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OCR for page 82
Validation of Time-Domain Prediction of Motion, Sea
Load, and Hull Pressure of a Frigate in Regular Waves
W. Qiu, H. Peng and C.C. Hsiung
(Centre for Marine Vessel Development and Research, DaThousie University, Canada)
Abstract
A time-domain code, SEALOADS, has been devel-
oped to predict ship motion, sea load and hydrody-
namic pressure distribution of ship. The theoretical
background of SEALOADS is outlined. Computa-
tions were carried out for a frigate in regular waves
at various wave headings and steepnesses for dif-
ferent forward speeds. The predictions of heave,
roll, pitch, shear force and bending moment, and
pressures at several locations were presented. The
validation study of computed results was carried
out by comparing with experimental data from a
hydroelastic model of the frigate.
INTRODUCTION
The predictions of ship motions, sea loads and hy-
drodynamic pressure distribution over a ship hull
are essential components of ship design. Strip the-
ory has been used as a practical prediction method,
but it gives unsatisfactory predictions at low fre-
quencies and at high forward speeds. As well,
the strip-theory approach is not able to compute
the hydrodynamic pressure distribution over the
hull surface except on sections. Some of the de-
ficiencies of strip theory can be removed by three-
dimensional theory. Several researchers, such as
Chang (1977), Inglis and Price (1982) and Guevel
and Bougis (1982), have used three-dimensional
panels to obtain solutions of ship motion in the
frequency domain. The frequency-domain panel
method has been employed for ship seakeeping
analysis using zero-speed Green function with a
"speed correction", since the frequency-domain
Green function containing the velocity term is com-
plicated to handle. An alternative approach is to
formulate the ship motion problem directly in the
time domain. When the forward speed is involved,
the time-domain Green function is in a simpler
1
form and requires less computational effort than
does the frequency-domain counterpart.
The concept of direct time-domain solution
is based on the early work of Finkelstein (1957),
Stoker (1957) and Wehausen and Laitone (19604.
Cummins (1962) and Ogilvie (1964) discussed the
use of time-domain analysis to solve unsteady ship
motion problems. The zero forward speed problem
has been discussed in detail by Wehausen (1967,
19714.
In the linear time-domain formulations, the
time-dependent Green function is applied to derive
a boundary-integral equation at the mean wetted
surface of the body under the assumptions of small
motion and small amplitude incident waves. The
linearized radiation and diffraction forces acting on
the body can be expressed in terms of convolution
integrals of the arbitrary motion with impulse func-
tions. These methods have been developed by Li-
apis and Beck (1985), Beck and Liapis (1987), Beck
and King (1989), Beck and Magee (1990) and Lin
and Yue (19944.
Efforts have been made to directly incorpo-
rate the nonlinearity into time-domain formula-
tions. One extension of the linear time-domain
model is to impose the body boundary condition
on the instantaneous wetted surface of the body.
The free surface boundary condition remains lin-
ear so that the time-dependent Green function can
still be applied. The body-exact problem has been
solved with various degrees of success by Lin and
Yue (1990), Magee (1994) and Danmeier (19994.
Huang (1997) combined the exact body boundary
condition with a free-surface condition linearized
about the incident wave profile. In the results of
these studies, the application of the exact body
boundary conditions showed promise of improve-
ment for cases of computations dealing with large-
amplitude motions.
The computer program SEALOADS was devel-
OCR for page 83
aped at the Centre for Marine Vessel Development
and Research (CMVDR), Dalhousie University for
predictions of ship motions, sea loads, and hydro-
dynamic hull pressure in the time domain. The
linear time-domain model is applied to compute
the radiation and diffraction forces. The Froude-
Krylov forces and restoring forces are computed
on the instantaneous wetted surface under the in-
cident wave profile. The other nonlinear forces
such as viscous damping forces and maneuvering
forces are also taken into account. The nonlin-
ear equations of ship motion in SEALOADS can
be solved in the time-domain either by the fourth-
order Runge-Kutta technique or the Extrapolation
Method (Magee, 19944. The uniqueness of the code
is that a direct solution approach (Cong et al.,
1998) is applied to solve the impulse response func-
tion, and the analytical solution (Qiu and Hsiung,
1999) of the time-dependent Green function is com-
puted by solving an ordinary differential equation
(Clement, 19984.
Ship motions, sea loads, and hull pressures
predicted by the computer program SEALOADS
for the Canadian Patrol Frigate (CPF) in regular
waves at various wave headings, steepness, and for-
ward speeds were validated against the test data
with a 1/20-scale hydroelastic model of the CPF.
THEORETICAL ANALYSIS
Equations of Ship Motion
Three right-handed coordinate systems (as shown
in Figure 1) are employed for the ship motion anal-
ysis. A space-~;xed coordinate system, OXYZ, has
the OXY plane coinciding with the undisturbed
water surface and the Z-axis pointing vertically
upward. In the steady-moving coordinate system,
°m~mymzm, the °m~mYm plane coincides with the
calm water surface and °mZm is positive upward.
The third coordinate system, Os~csyszs' is fixed on
the ship, and Os is at the point of intersection of
calm water surface, the longitudinal plane of sym-
metry, and the vertical plane passing through mid-
ships. The Os~csys plane coincides with the undis-
turbed water surface when the ship is at rest. The
positive -axis points toward the bow and the Ys~
axis to the port side.
Denoting a column vector by braces
{}, ship motions in the °m~mYmZm sys-
z
Y
O tax
x
as
Act_ J ~
Figure 1: Coordinate systems
tem are represented by the vector Xm =
{~m I ~ ~m2 ~ ~m3 ~ ~m4 ~ arms ~ ~m6 } ~ in which
{~m I ~ ~m2 ~ Ems } are the displacements of the
center of gravity (CG), and {~m4,~m5,~m6} are
the Eulerian angles of the ship. The Eulerian
angles are the measurements of the ship's rotation
about the axes which pass through the CG of the
ship. The instantaneous translational velocities of
ship motion in the directions of Osiris' OsYs and OsZs
are {~1, ~2 ~ ~c3 }, and the rotational velocities about
axes parallel to Os9Cs' Osys and Oszs and passing
through CG are {0c4, ice, Em}. The equations of
ship motion are
..
MijXj + Si = Fi, i = 1, 2, ..., 6
..
where X = {~1, ~2 ~ ~3, ~4, ~5, ~6 } ~ F is the external
force vector, and
M=
m
O
O
O
O
O
O O
O O
O O
O —I13
I22 0
O I33
m(9Cs~3—~6~2) ~
main - ~4~3) 1
m(0c4~2—~5~1) (3)
5~6(I33—122)—I13~4~5
(I1l—133)—I13~6—~4)
~ ~4~5 (122—Ill ~ + Il3~s~6
where m is the ship mass and Iij is the moment of
.
inertia.
The total external force acting on the ship is
Fi = Fir a't + Fief + Fife + Firs + Fir
+FimC' for i = 1,2,...,6 (4)
2
OCR for page 84
where Fired and Fief are the radiation and diffrac-
tion forces, respectively; the Fife are the nonlin-
ear Froude-Krylov forces; the Firs are the restor-
ing forces; the Fin are the viscous forces; and the
FimC are the miscellaneous forces which include the
propeller thrust, the maneuvering forces, and the
rudder forces.
The velocities of motions in the °m~mYmZm
system are related to those in the Os~csyszs system
as follows:
Xmi = TijXj, i = 1,2,...,6 (5)
where Xm represents the ship perturbation veloci-
ties in the steady-moving coordinate system. The
transformation matrix T is
[ 0 B ]
where
and
~ c2c3 sls2c3—cls3 cls2c3 +S1S3 ~
R = 1 c2s3 s1s2s3 + c1c3 c1s2s3—s1c3 1
2 S1C2 ClC2 ~
(7)
1 Slt2 Clt2
B= 0 c1 - s1 (8)
O S1/C2 Cl/C2
where ci = cost si = sin(~)) and ti = tan(~))
for i=4, 5 and 6.
Ship motions in the steady-moving coordinate
system can be solved from Equations (1) and (5)
either by the Runge-Kutta scheme or by the ex-
trapolation method.
External Forces
The boundary integral equation of linearized ra-
diation and diffraction problem can be expressed
by the source distribution and then solved by the
panel method (Liapis and Beck, 19854. The oscilla-
tory part of the time-dependent Green function and
its derivatives can be solved from the fourth-order
ordinary differential equations by using a Runge-
Kutta scheme (Clement, 19984. In the computer
program SEALOADS, a series expansion method is
used to achieve an analytical solution of the ordi-
nary differential equations (Qiu and Hsiung, 19994.
The linearized radiation force at time t can be
obtained from
Fi p (t) = — pi p ~k (t)—Aid ~k (t)—Aid ~k (t)
at
J KiR~(t—Id (9)
o
Here, Hi, Air and BYTE are the added-mass, the
damping coefficient and the coefficient of the restor-
ing force of the ship in the time domain, respec-
tively, and KiR~(t) is the impulse response func-
tion. This function can be solved from Eq (9) by
substituting ~~ for a non-impulsive input (~(t) =
~/7e-~t . In SEALOADS, a direct solution
scheme (Cong et al., 1998) is applied to solve the
response function instead of using Fourier transfor-
mation. The total radiation force is obtained from
Firad (t) = ~6~=1 Fi p (t) .
In a similar way, the diffracted wave forces can
(6) be computed from
r°°
Fief= / KiD7(t—74Ho(~)d~ (10)
—Go
J
where KiD7(t) is the impulse response function for
the diffraction force in the ith mode and r10(t) is
the free surface elevation of the incident wave at
the origin of the steady-moving coordinate system.
The Froude-Krylov forces and restoring forces
were computed on the instantaneous wetted surface
under the incident wave profile. The rudder forces,
maneuvering forces and viscous forces have been
discussed by Huang and Hsiung (19964.
Pressure
The pressure at a point Pin, y, z) on the mean wet-
ted hull surface can be expressed as
p(P; t) = PR(P; t) + pD(P; t)
+pi(P; t) + bPst(P; t) (11)
where PR (P; t), PD (P; t) and pi (P; t) are the pres-
sures due to the radiated, diffracted and incident
waves, respectively, and bPst(P; t) is the hydro-
static pressure fluctuation due to the oscillatory
ship motion. The pressures due to the radiated
waves and diffracted waves are obtained from
6 t
PR(P; t) = ~ J Kpk (P; t—T)~)dT (12)
k=1 0
3
OCR for page 85
PD(P; t) = | Kp (P; t—7)Ho(~)d~ (13)
J-OO
where KRk (P; t—T) is the pressure response func-
tion due to the kth mode of motion and KD(P; t)
is the pressure response function due to diffracted
waves.
If a point is below the incident wave profile,
the nonlinear pressure due to the incident waves is
directly computed by
pi(P;t) = - p9~Z-Ho(P;t)] - p i; ~
2P~V~O(P; {)~2 (14)
where ~O(P; t) is the velocity potential of the inci-
dent wave.
Sea Loads
The sea load acting on a cross section He can be
expressed as
6
Vp (t) = ~ FrJk (t) + F4k (t) + Ff ok (t) + rSk ( )
j=1
+Fink(t), for k= 1,2, ,6
where Vie (t) is the total sea load in the kth mode of
motion; The terms on the right-hand side are the
forces acting on the body forward of station ~c.
Frjk (t) and Folk (t) are the forces due to the radi-
ated and diffracted waves, respectively; Ff,~Ck (I) and
Frsk (t) are the Froude-Krylov forces and the restor-
ing forces, respectively, and F~s k (t) represents the
inertial forces.
Equations for computing sea loads caused by
radiated and diffracted waves are similar to Eqs.(9)
and (10). Sea loads at the section He caused by in-
cident waves are obtained by directly integrating
pi(P; t) over the wetted surface forward of the sta-
tion He
VALIDATION
An effort was made to validate the ship mo-
tions, sea loads, and hull pressures computed by
SEALOADS for a Canadian Patrol Frigate in reg-
ular waves in the deep departure condition. This
took about 25 minutes to compute using 10,000
time steps (At = 0.02 sec.) for a single speed and
wave condition on a Pentium III 700MHz PC.
.~
it-- 12-m WL
it_
-
1~: __ _
~ |~ BL
Figure 2: Model frigate body plan (dimensions in
full scale).
SUPER Err _ in ~ = r~r~TR~
n I n I n I n /
~ ~ ..' ' PAL ' ~ ' ~
ACtELERIIMETER ~ ELASTIC
(ONE FOR EAtH SEGMENT) BA[~RONE
Figure 3: Backbone foundations and superstruc-
ture profile.
Model Test
Experiments with a self-propelled 1/20-scale model
of the CPF were conducted in both regular and ir-
regular waves in the towing tank (200 m x 12 m x
7 m) and the Offshore Engineering Basin (75 m x
32 m x 3.5 m) at the Institute for Marine Dynam-
ics (IMD) in St. John's, Newfoundland, Canada.
The steepness, H/A, of the regular waves ranged
from 1/50 to 1/15, where H is the wave height
and ~ is the wavelength. Wavelength was varied
from 0.5L to 1.6L (the model length between per-
pendiculars L = 6.225 m). Smaller wave ampli-
tudes were used to measure linear response, while
large amplitudes were for investigation into non-
linear responses. Built with solid fiberglass, the
model was segmented into 5 sections with a contin-
uous backbone to enable the measurement of bend-
4
OCR for page 86
ing moments and shear forces on the hull girder.
The model and the earlier tests were described by
McTaggart et al. (19974. Pressure sensors were
deployed in the later tests (Ando, 20004. Table
1 gives the particulars of the ship and the model.
The model was equipped with a hull-mount sonar
dome, a rudder, and propeller brackets, but no
bilge keels. Table 2 gives the locations of the 11
transducers (Ando, 20004. Figures 2 and 3 show
the body plan and the backbone foundations and
superstructure profile. In Fig. 2, the positions of
pressure transducers are also indicated. The model
was fitted with twin five-bladed, highly skewed pro-
pellers. Figure 4 shows the stern profile. The shal-
low draft near the stern is notable. Wave height
was measured by a resistor-type wave probe at-
tached to the carriage at 7.84 m forward of the for-
ward perpendicular. All pressure transducers were
zeroed at rest in calm water. The hydrostatic pres-
sure was balanced out initially in the transducer-
bridge monitoring circuit. The recorded quantity
was therefore the periodic variation of pressure
about the average hydrostatic value.
Table 1: Hydrostatic particulars of ship and model
in deep departure condition.
| Designation | Ship | Model l
water
Scale ratio
Length overall(LoA)
Length between
perpendiculars (LPP)
Length of waterline (LWL
Beam (B)
Draft (T)
Maximum section
abaft amidships
Area of midship section
Area of maximum section
Centre of buoyancy
abaft amidships (LCB)
Centre of buoyancy
above the baseline
Volume of displacement
Wetted surface area
Displacement (I\)
Centre of flotation
abaft amidships (LCF)
Area of the waterplane
salt
134.7m
124.5m
124.91m
14.88m
4.97m
3. 73m
59.48m2
59.66m
2.46m
3.06m
4548m3
1992m2
466!Nt,nn
8.02m
1 449m2
fresh
1/20
673.5cm
622.5cm
624.6cm
74.4cm
24.9cm
18. 7cm
O. 149m2
O. 149m2
12.3cm
15.3cm
0.568m3
4.979m2
567.8kg
40. lcm
3.604m2
~ —
Figure 4: Stern profile of CPF.
Motions, Sea Loacis anc! Pressures
Selected predictions of motions, sea loads, and hull
pressures together with the experimental results in
regular waves at the deep departure condition are
presented below. Predicted heave, roll, and pitch
motions are compared with experimental results.
For sea loads, vertical shear forces and bending mo-
ments at stations 2.5, 5.0, 7.5 and 10.0 are given.
Pressures are given at sensors 5, 6, 8, 9, 10 and
11 (see Table 24. The matrix of validation work is
summarized in Table 3 where Fn and ~ denote the
Froude number and heading, respectively. A head-
ing of 180 degree corresponds to head seas. The
experimental data on pressures are available only
for head seas at Fn=0.05, 0.12 and 0.18. The mea-
sured pressures at Fn=0.12 are chosen to validate
the computational results. Amplitudes (,a of the
incident waves corresponding to H/A = 1/30 and
H/A = 1/20 are listed in Table 4, where c~ denotes
the wave frequency.
Table 2: Location of pressure sensors (in full scale).
Sensor Station Distance Height
No. from CL (m) above BL (m)
0
11
5
1.0
1.0
1.0
1.0
1.0
3.0
3.8
7.2
9.5
13.0
18.5
4.6
3.3
2.0
0.7
0.0
0.0
0.0
0.0
0.0
0.0
0.0
* son Lar-dome bottom
11.5
9.70
7.0
3.0
0.0
0.0
-1.75*
0.0
0.0
0.0
3.3
OCR for page 87
Motions, sea loads and pressures are nondi-
mensionalized as follows:
(16)
(17)
Vi/ = Vi/(pgLppB(a), i = 1,2,3 (18)
(19)
(20)
pi = ~i/~(a)' i = 4,5,6
Vi/ = Vi/(pgLppB(a)' i = 4,5,6
where ~ is wave number; hi is nondimensional mo-
tion amplitude; Vi' is nondimensional load ampli-
tude; and p' is nondimensional pressure amplitude.
In Figure 5, the nondimensional heave and
pitch in head seas at Fn=0.06 are given along with
vertical shear forces and bending moments at sta-
tions 2.5, 5.0, 7.5 and 10.0. The responses were
computed for two wave steepnesses (1/30 and 1/20)
and 7 wavelengths (~/L from 0.70 to 1.37) for each
wave steepness. As shown in figures, the predicted
heave and pitch agree well with experimental re-
sults. Predicted sea loads show correlation with
test data.
Figure 6 presents the predicted ship responses
in oblique waves () = 165°) at Fn=0.06. The pre-
dictions for heave, roll and pitch in oblique waves
are generally in good agreement with test data.
Predicted sea loads agree well with test data.
Figure 7 gives the computed heave, pitch and
sea loads in head seas at Fn=0.12. The corre-
sponding pressures at six sensor locations are also
presented in Figure 8. The predicted pitch agrees
well with the experimental results, whereas heave
is over-predicted when 1.0 < A/L < 1.6. The pre-
dicted bending moments at four stations show rea-
sonable agreement with experimental results. The
shear forces are however over-predicted. The pre-
dicted pressures at sensor 5, 6, 9 and 10 are in
general agreement with model test results for cases
Table 3: Summary of the validation matrix
| En | Ship Speed | ~ (deg.) | H/A
0.06
0.12
0.20
0.25
(knot) | l
4.1 1 180, 165
8.2 1 180, 165, 135
13.6 1 180, 165, 135
17.0 1 180
1/30, 1/20
1/30, 1/20
1/30, 1/20
1/30
Table 4: Amplitudes of regular waves in head and
oblique seas.
A/L
0.59
0.70
0.80
0.89
1.01
1.09
1.19
1.36
1.57
1.94
.
rad/s)
0.92
0.84
0.79
0.75
0.70
0.67
0.64
0.60
0.56
0.51
(a (m,
H/~=1/30
1.224
1.453
1.660
1.847
2.096
2.262
2.469
2.822
3.258
4.026
H/~=1/20
1.836
2.179
2.490
2.770
3.144
3.393
3.704
4.233
4.887
6.038
of H/A = 1/30. The discrepancies between the pre-
dictions and test results for the case of H/A = 1/20
may be due to the assumption of linear radiation
and diffraction. Figure 9 shows predicted time se-
ries of heave, pitch, and pressures at sensors 6 and
11 for A/L = 1.01 and H/A = 1/30. Compared
with responses of heave, pitch and pressure at sen-
sor 6, spike-like responses are shown at sensor 11.
This could be because sensor 11 is located close
to the stern and the pressure due to incident waves
was computed on the instantaneous wetted surface.
The wetted surface could change drastically due to
the shallow draft at the stern of CPF.
Figure 10 presents the computed motions and
sea loads in oblique waves () = 135°) at Fn=0.12.
Predicted heave, pitch and sea loads show reason-
able agreement with test data. Predicted roll is
smaller than experimental results. This indicates
that the viscous roll damping coefficients might be
over-estimated.
Motions and sea loads are also given in Fig-
ure 11 for the case of head seas and Fn=0.20. It
is shown that motions and sea loads are in good
agreement with experimental results.
Numerical simulations were also conducted in
oblique seas (Fn=0.2) and head seas (Fn=0.254.
It was found that irregularities were observed in
the time series of ship responses as ship speed in-
creased. This suggests that the assumption of lin-
ear radiation and diffraction might not be valid
for these cases, where the wetted surface changed
significantly due to shallow draft and large waves.
This applied to very long waves as well as to very
short waves.
6
OCR for page 88
1.4 _ I I I
1 .2 _
1 _
- 0.8 _
0.6 _
02 _
0.6 0.8 1
\/L
1.2 1.4
Lc, 20 _ _
CM
`u 1 5 _ _
`u 1 0 _ _
S 5
o
0.6 0.8 1 1.2 1.4
\/L
25 1 1 1
Lc, 20 _ _
c'' 1 5 _ _
~ 10
> 5
_ ~==~==~=:
_
O 1 1 1
0.6 0.8 1 1.2 1.4
\/L
25
20
15
10
5
O 1 1 1
0.6 0.8 1 1.2
\/L
1 .4
o 20 _
15 _
i~ 10 _
5 I ~ ~ ~ ~ ~
0.6 0.8 1 1.2 1.4
\/L
1 .4
1 .2
1
0.8
0.6
02 ~
0.6 0.8 1 1.2
\/L
L~
CM
cn
Ln
S
. .
Lc, 40
c'' 30
~ 20
S
10
1 .4
15,
10 _ _
O ~7 ~=1~
0.6 0.8 1 1.2 1.4
-- ~ 1~-
o
0.6 0.8 1 1.2 1.4
\/L
50 1 1 1
Lo 40 — _
30 _ _
`u 20 _ _
S 10 _
O 1 1 1
0.6 0.8 1 1.2 1.4
\/L
~ 1 1 1
o 40 _ _
c,, 30 _ _
i~ 20
Ln
> 10
_ ~ ~ ~ ~ ~ _
1 1
1 1.2
\/L
1 .4
Figure 5: Predicted motions and sea loads in regular waves, ~ = 180°, Fn=0.06 (Legend: o experimental,
H/~= 1/30; x experimental, H/~= 1/20; SEALOADS, H/~= 1/30; -—SEALOADS, H/~= 1/204.
7
OCR for page 89
Legend
1 .4
1 .2
0.&
0.6
0.4
0.2
o
. _
_
- 5~ ,:5~ ~
0.6 0.8 1 1.2
\/L
0.8 1 1
0.7 _ _
0.6 _ _
0.5 _ _
0.4 _ _
0.3 _ ><
02 _ ^~1
0.6 0.8 1 1.2
\/L
~, 20
c~
~ 15
cn
`~ 10
S 5
~ _
o
0.6 0.8 1 1.2
\/L
25,
~, 20 _ _
c'' 1 5 _ _
~ 10 _ _
>m 5 _
O 1 1
0.6 0.8 1 1.2
25
O 20
cn
i~
>
Experimental, H/~=1/30 O
SEALOADS, H/~=1/30
Experimental, H/~=1/20 X
SEALOADS, H/~=1/20 -----
L~
. 10
cn
i~
>
5
C'
~, 40
c'' 30
~ 20
> 10
\/L
15
10
1 .4
1 .2
0.8
0.6 - 9~~=~
0.6 0.8 1 1.2
\/L
15 I
0.6 0.8 1 1
\/L
.sn I
I _=~'W~ i
o
0.6 0.8 1 1.2
.2
_ _ c'' 30
~ _ _ ~ 20
5 _ ~ > 1C
0.6 0.8 1 1.2
\/L
Figure 6: Predicted motions and sea loads
8
O 1 1
0.6 0.8 1 1.2
\/L
l regular waves, ~ = 165°, Fn=0.06.
OCR for page 90
1.4 _ I I I I _ 1.4
1 .2 _ _ 1 .2
1 _ _ 1
~~ 0 8 ~ x 0 8
02 ~ ~ O X - 02
O O
0.8 1 1.2 1.4 1.6
\/L
2.5
15
_1 1 1 1 ~
_ .~
W~ x — _
~ X~
~ 1 1 1
0.8 1 1.2 1.4 1.6
\/L
L`, 20 _ _ Lo
c~ c~
`u 15 _ _
`~ 1 0 _ _ i~
O ~1 -g >m 1 ~
0.8 1 1.2 1.4 1.6 0.8 1 1.2 1.4 1.b
\/L \/L
20
15
10
5
o
25
20
~ 15
cn
`~ 10
S 5
20
15
10
5
o
O -
I ~ ~ ~ ~1 ~.
0.8 1 1.2 1.4 1.6
\/L
c
4C
~ 3C
cn
i~ 20
Ln
> 10
o
_, =:=~=
_ ~ ~ ~ ~ ~ ~ ~
0.8 1 1.2 1.4 1.6
\/L
4C
3C
2C
~ 10
~ I I I I ~
o
0.8 1 1.2 1.4 1.6
\/L
50
_ ~ 40 _
~== __4 ~ 20 t --- ~
3~ Q ~ _ S 10
I I I I n
0.8 1 1.2 1.4 1.6
~1
_ ~ ~ ~ ~ q--~
1 1 1 1
0.8 1 1.2 1.4 1.6
\/L
50 1 1 1 1
:: ' =~__
C
1 1 1 1
0.8 1 1.2 1.4 1.6
\/L
Figure 7: Predicted motions and sea loads in regular waves, ~ = 180°, Fn=0.12 (Legend: 0 experimental,
H/~= 1/30; x experimental, H/~= 1/20; SEALOADS, H/~= 1/30; -—SEALOADS, H/~= 1/204.
9
OCR for page 91
3 ~
2.5 _
Lo
l
X
, 1.5 t ~ ~c ~
A 1 _ 'a ]
0.5 _
O l l l l l
0.8 1 1.2 1.4 1.6
\/L
1 .4 _
1 .2 _
Go
JO
0.8
0.6
0.4
0.2
2.5
0.5
O
3
2.5
o
(n
~ 1.5
(n
Q
2
1
0.5
o
1 .4
1 .2
_ ~
1 ~
0.8 1 1.2 1.4 1.6
\/L
0'-~--
0.8 1 1.2 1.4 1.6
\/L
_ ~
— _ _ _ _ _ _ .
~ 1 1 1
0.8 1 1.2 1.4 1.6
\/L
1
o
a' 0.8
(n
`u 0.6
0.4
0.2
o
3
2.5
2
o
(n
a, 1.5
(n
i~
Q
0.5
o
-O ~Q
~ 1 1 1
0.8 1 1.2 1.4 1.6
\/L
Figure 8: Predicted pressures on six sensor locations in regular waves, ~ = 180°, Fn=0.12 (Legend: o
experimental, H/~= 1/30; x experimental, H/~= 1/20; SEALOADS, H/~= 1/30; -—SEALOADS,
H/~= 1/20)
10
OCR for page 92
REDD1 2-30-1 80-05
0.5 1 , ,
0 50 100 150 200
n
I I as expected, computed pressures show peculiarities
at locations near the stern.
Ann
l An 200
1 50 200
Figure 9: Predicted time series of heave, pitch, and
pressures at sensors 6 and 11 (~/L = 1.01, H/A =
1/30, id= 180°, Fn=0.124.
CONCLUSIONS
Validation of the computer program SEALOADS
on ship motions, hydrodynamic pressures and sea
loads has been carried out for CPF. The ship
motions, sea loads and hydrodynamic pressures
predicted by SEALOADS, in general, agree well
with experimental results under the following con-
ditions: a) up to medium speed (Fn=0.204; b)
medium waves (0.7 < A/L < 1.64; and c) wave
steepness up to 1/20.
Some of the differences between the computed
sea loads and test data may be due to the fact
that the physical model was flexible whereas the
SEALOADS computations were based on the as-
sumption of a rigid ship.
The computed results show deviation from
measured data as forward speed increased, espe-
cially in short waves: A/L < 0.59, long waves:
A/L > 1.94, and steep waves: H/A > 1/20. Also
Since the draft of CPF is very shallow at the
stern, i.e., the instantaneous wetted surface can
change drastically during ship motion, the assump-
tion of mean wetted-surface would be no longer
valid, especially for large waves. As a step fur-
ther to improve the current code, the varied added
mass, damping and restoring forces, and the re-
sponse functions should be taken into account for
the varied wetted surfaces. The effect of varied
added mass is being examined by the CMVDR re-
search group and has shown promising improve-
ment to the current code for ship seakeeping com-
putations. Stokes waves should be used for the
computation of ship responses in steep large waves
in order to examine the nonlinearity in responses.
ACKNOWLEDGMENTS
The authors are grateful for the research support
from the Defence Research Establishment Atlantic,
Canada. The useful discussions with Mr. Sam
Ando and Dr. Xin Lin are very much appreciated.
REFERENCES
Ando, S. (20004. Wave-Induced Motions, Loads
and Hydrodynamic Pressures on a Model Frigate.
DREA Technical Memorandum, in review.
Beck, R. F. and Magee, A. (19904. Time-Domain
Analysis for Predicting Ship Motions. Proceedings
of IUTAM Symposium, Dynamics of Marine Vehi-
cles and Structures in Waves, London.
Beck, R. F. and King, B. (19894. Time-Domain
Analysis of Wave Exciting Forces on Floating Bod-
ies at Zero Forward Speed. Applied Ocean Re-
search, Vol. 11, pp.19-25.
Beck, R. F. and Liapis, S. J. (19874. Transient
Motion of Floating Bodies at Zero Forward Speed.
Journal of Ship Research, Vol. 31, pp.164-176.
Chang, M. S. (19774. Computation of Three-
Dimensional Ship-Motions with Forward Speed.
Proceeding Second International Conference on
Numerical Ship Hydrodynamics, University of Cal-
ifornia, Berkeley, pp.124-135.
Clement, A. H. (19984. An Ordinary Differential
Equation for the Green Function of Time-Domain
Free-Surface Hydrodynamics. Journal of Engineer-
11
OCR for page 93
ing Mathematics, Vol. 33, pp.201-217.
Cong, L.Z., Huang, Z.J., Ando, S. and Hsiung,
C.C. (19984. Time-Domain Analysis of Ship Mo-
tions and Hydrodynamic Pressures on a Ship Hull
in Waves. 2nd International Conference on Hydroe-
lasticity in Marine Technology, Fukuoka, Japan.
Cummins, W. E. (19624. The Impulse Response
Function and Ship Motions, Schiffstechnik, Vol. 9,
pp.101-109.
Danmeier, D. G. (19994. A High-Order Panel
Method for Large-Amplitude Simulations of Bodies
in Waves. Ph.D. thesis, Massachusetts Institute of
Technology.
Finkelstein, A. (19574. The Initial Value Problem
for Transient Water Waves. Communications on
Pure and Applied Mathematics, Vol. 10, pp.511-
522.
Guevel, P. and Bougis, J. (19824. Ship Motions
with Forward Speed in Infinite Depth. Interna-
tional Shipbuilding Progress, Vol. 29, No. 332,
pp.105-117.
Huang, Z.J. and Hsiung, C.C. (19964. Nonlinear
Shallow Water Flow on Deck Coupled with Ship
Motion. Proceedings of the 21st Symposium on
Naval Hydrodynamics, Trondheim, Norway.
Huang, Y. (19974. Nonlinear Ship Motions by a
Rankine Panel Method. PhD dissertation, Depart-
ment of Ocean Engineering, Massachusetts Insti-
tute of Technology.
Inglis, R. B. and Price, W. G. (19824. A Three-
Dimensional Ship Motion Theory - Comparison
between Theoretical Prediction and Experimen-
tal Data of the Hydrodynamic Coefficient with
Forward Speed. Transaction Royal Institution of
Naval Architecture, Vol. 124, pp.141-157.
Liapis, S. and Beck, R. F. (19854. Seakeeping Com-
putations Using Time Domain Analysis. Proceed-
ings of the Fourth International Conference on Nu-
merical Ship Hydrodynamics, Washington, D.C.
Lin, W. M. and Yue, D. K. (19944. Large Am-
plitude Motions and Wave Loads for Ship Design.
Proceedings of the 20th Symposium on Naval Hy-
drodynamics, Santa Barbra, California.
Lin, W. M. and Yue, D. K. (19904. Numerical Sim-
ulations for Large Amplitude Ship Motions in the
Time Domain. Proceedings of the 18th Symposium
on Naval Hydrodynamics, Ann Arbor, Michigan.
Magee, A. (19944. Seakeeping Applications Using
a Time-Domain Method. Proceedings of the 20th
Symposium on Naval Hydrodynamics, Santa Bar-
bra, California.
McTaggart, K., Datta, I., Stirling, A., Gibson, S.
and Glen, I. (19974. Motion and Loads for a Hy-
droelastic Frigate Model in Severe Waves. Trans.
SNAME, pp.427-453.
Ogilvie, T. F. (19644. Recent Progress toward
the Understanding and Prediction of Ship Motions.
Proceedings 5th Symposium on Naval Hydrody-
namics, ONR, Washington, D.C., pp.3-128.
Qiu, W. and Hsiung, C. C. (19994. Theoretical
Manual for SEALOADS version 1.0 - a Computer
Program for Prediction of Nonlinear Ship Motions,
Sea Loads and Pressure Distribution in the Time
Domain. Technical Report NAP- 1999-005, Centre
for Marine Vessel Development and Research, Dal-
housie University, Halifax, Nova Scotia, Canada.
Stoker, J. J. (19574. Water Wave. International
Science Publishers, Inc., New York.
Wehausen, J. V. (19674. Initial Value Problem for
the Motion in an Undulating Sea of a Body with
Fixed Equilibrium Position. Journal of Engineer-
ing Mathematics, Vol. 1, pp.1-19.
Wehausen, J. V. (19714. The Motion of Floating
Bodies. Annual Review of Fluid Mechanics, Vol.
3, pp.237-268.
Wehausen, J. V. and Laitone, E.V. (19604. Surface
Waves. Handbuch der Physik, Springer-Verlag,
Vol. 9.
12
OCR for page 94
Legend
1 .4
1 .2
0.8
0.E
0.4
0.2
o
. _
; - :'
0.6 0.8 1 1.2
\/L
0.8 1 1
0.7 _ _
0.6 _
03L:
o
0.6 0.8 1 1.2
\/L
~, 20 _
c~
`~ 15 _
cn
`~ 10 _
S 5 _
25
0 20
cn
i~
>
15
10
5
Experimental, H/~=1/30 O
SEALOADS, H/~=1/30
Experimental, H/~=1/20 X
SEALOADS, H/~=1/20
1 .4
1 .2 _
~x08 L~—
o
0.6 0.8 1 1.2
\/L
15 I
. 10
cn
i~
>
0.6 0.8 1 1.2
\/L
~, 20 _ _
c'' 1 5 _ _
~ 10 _ _
>m 5
o
0.6 0.8 1 1.2
\/L
50
_ _ c'' 30 _
_ _ ~ 20 _
_ ~ > 10 _
O ~ ~ ~ ~ ~ ~ ,
3.6 0.8 1 1.2
\/L
~ _ _
~--~--~ ~
0.6 0.8 1 1.
\/L
.sn l l
~, 40 _ _
c'' 30 _ _
(a 20 _ _
> 1 0 ~
0.6 0.8 1 1.2
\/L
1 1
0 40 _
O 1 1
0.6 0.8 1
\/L
Figure 10: Predicted motions and sea loads in regular waves, ~ = 135°, Fn=0.12.
13
1 .2
OCR for page 95
1.4 _ I I I
1 .2 _
1 _
0.8 _
0.6 _
0.6 0.8 1
\/L
1.2 1.4
Lc, 20 _ _
`u 1 5 _ _
`u 1 0 _ _
> 5
o
0.6 0.8 1 1.2 1.4
\/L
Lc, 20 .
c'' 1 5 .
~ 10 .
> 5
20 _
15 _
10 _
5 _
_ ~
O 1 1 1
0.6 0.8 1 1.2 1.4
\/L
25
_ - - _ ~_
O
o 20
~ 15
cn
i~ 10
> 5
1 1 1
0.6 0.8 1 1.2 1.4
\/L
O ~ ~ ~ ~ ~.
0.6 0.8 1 1.2 1.4
\/L
-
1.4 _
1 .2 _
0 8 _
02
0.6 0.8
10
5
°r
Lc, 40 _
c'' 30 _
~ 20 _
S
10 _
~_~-~--~_~_
1 1 1
0.6 0.8 1 1.2 1.4
. .
, . .
_
L~ 40 _
~ 30 _
cn
`u 20 _
Ln
S 10
o 4C
c,, 30
i~ 20
Ln
~-~-~--~U
O
ns n~
~ ~Q
0.6 0.8 1
\/L
Figure 11: Predicted motions and sea loads in regular waves, ~ = 180°, Fn=0.20 (Legend: o experimental,
H/~= 1/30; x experimental, H/~= 1/20; SEALOADS, H/~= 1/30; -—SEALOADS, H/~= 1/204.
14
OCR for page 96
DISCUSSION
D. Murdoy
Nahona Research Commci /Institute for
Ma me D namics, Cmada
The auhhou are to be coug ahdated for
mahug progress iu hhe very c mplex md
dhfficu t task of improving aud vs idabug
uumeucal predhchou medhods to assess
opeu hous perfommauc aud loads imposed
ou uew sh~p des~gms m vanou
euv roumenh I coudhhous
We wou d like to mske hhree observahous,
each les hug to a queshou
The fiu t couc ms hhe u uge of coudhhous
umder which hhe hme-domam predhchous
were validated lu validabug hheir
SEALOADS hme domsiu code hhe auhhors
have selected
respouses iu regu ar waves wihh modeu te
wave heighh aud low Froude uumbers
While mch validahou
demoushvtes hhe perfommauce of hhe
program for much of hhe operahous u uge
for hhe ship, it does uot
exe cd hhe predhchou expech hous of a
linear ship hheory based program We
wouder if hhe auhhou have
hied t validate hheir code for predhchous of
perfommauce iu inegu ar waves, for higher
Froude uumber aud
possibly exheme sea coudhhous? The
uec ssary expeumeut dah are available
firom tesh camed out at
IMD wihh hhe same fiigate model u cd by
hhe auhhou
O r secoud observahou c ucems hhe u e of
qualih hve validahou cuteua The majouty
of hhe validahou shudhes, such as hhat
preseuted iu hhis paper, have u cd qus ih hve
uoums such as: good, sahsfactory, fair aud so
ou to desc ibe gooduess of fit betweeu hhe
uumencal simu ahou aud hhe expeumenh]
resu h We wou d like to ask hhe auhhou if
hhey have cousidered hhe u e of qumhh hve
validahou c iteua wheu judging hhe
compmsonofhhenumencal md
expenmenkl resu h? A key pu chcal isme
is to decide how close hhe uumeucal md
expenmenh I resu h ueed to be for hhe
ag eemeut to be cousidered, firom a ship
desigmer s peu pechve, "sahsfactory" For
example, s hhough hhe sms I scale of fig res
5 to 8 makes it dhfficu t to mske a precise
quandh hve evaluahou of hhe dhffereuces, it
appeau hhat pred cted md meas red loads
close to amidships dhffer, by as much as
100% Shou d hhis be cousidered fair,
sahsfactory or umsahsfactory, importaut or
umimpor mt?
Third y, We wou d like to buefly sddress
hhe is me of umc rtainty The resu t of any
expeumeut or simu ahou is uot a umiqme
value, but u hher a u uge wihhiu which hhe
res value is located wihh a defiued level of
coufideuc While it is well knowu hhat all
meas remeutaudcalcuahouare mbjectto
umcerh inly, hhis knowledge is uot ofteu u cd
m assessmg compausous of uumeucs
simu ahous aud resu h of expeumenh Au
umcertainty analy is is especially importaut
iu any process for validahou of uew
simu ahou medhods A fommal umcertainty
aus yses wou d also preseut au oppor mity
to evaluate qus ity of hhe dah, to idendfy hhe
biggestsources of enor audgive dhrechou
for fuh re improvemenh iu expeumeut
techmques or uumeucal medhods We
wouder if hhe auhhou have camed out such
au aus ysis or if hhey have plau t do so iu
fuh re?
lu couclu iou, we wou d like to
acknowledge hhe importauce of hhe work
being camed out by ITTC c mmittees to
develop g idelines aud procedures for
expeumenh aud uumeucs code validahou,
includ ug umcertainty analysis aud
publishiug beuchmark model aud full scale
data This work is au essenbs foumdahou
for eusuring hhat hheoredcal aud
expeumenh~ly based predhchou of ship
perfomm mce may be u cd wihh coufideuce to
meet hhe ueeds of pu chcal ship desigmers
aud ship opeu tou
OCR for page 97
AUTHOR'S REPLY
First of all, we would like to th mk all discussers
for their thoughtful remarks Ed comments
In reply to questions Raised by M Murd y: (1)
on of the goals of SEALOADS time domain
code is to predict the ship motion responses
under extreme sea conditions We are in the
process of extending the validation to extreme
seas Ed Regular waves (2) We bay
considered the use of a qu mtitativ validation
criterion, the total-factor-en or IPEI (Ando,
199S) The TFE analysis has been used to
validate our fiequen y-domain code,
WA ELOAD Am, et al, 1999) Although we
did not apply it when examining the mmmerical
Ed experimental recolor at f is time, it is our
intention to carry out TFE analysis for further
validation Sea loads close to the midship section
are import mt, but the computed recolor as showm
in Figmes 5 to 5 are unsatisfacto y, Ed the
reason for this will be m. in pled We are
contmuing to refix the program to in ease its
efficiency Ed accuracy (3) We bay not
considered un ertamty analysis yet, but would
I ke to in She future
DISCUSSION
M Thin
University of Califo nia, Santa Barbara,
USA
I wonder whether you Ho ght about
st dying the mohon of ships in wave g oups
(modulahng waves) where Here is in the
ocean a considerable accumulahon of
ene gy at the peak of She wave g oup It is
not difficult to create wave g o ps in t wing
talks ant test ships m Hem
AUTHOR'S REPLY
We agree with Professor Tulm that wave groups
could be considered Ed in orporated into She
code
ADDITIONAL REFERENCES
Ando, S. (1995) Qu notification of correction of
predicted Ed measured tr msfer fun tions for
ship motions Ed wave loads R1NA
Intemational Conferen e on Ship Motions Ed
Maneuv mblity, London
Qm, W. Ando, S. Ed Hsiung, CC (1999)
Applying the FE analysis to validate the
software WA LOAD 22 International
Towing Tmk Conferen e, Soul, Korea Ed
Sh mghai, China
Representative terms from entire chapter:
ship motions
