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OCR for page 595
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Validation of Numerical Method for Predicting
Hydrodynamic Characteristics of a High-speed Ship
H. Orihara (Hitachi Zosen Corporation, Japan)
ABSTRACT
The capability of a CFD code is validated for predict-
ing the hydrodynamic characteristics of a high-speed
ship advancing in calm water. The CFD code
WISDAM-VIII is used for the validation study.
practical high-speed ship hulls advancing in calm
water over a Froude number range from 0.4 to 1.0. The
validation of the code is conducted by comparing the
computed results with a set of experimental data for a
number of mono-hull type hull forms. Theses
comparison include ship running attitudes, wetted
surface at running condition, total resistance
coefficients and surface pressure distributions. Also the
code is validated for the prediction of the effects of
hull shape on the hydrodynamic characteristics of the
ship and the results are compared with the available
experimental data.
method. These methods were capable of treating the
change of running attitudes and computing the flow
about a hull in the free to sink and trim condition. It
was reported that the computed results from these
methods agreed qualitatively well with the
experimental data.
In this study, simulations are carried out for More recently, with the development of computer
- ~ ~~ ~ ~ ~~ ~ ~~ ~ ~ ~ ~ hardware and the numerical solution methods, CFD
simulation methods have been developed, which is
applicable for the prediction of flows about a
high-speed ship, such as Subramani et al (2000), Lin
and Percival (2000), Orihara and Miyata (2000~. These
methods were based on the solution of
Reynolds-Averaged Navier-Stokes (RANS) equations.
In contrast to the above-mentioned theoretical methods,
these methods had the advantages in that they could
treat the nonlinear free-surface conditions without any
linearized approximations and that the viscous effect
can be taken into account.
The computed results from these CFD simulation
methods showed that the trends in the measured
running attitudes data could be predicted correctly and
the quantitative agreement between the computations
and the experimental were generally well. However,
these computations were conducted mainly for low
speed cases in the context of a high-speed ship, i.e. at
Froude number (Fn) below 0.65.
The principal objective of the present study is to
validate a CFD code for predicting the hydrodynamic
characteristics of a high-speed ship advancing in calm
water. In the present study, WISDAM-VIII code is
selected for the validation. WISDAM-VIII was
originally developed at the University of Tokyo by
Orihara and Miyata (2000) for the performance
prediction of a high-speed ship. The code has been
used for the performance prediction for practical
high-speed ships in Hitachi Zosen Corp. The code
solves the Reynolds-Averaged Navier-Stokes (RANS)
equation and continuity equation with the nonlinear
free-surface conditions. The code has already validated
for some cases of high Froude number flows about
high-speed ship models, including wave height near
INTRODUCTION
The prediction of hydrodynamic characteristics of
a high-speed boat advancing in calm water has been
challenging task due to the complex flow features
around a hull. From a hydrodynamic point of view,
these complexities are consisted of two distinctive
features. One is the highly nonlinear waves generated
about a hull, and the other is the change of running
attitude with the increase of ship speed. Due to these
flow features, there has been little work on the
development of the prediction method of flows and
performance of a high-speed ship, and the performance
prediction of a high-speed ship has been made almost
all cases by means of model tests.
In recent years, several theoretical prediction
methods for high-speed ships has been developed, such
as Xia (1986), Larson and Xia (1987), Wang et al
(1996), Eguchi (1998), Kawashima (1998), Brizzolara
et al. (1998~. Most of these method were based on the
linear potential theory and using the Rankine-source
OCR for page 596
the semi-planing boat at Fn = 0.513 and the running
attitudes and resistance coefficient of semi-planing
boats at Fn = 0.6. Most of these validation cases,
however, are mainly concerning the cases of relatively
lower speeds. The systematic validation of the
predicted running attitude and resistance attitudes,
which is of great importance for the evaluation of the
performance of high-speed ships, has been conducted
as yet. Also the validation of surface pressures have
not been conducted. So in the present study, the
validation of the surface pressures, running attitudes
and resistance coefficients are conducted for a number
of mono-hull type hull forms over a wide range of Fn
from O.4to 1.0.
In the next section, the outline of WISDAM-VIII
will be briefly described. The descriptions of
experimental data used for the validation study will be
followed. Then, comparisons of computed results and
experimental data are presented. Finally, some
conclusions will be mentioned.
NUMERICAL METHOD
In the present study, computations of flows around
high-speed hull forms are carried out using
WISDAM-VIII (Orihara and Miyata, 2000~. Since
details of the computational procedure used in the code
can be found in Orihara and Miyata (2000), the outline
of the code is described in the following.
The code solves the RANS equation and
continuity equation. These can be written in the
following conservative form for time-dependent
arbitrary control volume Q(t) as:
~' A,) u dV = im( ) dS - T.
0t [ea(,)dS-(U-V), (2)
where u is the velocity vector, v is the velocity vector
of the face of the control volume. All the variables are
made dimensionless with respect to the constant
reference velocity Uo and the ship length
on waterline Let . The stress tensor Tis written in
ALE form as:
T = -¢I-tU-v~u+—[VU+(Vu) ]-U'u (3)
where I is the identity tensor, v is the gradient opera-
tor, ()T denotes the transport operator, -utu' is the
Reynolds stress. ~ is the nondimensionalized pressure
excluding the hydrostatic pressure defined as:
Fn2
(4)
where z is the vertical position. The stress term which
comes from the Reynolds stress is incorporated in the
diffusion term using the turbulence model of eddy
viscosity type. In the present study, the algebraic
Baldwin-Lomax turbulence model is used.
A finite-volume method is used to discretize the
governing equations (1) and (2~. Except for the
convective term, all the terms of Eq. (2) are
approximated with second-order accurate central
differencing, while the convective term is approximat-
ed with third-order accurate upwind differencing.
The code employs a body fitted coordinate system
and uses single-block H-O grid topologies. The
computational grid are generated algebraically. One of
the principle features in grid generation of
WISDAM-VIII is specifying the grid point clustering
along both the hull surface and the undisturbed free
surface such that the grid spacing near these
boundaries is sufficiently small for resolving free
surface waves and flow separation behind the transom
stern.
For a time-accurate solution of the incompressible
flow, pressure and velocities are coupled by a MAC-
type solution algorithm and a Rhie-Chow interpolation
scheme is employed to avoid the checkerboard type
oscillations of the pressure field.
The free-surface treatment is based on the
density-function method (Miyata et al. 1988,
Kawamura and Miyata, 1994), which is a kind of a
so-called front capturing method and corresponds to a
generalized interpretation of the VOF method.
In WISDAM-VIII, the kinematic condition is
satisfied by solving the following transport equation
for the density function Pm
t(') ~ U dV |~(,)dS Pm (u v) (5)
where Pm is the density function which is defined as
;~1, in fluid region
m tO, in external region
This implies that Pm is unity at any point occupied by
the fluid and the value of Pm changes from unity to
zero at the free surface. In WISDAM-VIII, Eq. (5) is
descretized by the finite-volume method and solved in
a time marching manner and the free surface location
OCR for page 597
is determined as the iso-surface of Pm=O.S.
The dynamic condition, which denotes the stress
equilibrium at the free surface, is approximately
satisfied by the extrapolation of the pressure and
velocity components above the free surface.
The change of running attitude is treated by
combining the solution of the equation of the rigid
motion of the hull with the flow solution. This is
performed by calculating the solution of flows and
rigid motions iteratively. At each time step, the force
and moment acting on the hull were obtained by
integrating the pressure and shearing stress on the
whole wetted surface. Then the equation of motion for
heave and pitch motions are integrated in time and the
new position of the hull is obtained. After obtaining
the ship position, computational grid is regenerated in
accordance with the movement of the hull surface. The
effect of grid movement is accounted for in the flow
solution by including the velocity vector of the face of
the control volume v in Eqs. (2), (3) and (5). These
procedure are repeated until the motion in heave and
pitch are converged. Then the running attitudes of the
hull are obtained as the converged solution of the
heave and pitch motion.
RESULTS AND DISCUSSION
In the present study, the WISDAM-VIII code is
validated for surface pressure distributions, running
attitudes and hull resistance. The validation of the code
is conducted by comparing the computed results with a
set of experimental data for selected mono-hull type
high- speed ship hull forms. Computations are carried
out for the hulls advancing over a range of Froude
number, based on the length on waterline, from 0.4 to
1.0. Also the code is validated in terms of the
capability of predicting the effect of the change in hull
shape on the running attitudes and resistance of the
hull. The details of the Experimental data, the
condition of computations and the representative
validation results are described in the following.
Experimental data
In the present study, experimental data for two
selected hull forms of high-speed ships are used for the
code validation.
For the validation of computed running attitudes
and resistance coefficients, experimental data for NPL
round bilge series hull forms (Marwood and Bailey
1969, Bailey, 1974) is used. The body plan and
principal dimensions of the basic form of the series,
NPL Model lOOA, are given in Table 1 and Fig.1,
respectively.
Table 1 Principal dimensions of NPL Model lOOA.
Length on water line ( L'`, )
Breadth ( B ~
~ , .
Draft ( ~ )
~ ,
Block Coefficient (c )
~ h .
Longi. Cent. of Buoyancy ( LOB )
2.54 m
0.4064 m
0.140 m
0.397
6.4% Lo, aft
NPL series models were derived by producing
geometric variations of the basic form (NPL Model
lOOA) and all have constant block coefficient,
prismatic coefficient, maximum section area coeffi-
cient and longitudinal center of buoyancy.
In the present study, the basic form (1OOA) and
two derived forms, 80A and 150A are selected for the
validation study. 80A and 150A are the forms having a
same Length to Breadth ratio (L/B = 6.25) as lOOA, L,
and a displacement of 80 and 100 tons for a 30.48 m
ship length, respectively. The comparisons of principal
dimensions between the three models are shown in
Table 2.
Table 2 Comparisons of dimensions between
selected NPL series models.
Model
number
80A
l OOA
_150A
UB B/d Llvil3
6.25 3.63 7.09
6.25 2.90 6.59
6.25 1.93 5.76
cb
_ 0.397
.
0.397
.
_ 0.397
In Table 2, d denotes the draft of the ship, and
L/V/3 denotes the length to displacement ratio
where V is the volume of displacement.
In the validation study, the experimental data for
NPL series models obtained in No. 3 tank of Ship
Division at the National Physical Laboratory (NPL) is
used, which is reported in Marwood and Bailey (1969)
and Bailey (1974). In the experiments, the models
were tested in the bare hull condition. The models
were tested in calm water over a En range from 0.1 to
1.2. The maximum model Reynolds number based
onLwLwas 1.3x107. Each model of the series was
given a level trim at rest and towed horizontally at the
position of the longitudinal center of buoyancy. For
each run, model speed, resistance and running attitudes
were measured. Photographs of the wave profile along
the hull were taken to assist for the assessment of the
OCR for page 598
running wetted surface. Further details of the model
tests of NPL series can be found in Marwood and
Bailey (1969~.
For the validation of computed surface pressure
distributions, the pressure measurements on the hull
surface are conducted in this study. The pressure
measurements are carried out at the Akashi Ship
Model Basin (ASMB) Co., Japan. The towing tank at
ASMB has a length of 200m and a section of 13m
wide and 6.5m depth with a maximum carriage speed
of 6.0 m/sec. The tank tests are carried out with a 4.0
m model of a mono-hull type high-speed ship with a
transom stern, which is designated as Hull B in the
following description. The picture of the model towing
in the tests is shown in Fig.2. The model is fitted with
12 static pressure gauges on the keel line. The pressure
gauges are placed closely near the bow and stern so
that the pressure peaks can be measured in the tests.
The locations of the pressure measurements are shown
in Fig. 3. Initially, the model is given a level trim at
rest. The pressure measurements are carried out at five
different speeds (Fn = 0.434, 0.514, 0.612, 0.685,
0.787~. To check the accuracy of the measurements,
surface pressure distributions measured three times at
each speed. The scattering of the measured data were
within + 1% of the static head at the bottom. The
running attitudes were obtained by measuring the bow
and stern sinkage with two potentiometers mounted on
the bow and stern of the model.
Condition of computations
The computations of models of three NPL series
(80A, lOOA and 150A) and Hull B are performed on
the O-O type structured grid with a total of 168,000
grid points, with 80 points in the axial direction, 30
points in the direction normal to the hull and 70 points
in the girth direction. A partial view of the gird for
NPL model lOOA and Hull B model are shown in Fig.
4 and Fig. 5, respectively. In these figures, grids on the
hull surface, still water plane and the center plane are
shown. The minimum grid spacing normal the hull
surface is set 0.001 LO . The outer boundary extends
eight ship lengths from the center of the hull.
In order to make comparison exactly of the
computed results with the experimental data, the
Reynolds number in the computations should be set the
same value as the experiment. For the case of
high-speed ships with a transom stern, however, since
the flow detaches smoothly at the corner of the
transom stern and stern waves formed continuously
from the bottom of the hull, the boundary layer does
not become so thick as in the case of
displacement-type ships. Thus, it could be considered
that the flows about the hull are not so sensitive to the
Reynolds number. For this reason, in the present study,
a smaller value of Reynolds number, Rn =l.Ox106, is
specified for all the computations to avoid the
numerical instability and save computational expense.
Surface pressure distributions
The computed surface pressures are shown in Figs.
6 - 19. The Froude number is varied from 0.434 to
0.785, and the Reynolds number is set at Rn = 1.0 x 1 o6 .
All the computations are performed with the hull free
to sink and trim. In these figures, pressure is shown in
the nondimensional coefficient c. c. is the
—(Da - —(Da
pressure coefficient excluding the hydrostatic com-
ponents and made dimensionless with respect to the
hydrostatic pressure at the bottom of the midship as
follows:
c" = ~ P d ]. ~
(6)
where do is the midship draught at rest; g is the
acceleration due to gravity, ~ is dimensionless
pressure defined in Eq. (4~. As shown in Eq. (6),
ascot is scaled with Fn, the effect of Fn on surface
pressure distributions can be shown more directly with
Cal than the ones shown in ~
Computed pressure contour plots on the hull
surface are shown in Fig. 6. Since the surface pressure
is only measured on the keel line, surface pressure
distributions are only qualitatively examined for Fn =
0.511 and 0.787. It is seen that surface pressure
decreases rapidly near the stern for all the Froude
numbers. This shows that the surface pressure
decreases to the atmospheric pressure, i.e.
c,k =zS``rnlFn2 ~ where A, is the vertical position of the
transom stern. It is also shown that the smooth flow
detachment at the transom stern is reasonably predicted
by the computation. Also seen in these figures is that
the increased positive pressure region exist at higher
Froude numbers.
The comparison of computed surface pressure
distributions on the keel line for Hull B with the
experimental data are shown in Figs. 7 - 11. In general,
the computed surface pressures agree well with the
. .
exit perimental data, indicating the capability of
WISDAM-VIII for predicting the flow about a
high-speed ship hull form is excellent over a wide
range of Froude number. In particular, computed
surface pressures in the aft part of the hull agree quite
well with experimental data. This may show that the
viscosity has minor effect on the surface pressure
OCR for page 599
distributions on the high-speed ships considered. On
the fore part of the hull, however, the computed results
deviate from the experimental data with the increase of
Froude number, as shown in Figs. 10 and 1 1. A
probable cause of this disagreement is that the
computed grid used is not sufficiently fine for
capturing the pressure.
The effect of Froude number on surface pressure is
shown in Figs. 12 - 15. In these figures, pressure
coefficient Cal is plotted as a function of Fn at four
points on the hull surface. The locations of these points
are shown in Fig. 3. It is seen that the computed results
agree qualitatively well with the experimental data. At
point Pi which is located 0.025 ~ from the transom
stern corner, c,~ value is nearly constant at speeds Fn >
0.6. This may implies that the vertical position at the
stern is almost constant at these speeds. At points P5,
P6 and P8, which are located 0.2~, 0.3 ~~ and
0.8 ~ from the transom stern corner, respectively,
c,k values increase with the increase of Fn. This is
consistent with the increase of rise of the hull shown in
Fig. 19, which is considered to be due to the increase
in dynamic lift acting on the hull.
Running attitudes
The prediction of running attitude of the ship is
made for NPL hull 80A, 1 00A, 1 50A and Hull B. The
comparisons of computed running attitudes, which
include running trim angle and rise at the longitudinal
center of gravity (LCG), with the experimental data are
shown in Figs. 16 - 19.
The computed running attitudes agree fairly well
with experimental results. In particular, the computed
running attitudes for Hull B agree quite well with the
experimental data. Since computed surface pressure
distributions correlate fairly well with the experimental
data as shown in Figs. 7-11, the agreement of running
attitudes between the computation and the experiment
is considered to be reasonable. For the NPL series
cases, however, some discrepancies are seen in the rise
at LCG, which is shown in lower graph in each figure.
Except for the case of NPL 80A at Fn>0.8,
computations underpredict the rise at LCG by about
0.001. While no detailed investigation for this
discrepancy is conducted, one of the probable cause is
measurement errors since the trend in the computed
rise is almost same as the experiment.
Wetted surface area
The computed wetted surface areas are compared
with the experimental data as shown in Figs. 20 - 22.
The computed wetted surface area So is obtained by
integrating the density function over the wetted surface
of the hull as follows:
so = f Pm~ dS
H
(7)
where SH denotes the surface of the hull; Pm iS the
density function; n =(nx, ny, n ~ is the unit normal
vector to the hull surface.
Due to a change in running attitude and large-
amplitude bow waves developed along the hull surface,
the wetted surface area of high-speed ships changes
with Fn. As described earlier, since the measured
wetted surface area were obtained from photographs
and it is difficult to measure the edge locations of bow
spray on the hull, it is difficult to make direct
comparison of the wetted surface area between the
measurements and computations. Thus the
comparisons are made only qualitatively. The
computed wetted surface areas correlate fairly well
with the experimental data.
Resistance coefficient
To make a direct comparison of computed
resistance coefficients with the measured ones, total
resistance coefficient CTM] was estimated from the
computed flow data. Since the computations were
conducted at smaller Reynolds number than the
experiment, the correction of the difference of
Reynolds number had to be made on the computed
results. To this end, the model-scale total resistance
coefficient of the hull CTML is divided into two parts,
frictional resistance coefficient CFM! and residuary
resistance coefficient A, respectively. These
coefficients are obtained by the following resistance
breakdown:
RTM
C =
= CRL + CF.~L
(8)
where RTM is the total resistance; p is the density; u is
the velocity of the ship; So is the wetted surface of the
hull. It is noted that the frictional resistance
Coefficient CFMZ is made dimensionless with the
reference area of ~,,7'
The residual resistance coefficients C.R1 is obtained
by integrating the longitudinal component of the static
pressure p over the hull wetted surface as follows:
CRL = PU2LWL I PmPnx dS
(9)
OCR for page 600
The frictional resistance coefficient CAM] is obtained
by using the frictional resistance coefficient of a flat
plate CFO as follows:
CT7I~. = (—)CFO
,where CFO is evaluated using the Schoenherr line as:
= loge (Rn x CFO ~
(10)
(1 1)
The comparisons of resistance coefficients bet-
ween the computations and experiments for NPL
models 80A, 100A and 150A are shown in Figs. 23 -
25. In these figures, the computed total resistance
coefficients estimated using Eqs. (7) - (11) are
compared with the measured total resistance coeffi-
cients. Also shown in these figures is the computed
frictional resistance coefficient CFM] estimated using
Eqs. (10) and (11). As can be seen from Figs. 23 - 25,
the computed results correlate fairly well with the
experimental data for all the three different models
selected. This is surprising since the present
computations are carried on relatively coarse grid
consisting of 168,000 grid points. In the case of
computations for low-speed displacement type ships,
the resistance coefficient, in particular, the residual (or
wave-making) resistance is known to be quite difficult
to predict. In general, the use of fine grid consisting of
nearly million grid points is considered to be required
for the accurate prediction of the resistance coefficients
for this type of ships. The reason for this may be
considered as follows. For high-speed ships running
with the dry transom, since the pressure increase in the
aft part of the hull are not occurred as shown in Fig. 6,
so the pressure integral in Eq. (9) can be made
accurately on the coarse grid. Also seen from Figs 23 -
25 is that the frictional resistance component becomes
predominant in the total resistance with the increase of
En and that the resistance coefficient is almost same
over a En range from 0.6 to 1.0.
From the results described above, it may be
considered that the resistance prediction method used
in the present study which is based on Eqs. (7) - (l l),
is valid for high-speed ships of mono-hull type. Also it
may be considered that the effect of viscosity on the
residual resistance is relatively small and that the
resistance coefficients can be estimated with certain
degree of accuracy from computations conducted at
Reynolds numbers lower than the experiment. From a
practical point of view, this is advantageous in that the
time required for computations can be reduced and
design alternations by means of computations can be
made more easily.
Effect of hull shape on running attitudes and
Resistance coefficient
To validate the capability of predicting the effect
of the change in hull shape on the running attitudes and
resistance coefficients, the variations of the running
attitudes and resistance coefficient with the hull form
factor are considered. Since the NPL series models
cover a wide variety of hull form parameters, e.g. L/B,
B/d, LIV~'3, validations can be conducted on the
effect of these hull form parameters. Among theses
factors, the length to displacement ratio LIV~'3, which
is known to be the predominant factor on the running
attitudes and resistance of high-speed ships, are
selected for this validation study.
The effect of LIV"3 on the running attitudes and
resistance coefficients are shown in Figs. 26 - 31 for
the selected Froude numbers of 0.6, 0.8 and 1.0.
Running attitudes, running trim angle and rise at LCG,
are plotted functions of LIV"3 and compared with the
experimental data in Figs. 26 to 28. In general, the
computed results show well agreement with the
experimental data for all the Froude numbers.
Although some discrepancies are observed in rise, the
trend in the experimental data, i.e. the variations of
running attitudes with LIV"3 are predicted favorably
well by the computations. In Figs. 29 - 31, total
resistance coefficient c, is plotted as a function of
LIV"3 and compared with the experimental data. As
shown in these figures, the computed results agree
quite well with the experimental data as in Figs. 22 -
24 shown earlier. From these comparisons, it may be
considered that the present code has capability of
predicting the effect of change in hull shape for
high-speed ships considered.
CONCLUSIONS
Validation of the CFD code WISDAM-VIII is
carried out for a number of mono-hull type high-speed
ship hull forms. Between the computed results and
experimental data, comparisons are made of surface
pressure distributions, running attitudes and resistance
coefficients. The computed surface pressure
distributions agree well with the experimental data.
The computed running attitude also agree well with the
experimental data, except that the computed rise at
LCG for NPL series models are slightly underpredicted.
The estimated total resistance coefficients correlate
well with the experimental data. The running attitudes
and the resistance coefficient are also validated in
OCR for page 601
terms of the effect of the length to displacement
ratio LIVE, and it is shown that the code can predict
the effect of L/V~'3 on these quantities with reasonable
accuracy. From these results, although the degree of
accuracy of the code is not completely satisfactory, and
further study is needed to improve the code, it is
confirmed that the capability of the present code is
generally sufficient to analyze the flow about a
mono-hull type high-speed ship over a En range from
0.4 to 1.0 and that the present code is very promising
as a design tool for predicting the still-water
performance of mono-hull type high-speed ships.
ACKNOWLEDGEMENTS
The author would like to thank Mr. Mitsuyasu Na-
gahama and Mr. Kazuya Hatta of Hitachi Zosen Corp.
for their valuable help and discussions provided during
this research. The author wishes to express his
gratitude to the member of the test section of Akashi
Ship Model Basin Co. for conducting the model test of
Hull B.
REFERENCE
Bailey, D., "The NPL High Speed Round Bilge
Displacement Hull Series," Maritime Technology
Monograph, No.4, RINA, London, 1974.
Brizzolara, S., Bruzzone,D., Cassela,P., Scamardella,
A., and Zotti, I., "Wave Resistance and Wave Patterns
for High-Speed Crafts; Validation of Numerical
Results by Model Tests," Proceedings of the
Twenty-Second Symposium on Naval Hydrodynamics,
Washington, D.C., 1998, pp. 69-83.
Eguchi, T. "On the Prediction of High-Speed Boats by
a Rankine-Source Method," Transaction of the
West-Japan Society of Naval Architects, No. 95, Mar.
1998, pp. 9-16 (in Japanese).
Kawamura, T., and Miyata, H., "Simulation of
Nonlinear Ship Flows by Density-Function Method,"
Journal of the Society of Naval Architects of Japan,
Vol. 176, Dec. 1994,pp. 1-10.
Kawashima, T., and Suzuki, S., "Development of
Program based on Rankine-Source Method for
Transom-Stern Hull Forms," Bulletin of National
Research Institute of Fishery Engineering, No. 19, Mar.
1998, pp. 61-70 (in Japanese).
Larsson, L., and Xia, F., "Numerical Hydrodynamics -
A Useful Complement to Model Testing," Proceedings
of the Third Symposium on Practical Design of Ships,
London, 1987, pp. 171-183.
Lin, C.W., and Percival, S., "Free Surface Viscous
Flow Computation Around A Transom Stern Ship By
Chimera Overlapping Scheme," Proceedings of the
Twenty-Third Symposium on Naval Hydrodynamics,
Rouen, 2000.
Marwood, W.J., and Bailey, D., "Design data for high-
speed displacement hulls of round-bilge form," NPL
Ship Report, No. 99, 1969.
Miyata, H., Katsumata, M., Lee, Y.,G., and Kajitani, H.,
"A Finite-Difference Simulation Method for Strongly
Interacting Two-Layer Flow," Journal of the Society of
Naval Architects of Japan, Vol. 163, Dec. 1994, pp.
1-16.
Orihara, H., and Miyata, H., "Numerical Simulation
Method for Flows about a Semi-Planing Boat with a
Transom Stern," Journal of Ship Research, Vol. 44, No.
3, Sep. 2000, pp. 170-185.
Subramani, A.,K., Paterson, E.,G., and Stern, F., "CFD
Calculation of Sinkage and Trim," Journal of Ship
Research, Vol. 44, No. 1, March 2000, pp. 59-82.
Wang, Y., Sproston, J.,L., and Millward. A.
"Calculations of Wave Resistance for a High-Speed
Displacement Ship," International Shipbuilding
Progress, Vol. 43, No. 435, 1996, pp. 189-207.
Xia, F., "Numerical Calculations of Ship Flows, With
Special Emphasis on the Free Surface Potential Flow,"
PhD thesis, Chalmers University of Technology,
Gothenburg, 1986.
OCR for page 602
(mm)
30
NPL-1 OGA
loo
o
` t t~D.W.L._ _
-200 0 200 ( mm )
Figure 1: Body plan of NPL model l OOA.
- :~
1 11'1~f Cat
Figure 5: Computational grid for NPL Model lOOA.
Figure 2: Model of Hull B towing at En = 0.687.
W.L. at rest | P' i.L. at rest
~0 Q- 0 0 0 0 PtOP`1~ ~—
A.P. 1 2 3 4 ~ 6 7 8 9 F.P.
S.S.
Figure 3: Locations of pressure measurements for Hull B.
i__
_ ~ Il111J,1Jr
i_ ~ .
I
B.
111'/~
Figure 4: Computational grid for Hull B.
A.P. 1 ~
( Cody 10 ):
~ 3 4 3g~ 6 7 8 9 F P S.s.
Figure 6: Computed surface pressure distributions for Hull
c.
o.,
o.`
0.1
—o..
—o.'
. .
~ W.L. at rest | ~ F~W/.L. at nest
,.~ - - ~ _ .~ J
~ ~ : Mes. (ASMB)
I _: Cal. (WISDA - Va)
..J · ,1 , , , , I , , , , _
A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S S
Figure 7: Comparison of pressure distribution along the keel
line for Hull B. Fn=0.434.
OCR for page 603
-'-~1
GAL
o.ol
4A _ ~
,r · : Mes. tAsMs)
t Cal. (WISDAM-V~)
- .R . .' . . . . ~ . . . · . .
A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S.
Figure 8: Comparison of pressure distribution along the keel
line for Hull B. Fn=0.5 11.
cod
us
o.~. :
O.t _
4.4
4.8
_n.2 , . , ., . .
P1
-0.4 _
-0.6
I
l
—V.Q
Fn - 0.590 ' ' ' ' ' ' ' ' ' ~ Fn
, /
W.L. at neat ~W.L. at test
1 _ ~- 9-
~-
· : Mes. (ASMB)
— : Cal. (WISDAM-VUg
I, , , , , I , , ,
A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S.
, , ,
Figure 9: Comparison of pressure distribution along the keel
line for Hull B. Fn=O.S90.
O.' .
Fn - 0.688
, ' __~
it' /
W.L at rest _ ~ ~.L 8t rest
0.0 _ - ~ ~ .
4.4 ~ _
· : Mes. (ASMB) ·
—: Cal. (\NISDAM-VUg
4.8 , ,~, , , , ~ , , , , , _
A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S
Figure 10: Comparison of pressure distribution along the ke-
el line for Hull B. Fn=0.688.
u ~
o.`
4.~-
f
· : Mes. (ASMB)
: Cal. (WISDAM-V00
A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S
Figure 11: Comparison of pressure distribution along the ke-
el line for Hull B. Fn=0.787.
Figure 12: Effect of Fn on surface pressure for Hull B. at Pi.
0.2
0.0
-0.2
7
Fn
Figure 13: Effect of Fn on surface pressure for Hull B. at PS.
0¢0.0
—0.2
''0.4 0.6 0.8
Fn
Figure 14: Effect of Fn on surface pressure for Hull B. at P6.
OCR for page 604
_3.0
~ NPL-1 OOAF
2 5 ~ = _ _ : _ `, r
· _ _ _ _ _ _ ~ ~ ~ ~ 1 ~ ~
~ .5 _ _ _ _ _ _ _ _ _ _ _ _ _
., _ _ _ _ _ _ _ _ _ _ _ _ _
~ 10 _ _ _ _ _ _ _ _ _ _ _ _ _
.= _ _ _ _ _ _ _ _ _ _ _ _ _ ~ l
=0R _ _ _ _ _ _ _ _ _ _ _ _ _ ~ V
~ .- _ _ _ _ _ _ _ _ _ _ _ _ _ ~ZC
~ _ _ _ _ _ _ _ _ _ _ _ _ Z ~
O. O _ _ ~ . _ _ _ ~ ~ ~ ~; ~ ~ (T ~
0.0 0.2 0.4
0.4~
02L
o.o ~70.4 0 6 0.8
Fn
1
4.0
1
~ 2.0
J 0.0
Figure 15: Effect of Fn on surface pressure for Hull B. at P9. ~
~ 20
_3.t~
cn
O 25
~ I I I I Ttll T
_ _ _ _ _ _ 1 1 1 1
O On _ _ _ _ _ 1 1 1 1
=^ v fLFI :
5 _ _ 1 1 1 1
1 ~ _ _ _ _ _ T 1 r T
~ .- _ _ _ _ _ - 1- ~
~ 1.0 _ _ _ _ _ ~
~ _ _ _ _ _ 1 1 1 1
·co 1FT: :
.5 _ _ _ _ _ 1 ~ 1 1
_ _ _ _ _ 1 1 1 1 .
oo 1 1 1 1
0.0 0.2 0.4
(X10-3 )
4.0 11
~ 2.0 n
I nc
4.O—
- : Mes. (NPL)
· : Cal. ( WD-VIII ) ~
0.6 0.8 1.0 1.2
Fn
~ : Mes. (NPL) I I I I I I I I Lll I I I
· : Cal. (WD-VIII ) IITI IT~ ITTTIT~
E
E
11..
a.o 02 0.4 0.6 0.8 1.0 1.2
Fn
Figure 16: Comparison of running attitudes for NPL 80A.
C| : Mes. (NPL)
· : Cal. ( WD-VIII )
0.6 0.8 1.0
| : Mes. (NPL)
| · : Cal. (WD-VIII )
ll
1 .2
Fn
II
Figure 17: Comparison of running attitudes for NPL lOOA.
~3.0lr
~ H
=2.5~
_ ~
O2.0R
~ 1.5
T 1.0 121
0.5
00
0.0 0.2 0.4
| NPL-1 50A|| | | |- | | |
~ 1 1 1 1 1 1 1 1 i ~ 1 1 1 1 1 1
l I r T7 [T7 [Tl ITTTTT7 1 1
llL111~ ll:FTT FTTItT FT
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-lllTIITlllILLllillll
T ~ T T 7 I T 7 ~ T 1 I T T T T I I I I
1 ITTI ITI ITI IT1 ITTI 1)
l I T T I r T 7 r T l r T T T T I I 1~1
I I I I I 111 I T I TT1 ll 1 T~r
T ~ T T 7 ~ T 1 ~ T 1 T T T T I T 1~1 1 '
I I I I I r1 T rT1 rTrTrr'TT
1111111111L1~111111
(X 10~ )
4.0u 1
R
=~2.0~
0.0 L
t
~~!-2.0~
C: Mes. (NPL)
| · : Cal. (WD-VIII )
0.6 0.8 1.0
: Mes. (NPL)
: Cal. ( WD-VIII )
i
111111111~1
111111111~1
~11111111111
T 1 1 T I I I I I T
N~ 1 1 T I r 1 1 I T
NPL-150A
_401 1 1 1 1 · I I I I I ~ 1 1 1 1 1 1 1 1 1 1 1 1~1 1 1 1 1 1 1 1 1 11 ~
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fn
Figure 18: Comparison of running attitudes for NPL 1 SOA.
OCR for page 605
25
C~
2.0
a)
°0 1.5
.~ 1.0
~ 0.5
~ Hull B |
1 1 1 1 1 ~ _
IIITI
1 1 1 :1~1~
~TTW2
_ I I rv _
_ 1 1 ~
_ ~ ~ _
_ ~ _
: Mes. ( ASMB ~
· : Cal. ( WISDAM-VIII )
0.0 _ ,,,,, , ·,,,, ,-
0.4 0.5 0.6 0.7
Fn
(X10 - )
4.0 l ~ _ _ _ 1
l l : Mes. (ASMB ) ~ _ _ _ _ _ _ _ _ _ _ _ _ _
, 2.0 ~ · : Cal. ( WISDAM-VIII ) E _ _ _ _ _
= = = = = = _ 111111''' _ _ _ = _ _ = _ _ _ Z _ _
. _ _ _ _ _ I I I I I I I I I ~ , ~ _
_ _ _ _ _ _ _ _ 1 1 1 1 1 1 1 1 1 _ = _ _ = = _ _ ~ _ _
~ o.o _ _ _ _ _ ~ _ ~ _ ~ _ ~
o5 ~^ _ _ _ _ _ _ _ ~ 1 ~ ~ ~ 1 1 1 1 ~ ~ _ _ _ = = = ~ = = 1
~ ~.u _ _ _ _ = _ _ _ 1 1 1 1 1 1 L'-- _ _ = = = =F = ~
._ _ _ _ _ _ _ _ _ 1 1 1 1 1 ~1 1 _ _ _ _ = _ _ = 1 _ _ 1
~-4.0 _ _ ., _ _ = _ _ ~ 1~1 1 1 1 _ _ _ _ _ _ _ _ ~ _ _
_ _ _ _ _ _ _ _ E11111111 _ _ _ _ _ _ ~ u _ ~
-60 _ _ _ ~ _ _ _ ~ 1 ~ ~ I 1 1 1 1 1 _ _ ~ _ ~ ~ _ _ ,1
· 0.4 0.5 0.6 0.7
Fn
Figure 19: Comparison of running attitudes for Hull B.
0.2sp
~ 0.2t
~_
U. 3 0.1'
~J
r ~
° 3 01(
~ C
.= 0.05 t
' t
~ 0.00 ~
: Mes. (NPL) l
· : Cal. (W~V111) |
~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fn
Figure 20: Comparison of wetted surface area for NPL 80A.
a.) 0.25
~ ~ NPL-100At
O 0.2C' "
_
~0.1:
~J
a)_
a) ~ 0.1C
=~ r,, ,, I I ,,
~ ri r~e Ll 1 1 I nTT
·= U.~7tl 1 1 1 1 1 1 1
Ll I l ~ i I T I
~, r I I I I r I n
r~ o.oorl rl I I ITl
0.0 0.2
,, ~ 1 1 1 11
: Mes. (NPL) ~
: Cal. ( W~VIII ) |'
0.4 0.6 0.8 1.0 1.2
Fn
Figure 21: Comparison ofwetted surface area for NPL lOOA.
0.2b
0) 0.20~ ~; ~ ~ ~ ~ ~ ~ ,`
I ~ 1 1 1 1 1 1 1 1 1
=_ rl Ill I rTr
c\' ~ 1 1 1 1 1 1 1 1 1 ~
¢0.150~|~| 1 1 1 1 1
=' F11111111-
, — I 1 1 1 1 1 1 1 ~ 1 1
~0.10llllllllI4l
005FlTIII nm
IIIT7TIlllI
rllllllllll
° °8' 1 " " ' 1 ' ~ '
.. ^~ .............
I NPL—15nA~
1
T1 T T I I
ITITLL
I T I T 1 1
TTTIT1
1 1 1 1 Tl~
I T I T I I
~ I I TT~
1 1 1 1 1 1
iTTT '
1llllllllIl!~II
~1~1
1 l~l ' _ I I I T ~ T I I T
_t_rl I I I I 1 I T 7 T I I T I I
1 1 ~ 1 ~ 1 1 1 1 1 1 1 1 i 1 1 1 17]
r' I I I ~ l I l I T I ~ I I I I I
I I I I I I ~ I I I I I Ll ~ I ~ I I
f ~ I ~ ~ 1 1 ~ ~ TiT ~ ~ T'
r~ ~ ~ l I l I T L T I I I ~ I
i ~ T ~ ~ I I ~ I T I T I Ll I I
T ~ I 1 ~ 1 I T I T I Ll I
T ~ I 1 ~ ~ ~ Lj ~ ~ ~ ~
I I ~ I I I ~ I I I I I I i 11 ~ ~ I
IIITlTIlllIITIlIIII
1 I I I 1 T I 171 I 1 T I 17
ii : Mes. (NPL)
· : Cal. (W~V119)
0.6 0.8 1.0 12
Fn
Figure 22: Comparison of wetted surface area for NPL 1 SOA.
( X 1
1,
-
-
. _
c)
C~ ~~ 7~r~ ~F~-
`' ~ Mes. Cal. L~l Llil I I4lTL:
,,, ~ (NPL) (WD-VIII) II ;~ I ~ ~ I ~+l I l - ~ ~ I I I I
·_ Ll CTML ~ IL~ I ~ ~ ~ I ~ ~ ~ I ~ I ~ I ~ ~ I I ~ I ~ I
cn ~ 1~ ~ I ~ ~ ~ I I ~ ~ I I ~ I ILlTI ~ I ~ I I I ~
IICF~ O II I I I I I I I I I i 11n 11111 I Ll I I I
011 111 1 1 1 1 1 1 T 1 1 1 1 1 111 1 I 1 1 1 1 1 I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fn
Mes. Cal.
( NPL ) (WD-VIII)
CTML ·
CF~ O
Figure 23: Comparison of resistance coefficients for NPL
80A.
(X10 4'
1-
c'
.a
o
c'
Mes. Cal. || |,`| | |,~| | |,`| | |~| | |~| | | | | | | |
U) ~ (NPL) ~D-VIII) II lTI I l~l 1 ~TI 1 ITI I ITI I I I I I I I
·_ 11 CTI\L ~ I I I I I I I I I I I I I I I I I I I
11 11 1 1 1 1 1 1 1 1 1 1 1 1 1 11 L I I I I I I I I I I
CFNL O Ll11 I I I I I I I I I I I I I I I I I I I I I I I I
ol' Il I I I I rTI ~ ~ ~ I I I I ~ I I I I ~ I I I I ~ ~
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fn
Figure 24: Comparison of resistance coeff~cients for NPL
1 OOA.
OCR for page 606
(x~o-)
~e
~150;
o
o
o
o
o
1 4 !11I!I!I!I1I !11!I1I1 11111 I ! 11 111111111 I I I I I I 111
~ (~ ~ < ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . ~
CT~ ~ _ _ _ 11II[1II[T _
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 1 1 1 1 1 1 i I l?
° 1CF~ O ~ ~ ~ ~ ~ ~ ~ ~ 111.11II11
0.0 0.2 0.4 0.8 0.8 1.0 1.2
Fn
.
F1gure 25: Co~~son of ~si~ance coe~dents ~r NPL
1 30A.
~ 3
2.5
2
E1~ ~ ~
1~ ~ ~
~ o~ ~ ~
o.o _ _ _
~ 1 1 1 1 1 1 1 1
I1 11 1 ~OI1
11 I 1 T 1 I 1 Ill
illT11111d
11 I TI1I)
1I11[1T[11[
1 1 1 1 1 1 1 1 1 1 1
~ 1 1 + + LI 1 L1 1
11111111111
1 1 1 1 1 1 T 1 1 1 [
I I I 1 I 1 I ~ I 1 I
1 1 1 1 I 1 I I 1 1 T
NPL UB=6.25, Fn=0.60 I
~BS.(NPL)
:CS1.~D~II1)
_
-~ 5~ 6~ 6~ ~ 7~
(X10~) L/V1~
~{
q _:
o
e
.s
[NPL L/8=6.25, Fn=0.60 k
H ~u ~
~ ~ :C~]WD~I~ ~#
NPL L/8=6.25, Fn=0.80
,-I!I111IIII1I1i111iI ~PU
e c8l. (WD~III)
wu-
5.0 5.5 6.0 6.5 7.0 7.5
(X10~) L/V1
1NPL L/8=6.25, Fn=0.80 I
:~eS.(NPL) 1
~I ~ CaI.o -
f f l l f 1 1 1 1 1 1 f l 1
I I I I I I I 1 1 ]~l~lT1
ol I 1 1 1 1 1 1 1 1 1 1 1 1
I! 1 1 lILllllH
[--I-+-l--lIll+I
-2~1 I 1 1 1 1 +1F
~IIII1TI)
5.0 5.5 6.0
~u-vllI) I
+IT1I11
llTlTF
IIB1#I
IllII~I
11lJlII
7.0 7.5
L/
P1gure 27: E~C1 of L/V 1~ on n~ning athtudes, Fn = 0.8.
30F
2.5~
k
2.0F
~ r
~ le5l
|~[IIllIlIIllIlIIl I!!~ ~ I
F+Er++ H+~ :~eS.(NPL) I
F111111 I 1111 T 111 I 111 ~ C~l.~D-I'0 1
5.0 5.5 6.0 6.5 7.0 7.5
X10~) L/V1
4,. ..
I NPL ~ F~1~0 ~
H :~eS.(NPL) H
2# @ :CB1.(WD^~1) ~
6.5 7.0 7.5
L/V1
P1gure 26: E~ct of LV'/3 on nmning atti~dcs, Fn = 0.6.
IlIII'lII
L3I 1 1 1 1 1
1 1111111 1
1 1~111 1 1
~1111E
Illlllll?
llllIFlI
111111111
5.0 5.5 6.0 6.5 7.0 7.5
L/V1
F1qure 28: E~ct of L/V 1~ on muning aui~des, Fn = 1.0.
OCR for page 607
.O
!t
o
a
c
cO
. -
~n
a
ct
-
c
.a
c~
o
-
. -
u)
........... >, `,,,, I,, I I L I I I I I I I _
~ _
I I I I I I I I T 1 I T 1 I T 1 1~1 I T 1 I T 1 I T T I F _ = =
_ = _ _ = _ _ 1 1 1 1 1 1 1 1 1 1 IU 1 1 1 1 1 1 1 1 1 1 _ _ _
_ _ _ _ _ _ _ I I I ~ I ~ r r I T I _ r 1ll 1: 1 1 ~ I ~ T _
: _ _ = = = I I 1 4~TT T 1 I T 1 I T ~ T 1 I T T I I ~ _
_ _ = = _ I I I I 11 I T 1 I T 1 I T 1 1011 T T It: ~ =
_ _ _ _ _ I T 1 I T 1 I T 1 I T 1 I T 1 I T I`LI I I ~ =
_ _ = = _ 1 T 1 I T 1 I T 1 I T 1 I T 1 I T 1 1 1~1tl ~ =
_ _ _ _ _ r ', r r 7 T r ~ T r, T ~ I T r, T ~ I I I T _
_ _ _ = _ _ T., I,, T r 1 r,, T., r I j I I 1 1 1 T _
_ _ _ = = _ I T1 I T1 I T1 I T1 I T1 I T1 1 1 1 1 1
T r ~ r ~ 1 I T 1 I T 1 I T 1 I T 1 11 ~ I I
1 I T1 I T1 I T1 I T1 I LT 11
1 1 T1 1 T1 I T1 I T1 1 1 1 1 1
1 1 T1 I T1 I T1 I T1 1 1 1 1 1
_ _ _ _ _ _ IT1 I T1 I T1 I T1 I Tl Ll
2 NPL L/B=6.25, Fn=0 60 |1 I T I I T I I T I I T I I I I ~
:Mes.(NPL) 11 T I T1 ~ T1 I T1 ~ TT
11 1 111 I T1 I Tl I I Tll:
· : Cal.(WD-V111) 11 1 1 1 ~ I ~ I i I I I ~ I I I
1l 1 I r 1 T r 1 T r 1 T r I I r:
O , Illilid1~111161 i.
5.0 5.5 6.0 6.5 7.0 7.5
L/v1/3
Figure 29: Effect of L/V l/3 on total resistance coefficient,
Fn=0.6.
( X104 )
4O
14[ 1 1 1
L T 1 1
l
l
11 1
10
8~
6:
— 2
~L
1 1 1 1 T 1 1 T I T 1 I T Tl 1~1 1 1
1 TT I T1 I T I 1 1 I T I 1 1 1 1 1
1 1 1 I T1 I T I 1~1 T1 TT I r7
1 1 1 I T1 1 T I I 11~1lEl I
I I I ITT T T TTl T T~T 1 T r 1
1 1 ' ' ' ' ' I 1 1 1 1 1 1~ 1 1 1 1
1 _ 1 1 1
rr1
1 11
~H
~3
1 1 1
I T I
T r l
T Pl
~H
I r ~
I NPL UB=6.25, Fn=0.80
. : Mes. (NPL)
· : Cal. (WD-VOf)
i
eF j ~ T
1 1 1 1
F j ~ ,F
F T r r
~F T r r
I I IT
I I Ir
T T r I
rT I I
I Trr
T Ij jl T
1 1 1 1
1111
I IIT
T T rr
_LlL1
1 1 1 1
T I jl
1 1 1 1
1 1 1 1
T T r
I Tr
l l l l
I I j I
5.0 5.5 6.0 6.5 7.0 7.5
L /v1/3
Figure 30: Effect of L/V "3 on total resistance coefficient,
Fn=0.8.
F I I I I I I I I I I I 11 1 1 1 1 1 1 1 ~ I I I I I I I I I I I I I I I I I I
~ _ ~
6~1 1 1 1 1 1 1 1 1 1 1 ~1 171TIITI1 111 ITIITITII
01 1 1 11 ~:
I- I I I I I I I I I I ~ I f I I I I I I I I r I ~ I I I
rl I 111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~1 1 1 1 1 1 1 1 1 1 1
4FI I T I I I I I I I I I I I I I I I I I I I I LPI 1 1~1 1 1 1 1 1 1
~ r ~ F ' ' I 1 IF I I T 1 1 1 1 | I I I | | L | |
2|| NPL L/B=6.25, Fn=1.00 |1 1 | | T I 1 1 I T I I I I T I I I I
: Mes. (NPL)
: Cal. (\ND-VIll)
U I I I I I I F 1 T j T F 1 F j T I 1 F ,]
o n · . ~
5.0 5.5 6.0 6.5 7.0 7.5
L /v113
N PL L/B=6.25, Fn=1.00 1
: Mes. (NPL) ~
~ : Cal. (\ND-V111) |
Figure 31: Effect of L/V 1/3 on total resistance coefficient,
Fn= 1.0.
OCR for page 608
Representative terms from entire chapter:
surface pressure
DISCUSSION
Masashi Kashiwagi
Kyushu University, Japan
As validation for a wide variety of hull forms,
you compared with the experiments of NPL
series model. The data was published in the
1970's, and thus I guess those have been used for
comparisons with other numerical models in the
past.
If this is true, what are the main differences
between the present results and published results
in the past?
AUTHOR'S REPLY
The comparison of the present computed results
using WISDAM-VIII with the computed results
of Wang et. al. are shown in Fig. A-1. In Fig. A-
1, two types of computed results of Wang et. al.,
the one is computed by the Rankine source
method (RSM) and the other by the Tulin's
theory (1986, cited below).
Since only the comparison of wave making
resistance coefficients (Cw) is shown in Wang et.
al. (1996), comparison of residuary resistance
coefficient (Crl) are shown in Fig. A-1 where
computed Cw of Wang et. al. are compared with
the experimental data along wit h the present
computed data.
As can be seen clearly from Fig. A-1, computed
results of Wang et. al. fail to reproduce the
Thank you for your kind remarks. trends, i.e. the slope of the experimental data,
and the quantitative agreements with the
experimental data seem to be poor. That is, the
mean differences of computed Cw of Wang et.
al. compared with the experiment are greater
than 10% while that of the WISDAM-VIII result
is about 4% for a speed range 0.6
