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

-------
                     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.

-------
                                              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

-------
                             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

-------
                             CONTENTS
Section
  I       Conclusions                                         ^
 II       Recommendations                                     3
III       Introduction                                        5
 IV       Experimental Methods                                9
  V       Results                                            15
 VI       Reference                                          "
VII       Appendix                                           49

-------
                            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

-------
                                                                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.

-------
                              TABLE
1          Matrix of experimental  parameters.
                                viii

-------
                             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.

-------
                            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.

-------
                           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
cj
g !
ni *
r— • i
3 !
1 '
0 '
•z.
With Turbulence

e\j
s
r-*
CO
u
u_
CVJ
£
r-
CO
»
u_


cvJ
u
££.
lO
II
.i£
CM
II
.i£
».o
ii
_je
r-
•
00
u
^.
r«.
M
^<:
CO
n
J5£
CO
«
^.
Discharge Angle
0°
Fig. Nos.
4
12
6
14
5
13
7
15
	 ^
8
16
10
18
9
17
11
19
15°
4
12
6
14
5
13
7
15
8
16
10
18
9
17
n
19
45°
4
12
6
14
5
13
7
15
8
16
10
18
9
17
11
19
90°
4
12
6
14
5
13
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

-------
                            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

-------
                                                                                   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

-------
                           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

-------
   .30
    .25
o


o   .20
«r-
+J
(O

-------
00
         .30
         .25
     E  .20
     IB
     fe  -15

     Q.


     0)
    •9   -10
     LU
         .05
90
                     10
20
30
40
50
60
70
80
90
                                              Horizontal Distance  (X/D)


                            FIGURE 5.  Temperature Decay Chart:  No Turbulence,  F=37,   k=2,

-------
                Horizontal Distance (X/D)




FIGURE 6.  Temperature  Decay Chart:  No Turbulence, F=12, k=6.

-------
ro
o
          .30
          .25
     <

     o
     £   .20
en


2
3
+J

J-
01
Q.

0)
     VI
     V)
     
-------
    ,30
•••*
as
CC
t
(O
<"
o_
0)
01
LJL)
    .25
.20
,15
    .10
    .05
                                                                                            Normal
                10
                      20
30       40         50        60
      Horizontal  Distance (X/D)
70
80
90
                      FIGURE 8.  Temperature Decay Chart:  With Turbulence,  F=12, k=2.7.

-------
ro
          .30
          .25
<^
o
to
          .20
      •M
      2   .15
      Q.
      0)
      g   .10
          .05
                          15
                                   90
                      10
                          20
30
40
50
60
70
80
90
                                                 Horizontal  Distance (X/D)
                               FIGURE  9.   Temperature  Decay Chart:   With Turbulence, F=37, k=3.

-------
ro
        .30
        .25
      o
     o

     £  .20
     (O
     0)
        .15
        .10
     x
     Ul
        .05
                    45
                    Normal
                    10
20
30
40
50
60
70
80
90
                                               Horizontal  Distance  (X/D)
                            FIGURE  10.  Temperature  Decay  Chart:   With Turbulence,  F=12,  k=7.

-------
    .30
    .25

-------
en
         10
          8 -
      OJ
      o

      10

      £   6
      to
      o
      0)
                    10
20
30
40
50
60
70
                                                                                                  Oc
80
90
                                               Horizontal  Distance (X/D)
                             FIGURE 12.  Trajectory  - Temperature  Chart,  No Turbulence:   F=12, k=2.

-------
ro



      0)
                      10
                                                 Horizontal  Distance (X/D)
                           FIGURE 13.  Trajectory - Temperature  Chart,  No Turbulence:  F=37, k=2.

-------
        10  •
         8  '   /  —>
ro
      
          2 -
                                                 Horizontal  Distance (X/D)
                          FIGURE 14.  Trajectory  -  Temperature Chart, No Turbulence:  F=12, k-6,

-------
rsi
oo
           10
£1  8


 a

 to
 •M
 CO


 5  6
        0)
ATC/ATQ=.075
                      10        20       30        40       50        60       70        80         90
                                                 Horizontal Distance  (X/D)
                           FIGURE 15.   Trajectory - Temperature Chart, No Turbulence:   F=37,  k=6,

-------
M

-------
u>
o
          10
a


3  8


-------
        10
CO
    M




     O
     c
     10
     cd
     o
         8
                    10
20       30        40       50
60
70       80
90
                                                Horizontal  Distance  (X/D)
                             FIGURE  18.   Plume  Trajectory,  With  Turbulence:   F=12,  k=7.

-------
CO
ro
         10
      a

      M   8
I
to
+J
">    R
5    6
      ItJ
      O
      O)
                90
                     10
                         20
30
40
50
60
70
80
90
                                                Horizontal Distance  (X/D)
                             FIGURE 19.  Plume Trajectory, With Turbulence:   F=37,  k=8.

-------
          10
CO

CO
      a

      M
       8
       c
       01
8
      £   6
       (O
       o
       O)
                                                                                               F=12,  k=6
                                                                                        =12, k=2
                     IU
-*	4ir
                                                          -for
                                                Horizontal Distance  (X/D)
                           FIGURE 20.  Plume Trajectory, Normal Configuration,  No  Turbulence,

-------
          10
CO
           8
       
                     10
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

-------
en
           10
       z
       D
5  -
                       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.

-------
         .30
         .25
CO
00
      o
     °-M
      (XJ
      S-
         .20
         .15
      (V
     LU
         .10
.05
                                                                                         F=12

                                                                                         F=37
                                                                                                    k=2

                                                                                                     k=2
                                                                                                     k=6

                                                                                                     k=6
                     10
                      20
30
50
60
70
80
90
                                                Horizontal  Distance (X/D)
                                FIGURE 24.  Temperature  Decay Chart:   9=45°, No Turbulence.

-------
        ,30
    "b  .25
                                                                              	F=12


                                                                              	  F=37
                          k-7
ID
o
•I—
-M

o:
    frf
    S-
    
        .20
            -   k=8
               k=3
        .15
        .10
        .05
                k=2
                    10
                          20
30       40         50        60


        Horizontal  Distance (X/D)
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

-------