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OCR for page 361
Turbulence Measurements in a
Submerged Jet Near a Free Surface
D. Anthony, W. WilImarth, K. Madnia, A. Bernal
(The University of Michigan, USA)
ABSTRACT
The results of two experimental investigations on
the flow structure of a circular jet issuing beneath a free
surface are presented. The mean flow scaling was
determined from velocity measurements made with a hot-
film anemometer. The free surface is shown to decrease
the decay rate of the maximum velocity in comparison to
a free jet. The similarity scaling of the flow is discussed
based on a simple model. The mean flow and all
components of the Reynolds stress tensor were
measured with a three-component LDV system.
Measurements beneath a clean free surface show that the
mean flow spreads laterally in a shallow surface current,
and the turbulent velocity fluctuations become
anisotropic as the surface is approached. Flow
visualization reveals that the surface current contains
fluid structures ejected from the jet, and the current is
suppressed with the addition of surface active agents.
NOMENCLATURE
cl
d
Similarity constant.
Similarity constant.
Jet exit diameter.
h Jet centerline depth.
hm Maximum velocity depth from the free surface.
Jet momentum flux.
Half velocity width.
Streamwise velocity component.
Horizontal velocity component.
Vertical velocity component.
x Streamwise coordinate, positive downstream.
Go Streamwise location of virtual origin.
Horizontal coordinate, positive for right-handed
coordinate system.
Vertical coordinate, positive upward.
Water density.
u
w
z
Po
c
m
z
(subscript) Surface.
(subscript) Half velocity width measured in y
direction.
(subscript) Half velocity width measured in z
direction.
Capital letters are used for mean qualities, primes to
denote RMS fluctuations, and overlines to indicate
Reynolds stresses, e.g., U. w',
INTRODUCTION
Synthetic Aperture Radar (SAR) images of ship
wakes have generated a great deal of interest in the
interaction of turbulent shear flows with a free surface.
These images show a dark band along the track of the
ship believed to be related, either directly or indirectly, to
the interaction of turbulence in the wake with the free
surface. The study of a turbulent jet beneath a free
surface was undertaken to gain some insight on the
interaction of turbulent shear flows with the free surface.
The surface signature of a submerged turbulent jet
was documented by Bernal and Madnia (19881. They
found that the large scale structures in the jet cause
surface deformations and the generation of surface
waves as they interact with the free surface. Farther
downstream, in the region of interaction of the
turbulence in the jet with the free surface, persistent
surface dimples are observed associated with vortex lines
terminating at the free surface. This phenomenon has
been studied in detail by Bernal and Kwon (1989) and
Kwon (1989) for the case of a vortex ring interacting
with a free surface.
(subscript) Jet centerline.
(subscript) Jet exit.
(subscript) Profile maximum.
In this investigation we consider the interaction of
a submerged jet with the free surface. The flow geometry
and coordinates system used is shown schematically in
Figure 1. Here we focus on the velocity field beneath the
surface. We discuss first the similarity scaling of the
mean velocity profiles based on velocity measurements
obtained with a hot-film anemometer at several jet
361
OCR for page 362
z
Ue ~~
- ~-
-
Figure 1. Schematic diagram of the flow geometry
depths. In the second part of the paper the results of
measurements of the mean flow and turbulence stresses
are presented. These measurements were obtained with a
three-component Laser Doppler Velocimeter.
SCALING OF THE FREE SURFACE JET
Rajaratnam and Humphries (1984) studied the
mean flow characteristics of free surface jets when the
free surface is located at the edge of the jet nozzle. In
their investigation they did not study the free surface
motion caused by the jet/free-surface interaction.
However they reported a reduction of the mean velocity
near the surface at high Froude numbers which was
attributed to surface wave generation. Self-similarity
was found for the mean velocity profiles. Rajaratnam
and Humphries (1984) and more recently Ramberg et al.
(1989) have studied two-dimensional free-surface jets.
Ramberg et al. noted the pervasive effects of jet
confinement in their tank. These confinement effects
have been studied by Kotsovinos (1976, 1978~. These
effects can lead to breakdown of the similarity scaling
laws because of the momentum flux associated with the
entrained fluid.
Experimental Apparatus
The scaling experiments were conducted in a water
tank facility consisting of a free surface tank and a jet
tank. The free surface tank was made of glass and was
76.2 cm wide, 76.2 cm high and 167.6 cm long. The jet
flow was generated by a jet tank located inside the free
surface tank. The jet issues from a circular orifice 0.64
cm in diameter located on the side of the tank. A
circular-arc-shaped nozzle with radius 1.27 cm provides
a smooth transition from the side wall of the tank to the
jet exit plane. For the data discussed here the exit
velocity was 200 cm/s which gives a Reynolds number
of 12,700.
Velocity data were obtained using a constant
temperature hot film anemometer. A standard TSI quartz
coated cylindrical sensor was used in the measurements.
The sensor length was 0.51 mm and the diameter 25 ,um.
The sensor axis was positioned perpendicular to the flow
direction and parallel to the free surface. The hot film
was operated at the overheat ratio of 1.09. The output of
the anemometer was DC shifted and amplified using a
Tektronix AM501 operational amplifier wired as a
differential amplifier with a gain of 2.6. The output of
the differential amplifier was digitized using a Lecroy
8210 Transient Digitizer. Typical sampling rates used
were between 200-800 Hz. The digitized output was
then stored on permanent files using an IBM CS9OOO
computer. Additional details on the facility and
instrumentation can be found in Madnia (1989~.
Scaling
A simple model is proposed based on dimensional
reasoning and similarity concepts which describes the
scaling in the far field of the free surface jet. In this
model we consider the momentum flux of the jet Jo as
well as the momentum flux of an image jet above the
surface as shown schematically in Figure 2. Thus the
free surface is assumed to be a plane of symmetry for
the flow. It is further assumed that the dominant length
scale is h, the distance from the jet centerline to the free
surface. The jet exit diameter plays an indirect role
through its effect on the jet momentum Jo.
l
14 ~
~ Free Surface
\ /
UmN
/
Figure 2. Far field scaling of the free surface jet
The similarity scaling in the far field of the
turbulent axisymmetric jet has been discussed by several
authors (e.g., Rajaratnam 1976~. If the jet momentum
flux is constant, the linear growth of length scales with
downstream distance implies that sufficiently far
downstream compared to the jet exit diameter the mean
centerline velocity, Um, can be written as:
r
~ Po Um
362
OCR for page 363
where pO is the fluid density and c is a constant. It
follows that for the free surface jet at sufficiently large
distance compared to the jet depth h, the maximum
velocity Um is given by
~ I °
-= c (x - xO)
Am
where 2Jo is used instead of JO to account for the
momentum of the image jet above the surface. The
constant c should be the same as for the free jet while
the location of the virtual origin xO depends on the
geometry of the jet and consequently can not be expected
to be the same as for the free jet.
In order to verify this scaling arguments, the
equation for the free surface jet can be written in terms of
the jet exit parameters as follows
Ued crux xO)
Um h - ~2 (h - h J
where we have used the relation JO ~ Po (Ue dj2. The
same analysis applied to the free jet gives,
Ue C (X TO:
Thus, the constant cat can be determined from free let
data, which gives cl- 0.162 (Madnia, 1989~. It should
be noted that in order for the constant car to have the same
value for a free jet as for a free surface jet it is required
that the selfsimilar velocity profiles in both of these
flows have the same shape.
These arguments are based on the assumption that
JO is a constant independent of x. As discussed bv
Kotsovinos (1976,1978) this fails to account for the
momentum flux of the entrained fluid which tends to
reduce the momentum flux as the flow evolves
downstream. Also in the free-surface jet problem,
surface waves generated at the interaction will carry
momentum away from the jet which will result in a lower
effective value of JO. Another important effect is the
presence of surface active agents which may contribute
to a reduced momentum flux.
-
In summ~y7 the similarity arguments presented
above suggests that: (i) the proper velocity scale for the
free-surface jet is Ued/h; (ii) the proper length scale for
the interaction is h, the depth of the jet; and (iii) the
maximum mean velocity an~rnache~ the. free c',rf~r`~ faith
downstream distance.
--a Errs _ vent
Results and Discussion
Figure 3 is a plot of UedlUmh as a function of xlh
for free-surface jet data obtained at several values of hid.
It is apparent that the proposed similarity scaling results
in good collapse of the data throughout the interaction.
Yet the slope of the data is somewhat smaller than the
expected value of c/2=0.115. It is only when the
values at xlh=24 and 32 are used to determine the slope
that there is good agreement of the measured slope 0.114
with the calculated value.
h/d=1 n h/d=3.5
h/d=1.5 Free Jet Data
~ h/d=2.5
7-
6-
s
4
3
2
1
O
/~
~'
'1 1 1 1 1
0 10 20 30 40 50
/: a
/
/
o
x/h
Figure 3. Decay of maximum mean velocity.
The collapse of the data in Figure 3 throughout the
interaction region suggests that velocity profiles
measured at the same value of xlh for different hid
should collapse on a single similarity curve. Similarity
profiles for various values of x/h are presented in
Figures 4 and 5. In each figure, plot (a) presents the
similarity profiles in the direction normal to the free
surface and plot (b) presents the profiles parallel to the
free surface. For a normalized distance of x/h-12,
Figure 4(a) shows a significant reduction of the mean
velocity close to the free surface (the free surface is
located at zlLz al). The mean velocity profiles atxlh=24
and 32 are given in Figure 5. The profile in the direction
perpendicular to the surface at xlh=24, Figure 5(a),
shows that the maximum velocity occurs away from the
surface. At xlh=32 the maximum occurs closer to the
free surface. It is apparent that only downstream of
xlh=32 do the similarity profiles of the free surface jet
resemble those of a free jet. We expect that the far field
slope c/2 can only be obtained downstream of this
location.
363
OCR for page 364
~ x/h_10.67 o x/h=12
ll
0.83
. _
0.6
0.4
0.2
O- q° 1~'
-3 -2
· ~e
· ~
· x/h=13.33
1-
0.8
63 0.6
-
0.4
n'._
o_
~. I . I . I
-1 0 1 2 3
z/Lz
(a)
.
a
~0
o
of
a
.· I I ~ ~
-10 1 2 3
Y~Y
(b)
Figure 4. Mean velocity similarity profiles. Ue=200 cm/s
x/h = 10.67,12,13.3. (a) Profiles perpendicular to the
surface. (b) Profiles parallel to the surface.
The growth rate of the mean velocity profiles was
characterized by the half velocity widths Lo, and Lz in the
directions parallel and perpendicular to the free surface.
These half velocity widths were determined with
reference to the location of the maximum velocity in the
profile. The similarity argument suggests that in the far
field the maximum velocity should be found on the free
surface, i.e. hm~0, and also Ly~Lz. Thus, in the far
field Ly ~LZ+hm' where LZ+hm is a measure of the
thickness of the high momentum region on the vertical
symmetry plane. The normalized widths Lylh and (Lz
+hm JIh are plotted in Figure 6 as a function of xlh for all
values of hid. These results show that the high
momentum region is deeper than it is wide throughout
the interaction region. The asymmetry persists for large
~ _
0.8
~3 0.6
=) 0.4_
0.2
0.8]
Is 0.6
0.4
() 2_
1 0 x/h=24
· x/h=32
o
n
-2 0
zJLz
(a)
. I . I
2 4
o-
g
a
a
to
to
._
0 ~ ~on.
-4-2
o
y/Ly
(b)
Figure 5. Mean velocity similarity profiles. Ue=200
cm/s, x/h = 24, 32. (a) Profiles perpendicular to the
surface. (b) Profiles parallel to the surface.
2 4
distances downstream. Only for xlh=32 the values of Ly
and Lz +hm begin to converge toward each other as is
expected in the far field. Both L'lh and (Lz +hm)lh grow
almost linearly with x. The slope of these lines, 0.078, is
in good agreement with the results for a free jet. This
result is not consistent with reported measurements in
free surface jets by Rajaratnam and Humphries (1984).
The downstream evolution of the normalized mean
surface velocity along the jet centerline, measured at a
distance of approximately 2 mm below the surface, is
shown in Figure 7. The mean surface velocity is very
small for xlh ~ 5. The mean surface velocity reaches a
maximum at x/hzl 1 and decreases downstream of this
point. The solid line in this plot is a least squares curve
fit through the normalized maximum mean velocity data
364
OCR for page 365
7;: h/d=2.5 0 h/d=3.5 1
~ ' ~
~ 2- do
1 ~ -e
_.,~%
. ~r
a o
.
1
0 10 20 30 40 50
x/h
Figure 6. Evolution of half velocity width. Solid
symbols, Ly/h; open symbols Lz/h+hm/h.
presented in Figure 3. From Figure 7 it can be seen that
the surface velocity approaches the maximum mean
velocity in the profile for large values of xlh. It appears
that the rate of decay of surface velocity is much slower
than its initial rate of increase in the axial direction. This
can have a significant effect in the dynamics of surface
waves in this region. It is interesting to note that the
location of the maximum velocity, x/in= 11, is
downstream of the location of maximum surface activity
as determined by surface curvature measurements, xlh~
5tolO(Madnia, 1989).
0 in/d= 1 · h/d=3.5
~ hid- 1.5
0 h/d=2.5
0.6-1
- Um h/Ue d
~ ~1
._
=, 0.4
~ 0.3
con ,
0.2
0.1
o
0 10 20 30
x/h
Figure 7. Evolution of mean velocity near the surface.
TURBULENCE MEASUREMENTS
Experimental Apparatus
Measurements of jet turbulence beneath a free
surface were made using a three-component,
underwater Laser Doppler Velocimeter (LDV) designed
for wake measurements in a towing tank. The LDV
used the three strongest lines, 514.5 nm (green), 488.0
nm (blue), and 476.5 nm (violet), of an Argon ion laser
in a three-color, six-beam configuration. The green
and blue beam pairs determined the velocity
components in a plane, and the violet beams determined
the component perpendicular to this plane (Figure 8~.
The LDV used optical fibers to carry the transmitted
beams to two watertight optical probes and to carry
backscattered light from the probes to the
photodetectors. The submerged probes were mounted
oppositely in a cylindrical housing, and a pair of
underwater mirrors folded the six beams to a crossing
approximately 1.25 m from the housing axis. The
measurement volume diameters were approximately
.020 cm on all three components, and frequency shifting
using Bragg cells was employed to allow discrimination
of reversed flow of any component. The Doppler bursts
t
r.~ =.
+Y
Figure 8. Plan and side views of the three
component LDV and jet nozzle. The LDV translates
perpendicular to the jet and rotates about its own axis;
the jet nozzle translates on its axis.
365
OCR for page 366
were processed using counter-type processors, and the
burst information from all three processors was tested
for simultaneity or was rejected. The data were stored
on an IBM PC. See Willmarth (1987) for a more
complete description of the LDV design.
The LDV was operated in a 2400-gallon small
towing tank facility at the University of Michigan. The
LDV probe was suspended from a carriage that allowed
translation in one direction. A stepping motor attached
to the underwater housing allowed the LDV to be
rotated about its axis.
The jet itself consisted of a brass nozzle attached
to a pair of concentric PVC cylinders; within the
cylinders were screens and honeycomb for turbulence
management. The jet was suspended from the facility's
towing carriage and was moved axially to provide the
third axis of positioning. This 'free' jet arrangement
allowed entrainment from all directions, in contrast to
that used for the scaling measurements of Part I where
the jet issued from a wall that spanned the facility. The
jet exit diameter was .635 cm, and the jet exit velocity
was 200 cm/s. Figure 8 shows the LDV probe, the jet,
and the coordinate system.
The water in the towing facility was continuously
circulated and filtered when not taking measurements,
so as to maintain a uniform temperature throughout the
tank. A submersible pump drew from the towing tank,
and the jet discharged back into the tank; in this
manner, seeding uniformity between jet and ambient
fluid could be assured. Titanium dioxide was added to
the water to seed the fluid with scattering particles prior
to taking measurements.
Results and Discussion
Three-component LDV measurements of the flow
velocity in a submerged turbulent jet at depths of 60
and 2 diameters were made to quantify the behavior of
turbulence beneath a free surface. The jet Reynolds
number based on exit velocity and jet diameter was
approximately 12,700. The data were obtained using a
simultaneity window set equal to the time required for
a scattering particle travelling with the measured mean
speed to traverse the diameter of the measurement
volume. Data rates tended to be low, around 30 Hi
near the jet centerline and less than 10 Hz at the jet
edges. For the data reported here, at least 1000
individual measurements were recorded at each location;
this number was chosen based on the appearance of the
velocity histograms for each component. Ensemble
averages were corrected for particle arrival bias using
the reciprocal of the magnitude of the instantaneous
velocity vector (McLaughlin and Tiederman, 1973) to
weight the individual measurements.
Measurements of the flowfield of a deep jet
(h/d~60) were made as a baseline from which to
compare measurements made in a shallow jet (h/d=2)
beneath a free surface. The streamwise velocity
component on the jet centerline is shown in Figure 9,
plotted so as to reveal its inverse dependence on x, as
expected from similarity considerations. The measured
slope of this line gives Uc/Uc~6.3/(x/d), in agreement
with that reported elsewhere, e.g. Rajaratnam (1976~.
However, at 32 diameters downstream, the flow can still
not be considered fully developed, in the sense that the
turbulence quantities become self-similar. Wygnanski
and Fiedler (1969) have shown that the turbulence
;
o
o o o
o
o
; 1'0 2'0
x/d
o
o
,
30 40
Figure 9. Variation of jet centerline velocity with
downstream distance, h/d~60. Scaling determined
from straight line segment shown.
quantities in an axisymmetric jet do not become self-
preserving until about 80 diameters downstream.
Profiles of mean velocity, RMS turbulent
fluctuations, and Reynolds stresses were measured at
downstream stations of 16, 24, and 32 diameters.
Shown in Figs. lOa-d are profiles at x/d=32 for varying
z at y=O; corresponding profiles for varying y at z=O,
though not shown, are in excellent agreement and serve
to verify that the jet is indeed axisymmetric. The
profiles are plotted using similarity variables,
normalizing the vertical coordinate z by the downstream
distance x and the velocity components by Uc, the mean
velocity on the jet centerline. The vertical mean
velocity component W. shown in Fig. fob, shows
outward flow near the jet centerline, and inward flow
(entrainment) at the jet edges. This behavior is
expected to differ when the jet discharges near a free
surface, because of the restrictions the boundary places
on the vertical growth of the jet and on the entrainment
366
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of fluid into the jet from above. The RMS turbulent
fluctuations (Fig. lOc) show the horizontal and vertical
fluctuations v' and w' to have the same magnitude,
while the magnitude of the streamwise fluctuations u' is
somewhat greater. By symmetry, the cross-stream
mean velocity V(Fig. lOb) and the Reynolds stresses u v
and v w (Fig. lOd) should be zero; to within the limits of
experimental error, these terms are effectively zero.
Shallow jet data (h/d=2) were obtained at x/d=32,
for the same Reynolds number, and are presented in
Figs. [la-d. The same similarity variables are used so
that direct comparison between Figs. 10 and 11 is
possible. Comparison of the streamwise mean velocity
profiles (Figs. lea and lla) reveals that the location of
maximum mean velocity approaches the surface, in
agreement with the scaling results of Part I above. Fig.
Fib shows a profile of the vertical mean velocity; near
the jet centerline, the flow is again outward, and well
below the centerline, the flow is entraining inward. The
flowfield above the jet centerline shows the effects of
the free surface, driving the vertical mean velocity to
zero as it is approached. The RMS turbulent
fluctuations, Fig. tic, reveal a distinctive behavior as
the surface is approached: The fluctuations normal to
the free surface are significantly diminished, while those
parallel to the surface are enhanced. The Reynolds
stresses are plotted in Fig. lid, showing that the
principal stress uw diminishes to zero as the surface is
approached.
Measurements of turbulence beneath a free surface
in inherently two-dimensional flows such as the
channel flows reported by Komori, et. al. (1982) and
Rashidi and Banerjee (1988), and the plane surface jet
flow reported by Ramberg, et. al. (1989) have
previously shown that the turbulent fluctuations become
anisotropic beneath a free surface. Beneath a sheer-free
plane surface as is appropriate to the image model
outlined above, the vertical velocity and vertical
fluctuations must go to zero as a consequence of the
plane boundary. However, the interaction of the jet
with a free surface shows considerable surface activity,
including the generation of surface waves, and the
vertical fluctuations need not go to zero as the surface
is approached. Recent research investigating the
dynamics of vortex rings at a free surface (Bernal and
Kwon, 1989) revealed a process of vortex reconnection
to the free surface. The vortex lines comprising the
rings were found to disconnect and become attached to
the surface, resulting in open vortex lines beginning and
terminating at the free surface. We suggest that the
physical mechanism acting to redistribute the turbulent
energy from the vertical to lateral fluctuations is a
process whereby vortex filaments in turbulence become
attached to the free surface.
Lateral velocity profiles were taken between the
jet centerline z=0 and the free surface z=h, again at
x/d=32. Those points nearest the free surface were
within 1 mm of the undisturbed surface and were as
close to the surface as was possible without the
measurement volume being interrupted by surface
deformations. Though not shown, these data reveal a
significant increase in the jet width as the surface is
approached. The flow is inward at the jet edges on and
just above the jet centerline, corresponding to
entrainment, but is outward in a thin layer just beneath
the surface that extends laterally to several jet widths
from the jet centerline. We refer to this thin layer as
the surface current.
To investigate this surface current, the LDV was
operated without requiring simultaneity among the three
components; this allows determination of the mean
velocities, but sacrifices the turbulence quantities in
favor of a higher data acquisition rate. The data shown
in Figs. 12a-d are averages of at least 2000 individual
measurements per channel at each location, and are not
corrected for bias. Shown are vector plots of the mean
velocity components V and W at various downstream
stations. At x/d=16, the data show the beginnings of
the surface current in the data taken at the surface, but
not in that taken below it. Proceeding downstream to
24 and 32 diameters, the current is seen to develop,
growing significantly wider than the turbulent jet flow
beneath it, but remaining confined to a shallow layer
just beneath the surface. At 48 diameters downstream,
the surface current dominates the flowfield, the velocity
components throughout the jet having diminished with
increasing distance downstream.
Near the jet centerline, the mean flow has a
component outward (as the jet grows wider
downstream), and well below the jet centerline, the flow
is inward as ambient fluid is entrained. In the current
layer, a strong outward flow causes the entraining flow
below it to be turned outward. One might attribute such
turning to the action of a streamwise vortex lying just
outboard of the jet, as the flowfield is suggestive of a
vortex pair lying just beneath and parallel to the free
surface. A similar flow pattern appears in wake data
taken behind surface ships, and this pattern is
sometimes attributed to the action of large streamwise
vortices shed from the stern or bilges of the ship. In
the case of the jet, stretching of ring-like or helical
vertical structure within the jet could yield streamwise
structure in the mean. Far from the free surface, there
should be no preferred azimuthal position for these
structures, but in close proximity to the surface, a stable
configuration of streamwise vorticity could develop.
This feature might be characteristic of the interaction
between a three-dimensional turbulent shear flow and
a free surface.
367
OCR for page 368
1.00
0.80
0.60
0.20
of
-
o o U o
0.30
o ~
o o
o ¢0.20
o
o o
o o
o
o
o o
0.00 - Go Oo
-0.20 -0. 10 0.00 0.10 0.20
Z/X
Figure lOa. Profile of streamwise mean velocity
component, x/d=32, h/d~60.
0.10;
0.05
0.00
-0.05
oo U' o
V' o
I'
o
°° °8°° °
o
it, 0 ~ ~ ~ [; 0
0
i,\ 0
o
r'
~ 0
o8
0.00 1 , , , ~
-0.20 -0. 10 0.00 0.10 0.20
Z/X
Figure lOc. Profiles of RMS turbulent fluctuations,
x/d=32, h/d~60.
0.025
V o C`2
W
~o
o O a O C O o U
~ A O C C O ~O A ~ 0.000
~ ~ ~ear,
UV O
veer 0
^~^ US
O Oo O
~ ~ 8 ° ° ~ ~ ~ ~ 0 0 O8 ° of ° o8g gone ~
-0.10~, , , , -0025 1 , . . .
20 -0.10 0.00 0.10 0.20 · -0 20 -0.10 0.00 0.10 0.20
Z/X Z/X
Figure fob. Profiles of horizontal and vertical mean Figure led. Profiles of Reynolds stresses, x/d=32,
velocity components, x/d=32, h/d~60. h/d~60.
The surface current does not obviously follow
from the considerations of Part I for a shallow
submerged jet merging with its image above the surface,
although the concept of image vorticity is essential to
understanding the surface current. To understand the
origin of the surface current, flow visualization using
laser-induced fluorescence (LIE) was used. A small
amount (3 ppm) of fluorescein dye was added to the
reservoir supplying the jet, and a cross-stream plane
(x/d=32), normal to the free surface and the axis of the
jet, was illuminated with a laser light sheet. The
boundary of the jet was observed to be very uneven and
unsteady, appearing to emit puffs of dyed, vertical fluid
in random directions; these puffs initially propagated
outward and away from the jet. The puffs that were
emitted downward slowed rapidly and were rarely
observed to propagate far from the jet boundary.
However, those that were ejected near the surface,
having little downward velocity, were observed to
368
OCR for page 369
l.
o.8
0.60
c,
0.40
0.20
0.00- 00 , . . .
-0.20 -0. 10 o.oo o. 10 0.20
z/x
Figure 11a. Profile of streamwise mean velocity
component, x/d=32, h/d=2.
o
'it.
o to U o
o
o
o
o
o
0.10
0.05
c,
0.00
-
c,
0 ° 0 ° ~ ~ ~
-0.05
o. 100 20 -o. to o.oo o. to 0.20
z/x
Figure lib. Profiles of horizontal and vertical mean
velocity components, x/d=32, h/d-2.
continue to propagate parallel to the surface away from
the jet boundary. These emissions persisted to several
jet half-widths hom the boundary in a thin layer just
below the surface. The average of many such emissions
and their subsequent propagation outward gives rise to
a mean outward flow which is observed as a surface
current.
0 30 ~
-
~ 0.20
-
-
~n 1n
a
Coo
0 0
~ ~ ~ B
o
o
U' O
V' O
in'
0-00-
-0.20 -0.10 o.oo 0.10 0.20
z/x
Figure 11c. Profiles of RMS turbulent fluctuations,
x/d=32, h/d=2.
0.025
v ~C`2
w ~
~ 0.000
1>
1>
car
1=
uv 0
veer 0
user ~
oo 28 8°~°°°~
~ AL
-0.025 l l l l
-0.20 -0. 10 o.oO 0.10 0.20
z/x
Figure 11d. Profiles of Reynolds stresses, x/d=32,
h/d=2.
Using a horizontal light sheet, planes parallel to
the surface were illuminated. With the sheet just
beneath the surface, a plan view of the surface current
was obtained. The layer appears to originate near
x/d=16 for a jet depth h/d=2. Ibe current layer shows
puffs of dyed fluid ejected from the jet propagating
outward at an angle of about 35 degrees to the jet axis,
whereas the jet flow itself spreads at about 12 degrees.
369
OCR for page 370
2
o'
z/d
-2
4
yld
0 2 4 6 ~10 12 0
.h .~.1 ~ ~1 1 1 1
, ~ ~ - ~ + ~
9 ,.^ an____`
%~_4~`
_ , , _~ t t ~ ~ ~
10 cm/s
Figure 12a. Vector plot of horizontal and vertical mean
velocity components, x/d=16, h/d=2. Shaded circle
shows jet nozzle, shaded triangle shows location of free
surface.
y/d
o
4
1 ~ b ~ ~ t
Figure 12b. Vector plot of horizontal and vertical mean
velocity components, x/d=24, h/d--2.
The ejected structures remained relatively coherent, and
high concentrations of dye in the ejected fluid suggest
that turbulent mixing is greatly reduced within the layer.
Illuminating a plane through the jet centerline, z=O,
reveals characteristic deep jet behavior up to
approximately 24 diameters, at which distance the
structures emitted in the surface layer have grown in
scale sufficiently to intercept the sheet from above, well
outboard of the 12 degree jet boundary. In a plane
beneath the jet, z/d=-1, the only evidence of the layer
comes from the few structures large enough to reach the
light sheet.
y/d
2 4 6 8 10 12
Lit 1 ~ __ _ ~ _
- 4
10 cm/s
Figure 12c. Vector plot of horizontal and vertical mean
velocity components, x/d=32, h/d=2.
~U
2
z/d
-2
-4
ma. ~
10 cm/s ,
370
~ . 10 cm/s
Figure 12d. Vector plot of horizontal and vertical mean
velocity components, x/d=48, h/d=2.
Although we have not directly measured the
vorticity, the fact that the surface puffs continue to
propagate away from their origin near the jet boundary
indicates that they consist of vertical fluid. The dye
concentration of the fluid carried with the surface puffs
indicates that this fluid has not mixed with the
surrounding (non-dyed) fluid as the puffs propagate
outward along the surface.
The recent work of Bernal, et. al. (1989) and Hirsa
(1990) in determining the behavior of a vortex pair
OCR for page 371
beneath a free surface revealed the importance of
surface-active agents in determining the vortex
trajectories and the generation of secondary vorticity
beneath surfaces contaminated with such agents.
Discrete vortices travelling toward a free surface
propagate outward beneath the surface when the surface
is relatively free of surfactant, but rebound from the
surface when surfactant is present. The rebounding is
caused when secondary vorticity of opposite sign to the
primary vortices is generated beneath a surfactant
covered surface. Oleyl alcohol, an insoluble surface-
active agent for which the constitutive relation between
surface pressure and concentration is known, was added
to the free surface, and the LIF flow visualizations were
repeated. The surface current did not form, and vertical
ejections from the jet, emitted near and parallel to the
free surface, were confined laterally through interaction
with secondary vorticity generated beneath the
surfactant layer.
Acknowledgements
This work is supported at the University of
Michigan by the Office of Naval Research University
Research Initiative Program in Ship Hydrodynamics,
Contract Number N000184-86-K-0684 and at the
David Taylor Research Center by the ONR Surface Ship
Wake Consortium, Contract Number N0001490-WX-
22034.
References
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371
OCR for page 372
DISCUSSION
John P. McHugh
The University of New Hampshire, USA
Did you notice any pattern on the free surface near the jet? Were
there any distinct streamwise or transverse waves visible?
AUTHORS' REPLY
Under the conditions investigated, the interaction of the jet flow with
the free surface led to the generation of surface waves near the jet
centerline. These waves, generated continually and apparently at
random by the large-scale structures in the jet flow, were observed to
coalesce and to propagate in a direction almost perpendicular to the
jet axis. Measurements of the wavelength and wavespeed from
shadowgraph images of the free surface showed the waves to be
gravity-capillary waves of wavelengths between 1 and 4 cm,
travelling with approximately the minimum wavespeed, 23 cm/s,
attainable on deep water having a clean free surface.
372
Representative terms from entire chapter:
mean velocity
