|
Items in cart [4] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 368
Prediction of Wave Pressure and Loads on Actual
Ships by the Enhanced Unifed Theory
M Kashiwagi (Kvushu University, Japan)
S. Mizokam i, H Yasul~awa, Y. Fukushim a (Mitsubishi Heavy Industries, Japan)
ABSTRACT
To establish n new practical calculation method
in place of the conventional strip method, perfor
mance of the enEnnced unified theory is investigated
through the comparison of computed rmults with n
large number of experiments conducted with VLCC
tanker and container ship models in this paper,
compared are the ship motions the pressure dis
tribution, and the wave loads The enhanced uni
fled theory is msentinllJ based on 2 D computations
but takes account of 3 D and forw rd speed effects
Furthermore the e' ts of wave diffraction from the
b w part near the waterline are taken into account
in n rational WAN Despite these theoretical improve
meats, the results of comparison for the w we loads
are not so good as expected Since the pressure and
wave loads are strongiJ influenced -- the nccuracJ
of ship motions, more improvement is needed for
precise prediction of the ship motions particularly
near the resonance of he we, roll, and pitch
INTRODUCTION
In the design stage of actual ships, the strip the
ore is still in routine use for computing the ship mo
tions, added resistance in warm, pressure distribu
ti on, and so on Recentl J. 3 D computnti on meth
ods based on the free surface Pnnkine panel method
have been developed, but they are time consuming
from n practical viewpoint, and validity for various
ship shapes is not confirmed
On the other hand, the strip method is verse
tile and its prediction is relatively good, consider
ing that the computation time is short and the the
ore is simple However, several shortcomings in the
strip method have been recognized; for instance, the
pressure distribution near the ship bow and stern
and the added resistance in short waves are not in
good agreement with experiments These shortcom
ings are related to improper treatment of 3 D and
forward speed effect
To account for these effect in the framework
of slende~ship theory, many theoretical works h we
been made Among them, the unified theory, orig
inally developed by Newman (1978) and extended
to the did action problem by Scla:vounos (1984), is
recognized as one of the succmsful slender ship the
orim The unified theory could bring in n certain
amount of 3 D effect to n strip theory type solo
tion in n rational manner However, it was still not
sati factory For instance, the w e did action from
the b w part near the waterline could not be taken
into account, and thus the wave exciting force in
surge and the added resistance in short waver were
usually underestimated
To incorporate the effect of the wave difirac
tion nenr the b w and other effects dismissed as
higher order in the slender ship theory, the original
unified theory was enEnnced by Kashtwngi(1995);
in which the radiation problem of surge is solved
in the same fashion as the he we and pitch modes,
and the effects of wave diffraction from the b w part
near the waterline are taken into account -- retain
ing the x component of the ~ al vector in the
body boundary condition of the diffraction prob
lem F rthermore, 3 D and forward speed e' ts on
lateral modes of motion are incorporated as well
Validity of this enhanced unified theory (nbbrevi
Ted as BUT in the present paper) has been con
firmed only for mathematical ship models like n pro
late spheroid and n modified Wigley model (Kashr
wngi et cl 2000) The unified theory is essentinllJ
based on 2 D computations and thus the compu
Lotion time is very short compared to that needed
in 3 D Pnnkine panel codes; this feature is promis
ing as n practical design tool in the design stage of
actual ships
For the purpose of establishing n new pro ti
cal calculation method in place of the strip method,
we have investigated usefulness and applicability of
the enhanced unified theory, through comparison
of computed results with n large number of experi
OCR for page 369
meets using actual ship models. In the present pa-
per, some results of comparison are shown for mod-
els of a VLCC tanker and a recent container ship.
The experiments were conducted in regular waves,
and the incidence angle of the wave was changed
rather densely. Although there are many experi-
mental data, shown in this paper are the ship mo-
tions and pressure distribution of a VLCC tanker
and the wave loads (vertical bending and torsional
moments) of a container ship.
We can see some noticeable improvements over
the strip method particularly in the pressure distri-
bution and wave loads, but predictions of the en-
hanced unified theory are still not perfect in some
cases when compared closely with experiments. Dis-
cussion is made on possible reasons of disagreement
with experiments.
ENHANCED UNIFIED THEORY
Mathematical formulation
We consider a ship advancing with constant
speed U and undergoing oscillatory motions with
circular frequency ~ in deep water. The analy-
ses will be performed using a Cartesian coordinate
system, which moves steadily with the same con-
stant speed as a ship. The x-axis is directed to the
ship's bow and the z-axis is directed downward (see
Fig. 1~.
\~ Incident wave
Yet
i.
Fig. 1 Coordinate system and notations
Assuming the inviscid fluid with irrotational
motion, the flow can be described with the veloc-
ity potential, which is expressed as
4> = Ut—x + Us (x, y, z) ~ + Ret ¢(x y z) eiwt ~ (1)
6
:,,0 (A + >7) +iw~Xj <;,j (2)
j=1
¢0 = e-koz-i~oy sin x cite _ ¢~0 (y z) bier (3)
is= ~70—koU cOs X' ko = 0 ~ ~ =—ko cOs X (4)
9
where j0 denotes the incident-wave potential; A,
we, ko, X are the amplitude, the circular frequency,
the wavenumber, and the incidence angle of incom-
ing wave, respectively; y is the gravitational accel-
eration. Us in (1) denotes the steady disturbance
potential due to the forward motion of a ship. ¢7
in (2) denotes the scattering potential and Hi the
radiation potential of the j-th mode with complex
amplitude Xj, where in particular j = 1 for surge,
j = 3 for heave, and j = 3 for pitch.
To obtain a solution for the purpose of practical
calculations, the enhanced unified theory (hereafter
abbreviated as EUT) is applied in this paper. In
the subsections below, the outline of the theory will
be given. For more details, we refer the readers to
Kashiwagi(1995, 1997~.
Radiation problem
In the inner region close to the ship hull, varia-
tion of the flow along the x-axis is small compared
to that in the transverse section and the wave ra-
diation at infinity is out of concern. Therefore, the
velocity potential in the inner region satisfies
y2 + ~Z2~¢i = 0 for z > 0 (5)
Gil + Kfj = 0 on z = 0 (6)
0¢j = ~,j +—nit on CH (7)
where K = W2/9. ~j and mj in (7) denote the
j-th component of the unit normal directing into
the fluid and of the so-called m-term representing
interactions with the steady flow; these are consid-
ered on the contour (CH) of the transverse section
at station x along the ship's length.
The general inner solution satisfying (5~-~7)
takes the following form:
(j = enjoy, z) + . Arty, z) + Cj~x) ~, (y, z) (8)
where Gil and Hi are the particular solutions, corre-
sponding to the first and second terms on the right-
hand side of (7), respectively. AH denotes a home-
geneous solution, which can be explicitly given by
AH =~3 _ ~3 for the symmetric modes (j = 1, 3, 5)
and by AH =~2—i2 for the antisymmetric modes
(j = 2,4,6), where the asterisk means the complex
conjugate.
OCR for page 370
In the present paper, contributions of f6 are
neglected in computing the m term and thus m: = 0
for j = I ~ 4, me = ~3, and m6 = ~2 Moreover,
with slenderness assumption, as = x -: ~ and ~6 =
~2
In accordance with these zpprcximations, we
can obtain the toll wings:
f =0(j=1~4), fs=73.
Gus = ~f3, f5 = ~f2
. ~~ = no 1
The unkn wn coefficient C: (x) in (8) can be de
termined by the matching with the outer solution
In the outer region far way from z ship, the so
lotion can be represented by z line distribution of
singularities along the x axis Considering only the
symmetric modes (j = 1,3,5), the source distribu
tion may be used, in which its strength f>(X) is
unknown due to lack of the body boundary condi
tion
The method of matched asymptote
gives the toll wing rmults:
expansions
I (~)+ ~ () 03); I Oft Odin
Up
C>(x){ O3 O3 } = f >(I) {07 + ID f } (11)
(10)
where or Ed f are the 2 D Kochin functions to
be computed from f and f, respectiveiJ The
kernel function f (x f ) in (10) represents the 3 D
and forward speed effects; the Fourier transform of
which is expressed as
i~f(~)}=ln +7
~ >/~{7
Lit
6b+cosh ( k )} 1 .~.
~ = ~ (D + kU), 6U = s3n(D + kU) (13)
and the upper and lower expressions in the brackets
are tzLen according as ~ > k and ~ < ., respec
tiveiJ
Once the integml equation (10) for f>(X) is
solved, it is straightforward to compute C: (x) from
(11), thereby completing the inner solution, which
will be used for computing the pressure, the added
mass and damping coefficients, and the wave loads
Diffraction problem
Unlike the mdiation problem, we assume that
the rapidly varying part with respect to x is of
the same form as fo; that is, em Thus the
scattering potential may be sought in the form of
f7 = D7(X; y, e) 6~'
The governing equation and houDdary condi
tions for the slowly varying pa t Do are given as
( yi + Bet e ) .7 = 0 for z > 0
~ + .: Do = 0 on z = 0
~ = (~3+f~cosx+f~2sinx)
x kD 3 uOz \uoysinx onyx (16)
(14)
(15)
It is noteworthy that the governing equation
is the 2 D modified Helmholts equation and the
wa:venumber in (15) is not K but ko The effect
of w we did action from the bow part near the war
terline are t ken into account -- retaining ~~ term
on the body boundary condition
Considering only the symmetric component
with respect to y = 0, the inner solution can be
constru ted in the form
f7 = DD (Y. Z) Z
+C7 (x){ mD (a; y, 2) + DD (9
DD By, Z)} Z (17)
where DD (Y. 2) = Z cos(koy sin X
notes z numerical solution of (14) (1,
Here c7 (x) is the unkn wn coefficient of z n
mogeneous solution, which can be determined by
matching (17) with the outer solution
The results of the matching are expressed as
f7(~)+7 07{ f 7(~) hs(x)
X), ad ED de
(16)
ho
+ J f7(~)f(~ :) d6} = 07 e (18)
C7 (a) 07 6 = f 7(~) (19)
where hs(x) = cscxco6h ( secx ) In(2 sec X )
and 07 is the 2 D Kochin function to be computed
from ED The kernel function f(x A) is identical
to that used in the mdiation problem
The numerical method adopted here for solving
the integral equations, (10) and (18), is essentially
the same as that shown in Scla:vounos (1985), us
ing ChebJshev polynomials for representing the un
En wn source strength and using z Gherkin scheme
with o thogonal prope tim
OCR for page 371
Hydrodynamic and hydrostatic pressure
P taining only the first order linear terms in
Bernoulli's pressure equation, the spatial part of the
un teadJ pressure is given by
p(~,y,z) = p(fh3+UV V)f
+pg ( X3 + y X~ ~ Xs ) (20)
Here the first term on the right hand side is the
hydrodynamic part, with V defined as V{ x +
fs(x,y 2)}, and the second term represent the
cEznge in the hydrostatic pressure due to ship mo
tions from the equilibrium position in accordance
with neglect of fs in computing the m term, an up
proximation of V ~ i is employed in the present
paper
Substituting (2) as f in (20), the total oscillate
tory pressure can be divided into three components;
those are written as
P= PD +PR Ups
(21)
where PD, PR, and ps denote the did action pres
sure, the r diction pressure, and the cEznge in the
hydrostatic pressure, respectively
In the did action problem, difierentiation with
respect to x may be applied only to the rapidly
varying term, ear, and thus PD is given by
p A al O ( act :~ ) (do + 467 ) em
= (fo+f7)
(22)
Lik wise, PR Ed ps are given in the nondimen
signal form as
pgA 9 ~ A ( Ihl~x)f: (23)
ps X3 + X~ X
(24)
The symmetric part of fo + f7 -- EUT can
be expressed by the homogeneous component (the
second line) in (17) The same is true for the azJm
metric part, although it explicit form is not sh wn
here
The radiation potential fj -- EUT is given by
(8) Consistent with zpprcximations for the m
term and the hJdrodJn mic forces (which will be
explained ne t), difierentiation with respe t to x in
(23) is performed only for j = 5 and 6
The complex amplitude, X>/A, of the j th mode
of motion will be given as z solution of the ship
motion equations
Hydrodynamic forces
In the radiation problem, the force acting in the
f th direction is computed in terms of PR and the
results can be summarized in the form
FV // PR A Is
JJS~
6
= (fee) ~,[A\> + B\~/fh~] X: (25)
)=t
AV+B\~/fh~
Jx Jc~( f m\) { f + ace f } Is
p J do C: (x); (ma\ i m\) ~ Is (26)
where An and B,j are the added mass and damp
ing coefficients in the f th direction due to the j th
mode of motion
In this paper, as sh wn in (9), m\ and f can be
expressed with by and f Therefore, all integrals
in (26) along the contour (Cur) of the transverse
section at station x are evaluated using the toll wing
2 D results:
p / of f Is = ()
JC~
The w we exciting force in the f th direction can
be computed -- integrating PD multiplied by by over
the ship hull Using (22) and (17), the symmetric
component (f =1, 3, 5) are expressed as
E,= pgAJJ (fo+f7)~\dS
= pgA J 4~ 7 (a) em
x J ~,{~62D(~;y 3) + Hi (a 2)} do (23)
cat
We note that hydrodynamic forcm related to
surge (f = 1) are computed by EUT, with 3 D and
forward speed effects tzLen into account
F6~(~)/fh~ (27)
Ship motions
In the linear theory, the symmetric modes (f =1,
3, 5) of motion can be computed independent of
the zntisJmmetric modes (f =2, 4, 6) for z ship
symmetric with respect to y = 0 Therefore, the
longitudinal motions (surge, he we and pitch) can
be computed from the coupled motion equations:
~ [ hi (My + An) + i B,j + C\> ] X: = E\
>=t,3,z
for f = 1, 3,5 (29)
OCR for page 372
where Mij is the mass matrix and Cij is the
restoring-force matrix to be computed from the hy-
drostatic pressure Ps given in (243. Nonzero ele-
ments in these matrices are
M1l = M33 = pV, M55 = Iyy = pay ~
C33 = pgAw, C35 = C53 =—pgAW~w ; (30)
C55 = pgV GMt J
where V is the displacement volume; Iyy is the mo-
ment of inertia about the y-axis and Ale is the cor-
responding radius of gyration; Aw is the waterplane
area and tow is the x-coordinate of the center of wa-
terplane area; and GM is the distance between the
center of gravity and the longitudinal metacenter.
The transverse motions (sway, roll and yaw) are
computed in the same way. However, the damping
coefficient in roll is modified to take account of vis-
cous effects, which are crucial especially near the
resonance frequency. Namely
B44 = kW BW + B4V4 + BU4 (31 )
where Bw denotes the value computed by EUT and
kw is a correction coefficient, B4V4 represents nonlin-
ear components due to the vortex shedding and the
shearing force on the wetted surface of a ship, and
BU4 represents the lift component in the presence of
the forward speed.
Wave loads
We consider first the vertical shearing force on
the transverse section at ~ = x0 along the ship's
length. As shown in Fig. 2, the vertical shearing
force is defined as positive when acting in the neg-
ative z-direction.
:,,,~'
the vertical shearing force can be given by
JXo ~
FV(~O) =— do / (PD +PR +PS ) rl3 Is
XA CH
J ~ )(i~)2{X3-~xs} do (32)
where ~cA denotes the aft end of a ship and we) is
the weight distribution along the x-axis.
When computing the pressure force from PR
given by (23), 0:j /~x may be discarded, which
is consistent with the treatment in computing the
added-mass and damping coefficients in heave.
The result after substituting the pressure can
be expressed in the nondimensional form as follows:
prearm' /~l d:X; JC 773 ( A + :7 ) dS
(TO ~
—K it, (j / do/ rl3:jdS
j=1,3,5 —1 CH
[do
—(3 / {By)—m(~)K} do
-1
to
+65J ~{B(~)—m(~)K} do (33)
where the nondimension is made in terms of a =
L/2 (L being the overall length) for the x-axis, and
b = B/2 (B being the breadth) for the y- and z-
axes. Therefore ~A/a = - 1 and other quantities
are defined as
(1=X1/A, (3=X3/A, (5=aX5/A ~
m(~) = W(0C)/P9b2, K = b`~2/p ~ (34)
The hogging moment is defined as positive for
the vertical bending moment (see Fig.2). With
this definition, the vertical bending moment on the
transverse section at ~ = x0 is computed by
{SO ~
Mv(~o) = / (a—no) dot (PD + PR ) rl3 Is
XA CH
to ~
—/ do / PS { (a—(G)~1 - (A—x;O)rl3 } Is
~ XA CH
lox +J (x no) ' )(i&,)2{X~ xX5}dx (35)
Y . .
J?ME z
Fig. 2 Positive directions of the wave loads
Since the force is the sum of the pressure force
and the inertia force due to the body acceleration,
Here, to be consistent with the pitch restoring
moment, C55, in the motion equation, the contribu-
tion of rll-term is included in computing the hydro-
static pressure force. ( (G is the z-coordinate of the
center of gravity.)
It should be also noted that the integral asso-
ciated with the radiation pressure including differ-
entiation of Hi with respect to ~ may be treated
OCR for page 373
J. (a no) ~fJdx~ J 73f~dx (36) PsA~e2 JO art ~ (fo+f7)ds
This transformation is consistent with the treat
ment in computing the added mass and damping
coefficients in pitch
With these tzLen into account
sional calculation formula for the
moment tzLes the form
pgA~2e J ~ Jc~
+ K it, i J d ~ { ( ~ i,
pro
+63 J. (a ~r
J s(~){c~(~) cc} do
+~oS(~o){eB(~o) en}] (37)
where S(x) denotes the area of the to Dsverse sec
tion and (x) is the z coordinate of the center of
transverse se tion area
The expressions for other components of the
wave loads c D be obtained in an analogous manner
For the subsequent comparison with experi
meats, let us describe the expression for the tor
sional moment Defining the torsional moment act
ing counterclockwise about the x axis to be positive
(see Fig 2), the torsional moment on the transverse
section at x = no is computed by
pro ~
MT(~O) = / do / ( PA + PR + PS ) ~ Is
Jig JCH
J f i(~) (fh3)2X~ do
(38)
where 7C = y~3 (z cc)~z, and f;(x) is the
distribution of the moment of inertia in roll
A is the same as the vertical shearing force,
we note that ~f>/5x in the radiation pressure mzJ
be discarded from z vi wpoint of consistency with
the computation of the added mass and damping
coefficients in roll F rthermore, since only the an
tisJmmetric components of the pressure contribute
to (38), the nondimensional calculation formula for
the torsional moment is given as follow:
~3(fo+f7)ds
7 } Jc~
o){B(~) m(~)K}d~
+s(~o){c~(~o) cc}]
To ,
K ~ i J. dxJ 7C f: do
~=2,9,6 ~ con
:4J {S(X) M(X) m(7)'9~i(7)K}d7 (39)
where M(X) is the transverse metacentric height
and of (x) is the gyratioDzl radius of roll in the
transverse section; both are nondimensionalized in
term of e
It should be noted that the 3 D and forward
speed effect are tzLen into account in EUT even for
the aDtisymmetric part of f 7 and the lateral modes
of the radiation potential f: (Kashtwagi, 1997)
RESULTS AND DISCUSSION
+:st/ (a ~o)~{B(~) m(x)K}dx Outline of the strip method
In this paper, the results of the trip method
established by Szlvesen, T ck and Fzltinsen (1970)
(which is abbreviated hereon er as STFM) are shown
and compared with the results of EUT and model
experiments
In STFM, the contour of the transverse section
is appro im ted by the Lewis form, and 2 D hJdro
dynamic computations are implemented -- Ursell
Tasai's method Surge is treated as an independent
mode, with only the F oude KrJIOV force and the
inertia force due to the ship's mass tzLen into zc
count The computer code used in this study solves
the difirz tion problem dire try, in which the free
surface condition of (15) is satisfied; that is, the
wa:venumber in the free surface condition is not K
but ko
The experimental data of ship motions and the
pressure distribution used for comparison in this par
per are for z VLCC tanker model The principal
particulars of this tanker model are shown in Ia
ble I The experiments w re carried out at Ship
Pesearch institute and their results were reported
by Tzniz we he cl (1993)
Although many experimental data exist, only
the amplitudes of heave and pitch are shown in
Fig 3 for various angles of the wave incidence,
together with corresponding result by EUT and
STFM The F oude number was set equal to Fr =
0 131 EUT tzLes account of 3 D and forward
speed effects in the mdiation and difiraction forces
OCR for page 374
~2
2 ~ .
2 ~ ~_ ~ 0s
s ~ i~ \ 0 s
02 _ ~ :~: 02
i Lpp
~2
95 , _ .
95 ' . ~"
92 I ~~- 1
~o - ~C 1 1
_ ~/Lpp
s I I I . i2 I I I
| 2 ~~~~~~ i ~ =°s ~| ~ tO dYg~
_~ ~ _ _ i
o z71 ~ oo c—'~ ~ !
00 Ob i° A/LPP 20 00 Os l/LPP 20
, s E:3z~ i ~ ~ ~ ~ . , 2 - j ~ = 12 0 dYgt r I ~
<, 2 ~ t - - tf2 -!- - -~ ~= os
~ o s ~ . o s . , ~
os :~!~-~!~: i:~. ~ 04 ~ ~ ~ 1
02 -__ 4'2 ~ ~ 02 ~ ~ I
I/LPP 20 00 Os A/LPP 20
i s . ! ! ! . i 2 ! ~ ~
,2 - 12 = 120 d~g| ~ j 10 -1 ~ = 120 dYg|-~ ~~~ ~ _ Z
<~ io -~ j~ '2 °6 ~', ~i~
02 i ~ i i 02 ~ ~ ~( i i
t/LPP 20 00 Os I/Lpp 20
Fig 3 Amplitudes of hea:ve (left) nnd pitch (right) of n VLCC tanker in w wes (F~ = 0 131)
Tnble I Principal particulars of n VLCC
tanker model
L~ (m) 4 500 GM (m) O 100
B (m) 0 793 ~yy/L~ 0 241
d (m) 0 285 ~/B 0 355
Cb 0 807 F~ 0 131
Therefore, EUT is expected to give n better pre
diction for the ship motions H wever, the numeri
cal results bJ EUT nnd STFM nre almo t the snme
th experimental datn
EUT tends to underpredi t the pitch motion in the
longer w welength region nt X = 120 ~ 180°, which
is due to underprediction of the pitch exciting mo
ment nnd overprediction of the pitch damping co
efficeint, nccording to n recent studJ (Kashtwngi et
21 2000)
Premure distribution
Comparison of the pressure distribution is
shown from Fig 4 to Fig 6 for n VLCC tanker model
OCR for page 375
- F i-
........
= 120 deg| -
-F~ i---F-
i - - -i- - - i ~
. . i~
30 _
26 .
rL 2 o ~
30, .., .., .., .
j.
26
20
k
,~ .
~ _ _ I _ _ _i~ | ~ _ sO d~g |
i5~-r---i---~---r--~
30
26
2
, 6 .
~ ,
o ~
~ ~ I ~ - | ,, _ lf O deg | -
--t- --r ---I--- l-- -r- --
~t ~1~-
i J ~ ~
. . ,'~L=~'
Oo go ~o o 30 go Oo
Of d~0
30 : ' ' 1 ' 1 ' ' ' 1 ' 1 ' ':
26 4 | ~ = 9O degl~
~ ~ t - - -1- - - J - - - L 1
oo - . . 1 \~J
90 90 ~o o 30 90 90
9fd~0
Fig 4 Pressure distribution nt S S 4 22 of n VLCC t
..... - :
_ . _
~f91 ~ ~ I L
t~~
90 90 ~o o 30 90 9
9fd~g)
- Cul by k~T
Cul by STFk
f9 kxperime=t
Preooure Diotributio=
A/Lpp = 0.3. F= = 0.131
ut 5.5.4.22 of VECC Tu=ker
tanker (~/Lpp = 0 3, F~ = 0 131)
nt F~ = 0 131 The pressure was measured nt some Figure 4 sh ws the results of N/L~, = 0 3, nt
points on the contour of the transverse section nt which the ship motions nre nlmost zero eccept for
S S 4 22 ( O I m nhend of S S 4 ) The nbsci~sn of the roll motion nround X = 30° Therefore the
ench figure is the position nlong the contour and pressure distribution in Fig 4 mnJ be regarded as
f = 90°, 0°, nnd 90° correspond to the wenther the pressure induced bJ the w e difiraction onlJ
side, the centerline, nnd the lee side, respectiveiJ The overnll ngreement between computed results bJ
OCR for page 376
30 _
26
20
:~
! I ~ I ,~ = 0 d~g 1
06
~o
90 90 ~o o 30 90 90
·fd~0
- 1 1 "r, 1" 7
r i 7 - | A = 90 d~g I
--r---|---l---r---|---
- '..',~
: i~
F
30
26
2
rt ~ 6
~ ,
o ~
-~-~- I ~ - ~ 't - 1f 0 deg |_
~-t- --r ---I--- l-- -r- --
.^ ~ I 1
t~ t ! t ~ .
T~
30
26 .
2 0
~o
06 _
oo o
30
26t
r 2 0
, 6
26
_ ~ .
..7..~.-r- r- 7
! I ~ I3-fOd~gl
t' ! ~ -! - ~ ~ ~ ~ ~ - i - - - i- - -
i - .:: — — — — . — — — _ _ .
~ 7,~~~1~ ! °
. :i.~zK'i . .
Do 90 ~o o 30 90 90
Of d~0
30 ' ' 1 ' ' 1 ' ' ' ' ' 1 ' ' 1 ' '
'6 ~Op I ~ |, = 90 deg |
o ~ ! · L !
6 ~ i i i i
~0 L\ ~ 1 ! ~ -7
06 I ~
00 .. ! .. ! .., .. i .. ! ..
90 90 ~o o 30 90 90
9fd~0
Fig 5 Pressure distribution nt S S 4 22 of n VLCC
EUT nnd the measurements is sati factorJ Com
pared with the results of STFM, EUT gives n no
ticenble improvement nenr the ship bottom nt X =
180° H wever, EUT tends to overestimate the
pressure on the wenther side in oblique wa:ves
Figure5 sh ws the results of N/L~, = 0 75, nt
~ .
|, - 190 deg |_
.
~ ~ ~ I ~
~_,~
90 90 ~0 0 30 90 90
9fd~g)
- Cul by k~T
Cul by STFk
f9 kxperime=t
Preooure Diotributio=
A/Lpp = 0.75. F= = 0.131
ut 5.5.4.22 of VECC Tu=ker
hnker (~/Lpp = 0 75, F~ = 0 131)
which the pressure is influenced bJ the ship motion
Because of the paucitJ of measured points on the
lee side, the definitive judgement on the superioritJ
of EUT cnnnot be made However, EUT seems to
give better result thnn STFM, particularlJ in the
following wa:ve ( X = 0° )
OCR for page 377
rL
30 _
26
rL 2 0
~ -1 2 - 80 derf ~-
---r---r--~---r---r ---
30,
26
r:L
o L
o
~:
___~
30
26
i 2
r ,
~ lO .
O ;
~ ~ I ~ - | ~ _ 1f 0 d~g |—
---T---r---l---i---r---
~ ~ ~ ~t ~ ~ ~1~ ~ ~ i ~ ~ ~ ~ ~ ~ -.
O;~j .___i___ J~
1 °1 --'9:'' j,, 1 ., .
30
26
rL ~ 6
~o
06 Li
26
i 20
kL
— ,6
~o =
_ ~ .
7 . .~ .. r- r" 7 'i
! ~ |r2 = co d~g|4
I I ~ I I ~
X~.
Of d~0
r- r" 7
| |, = 90 deg |
_ L _ J _ L
6 ~ I ~_1___~
90 90 ~o o 30 90 90
~fd~0
Fig 6 Pressure distribution nt S S 4 22 of n VLCC
We cnn see that the w we pressure nt N/L~
1 25 sh wn in Fig 6 is relativelJ smnll in nmplitude
except for X = 90° in the present case, the roll mo
tion becomes Intge nround X = 90° due to the roll
resonnnce in fact, the chnnge in the hJdrostntic
- r- 7 ~ ' ' r-
~ ~|, - 180 degl_
- Cul by kL7T
Cul by STFk
ffi kxperime=t
Pre88ure Di8tributio=
A/Lpp = 1.25. F= = 0.131
ut 5.5.4.22 of vcoc Tu=ker
hnker (~/Lpp = 1 25, F~ = 0 131)
the right hnnd si
the roll rmonnnc~
the roll motion i:
For that purposc
nonlinenr viscou~
equntion is verJ
de of (24), becomes dominnnt near
Therefore precise prediction of
. crucial in estimating the pressure
, as shown in (31), inclusion of the
ms damping force in the ship motion
important it should be noted that
OCR for page 378
o ~ 1 `" ~~ o ~ OF C it,, ' -
o ohs ~ — j o 4 o ohs If j j it=
o coo o coo
o 3 ° s ~ ° A L 2 0 A to to 3 A/L 2 0
to 030 , , , to 030 , , , ....
0023 j | A = to dreg | - ~ 0023 i
0020 ·`t i i ~ 0020 i .~*~ i i
~ oozes - ..'{~-C o i I ~ oozes - i.if i my, -
~ O Oi O ~ ~ I ~ O Oi O ~ i ~ .
ooos . 1::: i~..=.. ooos - ! i i
20
Fig 7 Vertical bending moment at S S 5 of
the s me modification for the roll damping coeffi
cient using (31) is made both in EUT and STEM
(Unlems the nonlinear viscous damping is taken into
account in roll, the premsure at X = 90° in Fig 6
becomes tremendously large )
Wa d loads
In orderto make Thorough investigation on the
wave loads, measurement of the vertical bending
moment and the torsional moment h we been car
Lied out using a container ship model at Nagasaki
R&D Center of Mitsubishi Heavy industries The
| _ Cal by BUT
Cal by Stiff
O Brperimen t
Vertical Bending Yomenc
In = 0.215
at S.S.5 of Container Ship
a container ship (Fn = 0 215)
experiments were conducted for various angles of
the w we incidence and at five different F oude num
hers F rthermore, the wave loads were measured
at seven stations along the ship's length
The length to breadth ratio, L/B, and the
block coefficient, Cb, of the te ted ship model are
6 45, and 0 59, respectiveiJ The nondimensional
met centric height in roll, GM/B, was set to 0 03
and the gyrational mdius in pitch, 9,/L, w 0 25
in the experimental setup
Figurm 7 and 8 show the vertical bending mo
ment and the torsional moment, respectively Thme
OCR for page 379
A/L
| ~ ~ ~0 d~g |.
..4—~
0 ooo
A/L
~ ..., ....
. _ 2 90 d~Tl
0 003 I I
0002 _ ~ ~ ~ ~ ~ ~ ~ ~ ~ i
\ .
o 00i _ ~ i I
... - , 0 0 0 C
....... ,,.= ~ ,,,'t ~
oooo 0 os lo is 2 0
A/L
Fig 8 TorsionTI moment Tt S S 5 of T contTiner
were meT lured Tt S S 5 Tnd F~ = 0 215 Look
ing Tt closelJ, computed results of EUT differ from
the meT lured results in some respects FirstiJ
for longer WT elengths in foil wing Tnd quTrtering
WT es, EUT tends to overe timTte the verticT I bend
ing moment, T d secondiJ in beT m WT e(X = 90°),
EUT is different from the meT lured results even in
the variTtion tendencJ Th ie discrepTncies mTJ be
Tttributed to imperfect Tgreement of ship motions,
becTuse the WT e ioTds Tre strongiJ dependent on
the r inlts of ship motions
RegTrding the torsionTI moment Tt S S 5
(Fig 8), the overTII Tgreement between computed
Tnd meT lured r inlts is fT rTble, considering the
vTIue itself is smTII compTred to the verticTI bend
the variTtion tendencJ for oblique WT es (X = 60°
~nA 1211°N
0 003
0 002 _ _ _,~—~ _ _ _i_ ~3
o oo~ ~ ~ . _ _
- I * ~0 i
o ooo 1 1 ~ i . ~
O O 0 5 ~ O A/L 2 0
| - Cal by FT T
Cal by STFM
O Sxperiment
Toraional ~ = ent
Fn = 0.215
at S.S.5 Of Container Ship
r ship (F~ = 0 215)
the Tmptitude of the verticTI bending moment de
creT i i but the variTtion tendencJ with respect to
N/L Tnd X is more or iesi the sTme
Looking Tt the torsionTI moment Tt S S 7
(Fig 10), T noticeTbie improvement bJ EUT over
STFM CT be seen in the shorter wTweiength region
for the CT ie of X = 30° H wever, in other Tn
gles of the wTwe incidence, there Tre still discrepTn
cl i between computed Tnd meT lured results Since
nontineTr Tnd fOrWTr] Spi
force Tre importTnt in th
might be T rm ion of dis
moment
Figurell sh ws ths
number on the verticTi I
heTd wTwes ( X = 180
increT ies slightlJ T i tl
_ _ ._~ J the ovemll variTtion t~ _
Figures9 Tnd lOsh wthesTme itemi ofthever is the sTme
tiCTI bending Tnd torifonTI moments, respectivelJ, RegTrding the degree of Tgreement, we cTn
but the meT lured section Tiong the ship's length is point out thTt EUT tends to underestimTte _.
S S 7 CompTred to the results Tt S S 5 (Fig 7), N/L = 0 7 Tnd this tendencJ becomes promir
peed effects on the dTmping
the roll mode, those effect
i~ nr;/ in tR~ t~r~imn~l
.~ dependence of the Froude
bending moment Tt S S 5 in
, We cTn see thTt the vTIue
~e ship's speed increT ies, but
~nA~nr;/ ~zAtR r~ rt tm ~ / T
~rnnnA
OCR for page 380
A As
it ~
~~ooost Of= . ~::]
0 0 s s ~ ° A/L 5 2 0
f 000:~
0 000
00 05 I ° A L 20
0015 ...., ...., ...., ....
| ~ = '7 deg |-
too · i i ~
. ^.-g-O .
~ooos ~ Am:
..............
0000 0 05 i0 i5 2 0
A/L
a, It
Solo
~~ r
with increasing the Froude number in fact, the
forward speed effects are not properly taken into nc
count in EUT especially for higher F oude numbers
To improve in this respect, the forw rd speed terms
mu t be incorporated into the fre~surtace condition
even in the inner problem of the slendeaship theory
CONCLUDING REMARKS
The enhanced unified theory (EUT) encom
passes the strip method and takes account of the
3 D and forw rd speed effects in n rational way
Moreover, EUT can compute the surge related ho
... r .... r....n ....
I A 120 dog l
:~:
r ~ r "n
i i | 2 = 180 dog |
-----i jo-^i---r----
/4 lo'_.
i i i .
to oS I ° A L S 20
| _ Cal by BAIT
Cal by STFlf
O Brperimen t
Vertical Bending Yomenr
In = 0.215
at 5.5.7 of Container Ship
n m -- a- or ship (Fn = 0 215)
drodJnamic forces in the same manner as for he we
and pitch, and thus the longitudinal ship motions
(surge, hewe and pitch) are computed from fully
coupled motion equations among these three modes
In the diffraction problem, EUT can also account
for the wave diffraction from the b w part near the
free su face, because contributions of the at term
are retained in the body boundary condition We
expected that these theoretical improvements over
the strip method w uld result in good prediction
of the di tribution of w we pressure and wave loads
even for actual ships
OCR for page 381
0 004
~ ~ ~ ~ ~ ~ 1 1i ~~ ~ ~ 1, - 120 dog 4
0002 i i
~ 000i ~~ V -o - 3 - ~ =- - ~
Fig 10 Torsional moment at S S 7 of n c
With this expectation, EUT was applied to n
VLCC tanker model and n recent container ship
model, and computed results were compared with
experiment to confirm applicability of the theory
However, the results were not so good as expected
before starting this study One important reason
of this is that the prediction of ship motions is not
improved so much when compared to the results of
STEM, since the ship motions are influential in the
prediction of the w e pressure and resulting wave
loads
Of course, the effects of noffiinenritJ and three
dimensionalitJ of the fl w may be impo tant partic
ularly around the bow part, and viscous effect are
also important near the stern These effects mu t be
accounted for -- more sophisticated 3 D computed
tion methods However, EUT is till advantageous
from n practical viewpoint, because it is efficient
in computations F :- e- study is needed for pre
cise predi tion of the ship motions, for which the
forward speed eke ts on the free surface condition
i| ~ _ :5~ deli]
| - Cal by IT
Cal by STEM
O Experiment
Torsional ~ = eat
EN = 0.215
at 5.5.7 of Container Ship
container ship (Fly = 0 215)
Ackn wledgmentz
The authors would like to thank Mr H Sueck
and Dr T KuroLwn of Mit ubishi Heavy Indu trim
for their help in the course of the present study
Mr Y Tozaki in assisting numerical computations
is also greatly acknowledged
REFERENCES
Kashtwngi, M, "Prediction of Surge and its Effect
on Added Pesistance by Means of the Enhanced
Unified Theory," Tmrsactlors of West JcparSocl
say of NCDCI Archdeces~ No 89, 1995, pp 77 89
Kashtwngi, M, 'Numerical Senkeeping Calculations
Based on the Slender Ship Theory," Ship Tschrol
ogy Rsssamh, Vol 4, No 4, 1997, pp 167 192
Kashtwngi, M, K wasoe, K and Inadn, M, "A
Study on Ship Motion and Added P distance in
Wwm (in Japanese)," Jourrcl of Kcrscl Society
of N A, Japan, No 234, 2000, in press
OCR for page 382
003 ...., ..............
1 ==0.152
~ 002 ~ ~:: :b.-
>~ ~.,.
' _:<
000 0 05 i0 i5 2 0
A/L
i~ ,~_:_:_~
0i ~ i ~~.:, ~D 0 0i .V i ! ~
' . ?~. . . . i . . . . i . .— - , ~i, , , , . il,~=o 2 s! . . -
ooo ooo
o o ° s ~ ° A/L ~ s 2 0 0 0 0 5 A/L 2 0
003 ...., ...., ...., ....
i~ ~ 1 ~=0.215 1-
~ 002 . O~ j~
\ . ~ W.. .
~ O Oi _ ~ _ ~.
... r .... r....n ....
I i[~.
o o o s ~ ° A/L o
Fig 11 Vertical bending moment nt S S
Newman, J N. 'The TheorJ of Ship Motions," Ad
D2rces of Appiled Mecharics, Vol 18, 1978, pp 221
283
Salvesen, N. T ck, E O nnd Fnltinsen, O M, "Ship
Motions nnd Sen Londs," ~ 2rsactlor3 of SNAME,
Vol 78, 1970, pp 1 30
Scl wounm, P. D, 'The Difiraction of Free Surtace
Wa:ves bJ n Slender Ship," Jourr21 of Ship Re
search, Vol 28, No 1, 1984, pp 29 47
| - Cal by B7T
Cal by STFM
O Brperiment
Vertical Bending Moment
A' = l SO deg
at S.S.5 O f Container Ship
5 of n contniner ship (X = 180°)
Scl wounos, P. D, 'The Unified Slende~BodJ The
orJ: Ship Motions in Wwes," Proceedirgs of the
15th Symposlum or N2D21 Hyd 2dy 2mics, Hnm
burg, 1985, pp 177 192
Tnniz wn, K, Tnguchi, H Snrutn, T nnd Wntan
nbe, I, "Experimental StudJ of Wwe Pressure on
VLCC Punning in Sho t Wa:ves (in Jnpanme),"
Jourr21 of 5odety of N2D21 A~chitect3, J2par,
No 174, 1993, pp 233 242
OCR for page 383
DISCUSSION
P. Sclavounos
Massachusetts Instit te of Tech olo :, USA
I would like to con rat late the mfhors for c
series of Thorough st dies, including the present
one, reti Ding He unified slender body theory for
the prediction of motions md wave induced loads
of realistic ship hulls I would I ke to commend
the mthors' diligent refinement of the theory md
its validation cgamst careful experimental
measurements it is the experience the mthors are
repo ting that ht. led me to swit h my energies
since She mid 30's to the development of She 3D
R nkine Panel Method SWAN I cm however
very pleased to see chat se- end of She
short om ings of the unified slender body Theory
with forward speed have been removed by She
mthors
I have c few comments md questions to which I
w Icomethe mthors'response:
O The good conelation of STEM md
EUT for the motions of the t taker
is probably due to her low Frau de
mmmber it would be inte~estmg to
e ho.. both methods perform at
U=0 We have seen some very
good perfommance of unif ed theory
inthatlimitwhichseemstobe
corroborated by She results She
mthors present
O in our experience with SWAN, one
of the most importmt forward
speed effect arises from the careful
mdcomplete treatment of She m-
term s on the body boundary
condition These terms may
actually be computed from She
double body flow without She need
to model surface wave
di turbances Their evaluation
would require the use of c 3D p mel
method, yet their values c m be
input mto EUT es fmcing terms in
thebodyboundarycondition it
ld he interesting to see the
effect of this "experiment" on She
performance on She EUT it ht.
been our experience Nat She m-
temms mthebodyboundary
conditionconhibute muchmore
signific mt forward speed effects
th m their countemart on the free
su face condition, es She mthors
appear to suggest
O Whet is the behavior of the EUT
near the ~114 singularity m
q artermg waves it is my
rec ol lecnon that She unified theory
solution developed in the late 70's
mdesrh go sib Nick mdmyseff
was predicting c singular it in the
motionpredictionsat~=l/4 We
have since seen that this smgukr ity
is not really present in SWAN, yet it
remains difficult to resolve How
does EUT de tl with this delicate
regime when it arises in your
computations md experiments?
AUTHOR'S REPLY
1) Conceming good performance of EUT m the
limiting case of U=0, we have shown m my
suppo ting results not only for c single body
m open see but also She to k-wall
Interference md catamarm problems (see
relerence [Al]) Prom Theoretical viewpoint,
She unified theo y is c perfect one in the
ficmework of slenderbodytheo y
2) Regardmg the effect of She d-. disturb mce
m the body bounds y condition, our
recognition seems to be different fi om that of
discusser Firstly, our purpose is to develop c
practical cclcubtion method which must be
easy to implement but Elide m the design
tage Secondly, She results of the radiation
forces (especially the diagonal coefficients)
by the present method are in good agreement
with experiments Recent results for
mod tied Wigley model with L 7=6 67 te
show in reference [A2] The degree of
cgreementbymems of EUT is ammo t perfect
in A;;. E 3, cod A 3 The results of High-
Speed Slender-Ship Theory HSSST I are also
shown m reference [A2] md HSSST gives
obvious improvement in E3 This tendency
coupling temms HSSST uses also She uniform
flow assumption m the body boundary
condition, but the forward-sped effects m
She fiee-su face condition are fully taken mto
account In fact, w have learned from
Rctiorurl Ship Theo y RSTI of Of il ie &
Tuck that the forward-speed effect in the
fiee-su face boundary condition is importmt
m the cross~oupling terms, which improves
clearly over the strip theory HSSST
encompasses RST, md thus it is natural to
see good agreement with experiments Prom
experiences mentioned clove, w suggest
Nat She forward-speed effects in She free-
surface condition may be more significmt
f m the effects of disturbance potential m the
OCR for page 384
3) As shown in some figures m references [Al]
md [A2], EUT shows singularity et the
frequency equal to ~114, md experimental
date also show mpid variation near ~114 1
suppose She results of SWAN are impe feet
near ~=1/4, md we carmot discuss this
sensitive behavior with questionable
mmmericcl reecho
[Al] M Kcshiwagi (1997); Numerical
Seckeeping Calculations Based on She
Slender Ship Theory, Ship Techmology
Research ~Schff~tech kg Vol. 4, No 4,
pp 1 67-1 92
[A2] M Kcshiwagi (2000); The State of the A t
on Slender-Ship Theories of Seckeeping,
Proceedings of the Ah Osaka Colloquium on
Seckeeping Pe form mce of Ships, October,
2000
Representative terms from entire chapter:
unified theory
