|
Items in cart [0] |
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 458
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Validation and Application of Chimera RAN S Method for
Ship-Ship Interactions in
Shallow Water and Restricted Waterway
Hamn-Ching Chenl, Woei-Min Lin2, and Wei-Yuan Hwang3
(~Texas A&M University, 2Science Applications :International Corporation,
3Us Merchant Marine Academy, USA)
ABSTRACT
A Reynolds-Averaged Navier-S tokes (RAN S) method
has been employed in conjunction with a chimera
domain decomposition approach to compute the
effects of unsteady ship-ship interaction in shallow
water and restricted navigation channels. For the
simulation of ship-ship interactions, it is convenient to
construct body-fitted numerical grids for each ship and
the navigation channel separately. The numerical
grids around the passing ships and the own ship are
allowed to move relative to each other and relative to
the grid of the navigation channel. The computation
results were first validated by comparing directly with
the time record of the experimental measurements by
Dand ( 1981 ) for ship-ship head-on encounter and
overtaking cases. The method was then applied to
navigation channel design problem of computing the
effects of moving ships on a ship moored next to a
pier. More than 40 time-domain simulations were
carried out parametrically for different ship types,
wharf line distances, ship speeds, and wind directions
that are manifested in ship crabbing angles. The
results of these computations were systematically
organized and compared to investigate the ship speed
effect, wind direction effect, wharf line distance effect,
ship type effect, ship sheltering effect, and bottom
clearance effect. Although a great deal of further
study is required, the results in this paper clearly
demonstrate the potential of using the chimera RANS
method for ship-ship interaction and navigation
channel design problems.
INTRODUCTION
water effects as well as ships are operating near
obstacles such as other ships and piers. Traditionally,
for various ship maneuvering simulation purposes, the
semi-empirical formula are used to report and
represent the towing tank test based ship-ship
interactions in deep as well as shallow water when
these vessels meet or overtake each other on parallel
course. In ship maneuvering simulator community,
these formulae are typically used to calculate the ship-
ship interactions during real-time simulation. There
are simulators that calculate the ship-ship interactions
by solving potential flow in real time with the
assumptions of open water, rigid free surface, parallel
course, and single passing ship. Whether the
simulated interactions on parallel course are calculated
empirically or solved numerically, further adjustments
are applied to account for crabbing angle and various
bank effects. When multiple passing ships are in the
proximity of own ship in a simulation scenario, the
passing ship effects are typically superimposed. This
approach certainly has a great deal of room for
improvements in order to provide better quality of
simulator research and training.
In order to more accurately capture the
complex phenomena of ship-ship interactions with the
presence of variable bottom in a navigation channels, it
is desirable to use more sophisticated numerical
methods that are capable of dealing with three-
dimensional turbulent flows induced by arbitrary
vessel motions in confined shallow water channels. In
the past several years, Chen and Chen (1998) and
Chen et al. (2000) developed a chimera RANS method
for the computation of ship-fender coupling during
berthing operations. The method was generalized
recently by Chen et al. (2001~ 2002) for time-domain
The ship maneuvering and ship-ship interaction in
confined water have been important problems in
channel design and ship operation in harbors. The
problems are very complicated because of the shallow
1
~ . ,
simulation or large amplitude ship roll motions
including capsizing. In the present study, the chimera
RAN S method was further generalized to compute the
interaction of two moving ships and the effects of
OCR for page 459
moving ships on a ship moored next to a pier.
To demonstrate the validity of the current
approach, the numerical results were first compared
with experimental measurements by Dand (1981) for
ship-ship head-on encounter and overtaking cases.
The method was then applied to compute the effect of
moving ships on a ship moored next to a pier. A total
of 44 runs were carried out parametrically for various
combinations of ship speeds, wind directions, ship
types and wharf line distances. The results of these
computations were systematically analyzed to
determine the ship speed effect, wind direction effect,
wharf line distance effect, ship type effect, ship
sheltering effect, and bottom clearance effect.
NUMERICAL METHOD
In the present study, calculations have been performed
using the free-surface chimera RANS method of Chen
and Chen (1998) and Chen et al. (2000, 2001, 2002) to
determine the multiple-ship interactions in a shallow-
water navigation channel. The method solves the non-
dimensional RAN S equations for incompressible flow
in general curvilinear coordinates (5~;, i):
u'!i =o
(1)
au + u jUt + U'U] j + g j p j ——g U,jk O (2)
where ~ and ui represent the mean and fluctuating
velocity components, and go is the conjugate metric
tensor. t is time p is pressure, and Re = ULIv is the
Reynolds number based on a characteristic length L, a
reference velocity U. and the kinematic viscosity v.
Equations (1) and (2) represent the continuity and
mean momentum equations, respectively. The
equations are written in tensor notation with the
subscripts, ,j and ,jk, represent the covariant
derivatives. In the present study, the two-layer
turbulence model of Chen and Patel (1988) is
employed to provide closure for the Reynolds stress
tensor uiuj
The RAINS equations have been employed in
conjunction with a chimera domain decomposition
technique for accurate and efficient resolution of
turbulent boundary layer and wake flows around the
moving and moored ships. The method solves the
mean flow and turbulence quantities on embedded,
overlapped, or matched multiblock grids including
relative motions. Within each computational block,
the finite-analytic method of Chen, Patel and Ju (1990)
is employed to solve the RAN S equations in a general,
curvilinear, body-fitted coordinate system. The overall
numerical solution is completed by the hybrid
PISO/SIMPLER pressure solver of Chen and Korpus
(1993) that satisfies the equation of continuity at each
time step. The present method was used in
conjunction with the PEGSUS program of Subs and
Tramel (1991) that provides interpolation information
between different grid blocks.
The free surface boundary conditions for
viscous flow consist of one kinematic condition and
three dynamic conditions. The kinematic condition
ensures that the free surface fluid particles always stay
on the free surface:
77,+U0x+v~y-w=o on
z = ~ (3)
where ~ is the wave elevation and (U,V,W) are the
mean velocity components on the free surface. The
dynamic conditions represent the continuity of stresses
on the free surface. When the surface tension and free
surface turbulence are neglected, the dynamic
boundary conditions reduce to zero velocity gradient
and constant total pressure on the free surface. A more
detailed description of the chimera RANS/free-surface
method was given in Chen and Chen (1998) and Chen
et al. (2000, 2001, 2002~.
VALIDATION OF SHIP-SHIP INTERACTION
Although the chimera RANS method has been
validated and successfully applied to many different
hydrodynamic and body fluid interaction problems, it
is necessary to validate its capabilities in predicting the
ship-ship interaction in shallow navigating channel due
to the complexity of the problem involving multiple
moving ships, stationary ship, variable bottom
topography, and channel banks. The whole procedure
of dealing with multiple moving vessels needs to be
checked to make sure the results are valid. The
capabilities of chimera RANS method, including its
supporting pre-processing and post-processing
software modules, to handle the ship-ship interactions
are thus validated against the model test data. A
favorable comparison would provide the confidence to
apply the code to full-scale predictions.
Ship Model and Experimental Setup
The validation data used here are the towing tank test
results reported by Dand (1981). That experiment
study was designed to provide insights into the
hydrodynamic interactions between ships moving on
parallel courses in shallow water for: (1) overtaking
encounter, both ships moving; (2) head-on encounter,
both ships moving; and (3) a stationary vessel when
passed by another.
2
OCR for page 460
Two 48.2:1 scaled models were used. As
shown in Figure 1 and Figure 2, both models were
chosen as representative of"averaged" vessels, model
5232 being of the single-screw cargo-liner type while
model 5233 represented a tanker. A fully instrumented
model 5233 (own ship) was attached to the towing
carriage with its track on the tank centerline. Model
5233 has a Lpp of 3.962m, a beam of 0.506m, a draft
of 0.208m at FP and 0.218m at AP. Model 5233 was
restrained in surge, sway, and yaw; but allowed to
pitch and heave freely, and roll to a limited extent.
Model 5232 (passing ship) was running on a track and
carried no measuring instrumentation. Model 5232
has a Lpp of 3.323m, a beam of 0.473m, a draft of
0.162m at FP and 0.170m at AP. Both models were
fitted with propeller and rudder.
tI\\\~ TO I I I I 1 1 11
\ \ \ \ \ ~
Figure 1. Body Plan of Model 5232
11\ \ \ \
i\ \ \ \ \
A\\ \ \ \
\\\\-\ \ \
\\\\\\~\\\ ~
\ \\\ \ \ \
\ \ \ \ \
\ \ \ \ ~~—
54\ \ \ N
\ \ \ \. \ \
\\ \ Aft\ \\
\ \ \,9. \ \ \ \
i\ \e X\ \\ \ ' 1
\\.~'\\ \\ 5~\
~ fib\ \ ~ \ \ \ ~
1 i;
1 / / / / /
I / / / / /
1 7 /_/ - l it
I / / / /7 [l
11 11
/ / / 7 1~ r,
_ I -4/ / / 7 1 11
/ l I I rI
1 7 I I 11
. I I ~ I I I
111~7
1 7 ITS
' 47/ ~ PI
Figure 2. Body Plan of Mode 5233
The model tests were conducted in a towing
tank of 90m long, 6.1m wide, and a depth that can be
adjusted between O and 0.56m. Note that the
combined width of the tanker and the cargo liner is
about 16% of the tank width. It was decided to model
the tank walls in the numerical simulation as solid wall
boundary conditions.
A low-pass filter set at 10 Hertz was used to
eliminate the noises originated from the vibration of
towing carriage. In addition, the model test data
underwent a screening process to reject 'wild' data
values and also a curve-fitting procedure to fit the data
into a modified sine function format. The curve fitting
strategy was probably influenced by the observations
of typical calculations of interactions based on
potential flow and rigid free surface flow assumptions.
The original measured data was not available in the
original report.
Comparison between Numerical Results and
Experimental Measurements
To provide a critical assessment on the capability of
using the chimera RANG method for time-domain
simulation of ship-ship interactions in shallow and
confined water, computations were performed for two
selected cases and compared with the experimental
data. These two cases are a head-on encounter case
(case 1) and an overtaking case (case 2~. In order to
facilitate a direct comparison with the experimental
data, the governing equations were normalized using
the water depth h, a characteristic velocity A= ,/~,
and a characteristic time of T = h I U = it. The
Froude numbers are defined by Fnhp = UplU for the
passing ship with speed Up and Fnho = UOIU for the
own ship with speed UO.
In case 1 (the head-on encounter case), the
Froude numbers for the passing and own ships were
chosen to be 0.421 and 0.250, respectively, in the time-
domain simulation. The lateral separation distance YO
between the centerlines of the passing and own ships is
1.6 Bo' where Bo = 0.506m is the beam of the own
ship. The water-depth-to-draft ratio was chosen to be
hlTo = 1.19, where To = 0.213m is the mean draft ofthe
own ship. The present chimera grid system consists of
7 computational blocks (3 blocks for each ship and one
block for the channel) with 811,587 volume grid points
and 5 free-surface blocks with 29,895 free surface grid
points. A close up bird-eye view of the free surface
grid is shown in Figure 3 at two different time instants
during the head-on encounter.
In case 2 (the overtaking case), the Froude
number of the passing ship was chosen to be Fnhp =
0.411 while the own ship was stationary with Fnho =
0. The water depth for this case is identical to that for
the head-on encounter case with hlTo= 1.19, but the
lateral separation distance YolBo was reduced to 1.3.
Bird-eye views of two time instances of the chimera
grid system used in the computations of the overtaking
case are shown in Figure 4. Due to the small lateral
separation, a significant portion of the ship grids was
found to fall within the hulls of another ship during the
overtaking encounter. During the computations, these
hole-points were automatically removed from the
computational domain using the PEGSUS program of
Subs and Tramel (1991). It is quite obvious that the
use of grid overlapping and embedding techniques
3
OCR for page 461
greatly facilitates the simulation of ship-ship
interactions during close encounters without tedious
regeneration of numerical grids at each time step.
Figure 3. Chimera grids for head-on encounter case
(case 1)
Figure 4. Chimera grids for overtaking case (case 2)
Computations were performed for both the
head-on encounter case (case 1) and overtaking
encounter case (case 2) using a constant time
increment of t/T = 0.1. In both simulations, the
passing ship was accelerated from zero speed to V=
Fnhp between t/T = 0 and 4, and then maintained a
constant speed for the remaining excursion. The same
starting condition was also specified for the own ship
for the head-on encounter case. In both numerical
simulations, both the passing ship and the own ship
were held fixed in sway, heave, roll, pitch, and yaw
directions. The ships were moving in straight courses
and no equations of motions were solved.
Figure 5 shows the computed longitudinal
velocity and pressure contours at several time instants
to illustrate the general flow characteristics during the
head-on encounter (case 1~. It is noted that the
pressure field generated by the passing and own ships
propagated in front of the ship bows and induced
strong ship-ship interactions well before the ships meet
at Xo/Lo = 0. The reflection of the pressure waves
from the tank walls produced nearly two-dimensional
wave fronts as seen in Figure S(b)-(c). The collision of
these wave fronts produced a sharp rise in pressure
field near the middle of the towing tank at t/T = 36.
These wave fronts continue to propagate towards the
other ends of the wave tank and produced a complex
wave pattern before the ships meet at t/T = 72. A
close examination of the pressure contours shown in
Figure S(c) clearly showed that the two pressure wave
fronts met near the center of the towing tank even
though the passing ship travels at a significantly higher
speed than the own ship. This indicates that the
propagation speed of the pressure waves is nearly
independent of the actual ship speed.
For the present head-on encounter case, the
two ships met at t/T = 71.9 (Xo/Lo = 0) and completely
passed each other at t/T = 114.7 (Xo/Lo = 2~. It can be
seen from the pressure and velocity fields shown in
Figure S(e)-(h) that there is a very strong interaction
between the passing and own ships during the
encounter. A low-pressure region was developed in
the narrow clearance region between the two ships due
to the Bernoulli effects. After the ships completely
passed each other, the pressure interactions reduced
gradually but the ship wakes remain clearly visible at
the end of the simulation.
For completeness, we shall present also the
longitudinal velocity and pressure contours for the
overtaking case at several time instants as shown in
Figure 6. It is clearly seen from Figure 6(b)-~0 that
the pressure waves generated by the passing ship travel
considerably faster than the ship itself. The wave front
is again nearly two-dimension due to the tank wall
effects. The bow of the passing ship crossed the stern
of the stationary own ship at t/T = 40 (XJLo = 1.0) and
completely overtook the own ship at t/T = 110 (XJLo
= -0.8387~. As noted earlier, the lateral separation
distance YolBo for the overtaking case is only 1.3. This
resulted in a sharp reduction of pressure in the narrow
passage between the two ships. After the passing ship
completely overtook the own ship, the pressure field
around the own ship returns gradually to zero.
However, the reflection of pressure waves from the
tank wall was still quite significant at t/T = 150.
In order to facilitate a direct comparison with
the experimental measurements of Dand (1981), the
computed forces and moments on the own ship (model
5233) were non-dimensionalized as follows:
Surge force coefficient: Cx = FX 1( 2 pBoTou2 )
Sway force coefficient: Cy = Fy 1~2 pBoToUp )
Yaw moment coefficient: Cn = Mz 1~2 pBoToUp)
4
OCR for page 462
-
- ~
_11
c
- -
_11
- -
- -
- -
_11
- -
_11
- -
_11
- ~
- ll
- -
-
1
l
1
b
1
i
i
~ .
_
_ _
l _
_—r
_
_
__
at_ _
-
l
-
_
_
_
_
- _
3_
_
1 _
1
Hi
l
-~1 -uw -O.OB ¢04 002 0 002 004 006 008 01 _ _ ~' _ 4~02 001 0 001 0~02 003 004
Figure 5. Longitudinal velocity (left) and pressure (right) contours for head-on encounter case (case 1)
5
OCR for page 463
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -0.06 -0.05 -0.04 403 -0= -0.01 0 0.01 0.02 0.03 0.04
Figure 6. Longitudinal velocity (left) and pressure (right) contours for overtaking encounter case (case 2)
6
OCR for page 464
~ 0.4 (a) Cx
~-02 ~
~0.4 Cakuladons
: ~ Experkr~ (Filleted
~0.6 -2 -1 xiLo
2 . (b) Cy
5 o ,~\:
of -2 . Cartons
4r
2
E
~ O .
~ -2
~ ~ ._ ,. es_w,
~ . . . . . . . . . . . . . . . . .
-2 -1 x IL O 1 : ~
~ o
_ T/\~/~{ I-/—
Cakubdons
~ Eat rr~ (Fllb~
-2 -1 XolLo 0 1 2
Figure 7. Force and moment coefficients on the own
ship for head-on encounter case (case 1)
:
(a)cy
50.4~.-~
~ ~0. 4 - -- CakubUons
U) ~ Expert (FIlbred)
-1 .5 -1 -0.5 XJLo ~ 1.5
2
is:
1
~ U
o
,, -1 .
o
2
(b) Cy
N~ ,' Cakuh~ons
~ E~tperltr~ (Fllbred}
-1.5 -1 -0.5 0 XJLo05 1 1.5
4,
2~(C) Cn
,~ ~ it' ~
]-2
Is Cakubffons
: ~ E~tperbr~ (Fllbre~
-41 .5 -1 -0-5 0 xJ~ 05 i 1 5
Figure 8. Force and moment coefficients on the own
ship for the overtaking case (case 2)
Figure 7 and Figure 8 show the comparisons of the
computed and measured Cx, Cy' and Cn for the head-
on encounter case (case 1) and overtaking encounter
case (case 2), respectively. The blue solid lines
represent the numerical results and the red dash lines
represent the filtered experimental measurements by
Dand (1981~. As mentioned before, the model test
data went through a curve-fitting procedure to fit the
data into a modified sine function format. The
original measured data was not available in the
original report. In general, the numerically predicted
force and moment coefficients are in fairly good
agreement with the filtered model test data, although
the numerical results contain more oscillatory
components. The observed discrepancy may be
attributed to the following factors:
.
.
· Due to the removal of the wild data points and
the curve fitting of test data, the more oscillatory
components of the interactions might have been
lost in the figures presented by Dand (1981~.
· The forward speed of the ships were assumed to
be constant (except the initial ramp start) in the
numerical calculations, while the actual speed of
the ship models might not be constant, as
reported in Dand (1981), due to increase of
resistance while one ship passes another.
· The ship acceleration during ramp start produced
strong pressure waves that is responsible for the
initial oscillations in the surge forces.
The motions of the ship models in the numerical
calculations were constrained, while the test
model was allowed to pitch and roll. In addition,
the tank walls were assumed to be perfectly
reflective in the simulations.
· The more oscillatory components observed in the
computations could also be attributed to vortex
shedding, the free wave system of each vessel, or
a local wave system induced by the interacting
vessels. These phenomena have been reported
and discussed by Norrbin (1985), as well as by
Kaplan and Sankaranarayanan (1986~.
The physical test models were equipped with
rudder and propeller. Dand (1977) showed that
the effects of rudder and propeller are
recognizable although not overwhelming.
SHIP-SHIP INTERACTION IN CHANNEL
With validations established for ship-ship head-on
encounter and overtaking cases, the chimera RANS
method was applied to study a more complicated
navigation channel design related problem. In this
study, the effect of one and two passing ships on a
ship moored next to a pier was examined. A total of
44 simulations were performed to examine the effects
of passing ship speed, wharf line distance from the
channel boundary (i.e., lateral separation distance),
crabbing angle of the passing ship (a manifestation of
the wind effects), bottom clearance, and sheltering
effects in two passing ships cases. A complete listing
of the numerical simulations performed in this study
is shown in Table 1. Note that h represents the
reference water depth. Figure 9 shows the cross-
sectional view of the navigation channel. In most of
7
OCR for page 465
the simulations performed, the wharf line (denoted
shape A) consists of a 2:1 bank slope which
terminates at a water depth of 0.5h. A second wharf
line shape (shape B) was considered in case 17 to
examine the sensitivity of the bank shape on the ship-
ship interactions. In this case, the 2:1 bank slope was
extended further up to the shallow water region with
a minimum water depth of 0.125h. It should also be
noted that the water depth in Case 36 is 0.2h deeper
than the other cases everywhere. In addition, there is
no 2:1 slope at the wharf line and the vertical quay
wall is located at a distance of 2h away from the
moored ship-C (to the starboard side). In all
simulations, the North (N) is going into the paper,
East wind (E) means the wind is from the East, and
West wind (W) means the wind is from the West.
The wind effects were represented by a 5° crabbing
angle of the ships to counter the wind action.
~ !
1 1
West Side ' N ~ CL
Channel, I
Boundary '
8h
_ .
.
East Side
Channel
Boundary
~1
Distance to, i , Constant
Wharf Line ' ; ' Depth
, ; ,
Figure 9. Navigation channel cross section
The coordinate system convention used in the present
study is shown in Figure 10, with the Taxis going
into the water. The forces and moments shown in all
Run#
01-03
04-06
07-09
10-12
13-16
17
18
19
20-21
22-24
25-27
28-30
31-33
34
35
36
37-38
39-41
42-43
44
Wharf Line
Distance
10h
10h
10h
16.6h
6h,8h,12h,14h
10h (Shape B)
Open Water
10h
10h 16.6h
,
10h l
16.6h
10h
12h
10h
16.6h
.
10h (Deep)
10h,12h
10h
12h
16.6h
the plots are consistent with this coordinate
convention and represent the hydrodynamic forces
and moments acting on the moored ship. As noted in
Table 1, three types of ships were considered in the
present simulations. The dimensions (i.e., length,
beam, and draft) for these three ships are (19.3h,
2.112h, 0.86h) for ship-A, (l9.Oh, 2.9h, h) for ship-B,
and (25.92h, 3.6h, 0.94h) for ship-C, respectively. In
all simulations, ship-A is the inbound vessel moving
from North to South and ship-B is the outbound
vessel moving from South to North. Two different
moored vessels were considered with ship-A moored
at the pier in the first 27 cases while the much larger
ship-C was the moored vessel for the remaining 17
simulations. In order to facilitate the comparison of
the forces and moments, the length of ship-A was
chosen as the reference length L = 19.3h for all the
figures presented in this paper. The forces and
moments obtained by the chimera RANS method
were non-dimensionalized as follows:
For Forces: 1/2p(VV p )l'3 Up (4)
For Moments: 1/2p(VVp)~'2U2 (5)
where p is the water density, V is the displacement of
the moored ship, Vp is the displacement of the
passing ship, and Up is the speed of the passing ship.
When more than one passing ship is present, the ship
that tracks closer to the moored ship is regarded as
the reference passing ship for non-dimensionalization
purpose.
Table 1. Simulated Cases
Ship
A
A
A
A
A
A
A
A
A
A
A
A
A
A
-
A
A
A
8
. ~
Sneed Wind
U. 1.33U 1.67U Calm
, ,
U,1.33U,1.67U E
U,1.33U,1.67U W
.
U,1,33U,1,67U E
1.33U E
U W
1.67U Calm
W
W
W
W
Calm
. W
W
W
W
W
U,1.33U,1.67U
U. 1.33U 1.67U
, ,
U,1.33U,1.67U
U,1.33U,1.67U
1.67U
1.67U
1.67U
U. 1.33U, 1.67U
U. 1.33U
_ U
OCR for page 466
An overview of the computational grid for a two-way
passing calculation is shown in Figure 11. As can be
seen in the figure, both inbound and outbound ships
have a 5-degree crabbing angle to counter the wind
from the West (west wind condition). Both the
inbound and outbound ships travel approximately 5
ship lengths (depending on ship speed) and the
longitudinal extent of the computational domain is
about 150h. For the two-way passing cases, the
numerical grid consists of 15 computational blocks (3
blocks for each ship, 4 blocks for the harbor, and two
phantom grids) with 995,776 volume grid points and
10 free-surface blocks with 43,055 free surface grid
points. A close up view of the grid surrounding the
moored ship-C is shown in Figure 12, and a bird-eye
view of the blanking scheme between grid blocks is
shown in Figure 13. In the present simulations, the
numerical grids for the inbound and outbound ships
were allowed to move in prescribed translational
motion relative to the moored vessel and the
stationary harbor grids. Other than the forward
direction, motions of the passing ships were fixed in
all directions. The moored ship was also assumed to
be fixed. No equations of motions were solved in the
current study.
Figure 10. Simulation coordinate system
Figure 11. Numerical Grid for Two-Way Passing
Configuration
:'~^'~-~--~: . ~ ~~ :: ~ ~
Figure 12. Close-up view of grids for moored Ship-C
next to a pier
~ i: ~ i :i:::i~: i :~i :lR~ i-l-!-i-E ~1 ~ ~ -~-~-~--~-1-l ~ I i-t ~ it ~ 1.~ 1~4 1 ~ I Lt til ! ~ li - ~:~f~
Figure 13. Bird-eye view of blanking between grid
blocks
Detailed Flow Field
Time-domain simulations were performed for each
case listed in Table 1 with various combinations of
ship speed, wind direction, and wharf line distance.
A total of 2000 time steps were used for each
simulation with a constant non-dimensional time
increment of 0.0025. The initial positions of the
passing ships are about 2.0L from the center of the
moored ship. In all simulations, the passing ship (or
ships) was accelerated from zero velocity to the
designed speed between tlT= 0 and 0.2, where T =
LlUp is the characteristic time. The passing ship
travels 0.1 ship length during the initial acceleration
and then maintain a constant speed for the remaining
excursion. The Reynolds number is 7.78 x 108 and
the Froude number is 0.0575 based on the length of
ship-A and the reference speed U. In all simulations,
the time histories of the surge, sway, and heave
forces, as well as the roll, pitch, and yaw moments
9
OCR for page 467
acting on the moored ship were recorded. In
addition, a 500-frame movie was made for each
simulation to provide more detailed understanding of
the flow field induced by the passing ships). It
should be noted that the center of the passing ship
(closest to the moored ship) was aligned with the
center of the moored ship at tlT= 2.1 for all the
simulations considered.
Due to the large number of simulations
performed, it was not possible to present detailed
velocity and pressure fields for every case. For the
sake of brevity, we shall present the free surface
velocity and pressure contours for Case 39 to
illustrate the general flow features for two passing
ships in the navigation channel. In this case. the
inbound ship-A is moving from the left to the right,
and the outbound ship-B is moving from the right to
the left. Figure 14 shows the computed longitudinal
velocity and pressure contours for Case 39 at several
different time instants of tlT= 0.25, 0.5, 0.75, 1.0,
2.1, 2.25, 3.0, 4.0, and 5.0. It is seen that the pressure
field generated by ship-B is considerably stronger
than that induced by the ship-A. This is clearly due
to the fact that ship-B has significantly wider beam
and larger draft compared to ship-A. The rather blunt
bow shape for ship-B also produces larger pressure
waves in front of the bow. Furthermore, the bottom
clearance for ship-B is only 10% of its draft and is
significantly smaller than the 18% bottom clearance
for ship-A. A close examination of the movie file for
this simulation showed that the pressure waves
induced by the passing ships reached the moored ship
at around tlT= 0.6 with each passing ship travel
about 0.5 ship length. It is also interesting to note
that ship acceleration during the initial ramp start
produced very strong pressure waves that are
significantly higher than those observed after tlT= 1
when both the inbound and outbound ships were
traveling at constant speeds.
As noted earlier, the ship-ship interactions in
navigation channel is very complicated due to the
shallow water effects and the presence of channel
bank and mooring piers. In addition to the
interactions between the passing and moored ships, it
is also clearly seen that there are very strong
interactions between the inbound and outbound ships
when both ships were in the vicinity of the moored
ship. This is particularly evident at tlT= 2.35, shortly
after the inbound and outbound ships passed the
center of the moored ship. The influence of the
passing ships diminished gradually after tlT= 3.0
with the free surface pressure returns slowly to its
ambient value around the moored ship. However, the
trajectories of the wakes behind the passing ships
were still clearly visible at tlT= 5.0.
Forces and Moments
In order to analyze the mooring line forces induced
by moving traffic vessels, the computed pressure
and shear stresses were integrated over the hull
surface of the moored vessel. Figure 15 shows the
computed hydrodynamic forces and moments on the
moored ship-C. For all cases, the force and moment
coefficients were plotted as a function of XIL instead
of tlT with the initial position of ship-A located at
XIL = -2.0 and the center of the moored ship located
at the origin (XIL = 0 and tlT= 2.1~. It is noted that
the moored ship experienced a large downward heave
force after the inbound and outbound ships passed the
center of the moored vessel. This is clearly
associated with the depression of water elevation in
the narrow navigation channel due to ship motions.
It is also noted that the pitch moment history
exhibited some high frequency oscillations. This
high frequency oscillation was not caused by the
numerical instability since the oscillation period
(about 0. 11) was found to be significantly longer than
the time increment used in the simulation.
Furthermore, the high frequency oscillations were
present only when the ship-C is the moored vessel
and was completely absent for ships A-A-B
configuration (Case 22) shown in Figure 16 when
ship-A was moored at the pier. It is believed that
these high frequency oscillations were caused by the
small underkeel clearance of the moored vessel and
will be discussed in more details later when the
effects of bottom clearance is considered.
In the mooring line analysis, the sway forces
and yaw moments are of particular concern because
they produce lateral displacements and rotations
perpendicular to the wharf line. It is seen from
Figure 15 that the sway force reached a maximum
value at XIL = 0.6 (i.e., tlT = 2.7), long after the ships
passed the center of the moored ship. In the quasi-
steady, semi-empirical formula for deep water or
shallow open water ship maneuvering, the sway force
typically reached a maximum value at XIL = 0 when
the vessels meet on parallel course. The shift of the
maximum sway in the present simulation is most
likely due to the combined effects of wharf line
(bank) shape and small underkeel clearance that were
not included in the traditionally open water
simulations. Finally, it is also worthwhile to note that
both the sway force and yaw moment diminish
gradually after XIL = 1.0. Therefore, it is reasonable
to terminate the simulations after the passing ships
have traveled 3 ship lengths beyond the center of the
moored ship if our primary interest is to determine
the maximum mooring line forces.
10
OCR for page 468
.0.4 0.2 0.0 0.2
0.6 0.8
Figure 14. Longitudinal velocity (left) and pressure (right) contours at t/T= 0.25, 0.5, 0.75, 1, 2.1, 2.25, 3, 4, 5.
11
OCR for page 469
2.5'
' ~ Surge force
Sway to roe
Heave force
Roll moment
~ Pitch moment be,
Yaw Nero T ent !
2
1.5
~ 1
E 0.5 - .~' I--!
E o ~_~
_
_ ~ ~ ~~#~ —_ ,,h~
, .
i.
-1 .~ ~ .
-2 -1 o 1 2 3
X/L
Figure 15. Force and moment coefficients for Case 39
.:, 2
._
0 1
E
~ :
0 0
E
8
o -1
~ Surge force
Sway force
I Heave force
. Pitch rnornent ,~ %N
Yaw moment ,' -"
t_~_~
"A
........................
-2 -1 0 1 2 3
X/L
Figure 16. Force and moment coefficients for Case 22
The present study seeks to determine the
effects of passing ship speed, wharf line distance, wind
direction, bottom clearance, and ship sheltering while
there are more than two ships in the navigation
channel. In the following sections, we shall compare
the sway force andfor yaw moment time histories to
quantify these effects.
Passing Ship Speed Effects
In the present simulations, three different ship speeds
of U. 1.33U and 1.67U were considered for the
inbound ship-A while the speed for the outbound ship-
B is always the same. It is seen from Table 1 that the
speed effects were investigated for various
combinations of wind directions, wharf distance, and
ship types. Cases 1-12 examined the speed effects for
ships A-A in calm, east, and west wind conditions at
two different wharf line distance of s = lOh and 16.6h.
The speed effects were also investigated in Cases 22-
33 and 39~1 for other ship types involving A-A-B, C-
A, and C-A-B configurations. Figure 17 shows the
sway force and yaw moment coefficients for Cases 1-3
with ships A-A under calm wind condition at a wharf
distance s = lOh. The results are normalized by the
corresponding forward speed of the moving ship Up.
It is seen that both the phase and magnitude of the
peak sway force and yaw moment change with the ship
-0.1
0.2
speed. The phase lag for higher speed cases is to be
expected since the faster ship will be closer to the
moored ship when the pressure waves generated by
initial ship acceleration reach the moored vessel.
Although the yaw moment coefficient is higher for the
lower speed case, the magnitude of the yaw moment
actually increases with the ship speed since the
dimensional yaw moment is obtained by multiplying
Up to the coefficients. Similar trends were also
observed for other cases although the effect varies
somewhat with different wind directions, wharf
distance, and ship types.
0.2
0.1
~ O 4''V`;!
In
· Up= 1.67U
Up= 1.33U
Up=U
(''1'.\'~
~ (a) Sway Force
~ — Up - 1.67U
- - - - Up= 1.~JU
Up=U
Q 0.1
E O 1 'l' i
-0.1
(b) Yaw Moment
2 ... ...........
-2 -1 ° X'L 1 2 3
Figure 17. Speed effects for ship A-A in calm wind:
(a) sway force, (b) yaw moment
Further insight was gained when the numerical results
were examined in dimensional quantity. Table 2
summarizes the peak sway forces when a ship A is
passing a moored ship A or ship C at U. 1.33U, and
1.67U in the s = lOh wharf line configuration. The
moving vessel crabbed to the west in simulating a
transit to cope with a 3 U westerly wind. It was noticed
that the speed effects on the ships A-A interactions are
different from the speed effects on the ships C-A
interactions. In the ships C-A cases, the speed effect is
approximately proportional to the square of speed.
This is what one would expect from a fluid flow
phenomenon. However, the speed effect is almost
negligible on the ships A-A interactions. It is
hypothesized that when the moored vessel is a ship C,
the much wider beam, longer length, deeper draft and
very small underkeel clearance (1.064 water depth to
draft ratio) have made the pressure pulse contribution
12
OCR for page 470
to the interaction dominant over other contributions to
the interaction. With smaller dimensions and more
space under the keel for a moored ship A (1.163 water
depth to draft ratio), the predominant contribution to
the interaction seemed to come from ship wave trains,
local waves induced by interacting vessel pressure
fields, vortex shedding or other physical mechanisms.
This finding shows that in a complicated
setting of a ship next to a pier environment we cannot
rely only on one generic set of non-dimensionalized
ship-ship interaction curves for sway force
calculations. Significant errors could be introduced in
estimating the real effects of passing ships if the sway
forces are used in dimensional form based on
instantaneous passing ship speed.
Table 2. Speed Effects with Wind from West
CFD
Run
7
8
9
21
22
23
M-P
Ships
.
A-A
A-A
A-A
C-A
C-A
C-A
Max Sway
Coeff
0.0725
0.1100
0.1800
0.2050
0.2010
0.2150
Wind Direction Effects
Passing
Speed, U
1.67
1.33
1.00
1.67
1.33
_ 100
Max Sway
Force, pU2
.
0.2014
0.1955
0.1800
0.5695
0.3555
0.2150
The wind effects for a moored ship-A with a passing
ship-A or ship-B were investigated in Cases 1-9 and
19-20, respectively. For the East (E) wind condition,
the bow of the inbound ship will turn 5° in the
counterclockwise direction, and the bow of the
outbound ship will turn 5° in the clockwise direction.
On the other hand, the bow of the passing ships will
turn 5° in the opposite direction under West (W) wind
conditions. In Figure 18, the wind effects for ship
speed Up = 1.67U cases are shown for the ships A-A
configuration at a wharf line distance s = 10h. Figure
19 shows the wind effects for ships A-B configuration
with Up = U and s = 1 Oh. For the ships A-A
configuration, the wind directions and the related
crabbing angles show varying yaw moments from the
calm wind cases, but the effects are relatively small.
The yaw moment coefficients shown in Figure 19 for
ships A-B case are more sensitive to the wind
directions. In addition, the yaw moments and sway
forces induced by the larger ship-B are also
considerably higher than those observed in Figure 18
for ships A-A configuration. In general, it was
observed that crabbing angle introduced additional
interaction forces and moments depending on the
passing ship speed and crabbing direction. A typical
simulation adjustment of crabbing angle on passing
ship effects is to multiply the parallel course testing
data with a cosine function of the relative heading.
However, the finding from present calculation does not
support that approach.
0.2 t
c' 0.1
E° o
3 -0.1
CalmWind
East Wind
------- West Wind
-2 -1 ° XL 1 2 3
Figure 18. Wind effects for ship A-A at Up=1.67U
0.2 t
West Wind
<, 0.1
~ 0 ~N f ~ take],
o
3 ~.1
fY I'm ~ /\
-3 -2 -1 X'L ° 1 2
Figure 19. Wind effects for ships A-B at Up= U
Wharf Line Distance Effects
The wharf line distance effects for single and two ship
passing configurations were examined in Cases 4-6,
10-16, 20-33 and several other runs listed in Table 1.
For the sake of brevity, we will present mainly the
results for ships A-A configuration under East (E)
wind condition at a speed Up= 1.33U. Figure 20
shows the sway force and yaw moment histories for
moored ship-A at six different wharf distances of s =
6h, 8h, 10h, 12h, 14h, and 16.6h, respectively. It is
interesting to note that the peak sway force, in general,
reduces with increasing wharf distances. On the
contrary, the peak yaw moment tends to increase with
increasing wharf distances. However, the phase and
magnitude variations with wharf distance are not
completely monotonic. It should be noted that the
wharf line is still within one ship length of the passing
ship even for the longest wharf distance considered.
The hydrodynamic interactions between two
ships can be attributed to at least two major physical
13
OCR for page 471
phenomena: the pressure pulse and the ship generated
wave train. The pressure pulse can be explained by
Bernoulli's effects in the fluid flow surrounding the
vessels. The contribution of this mechanism is very
strong and dominant in close separation distance. But
the effect decreases rapidly when the vessels move
apart from each other. The effect of a ship-generated
wave train is of smaller order of magnitude, but the
effect can reach greater distance. There may be
contributions from other mechanisms that can also
reach greater distance, such as the "local waves"
mentioned by Dand (1981) and the vortex shedding
pointed out by Kaplan and Sankaranarayanan (1986~.
0.2
~0 O. ~
O
3
u'
E
E
s= 16.6 h
------ s=14h
--- s= 12 h
. s= 10 h
— s= 8 h
~ -— such
0.2
0.1
c ~ 1 ~ ~ h
s = 14 h
s = 12 h
A .~ s=10h
------- s=8h
s=6h
-0.1
(b) Yaw Moment
-2 -1 0 X/L 1 2 3
Figure 20. Wharf line distance effects: (a) sway force,
(b) yaw moment
Most of the towing tank tests only cover small lateral
separation distances where pressure pulse dominates
the ship interactions. For example, the test range of
separation distance covered by Dand (1981) was 1.1 to
3.66 of own ship beam widths. It is noticed that at
3.66 beams lateral distance, the interaction curves of
overtaking started to show more oscillatory behavior.
When a moored vessel is moored at a pier that
is built on top of a sloped bank, the physics of ship-
ship interaction hydrodynamics becomes more
complicated, especially with small underkeel clearance
for one or all of the interacting vessels. There might
be even "resonant phenomenon" when snipes) passes a
moored ship in the presence of a sloped bank because
the wave train could reflect and refract. This is an area
needs more research to understand the underlying
mechanism and harness the knowledge for simulation
applications. The results of SSPA model tests reported
by Li (2000) on bank effects clearly demonstrate the
complex hydrodynamic phenomena when a vessel is
sailing near a bank of various configurations.
Bottom Clearance Effects
The comparisons of pitch yaw moment coefficients in
Figure 21 for Cases 30 and 36 provide evidence for the
physical nature of the high-frequency force oscillations
detected in the ship-C runs discussed earlier. Such
oscillations are induced when a small clearance
between the ship and the bottom of the channel is
present. As noted earlier, Case 36 has the same
conditions as those in Case 30 except that the water
depth is 0.2h deeper throughout the channel and the 2
to 1 bank slope at the wharf line was replaced by a
vertical wall at a distance s = 2h away from the ship-C.
For the shallow water cases, the underkeel clearance is
only 0.06h or 6.4% of the ship draft. Therefore, the
water flow induced by the passing ships was forced to
move back and forth across the bottom of the ship hull
through small clearance. When the bottom clearance
was increased from 0.06h to 0.26h for Case 36, the
water was able to move more freely around the moored
vessel and the high frequency oscillations were
completely eliminated.
2
~ 1
0
o
-1
0.06h underkeel clearance
-- 0.26h underkeel clearance
-2 -1 2 3
Figure 21. Sway force and yaw moment for bottom
. .
c ~earance varlatlon
Ship Sheltering Effects
Traditionally, the superposition of forces and moments
has been used as a simplified way of obtaining the
influence of multiple ships passing the moored ship in
a simulator environment. In order to determine the
validity of superposition and the influence of
sheltering effects, a comparison between the
superposition of Case 7 and Case 20 and the combined
simulation of the same ships in Case 22. Figure 22
shows a comparison of the free surface pressure
contours for Cases 7, 20 and 22 at two different time
instants t/T= 2.0 and 2.5, respectively. The addition
of forces and moments from Cases 7 and 20 are shown
in Figure 23 and the comparison of Case 22 to the
14
OCR for page 472
superimposed solutions is shown in Figure 24. The
comparison of the superimposed solution to the direct
multi-ship solution shows that there are significant
sheltering effects from Case 22 that are neglected in
the superimposed solution. The free surface pressure
contours shown in Figure 22 clearly illustrates the
complexity of the nonlinear interactions between the
(a) Case 7, Ship A-A, t/T = 2.0
inbound ship, outbound ship, moored ship, and the
bank. These highly nonlinear multi-ship interactions
highlight the inaccuracy of a superposition method for
the multi-ship interaction problem needed to establish
the lashing loads on the moored ship.
(b) Case 7, Ship A-A, tot = 2.5
(c) Case 20 Ship A-B t/T = 2.0 (d) Case 20, Ship A-B, tlT = 2.5
(e) Case 22 Ship A-A-B t'T = 2.0 (f) Case 22, Ship A-A-B, tfT = 2.5
. ~ .... . _ _ _ _ . _ _ _ . _ _ _ _ .
-0.4 -0.2
0.6
0.4
`~ 0.2
ID
o o
-0.2
-0.4
, ,
- ....
o
0.6 t
0.4
0.2
E o ~ 5
-02
-04
-0.6( )
Shlps 1A ~ A1
~ - - Ships 1A ~ B]
_ - - - - - Superpose ~ ~ Ad
fib
~1
(a, sway Force
. . . . . .
j ... -
Ships ~ ~ ~ |
- ships CAT ED
- ---- -- Supelposiffon [A ~ A] ~ p~ ~ ED
l' ~ ~ ~ ~
-a' it;
, . . . .
1 2 tlT
5
(b) Yaw Moment
, . . . . .
3 4 ~
Figure 23. Superposition of (a) sway forces and (b)
yaw moments for Case 7 and 20
0.0 0.2 0.4 0.6 0.8 -0.4 -0.2 0.0 0.2 0 4
Figure 22. Sheltering effects at t/T=2.0 (left) and 2.5 (right), respectively
0.6
0.4
ID
`' 0.2
~ O
LL
~ -0.2
u,
-0.4
0.6
-0.4
O.B 0.8
~ - Superposl~don [A+AJ ~ [A ~ B]
lo Ships IA ~ A ~ B1
0 1
) ', ........
0 1 2 VT 3
'\1~
(M rob F x"
, . . . . . . . . . . . . . .
2 tlT 3 4 ' i
Superposition [A+Al + Urn E]
alps pa ~ A ~ ~
- V~'~
(b) Yaw Moment
.
4 1
Figure 24. Ship sheltering effects: (a) sway force, (b)
yaw moment
15
OCR for page 473
CONCLUDING REMARKS
In this paper, the unsteady chimera RAN S method has
been validated against some available experimental
measurements and employed to study the effects of
multiple-ship passing effects in a navigation channel.
In the validation study, the time-domain surge force,
sway force, and yaw moment results track the
experimental measurements very well even though
there are minor differences in the settings of the
numerical study and the original experiments. In the
navigation channel design study, the numerical results
were systematically organized and compared to
investigate the ship speed effect, wind direction effect,
wharf line distance effect, bottom clearance effect, and
ship sheltering effect while there are more than two
ships in the channel.
For safe operation of a ship while operating in
the proximity of other ships and near obstacles with
variable-depth bottom topography, accurate interaction
forces and moments acting on the ships are required.
At the current time, this vital information is typically
obtained from extrapolation of model test data and
from operator's experiences over the years. There are
very few systematic and reliable data exist at the full
scale. Advanced physics-based computation method
allows us to model the actual viscous flow phenomena
of the problem at a level not previously possible. The
current computation method offers the ability and
flexibility of modeling complex ship geometry,
multiple ships operating in the proximity of each other
and near obstacles, and channel bottom topography,
etc. In addition, computations can be done at full scale
Reynolds number where the viscous effects on the
ships are very difference from those at the model scale.
Although a great deal of improvements and further
studies are still required, the results presented in this
paper clearly demonstrate the potential of using the
chimera RANS method for ship-ship interaction and
navigation channel design related problems.
ACKOWLEDGEMENT
The authors would like to thank Mr. Kenneth Weems,
Mr. Paul Jones, Dr. Daniel Liut, and Mr. Michael
Meinhold for their help on geometry generation and
data processing of the results in this paper.
REFERENCES
Chen, H.C. and Chen, M., "Chimera RANS Simulation
of a Berthing DDG-51 Ship in Translational and
Rotational Motions," International Journal of Offshore
and Polar Engineering 1998, Vol. 8, No. 3, pp. 182-
Chen, H.C. and Korpus, R., "A Multi-block Finite-
Analytic Reynolds-Averaged Navier-Stokes Method
for 3D Incompressible Flows," ASME FED-Vol. 150,
pp. 113-121, Proceedings of the ASME Fluids
Engineering Conference, 1993, Washington, D.C.,
June 20-24.
Chen, H.C., Liu, T., Chang, K.A., and Huang, E.T.,
"Time-Domain Simulation of Barge Capsizing by a
Chimera Domain Decomnosition ~Ol)It)~!
Domain Decomposition Approach,"
Proceedings of the 12th International Offshore and
Polar Engineering Conference, KitaKyushu, Japan,
May 26-31,2002.
Chen, H. C., Liu, T., and Huang, E.T., "Time-Domain
Simulation of Large Amplitude Ship Roll Motions by
a Chimera RAN S Method," Proceedings of the 11th
International Offshore and Polar Engineering
Conference, Vol. III, 2001, pp. 299-306, Stavanger,
Norway.
Chen, H.C., Liu, T., Huang, E.T. and Davis, D.A.,
"Chimera RANS Simulation of Ship and Fender
Coupling for Berthing Operations," International
Journal of Offshore and Polar Engineering, Vol. 10,
No. 2, 2000, pp. 112-122.
Chen, H.C. and Patel, V.C., "Near-Wall Turbulence
Models for Complex Flows Including Separation,"
AIAA Journal, Vol. 26, No. 6, 1988, pp. 641-648.
_. . . ..
Chen, H.C., Patel, V.C. and Ju, S., "Solutions of
Reynolds-Averaged Navier-Stokes Equations for
Three-Dimensional Incompressible Flows," Journal of
Computational Physics, Vol. 88, No. 2, 1990, pp. 305-
336.
Dand, I.W., "Ship-Ship Interaction in Shallow Water,"
Report R 8, 1977, National Maritime Institute,
Feltham, Middlesex, United Kingdom.
Dand, I.W., "Some Measurements of Interaction
between Ship Models Passing on Parallel Courses,"
Report R 108, 1981, National Maritime Institute,
Feltham, Middlesex, United Kingdom.
Li, D-Q., "Experiments on Bank Effects under
Extreme Conditions," SSPA Report No. 113, 2000,
Goteborg, Sweden.
Norrbin, N., "Model Tests for CAORF Panama Canal
Study- Part 7: Ships in Straight Channels," S SPA
Report 3062-7, 1985, Goteborg, Sweden.
Kaplan, P. and Sankaranarayanan, K., "Analysis of
Asymmetric Channel Hydrodynamic Interaction of
Ships." Report No. VPI-AERO-156, 1986, Virginia
Polytechnic Institute and State University, Blacksburg,
VA.
Subs, N.E. and Tramel R.W., "PEGSUS 4.0 Users
Manual," Report AEDC-TR-91-8, 1991, Arnold
Engineering Development Center, Arnold Air Force
Station, TN.
16
OCR for page 474
DISCUSSION
Hoyte C. Raven
MARIN, The Netherlands
Your Figure 14 and the animations in your
presentation show large waves being generated
at the initial startup of the vessels. There are
solitary waves running ahead, interacting with
ships and reflecting at the far boundaries.
How did you separate the true interaction forces
and those caused by the transient waves?
Would it not be more accurate to neglect free
surface effects all together for these cases?
AUTHORS' REPLY
We would like to thank Dr. Raven for his
valuable discussion. If the ship starts from rest
in the real scenario, then the true interaction
should obviously include the transient wave
effects. Depending on the test condition, it is
actually quite common to observe solitary waves
running in front of the ship in shallow water ship
model tests. In the current study, the ship speed
was ramp up from zero to a constant value in a
fairly short distance. In an ideal setting, we
should allow the ships to run for a while so that
it can reach steady-state condition before them
encounter each other. However, this approach
will require a fairly large computation domain
and the large amount of computation time.
The ship speed is not high (less than 5 knots in
most cases), and the wave effect should be small.
I would not say the calculations without the free
surface effects would be more accurate. But,
based on the fact of low ship speed, we should
be able to neglect the free surface effects and
expect the error to be small. However, if the
ships are very close to each other during passing,
a rigid surface condition on the free surface
(neglect the free surface effects) will create an
unrealistic pressure between the ship since the
fluid will be forced to escape in the horizontal
direction rather than both the horizontal and the
vertical directions.
DISCUSSION
Tao Jiang
VBD European Development Centre for Inland
and Coastal Navigation, Germany
I would like to congratulate the authors for their
comprehensive study on a practically relevant
subject. The proposed method seems to work
well for such complex interaction problems near
a harbor basin.
Looking at Figure 5, one can observe that there
is a strong interaction of bow-wave systems of
the two ships subjected for head-on encounter
case. However, bow-wave systems do depend
on the start contributions which are quite
different from the real situation. Could the
authors comment on their experience regarding
the influence of numerical accelerations of the
ship for truly unsteady problems?
AUTHORS' REPLY
We would like to thank Dr. Jiang for his valuable
comments. As discussed in the previous reply,
in an ideal setting, we should allow the ships to
reach a steady-state condition before they pass
each other. In that case, the bow waves would
not be an issue. However, there are practical
limitations of this approach based on domain
size and computation effort considerations. Our
observation indicated that the effect of the bow
waves were relatively minor comparing to the
actual interact between the ships. However,
more study is required to quantify the true
impact.
Representative terms from entire chapter:
wharf line
