EPA-660/2-73-001
January 1973
Environmental Protection Technology Series
PLUME TEMPERATURE MEASUREMENTS
OF SHALLOW, SUBMERGED MODEL
DISCHARGES WITH CURRENT
No.2
National Environmental Research Center
Office of Research and Development
US. Environmental Protection Agency
Cof»allis. Oregon 97338
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development,
U.S. Environmental Protection Agency, have been grouped into
five series. These five broad categories were established to
facilitate further development and application of environmental
technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface
in related fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL PROTECTION
TECHNOLOGY series. This series describes research performed
to develop and demonstrate instrumentation, equipment and
methodology to repair or prevent environmental degradation from
point and non-point sources of pollution. This work provides
the new or improved technology required for the control and
treatment of pollution sources to meet environmental quality
standards.
EPA REVIEW NOTICE
This report has been reviewed by the Office of Research and
Development, U.S. Environmental Protection Agency, and approved
for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the U.S. Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
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EPA-660/2-73-001
January 1973
PLUME TEMPERATURE MEASUREMENTS OF SHALLOW, SUBMERGED MODEL
DISCHARGES WITH CURRENT
By
Lawrence Winiarski
James Chasse
National Thermal Pollution Research Program
Pacific Northwest Environmental Research Laboratory
National Environmental Research Center
Corvallis, Oregon
Program Element 1B1032
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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ABSTRACT
Laboratory studies were conducted with a shallow-submerged thermal
discharge model in a flowing ambient stream. Plume behavior,
characterized by excess temperature, trajectory, and width, was
observed to determine the qualitative effects of the discharge angle,
Froude number, relative stream velocity, and turbulence in the ambient
water.
Increasing the angle of discharge in a vertical plane parallel to
the direction of stream flow, caused increased dilution and lower
temperatures along the trajectory. Jets of higher Froude number
diluted less than those of lower Froude number for the same discharge
angle and relative stream velocity. With no turbulence in the ambient
stream, dilution was increased by a reduction in the ambient stream
velocity. However, in a turbulent stream, dilution was decreased by
a reduction in the ambient velocity.
iii
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CONTENTS
Section
I Conclusions ^
II Recommendations 3
III Introduction 5
IV Experimental Methods 9
V Results 15
VI Reference "
VII Appendix 49
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FIGURES
Page
1 Experimental apparatus. 1°
2 Typical temperature traverses: 8=15°, F=12, k=2 12
3 Water velocity behind the towed grid as a function 14
of carriage speed.
4 Temperature decay chart: no turbulence, F=12, k=2 17
5 Temperature decay chart: no turbulence, F=37, k=2. 18
6 Temperature decay chart: no turbulence, F=12, k=6. 19
7 Temperature decay chart: no turbulence, F=37, k=6. 20
8 Temperature decay chart: with turbulence, F=12, 21
k=2.7.
9 Temperature decay chart: with turbulence, F=37, k=3. 22
10 Temperature decay chart: with turbulence, F=12, k=7. 23
11 Temperature decay chart: with turbulence, F=37, k=8. 24
12 Trajectory-temperature chart; no turbulence F-12, K=2. 25
13 Trajectory-temperature chart: no turbulence F=37, k=2. 26
14 Trajectory-temperature chart no turbulence F=12, k=6. 27
15 Trajectory-temperature chart: no turbulence F=37, k=6. 28
16 Plume trajectory, with turbulence: F=12, k=2.7. 29
17 Plume trajectory, with turbulence: F=37, k=3. 30
18 Plume trajectory, with turbulence: F=12, k=7. 31
19 Plume trajectory, with turbulence: F=37, k=8. 32
20 Plume trajectory, normal configuration, no turbulence. 33
VI
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Page
21 Plume trajectory, normal configuration, with 34
turbulence.
22 Effect of discharge angle on plume spread: F=12, 36
k=2.
23 Effect of discharge angle on plume spread: F=12, 37
k=6.
24 Temperature decay chart: 0=45°, no turbulence. 38
25 Temperature decay chart: 0=45°, with turbulence. 39
26 Effect of ambient velocity on plume spread: 0=15°, 42
F=37.
27 Effect of ambient velocity on plume spread: 0=45°, 43
F=37.
2&. Effect of turbulence on temperature-velocity 45
relationship: 0=45°, F=37.
29 Effect of turbulence on temperature-velocity 46
relationship: 0=45°, F=37.
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TABLE
1 Matrix of experimental parameters.
viii
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SECTION I
CONCLUSIONS
1. For the range of experimental variables in the reported program,
jet dilution was increased (i.e. centerline excess temperature ratio
decreased) as the discharge angle was increased with respect to the
horizontal (coflow) configuration. For the horizontal discharge
perpendicular to the ambient current (normal), plume temperatures
at a given downstream location were usually between those of the
vertical (90°) and the 15° discharges of the same Froude number (F)
and the same ratio of jet velocity to stream velocity (k).
2. For jets of the same discharge angle and velocity ratio (k),
decreasing the Froude number caused centerline excess temperature
ratio to decrease more rapidly with respect to distance. Decreasing
the Froude number also caused more rapid plume rise with respect to
distance.
3. With the exception of the normal discharge, decreasing the ambient
velocity in a non-turbulent field promoted dilution of jets with the
same Froude number and discharge angle. Decreased ambient velocity
also resulted in more rapid plume rise.
4. In general, turbulence in the ambient stream caused a reversal
of the relationship between ambient velocity and temperature. With
turbulence, decreasing the ambient velocity resulted in less dilution.
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SECTION II
RECOMMENDATIONS
1. In order to promote the most rapid mixing, it is recommended that
effluent nozzles discharge at large angles relative to the river bottom
and the direction of stream flow.
2. In as much as the largest temperature drop occurs in the immediate
vicinity of the nozzle and this temperature drop is greater when there
is large angular deviation between the nozzle and the stream, it is
recommended that more study be devoted to understanding and predicting
the initial mixing in this region.
3. This program was limited to laboratory models and a narrow range
of parameters. Where possible these results need to be compared with
other laboratory studies and field data.
4. In order to show a more significant effect of turbulence, it is
recommended that turbulence be generated on a scale large enough to
actually fluctuate the plume trajectory.
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SECTION III
INTRODUCTION
One of the primary means of waste heat disposal available to the
electric power generating industry and other industries is the direct
discharge of heated cooling water to the aquatic environment. Although
such disposal schemes may be economical from the standpoint of capital
costs and operating expenses, once-through cooling may create a
thermal pollution problem in the receiving water body. This potential
problem can be minimized through proper design of the effluent outfall
and diffuser so that the heated water is adequately mixed and diluted
with the ambient water. Details affecting this design are the depth
of the receiving water body and the location of the discharge port
relative to the water surface and/or bottom.
With respect to these factors, diffuser design and evaluation has been
categorized as either submerged or surface. In the former, the diffuser
is located at a depth where the effects of boundary conditions are assumed
negligible or nonexistent. With the latter, the diffuser is located at
the water surface and produces a layer of relatively high temperature
water above the colder unmixed water. Shirazi and Davis (1972) have
evaluated and combined predictive models for the analysis of submerged
diffusers. Their work is presented in the form of nomograms that
provide estimates of the physical spread and temperature distribution
of a discharge plume. Work of a similar nature is being advanced with
respect to surface discharges.
There is, however, an intermediate situation, that of a shallow submerged
diffuser, wherein the discharge port is located on or near the bottom
of a shallow water body. Located as such, the plume temperature and
-------
trajectory may be influenced by the bottom, the water surface, or a
combination of those two boundaries. The condition of shallow submergence
has numerous examples where a diffuser pipe is located on a river bottom.
Because of the uncertainty of predictive methods and scarcity of experi-
mental data relative to the shallow submergence situation, predesign
analyses and diffuser performance estimates are limited. This study
was undertaken to provide information on the behavior of shallow
submerged jets. The data in this report can be used for the purpose
of verifying analytical models as they are developed. A future laboratory
study dealing with deeply submerged discharges will compare laboratory
data with existing analytical models.
Plume behavior is usually characterized in terms of its trajectory,
width, and temperature distribution along the trajectory. In this
report trajectories are plotted with respect to vertical and horizontal
coordinates, made dimensionless by dividing by the discharge nozzle
diameter. Plume widths along the trajectory are made dimensionless in
a similar manner. Temperatures along the trajectory are expressed as the
ratio of the excess temperature at a point.to the excess discharge
temperature. The temperature excess is with respect to the temperature
of the ambient water body.
The primary objective of the study was to determine qualitatively how
the plume characteristics of temperature, trajectory, and width are
affected by the different parameters which influence these characteristics,
These parameters include:
1. the angle of discharge with respect to the ambient current;
2. the ratio (k) of the jet velocity (U,) to the ambient velocity
(Ua);
3. the turbulence level of the receiving stream; and
4. the Froude number (F).
-------
.."j
The Froude number is defined as F = yftp where D is the nozzle
o^ gD
diameter, ° is the normalized excess density, and g is the
po
gravitational constant. Other factors to be considered include:
5. the depth of the water body and
6. the existence of any temperature (density) gradient.
To study the above relationships, experimental parameters were chosen
to facilitate measurement and duplication in the laboratory. In all
cases, the ambient water body was isothermal and ten diameters in depth
and the discharge port was located on the bottom. Two jet/ambient
velocity ratios (k) were selected: k=2 and k=6. Similarly, two Froude
numbers were evaluated: F=12 and F=37. The two jet velocities of one (1)
and three (3) feet per second provided Reynolds numbers greater than 5,000.
Four different discharge angles to the direction of flow were studied.
Measured from the horizontal, these are 0° (coflow), 15°, 45°, and 90°
(vertical). Additionally, a horizontal discharge normal to the direction of
the ambient current was studied. With respect to turbulence, plume behavior
was examined under two conditions: in the absence of any turbulence and in
the presence of an artificially generated turbulence. Combinations of the
previously described parameters provide a total of forty different test
conditions (see Table 1) from which qualitative conclusions are drawn.
The conditions in the laboratory do not necessarily represent any field
situation. However, they do represent typical parameters that might be
encountered in the field. These conditions were selected so that trends
predicted by analytical models could be checked against laboratory conditions,
One should be cautioned about using the reported data as design criteria
inasmuch as several important conditions which might occur in the field
have been omitted from these experiments. For example, near a field
installation, natural barriers may serve to limit the amount of ambient
water available for dilution. The resulting recirculation would be difficult
to quantify. Also, the single port nozzle configurations studied here do
not represent best available techniques for maximizing the amount of heated
water that can be discharged.
-------
TABLE 1. Matrix of Experimental Parameters
1
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Fig. Nos.
4
12
6
14
5
13
7
15
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8
16
10
18
9
17
11
19
15°
4
12
6
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5
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7
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8
16
10
18
9
17
n
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45°
4
12
6
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5
13
7
15
8
16
10
18
9
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90°
4
12
6
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5
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7
15
8
16
10
18
9
17
11
19
Normal
4-
20
6
20
5
20
7
20
8
21
10
21
9
21
11
21
8
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SECTION IV
EXPERIMENTAL METHODS
Experiments reported herein were conducted in a towing channel forty
(40) feet long and two (2) feet wide. The discharge nozzle and a
simulated river bottom were suspended from a carriage mounted on rails
along the top of the channel (see Figure 1). The nozzle and attached
bottom were towed through the water to obtain the desired relative
velocity. The diffuser orifice was one-half inch in diameter. Heated
effluent was discharged from a constant head tank which was also
mounted on a carriage. This reservoir was periodically refilled with
hot water from a constant temperature bath. Discharge velocities were
controlled by valves at the effluent reservoir.
A third carriage supported the temperature transducer and cable.
Transversing vertically through the discharge plume, the transducer
monitored temperature profiles at predetermined distances downstream
from the nozzle exit. The traversing mechanism was directly linked
to the horizontal movement of the carriage through a simple pulley
arrangement.
Because of its characteristics of fast response and verstility, the
transducer selected was a hot film anemoneter. Signals were processed
through a TSI Model 1050 anemometer and recorded on an XY recorder.
To facilitate data reduction, an intermediate circuit was inserted
between the signal processor and the recorder. This circuit allowed
adjustment of the time response of the anemometer, analogous to
increasing the thermal mass of the transducer, so that temperature
oscillations were effectively averaged.
-------
Cable drum
Constant head
hot water supply tank
O
Bottom support carriage
\
Vertical
Traversing
Carriage rail
Water Surface
Mechanism
Simulated Bottom
Temperature
Sensor
Turbulence
Generating Grid
Flume bottom
FIGURE 1. Experimental Apparatus
-------
Test procedure entailed calibration of the recorder for temperature
and position and adjustment of the discharge valves to attain the
desired effluent flow rate (hence discharge velocity). With an
attached chiller/boiler system, the water in the channel was brought
to approximately 68°F (20°C). The constant head reservoir was then
filled with heated effluent such that the excess temperature at the
orifice would be approximately 30°F (16.7°C). Prior to each series
of test runs the actual exit temperature was monitored with a Hewlett
Packard Model 1801A quartz thermometer. The transducer carriage was
then located at a predetermined distance from the orifice with the
anemometer probe positioned near the simulated bottom. Next the
nozzle was opened and the carriage assembly was towed through the
channel at a uniform velocity. To insure accuracy and eliminate
inconsistencies, the above procedure was repeated three times at
each station downstream from the nozzle. The stations at which the
temperature profiles were recorded were at 10, 20, 30, 40, 60, and
90 nozzles diameters along the horizontal axis. An example of the
data display is provided in Figure 2. For the case illustrated the
discharge angle is 15°, the Froude number is twelve (12), the discharge
velocity to ambient velocity ratio (k) is two (2) and the damping of
the transducer signal is minimal.
Figure 2 also illustrates the effect of ambient turbulence.
To qualitatively determine the effect of turbulence levels in the
receiving stream, turbulence was generated by a removable grid ahead
of the discharge nozzle (see Figure 1). The grid was made of three-
eighths inch (3/8 inch) round bars spaced at one inch on center.
11
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22 TZHFEkATUJtE (ClKTICRXl E)
ro
fRUM KO2ZLE (X/D)
With Turbulence
TEMPEMTURI (CENT 1C BADE )
USTANCt FROM KOZZU (X/L i
FIGURE 2. Typical temperature traverses: 6=15°, F=12, k=2.
-------
So that data collected in this study might properly be interpreted
and compared with other data, an effort was made to quantify the
turbulence generated by the grid at different towing velocities.
For that purpose the anemometer was calibrated and used in the velocity
mode. The turbulent velocity fluctuations behind the moving grid were
then monitored and passed through a TSI Model 1060 RMS voltmeter.
Despite the fact that it was difficult to differentiate between
oscillations introduced by the carriage movement and the true turbulent
fluctuations, some quantitative observations were made. In general,
the carriage oscillations produced an apparent turbulence intensity (i.e.
ratio of the root-mean-square of the velocity fluctuations to the mean
velocity) on the order of six percent (6%). The turbulent intensity
behind the moving grid was on the order of 9 percent at all stations
for the different towing velocities.
An additional problem introduced by the grid, however, was its effect
on mean velocities. By its arrangement, the grid presented a blockage
for flow over the simulated bottom and forced a portion of the water
mass to move beneath the bottom. As a consequence, the relative
velocity of the water body behind the grid differed from that of the
carriage. The velocity correction curve is shown in Figure 3. The
significance of this is that for the same carriage velocity, the
corresponding k ratios for the conditions of "no turbulence and
"turbulence" are different and direct comparisons are difficult.
13
-------
1.50
1.25
1.00
o
o
(O
I
S-
0.75
0.50
0.25
With Grid
Without Grid
0.25 0.50 0.75 1.00 1.25
Ambient Water Velocity (fps)
FIGURE 3. Water Velocity Behind Towed Grid as a Function of
Carriage Speed
14
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SECTION V
RESULTS
Plume behavior is usually characterized in terms of its trajectory,
width, and temperature distribution along the trajectory. In this
report trajectories are plotted with respect to vertical and horizontal
coordinates, made dimensionless by dividing by the discharge nozzle
diameter. The trajectory is delineated by the vertical location of
peak temperatures along the horizontal axis. Vertical plume widths along
the trajectory are made dimehsionless in the same manner. Temperatures
along the trajectory are expressed as the ratio of the excess temperature
at a point to the excess discharge temperature. The temperature excess
is with respect to the temperature of the ambient water body. Algebraically
that is:
ATC Tc - T0
AT0 TJ - T
where TJ is the discharge temperature; T0 is the ambient temperature;
and Tc is the temperature in the plume at point c.
When
ATC
the above mentioned characteristics of temperature (TT ) » vertical
A I o
Z W
trajectory (^-) , and width (jr) are plotted versus the horizontal distance
Y
from the jet (£) , a description of the plume is obtained. Test results
are presented in terms of how these plume characteristics are influenced
by the previously discussed parameters: configuration (0); Froude
number (F); relative velocity ratio (k); and turbulence.
Jet Configuration
The greatest influence on plume characteristics was exerted by the
jet configuration, i.e., the angle of discharge relative to the ambient
15
-------
current. Neglecting temporarily the horizontal discharge perpendicular
to the angle of flow (normal), Figures 4 through 7 show that larger
discharge angles increased the plume dilution. The same result was
obtained in a turbulent stream (see Figures 8 through 11). The normal
configuration, discharging across the flow at zero angle relative to
the bottom, diluted at a rate which was often intermediate between
a high angle (90°) discharge and a lower angle (15° or coflow) discharge
Figures 12 through 15 show the trajectories of the peak temperatures
for the various test conditions without turbulence. Portions of the
temperature decay curves are superimposed on the trajectories. Small
deviations from the coflow configuration have a greater effect on the
trajectory (and plume temperature) than do similar deviations from 90°.
It is suspected that this result is related to the effect of the bottom
which inhibits entrainment of the coflow plume from the underside.
With approximately half of the effective dilution water eliminated,
the plume attaches to the bottom. This results in low trajectories
and high temperatures (Figures 4 to 7). When the discharge angle is
increased slightly from horizontal, entrainment of ambient water is
promoted. The same trend is again apparent in Figures 16 through 19
which are for conditions of a turbulent stream.
The peak temperature trajectories for the normal configuration are
shown in Figures 20 and 21. Generally, the trajectories are low and
flat, although not as low as with the coflow configuration. When the
trajectories are compared with the temperature decay curves, it is
apparent that the normal discharge is not influenced by the bottom.
It is instead swept up and diluted near the source.
16
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FIGURE 5. Temperature Decay Chart: No Turbulence, F=37, k=2,
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Horizontal Distance (X/D)
FIGURE 6. Temperature Decay Chart: No Turbulence, F=12, k=6.
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FIGURE 8. Temperature Decay Chart: With Turbulence, F=12, k=2.7.
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FIGURE 9. Temperature Decay Chart: With Turbulence, F=37, k=3.
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FIGURE 10. Temperature Decay Chart: With Turbulence, F=12, k=7.
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FIGURE 12. Trajectory - Temperature Chart, No Turbulence: F=12, k=2.
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FIGURE 13. Trajectory - Temperature Chart, No Turbulence: F=37, k=2.
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FIGURE 14. Trajectory - Temperature Chart, No Turbulence: F=12, k-6,
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FIGURE 15. Trajectory - Temperature Chart, No Turbulence: F=37, k=6,
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FIGURE 18. Plume Trajectory, With Turbulence: F=12, k=7.
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FIGURE 19. Plume Trajectory, With Turbulence: F=37, k=8.
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FIGURE 20. Plume Trajectory, Normal Configuration, No Turbulence,
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20 30
40 50
60 70
80
90
Horizontal Distance (X/D)
FIGURE 21. Plume Trajectory, Normal Configuration, With Turbulence.
-------
For a given combination of k and F, plume widths were generally as
dependent upon the boundary conditions as the discharge angle. Figure
22 illustrates plumes from two different discharge configurations,
both with a k of 2 and Froude number equal to 12. The plume of the
45° jet is seen to be a bit wider and higher than that of the horizontal
jet which is attached to the bottom. However, when the ambient velocity
is reduced, such that K equals 6, the situation is reversed. Figure 23
shows that the coflow plume, still on the bottom, is wider than that
of the 45° discharge which is a relatively narrow band at the surface.
Froude Number
The effect of the Froude number (F) on jet dilution was more subtle
than the effect of discharge angle. Generally, the test results showed
that the higher Froude number jets diluted less rapidly than those
of a lower Froude number, irrespective of discharge angle. The result
is more pronounced at higher relative velocities (lower k) than at
the lower relative velocities. This is illustrated in Figure 24 for
an angle of 45°. For k equal to 2, the lower Froude number jet has
lower peak temperatures along the trajectory. At a k of 6 however,
there is little difference between the plumes.
The same general relationship held true in conditions of turbulence
although the data does not allow Froude number comparisons with the
same relative velocity (i.e., F = 12, k = 7 is compared with F = 37,
k = 8). Figure 25 illustrates this relationship for a jet angle of
45°. Additional comparisons for the Froude number effect can be made
from the data in Tables A-l through A-5.
35
-------
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D
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10
20
30
40 50 60
Horizontal Distance (X/D)
80
90
10
Z
D 5
20
30
40 50 60 70
Horizontal Distance (X/D)
80
90
FIGURE 22. Effect of Discharge Angle on Plume Spread: F=12, k=2.
-------
CO
10
Z 5
a
20
30
40 50 60
Horizontal Distance (X/D)
70
80 90
20
30
40 50 60
Horizontal Distance (X/D)
70
80
90
FIGURE 23. Effect of Discharge Angle on Plume Spread: F=12, k=6.
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F=37
k=2
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70
80
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Horizontal Distance (X/D)
FIGURE 24. Temperature Decay Chart: 9=45°, No Turbulence.
-------
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F=37
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70
80
90
FIGURE 25. Temperature Decay Chart: 6=45°, With Turbulence.
-------
The peak temperature trajectories also demonstrated a slight Froude
number dependency such that lower Froude number jets had a higher
trajectory. This result may be seen by superimposing Figures 12 and
13, and Figures 14 and 15. The same result in a turbulent field is
apparent in Figures 16 through 19. Froude number comparisons for the
normal discharge angle are directly available from Figures 20 and 21.
Relative Velocity
When considered without turbulence, the velocity ratio had an inverse
relationship to the plume temperature ratio: as k was increased,
ATc
decreased. Again, using 45° as an example, Figure 24 shows
this effect of k. At angles of 0°, 15°, and normal with F equal
to 12, the temperature decay curves nearly overlap and the result
is less apparent.
When turbulence was introduced, the above relationship appeared to
be reversed in several instances. Figure 25 shows the temperature
decay curves in a turbulent stream when the discharge angle is 45°.
It can be seen that with both Froude numbers, higher velocity ratios
are associated with higher plume temperatures. Because of the
limited range of data, it is not known if this apparent reversal
with turbulence is significant. Furthermore, an exception occurs
ATc
at cof low, where for the lower k is equal to or greater than
o
for the higher k. Also, for the normal and 90° discharges, with
F equal to 37, the excess temperature values are very nearly the
same with both k's (refer to Tables A-4 and A-5).
40
-------
A change in relative velocity has a more pronounced effect on trajectory
than it has on the temperature decay. This is apparent from Figures 12
and 14, and Figures 13 and 15. As may be expected, the coflow trajectory
is affected least by changing k.
Evaluating the effect of k on plume widths is complicated by the influence
of the boundary surfaces. For example, Figure 26 shows the plume from
a 15° jet with F equal to 37. With k = 6 (slower ambient velocity)
the plume is much wider than when k = 2. For an angle of 45° (Figure 27)
the vertical spread is restrained and the centerline widths of the two
plumes are nearly equal.
Turbulence
As previously discussed, the effect of turbulence on plume behavior is
difficult to isolate because of the different relative velocities.
To adequately describe the influence of turbulence, plume temperatures
for a given F and k in a non-turbulent medium must be compared with
temperatures obtained in a turbulent field for a jet of the same F
and k. Exact comparison can not be made with the data presented in
this report. Approximations may be derived when a k = 2 is matched
with a k = 3, and k =6 is matched with k = 8 for F = 37. Similarly
for F = 12, k = 2 is compared with k = 2.7 and k = 6 is compared with
k = 7.
When caution is applied with respect to the above limitations, some
generalizations may be made as to the effect of turbulence on this
particular set of data. That is, for a given Froude number, at low k
the temperatures in the non-turbulent stream were higher than those
of the turbulent stream, while at the higher k the situation was reversed.
41
-------
10
20
30
40 50 60
Horizontal Distance (X/D)
70
80
10
20
30
40 50 60
Horizontal Distance {X/D)
70
80
FIGURE 26. Effect of Ambient Velocity on Plume Spread: 6=15°, F=37.
-------
CO
10
10
20
30
40 50 60 70
Horizontal Distance (X/D)
20
30 40 50 60
Horizontal Distance (X/D)
70
80
80
FIGURE 27. Effect of Ambient Velocity on Plume Spread: 0=45°, F-37.
-------
Figures 28 and 29 exemplify this result for an angle of 45° and F of
37. Data in the appendix indicates that in several instances the trend
is less distinct.
In general, turbulence caused a slight spreading of the plume. However,
the same observation is consistent with the decreased ambient -velocity
caused by the grid. A specific example is illustrated in Figure 2.
The plume with turbulence is slightly wider than that without. Never-
theless, the altered trajectory might also be noted.
44
-------
.30
.25
.20
en
QL
01
CU
0
X
.15
.10
k=2 (no turbulence)
k=3 (with turbulence)-^
.05
J L
J 1 1 L
10 20
30 40 50 60
Horizontal Distance (X/D)
70 80 90
FIGURE 28. Effect of Turbulence on Temper 'ure - Velocity Relationship: 0=45, F-37,
-------
T»
.36
o .25
.° .20
+>
re
I'
« .15
-------
SECTION VI
REFERENCE
1. Shirazi, Mostafa A., and Davis, Lorin R., "Workbook of Thermal
Plume Prediction, Volume I, Submerged Discharge," Environmental
Protection Agency, EPA-R2-72-005a, August 1972.
47
-------
SECTION VII
APPENDIX
49
-------
TABLE A-l. Plume Characteristics for Discharge Ang.le of 0£
X/D
Ho Turbulence
F =
k=2
12
M
F =
*=2
37
k=6
With Turbulence
F =
k=2.7
12
k=7
F =
k=3
37
k=8
.
Peak Temperature (AT /AT )
0
0
0
0
0
0
0.47
0.31
0.23
0.18
0.13
0.08
0.50
0.295
0.205
0.16
0.11
0.07
. .. .... _J
0154
0.38
0.29
0.23
0.145
0.115
I
0.54
0.36
0.24
0.175
0.115
0.08
0.45
0.275
0.20
0.155
0.10
0.065
0.49
0.31
0.20
0.15
0.105
0.075
0.53
0.33
0.245
0.185
0.125
0.075
0.54
0.335
0.22
0.16
0.11
0.085
Vertical Trajectory (Z/D)
10
20
30
40
60
90
0.6
0.8
1.0
1.2
1.7
3.0
0.6
0.8
1.0
1.3
2.0
3.5
0.6
0.6
0.6
0.7
0.8
.. 1*0
005
0.6
0.6
0.7
1.0
1.6
0.6
0.6
0.8
1.0
1.7
3.9
0.7
0.9
l.l
1.5
2.5
5.6
i
0.6
0.6
0.6
0.5
0.6
0.9
0.6
0.6
0.6
0.6
0.7
0.9
Plume Width (W/D)
10
20
30
.
40
60
90
2
3
3.5
4
5
5.5
3
4
5
6
8.5
9
2
2.5
2.5
3
3.5
4
2.5
3
3.5
4
4.5
5
2.5
3
3.5
4.5
5
6
3
4
5
7
10
10
2
2.5
3
3.5
4
4
3
3.5
t\ i
!
*'* \
4.5
6
50
-------
TABLE A-2. Plume Characteristics for Discharge Angle of 15'
X/D
No Turbulence
F «
k=2
12
k=6
F = 37
k=2
k=6
With Turbulence
F = 12
k=2.7 k=7
F =
k=3
37
k=8
M* '
Peak Temperature
10
20
30
40
60
90
0.35
0.19
0.14
0.11
0.08
0.065
0.425
0.21
0.155
0.11
0.08
0.06
0.365
0.20
0.155
0.13
0.10
0.08
0.47
0.255
0.16
0.115
0.07
0.06
^ ---!-. -1-1 111 111.^^
0.355
0.16
0.115
0.09
0.065
0.05
0.43
0.22
0.165
0.13
0.09
0.06
0.385
0.20
0.135
0.10
0.075
0.06
0.51
0.255
0.17
0.125
0.09
0.07
Vertical Trajectory (Z/D)
10
20
30
40
60
90
2.5
3.3
3.8
4.0
4.6
5.8
3.5
6.1
8.0
9.2
10.0
10.0
2.5
3.1
3.6
3.9
4.2
4.8
3.1
4.9
6.4
7.2
8.8
10.0
3.2
4.5
5.7
6.6
8.0
9.5
4.0
7.2
9.6
10.0
10.0
10.0
3.0
3.7
4.1
4.2
4.4
4.4
3.8
6.0
8.0
10.0
10.0
10.0
Plume Width (W/D)
10
20
30
40
60
90
3.i
4
4
4.5
5
5
4
5.5
6
6
3.5
3
2.5
3.5
4
4'
4
4
3.5
5.5
8 .
8
8.5
8.5
3.5
5
6
7.5
6
7
4
6.5
5.5
4
3.5
3
3
4
5
5.5
6
6.5
4
6,5
8.5
8
8
7.5
51
-------
TABLE A-3. Plume Characteristics for Discharge Angle of 45C
x/tr
No
F =
k=2
Turbulence
12
k=6
F = 37
fc=2
k=6
With Turbulence
F = 12
k=2.7 k=7
TJI .^
k=3
37
k=8
Peak Temperature-(AT /ATn)
\* U
10
20
30
40
60
90
0.19
0.135
0.10
0.08
0.065
0.05
0.20
0.13
0.09
0.065
0.045
0.035
0.20
0.15
0.12
0.10
0.075
0.06
0.19
0.125
0.095
0.07
0.05
0.035
0.16
0.105
0.08
0.065
0.05
0.04
0.215
0.155
0.115
0.095
0.07
0.065
0.17
0.13
0.10
0.085
0.065
0.05
0.265
0.175
0.125
0.10
0.085
0.05
Verti cal Trajectory (Z/f)
10
20
30
40
60
90
3.0
4.4
5.2
5.5
b.O
7.0
7.9
10.0
10.0
10.0
10.0
10.0
3.2
4.0
4.5
4.9
5.5
. 6.1
6.5
9.5
10.0
10.0
10.0
10.0
4.9
6.0
6.4
6.7
7.5
9.0
9.4
10.0
10.0
10.0
10.0
10.0
4.4
5.6
6.2
6.6
7.3
9.5
9.4
10. 0
10.0
10.0
10.0
10.0
Plume Width (W/D)
10
20
30
40
60
90
3.5
4
4.5
5.5
5.5
6
6
5
4
2.5
2
2
3
3.5
3.5
4
4.5
5
4.5
6
4.5
4.5
4.5
4
4
6
6
6.5
6
5.5
5.5
3.5
2
2.5
3
3
4
5
6
6.5
7
6.5
6
4
3
3
3
3
52
-------
TABLE A-4. Plume Characteristics for Discharge Angle of 90C
UD
No
F =
k=2
Turbulence'"
12
k-6
F = 37
k=2 k=6
With Turbulef^e^
F = 12
k=2.7 k=7
F =
k=3
37
k=8
Peak Temperature .(AT /AT, )
C U
10
20
30
40
60
90
0.14
0.09
0.07
0.06
C.05
0.135
0.06
0.035
0.025
0.015
0.04 ]- 0.01
0.16
0.11
0.08
0.06
0.045
0.04
0.13
0.08
0.055
0.04
0.03
0.02
0.14
0.095
0.07
0.06
0.05
0.04
0.14
0.105
0.09
0.085
0.075
6-07
0.15
0.105
0.08
0.065
0.05
0*04
0.175
0.105
0.075
0.055
0.05
0.045
Vertical Trajectory (Z/D)^
10
20
30
40
60
90
3.4
4.4
5.7
6.2
6.6
7.8
10.0
10.0
10.0
10.0
10.0
10.0
3.5
4.3
4.8
5.1
5.6
.6.3
10.0
10.0
10.0
10.0
10.0
10.0
4.4
6.0
7.1
7.9
9.1
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4.4
5.6
6.4
6.9
7.7
8.2
10.0
10.0
10.0
10.0
10.0
10.0
Plume Width (W/D)
10
20
30
40
60
90
4.5
4.5
5
5.5
6
6
4
3
2
2.5
2
2
4
4.5
5
5
5.5
6
5
4
4
5
4.5
4.5
6
6.5
R
7.5
6
5.5
3
2.5
2.5
2.5
2.5
3
5.5
6
7
7
6.5
6.5
4
3
2.5
3
3.5
3
53
-------
TABLE A-5. Plume Characteristics for Normal Discharge Angle.
X/D-
NXJ Turbulence^
F *= 12
k=2 k=6
F = 37
k=2 1 k=6
With TurtnrFelfeir
F = 12
k=2.7 k=7
F = 37
k=3 k=8
C 0
10
20
30
40
60
90
0.14
0.11
0.09
0.07
0.05
0.14
0.12
0.095
0.075
0.06
0.03 i 0.05
0.225
0.155
0.125
0.105
0.08
0.065
0.155
0.115
0.09
0.075
0.06
0.045
0.13
0.085
0.065
0.045
0.03
0.125
0.10
0.085
0.08
0.07
0.05
0.18
0.135
0.105
0.09
0.065
0.04
0.13
0.11
0.09
0.08
0.06
0.05 S
VWWcrf-Trifceto* W
10
20
30
40
60
90
2,
2.6
2.9
3
3.4
4.6
3
3.7
4.1
4.5
5.2
7.2
1.2
1.7
2
2.2
2.3
. 2.5
3
3.5
3.5
3.5
3.5
4
2.5
3.4
4.3
4.9
5.9
6.5
5
5.7
7
7
7
9
2.3
3.6
4
4.3
5
7
4.4
5
5.1
5.2
5.5
7
Plume Width-(W/D)
10
20
30
40
60
90
3.5
4
4
4
4.5
5
5.5
7.5
9
9.5
9
8
4
4.5
4.5
5
5
5
5
6.5
7.5
8.5
8
8
4.5
5
5.5
6.5
7
7
6
7.5
6.5
8.5
8
7.5
4.5
5.5
6
6.5
6.5
7
6
8
8.5
8.5
9
8
54
------- |