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DISCLAIMER
This report has been reviewed by the Corvallis Enviromental Research Labora-
tory, U.S. Environmental Protection Agency, and approved for publication.
Mention of trade names or commercial products does not constitute endorsement
or recommendation for use.
11
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FOREWORD
Man and his environment must be protected from the adverse effects of
pesticides, radiation, noise, and other forms of pollution, and the unwise
management of solid waste. Efforts to protect the environment require a
focus that recognizes the inter play between the components of our physical
environment—air, water, and land. The Corvallis Environmental Research
Laboratory contributes to this multidisciplinary focus through programs
engaged in
0 studies on the effects of environmental contaminants on the
biosphere, and
0 a search for ways to prevent contamination and to recycle
valuable resources.
This report presents the results of a study to determine some of the
dilution characteristics of single and multiple port buoyant discharges
typical of modern natural and mechanical draft cooling towers.
A. F. Bartsch
Director, CERL
iii
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ABSTRACT
An experimental investigation was conducted to determine the dilution
characteristics of single and multiple port buoyant discharges typical of
modern natural and mechanical draft cooling towers. Simultaneous measurements
of velocity and tracer concentration profiles were taken at various downstream
locations in the three-dimensional plumes discharged into a stagnant ambient
using a hot film anemometer and conductivity probe. The number of discharge
ports was varied from one to seven. Discharge densimetric Froude numbers
were varied from 1.5 to infinity. Numerical integration of the profiles gave
dilution, tracer conservation, and momentum fluxes. The effect of reducing
Froude number was to increase entrainment considerably. Increasing the
number of discharge ports reduced the rate of entrainment. In multiple port
discharges the shape of the plume changed from an elongated configuration to
nearly axisymmetric within the first 20-30 diameters of discharge. This
report covers the period from July 1975 to December 1976 and work was com-
pleted as of December 1976.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures vi
List of Symbols vii
1. Introduction 1
2. Conclusions and Recommendations 3
3. Apparatus and Procedure 4
4. Results and Discussion 9
References 22
Appendix 24
A. Table A-l Complete List of Data 24
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FIGURES
Number Page
1 Sketch of Test Apparatus in Towing Channel 5
2 Sketch of Multiple Port Discharge System 6
3 Dilution versus Distance for single Jet, F = 1.5 - ~ 12
4 Plume Half Width versus Distance for Single Jet Discharge 13
5 Center!ine Velocity Ratio versus Distance for Single Jet, F =
1.5-°° ° 14
6 Development Zone Velocity Profiles for Single Jet, F = 2.2 16
7 Froude Number Effects on Velocity Profiles at Fixed Downstream
Distance 17
8 Dilution versus Distance for Multiple Port Discharge, F = 6 18
9 Variation in Plume Shape for Multiple Port Discharge at Various
Downstream Distances, F = 6 19
10 Centerline Salinity Concentration versus Distance for Multiple
Port Discharge, FQ = 6 21
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LIST OF SYMBOLS
A Number of discharge ports aspect ratio
b Local characteristic width of jet = /2 a
bn c Local characteristic width of jet where U/U =0.5
u * o c
D Port discharge diameter
F Densimetric Froude number at outlet, U //g'D
F, Local densimetric Froude number U //g'b
l_ C C
g Acceleration due to gravity
g1 Reduced gravitational acceleration, g Ap/p,
a
J Mass flux of salt - /USdA
m Mass flux - /pUdA
M Momentum flux - /VdA
Q Volumetric flow rate
r Radial coordinate perpendicular to jet centerline
S Salinity - mass fraction
AT Excess water surface temperature on jet centerline
\f
AT Discharge excess water temperature
U Jet velocity - variable in all directions
U Discharge velocity from outlet
X Rectilinear horizontal coordinate parallel to port connecting line
Y Rectilinear horizontal coordinate perpedicular to X
Z Coordinate in vertical direction
Ap Difference between jet centerline and ambient water densities
vii
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p Fluid density
a Standard deviation of Gaussian profile
SUBSCRIPTS
a Ambient conditions
c Centerline value
o Discharge conditions
vm
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SECTION 1
INTRODUCTION
With the changing emphasis of waste heat disposal to large cooling
towers instead of once-through cooling systems, an increased interest has
developed into the dilution characteristics of a finite number of neighboring
jets discharging at relatively low densimetric Froude numbers, F , such as
found in mechanical draft cooling towers. This system produces a three-
dimensional plume whose dilution depends on combined turbulent heat and mass
transfer with the environmental ambient fluid.
Once-through cooling systems consist mainly of surface discharge or
submerged discharge from a large single port or from a multiple port diffuser
that may be several hundred feet long with many discharge ports. However,
mechanical draft cooling towers usually have fewer than ten discharge ports.
Thus, end effects cannot be neglected and, because of the initial merging
process, they cannot be considered as single axisymmetric jets.
Buoyant jets have been investigated extensively in the past. Excellent
reviews can be found in Hirst [1], Baumgartner and Trent [2], Briggs [3], and
Silberman and Stefan [4]. Therefore, only those references directly related
to this work will be discussed. Most of the reports in the above reviews
deal with single jets with dilution expressed as excess temperature decay
AT /AT . However, true dilution is defined in terms of the ratio of local
mass flow rate of fluid in the plume to the discharge mass flow rate, m/m .
The latter definition is related singularly to excess temperature only in the
fully developed region of the plume where similarity of profiles exists and
in non-stratified ambients. Since multiport discharges of finite number have
non-axisymmetric, non-similar velocity and temperature profiles, both must be
measured to determine dilution and its relation to excess temperature decay.
One of the classic papers on single port buoyant plumes in which both
temperature and velocity were measured was presented by Schmidt [5]. He
created a purely buoyant or thermal plume by placing a heating coil in a hole
in a horizontal board inducing flow through it. No measurements were reported
at the hole so neither a discharge flow rate nor Froude number could be
determined. The rate of dilution determined from his data, however, falls
below the values of F = 1.5 determined in this study. Integrating his
published values of velocity and temperature at different cross sections in
the plume shows a variation in the conservation of energy by as much as a
factor of 2.0. This indicates the difficulty in obtaining accurate simultane-
ous readings of temperature and velocity, especially in stagnant ambients
where the tail of the profile goes to zero. Similar problems occurred in the
present study.
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Rouse, et^ al_. [6] also investigated buoyancy-induced flows from a point
heat source. Although interesting to look at, an idealized point source is
difficult to relate to results of a finite discharge with initial turbulence,
momentum and development length. The inability to determine an initial mass
flux and Froude number further complicates the problem. However, such studies
are useful in determining trends in plume dynamics in the far field. The
authors were able to do this very successfully. Jirka and Harleman [7]
investigated multiport discharges into shallow water from submerged outfall
diffusers. Both two- and three-dimensional configurations were examined.
They developed stability criteria useful in analyzing plume spreading at the
water surface but due to the shallowness of the water and the long length of
the diffusers, their data do not apply directly to this study. Kannberg and
Davis [8] experimentally investigated temperatures in deep submerged multiport
discharges and developed models primarily applicable to two-dimensional
diffusers with no end effects. Sforza, et a]_. [9] investigated velocities in
the isothermal discharge of air into air from a variety of discharge shapes
including rectangular slots. Their findings will be compared with the results
of this investigation.
Kotsovinos [10] studied the entrainment of plane (two-dimensional)
turbulent buoyant slot jets. As in the present study, he conducted simultane-
ous measurements of temperature and velocity within the plumes for a variety
of Froude numbers and was able to determine both dilution and excess tempera-
ture decay directly. His is an excellent study but it does not include end
effects or mixing and merging of plumes.
The emphasis in the present investigation was to obtain simultaneous
measurements of velocity and tracer across the plume in a variety of single
and three-dimensional multiple jets discharging into stagnant ambients. The
objective was to obtain direct entrainment data to facilitate modeling of a
three-dimensional plume from cooling towers with one or more neighboring
cells.
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SECTION 2
CONCLUSIONS
The measurement of dilution from single and multiple port buoyant jets
with no ambient current has been made along with the decay in centerline salt
concentration by simultaneously measuring velocities and salinity within the
plumes. The effect of Froude number on dilution was considerable with greater
dilution at lower Froude numbers. The approximate expression showing this
effect was given in terms of the entrainment coefficient,
a = 0.057 + 0.083 Fo"°'03.
For multiple port discharge the effect of aspect ratio (number of dis-
charge ports) was to decrease dilution with increasing aspect ratio. The
approximate expression showing this effect was found to be
Q/Q0 = 1-0 + 0.46(Z/D)1J(A)"°'52
It was found that the shape of multiple port plumes changed from an elongated
configuration to nearly axisymmetric within the first 20-30 diameters of
discharge.
The experimental scatter in the results and the inability to accurately
measure the low velocities in the "tail" of the velocity profiles using a hot
film anemometer precludes the drawing of firm conclusions at present. It is
recommended that the results of this study be checked with a different anemom-
eter such as a Laser Doppler system with a "Bragg" cell so the lower veloci-
ties will be more accurate. It is also recommended that the work be extended
to include ambient velocity effects and discharge line orientation relative
to the ambient current.
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SECTION 3
APPARATUS AND PROCEDURE
Water was chosen as the working fluid with the buoyant jets being created
by discharging salt water downward into fresh water. Using this technique, a
wide range of Froude numbers could be obtained by adjusting the salinity of
the discharge water while maintaining Reynolds numbers high enough to insure
turbulent flow.
Figure 1 is a sketch of the test apparatus used in this study. The main
tank was a towing channel 12.1 m long, 0.61 m wide, and 0.91 m high located
at EPA's Corvallis Environmental Research Laboratory (Oregon). Both sides of
the tank were plexiglass so visual measurements could be made. The discharge
tank containing salt water was located on rails above the receiving tank. It
was airtight except for breather tubes which maintained a constant velocity
head regardless of the water level in the discharge tank. This system is
described in detail in Kannberg and Davis [8]. From this tank, the salt
water passed through a control valve into a plenum chamber with baffle and
discharge tubes as shown in Figure 2. Also shown in this figure is the
coordinate system used. The number of discharge tubes used were 1, 2, 3, 5
and 7. The tubes, 9.53 mm inside diameter and 12.7 mm outside diameter, were
placed as close together as possible. This gave a port spacing to discharge
diameter, L/D, of 1.33, approximating that of multiple cell mechanical draft
coolirfg towers. Since the ports were right against each other, the number of
ports approximately represented the discharge aspect ratio, A. The length of
the tubes was such as to give fully developed turbulent flow at discharge.
In addition, several runs were conducted with single discharge ports of
11.2, 11.6, 11.2 mm, 13.5 mm, and 38.1 mm inside diameter to give the range
in Froude and Reynolds numbers desired. The Froude numbers tested ranged
from 1.5 to infinity (a momentum jet). The Reynolds numbers were all greater
than 2100 which was sufficient to maintain turbulent discharge. This was
easily detected by observing the density waves created by the discharge of
salt water into fresh water.
Salinity within the plumes was measured with a conductivity probe and
carrier amplifier similar to those described by Keeler [11] and McQuivey, ejt
al. [12], Velocities were measured with a Thermal Systems, Inc. (TSI) con-
stant temperature hot film anemometer system. The two probes were mounted
side-by-side on a remotely controlled string. The tips of the two probes
were about 2.0 mm apart. The discharge system, traversing mechanism and
probes were attached to a carriage on rails above the receiving tank and
could be towed at desired velocities ranging from 0.5 to 50.0 cm/s along the
length of the receiving tank. This feature was only used for probe calibra-
tion since tests were conducted in stagnant water.
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Calibration of the conductivity probe was fairly stable as long as it
was kept free of dirt and oxidation. Considerable care was taken before each
test to clean the probe and adjust the gain of the carrier amplifier to bring
the signal output in agreement with a predetermined calibration curve. It
was found that this procedure insured that the probe response agreed with the
calibration curve over the full range of salinities of interest.
The overheat ratio for the hot film anemometer probe could not be set as
high as recommended by the manufacturer without causing vapor bubbles to form
on the probe, thus creating signal drift. Operation at a reduced overheat
caused the response to be sensitive to the water temperature. To resolve
this problem, a calibration curve was obtained at a desired nominal reduced
overheat by towing the probe through the tank for a full range of speeds.
Then, before each run the probe was towed at one known speed and the overheat
was adjusted until the signal reponse agreed with the previously determined
calibration curve. This brought the probe back into calibration as the tank
temperature changed from day to day.
After selecting the desired discharge configuration, the discharge
velocity and salinity were adjusted to give the desired Froude and Reynolds
numbers. Discharge flow rates were calculated from the measured time it took
a known amount of water to flow from the discharge tank. Most runs were with
sea water at a salinity of 32 ppt. For runs with F =1.5 and 3.0, the
salinity was increased so the discharge Reynolds number could be maintained
above the critical value. For F = 8.7, 23 and 36, the salinity was reduced
so discharge flow rates could be maintained, allowing longer run times.
With the system properly adjusted, runs were made while traversing the
plume horizontally at desired locations. The probes were left at each point
long enough to obtain a good time average reading. The velocity signal was
squared and averaged with several time constants using a true RMS meter. It
was found that a record length of up to one minute was required to provide
sufficient information for a stable variance. For single port discharges
where the plume can be assumed symmetrical, a single horizontal traverse was
made through the center of the plume at each downstream location, Z/D. For
multiport discharges, however, several horizontal traverses were made through
the plume at each Z/D location to provide sufficient readings for a three-
dimensional picture of the plume cross section. The usual spacing for these
readings was on 1.0 cm centers in both the X and Y directions. In high shear
areas, 0.5 cm spacings were used.
Downstream locations, Z/D, ranging from 0.09-40 diameters were investi-
gated with the bulk of the data taken at 10, 20, and 30 diameters. Readings
near the discharge ports were usually not taken due to the inaccuracies of
the probes in high gradient regions caused by their size relation to the
shear layer thickness. One run was made at a Froude number of 2.1 using a
large discharge diameter port (38.1 mm) with data taken near the discharge
port. This provided information on discharge profiles and their development
in the zone of flow establishment. In the far field, the hot film probe
could not give accurate readings in the low velocity tail of the expanding
plumes. Since this region grew more important in determining dilutions as
Z/D increased and because bottom effects began to appear, far field readings
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were not taken. The tank was drained after each series of runs and refilled
with fresh water to prevent salt build up in the ambient receiving water.
Several multiport runs were made with dye in the discharge water. This
was done with the line of ports both perpendicular and in line with the tank
side walls. Photographs were taken to determine plume spreading in both the
X and Y directions to support the data taken with the two sensors.
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SECTION 4
RESULTS
The appendix contains a listing of all the data taken in this study.
Each set of data contains the test number, Froude number, number of ports,
dimensionless X-Y-Z location of the point, the velocity, U/U , and salinity,
S/S (if applicable and available). A Froude number of 999 is for a momentum
jet? Salinity data for Froude numbers of 1.5 and 3.1 are unavailable due to
equipment failure
Table 1 presents the basic summarized results of this study, both for
single and multiport discharges. Given on this table are: number of ports,
discharge densimeteric Froude number, the plume half widths in the X and Y
directions, dilutions, and terms relating local momentum and salinity fluxes
to discharge conditions. These initial discharge conditions are also indi-
cated on the table. Dilution is defined as the local mass flow rate as
compared to the discharge flow rate or m/m . Mathematically this is given as
pUdA/p Q . Since the density across the plume changes less than 1.0% from
the ambient, the dilution can be determined approximately by considering
volume fluxes only. In this study, the dilution was calculated numerically
for the three-dimensional plumes by
Q/Qo = ZEUijAA/QQ (1)
where U.. were the velocities at each grid point and AA was the grid size.
For thensingle plumes, dilution was determined by using a best fit Gaussian
curve to the data in the expression
Q/QQ = 27rufexp[-(r/b)2]rdr/Qo (2)
where U was the maximum cross section velocity and b was the characteristic
width determined from the data.
An indication of the accuracy of the data was obtained from the expres-
sion
J/Jo = JUSdA/(QoS0) (3)
where S is the salinity. Since the receiving water was fresh, the mass flux
of salt in the plume should be constant or J/J = 1.0 at all Z/D along the
plume. The value of this ratio was determined in the same manner as dilution.
The momentum flux ratio, M/M
M/MQ = I U2dA/U2Q (4)
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is also helpful in evaluating plume dynamics. For momentum jets the value of
this ratio should be unity at all times due to the lack of external forces on
the plume. For buoyant jets, however, this ratio should increase under the
influence of buoyant forces. The values of M/M for each Z/D were calculated
by numerically integrating the velocity squared over each plume cross section.
Figure 3 is a plot of Q/Q versus Z/D for the single port discharges at
various Froude numbers. Lines have been drawn through the data to indicate
approximate trends. Even though the data are scattered, it can be seen that
the effects of Froude number are considerable. It can also be seen that the
trends are not necessarily linear, reflecting partly the influence of the
development zone. For the momentum jet, F = », the rate of dilution is
linear with distance and agrees well with published data [13, 14 and 15].
Most buoyant discharge experiments have been interested in temperature or
concentration decay. Dilution as such was usually not measured. Ricou and
Spalding [15] measured dilution for hydrogen discharged into air. The trend
in their data agrees with Figure 3; however, they suggest that m/m =
0.32(x/d)(p1/p2)1/2 where pi/p2 is the ratio of the heavier fluid aensity to
the lighter fluid density. This expression considerably underpredicts the
observed dilutions in this study.
The entrainment of ambient fluid causing dilution, E = dQ/dz, has been
expressed as a function of an entrainment coefficient and local plume proper-
ties [16, 17] such that E = aU b. In this expression a is the entrainment
coefficient. For momentum jets a = 0.057 has proven to be a good value.
Abraham [18] suggested a value of a = 0.085 for low Froude number discharges.
In this study entrainment coefficients varying from 0.06 for momentum jets to
0.14 for very low Froude numbers were found. The expression
a = 0.057 + 0.083 Fo"°'3 (5)
fit the general trend in data for the single port discharges without ambient
current.
An alternate expression, derived by Fox [19] using a combination of the
nical energy, momentum and continuity equations is E = (ai + a2/F?
where F, is the local Froude number given by F. = U /[Ap gb/pjv2. The
value of the first coefficient is the momentum jet value of 0.057. Hir
mechanical energy, momentum and continuity equations is E = (ai + a2/F?)U b
jv2. The
jet value of 0.057. Hirst
[1] suggested a value of 0.97 for the second. This expression does not
agree with the data from this study. For example it was 40% low for F = 36
and Z/D = 30 and 30% low for FQ = 6 and Z/D = 10. °
Figure 4 is a plot of plume half width, bQ r, versus distance for the
single port discharges investigated. These wiatns were based on the location
where U/U = 0.5 at each cross section. Only a slight increase in plume
width is observed as Froude number is decreased. The momentum jet plume
growth agrees with the experimental values of Albertson [13]. Figure 5 is a
plot of the plume center! ine velocities versus distance for Froude numbers
ranging from 1.5 to infinity. Lines indicating approximate trends have been
drawn through the data. It is seen that at very low Froude numbers the
buoyant forces maintain high centerline velocities which cause higher dilution
rates when compared to the higher Froude number discharges.
11
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VERTICAL DISTANCE - Z/D
Figure 5. Center!ine velocity ratio versus distance for single jet,
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Figure 6 is a plot of velocity profile measured close to the discharge
port for a Froude number of 2.2. The Z/D distances were 0.1, 1.0, 3.0, and
10.0 diameter downstream which cover the development zone. Due to the steep
velocity gradient near discharge, the profiles for Z/D =0.1 and 1.0 are less
accurate than for larger diameters downstream. The profiles on Figure 6,
however, do show the extreme variation of velocities within the development
zone. It is interesting to note that the boundary layer and buoyant forces
within the discharge tube have caused center!ine velocities to be greater
than the average discharge velocity near the source. It is noted from Table
1, however, that Q/Q for Z/D =0.1 is essentially 1.0, which it should be
for consistent data.
Figure 7 is plot of velocity profiles at Z/D = 10 for Froude numbers of
1.5, 3.1 and °°. The effect of buoyant forces on velocity is clearly seen on
this figure where the center!ine values for the low Froude number runs are
considerably higher than the non-buoyant discharge case. The minor effect
buoyancy has on plume width can also be run on this figure.
Figure 8 is a plot of dilution versus distance for several multiport
discharges at a nominal Froude number, F = 6. The single port discharge
values for this Froude number are also included for reference. Although the
data are scattered, the effect of aspect ratio A (number of ports) is evident.
The greater the number of ports, the lower the rate of dilution. This is
explained by the interference of the merging plumes on the entrainment mechan-
ism. Not only is the surface area available to entrain ambient fluid de-
creased upon merging, but neighboring plumes also compete for the same ambient
fluid thus decreasing the entrainment of each. Also included on this figure
are data points taken from Kotsovinos [10] for an infinite slot (A = °°) at
Froude numbers of 8.4 and 5.5. Within the experimental limits of this study
the dilution was found to approximately fit the expression,
Q/Q0 = 1.0 + 0.46 (Z/D)1'1(A)"°-52 (6)
One of the more interesting characteristics of the multiple port dis-
charges was the change in plume shape along its trajectory. Near discharge
the jets from each port maintained their individual character but soon merged
into a single elongated plume with the major axes in line with the line of
discharge ports. As the plume grew, perpendicular spreading was greater than
spreading along this line. Thus, this elongated character soon disappeared
and the plume became essentially round. Figure 9 shows four different cross
sectional shapes for A = 5. These are full widths as observed by dye studies.
Half widths in the X and Y directions are given in Table 1. This same phenom-
enon was observed by Sforza, et^ al_. [9] for rectangular slot jets of air.
They divided the flow into three regions as follows: 1) The potential core
or development zone where ambient mixing had not penetrated into the center
of the jet. 2) The characteristic decay region where major and minor axes of
the plume depended on discharge conditions but spreading in the minor axis
direction was faster than in the major axis direction. Velocity profiles in
the plane of the minor axis are similar; in the planes of the major axis they
are non-similar. 3) Axisymmetric decay region where the plume behaves as one
axisymmetric plume. These same regions were observed in this study.
15
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Z/D « 30
I I
I I I I
Figure 9.
0 2 4 6 8 10
X/D - DISTANCE
Variation in plume shape for multiple port discharge at various
downstream distances, F = 6
19
-------
Since the widths of the multiple port plumes within the characteristic
decay region are different in the X and Y directions, it is not correct to
express the entrainment in terms of either one alone. In addition since the
profiles in the plane of the major axis are not similar, it is probably not
correct to express the entrainment in the classic manner at all. As a result
this was not done.
The decay in maximum salt concentration S /S along the plume center!ine
is of interest since this represents the decay of excess temperature in a
thermal plume. Figure 10 is a plot of centerline concentration ratio versus
distance for the multiple port discharges. Again the effect of aspect ratio
is evident with a more rapid decrease in concentration as the number of ports
is decreased.
20
-------
o
CO
X
O
CO
I
o
h-
CO
UJ
QC
UJ
I-
LU
O
10 20 40 60 80
VERTICAL DISTANCE - Z/D
Figure 10. Center!ine salinity concentration versus distance for multiple
port discharge, F = 6
21
-------
REFERENCES
1. Hirst, E. A., "Analysis of Round Turbulent, Buoyant Jets Discharged to
Flowing Stratified Ambients," Oak Ridge National Laboratory No. ORNL-
4685, 1971.
2. Baumgartner, D. J. and D. S. Trent, "Ocean Outfall Design Part I:
Literature Review and Theoretical Development," U.S. Dept. of Interior,
Federal Water Quality Administration, 1970.
3. Briggs, G. A., "Plume Rise," AEC Critical Review Series Report, No. TID-
25075, 1969.
4. Silberman, E. and H. Stefan, "Physical (Hydraulic) Modeling of Heat
Dispersion in Large Lakes, a Review of the State of the Art," University
of Minn., St. Anthony Falls Hydraulic Lab., Project Report No. 115,
1970.
5. Schmidt, W., "Turbulente Ausbreitung eines Stromes erhitzter Luft,"
Zeitschr, Angew. Math, und Mech., Volume 21, 1941.
6. Rouse, H., C. S. Yih, and H. W. Humphreys, "Gravitational Convection
from a Boundary Source," Tell us, Volume 4, 1952.
7. Jirka, G and D. R. F. Harleman, "The Mechanics of Submerged Multiport
Diffusers for Buoyant Discharges in Shallow Water," MIT Ralph M. Parsons
Laboratory for Water Resources and Hydrodynamics, Report No. 169, 1974.
8. Kannberg, L. D. and L. R. Davis, "An Experimental/Analytical Investiga-
tion of Deep Submerged Multiple Buoyant Jets," EPA-600/3-76-101, U.S.
Environmental Protection Agency, Corvallis, Oregon, Sept. 1976.
9. Sforza, P. M., M. H. Steiger, and N. Trentacoste, "Studies on Three-
Dimensional Viscous Jets," AIAA Journal, Vol. 4, No. 5, May 1966.
10. Kotsovinos, N. E., "A Study of the Entrainment and Turbulence in a Plane
Buoyant Jet," W. M. Keck Laboratory, California Institute of Technology,
Report No. KH-R-32, August 1975.
11. Keeler, R. M., "Mixing and Chemical Reaction to Turbulent Flow Reactors,"
California University, Livermore, Report No. UCRL-7852, June 1964.
12. McQuivey, R. S., T. N. Keefer, and M. A. Shirazi, "Basic Data Report on
the Turbulent Spread of Heat and Matter," U.S. Department of Interior,
Geological Survey and the U.S. Environmental Protection Agency, Open
file Report, Fort Collins, Colorado, August 1971.
22
-------
13. Albertson, M. L., Y. B. Dai, R. A. Jensen, and H. Rouse, "Diffusion of
Submerged Jets," ASCE Transactions, 115, No. 150, 1950.
14. Becker, H. A., H. C. Hottel, and G. C. Williams, "The Nozzle-Fluid
Concentration Field of the Round, Turbulent, Free Jet," Journal of Fluid
Mechanics. 32(2),231-252, 1967.
15. Ricou, F. P. and D. B. Spalding, "Measurements of Entrainment by Axisym-
metrical Turbulent Jets," Journal of Fluid Mechanics, 11(1), 21-32,
August 1961.
16. Morton, B. R., A. G. Taylor, and J. S. Turner, "Turbulent Gravitational
Convection from Maintained and Instantaneous Sources," Proceedings of the
Royal Society of London. Vol. A234, 1-23, 1956.
17. Fan, L-N., "Turbulent Buoyant Jets into Stratified or Flowing Ambient
Fluids," W. M. Keck Laboratory, California Institute of Technology,
Report No. KH-R-15, June 1967.
18. Abraham, R., "Entrainment Principle and its Restrictions to Solve Prob-
lems of Jets," Journal of Hydraulic Research, 3(2),1-23, 1965.
19. Fox, D. G., "Forced Plume in a Stratified Fluid," Journal of Geophys.
Res., 75(33),6818-6835, 1970.
23
-------
TEST
FO
APPENDIX
TABLE A-l MEASURED DATA
Z/D
X/D
Y/D U/UO
S/SO
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999,00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
18 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
17 999.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1*00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
40.00
40.00
40.00
40.00
40.00
40.00
40.00
.09
.09
.09
5.00
5.00
5.00
5.00
5.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
10.00
0
.42
.83
1.25
1.67
2.50
3.33
0
.83
1.67
2.50
3.33
4.17
5.00
5.83
0
.83
1.67
2.50
3.33
4.17
5.00
5.83
0
1.67
3.33
5.00
6.67
8.33
10.00
0
.43
.49
0
.43
.86
1.29
1.72
0
.43
.86
1.29
1.72
2.15
2.58
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.56
.43
.35
.20
.11
.03
.02
.37
.29
.17
.08
.03
.01
.01
.01
.24
.23
.18
.12
.09
.05
.03
.02
.17
.14
.08
.04
.01
.01
.00
1.30
1.27
.12
.81
.59
.37
.11
.02
.65
.59
.33
.17
.10
.04
.02
.52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(Continued)
24
-------
TABLE A-l (continued)
TEST
FO
Z/D
X/0
Y/0
U/UO S/SO
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
16
16
16
16
16
11
11
11
11
11
11
9
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
999.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
36.00
8.30
8.30
8.30
8.30
8.30
8.30
8.30
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
l.UO
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
10*00
10.00
10.00
10.00
10.00
10.00
15.00
15.00
15.00
15,00
15.00
15.00
15.00
15.00
15.00
15.00
25.00
25.00
25.00
25.00
25.00
25.00
25,00
25.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
37.00
20.00
20.00
20.00
20.00
20.00
20.00
10.00
.43
.86
1.29
1.72
2.15
2.58
0
.43
.86
1.29
1.72
2.15
2.58
3.00
3.43
4.29
0
.86
1.72
2.59
3.45
4.31
5.17
6.03
0
.86
1.72
2.59
3.45
4.31
5.17
6.03
6.90
7.76
0
1.72
3.45
5.17
6.90
0
.86
1.72
2.58
3.43
4.29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.46
.34
.25
.12
.05
.01
.34
.29
.29
.23
.15
.15
.09
.03
.03
.01
.29
.28
.15
.12
.09
.05
.02
.02
.22
.19
.16
.11
.11
.08
.07
.03
.03
.02
.20
.17
.13
.09
.03
.39
.37
.24
.18
.09
.07
.64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.15
.15
.09
.09
.08
.06
.06
.05
.11
.09
.08
.05
.05
.06
.05
.05
.05
.06
.08
.08
.07
.04
.01
.18
.17
.11
.08
.03
0
.33
(continued)
25
-------
TABLE A-l (continued)
TEST FO A Z/0 X/0 Y/D U/UO S/SO
9
9
9
9
9
9
10
10
10
10
10
10
10
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
8.30
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
2.20
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
10.00
10.00
10.00
10.00
10.00
10.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
.09
.09
.09
1.00
1.00
1.00
1.00
1.00
3.00
3.00
3.00
3.00
3.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
.43
.86
1.29
1.72
2.15
2.58
0
.43
.86
1.29
1.72
2.15
2.58
0
.26
.52
0
.26
.52
.79
1.05
0
.39
.79
1.18
1.58
0
.52
1.05
1.58
2.10
0
.37
.74
l.U
1.45
1.85
2.22
2.95
0
.74
1.48
2.22
2.96
3.70
4.40
6.67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.60
.41
.27
.16
.09
.06
1.29
1.05
.35
.13
.07
.06
.05
1.66
1.76
.45
1.72
1.58
.82
.23
.14
1.27
.96
.42
.22
.07
.65
.60
.44
.25
.14
.84
.69
.67
.53
.32
.29
.12
.05
.69
.54
.28
.19
.17
.08
.08
.06
.30
.24
.17
.13
.11
.09
.56
.48
.19
.08
.02
.01
.01
.91
.80
.20
.64
.55
.42
.13
.07
.47
.42
.17
.14
.12
.22
.21
.17
.14
.12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
26
-------
TABLE A-l (continued)
TEST FO A Z/0 X/0 Y/0 U/UO S/SO
I
I
I
I
1
1
1
1
1
2
a
a
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
20
20
20
20
20
20
20
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
3.10
.50
.50
.50
.50
.50
.50
.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1.50
6.00
6.00
6.00
6.00
6.00
6.00
6.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
25.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
0
.74
1.48
2.22
2.96
3.70
4.40
5.19
5.93
0
.37
.74
1.11
1.85
2.59
3.33
0
.74
1.48
2.22
2.96
3.70
4.44
5.19
0
.74
1.48
2.22
2.96
3.70
4.40
5.19
0
.70
1.48
2.22
2.96
4.40
5.93
0
,52
1.05
1.57
2.10
2.62
3.15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.54
.54
.52
.45
.40
.33
.21
.09
.05
1.08
1.03
.61
.62
.19
.09
.08
1.04
.99
.73
.55
.32
.14
.10
.09
1.04
.95
.85
.57
.36
.19
.12
.09
.95
.90
.85
.80
.70
.38
.13
.58
.03
.56
.45
.22
0
.07
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.26
.25
.19
.10
.05
0
.00
(continued)
27
-------
TABLE A-l (continued)
TEST
FO
Z/D
X/0
Y/D u/uo s/so
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6*00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
21.00
21.00
21.00
21.00
21.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
0
.52
1.05
1.57
2.10
2.62
3.15
0
.52
1.05
1.57
2.10
2.62
3.15
0
.52
1.05
1.57
2.10
2.62
3.15
0
.52
1.05
1.57
2.10
0
0
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
.58
.53
.47
0
.17
0
.07
.47
.41
.30
0
.14
0
.02
.32
0
.26
0
.08
0
0
.18
0
.11
0
0
.03
.03
.39
.27
.14
.08
.01
.39
.41
.38
.24
.15
.05
.01
.24
.22
.18
.15
.05
0
.17
.16
.12
0
.06
0
0
.13
.12
.00
0
.04
0
0
.07
0
.05
0
.01
0
0
.03
0
.01
0
0
.00
.17
.10
.06
.03
.02
.00
.13
.12
.09
.04
.02
.01
.00
.06
.05
.04
.03
.01
0
(continued)
28
-------
TABLE A-l (continued)
TEST
FO
Z/D
X/0
Y/0 U/UO S/SO
21
21
21
21
21
21
21
21
21
21
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
23
23
23
23
23
23
23
23
23
23
23
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
6.30
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
0
5.25
6.30
0
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
0
1.05
2.10
0
0
1.05
2.10
3.15
4.20
5,25
6.30
7.34
0
1.05
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
3.15
4.20
4.20
0
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
4.20
4.20
4,20
4.20
5.25
5.25
5.25
6.30
0
0
0
0
0
0
0
0
1.05
1.05
1.05
0
.12
.08
.06
.03
0
0
0
.04
.02
.49
.08
.05
.38
0
.28
.24
.19
.15
.08
.01
.22
.21
.20
.13
.10
.02
.20
.18
.11
.02
.07
.06
.01
.02
.67
.67
.65
.51
.24
.11
.07
.04
.65
.65
.60
0
.05
.03
.02
.01
0
0
0
.02
.01
.11
.01
.01
.03
0
.05
.03
.02
.01
.01
0
.03
.03
.03
.02
.02
.00
.02
.02
.02
.01
.01
.01
0
.00
.21
.19
.11
.12
.06
.03
.01
.01
.21
.21
.17
(continued)
29
-------
TABLE A-l (continued)
TEST
FO
Z/0
X/D
Y/D U/UO S/SO
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
25
25
25
25
25
25
25
25
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
3.15
4.20
5.25
6.30
7.34
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
0
0
1,05
2.10
3.15
4.20
0
1.05
2.10
3.15
4.20
0
1.05
2.10
3.15
4.20
0
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
4.20
4.20
4.20
4.20
5.25
0
0
0
0
0
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
3,15
0
0
0
0
0
0
0
1.05
.38
.22
.10
.06
.03
.58
.55
.39
.21
.06
.01
.38
.03
.26
.22
.07
.05
.10
.11
.09
.05
.02
.60
.60
.60
.38
.05
.36
.36
.36
.24
.04
.07
.07
.07
.02
0
.02
.45
.43
.33
.25
.16
.09
.01
.45
.12
.06
.02
.01
.00
.21
.20
.15
.09
.02
.00
.09
.09
.08
.04
.01
.00
.06
.04
.03
.01
.00
.30
.32
.28
.14
.02
.28
.28
.25
.17
.02
.06
.08
.06
.03
.01
.00
.14
.11
.08
.06
.04
.02
.01
.11
(continued)
30
-------
TABLE A-l (continued)
TEST
FO
Z/0
X/0
Y/D U/UO S/SO
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7,00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
0
1.05
2.10
3.15
0
1.05
2.10
0
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
4.20
4.20
4.20
4.20
4.20
5.25
5.25
5.25
5.25
6.30
6.30
6.30
7.34
0
0
0
0
0
0
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
.40
.27
.18
.11
.06
.01
.38
.35
.27
.16
.09
.03
.25
.22
.16
.09
.04
.01
.19
.18
.10
.04
.00
.15
.12
.04
.00
.07
.04
.01
.02
.55
.53
.41
.24
.07
.18
.49
.49
.39
.22
.08
.03
.36
.34
.33
.10
.08
.05
.03
.01
.00
.10
.08
.06
.04
.02
.01
.08
.06
.04
.04
.03
.01
.05
.04
.03
.02
.01
.02
.01
.01
.01
.01
.01
.01
.00
.21
.16
.11
.05
.03
.01
.19
.19
.11
.06
.02
.01
.13
.13
.11
(continued)
31
-------
TABLE A-l (continued)
TEST
FO
Z/0
X/0
Y/D U/UO S/SO
26
26
26
26
26
26
26
26
26
26
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
6.40
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7«00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
3.15
4.20
0
1.05
2.10
3.15
0
1.05
2.10
0
0
1.05
2.10
3.15
0
1.05
2.10
3.15
0
1.05
2.10
3.15
0
1.05
2.10
0
1.05
2.10
3.15
4.20
5.25
6.30
7.34
8.40
0
1.05
2.10
3.15
4.20
5.25
6.30
7.34
8.40
0
1.05
2.10
2.10
2.10
3.15
3.15
3.15
3.15
4.20
4.20
4.20
5.25
0
0
0
0
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
3.15
3.15
3.15
0
0
0
0
0
0
0
0
0
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
.16
.03
.29
.19
.09
.03
.13
.10
.04
.06
.58
.56
.40
.05
.47
.47
.39
.06
.18
.13
.11
.02
.02
.02
.01
.58
.58
.58
.51
.41
.33
.25
.06
.03
.56
.56
.54
.51
.41
.33
.24
.11
.03
.26
.25
.21
.04
.01
.08
.06
.03
.00
.08
.05
.03
.02
.26
.26
.16
.02
.24
.24
.17
.03
.10
.08
.08
.03
.03
.03
.01
.21
.23
.23
.23
.18
.13
.09
.03
.01
.20
.19
.18
.15
.13
.11
.06
.03
.00
.15
.13
.18
(continued)
32
-------
TABLE A-l (continued)
TEST
FO
Z/D
X/D
Y/0 U/UO
S/SO
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
5.10
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
3.15
4.20
5.25
6.30
7.34
8.40
0
1.05
2,10
3.15
4.20
5.25
6.30
0
1.05
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
5.25
0
1.05
2.10
3.15
4.20
2.10
2.10
2.10
2.10
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
3.15
4.20
4.20
0
0
0
0
0
0
0
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
3,15
3,15
3,15
3,15
3,15
3.15
4,20
4,20
4.20
4,20
4,20
.16
.11
.11
.06
.04
.01
.21
.10
.12
.12
.07
.06
.03
.05
.05
.71
.01
.63
.46
.29
.20
.04
.63
.63
.58
.41
.26
.17
.04
.51
.45
.42
.33
.18
.07
.43
.39
.36
.29
.16
.06
.36
.36
.30
.26
.16
.18
.08
.08
.05
.03
.02
.08
.08
.06
.06
.06
.03
.01
.03
.02
.13
.13
.13
.08
.05
.03
.01
.13
.12
.12
.08
.04
.03
.00
.12
.12
.09
.07
.04
.01
.10
.09
.08
.05
.03
.01
.08
.07
.06
.04
.03
(continued)
33
-------
TABLE A-l (continued)
TEST
FO
Z/D
X/D
Y/0 U/UO S/SO
29
29
29
29
29
29
29
30
30
30
30
30
30
30
30
30
30
31
31
31
31
31
31
31
31
31
32
32
32
32
32
32
32
32
33
33
33
33
33
33
33
33
33
33
33
33
5.10
5.10
5.10
5.10
5.10
5.10
5.10
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
30.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
5.25
0
1.05
2.10
3.15
4.20
0
0
0
1.05
2.10
4.20
6.30
10.49
7.34
5.25
3.15
0
1.05
2.10
3.15
4.20
5.25
6.30
-1.05
8.40
-0.52
0
.52
1.05
1.57
2.10
3.15
2.62
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
4.20
5.25
5.25
5.25
5.25
5.25
6.30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.52
.52
.52
.52
.52
.05
.15
.14
.14
.11
.04
.04
.37
0
.39
.34
.30
.24
.04
.06
.15
.32
.51
.48
.32
.20
.11
.08
.05
0
0
.61
.71
.61
.36
.22
.12
.08
0
.62
.62
.62
.55
.42
.13
.02
.55
.55
.54
.51
.42
0
.05
.04
.03
.02
0
0
.12
0
.12
.10
.06
0
0
.03
.04
.10
.16
.15
.13
.08
.02
.01
0
0
0
0
.34
.31
.20
.13
.06
0
.01
.34
.34
.34
,32
.19
.09
.01
.30
.34
.34
.34
.21
(continued)
34
-------
TABLE A-l (continued)
TEST FO A Z/0 X/D Y/D U/UO S/SO
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
34
34
34
34
34
34
34
35
35
35
35
35
35
35
36
36
36
36
36
36
36
37
37
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
6.00
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
3.50
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
15.00
15.00
15.00
15.00
15.00
15.00
15.00
20.00
20.00
5.35
6.30
0
1.05
a. 10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
6.30
0
1.05
2.10
3.15
4.20
5.25
0
0
.52
1.05
1.57
2.10
2.62
3.15
0
.37
.75
1,12
1.49
2.24
2.99
.19
.56
.93
1.31
1.68
2.05
2.80
0
.37
.52
.52
1.05
1.05
1.05
1.05
1.05
1.05
1.05
2.10
2.10
2.10
2.10
2.10
2.10
2.10
3.15
3.15
3.15
3.15
3.15
3.15
4.20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.13
.01
.45
.45
.45
.45
.44
.17
.02
.14
.11
.10
.12
.10
.04
.04
.05
.02
.02
.02
.02
.01
.03
.60
.51
.34
.16
.11
.04
.01
.63
.61
.46
.33
.24
.10
.02
.48
.48
.43
.34
.30
.20
.04
.52
.51
.06
.01
.32
.32
.34
.29
.21
.11
.01
.13
.13
.13
.13
.11
.05
.03
.60
.40
.20
.10
.10
.01
.01
.17
.13
.12
.08
.06
.04
.03
.22
.20
.15
.10
.10
.02
.00
.15
.14
.12
.10
.07
.04
.02
.11
.10
(continued)
35
-------
4. TITLE AND SUBTITLE
"EXPERIMENTAL SIMULATION OF SINGLE AND MULTIPLE CELL
COOLING TOWER PLUMES"
7. AUTHOR(S)
Lorin R. Davis, Mostafa A. Shirazi, and
David L. Slegel
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO
EPA-600/7-77-070
3. RECIPIENT'S ACCESSION>NO.
5. REPORT DATE
July 1977
6. PERFORMING ORGANIZATION CODE.
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Corvallis Environmental Research Laboratory
Office of Research & Development
U.S. Environmental Protection Agency
200 S.W. 35th Street — Corvallis, OR 97330
10. PROGRAM ELEMENT NO.
EHE675A (AP#)
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Final Inhouse 7/75-12/76
SAME
14. SPONSORING AGENCY CODE
EPA/600/02
15. SUPPLEMENTARY NOTES
16. ABSTRACT
An Experimental investigation was conducted to determine the dilution characteristics
of single and multiple port buoyant discharges typical of modern natural and mechani-
cal draft cooling towers. Simultaneous measurements of velocity and tracer concentra
tion profiles were taken at various downstream locations in the three-dimensional
plumes discharged into a stagnant ambient using a hot film anemometer and conduct-
ivity probe. The number of discharge ports was varied from one to seven. Discharge
densimetric Froude numbers were varied from 1.5 to infinity. Numerical integration
of the profiles gave dilution, tracer conservation, and momentum fluxes. The effect
of reducing Froude number was to increase entrainment considerably. In multiple
port discharges the shape of the plume changed from an elongated configuration
to nearly exisymmetric within the first 20-30 diameters of discharge.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Cooling Towers, Plumes, Air Pollution,
Dilution, Dissipation
b.IDENTIFIERS/OPEN ENDED TERMS
Multiple cell
COSATI Field/Group
13-B
13. DISTRIBUTION STATEMENT
Unlimited Distribution
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
44
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
36
•k u 9 GOVERNMENT PRINTING OFFICE 1977—798-276/173 REGION 10
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