSm4----~.------'.-------'-------'----- -, Ll+C~ (15 m?L ~ L L ost-----~ o 0 02 04 06 08 1 12 14 16 //L (3) P7 .~ 4~P14 %=130deg. j+Cal(Scm) i . I~Ecp (10 m} ~-----~------ ------- ------~-----| ~ Cal (10 m)| ~ ' I ~ Exp (15 m] F _ -------- - - - -| + Cal (1 5 m) | f~.~. 0 02 04 06 Q8 1 12 14 16 L (4) P14 Fig 4 4 7he nonlinearities of 6he pressmes with re pect to the waveheight~l 80deg)

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(10 9) j—E p —Cal j 0 05 1 15 2 25 3 35 4 45 5 time(second) (1) P2, waveheight=lOcm, 2/l=0 75 (IOE21 j—E p —Cal j 0 05 1 15 2 25 3 35 4 45 5 time(second) (2) P10, waveheight=lOcm, 2/l=0 625 (IOE49) j—E p —Cal j 4 0 05 1 15 2 25 3 35 4 45 5 tlme(second) (3) P12, waveheight=lOcm, 2/l=0 75 Fig4 5 She comparison of time histories of measured mdcalculatedp~essuesmhecdwaves 4.4 Resudts and their comparison with es loci males 4.4.1 Frequency response eharaeteristies Fig42, Fig43 compare She results of the CF computation on She motions md on She p~essmes respectively in heed waves of lOcm height with the conespondmg experimental ones Since She experimental results me th Fou ier component that has She same beers ncy es She encoumtermg frequ ncy of She incident waves, th cciculation results w re also Fou ier-decomposed so that the component that has She encou termg f~equ ncy m be compared 7be pitch motion is predicted w 11 by She prese t computshop whereas the calculation results on She heave motion me c little smaller th m the corresponding experimental ones As for th pressu es, She lard p~essmes acting at She bow section PI is predicted quite accurately by th present ccl Elation On th other h md, pressures on P7, P8, P9, P10, Pll, P12, P13, which me located clo g She cross section close to the midship(see Fig2 1), are overe timated by c sig if ca t amount in She long wave r me it is characteristic At 6 is tendency persists for all the pressmes measured on the section Although th detailed cause of 6 is discrepancy is She subject of c future study, this may have to do somehow with the umde prediction of She h ace motion observed m Fig42(1) Asw gofubherdow sheamclongth ship hull, good cg cements betw en th present cciculation md She experime t me recovered es w observe in She comparisonsatP14,P15 4.4.2 Nonlinearides with respect to waveheight Fig 4 4 shows to what e tent She present CF compu ction c m reprodu e She nonlinear characteristics with re pect to waveheight that me observed in the experimental results on She p~essues She sig if cut nonlinear characteristics of the pressu e et She bow Pl) are accounted for fai Iy w 11 by She present computttioa 7be rather subtle difference of th pressures per Emit incident-wave amplitude m the th ee different waveheights observed et P4, P14 are also reprodu cd by She prese t computation quite w 11 On the other h md, et P7, which is located on the cross section close to the midship, She cciculation results differ form She experimental ones m two respects, that is, (1) She magnitude of th ccicoction results is sig fficmtly larger th m that of the e perimentcl ones in all the th ee waveheights, which was heady noted m 4 41 (2) the calculation results show distinct wase-height effect while the experimental evidence is that little wave-height effect exits among the experime till re mits obtained in She 6 ee waveheights 4.4.3 Time hdstories As example comparisons on time histories, Fig 4 5(1 Fig 4 5(3) compare th cciculated cod mecsu cd time hi tories on p~essmes measured et P2, P10 md P12 respectively The tru ction of th pressure observed in Fig 4 5(1) at the ctmo pheric pressu e level c m be accounted for quite w 11 by the present CF computation he limo level m the vertical axis does not necessarily represents She atmospheric pressure) At P10, which is located deep enough to always remain under She water su face, She

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time history of fhe pressu e shows c fai Iy smusoidal natme md it is w 11 ~eprodu cd by fhe pres nt computation As for the p~essue et P12 shown in Fig 4 5(3), the hough of the computed time hi tory is deeper thm th mecsu cd on cldhough fhe di torted natme from c simmsoidal cu ve is somehow reprodu cd by the computation S CONCLUSIONS A compreh mive experiment on ship motions md loads in krge waves was condu ted using c large contain r-ship model Some of the ~esults were compared with those obtamed by m mviscid CFD computation he followings may be con luded from fhese tudies (1) Nonlin arities with ~espect to waveheight me observed in mch c way that the motion md load responses per mit in ident-wave cmplit de actmg on fhe ship become smeller es the waveheight mcrecses hese nonlinear characteristics me especiclly m mffe ted m quartermg waves (2) Th time history of the p~essme mecsured et fhe location close to the water smface is sometimes hu cted et th ctmosph ric pressme level es fhe conespondmg pomt is exposed to fhe cir du to fhe k ge motion of the ship his may be the mcin c mse of fhe nonlin ar characteristics of the pressme wifh respect to waveheight th~t are observed in the e perimental ~esults How wx, fhe presm~es et fhe locations w 11 below fhe water su face still show n nlin ar characteri tics even though fhe conespondmg points clways stcy mder fhe water su fae (3) he csymmetricity of the ve ticcl bendmg moment acting et the midship is clearly observed m such c way fnat the sagging moment is larger f m fhe hog ing moment This tenden y is sig i f mtly enh mced es fhe waveheight becomes larger (4) he motions md loads are predicted fai Iy w 11 by fhe presented CFD computation he notable exceptiom are the pressu es on fhe cross section close to th midship in heed waves, where (c) th mcg it de of th cclcokted pressmes is sig ffi mtly k ger f m fnat of fhe mecsmed on s, (b) fhe cclcokted pressmes show distin t nonlin ar characteristics with re pect to waveheight whe~ecs fhe mecsmed on s show fairly lin ar natu e (5) Overcll, fhe nonlmear characteristics that me observed in the mecsu cd pressu es in large waves m be acco mted for fairly w 11 by the p~esented CFD comp htion On fhe other hmd, the~e exi t some distin t dismepancies m th cclcokted motions md pressu es fiom fhe mecsmed on s even in modercte waveheight, which may indicate fnat fhe presented CFD comp htion procedme still n eds futher improvements Acknowledgement: The cubhors w uld like to cck owledge D s Iwco Wctcrube, Shigesuke Ishidc, Kctsoji Tmizawc of Ship R search in titute, Ministry of Tr mspo t, hp m md Atsushi Kum mo of Nippon Kciji Kyokai for fheir support md valu~ble comments m condu tmg fhe experiments REFERENCES B.W.King, R.FBeek and A.R. Magee: Seakeeping ccl uhtions wifh forward peed usmg time-domcm crudy is, Proc 17fh Symposium on Naval Hyd odynsmics, The Hcgue, The Netherl mds, l 988 W-M. Lh and D.K.P Yue: Numericcl solu ions for large~mplitude ship motions m time domcin, Proc 18th Symposium on Naval Hydodynamics, Am Abor, Michigm, 1990 YHuang and P.D.Selavounos: Nonlinear ship motions, Jou nsl of Ship R search, Vol. 42, No 2, 120-130,1998 TKhostdta, H.Kagemoto and M.Fujino: A CFD cpplication to wave-indu cd flocti gbody dynamics, Proc 7fh h tl Conf on Numericcl Ship Hyd odynsmics, N mtes, F'ance, 1999 W-M L4 D.K.PYue: Large~mplitude motions cod wave loads for ship desig, Proc 20th Symposium on Na~l Hyd odynamics, S mtcBarbarc, Cclfformc, 1994 W-M L4 Y-S Shh, J-S Chung, S.Zhang and N.Salvesem Nonlinear p~edictions of ship motions md wave loads for stn tu cl crudysis, Proc 16th I tl Conf on Offshme Mech mics md A ctic Engmeermg, Vol. l -A, Yokohamc, Jcp m, l 997

Representative terms from entire chapter:

time history