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OCR for page 393
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Water Shipping on a Vessel in Head Waves
M. Wreck, O.M. Faltinsen2, M. Landrinii
(tINSEAN, The Italian Ship Model Basin, Roma - Italy, Department of Marine
Hydrodynamics - NTNU, Trondheim - Norway)
ABSTRACT
We present an investigation based on experimental and
numerical studies for the bow-deck wetness in head-sea
conditions of a stationary ship, with a blunt bow. Three-
dimensional water-on-deck experiments have been car-
ried out by focusing wave packets against the model of
a ESSO Osaka tanker. The experiments give a funda-
mental description of the dynamics of water shipping
and provide some useful data for the development of
three-dimensional numerical methods. In particular, the
observations confirm the formation of a cavity entrap-
ping air during the initial stages of the water shipping.
Near the fore portion of the deck, the local ship geom-
etry affects shape and complexity of the cavity evolu-
tion, always characterized by free-surface breaking and
dispersion of bubbles in the main water field. To deal
with this flow conditions, we present a Domain Decom-
position (DD) strategy to solve numerically the prob-
lem. A boundary element method (BEM) for the outer
field, where smooth though steep waves are present,
and a Volume-of-Fluid (VOF) method for the Navier-
Stokes equations in the breaking region have been cou-
pled by the DD. The present approach represents a com-
promise between efficiency, robustness and capability
of capturing the fragmentation of the air-water inter-
face, which occurs at several stages during the flow evo-
lution. The method is applied by assuming the flow to
be two dimensional in the longitudinal ship plane, but
no limitations exist to extend it to three dimensions. The
DD approach appeared rather promising, although com-
parisons with reference solutions demostrate that nu-
merical inaccuracies develop in the VOF solver so far
adopted.
INTRODUCTION
Reducing or preventing the occurrence of water ship-
ping is becoming an important issue for safety and op-
eration of ships. Compact masses of water entering and
flowing on the ship deck are a danger both for advanc-
ing and for moored vessels, whatever the considered
ship type is.
The present activity deals with the water on deck
in the context of stationary ships. This is an important
issue for FPSOs. These are ships with blunt bow forms.
A turret-mooring system supported by thrusters and a
dynamic positioning system are typically used. The ob-
jective is to keep the vessel closely to head-sea con-
dition. Green-water FPSO accidents documented deck
wetness in the bow region as well as from the ship sides,
with damages for deck house and equipment. In partic-
ular, the location of the deck house can vary. FPSOs
working in the North Sea usually have the deck house
with living quarters in the bow region. Our focus is on
the bow region, but green water has actually occurred at
many different locations along the ship.
Recently different projects have been program-
med andlor carried out for a deeper understanding of the
influence of ship geometry and wave parameters on the
occurrence and severity of this phenomenon. In general,
both experimental and numerical instruments are used
for this scope.
Our ongoing activity is aimed to understanding
the phenomenon and developing robust and efficient pre-
diction tools to be used in design and certification. In
recent studies, we focused our attention on a simpli-
fied prototype problem, Greco et al. (2000~. The how
has been assumed two-dimensional in the longitudinal
OCR for page 394
ship plane. The unsteady interaction between free sur-
face and ship has been accounted for, while viscous
and surface-tension effects have been neglected. The
problem has been solved numerically through a panel
method (BEM) with piecewise-linear shape functions
both for geometry and for boundary data. The method
was verified and validated through comparison both with
reference solutions and with experimental results. With
this instrument, a simplified parametric analysis was
carried out and the role taken by some of the main ge-
ometric and kinematic parameters involved in the wa-
ter on deck was discussed. Fundamental features of
the phenomenon have been highlighted. Both water on
deck resembling the breaking of a dam and water ship-
ping due to large scale plunging waves have been inves-
tigated. Two-dimensional water-on-deck experiments
analyzed in Greco (2001) identified the efficiency and
the limits of the numerical approach developed. During
the tests, a restrained nearly rectangular ship model was
exposed to head-sea waves generated by a flap wave-
maker in a small wave flume. We discovered that water
on deck starts in the form of a very localized plunging
wave that breaks onto the deck, close to the bow. At the
impact, an air cavity is formed. The post-impact evolu-
tion is not handled by the panel method. This could be
accomplished by using suitable high-speed local solu-
tions for short time scales, or by different methods able
to handle large deformation of the free surface, possibly
with multi-phase flows. On a larger time scale, the ex-
periments show a global behavior of the water along the
deck similar but not quantitatively the same as the flow
generated by the breaking of a dam, eventually hitting
the deck house. Through a proper Kutta-like condition
at the edge of the deck, the BEM method is able to cap-
ture both the initial plunging phase and the global be-
havior of the masses of water invading the deck. With
this approach the high pressures related to the initial im-
pact of the water with the deck house can be accurately
estimated. On the other hand, the BEM is not able to
handle post-impact phases, characterized by fragmenta-
tion of the free surface. This occurs after the impact of
the initial plunging wave with the deck and is associated
with the collapse of the cavity. Similar situation char-
acterizes the water field near the deck house in the late
stages of the impact. During the water run-down along
the wall a backward water overturning is observed, im-
pacting with the under water flowing along the deck to-
wards the deck house. Free-surface breaking and air en-
trapment are observed. Both mentioned phenomena are
potentially relevant from the structural point of view,
since they could be associated with large loads on the
structure. During the first stage, the loading due to the
compression of the cavity is of main concern. Therefore
its possible occurrence in the three-dimensional context
is of practical importance. On the deck house, large
loading occurs both when the water initially hits the
structure and when the backward overturning water im-
pacts and mixes with the under water flow, during the
run-down phase.
In this paper, the problem is analyzed experi-
mentally and numerically. Three-dimensional water-
shipping experiments have been performed to highlight
the dynamics of the water flowing along the deck. On
the numerical side, to deal with complex flow condi-
tions, a Navier-Stokes solver with a Volume-of-Fluid
(VOF) treatment of the interface is coupled via a Do-
main Decomposition (DD) strategy with a Boundary
Element Method (BEM), applied in the non-breaking
region of the flow field.
THREE-DIMENSIONAL WATER-ON-DECK EX-
PERIMENTS
Three-dimensional model experiments are ongoing to
study water-on-deck phenomena for stationary ships. In
the first part of our activity, we have focused our atten-
tion on the flow evolution along the deck during the wa-
ter shipping in head sea. A simplified analysis has been
carried out by combining the flow visualizations with
the wave elevation measurements around the used ship
model, in the vicinity of the bow.
Experimental Set-up
The tests have been carried out at INSEAN facilities in
a towing tank 220 m long, 9 m breadth and 3.6 m deep.
The experimental set-up, as well as the incident wave
parameters, have been decided by referring to PESO
ships and their usual operational conditions. The FPSO
water-on-deck accidents in North Sea documented that
the most interesting wavelengths are of order of the ship
length. In different cases, casualties occurred when the
vessel was full loaded, with an effective freeboard defi-
nitely smaller than the nominal value, Ersdal and Kvit-
rud (2000~.
OCR for page 395
|\ "' ,~; r
Figure 1: Body plan of the Esso Osaka ship model.
A Esso Osaka ship model (see figure 1 ) has been
used during the tests. The model has draft D ~ 0.284
m, length L ~ 4.44 m and beam B ~ 0.74 m. Since
the ship model is restrained from oscillating during the
experiments, and we wanted to have realistic heights of
water relative to the deck for representative design con-
dition, the upper portion of the bow has been modified
by reducing the freeboard to f = 0.064 m (see lateral
view in top plot of figure 2~. This means, D/L ~ 0.064,
B/L ~ 0.166 and f /L ~ 0.015. The tank dimensions
and the scale of the experiment ensure that the tests re-
produce water-on-deck casualties in deep and open wa-
ters. The ship bow has a conventional bulb, but this
is likely to be not relevant for water shipping (ci i.e.
Greco 2001~. Although the bow is quite blunt, at the
deck level the bow sides form an angle of about 100°
at the ship centerline. This is because the above water
portion of the bow has been realized in a transparent
material difficult to shape. This angle could affect the
features of the initial stages of the water on deck. Also
the deck has been realized in Plexiglas to permit visu-
alizations of the water run-up along the bow and of the
water front along the deck during the water shipping.
This is achieved by using a video camera in combina-
tion with a mirror placed under the ship deck (see left
center plot of figure 2~. The flow evolution was moni-
tored through a black/white video camera with a frame
rate of 30 Hz. The video camera was placed inside
the ship model and directed towards a mirror parallel
to the ship deck and located onto the internal bottom
of the model, as shown in the bottom sketch of figure
2. In this way, bottom views of the deck have been ob-
tained. For quantitative analyses, the false prospective
due to the mirror presence has to be filtered out. This
was done by post-processing after the video camera has
been calibrated. An additional color camera, with sam-
pling frequency of 25 Hz, was utilized to have captain
s~r~so~-
rn 10
wet
r
s10OS7 0 s4 0 slO
sllOs80 sl5° s20
sl20s90 s60 s30
camera
_,_.,-,:z ' ~
i,.
. I .
. I .
~ ~ I ~
r ~ . /,
~ ~ mirror
Figure 2: Experimental set-up: Lateral view (top), top
view (left center), sketch with the wave sensors used
in the experiments from top view (right center), and
sketch of the camera-mirror combined system from lat-
eral view (bottom).
and lateral views of the water shipping phenomenon.
A vertical wall in Plexiglas, perpendicular to the ship
center plane, has been introduced along the deck, at a
distance of 0.53 m from the bow (see right-center plot
of figure 2), mainly to protect the video cameras used
during the experiments.
In the real case the water shipping may be due
either to a single event, or to a summa of a small number
of events related to wave groups approaching the ship.
In the latter case, the first event is not necessarily the
most severe one. In the present tests, the water on deck
is studied as a single event. In this way, we also avoid
effects due to wave reflections from the tank walls. The
incident waves are wave packets. The used technique
is based on the focusing of the wave energy by linearly
decreasing the wavemaker frequency and thus increas-
ing the group velocity of the generated waves leading
OCR for page 396
to focusing of the dispersive waves. In this context the
energetic wave spectrum, the time instant for the focus-
ing occurrence, and the focusing point along the tank,
represent input data. In our case each wave packet is
characterized by an identical amplitude a for all the
generated wave components (see the amplitude spec-
trum in left plot of figure 3~. A wave-steepness param-
eter ha can be defined for the wave packet, k being the
wavenumber associated with the mean frequency fc in
the spectrum. In the tests, both fc and the frequency
bandwidth Af are kept fixed and equal to 0.6 Hz and
0.4 Hz, respectively. This gives ~ = 2~/k = 4.33 m
~ 0.98L as wavelength related to fc, while the shortest
and the longest wavelengths in each wave packet corre-
spond to ~ 0.5 and to ~ 2.6 the ship length L, respec-
tively. The wave steepness ha has been varied between
0.125 and 0.25. The focusing point has been chosen
almost at the bow location (about 85 meters from the
wavemaker). The typical time history of the wave ele-
vation at this location without the ship model present is
given in right plot of figure 3. The incident disturbances
at
0~
.
O
4J
\/ Am/
· ~ W ~ t
Figure 3: Left: example of amplitude spectrum associ-
ated with the wave packets used the tests. Right: exam-
ple of time history of the wave elevation at the location
along the tank where the focusing phenomenon occurs,
without the ship model present.
are two-dimensional but the wave field in the vicinity
of the ship will be three-dimensional due to the scat-
tering of the incident waves. Sixteen capacitive wave
sensors have been located around the ship model (see
right bottom sketch of figure 2) to measure the wave el-
evation and to quantify the effects due to the ship pres-
ence. Each probe has a diameter of 0.5 mm to reduce as
much as possible the disturbance to the flow field. Here,
our attention is focused on the flow developing onto the
deck during the water shipping and the wave scattering
due to the ship is not discussed.
General features of the water shipping
The flow along the deck Two-dimensional water-on-
deck experiments discussed in Greco (2001 ) have shown
that the water shipping starts in the form of a wave
plunging and hitting the deck near the bow of the ship
model (see figure 41. A cavity entrapping air appears
Figure 4: 2D water-on-deck experiments: plunging
wave phase characterizing the stages of the water ship-
ping. Time increases from left to right.
and it is stretched downstream by the main flow along
the deck and by the weight of new water entering the
deck. Eventually the cavity collapses. The three di-
mensional experiments confirmed the occurrence of a
wave plunging phase at the beginning of the water on
deck. The top plot in figure 5 shows a side view of the
water shipping at about 0.12 s after the freeboard ex-
ceedance. The incident waves propagate from left to
right, and the interaction with the restrained ship model
determines the bow deck wetness. In the case shown,
the wave packet has a steepness ha = 0.15 and central
wavelength ~ = 4.33 m (case b). The water shipping
starts first from the fore portion of the bow, where the
wave elevation exceeds earlier the freeboard. Then the
phenomenon developes along the bow sides, with a non-
uniform (decreasing) maximum freeboard exceedance
going from the fore portion towards the superstructure.
The water initially enters the deck in the form of a plung-
ing wave hitting the deck near the bow sides. The arrow
in the snapshot indicates the flow region characterized
by a plunging wave. To better emphasize the plunging
wave phase, the ship deck has been removed and the
resulting flow is shown in the bottom plot of the same
figure, for a time instant of about 0.16 s after the free-
board exceedance by the water. A top-captain view of
the water on deck in the same conditions is shown in
figure 6. The horizontal line visible in the snapshots in-
dicates the location of the vertical wall along the deck.
The time increases from left to right and from top to
bottom, with interval of 0.08 s between two snapshots.
In the pictures, the yellow color is the internal color of
the ship model. The green color in the water is due to
a mixture of natrium flourisenium powder placed in the
upper-front portion of the bow and partially convected
by the water flow during the run-up along the bow. The
mixture has been used to make clearer the water ship-
ping features. The water shipping starts first near the
OCR for page 397
~ ~ ~:~ -
- -a
i.
]
~ - -
~ - -
Figure 5: 3D water-on-deck experiments: side view.
The wave packet has ha = 0.150 and ~ = 4.33 m (case
b). Top: snapshot of the water shipping at about 0.12
s after the freeboard exceedance. Bottom: snapshot of
the water shipping at about 0.16 s after the freeboard
exceedance in the case when the ship deck has been re-
moved.
Figure 6: Water on deck caused by a wave packet with
ha = 0.150 and ~ = 4.33 m (case b), top-captain view.
Time increases from left to right and from top to bottom.
The time interval between two snapshots is ~ 0.08 s.
terline, resulting in a tongue of water moving towards
the superstructure. This one is clearly characterized by
a smaller layer of water than the two lateral jets gen-
erated from the impact. The latter leave the ship axis
of symmetry in the form of water humps entrapping
air. As a consequence of these reflected flows, the cen-
tral tongue enlarges its width with time and is delimited
by a non-smooth structure, likely characterized by mix-
ing of water and air bubbles. At this stage, along the
bow sides the two cavity arms have collapsed and two
jet flows (one for each side) are originated towards the
vertical wall, moving slower than the central tongue-
shaped flow. The described flow evolution along the
r: IF
ship centerline, and proceeds progressively from there I
on. Two non-uniform cavities are originated along the
bow sides.
The initial water-on-deck phase at the fore bow
is not very clear from the snapshots. There, the plung-
ing waves from the two sides of the bow interact with
each other and with the flow entering the deck along
the ship centerline. The water fronts coming from the
two ship edges interact along the ship center plane, and
are reflected outwards leaving laterally the deck. Air is
entrapped and convected by the two flows. The charac-
teristics and the collapse of the cavities are the result
of the local flow features and of the local bow char-
acteristics. The mentioned impact causes also an in-
crease of the velocity of the flow along the ship cen-
- ,\
1 11 1
Figure 7: Sketch of the flow evolution during the water
shipping, top-captain view. Time increases from left to
right and from top to bottom.
deck is qualitatively sketched in figure 7. The instan-
taneous water fronts along the deck are better observed
from the bottom view presented in figure 8. The time in-
OCR for page 398
creases from left to right and from top to bosom, with
a time interval of about 0.33 s between two snapshots
(the prospective error has not been corrected in these
images).
Figure 8: Water on deck caused by a wave packet with
ha = 0.15 and ~ = 4.33 m (case b), bottom view. Time
increases from left to right and from top to bottom. The
time interval between two snapshots is ~ 0.033 s.
The horizontal black lines visible in the snap-
shots are the result of the reflection from the mirror of
the lines drawn on a panel in front of the bow (the panel
is indicated by the arrow in the top plot of figure 2~.
From the pictures, near the fore portion of the
deck, a circular-shaped structure is formed at the be-
ginning of the water shipping, increasing as the time
increases. In the second snapshot, this structure is char-
actenzed by an inner-darker region, where the deck has
been already wetted, and an outer-lighter ring, where
air is present. At this instant two cavities are observed
along the bow sides, they have been colored in yellow
to make them more evident and are indicated by the ar-
rows. These are not perfectly uniform, with thickness
slowly reducing from the ship centerline on. At this
stage, the impact of the water with the deck has already
occurred. Two types of jet Rows have been originated
along the deck? almost perpendicular to the bow sides
and, respectively, entering and leaving the deck. This is
similar to the observations in the two-dimensional ex-
periments in Greco (2()01, see right plot of figure 41.
The evolution of the water near the centerline needs
additional comments. There, the flow is well three-
dimensional. After the cavity collapse, a main jet to-
war~is the superstructure is Unnerved, accompanied by
two lateral flows leaving the deck (C,76 second plot in
the figure). The former is faster than the water fronts
along the bow sides entering the deck, as well as the two
lateral flows are faster than the water fronts along the
bow sides leaving the deck (ct third plot in the figure
and the enlarged view given in figure 9~. The region of
~ . ,,~r~,;,,, . a: ,., ,:, .
Figure 9: Water on deck caused by a wave packet with
ka = 0.10 and ~ = 4.33 m (case b), bottom view. En-
larged view of the flow region near the ship centerline
at the time instant show n in third plot of figure 8.
the deck interested by the evolution of the cavity struc-
tures until their collapse is well delimited by two lines
of water (one at each bow side). The rest of the deck
is gradually wetted by the water flowing towards the
vertical wall. The collapse of the cavities leads to bub-
bles, first in the form of organized structures and then
as individual bubbles dispersed within the main bulk of
water. These are larger near the centerline. The volume
of air initially entrapped is larger near the ship center-
line and reduces moving along the edges of the deck.
Consistently, we observed larger bubbles near the ship
centerline. The flow of water towards Me vertical wall
does not appear completely smooth. Wavy structures
with relatively short wave length (order of one centime-
ter) are observed. Thes ripples are probably caused by
surface tension effects, relevant at the beginning of the
water shipping due to the high curvatures involved. The
global shape of the water fronts developing along the
deck is initially similar to a straight line, but it diverges
progressively from this behavior as the time increases.
OCR for page 399
At the same time the water fronts become less smooth.
Figure 10: Water on deck caused by a wave packet with
ha = 0.150 and ~ = 4.33 m (case b). Left: lateral view
of the water shipping before the water impact with the
vertical wall along the deck. Right: top-captain view
of the water shipping during the water run-up along the
vertical wall.
The water impact with the superstructure The im-
pact of the water with the vertical wall along the deck
occurs generally in a non-uniform way. This is shown in
figure 10 through a lateral view (left) of water shipping
just before the impact, and a top-captain view (right)
of the water shipping during the water run-up along
the structure, once the impact has occurred. The flow
run up along the wall is eventually reversed due to the
gravity action, and a backward water overturning is ob-
served (see top plots of figure 11~. The same phenome-
L__11~
it: -
~ i
~ BY 1
__ ~
_ I
_ -God ~ ~~ J
:~_d
_
_—_
_ _
___
~r'~
~ _
-
-
-
-
-
_~
l
_
Figure 11: Backward plunging wave formed after the
maximum run up has been reached. Top: 3D wa-
ter-on-deck experiments. Bottom: 2D water-on-deck
experiments. Time increases from left to right.
non has also been observed during the two-dimensional
experiments in Greco (2001, see bottom plots in the
same figure) and pressure measurements along the ver-
tical wall showed an increase of the structural loads due
to the plunging formation and its final impact with the
under water flowing towards the superstructure. It is
reasonable that the same happens in the three dimen-
sional case.
The water-off-deck phenomenon The water how gen-
erated by the reflection from the vertical wall causes
eventually a water-off-deck phenomenon (see left plot
of figure 12) modifying the flow field conditions around
the ship bow with respect to the diffracted wave field
without water-on-deck occurrence. As an example, at
the location of sensor 7 (indicated by the arrow in the
left plot of figure 12) a primary peak of the wave eleva-
tion corresponding to the water-on-deck occurrence is
followed by a sharp secondary peak (see right plot of
figure 12) associated with the disturbance of the water
leaving the deck. Therefore, in case of repeated water
Figure 12: Water on deck caused by a wave packet with
ka = 0.150 and ~ = 4.33 m (case b). Left: side view
during the water-off-deck phenomenon. Right: time
history of the wave elevation at the wave sensor 7 (indi-
cated by the white arrow in the left photo). At the time
instant of the left snapshot a sharp secondary peak in
the measured wave elevation is observed, as indicated
by the connecting arrow.
shipping, the second water on deck could be strongly
affected by the modifications in the wave field around
the ship bow due to the water-off-deck phenomenon as-
sociated with the previous event.
Steepness influence on the water shipping
Figure 13 shows snapshots of the water along the deck
after the collapse of the cavities associated with water-
on-deck events due to wave packets with ~ = 4.33 m
and ha = 0.125, 0.15, 0.175, 0.2 and 0.225, respec-
tively (cases a-e). The non-dimensional time instants
are not the same, and correspond to /\7wO~ = (t—twos)
/~/(H—f)/g ~ 0.95, 0.83, 0.87, 0.79 and 0.74, for
increasing values of the considered steepnesses. Here,
OCR for page 400
~ -
~ - -
~ —
-
- ~ ~
- - ~
- ~
Figure 13: Steepness influence on the initial cav-
ity. Water on deck caused by wave packets with
~ = 4.33 m and ka = 0.125, 0.150, 0.175, 0.200 and
0.225 (case a,.., case e, respectively), bottom view.
r
i\~ = (t—twod)/~\/(H—;)|g,whereH = 2a end twod
is the time instant when the water shipping started. The
spatial variables are made non-dimensional by (H - f ).
The prospective error has not been corrected.
twos is the time instant when the water shipping started.
In the case with the smallest incident wave steepness,
the region of the deck near the fore portion of the bow
appears almost completely wetted, differently for the
other cases the ring-shaped regions near the bow apex,
identifying the collapse of the two cavities at the fore
bow, and the related lateral flows, are visible. As the
steepness increases, the bubbly structures associated with
the two cavities become less uniform along the ship
sides, and thicker near the ship centerline.
Snapshots of the water along the deck, at the non dimen-
sional time instant i\rWO~ ~ 1.6 after the starting of the
water shipping and for the same cases, are shown in fig-
ure 14. As we can see, the bubbly structures subsequent
to the cavities collapse (especially near the ship cen-
terline) increase with the steepness. Also, the portions
of the deck interested by the evolution of two cavity
arms become larger as steepness increases. These can-
not even be clearly detected in the case with the small-
est steepness (case a). The water fronts during the water
shipping have been extracted by the video images and
are presented in figure 15. In the plots, the water en-
ters the deck from the bottom and the fore portion of
the ship deck is represented by the straight lines form-
ing an angle of about hundred degrees. The time in-
terval between two water-front configurations is equal
to the frame rate of the video camera (1/30 s). As the
wave steepness increases, the water fronts become less
Figure 14: Steepness influence on the water front evo-
lution. The water-on-deck is caused by wave packets
with ~ = 4.33 m and ha = 0.125, 0.150, 0.175, 0.200
and 0.225 (cases a-e, respectively), bottom view.
The snapshots correspond to the time instant
t ~ 1.6~/(H—f)/g from the starting of the wa-
ter shipping (H = 2a). The spatial variables are made
non-dimensional by (H—f). The prospective error
has not been corrected.
smooth and with a more marked interaction of the cen-
tral water flow with the lateral ones. In the last plot
(right bottom) of the figure, the estimate of the front ve-
locity along the ship centerline is given. This has been
obtained as ratio between the distance covered by the
water front and the related time interval. The different
cases are associated with non-dimensional front veloci-
ties of the same order of magnitude. Case a, for which
a longer non-dimensional time evolution is available,
shows a water front velocity slowly increasing with a
rate of change reducing with time. This suggests an in-
creasing shallow-water behavior of the water. A similar
behavior is also shown by case b. Differently the other
cases (cases c-e) show a relatively large change with
time of the water front velocities. The data available
for these cases refer to a non-dimensional time inter-
val smaller than for the two less steep cases. The large
rate of change in the front velocity implies that shallow-
water conditions are not yet reached by the flow along
the deck, and dispersion effects still matter.
TWO-DIMENSIONAL NUMERICAL STUDIES
Two- and three-dimensional tests evidenced breaking
and fragmentation of the free-surface, and air entrap-
ment during initial and late stages of the water ship-
ping. These phenomena are relevant for the resulting
OCR for page 401
and Valli 1999), where the flow field is divided into
sub-domains, each one modeled by a different numer-
ical method. In this way, the advantages of the BEM
method can be combined with the capabilities of a field
method. In particular, the latter will be used to describe
the flow evolution in proximity of the ship bow and on
the ship deck. The rest of the fluid domain will be ac-
curately described by the BEM, that is more efficient
and accurate in dealing with non-breaking free-surface
flows than field methods.
200
1X
200
1X
300 _
a
1=
0 1
300 ;
_~
WIt
case ~
Urn
Ann
100
a,~|t
~ \1// case b
. -~_
\ / case c
.... ~ . , .. I .... ~ ...
I^'~ fit
\- / can
0 _
200
1=
:~
0 \ /ca'cd
O lCO 200 30O
x (mill)
0 ease a
· ease b
.~ .
v
g(H-~) as
/ .
O-
ease c
card
_
. .
° ~ ~ Ax~/(HJ) 3
Figure 15: Case a to case e: water front propagation
along the deck (bottom view), time interval equal to the
rate of the video camera (1/30 s). The dotted lines in the
plots indicate the lines tangent to the bow sides and the
ship centerline. Right-bottom plot: water front velocity
along the ship centerline as a function of the distance of
the water front from the most fore bow point. H = 2a.
structural loads and should be correctly treated by any
prediction tool.
As shown in Greco (2001), a BEM approach is
able to detect and quantitatively capture several features
of water shipping but cannot handle the long-time evo-
lution, when free-surface breaking and two-phase flows
are observed. To the purpose, a field method with a
suitable treatment of the air-water interface could be
used. On the other hand, field methods are more expen-
sive in terms of memory and CPU-time requirements.
Moreover, the present experiments evidenced relevant
three-dimensional effects during the entire water ship-
ping, both around the ship and on the deck. The use
of field methods may become prohibitive when dealing
with the three-dimensional problem.
As a compromise between efficiency, robustness
and ability to handle the air-water interface dynamics
through the entire evolution, we decided to develop a
Domain Decomposition (DD) strategy (see Quarteroni
In the whole domain the flow is assumed incom-
pressible, while only in the BEM sub-domain it is con-
sidered inviscid and irrotational. Surface tension is ne-
glected everywhere. A free-slip condition along rigid
boundaries and pressure continuity across the air-water
interface are enforced.
In the region studied with a field method, the
problem is written in terms of primitive variables, ve-
locity and pressure, and the numerical solution is ob-
tained through a finite difference technique, on a stag-
gered Cartesian grid. A two-step projection algorithm is
used, where an auxiliary non-free divergence velocity is
introduced. The pressure field is governed by the Pois-
son equation and it is solved by an incomplete Cholesky
conjugate gradient method. The free-surface is treated
by a Volume-of-Fluid (VOF) technique, where the inter-
face is reconstructed by means of a passive scalar field
J(P, t) ~ LO, 1], representing the local water-volume
fraction. Details for the numerical algorithm can be
found in Hirt and Nichols (1981~. The BEM method
and the related numerical details are extensively descri-
bed in Greco (2001~.
Within the DD approach, BEM and VOF regions
are connected by a Transmission Domain portion (TD),
where the two sub-domains exchange information. In
this context, two different procedures have been ana-
lyzed (Campana and Iafrati 2001~. In the first one, cp
procedure a in the top sketch of figure 16, TD is a con-
trol surface and represents a boundary portion of the
BEM and VOF sub-domains. In this case, the velocity
distribution calculated by the BEM is used as boundary
condition for the field method. The latter provides the
pressure distribution used, through the Bernoulli equa-
tion, to update the velocity potential enforced along the
transmission boundary. Here a Dirichlet boundary con-
dition is enforced.
In the procedure b in the bottom sketch of fig-
OCR for page 402
a) I TD
---- --.
i
,
s
1
. : : :
: : ~
: :::
::: ::
: ::
13: :
.
BEM region
: : ::: :
:: : VOF: region i: :~: ~
I ~ ~ ~
i:
1 :: ~ :
-
i:~:~ ::~ ::::: :::~::::: :~::: ::: ~::
I::::: ::: :: :::: ::::::::: :::: ::: :::: ::::
:::: :: ::::: ::::::: :::::::::::: ::::::::::: :::::::
1::::: :::: ::: :: :::: :::: :::: :::::::::: :::::
I: : ::: :: :: : :: ::: ::::: :::::::
· : ~ : : : - ~ :: A:
: : : : : :::
............
BEM boundary" VOF boundary
hi)
1|, TD
. _ _
rid :
art::
r~
I ~:
r—
rid A:
BEM region
r~~
. ~
VOF boundary t ~ BEM boundary
::
~~VOF~:reg~on~ :~: Z
.
.
::
: : ::
: : :
Figure 16: Definition of the transmission region within
the Domain Decomposition approach according to pro-
cedures a and b explained in the text.
ure 16, the two sub-domains are partly overlapped, and
TD is the domain portion belonging to both of them.
In the computations, the VOF solution gives the normal
velocity component enforced along the BEM boundary
(Neumann boundary condition), while the BEM solu-
tion gives the velocity distribution required by the field
method along the VOF boundary.
In the numerical implementation, the time step is
governed by the stability constraints of the field method,
more stringent than those requested by the free-surface
evolution in the BEM domain, where a standard fourth-
order Runge-Kutta method is adopted.
Though the approach is rather general, at present
only the two-dimensional version of the method has been
implemented. Examples of application of the method
are presented in the following. In particular, we men-
tion that in the present case the emphasis is not on vis-
cous effects, and, for instance, the grid resolution has
not been chosen refined enough to capture boundary
layer effects and, consistently, a free-slip condition is
enforced along the solid boundaries.
Dam-breaking problem
As a preliminary study, the DD approach has been ap-
plied to a dam-break problem. A vertical (rigid) wall is
located downstream the initial dam position to mimic a
deck-house impact event. The considered reservoir of
water has a height h and a length 1. The DD results
shown in the following have been obtained by using
procedure a described above for the coupling between
the two sub-domains. The BEM solver is used to simu-
late the flow evolution up to a given horizontal distance
from the dam. Downstream this vertical section, the
problem is solved by the VOF method (see Figure 17~.
The VOF region is rectangular shaped, and its boundary
dam
~ ~W~W_~W~
BEM sub-domain ~ VOF sub-doma~n
I TD
~ :~ Hi: ~: : ~ ~ ~ A:: A: ::: ~ A:: ~
:::: ::: :::: ::::::: ::::: ::
~ ~ ~ ~ ~ ~ - ~ : ~
- ~ ~
.
. - ~
: ::: ::: :::::: :: :::::::::: ::::::
A: ~ : ~ .:
. .
: :::
~ A::: :::~:: ~ :~ : : A:: ~
.
: : ::: ::
_ ~ _
. ~~\~\~\~ ~
. ~ x
Figure 17: Definition of BEM and VOF regions for the
problem of dam breaking followed by the impact with
a vertical wall.
is made by TD (left side), the 'deck' (bottom side), a
vertical wall (right side) and the top boundary, which is
modeled as a rigid boundary. The velocity computed by
the BEM is enforced along the transmission boundary,
while a free-slip condition is enforced along the remain-
ing portions of the boundary. Once the dam has been
broken, the water flows along the initially dry deck. The
field method is switched on at t = t*, after the water
entered the VOF sub-domain. For t < t*, the BEM is
used to solve the whole problem. For t > t* on, the
BEM sub-domain is limited in the rightward extent by
the transmission boundary. A Lagrangian algorithm is
used in the BEM sub-domain, therefore, during the evo-
lution, those free-surface points entering the VOF sub-
domain are eliminated. Occasionally, new free-surface
points are introduced in the BEM domain by using cubic-
spline interpolation procedures.
Figure 18 gives snapshots of the free surface dur-
OCR for page 403
o DD sol.
—BEM sol.
x/n
o
x/n
x/n
. .
z o DD sol. , o DD sol.
—BEM sol. —BEM sol.
. Omission boundary . =
. —Am_ . it'
2 0 DD sol. ~ ' x~ 2 O DD sol. i · xl7
—BEM sol. —BEM sol.
O . . O
z o DD sol. ~ ' x~ ~ o DD sol. 2 ' me
—BEM sol. —BEM sol.
. , ~ e——e s e ~ ~ e ~
O l l O
2 o DD sol. ' x/h 2 O Dom. Decom.soL ' xAi
—BEM sol. —BEM sol.
' zip
. I'
o
0 7 ~ X 0 2 ~ X'7
Figure 18: Dam-Breaking problem (I = 2h) and im-
pact with a vertical wall at 3.366h far from the dam.
Free surface configurations at t~/~ =2.2, 2.6, 3.6,
4.1, 4.6, 5.1, 5.6 and 6.2. Time increases from left to
right and from top to bottom. DD results (circles) are
compared with BEM results (lines).
O DD sol.
—BEM sol.
a DD sol.
—BEM sol.
r/h
0 DD sol.
— REM ~1
r/h
o Dom. Decom. sot
—BEM sol.
r/h
ing the flow evolution after the dam break. In this case
I = 2h and the downstream wall is placed at 3.366h
from the initial dam. The studied case is the same as
discussed in Greco et al. (2000~. Results are presented
for the DD case (circles) with transmission boundary
located at 1.3h from the dam, and for the full BEM
simulation (lines). In the figure, the nondimensional
time t~/57; increases from left to right and from top
to bottom. The overall agreement between the two re-
sults is satisfactory. The initial impact and the water
rise up along the vertical wall are well captured by the
DD approach, although a flow instability seems to de-
velop during the water run-up along the vertical wall
(ct sixth plot of the figure). The results of the two
methods start to diverge quantitatively in the late stages,
during the water run down, when the backward plung-
ing is formed, finally hitting the underlying water. In
particular, in the DD solution, the impact phenomenon
occurs earlier and closer to the vertical wall.
The full BEM solution agrees quite well with
that obtained by the Smoothed Particles Method (SPH),
a Lagrangian meshless field method, Tulin and Landrini
(2000), as the comparison for the two latest time in-
stants confirms (ci figure 19, ct Colicchio et al. 2001~.
Therefore, we consider the full BEM solution as our
reference solution in verifying our DD algorithm. We
have seen that the present DD results are not affected
. SPH sol.
—BEM sol.
. SPH sol.
—BEM sol.
Figure 19: Dam-Breaking problem described in figure
18. Free surface configurations at t~7; ~ 5.6 (left)
and 6.2 (right). BEM results (lines) are compared with
SPH results (squares).
by the coupling procedure adopted, and we are prone
to believe that the accuracy of the field-method imple-
mented has to be improved to better handle the entire
evolution of the phenomenon.
Water-on-deck problem
The DD algorithm has also been applied to simulate the
water entering on a ship structure with finite draft. As
previously mentioned, in this case the VOF sub-domain
is restricted to the deck region and a relatively small
region of the flow in front of the bow (see sketch 20), the
rest of the domain is studied by using the BEM solver.
Also for this problem, we tested both the cou-
pling procedures and discovered that only the procedure
b gives reliable results for long-time evolutions. Specif-
ically, from our studies, both the procedures a and b are
applicable when the main flow travels from the BEM
sub-domain towards the VOF sub-domain. When the
main flow travels from the VOF sub-domain towards the
BEM sub-domain (e.g. in the case of wave reflections
by the ship bow as occurring during the water-on-deck
problem) the coupling procedure a breaks down.
=:= ~ ::
transmission ~~ ~ :~ :~ :
boundary - ~ VOF 5ub~domain
~"%, ',(, ........
BEM sub~domain
_.......
Figure 20: Definition of BEM and VOF regions for the
problem of water on deck on a ship structure with finite
draft.
Therefore, the following results are based only
on the coupling procedure b. Figure 21 gives snap-
shots of the free surface during the initial stages of the
OCR for page 404
water shipping onto the deck of a nearly rectangular
ship structure. The considered case corresponds to the
two-dimensional water on deck experiments reported in
Greco (2001, see figure 22 where the experimental re-
sults are satisfactorily compared with the BEM results
accounting for the surface tension effects). The DD re-
0.4
0.2
z/D
0.4
0.2
ED
.q .
0.2
. ' · ~
_1 7
—BEM sol. . —BEM sol.
. o DD sol. 0.2 . ° DD sol.
-3.9 X/Z) .3.6 -3.9 AD -3.6
-3-9 X/D -3.6
. .
ID ~
-_ 0.4 .
—BEM sol. . —BEM sol.
. o DD sol. 0.2 . ° DD sol.
-3.9 x./D -3.6
. . _
ID ~
0.4
0.2
\
r
—BEM sol.
o DD sol.
fit
_ 0 DD sol.
-3 9 x/D -3.6 -3.9 x/D .3.6
Figure 21: Water-on-deck on a nearly rectangular ship
structure: initial stages. Free surface configurations at
t ~ 55.5, 55.7, 55.9, 56.0, 56.3 and 56.4 >/~7; (the
initial time corresponds to the starting of the wavemaker
motion). The time increases from left to right and from
top to bottom. Domain-Decomposition results (sym-
bols) are compared with full BEM results (solid lines).
suits (symbols) are compared with the full BEM results
(solid lines). The two approaches are in good agreement
both during the water run-up along the bow and during
the formation of the plunging wave, after the freeboard
has been exceeded by the water. However, they progres-
sively diverge when large variations of the free surface
have to be handled. The results confirm the efficiency
of the DD strategy but still suggest the need to improve
the VOF treatment so far adopted.
CONCLUSIONS
Three-dimensional experiments have been presented to
highlight the dynamics of the water shipping and the
Figure 22: 2D water-on-deck experiments: initial
plunging phase. The red lines are obtained numerically
by the BEM method with included surface tension ef-
fects.
fluid flow evolution on the ship deck. In the experi-
ments, use has been made of wave focusing to gener-
ate a single water-shipping event. A restrained to move
ESSO Osaka model has been adopted. Previous two-
dimensional experiments have been confirmed in show-
ing that water shipping starts with the fluid plunging
onto the bow deck. At the impact, cavities of complex
shape, entrapping air, are formed. The cavity evolu-
tion is rather complicated and characterized by stretch-
ing and, eventually, fragmentation, leading to flow.
In more detail, after the freeboard is exceeded,
the water fronts plunge onto the deck, forming two non-
uniform cavities. These develop along the bow sides,
with the maximum cross sectional area at the ship cen-
terplane, decreasing along the bow edges. Soon after,
the water fronts move inwards, and meet each other
along the ship centerplane, giving rise to a vertical splash
up, eventually reversing outwards. In the meanwhile,
the cavities are stretched and finally broken into bub-
bles of variable size.
The details of this evolution depend on different
factors related both to the incoming waves and to the
ship bow shape. The influence of the incoming wave
steepness on the cavity and on the water front propaga-
tion has been analyzed. The importance of dispersion
effects during the water shipping has been discussed.
According to a simplified two-dimensional analysis car-
ried out in Greco (2001), the loads on the deck associ-
ated with the compressibility of the air entrapped into
the cavity can be relevant for deck safety. At present, no
pressure measurements have been performed to quan-
tify such loads and the related effects on the structure in
the three-dimensional case. However, the tests permit
to identify the extent of the cavity region near the bow
and the time scale of its collapse. Such information is
also useful for the set-up of further dedicated tests to
measure the pressure in areas where the cavity devel-
ops. A second-step experiment is planned for two dif-
OCR for page 405
ferent bow shapes, with different bluntness, to perform
a more systematic analysis of the three-dimensional ef-
fects in the context of the water-on-deck phenomenon.
As the numerical modeling of green-water phe-
nomena is concerned, we have presented a Domain De-
composition strategy to extend the investigations per-
formed by the Boundary Element Method, Greco et al.
(2000~. The underlying idea is to use a field method
with a more general treatment of the free-surface only in
domain regions where breaking and two-phase flow is
observed, and applying the BEM in the rest of the fluid
domain. In the present implementation, we adopted a
VOF technique to handle the free surface in the field-
method sub-domain.
Examples given show the potentiality of the com-
putational strategy, although a more refined VOF tech-
nique has to be developed to increase the reliability of
the whole method.
ACKNOWLEDGEMENTS
The INSEAN research activity has been supported by
the Italian Ministero per le Infrastrutture ed i Trasporti
through INSEAN Research Program 2000-02.
The authors are indebted with Dr. C. Lugni (INSEAN)
for his expertise and help in performing the three di-
mensional experiments.
REFERENCES
Campana, E. and A. Iafrati. "Unsteady Free Surface
Waves by Domain Decomposition Approach". Proc. of
16th Int. Workshop of Water Waves and Floating Bod-
ies. Hiroshima, Japan, 2001.
Colicchio, G., A. Colagrossi, M. Greco, and M. Lan-
drini. "Free-surface Flow After a Dam break: A Com-
parative Study". Proc. of 4th Numerical Towing Tank
Symposium (NuTTS). Hamburg, Germany, 2001.
Ersdal, G. and A. Kvitrud. "Green water on Norwe-
gian production ships". Proc. 10th Int. Conf. Offshore
and Polar Engg, ISOPE'2000. Seattle, 2000.
Greco, M. A Two-dimensional Study of Green-Water
Loading. Ph. D. thesis, Dept. Marine Hydrodynamics,
NTNU, Trondheim, Norway, 2001.
Greco, M., O. M. Faltinsen, and M. Landrini. "Basic
studies of water on deck". Proc. of 23 rd Symp. on Naval
Hydrod. National Academy Press, Washington DC, Vat
de Reuil, France, 2000.
Hirt, C. W. and B. D. Nichols. "Volume of fluid (VOF)
method for the dynamics of free boundaries". J. of
Computational Physics Vol. 39, pp. 201-225,1981.
Quarteroni, A. and A. Valli. Domain Decomposition
Methods for Partial Differential Equations. Oxford Sci-
ence Publications, 1999.
lblin, M. P. and M. Landrini. "Breaking waves in
the ocean and around ships". Proc. of 23r~ Symp. on
Naval Hydrod. National Academy Press, Val de Reuil,
France, 2000.
OCR for page 406
DISCUSSION
D.K.P. Yue
Massachusetts Institute of Technology, USA
The present paper is a very useful addition to the
literature on this important problem. The
presentation of three-dimensional data is of
particular value.
The authors' experimental observation that,
unlike dam breaking, water on deck starts in the
form of a localized plunging wave, is of special
interest. In general, one would expect that the
formation of a plunging wave during water entry
onto the deck must depend on the speed of the
oncoming wave crest and the geometry of the
hull (and deck). If the speed of the wave crest is
relatively small and/or the edge between the hull
and deck is smoother), the present conclusions
may not be valid. Did the authors investigate the
effects of wave speed and hull-deck geometry?
AUTHORS' REPLY
The wave speed parameter has been varied
during our three-dimensional experiments by
varying the wave steepness (see the paper). In all
the cases the plunging phase was observed. We
also performed two-dimensional laboratory tests
(see t13), and for the smallest wave amplitude we
observed a gentler overtopping. In this case,
surface-tension effects alter the particle
trajectory reducing the entrapped cavity and
helping a sort of blunter impact. However there
is still a cavity formed.
Rounded edges of the overdeck portion of the
hull sides are rarely seen in ships, therefore,
large scale experiments, and the actual geometry
of ships suggest that air-cavity formation is the
most frequent behaviour in practical cases.
DISCUSSION
M. Kashiwagi
Kyushu University, Japan
In the domain-decomposition method, we need
to transfer the data (like pressure, normal
velocity) from one domain to another domain. I
suspect this procedure decreases the accuracy,
and eventually the BEM might break down.
Aren't there any problems associated with
numerical instability and inaccuracy in the
domain-decomposition method?
AUTHORS' REPLY
Domain Decomposition (DD) strategies have
strong theoretical foundations which guarantee
that, under suitable refinement, the solution
converges to the solution of the single-domain
problem (see t23~. There are no indications that
the BEM method cannot be used within a DD
approach. Wang et al., t3], in fact, adopted the
DD strategy to speed up the solution of
Boundary Integral Equations (BIE) in large
domains and showed high accurate results. In
zonal approaches, where DD is used to couple
different solvers for different Boundary Value
Problems, the coupling procedure between the
sub-domains determines the accuracy and the
stability of the solution.
In the present paper, we have investigated two
coupling strategies, indicated as a and b, and we
found that procedure a has a poorer stability than
procedure b. We cannot ascribe this behaviour
just to the BEM but to the specific details of the
coupling between the BIE and Navier-Stokes
solvers.
1. Greco, M., "A Two-dimensional Study of
Green-Water Loading", PhD Dissertation, MTA-
rapport 2001-146, Dept. of Marine
Hydrodynamics, NTNU, Trondheim, Norway,
2001.
2. Quarteroni, A., and Valli, A., Domain
Decomposition Methods for Partial Differential
Equations Oxford Science Publications 1999.
, ,
3. Wang, P., Yao, Y., and Tulin, M. P., CCAn
efficient numerical wave tank for nonlinear
water waves, based on the multi--subdomain
approach with teem", Int. Journal for Numer.
Meth. in Fluids, Vol. 20, 1995.
OCR for page 407
O,04
0,03
0,02
0,01
0,00
-0,01
-0,02
-0,03
-0,04
0,10
0,08
0,06
E 0~04
0,02
0,00
-0,02
-0,0d
0,12
0,10
0,08
_ O,06
E 0,04
O,02
O,OO
-O,02
-O,04
O,10
O,08
O,06
O,04
0,02
0,00
-0,02
-0,04
0,08
0,06
0,04
E 0,02
0,00
-0,02
-0,04
-0,06
0,08
0,06
0,04
0,02
E 0,OO
-0,02
-0,04
-O,06
-O,08 _
o
_
1N
(i ='
0 5 10 15 20 25 30 35 40
,^ x=24.04m
o
1C
1
1
'`
.?
`
~ 5 10 -~
~E
t
25 30 35 40
0 5 10 15 20 25 30
30 44 m
_
10 15
x = 37.04m
~'~ ~ f`\/
-qll ~ V~
1 1 1
~ 1
1 l l
5 10 15 20 25
40
20 25 30 35 40
Figure 11: Records of wave elevation at 6 different wave-probe locations for an initially harmonic wave of period
2.525 s and amplitude 0.029 m propagating over an uneven bottom (see Figure 12) as measured by Dingemans
and calculated using BEShiWa (- - -)
13
OCR for page 408
Of 1
-0.2
-0.4
-0.6
-0.8
-1
\
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00
x [m]
Figure 12: The two-dimensional bar-type bottom topography investigated by Dingemans
REFERENCES
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Chen, X.-N. and Sharma, S.D.: "A slender ship moving at a near-critical speed in a shallow channel," Journal of
Fluid Mechanics 291 (1995, S. 263-285. - Presented at the 18th Int. Congress of Theoretical and Applied Mech.,
Haifa, Israel, 1992.
Chen, X.-N. and Uliczka, K.: "On ships in natural waterways," Proceedings of the RINA International Conference
on Coastal Ships and Inland Waterways, London, 1999.
Dingemans, M.W.: "Comparison of computations with Boussinesq-like models and laboratory measurements,"
MAST-G8M note, H1684, Delft Hydraulics, 1994.
Dingemans, M.W.: "Water Wave Propagation over Uneven Bottoms", Advanced Series on Ocean Engineering, Vol.
13, 1997, Part II, pp. 635.
Doctors, L.J., Philipps, S.J. and Day, A.H.: "Focussing the wave-wake system of a high-speed marine ferry," Pro-
ceedinas ofthe FAST 2001, Southhampton, UK, 2001.
Doyle, R., Whittaker, T.J.T. and Elsasser, B.: "A study of fast ferry wash in shallow water," Proceedings of the
FAST 2001, Southhampton, UK, 2001.
Feldtmann, M. and Garner, J.: "Seabed modifications to prevent wake wash from fast ferries," Proceedings of the
RINA International Conference on Coastal Ships and Inland Waterways, London, 1999.
Henn, R., Sharma, S. D. and Jiang, T. "Influence of Canal Topography on Ship Waves in Shallow Water," Proceed-
ings of the 1 6th Int. Workshop on Water Waves and Floating Bodies, Hiroshima, Japan, 2001.
Jiang, T.: "Ship Waves in Shallow Water," Fortschritt-Berichte VDI, Series 12, No. 466 with ISBN 3-18-346612-0,
2001.
Jiang, T.: "Investigation of waves generated by ships in shallow water," Proceedings of the 22n~ Symposium On
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Koushan, K., Werenskiold, P., Zhao, R. and Lawless, J. "Experimental and theoretical investigation of wake wash,"
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MacLarlane, G.J. and Renilson, M.R.: "Wake wave - a rational method for assessment," Proceedings of the RINA
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Raven, H.C. "Numerical Wash Prediction Using A Free-Surface Panel Code," Proceedings of the RINA Interna-
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Taylor, P.J.: "The Blockage Coefficient for Flow About an Arbitrary Body Immersed in a Channel," Journal of Ship
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Yang, G.-Q., Faltinsen, O.M. and Zhao, R.
Southhampton, UK, 2001.
.
. "Wash of ships in finite water depth," Proceedings of the FAST 2001,
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15
OCR for page 410
DISCUSSION
Stephane Cordier
Bassin d'Essais des Carenes, France
Ships inland waterway are confronted with
changes in maneuvering behavior in shallow or
restricted waters.
Could you please tell us how this method can be
used or extended to improve the prediction of
maneuvering forces for ships in restricted water?
AUTHORS' REPLY
We thank Dr. Cordier for his question. For
predicting the maneuvering forces on ships in
restricted water, we need only to improve our
approximation for the near-ship flow. Currently,
we examine the possibility of coupling the
BEShiWa program with different methods, such
as with a panel program or a Euler solver or a
RANSE solver. We hope to present our new
results in the near future.
DISCUSSION
L.J. Doctors
University of New South Wales, Australia
I would like to express my appreciation to the
three authors for a most interesting paper on the
subject of wave generation, a matter of interest
to many researchers who are aiming to reduce
the potential damage done by high-speed ferries
as well as traditional vessels, travelling near
coastlines and river banks.
The plots in Figure 1, in particular, are excellent
for displaying the wave patterns created by the
vessel at the various depth Froude numbers.
It is encouraging, also, to observe the good
comparison between the measured and calculated
wave profiles in Figure 2. It is particularly
impressive to see the calculations for the non-
uniform bottom topography in Figure 3 and
Figure 1 1.
Referring specifically to Figure 2, could the
authors comment on the likely relative accuracy
of the BeShiWa (Boussinesq's Equations for
Ship Waves) program, compared with, say, a
more traditional linearized-free-surface method,
in which no depth averaging is effected? That is,
what sacrifice has been made in losing the details
of the vertical distribution of the transverse
velocities within the flow domain, in order to
obtain the very impressive capabilities of
BeShiWa?
Secondly, can the authors verify that the effects
of sinkage and trim are not included in their
work? No doubt this would require a full near-
field calculation (presumably not done here).
The discusser feels that the effects of sinkage
and trim are probably not important in most
cases of practical interest.
AUTHORS' REPLY
We greatly appreciate Professor Doctors's
comments and questions.
The accuracy of predicting ship-wave
propagation in shallow water by using the
BEShiWa program is generally remarkable or at
least practically acceptable in comparison with
model tests. Till now, no attempt has been done
by us to compare with a traditional linearized-
free-surface method. A simple answer here
would be that we do not have such a linear code.
However, we would emphasize again our
statement that due to the nonlinear and unsteady
nature of ship waves in shallow water the linear
theory remains to be a restricted approximation.
Furthermore, it should be clarified that the
vertical distribution of the transversal velocity
components is explicitly described as an
analytical function of the averaged horizontal
velocity in the Boussinesq's shallow-water
theory. So the vertical effects are not neglected,
but analytically approximated in the BEShiWa
program.
Coming now to the second question, the effect of
the sinkage and trim as well as the free surface
elevation are simultaneously included in our
near-field solution, see paragraph
"Approximation of the Near-Ship Flow". As
shown by Jiang (1998), the sinkage and trim
could be well predicted by the BEShiWa
program. The agreement of our calculations with
model measurements was good not only in the
subcritical speed range, but also in the
transcritical and supercritical one.
J
OCR for page 411
DISCUSSION
H.C. Raven
MARIN, The Netherlands
This is an interesting paper on a topical subject.
The extensive results illustrate the richness of
wave phenomena occurring in practical
situations; and show how strongly the particulars
of the waterway determine which wave effects
dominate and whether any wash problems will
occur.
In order to predict these phenomena, there is a
need for a computational tool that incorporates
the essential features and has reasonable
efficiency. Boussinesq-type models seem to go a
long way toward that objective, as the
applications illustrate.
My question is on the boundary condition at the
ship hull; which is the one that generates the
waves. In the present work, a 'slender-body' type
condition is used: the passage of the ship
imposes a lateral velocity distribution, which is
averaged over the entire water depth. This is
consistent with Boussinesq theory; but
intuitively one would expect that this is less
accurate for higher water depth / draught ratio's.
Could the authors comment on their experience
in this regard, and mention the water depth /
draught ratio for the good results in Fig. 2?
Secondly, is there a way to compute and
incorporate the dynamic trim and sinkage in this
method?
AUTHORS' REPLY
We thank Dr. Raven for his comments,
particularly for his indication of our consistent
approximation in using the Boussinesq's
equations for the far-field flow and an extended
slender-body theory for the near-ship flow. We
agree with his presumption that our method is
less accurate for higher ratios of water-depth to
ship draught in the absolute sense of the
increased water depth, but not in the relative
sense of the ratio. For instance, the ratio for the
good agreement in Figure 2 was approximately
4. The crucial parameter for using the BEShiWa
program is the depth Froude number which
should not be below the associated lower limit
defined by Jiang (2001~.
For the answer to the second question we refer to
our reply to Professor Doctors on the previous
page.
DISCUSSION
H. S. Choi
Seoul National University, Korea
In this paper, you have used the depth-averaged
Boussinesq equations to describe wave field
generated by ships moving on Fairways.
Have you ever compared your numerical results
with those obtained by FEM based on ON
equations, which, for example, we presented at
the 1 8eh SNH in Ann Arbor, 1990?
AUTHORS' REPLY
We thank Professor Choi for the reference of his
work with the generalized Green-Naghdi (GN)
equations. In comparison with the Boussinesq's
equations the Green-Naghdi theory takes account
of the fully nonlinear effects. As discussed by
Jiang (2001), the application of the classical
Boussinesq's equations for most practical cases
is not limited by the nonlinear treatment but by
the dispersion treatment. Various methods are
derived in the work cited for the improvement of
the dispersion relation of the Boussinesq's
equations. Numerically we prefer the numerical
more efficient Boussinesq approximation.
OCR for page 412
DISCUSSION
H.C. Raven
MARIN, The Netherlands
This is an interesting paper on a topical subject.
The extensive results illustrate the richness of
wave phenomena occurring in practical
situations; and show how strongly the particulars
of the waterway determine which wave effects
dominate and whether any wash problems will
occur.
In order to predict these phenomena, there is a
need for a computational tool that incorporates
the essential features and has reasonable
efficiency. Boussinesq-type models seem to go a
long way toward that objective, as the
applications illustrate.
My question is on the boundary condition at the
ship hull; which is the one that generates the
waves. In the present work, a 'slender-body' type
condition is used: the passage of the ship
imposes a lateral velocity distribution, which is
averaged over the entire water depth. This is
consistent with Boussinesq theory; but
intuitively one would expect that this is less
accurate for higher water depth / draught ratio's.
Could the authors comment on their experience
in this regard, and mention the water depth /
draught ratio for the good results in Fig. 2?
Secondly, is there a way to compute and
incorporate the dynamic trim and sinkage in this
method?
AUTHORS' REPLY
We thank Dr. Raven for his comments,
particularly for his indication of our consistent
approximation in using the Boussinesq's
equations for the far-field flow and an extended
slender-body theory for the near-ship flow. We
agree with his presumption that our method is
less accurate for higher ratios of water-depth to
ship draught in the absolute sense of the
increased water depth, but not in the relative
sense of the ratio. For instance, the ratio for the
good agreement in Figure 2 was approximately
4. The crucial parameter for using the BEShiWa
program is the depth Froude number which
should not be below the associated lower limit
defined by Jiang (2001~.
For the answer to the second question we refer to
our reply to Professor Doctors on the previous
page.
DISCUSSION
H. S. Choi
Seoul National University, Korea
In this paper, you have used the depth-averaged
Boussinesq equations to describe wave field
generated by ships moving on Fairways.
Have you ever compared your numerical results
with those obtained by FEM based on ON
equations, which, for example, we presented at
the 1 8eh SNH in Ann Arbor, 1990?
AUTHORS' REPLY
We thank Professor Choi for the reference of his
work with the generalized Green-Naghdi (GN)
equations. In comparison with the Boussinesq's
equations the Green-Naghdi theory takes account
of the fully nonlinear effects. As discussed by
Jiang (2001), the application of the classical
Boussinesq's equations for most practical cases
is not limited by the nonlinear treatment but by
the dispersion treatment. Various methods are
derived in the work cited for the improvement of
the dispersion relation of the Boussinesq's
equations. Numerically we prefer the numerical
more efficient Boussinesq approximation.
Representative terms from entire chapter:
ship model
