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OCR for page 98
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
-
OCR for page 99
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)
OCR for page 100
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
OCR for page 101
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
OCR for page 102
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
OCR for page 103
~ 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
OCR for page 104
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
OCR for page 105
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
OCR for page 106
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
OCR for page 107
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)
OCR for page 108
~ ~ -
~ 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)
OCR for page 109
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)
OCR for page 110
(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
OCR for page 111
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
