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OCR for page 211
24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Bow Waves on a Free-Running, Heaving
And/or Pitching Destroyer
Howard B. Markle and T. Sarpkaya (Naval Postgraduate School, USA)
ABSTRACT
Measurements of the near-surface evolution of
the bow wave were made on a 1/250-scale model of a
destroyer and compared with those obtained from the
sea tests of the subject destroyer wherever possible.
The effects of steady motion, heave, pitch and
combinations thereof were subjected to controlled
experiments to quantify the base flow in comparison
to the prototype. The Froude Number for the majority
of the runs was 0.26. Model scale frequencies ranged
from 1 to 5 Hz, pitch angles from 0.85 degrees to
3.75 degrees and heave amplitudes from 3 mm to 15
mm. This resulted in a large amount of data. Here
only the most relevant and most unexpected ones are
discussed in some detail. Emphasis is placed on the
bow region where a ship's character is prescribed. The
model and the prototype data are shown to be in good
agreement and are expected to serve as a step towards
the validation of full-scale ship codes and the
improvement of the performance of such ships through
additional physical and numerical experiments.
INTRODUCTION
Brief Review
The interaction of a ship with the ocean gives
rise to numerous complex phenomena, dictated
primarily by the shape and motion of the bow. The
breaking of bow waves is a significant fraction of the
resistance experienced by the ship. It is because of
these reasons that warships, in particular, and
commercial ships, in general, have been studied for
many years. The present investigation concerns itself
with a typical destroyer. The ultimate objective of the
systematic investigation is to minimize the wave
resistance in all circumstances (free-run in waves, in
random seas, in heave and pitch) and to reduce the
spray formation, air entertainment and deck wetness.
The shape of the destroyer bows and the
sonar dome distinguish them from other commercial
ships. An extensive search of the relevant literature
have shown that there have been numerous studies
particularly during the past 50 years to predict the bow
wave and ship resistance (Miyata and Inui, 1984;
Grosenbaugh and Yeung, 1989; Longo et al. 1993;
Stern et al, 1996a; Fontaine and Cointe, 1997; Dong
et al, 1997; Beddhu et al, 1998; Cusanelli, 1998;
Larson et al, 1999; Subramani et al, 1999; Rhee and
Stern, 2001). In the earlier years, no special emphasis
has been placed on bow sheet separation and
subsequent spray. Technological advances have
necessitated higher speeds and increased protection
from the adverse effects of spray, particularly on the
deck. These efforts led to many physical and
numerical experiments.
The theoretical studies, while benefiting from
the advent of the computer, were primarily concerned
with 'thin ships' operating in inviscid fluids (see, e.g.
Fontaine and Cointe, 1997; Wu et al, 2000; and the
references cited therein). There is not, at present, a
computer code that could predict the response of a
destroyer in a random sea, the ship resistance, the bow
waves, bow sheet separation, jet/spray formation,
subsequent aeration, and the extent of the white water
region in the wake of the ship in a viscous fluid with
or without surfactants. However, significant advances
have been made (Beddhu et al, 1998) towards the
validation of the UNCLE solver with experimental
results tthe flow field around Series 60 CB = 0.6 at
Froude number of 0.316 (Stern et al, 1996b)] and by
Rhee and Stern (2001) for the simulation of the
boundary layer and wake and wave field for a surface
ship advancing in regular head waves, but restrained
from body motions, using an unsteady RAN S
method.
OCR for page 212
It is with the full realization of the
strengths and shortcomings of the existing
contributions that a major investigation has been
undertaken to delineate the characteristics of the bow
wave on a typical destroyer tshown in Figure (1~]
under a series of imposed motions (free running,
heave, pitch as well as combinations of heave and
pitch). The preliminary studies led to certain facts
which have not been previously realized. These will
now be described in some detail.
An. Ace_
~ ~~ - ~: -
.... :~ t. ~ ~ ~ ~ ,
~ . ... !
.. ...
as_
~e. ~
~ ~ ~ 'a,—_
_~"
-
~_
Figure 1: Bow wave and spray generation on a typical
Destroyer (Fr= 0.264.
Bow Wave, Sheet Separation, and Spray
When a ship is in free run in a calm ocean, it
has an imposed Froude number (Frs) given by
equation (1) where Vs is the velocity of the ship, g is
the gravitational acceleration and Ls is the length of
the ship.
V
Frs = 3W
(1)
The resistance is also influenced by the effect of
viscosity and surface tension. They are expressed as
the Reynolds number (Res) and Weber number (Wes)
in equations (2) and (3), respectively, where p is the
density, v is the viscosity and ~ is the coefficient of
surface tension.
Re = pVSLs
s ~
We = pV~ Ls
(2)
(3)
Figure 1 shows that the bow sheet for the
ship under consideration separates from the hull and
gives rise to spray. In general, the ship Froude
number, the shape of the ship (particularly the bow
geometry), the sea state, and the type of motion of the
ship determine the characteristics of the bow waves
and spray generation and, hence, most of the wave
resistance. However, all separated sheets do not give
rise to spray. The local Froude, Weber, and Reynolds
numbers, the hull curvature, and the surface roughness
at or near the point of separation must exceed certain
critical values. Obviously, the Froude number of the
separated sheet is not an independent parameter and is
uniquely determined by Frs and the other parameters
cited above. The same is true for the local Weber and
Reynolds numbers as shown by Sarpkaya and Merrill
(2001~. The fact of the matter is that the Froude
number of the ship is subcritical (Frs < 1) but the
Froude number of the breaking sheet is supercritical.
This leads to a well-known dilemma regarding the use
of models.
Since the physical properties of the fluid
(p, c,, A) and g must be kept constant, the
specification of the ship speed and length defines the
Froude number. Thus, for identical model and ship
Froude numbers (and physical properties), the Weber
and the Reynolds numbers for the model are smaller
by (Lm/Ls)2 and (Lm/Ls)3/2' respectively. Even for a
model of 1/25 scale, the Weber and Reynolds numbers
of the model are 625 and 125 times smaller,
respectively, than those of the ship. Likewise, the
specification of a supercritical Froude number and
sheet thickness for the separated-sheet embodies all the
effects of gravity, surface tension and viscosity. Thus,
one realizes the existence of two Froude numbers that
govern two distinctly different phenomena in two
different regions of the ship. This mandates two
2
OCR for page 213
(related but separate) investigations in two separate
facilities to examine the bow waves of a ship and the
separation of the bow sheet with all of its attendant
consequences. The result of utilizing a supercritical
jet facility is seen in Figure 2. The sheet separates
from the hull and breaks up into filaments and
droplets. There are no other alternatives unless one
wishes to conduct the experiments with very large
models or with the actual ship itself under the
influence of difficult-to-control environmental
conditions.
1 _1115
Figure 2: Representative supercritical flow and spray
generation about a bow model.
As to the effect of the more complex
motions, it is shown that one can extract the basic
bow wave from all other time dependent motions
(heave, pitch, yaw, etc.) experienced by the ship.
Consequently, the delineation of the excursions of a
given bow-wave above or below the maximum or
minimum of the basic bow wave may be very
important in assessing the operational resistance and
total hydrodynamic performance of a ship and the
spray generation as a function of the bow and sonar
geometry. This fact has been effectively used by
Cusanelli (1998) in improving the performance of
near-surface bow bulbs in irregular waves.
EXPERIMENTAL FACILITIES
Experiments have been carried out in two
distinctly different facilities. The first was for the
purpose of understanding the breakup of a bow sheet
and the formation of filaments and droplets, with or
without the effect of surfactants (both soluble and
insoluble in seawater). The second facility was for the
purpose of characterizing the bow wave. A typical
destroyer model was manufactured at the David Taylor
Model Basin to 1/250 scale out of resin material
utilizing a stereo-lithograph laser cutting system.
These are described in some detail below.
Supercritical Flow Facility
A rectangular supercritical wall jet
discharging into air from a carefully constructed nozzle
was used to study the transition, surface deformation
and filaments formation on the free surface with or
without surfactants. The nozzle was supplied by a
large water tunnel. Additional details about the
facility are described in Sarpkaya and Merrill (2001~.
The jet Froude numbers ranged from approximately 2
to 30 by varying the thickness and velocity of the jet
over smooth and rough surfaces. The filaments and
drop formations were photographed with several high-
speed imagers, including a digital camera and an
infrared laser. The data (filament geometry and drop
size) were deduced through the use of suitable software
in terms of the prevailing Froude, Reynolds, Weber,
and roughness numbers for the jet.
Bow Wave Facility
The ship models were mounted at the test
section of a recirculating water tunnel. A rendering of
the tunnel is shown in Figure 3.
__ _
1 1 __
1 ~ ~ __
1 __ 1 ~
Figure 3: The recirculating water tunnel.
At the top and to one side of the test section,
two motors of appropriate characteristics were
mounted and connected to the model to achieve heave
and pitch motions that were independent or phase-
coupled with one another. The base on which the
3
OCR for page 214
motors were mounted was pivoted to induce desired
angles of yaw to the models. The speeds with which
the tunnel operated corresponded to Froude numbers
of 0.26 and 0.65. The majority of the data were taken
at Frs = 0.26. The primary reason for this selection
was the availability of video footage of the prototype
destroyer in free-run tests in essentially calm seas with
Froude numbers in the range of 0.26. This was of
extreme importance for the comparison of the model
and sea experiments for the verification of the quality
of the model experiments and for the establishment of
the shape of the bow wave at the speed chosen.
The fluid motion, particularly in the bow
region, was recorded on video and analyzed through
the use of an analog to digital convertor. Fluorescein
dye was used during the videoing of the bow wave to
sharpen the ship/wave interface as shown in Figure
(4~.
Figure 4: Model of a typical destroyer (scale: 1/250)
Each test run was evaluated at different times
to minimize the errors in the measurement of tunnel
speed, wave height, stem height and the unsteady
oscillations of the wave surface on the ship bow. The
edge ofthe wave climbs up the hull, wets the surface
at some frequency, and gives rise to a string of 'pearls'
crowning the top of the bow wave. Their small
curvature reflects the light differently from the bow
wave itself.
The heave and pitch motions were conducted
independently as well as in combination (with
appropriate phase angle differences) in the range of
heave and pitch amplitudes deemed to be most
desirable. The establishment of the individual values
will be discussed later. The data were evaluated at
every frame (1/30-second intervals) for any given cycle
of oscillation. This was done partly to assess the
overall accuracy of the data and partly to account for
the aforementioned, relatively small, free-surface
oscillations.
RESULTS AND DISCUSSION
The results will be described in the following
order: the basic bow wave; the independent as well as
combined effects of heave and pitch on the model; the
surge phenomena (i.e., the differences between the
basic bow wave and mean heave as well as mean pitch
at Frs = 0.26~; the case of a higher Froude number
(only in the free running case); and the elect of
surfactants on the characteristics of free-surface
structures in simulated separated sheets at supercritical
Froude numbers.
Basic Bow Wave
Figure (Sa) shows plots of representative data
for the model at rest in uniform flow at Frs = 0.26.
The x-axis is the horizontal distance normalized by the
ship length. The y-axis shows the vertical position Y
of the free surface normalized by the mean of the water
elevations H(O)m~bar' at the stem. It is rather remarkable
that there is relatively little scatter. The bow wave
reaches its maximum at a value of X/L between 0.02
and 0.025. The initial rate of rise between the stem
and X/L = 0.025 is the strongest. After the wave
reaches its maximum elevation, it loses its height
gradually and at a value of X/L between 0.09 and 0.1,
it drops to the mean water level.
Figure 5a Y/H(O)m~bary versus X/L: bow-wave shape on
the model in steady flow (Frs= 0.26~.
Figure 5b shows the average of the data
shown in Figure 5a. It is interesting that the slope of
the wave elevation for X L > 0.05 is nearly linear.
4
OCR for page 215
Figure 5b: Y/H(O)m~bar' versus X/L: average model
data for the runs shown in Figure Sa.
Figure 6a shows, as before, Y/H(O)m~bar' versus
X/L for the data extracted from the videotapes of the
destroyer. It is not surprising that it exhibits larger
scatter due to the randomness of the sea state, the
changes in speed of the ship, the difficulties of
deducing precisely the scales from the photos, and the
variations in the ship direction. All measurements of
the model and ship have shown that the actual value
of H(O)m~ba~' at a Froude number of 0.26 is 2.2 feet.
Figure 6b shows the average of the data shown in
Figure 6a.
2.3' _
~ 2 --
o 1.5
o.s
Do
-os ~ _
.
. it_
~ .
X/L
Figure 6a: Y/H(O)m~bar' versus X/L: bow wave data for
the ship (Frs= 0.26~.
2S' .
H
15
Figure 6b: Y/H(o~m~bar' versus X/L: averaged bow
wave data for the ship (Frs = 0.26~.
is
Top line: Model
Bottom: Ship
M90~ To
X/L
Figure 7: Y/H(O)m(bar) versus X/L: comparison of the
basic bow wave shapes of the ship and the model (Fr
= 0.26 for both).
Figure 7 shows the average of Figure 6a
(basic bow wave shape) and its comparison with the
averaged model data (Figure Sb), at a Froude number
of 0.26. There is a remarkable similarity between the
two sets of data. The key parameters such as the
position of the maximum elevation on the ship and
the point at which the sea level is reached are either in
perfect agreement or very close to each other. The
ship data begin to deviate from those of the model at
approximately X/L = 0.04 and, as expected, is
slightly lower. The extensive observations of the
video of the ship show that the bow sheet begins to
separate from the ship and eventually break into spray
at approximately the same point as the deviation
between the ship and model data. However, the most
important feature of Figure 7 is that it points out the
establishment of the basic bow wave shape in the
subcritical Froude number regime and the point of
inception of the supercritical regime (X/L > 0.04~.
Heave Motions
Figure 8a is the average heave profile (the
mean of the maximum and minimum of the
elevations) plotted over the steady state obtained from
data of Figure 5b. One of the interesting features of
Figure 8a is that the surge due to the heave, for the
amplitude and frequency shown, is confined to the
bow region very near the stem, primarily reflecting the
effect of the sonar dome. Further away from the bow
region, the average heave is nearly the same as the
steady bow wave shape. It is of importance to note
that this, as well as the following two figures, is
plotted in terms of dimensional variables to give some
idea of the size of the bow wave on the model and to
simplify the presentation without distorting the
OCR for page 216
figures. Figures 8b and 8c show similar data at the
same frequency but at increasing amplitudes of heave.
Figure 8a: Y(cm) versus X(cm): comparison of the
average heave with the basic bow wave (for Frs = 0.26,
fm = 1.5 Hz, hm = 0.32 cm).
Figure 8b: Y(cm) versus X(cm): comparison of the
average heave with the basic bow wave (for Frs = 0.26,
fm = 1.5 Hz, hm = 0.96 cm).
0.75
E 05
0.2s
o
-0.2s
The previous three figures compared the
steady flow bow data with the mean of the heave at
one frequency and three different heave amplitudes. In
Figures 9a through 9c, the heave data are presented in
terms of Y/Hmax versus X/L for one frequency and one
amplitude, where Hmax is the maximum wave
amplitude.
Figure 9a begins at time 't-1' when the
model is at its maximum downward excursion.
Clearly, the bow wave at this time is not at its highest
position. As the model begins to go up, the wave
rises to its maximum height at time 't-3' and beyond
this point continues to decrease as shown from times
't-4' through 't-8'. The time of the maximum wave
height lags the maximum downward excursion of the
model by 2/45 seconds. In other words, if the model
reaches its maximum excursion at time 't-1', then the
maximum wave height occurs at time 't-3', as noted
earlier. Clearly, the rate of fall of the bow wave is not
uniform everywhere in the bow region. The smallest
changes in the amplitude are very near the stem as
noted by the labeled times of 't-9' through 't-17'. The
subsequent figures show heave at additional times.
The lowest position of the bow wave is
arrived at rather uniformly as evidenced by a cursory
examination of figures at times 't-11' through 't-15'.
Thereafter, the bow wave continues to rise as shown in
Figure 9c and the new cycle of the wave motion
begins at time 't-23' at which time the model is at its
maximum downward excursion at time 't-25'. Figure
9b, in particular, shows that the heave motion does
not induce uniform rise and fall of the bow wave
along the model.
When the bow wave reaches a minimum
position along the model (time 't-14'), the water from
the remainder of the ship rushes toward the lowest
point and gives rise to a wave breaking that is not
related to the breaking of the bow sheet. The wave-
break point is often below the design water line.
0.9
0.75
0.6
0.4s ~_
o0;3 ~~.z ~a
2 ~
o o~ = ~6 o.5
-o.~s _~ _ ~
fm= 1.5 Hz
hm= 1.28 cm
~_ . .
~,
t-2
t~3
t4
t~S
~ _t~
. ~ t-7:
t-X:
x (cm)
Figure 8c: Y(cm) versus X(cm): Comparison of the
average heave with the basic bow wave (for Frs = 0.26,
fm = 1.5 Hz, hm = 1.28 cm).
Figure 9a: Y/Hmax versus X/L: single cycle heave
history of the bow wave (Frs = 0.26, fm = 1.5 Hz, hm
= 1.28 cm)
6
OCR for page 217
rat ,(
015 =~==
-0.3
-0.45
X/L
Figure 9b: Y/Hmax versus X/L: the continuation of
Figure 9a for heave motion (Frs = 0.26, fm = 1.5 Hz,
hm= 1.28 cm).
,.05 1 fm= 1.5 Hz _
0 is ~ ~7 hm = 1 .28 —1
he 0.45 j ~=
=031 1 ~_ .
~ ~ .
O ' ' ~ ' ' .
o.oq 0.08 0.12 - _ 0.2
-0.15
-0.3 .
.45
X/L
_~-17:
_~-18:
t-l9:
a: ~~ ~ t-20:
~-21:
~_-22:
~-23:
.-24:
Figure 9c: Y/Hma'` versus X/L: the continuation of
Figure 9b for heave motion (Frs = 0.26, fm = 1.5 Hz,
Em= 1.28 cm).
Pitch Motions
Figures lea through lOc show the
comparison of the average pitch motion with steady
runs for a given frequency and three different
amplitudes (measured in degrees). As before, the
pitch affects the near stem region of the bow and
exhibits similar characteristics as those shown in
Figures 9a through 9c for the heave motion. The
differences are primarily due to the rotational motion
about the longitudinal center of buoyancy. Figures
1 1 a through 1 1 c show the variation of the
instantaneous position of the bow wave during one
cycle. As before, the bow-wave maximum lags the
model's maximum excursion by 2/45 seconds.
.. . . ~ . ..
E o
0.2s . r
o-
-Q25 ~
~ Eve P itch I
| E teddy |
l
1 2 3
Figure lea: Y(cm) versus X(cm): comparison of the
average pitch and steady motions (Frs= 0.26, fm= 1.5
Hz, pitch= 0.85 degrees
0.7s
E 05
>0.2s
-Q25
vgPitd~ I
tesiv I
me.
~ ~ ~ 1~
I
1 2 3 4
X(cm)
7
Figure lab: Y(cm) versus X(cm): comparison of the
average pitch and steady motions (Frs= 0.26, fm = 1.5
Hz, pitch = 2.5 degrees)
07
_
0.5- __
0.25
o-
~25
Of _
f ~
1
3
Figure lOc: Y(cm) versus X(cm): comparison of the
average pitch and steady motions (Frs = 0.26, fm = 1.5
Hz, pitch= 3.35 degrees.
7
OCR for page 218
1.05
o.s.
0.75 .
E , a===
1 0''5i 004~1
-0.3
-0.45
X/L
1 am.,
_= -2:
. t-3:
. .... ~~ ...~-4:
~-5:
_~-6:
_~-7:
t-8:
1
Figure lla: Y/Hmax versus X/L: single cycle Ditch
history of the bow wave (Frs = 0.26,
pitch = 3.35 degrees).
.
fm = 1.5 Hz,
.05
or
0.75
A ~ Y ~~ C~ ~
0.45 ;
0.3
0.15
.15
-0.3
-0.45
XIL
~==~
~ *~'2 ~ tar ~ . I
o.o~ my,_ ~ o.os #` ?:~' Oslo
~ '-— 1
~: ''he
-
_t- 10:
t- I 1:
t- 1_:
. ~< ~ A, 1 3:
t- 14:
t- 15:
mat- 16:
t- 17:
—t-18:
t-19:
t-20:
Figure Fib: Y/Hmax versus X/L: the continuation of
Figure 1 la for heave (Frs = 0.26, fm = 1.5 Hz, pitch =
3.35 degrees).
.05
0.9
0.75 r ^
06
0.15' ~` ~ =tt~,6
o _~ _< ~t-~7:
.15 0.04 o.og o.l~ —.,~
-0.3
-0.45
X/L
Figure tic: Y/Hmax versus X/L: the continuation of
Figure 1 lb for heave (Frs = 0.26, fm = 1.5 Hz, pitch
= 3.35 degrees).
Combined Heave and Pitch Motions
The data obtained for a heave-pitch
combination using a frequency of 1.5 Hz, a heave
amplitude of 0.32 cm, a pitch amplitude of 2.5
degrees, and a phase angle of 120 degrees (between the
pitch and heave) are shown in Figures 12a through
12c. These figures are not intended to convey the
impression that an attempt was made to optimize the
combinations of the controlling parameters (frequency,
heave amplitude, pitch amplitude and phase angle),
but rather to show that the combination of the two
motions produced the largest maximums as well as
the lowest minimums which were below the design
water line during some part of the cycle. It should be
emphasized that the frequency of 1.5 Hz does not
represent the natural frequency of the prototype. The
optimization of the various key parameters is left to a
future study.
1.05
0.9
0.75
0.6
0.4s
0.3
As
o
-o.tS -
-0.3 .
-0.4s
X/L
. 1
e? ~
~_ rtt23 I
. 1~- ~ t-4
- _t-s: I
—~ \~ _ 1 1
`~ - ~ l~t-6:
V ma,= - , -— tt-7: 1
~ of,—~ Off _- I A: I
0.04 o.o~r ~40 0.16 0.2 As_ 1
~ _ ~ 1 t-9 1
_y~~~ I t-10' 1
Figure 12a: Y/Hmax' versus X/L: single cycle time
history of the bow wave for Frs = 0.26, fm = 1.5 Hz,
hm = 0.32 cm, pitch =2.5°, phase = 120°, (t-1 - t-10).
~ 0.45
— 0.3-
0.~5-
o
-0.15 -
-0.3 -
-0.45- 1
X/L 1
Figure 12b: Y/Hmax versus X/L: continuation of
Figure 12a, (Frs= 0.26, fm = 1.5 Hz, hm = 0.32 cm,
pitch = 2.5°, phase = 120°), (t- 1 1 - t-20).
8
OCR for page 219
Laos
0.9 . .
0.75
0.6
# 0.4s
E
e: 0-3 i
0.15
o
-0.15
.0.3
t\ AC .
~ ' . .
~.2.' : ,
Figure 12c: Y/Hmax versus X/L: continuation of
Figure 12b, (Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm,
pitch = 2.5°, phase = 120°), (t-21 - t-294.
Figure 13 shows a single cycle time history of
the bow wave (times t-1, t-3, through t-13, and t-14)
for Frs = 0.26, fm = 1.5 Hz, hm = 0.32 cm, pitch =
2.5°, phase= 120°. The black line on the hull
represents the design water line along the ship. The
times at which the bow wave is below the mean water
level are seen clearly in the last three frames.
Ship at Higher Frs with Yaw
As previously stated, the existence of two
distinct flows and Froude numbers along the ship near
the bow necessitates two distinct experiments in two
separate facilities. Figure 2 was obtained in the
supercritical jet facility and shows that one must
utilize the supercritical values of the controlling
parameters (Froude, Reynolds and Weber numbers) to
accurately model sheet separation and subsequent
spray on any model smaller than the ship. Figure 14
shows representative pictures of a larger model of scale
1/150 at a Froude number of 0.65 with a yaw angle of
15 degrees. The separation of the sheet is precipitated
by the yaw of the model as well as by the speed of the
flow as evidenced by the breaking of the bow wave.
The point to be made here is that the bow-sheet
separation and the resulting jet breakup and spray
formation can be investigated either on very large
models or at very large Froude numbers (using a
separate supercritical jet facility).
Figure 13. A single cycle history of the bow wave.
9
OCR for page 220
Figure 14. Photographs showing the breaking of the
bow wave on the model at rest in uniform flow with
Frs= 0.65, yaw = 15 degrees.
Surfactants and Supercritical Flow
It is a well-known fact that clean surfaces are
relatively rare in nature and the presence of non-
dissolvable and/or adsorbable solutes provide a ready
means for the establishment of variations in surface or
interracial tension along the fluid phase boundary.
The surfactants render the free-surface more
rigid, reduce surface deformation, smoothen the free
surface, and enhance the generation of secondary
vorticity (Sarpkaya, 1996~. Thus, the shear-free free-
surface condition and the no-slip condition are
incompatible.
The consequences of surface tension
reduction may manifest themselves in various ways
under a variety of circumstances in both supercritical
and subcritical flows. These have been discussed by
Sarpkaya (1996, and references therein), and more
recently by Reed and Milgram (2002) in the context of
ship wakes. In spite of some favorable predictions of
the image features of ship wakes, the effect of
surfactants on the attenuation of the short sea waves
and surface structures by ship-generated currents and
turbulence remain in the realm of limited
measurements, empirical equations, and descriptive
knowledge. It is because of these reasons that a
comprehensive effort was undertaken to delineate the
effects of both soluble and insoluble surfactants on
both the supercritical and subcritical free surface flows.
Previously, Sarpkaya and Merrill (2001) have
shown, through the use of DPIV (See Fig. 15), that
the ejection of the filaments from the surface of a
supercritical flow is necessarily controlled by the
dynamics of the turbulent flow field.
Figure 15. DPIV measurements and the regions of
focussed areas with large upward velocities.
10
OCR for page 221
The circled regions in Fig. 15 show "focussed" areas
with upward velocities as large as large v'/UO ~ 0.2.
In view of this finding, the tip velocities of all
filaments, which eventually gave rise to one or more
drops, were evaluated from the Lagrangian
measurements, using only the images taken after the
initial acceleration period of 5 ms to 10 ms. A
typical plot is reproduced in Fig. 16 for the flow
without surfactants.
Some of the experiments described above and
in Sarpkaya and Merrill (2001) have been repeated
using 10 micron FluoSpheres (Molecular Probes, Inc.)
as surfactant. They do not dissolve in water and
contaminate only the free surface. The surface tension
for the concentrations used was about 55 dynes/cm.
The evaluation of the data along the jet at various
sections downstream has shown that the length of the
filaments (Figure 17) as well as their ejection
velocities decrease rapidly, showing the strong
damping effect of the contaminant on the free-surface
structures. The resulting data are shown in Fig. 18. It
is clear from a comparison of the two sets of data
shown in Figure 18 that the contaminant drastically
reduces the filament ejection velocities and the
focussing effect. The massive data is currently being
analyzed for the purpose of assessing the decay of the
kinetic energy of the grid-generated turbulence in
subcritical channel flows (Fr = 0.26) with non-
dissolving as well dissolving contaminants.
Figure 17. Ejection of filaments from the free-surface
of a supercritical flow with surface contaminants (10
micron FluoSpheres).
0.19
0.18
0.17
o
-
> 0.14
0.15
0.12
0.11
0.09
0.0 0.1 0.2 0.3 0.4
Frequency
Figure 16. Representative frequency distribution of
the vertical component of the normalized tip velocity
of the filaments in a supercritical wall jet.
0.19
0.18
0.17
~ 0.15
_ ~ 0.14
r
r _
0.12
0.11
0.09
0.0 0.1 0.2 0.3 0.4
Frequency
Figure 18. Comparison of the frequency distribution
of the vertical component of the normalized tip
velocity of the filaments in a supercritical wall jet
with (in red) and without (in black) contaminants.
11
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CONCLUSIONS
Measurements of the near-surface evolution of
the bow wave were made on a 1/250-scale model of a
destroyer and compared with those obtained from the
sea tests of the subject destroyer wherever possible.
The effects of steady motion, heave, pitch and
combinations thereof were subjected to controlled
experiments to quantify the base flow in comparison
to the prototype. The Froude Number for the majority
of the runs was 0.26. Model scale frequencies ranged
from 1 to 5 Hz, pitch angles from 0.85 degrees to
3.75 degrees and heave amplitudes from 3 mm to 15
mm. It has been shown that there exists two separate
Froude numbers that govern two distinctly different
phenomena in two different regions of the ship. The
subcritical flow dominates the region of unseparated
bow wave (X/L smaller than about 0.04~. The
supercritical regime corresponds to the region of
separated jet and spray formation (X/L larger than
about 0.04~. Remarkable similarity was found
between the corresponding bow-wave motions of the
model and the ship in free-run in heave, pitch, and in
combined heave and pitch motions.
The bow wave manifests its existence in all
other motions (heave, pitch and forced oscillations)
imposed on the ship and on a model. Conseouentlv.
the determination of the excursions of a given bow
wave geometry above or below the maximum or
minimum of the basic bow wave (say the vertical
surge) is an important measure of the resistance, spray
generation, and the overall performance of the ship.
All the motions examined produced a
minimum wave position below the DWL (design
water line) during some part of the cycle. The surge
due to heave and pitch motions is confined to the bow
region very near the stem with differences between the
two due to the rotational pitch motion about the LCB
(the longitudinal center of buoyancy).. The rate of rise
and fall of the bow wave is not uniform throughout
the cycle. The smallest changes in the wave
amplitude are very near the bow stem. In both heave
and pitch motions, the maximum wave height lagged
the maximum downward excursion of the ship by
2/45 seconds for a value of Frs = 0.26. The foregoing
has shown once that the character of a ship is, to a
large extent, ordained by the shape of its bow. A
better understanding of the bow hydrodynamics and
numerical methods may come from numerical
simulations which reveal details that are impossible to
measure.
Experiments with non-dissolving surfactants
have shown dramatic decreases in the size and ejection
velocity of the filaments from supercritical jets.
Detailed processing of data from experiments with
grid generated turbulence in subcritical channel flows,
with and without dissolving and non-dissolving
surfactants, will shed considerable light on the decay
of the turbulent kinetic energy of the wake and thereby
on the decay of short waves.
ACKNOWLEDGMENTS
This investigation has been supported by the Office of
Naval Research. We are particularly indebted to Dr.
L. Patrick Purtell, the Program Director, for his
continuous guidance and encouragement. A note of
special thanks is extended to Dr. Art Reed of DTMB
for providing a copy of the videotape of the ocean
experiments and for his careful reading of the
manuscript.
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13
Representative terms from entire chapter:
basic bow
