FULL-SCALE STUDY OF PLUME RISE
AT LARGE ELECTRIC GENERATING STATIONS
1968
TENNESSEE VALLEY AUTHORITY
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TENNESSEE VALLEY AUTHORITY
Division of Health and Safety
FULL-SCALE STUDY OF PLUME RISE
AT LARGE ELECTRIC GENERATING STATIONS
Muscle Shoals, Alabama
September 1968
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FULL-SCALE STUDY OF PLUME RISE
AT LARGE ELECTRIC GENERATING STATIONS
SUMMARY
Improved capability for estimating plume rise is needed for more
accurate and confident assessment of diffusion problems.
In 1963 the
Tennessee Valley Authority under sponsorship of the Public Health Service
initiated a comprehensive plume rise study at its generating stations.
Plume rise data were collected at six coal-fired. steam-electric generating
stations.
Unit ratings ranged from 173 to 704 megawatts with stack heights
varying from 76.2 to 182.9 meters.
An instrumented helicopter and special photographic equipment
were used to obtain 1,580 separate plume observations and values of
significant meteorological parameters during stable, neutral. and slightly
unstable conditions.
The 1,580 observations were resolved and consolidated
into 133 composite observation periods covering 30 to 120 minutes.
The data were evaluated in respect to six plume rise formulas in
general use:
Holland; Bosanquet; Davidson-Bryant; Csanady; CONCAWE; and
Lucas, Moore, and Spurr.
The CONCAWE formula showed best agreement with
observations.
Analysis of data indicates that, of all the variable
quantities in the formulas. wind speed and heat emission rate are the
principal determinants of plume rise.
Three of the formulas (Csanady;
CONCAWE; and Lucas, Moore, and Spurr) were modified for optimum agreement
with observations.
The optimized CONCAWE and Csanady formulas are judged
to provide estimates of plume rise which meet practical requirements in
diffusion calculations.
The optimized Csanady formula takes account of the
relatively minor variation of plume rise with stability and is therefore
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preferable for closer accuracy.
However, its use requires information on
meteorological parameters which is often not available.
The more simple
CONCAWE formula which requires information only on heat emission rate and
wind speed may therefore be preferable for general use.
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CONTENTS
Introduction, , . . , ,
II 0 0 e 0 0 .
Early Studies
<:> 'II . 0 . . 0 . 0 0
o . 0 . II
Current Studies
o 0 0 10
I.' . II 0 . e II
~ 0 0:1 0 . . .
III 0 . . .
Basic Workplan
. eo (I . 0 \) 0 . e I III . .
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Appendix A.
Appendix B.
CONTENTS
(con tinued)
Tables
1.
Plant Design and Operational Data. . . . . .
. . . 0
2.
Plume Rise Above Stack Top with Distance from Plant.
3.
Average Plume Rise with Distance from Source by
Stability Classes - Single Stack Operation
15 0 . .
4.
f and t Values - Initial Plume Rise Phase. .
Principal Meteorological Parameters and Haximum Plume
Rise II! 0 0 " e . . 0 . . . 0) . D . . II
. " . . . . .
5.
6.
Observed and Calculated Plume Rise - Single Stack
Operation . . . . . . . . . . . . . . .
Observed and Calculated Plume Rise - Single Stack
Operation . . . . . . . . . . . . . . . . . . . . .
7.
8.
Summary - Calculated and Observed Plume Rise Values by
Wind Speed and Stability Classification. . . . . . . . .
9.
Observed and Calculated Plume Rise - Multistack Operation.
Figures
1.
Instrumentation, Primary Pibal Station
. . . .
2.
Camera with Special Transit Mount. . . . .
. . . . .
3.
Plume Observational Plan by Modified Transit
. . II .
4.
Template on Plume Photograph
" . . II . . " . .
. . " . 0 .
5.
Data from Typical Day of Field Operation, April 1, 1965 -
Paradise Steam Plant. . . . . . . . . . . .
6.
z x
Initial Plume Rise Phase I vs I
. . . . . .
" 0 . "
. . 8 .
7.
Initial Plume Rise Phase ~ vs x
t I..
. . " . .
. . . .
8.
Z xl
End of Initial Plume Rise Phase - - vs -- . .
t t
" . . .
9.
Heat Emission vs Volume Emission
. . . . .
. . . . .
10.
Wind Speed vs Potential Temperature Gradient
. . 0 . . . "
Page
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CONTENTS
(continued)
11.
Average Wind Speed from Stack Top to Plume Top vs
Average Wind Speed at Stack Top. . . . .
. . . .
12.
Observed Plume Rise vs Average Wind Speed at Stack Top. .
13.
Observed Plume Rise vs Average Wind Speed Between Stack
Top and Plume Top. . . . . . . . . . . . .
14.
Relation - Observed and Calculated Plume Rise
15.
Relation - Observed and Calculated Plume Rise
. . II II.
16.
Relation - Observed and Calculated Plume Rise
II . II ..
17.
Relation - Observed and Calculated Plume Rise
o 0 . . . .
18.
Relation - Observed and Calculated Plume Rise
.. .
19.
Relation - Observed and Calculated Plume Rise
20.
Relation - Observed and Calculated Plume Rise
. . . . . .
21.
Relation - Observed and Calculated Plume Rise
22.
Relation - Observed and Calculated Plume Rise
23.
Relation - Calculated Plume Rise from the Original and
Optimized Csanady Formulas.. ..........
24.
Relation - Calculated Plume Rise from the Original and
Optimized CONCAWE Formulas. . . . . . . . . . .. ..
25.
Relation - Calculated Plume Rise from the Original and
Optimized Lucas, Moore, and Spurr Formulas. . . . . . .
26.
Variation of the Value of B with Stack Spacing.
. . . co .
27.
Relation - Observed and Calculated Plume Rise - Csanady
Formula - Mu1tistack . . . . . . . . . . . . . . .
28.
Relation - Observed and Calculated Plume Rise - CONCAWE
Formula - Mu1tistack . . . . . . . . . . . . . . .
29.
Relation - Observed and Calculated Plume Rise - Csanady
Formulas - Single and Mu1tistack . . . . . . . . .
Page
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CONTENTS
(continued)
Appendix C.
Formulas
Holland Plume Rise Formula
. II . e D . . Il1o
" . . II .
D . . C II
Bosanquet~ et al~ Plume Rise Formula - If G > 0 . . .
" . II II .
Bosanquet~ et al~ Plume Rise Formula - If G < 0
. II II Il1o .
Davidson-Bryant Plume Rise Formula
. . . . . . "
. Il1o . .
Csanady Plume Rise Formula
II . . e . . . to
. . II> II
CONCAWE Plume Rise Formula
~ Il1o . II 0
II . . II
. " 0 " II
" " II 0
Lucas~ Moore~ and Spurr Plume Rise Formula
. 0 Il1o II (I . 0
Optimized Lucas~ Moore, and Spurr Plume Rise Formula
. . . . .
Optimized CONCAWE Plume Rise Formula
. . . . . .
. a . . II . .
Optimized Csanady Plume Rise Formula
II II 0 "
Nomenclature.
e 0 0 II 0 . . II .
. . II e
II 0 II .
II . II II
Page
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FULL-SCALE STUDY OF PLDME RISE
AT LARGE ELECTRIC GENERATING STATIONS*
INTRODUCTION
Since the early fifties the Tennessee Valley Authority has had an
increasing interest in studying the rise of hot smoke plumes from its large
power plants in relation to the dispersion of atmospheric efflue~ts.
Studies
have progressively shown the need for more information on plume rise and
related meteorological parameters if satisfactory resolution of plume dis-
persion is to be achieved.
Special studies by TVA as well as by other groups
have provided sufficiently accurate diffusion parameters and coefficients to
describe, in most cases, rates of dispersion for principal meteorological
dispersion models.
However, in order to apply this information to practical
diffusion problems. effective stack heights must be known.
A number of plume
rise formulas derived primarily from data on small stack emissions are in
popular use.
Application of these formulas to increasingly larger emission
sources warrants a closer examination of their conformity with actual experience.
EARLY S TUDI ES
In 1951 TVA initiated plume rise studies by making observations at
the Watts Bar generating station which had four 60-megawatt units served by
two stacks extending 150 feet aboveground or 50 feet above the main building.
Plume rise data were collected by a simple perspex grid device operated on a
planetable at an established observation point.
In the midfifties a special
*Report prepared by S. B. Carpenter, Supervisor, Air Quality Studies
Fred W. Thomas, Chief, Industrial and Air Hygiene Branch; and F. E.
Assistant Director of Health, Tennessee Valley Authority.
Section;
Gartrell,
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peep sight and cross wire were adapted to a standard transit to obtain
greater plume coverage as well as improved accuracy.
This instrument was
used to collect plume rise data at the Johnsonville, Shawnee, and Kingston
stations with generating capacities ranging from 750 to 1,500 megawatts and
stack heights from 170 to 300 feet.
Data from these field observations
were very helpful in extrapolation of plume dispersion from the smaller
stations to the larger new stations.
However, classification of these plume
rise data according to principal diffusion models was not clearly estab-
1ished since the supporting meteorological data were collected from
relatively low tower installations and did not necessarily represent ambient
meteorological conditions at the higher plume elevations.
Improved plume rise information1 was collected during the 5-year
(1957-1962) research project titled "Full-Scale Study of Dispersion of Stack
Gases" conducted by TVA under sponsorship of the Public Health Service.
For the first time in TVA's experience, plume rise data were obtained along
with meteorological parameters, i.e., wind direction and wind speed profiles
and vertical temperature gradient, representative of the plume environment.
This limited information obtained on plume rise was incidental to the
principal study of plume ~ispersion.
CURRENr STUDIES
To meet a growing need for reLiable and comprehensive plume rise
data from large industrial-type stack emissions, TVA, under sponsorship of
PHS, initiated in 1963 a special 3-year research project titled "Full-Scale
Study of Plume Rise at Large Electric Generating Stations."
The study was
particularly timely because experience, techniques, and special equipment
developed in the preceding 5-year dispersion study were directly applicable.
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Also, the variability of available plant sizes. stack heights. and stack
configurations accommodated full-scale assessment of plume rise over a
wide range of conditions.
Valuable assistance and guidance were provided
by R. A. McCormick and Bruce Turner, Air Resources Field Research Office,
National Air Pollution Control Administration. PHS.
Basic Workplan
The objective of this study was to collect, compile, and analyze
data for documentation and definition of plume rise and related meteorological
parameters at a range of generating plants.
Six generating plants were chosen
for the study with unit ratings from 173 to 704 megawatts and stack heights
from 76.2 to 182.9 meters.
The first two years of the study, completed in the spring of 1965,
were devoted primarily to collection of field plume rise and meteorological
data at the six steam plant sites.
Fieldwork was scheduled in seasons of
the year when frequencies of desired meteorological regimes were expected to
be the highest, i.e., high winds and neutral stability in the spring (March-
April) and low winds and stable or inversion conditions in the fall
(September-October).
A third regime, i.e., low winds and unstable condi-
tions, was also documented whenever possible.
Procedural aspects of the
2
study were presented in an interim report at Toronto. Ontario, Canada.
Data Compilations
A comprehensive data collection program was devised.
The three
general categories of data included (1) plant design and operational
factors,
(2) meteorological information, and (3) plume profile, elevation
of plume top and bottom.
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Plant Design and Operational Factors
Principal plant design and operational factors for the six steam
plants are shown in table 1.
Operational data kept at the generating plants
were available for the study.
For each field study period the amount and
analysis of coal burned for each unit and the unit level of operation were
obtained for determination of stack effluent velocity and heat emission
rate.
Precise stack gas temperatures at the stack outlet were also
obtained from a special sampling program developed for the study and carried
out by TVA's Division of Power Production.
Meteorological Information
Wind direction, wind speed, and temperature profile data were
collected routinely.
Wind profile data were obtained at approximate
20-minute intervals by double-theodolite technique using standard Warren-
Knight Model No. 85 theodolites positioned at the ends of 1,000- to 1,500-
foot baselines.
Several baselines were established at each plant site to
ensure good angular separation between simultaneous instrument readings
for a wide range of wind directions.
Standard U. S. Weather Bureau-type,
helium-filled, 10-gram sounding balloons were used throughout the study
and provided a suitable ascension rate, i.e., approximately 500 feet per
minute throughout the 3,000- to 5,000-foot observational layer.
The use
of a balanced balloon also pe~itted single-theodolite operation in the
event the secondary station lost the balloon in flight or experienced
instrument or communication malfunction.
Communication between the two
theodolite stations was by two Cadre Model C-75 all-transistor, 2-way,
battery-operated radios.
A Warren-Knight Model No. 485 timer located at
the primary station (balloon release point) provided the 30-second time
signals.
Theodolite readings were recorded on an AC-operated portable
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Audograph at the primary station and on a DC-operated portable Audograph at
the secondary station.
Figure 1 illustrates instrumentation used at a
primary pibal station.
Vertical temperature profiles were obtained from a Bell Model
47-D-l helicopter equipped with a Cole-Parmer Model 8425 temperature indicator.
Profile runs were made at 45-minute intervals in the immediate plume area
about one mile from the power plant.
Individual readings were taken at
100-foot intervals from surface to about 500 feet above the plume top.
Additional meteorological information, i,e" surface wind direc-
tion, wind speed. and dry-bulb and wet-bulb temperatures, was recorded before
each pibal release at the primary station.
Also, cloud coverage and other
pertinent meteorological or plume observational information was recorded.
General synoptic weather information from U. S. Weather Bureau
radiosonde observations and surface and upper air charts was also compiled
for analysis and evaluation,
Plume Profile
The objective of this phase of data collection was to define the
plume profile for various combinations of generating unit sizes, stack
heights, and meteorological conditions.
Three separate simultaneous field
measurement techniques were used--ground level photography, ground level
modified transit readings, and helicopter observations.
Ground photography
was the principal source of data,
The three replicate plume profile measurement techniques were
designed to provide verification of data and to permit evaluation of the
several measurement techniques,
Photographic Technique--A 4- by 5-inch Super Graphic camera was
mounted on a modified transit head,
The focal points for both the 135-mm
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and telephoto lens were aligned to coincide with the vertical axis of the
tripod mount to provide accurate angular plume coverage.
The assembly is
shown in figure 2.
The camera was located at one of several referenced
sitest usually one to two miles from the power plant where right angular
orientation to the plume path, along with favorable light exposure, could
be maintained.
The l3S-mm lens with a horizontal field of 42 degrees was
used at sites from one to one and one-half miles from the source.
The
telephoto lens with a field of 16 degrees was used when the sites were about
two miles distant,
vfuen the plume was near perpendicular to the camera line
of sight, approximately six-tenths to one mile of the plume segment could be
photographed.
During the first two years of field studYt about ltSOO plume rise
photographs were taken.
Experimentation with various film types, camera
settings, etc., led to adoption at the end of the first year of a standard
photographic procedure consisting of I-second instantaneous and 1.S-minute,
time-exposed infrared photographs taken alternately at S-minute intervals.
Infrared film provided superior plume delineation in most cases and was used
in preference to standard black-and-white or Polaroid film types.
Excellent
quality control was also attained with infrared film.
For all daylight
infrared exposures, an f/32 aperture was used.
The I-second instantaneous
exposures required an infrared Wratten A filter.
The 1.S-minute time
exposure required an infrared Wratten A filter and a I-percent neutral
density filter.
Transit Survey Technique--Plume profile measurements were also
taken simultaneously by a modified transit located a few feet from the
camera.
Figure 3 shows the general plan for plume observation.
Observ~-
tions were made from an established surface location to the top and bottom
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of the plume at 10. 20. 30, 40, and 50 degrees horizontal from a selected
reference stack.
Helicopter Observation Technique--Elevation of top and bottom of
the plume was also recorded about every 45 minutes at one-half and one mile
and at two miles when possible by visual observation and helicopter altimeter
readings.
The helicopter was also used during each study period to maintain
continuous surveillance on the direction of plrnae travel.
These observations
were obtained by references to established ground control points.
Scope of Fieldwork - Data Collection
Fieldwork was conducted on 50 days totaling about 311 hours of
actual field sampling.
Data included 1,580 plume photographs, 494 double-
and single-theodolite pilot balloon runs, and 305 helicopter temperature
profile runs; total helicopter time was 188 hours.
Data Processing and Tabulation
All data from photographs, pilot balloon observations, and
temperature soundings were programmed for computer analysis and graphic
display.
Plume profile data from photographs were resolved by means of
special template overlays constructed for the respective lens type.
llie
template was designed to provide horizontal and vertical angular values on
all segments of the plume.
Horizontal and vertical angle ~eadings from
plume photographs were established with reference to horizontal and vertical
angles of the center of the photograph and the fixed point at the top of
the reference stack.
Spot checks made on selected segments of the plume
showed them in close agreement with readings obtained with the transit.
With concurrent plume directional information obtained through observations
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from the helicopter, these data were processed through the computer for final
resolution of the plume profile.
Elevation of plume top and bottom observed
from the helicopter agreed closely with corresponding points on the plume
profile obtained from the photographs.
Figure 4 illustrates the manner in which the template is super-
imposed on a plume photograph preparatory to analysis.
Each of the curved
horizontal and vertical grid lines represents 2 degrees.
Curvature of the
lines compensates for image distortion resulting from curvature of the
camera lens.
At the time of this photograph, the camera lens centerline
was positioned 20 degrees horizontal and 8 degrees vertical from the
reference point at the top of the upwind reference stack.
The vertical
angle to top of the reference stack is 7.9 degrees.
The overlay template
is superimposed on the plume photograph with the centerline elevation
reading of 8 degrees aligned along the center of the photograph.
Note that
the 20-degree horizontal line of the template coincides with the top of the
upwind referenced stack.
The sign at the center portion of the figure
displays code numbers necessary to identify each photograph.
For each series of photographs the mean height of top and bottom
of the plume was determined as a function of distance from the plant; and
from these values a plot of the centerline position was derived, the
centerline being defined as the arithmetic mean between the top and the
bottom.
From these plots, rise of the centerline as a function of distance
was determined.
Figure 5 illustrates a portion of the April 1 field data,
including the plume photograph taken at 0715, along with concurrent wind
and temperature profiles and computer-resolved plume profile plots.
Detailed data obtained on plant operation, wind speed and wind
direction profiles, temperature profiles, plume profiles from photographs,
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and other related data are not tabulated in this report but are available
from the files on request.
The 1,580 separate plume rise observations taken at 5-minute
intervals at the six plants were consolidated into 133 composite observa-
tions,3 table 2, each covering time periods of 30 to 120 minutes.
Duration
of composite periods was determined by the constancy of principal meteorologi. ,
cal and operational parameters.
Therefore each of the data points represents
from six to twenty-four 5-minute consecutive observations.
Data in table 2, the 133 composite observations, were next
classified into the following stability ranges based on the temperature
gradient from stack top to plume top.
Group
Inversion,
~ > 1. 00° K /100 meters
6z
o < ~ < 1.00
6z -
~ < 0
6z -
1
Stable,
2
Neutral and Unstable,
3
These classifications, along with heat emission rate, flue gas exit velocity,
and average wind speed from stack top to plume top, for single stack
operation are shown in table 3.
The average plume rise for wind speeds in
selected ranges for each stability group was also developed in this table.
Data Analysis and Evaluation
Point of Effective Plume Rise
Often the most difficult point to establish from a plume profile
is the height at which the rise attributable to buoyancy and momentvm
terminates.
A plume ascending and dispersing in neutral or unstable
conditions will continue to expand vertically because of turbulent diffusion
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after its momentum and buoyancy are spent.
A number of procedures have been
used by other investigators to establish the plume height resulting from
plume buoyancy and momentum.
In this study a relatively simple procedure~
considered to be quite realistic, was evolved.
This procedure, presented in
a paper4 coauthored by TVA investigators and Maynard E. Smith and John A.
Frizzola, Meteorology Section, Brookhaven National Laboratory~ was based on
preliminary results of limited analyses of these data.
Plume rise, ~h, was
defined as elevation of the plume at the point in distance and space where
rise of the plume centerline as a function of distance reached a minimum
value or became constant.
The plume often continued to ascend beyond this
point.
With this criterion, effective termination of plume rise occurred
457 to 1~2l9 meters from the source.
In most instances observations
extended well beyond this point.
In addition to a definition of criteria for establishing plume
rise,
it is desirable to determine whether one is observing the initial
phase where source effects and mean winds are important or the final phase
where the centerline asymptotically reaches a final height under the
influence of atmospheric turbulence and stability.
Difference in semantics
and interests on these questions probably accounts for a large portion of
the differences in plume rise reported by investigators.
The data may be
examined in respect to the initial plume rise phase in accordance with
relation set out by Csanady5 who defines the initial flux due to buoyancy
and momentum as:
2 ~T
F = g V r ---
s T
where
g
= acceleration due to gravity (meters per second2)
Vs = stack gas exit velocity (meters per second)
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r
= stack exit radius (meters)
6T = temperature difference between exit stack gas and ambient air (OK)
T
= ambient air temperature (OK)
If this fluxs Fs is divided by the cube of the wind speeds u3s a lengths
~ = ~, is obtained.
u
Then by dimensional analysis the distance variables
may be made nondimensional:
~ = a function of ~
~ ~
Xl
where z is plume rise and x is distance downwind. At the point ~ where
the plume levels off. the value of ~ becomes constant. Values of ~ and ~s
~ ~ ~
table 4. calculated for average plume rise at distances given in table 3,
are plotted in figure 6.
Because of the large number of points in figure 6.
it is difficult to note the near constant ~ values at the limit of the
~
plume observation.
z
The actual values of I near maximum x distances may be
The leveling at the limit of plume observation can be
noted in table 4.
seen more clearly in figure 7 where only 10 of the 27 groups in figure 6
are plotted.
The ~ and ~ values at the end of the initial plume rise for
9., 9.,
the 27 summary observations listed in table 3 are plotted in figure 8.
Here a two-thirds slope, as observed by otherss fits the data quite well.
The data are therefore considered representative of a close approximation
of the end of the initial plume rise phase.
Compilation - Estimates of Quantities for Plume Rise Calculations
In table 5 either direct measurements or reliable estimates of
every quantity needed for computation of plume rise according to all
principal formulas now in use are compiled for each of the 133 composite
observations along with observed plume rise.
These include:
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Vs - stack gas exit velocity (meters per second)
U4 - mean horizontal wind speed at stack top (meters per second)
u3 - mean horizontal wind speed at plume bottom (meters per second)
U2 - mean horizontal wind speed at plume top (meters per second)
Ul - mean horizontal wind speed at plume centerline (meters per second)
u
- mean horizontal wind speed between stack top and plume top
(meters per second)
68
/:,Z
change of potential temperature with height (OK
per 100 meters)
/:'T - temperature difference between exit stack gas and ambient air (OK)
Tl - temperature at which density of flue gases is equal to that of
the atmosphere (OK)
QH - heat emission per stack (calories per second), sensible heat
Q
- stack gas emission rate converted to temperature, Tl
(meters3 per second)
/:'h - observed plume rise above top of stack (meters)
e
- plume angle off the line of stacks (degrees)
Range of Plant Operation and Meteorological Conditions Covered
The range of principal plant operational and meteorological
conditions spanned by these observations is summarized as follows.
Stack gas velocity
7.7 to 29.2 meters per second
Volume emission rate
1.36 to 6.63 meters3 per second x 102
Stack gas temperature
106 to 145° C.
Heat emission rate
0.528 to 2.46 calories per second x 107
Wind speed, u
1.0 to 16.8 meters per second
Ambient temperature
273 to 304° K
Potential temperature gradient
-0.53 to 3.74° K
per 100 meters
The range and relation of volume emission to heat emission are shown in
figure 9.
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Wind Speed Relationships
Because of the predominant effect of wind speed on plume rise.
wind speed relationships were examined in some detail.
Average wind speed
occurring between stack top and plume top is plotted in figure 10 against
the potential temperature gradient between the same two points.
Most of
the observations fall within a 1- to l2-meter-per-second wind speed
covering a potential temperature gradient ranging from -0.5 to 3.70 K
per
100 meters.
Average wind speed measured at stack top is in most cases
slightly less than average wind speed occurring between stack top and
plume top, figure 11.
Plume rise from single stack operation when
associated with average wind speed observed at stack top, figure 12. shows
a slightly greater spread than when associated with average wind speed
between stack top and plume top, figure 13.
Therefore the average wind
speeds as observed between stack top and plume top were used throughout
this analysis unless otherwise indicated.
Comparison Between Observed and Calculated ~h Values from Principal
Plume Rise Formulas
The observed plume rise was examined with respect to fit with
principal existing plume rise formulas.
Formulas selected for comparison
were Holland;6 Bosanquet;7 Davidson-Bryant;8 Csanady;5 CONCAWE;9 and
Lucas, Moore, and Spurr.lO
In each case the formula has been applied as
recommended by the author without benefit of adjustment factors suggested
by later investigators.
The formulas used, together with complete
description of the various parameters, are given in appendix C.
Calculated
plume rise using the various formulas is given in table 6 and plotted
against observed values for single stack operations, table 5, in figures 14.
19.
In these plots points are coded according to wind speeds equal to or
less than 3 meters per second and greater than 3 meters per second.
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The relation of observed plmae rise with calculated plume rise
shown by the various formulas is as follows:
1.
Holland formula, figure 14, shows fairly good agreement with a
tendency to slightly underestimate plume rise.
2.
Bosanquet formula, figure 15, overestimates plume rise and induces
large scatter.
3.
Davidson-Bryant formula, figure 16, seriously underestimates plume
rise.
4.
Csanady formula, figure 17, shows good agreement for wind speed
equal to or greater than 10 meters per second.
However, it over-
estimates the plume rise for wind speeds less than 10 meters per
second; and the points for wind speeds less than 5 meters per second
fell off the plot or exceeded the ordinate scale.
5.
CONCAWE formula, figure 18, shows good agreement.
6.
Lucas, Moore, and Spurr formula, figure 19, has a tendency to
overestimate the plume rise and induce large scatter.
Individual points shown in these plots represent specific observa-
tions averaged over periods when some variability in meteorological
parameters was inevitable and some fluctuation would normally be expected
in the results.
Optimization of Formulas Based on Observed Plume Rise
On the basis of relationships shown in table 6 where observed and
calculated plume rise values are listed and in figures 14-19 where these
values are plotted, three of the six plume rise formulas were selected for
optimization by the process of multiple regression for best conformance with
the plume rise values observed in this extensive study.
In this process the
basic elements of each formula were retained, but coefficients and exponents
-------
15
were modified to yield best agreement with observations.
Fit of the basic
formula with observed values. amenability to the regression technique, and
inclusion of significant meteorological parameters were the basis of this
selection.
In optimizing these three formulas, only observations where
analyses indicated that full rise had been attained were considered; thus
the optimization was based on the 27 summary observations listed in table 3
according to wind speed and stability classification.
The Csanady formula with the u3 term in the denominator is
obviously not useful with low to moderate wind speeds.
However, it was
selected for optimization because it predicts a linear dimension and con-
tains the significant meteorological parameters required for evaluating the
effect of ambient conditions, especially stability.
The simple CONCAWE
formula was selected because of its superior agreement with observations.
The Lucas, Moore, and Spurr formula was selected because of its adaptability
to optimization.
It is considered that optimization of these formulas over
the broad range of plant designs, operational factors, and meteorological
conditions encompassed in this study should either confirm the efficacy of
the formula as initially presented or result in some improvement for
application to large power plants.
The equations for the optimized Csanady; CONCAWE; and Lucas,
Moore, and Spurr formulas are listed in appendix C.
When programmed for optimization the original Csanady formula
6h = 250 .L
-3
u
became
(F :\,27
6h = 133 "2")
for the full range of stability conditions.
-------
16
Data falling into each of the three stability classes were then
reprogrammed using the following formula
toh = C (: 3) , 2 7
from which the following values of C were determined:
Stability class 1 (0.013° K per meter) average potential temperature
gradient) = 119
Stability class 2 (0.003° K per meter) average potential temperature
gradient) = 131
Stability class 3 (-000006° K per meter) average potential temperature
gradient) = 137
These values of C plotted against the potential temperature
gradient, appendix C) show a straight-line relationship, that is) the
coefficient C becomes larger as the potential temperature gradient decreases.
Utilizing the final formula with the appropriate C values) the
values of toh were calculated and are plotted against observations in
figure 20.
As shown by this plot the optimized formula reduced the scatter
considerably from that shown in figure 17 when using the original formula.
The original CONCAWE formula derived by multiple regression from
observations of Rauchll in Europe showed very good agreement with observa-
tions at TVA steam plants, figure 18.
The original CONCAWE formula makes
no provision for difference in atmospheric stability and as stated by the
author is applicable to neutral and near-neutral conditions.
When this
formula
[ 1I2J
toh = 0,175 QH
_3/4
u
was optimized for best conformity with TVA data, it took the form
-------
17
6h =
[ .'+'+'+]
0.414 QH
_,69'+
u
While the apparent fit with TVA data was not significantly improved, figure 21,
optimization did result in slightly better agreement for particular points.
The Lucas, Moore, and Spurr formulas
o 7 [Q ]1/'+
6h = . aN -N for stable conditions
u GN
and
[Q 1/'+]
6h = aN Nu for
neutral or slightly unstable conditions
were adjusted by regression analysis to fit the data from single stack
operation.
Two regression analyses were made:
(1) by holding the stack
height factor aN constant and solving for the exponent and (2) by holding
the exponent constant and solving for the stack height factor aN'
The
calculated plume rise from both (1) and (2) gave approximately the same
values; however. there is slightly less spread shown when holding the
stack height factor aN constant which gave
0.7 aN
6h =
[ J. 22
~: for stable conditions
u
and
6h = aN
QN.20
for neutral or slightly unstable conditions.
u
The values of 6h calculated from this optimized Lucas, Moore, and Spurr
formula are plotted in figure 22 against the observed values.
As shown by
this plot there is a wide scatter; however, optimization reduced the spread
somewhat from that shown in figure 19 when using the original formula.
The
-------
18
relation of the original formulas to the optimized forms is illustrated in
figure 23 for the Csanady formula, in figure 24 for the CONCAWE formula, and
in figure 25 for the Lucas~ Moore, and Spurr formula where values calculated
by both forms of these formulas are plotted.
Values of plume rise based on the three optimized formulas, along
with observed plume rise values~ are shown in table 70
In table 8 the values
are classed in three stability categories (inversion, stable, and neutral and
unstable) and in two wind speed ranges (equal to or less than 3 meters per
second and greater than 3 meters per second).
The range of calculated values
in each category in relation to observed values is shown.
From this summary
table it can be seen that values for the optimized CONCAWE and Csanady
formulas are comparable.
The average of all calculations for the CONCAWE
formula is 105 percent of observed and 106 percent for the Csanady formula.
Greater variability is indicated for the Lucas, Moore, and Spurr formula
where the average of all calculated values is 117 percent of the observed
values.
Plume Rise When More Than One Stack is Operating
When more than one stack is operating, plume rise varies with
plume direction off the line of stacks.
Minimum rise occurs when the
plume is 90 degrees off the line of stacks, and maximum rise occurs when
the plume direction is along the line of stacks.
Of the plume rise observa-
tions, table 5, 62 observations, or 47 percent, were obtained from a 2- to
9-stack operation with stack spacing ranging from a minimum of 25.2 meters
to a maximum of 77.4 meters.
The optimized Csanady formula
( ),27
L1h = c. :3
-------
19
shows an increase in plume rise of 22 percent with the addition of a second
unit to the same stack when maintaining the same stack gas velocity.
There-
fore the plume rise would be increased by the following factor:
( ).27
.22 C ~3
If two stacks are used, one for each unit, the above factor would become
smaller depending on the spacing between the stacks and the plume direction
off the line of stacks.
The above factor would become
( ).27
6h (increase) = .22 B C ~3 (n-l) Cos e
where
n
= number of stacks
e
= plume angle off the line of stacks
B
a value ranging from 1 at zero stack spacing to 0 at an
approximately 3.000-foot stack spacing
On the basis of observations in this study, maximum initial plume
rise was usually attained about 3,000 feet from the point of emission.
Thus as a first approximation the assumption is made that a plume from
stacks spaced 3.000 feet would not rise higher because of the second plume.
However, as the spacing of stacks is made less than 3.000 feet and as the
number of inline stacks is increased, an increase in plume rise does occur
when the travel is in line with the stacks.
The effect on plume rise of
multiple stacks diminishes as the angle from the line of stacks increases
and is minimal when the plume direction is normal to the line of stacks.
Analysis of data from this and other related studies indicates that the
term B, a coefficient related to stack spacing, is approximated by the
values plotted in figure 26.
On the basis of this relationship, the
-------
20
incremental plume rise attributable to multiple inline stacks as calculated
by the optimized CONCAWE formula would be
6h (increase) = .22 B 0.414 l-QH'444]
'694
U
(n-l) Cos e
Calculated 6h values when two or more stacks were in operation, table 5,
using the optimized Csanady and CONCAWE formulas are given in table 9
along with the observed 6h values.
Calculated values plotted in figures 27
and 28 against observed values show rather good agreement for wind speeds
greater than 3 meters per second.
For lower wind velocities the scatter
is greater than that for comparable single stack operation in figures 20
and 21.
The calculated values for both the single and multiple stack
operations are plotted against observed values in figure 29.
Application of this empirically derived relationship for
estimating the increase in plume rise attributable to in line stacks to
practical problems and experience indicates that it has considerable
validity in the range of our experience.
Obviously, it results in appre-
ciable increase in plume rise for a line of stacks, say 8-10, when the
plume travels in line with the stacks.
This would result in a significant
reduction in concentration were it not compensated by the much smaller
spread of the plume under such conditions.
As a practical matter extensive
monitoring at many TVA plants has indicated that the level of the maximum
ground level concentration from multiple stack plants is closely comparable
for all wind directions.
We estimate that this empirical relation provides
a reasonably sound basis for treating modern large generating stations which
are unlikely to have more than four in line stacks.
If stacks for such a
plant were spaced 200 feet, the maximum plume rise increment over that of
a single stack would be only 22 percent.
-------
21
CONCLUSIONS
Several of the semi-empirical plume rise formulas in current use
were derived from data or observations on relatively small sources.
Frequently, these formulas are applied to sources which are of a different
order of magnitude from those on which they were initially based.
Extrapola-
tion of the relations inherent in these formulas may lead to significant
errors in estimates of stack height requirements and pollution levels.
A comprehensive investigation of plume rise from large modern
plants was therefore undertaken to establish the principal determinant
factors and to strengthen the degree of confidence now afforded in estimates
of diffusion by available formulas and procedures.
Plume rise observations
were made for units with capacities of 173 to 704 megawatts and stacks from
76.2 to 182.9 meters high.
Observations were made over a relatively wide
range of weather conditions.
Also. direct measurements were made of
significant meteorological parameters at the time of the observations.
Analysis of data indicated that most observations extended to the point
of maximum plume rise attributable to effluent forces such as velocity and
buoyancy.
Preliminary results of limited analyses of these data were
presented in an earlier paper.4
However, study and analyses of the plume
rise data have continued since that time and a more complete assessment is
now possible.
Plume rise data plotted against calculated values according
to six formulas in general use indicated that of all terms in all formulas
the wind speed and heat emission rate are the principal determinants.
When
plume rise observations were plotted against calculated values according
to the formulas as originally presented by the author. the simple CONCAWE
formula provided the best fit.
Of the three formulas optimized to give best
fit with TVA observations, both the CONCAWE and Csanady formulas were good.
-------
22
Because of the simplicity and ease of calculation, use of the
CONCAWE formula is considered preferable for general investigations.
When
a particular event such as an inversion breakup or limited mixing layer
fumigation is being analyzed, use of the optimized Csanady formula is
considered preferable, provided information is available on the meteorologi-
cal parameters in this formula.
This linear dimensional formula embodies
the principal physical quantities normally associated with rise of a plume
and permits some accounting for up to lS-percent difference in plume rise
attributable to variation in atmospheric stability.
In conclusion, the study served to validate two plume rise
formulas which can be used effectively over a range of meteorological and
operational conditions.
Plotting of the observed and calculated values
shows some scatter even for the two best formulas.
However, the scatter
is limited and is equally distributed about a line of best fit.
We doubt
that the scatter can be reduced unless wind speed profiles are taken at
less than 3D-minute intervals and related to shorter observation periods,
say S-lO minutes.
However, it is unlikely that even a reduction in scatter
would result in any substantive change in the formulas that have been
developed.
The common agreement of the original CONCAWE formula derived
by regression analysis from several hundred observations in western Europe
with the TVA observations is judged to lend strength to this simple formula.
-------
23
REFERENCES
1.
Tennessee Valley Authority and Public Health Service. "Full-Scale
Study of Dispersion of Stack Gasest A Summary Report."
Chattanoogat Tennesseet August 1964,
2.
Jack
M. Leavittt S. B. Carpentert and Fred W. Thomas. "An Interim
Report on Full-Scale Study of Plume Rise at Large Generating
Stations," Presented at Annual Meeting of Air Pollution Control
Association, Toronto. Canada. June 1965,
3.
Gary A. Briggs, Atmospheric Turbulence and Diffusion LaboratorYt
Oak Ridge, Tennessee. Personal communication. 1966.
4.
S. B. Carpenter, John A. Frizzola. Maynard E. Smitht J. M. Leavittt
and Fred W. Thomas. "Report on Full-Scale Study of Plume Rise
at Large Electric Generating Stations." Presented at Annual
Meeting of Air Pollution Control Associationt Cleveland. Ohio,
June 1967.
5.
G. T. Csanady. "Some Observations on Smoke Plumes." Int. J. Air
and Water Poll't vol. 4. Nos. 1/2 (196l)t pp. 47-51.
6.
J. Z. Holland. "A Meteorological Survey of the Oak Ridge Areat"
U. S. Atomic Energy Commission Report ORO-99t November 1953t
pp. 554-59.
7.
C. H. Bosanquet, W. F. CareYt and E. M. Halton. "Dust Deposition
from Chimney Stackst" Proc. Inst. Mech. Eng.. 162 (1950)t
pp. 355-65.
8.
W. F. Davidson. "The Dispersion and Spreading of Gases and Dust
from Chimneys t" Trans. Coni. on Industrial Was tes t 14th Annual
Meetingt Ind. Hygiene Found. Am. (November l8t 1949)t pp. 38-55.
9.
K. G. Brummaget et al. The Calculation of Atmospheric Dispersion
from A Stackt The Haguet The Netherlandst Stichtingt CONCAWEt
August 1966.
10.
D. H. Lucas, D. J. Mooret and G. Spurr. "The Rise of Hot Plumes
from Chimneys," Int. J. Air and Water Poll.. vol. 7 (1963)t
pp. 473-500.
11.
H. Rauch. "Zur Schornstein Uberhohungt" Beitr. Phys. Atmos.t
vol. 37t No.2 (1964)t pp. 132-58.
-------
APPENDIXES
-------
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TENNESSEE VALLEY AUTHORITY
Division of Health and Safety
APPENDIX A
TABLES
Muscle Shoals. Alabama
September 1968
,.
,.
.~~
" ~. <,
-------
Table 1
PLANT DESIGN AND OPERATIONAL DATA
Paradise Galla tin Shawnee Johnsonvi11e Colbert Widows Creek
Number of Units 2 4 10 4 4 1
Rated Capacity,
per unit (megawatts) 704 314 175 172.8 206 575
Stacks, Number 2 2 10 2 4 1
Height (meters) 182.9 152.4 76.2 121. 9 91.4 152.4
Diameter (meters) 7.9 7.6 4.3 4.3 5.0 6.3
Spacing (meters) 61. 9 77.4 25.2 49.4 30.2
Temperature of flue gas
leaving stack (OC.) 140.0 136.7 140.0 151. 7 170.6 141.1
Orientation N 38° E N 39° E N 56° W N 5° W S 45° E
N
0'\
-------
Table 2
PLUME RISE ABOVE STACK TOP WITH DISTANCE FROM PLANT
Obs. Plume Rise (meters} at Distance Downwind, x (meters)
Steam Plant No. x = 0 76 152 305 457 610 762 914 1,067 1 ,219
Paradise 1 0 20 32 46 44 49 62 74 86 89
2 0 31 50 67 71 95 119 143 167 179
3 0 59 93 109 110 147 184 221 256
4 0 31 44 66 84 96 100 98 104 115
5 2 59 80 112 136 153 165 173 182 188
6 1 97 160 228 269 304 327 340 354 375
7 0 57 104 160 185 191 195 193 183 187
8 25 48 77 126 166 203 230 255 275 295
9 12 92 145 203 217 250 283 313 338 363
10 14 118 168 261 302 307 331 323 330 307
11 3 66 107 169 214 247 273 292 309 329
12 12 80 124 175 214 247 277 307 334 363
13 94 178 240 312 358 394 417 433 447 457
14 4 39 62 98 132 162 184 201
15 2 43 66 106 134 163 198 226
16 1 29 53 90 121 148 175 207 217 251
17 0 25 39 62 81 92 102 115 119 127
18 1 30 55 91 117 136 156 167 172 183
19 0 22 42 79 117 150 174 194 215 237
20 0 10 21 53 82 106 128 149 170 176
21 0 34 54 78 102 126 148 167 188 242
22 0 33 62 92 115 140 159 182 201 219
23 0 25 44 65 84 112 115 133 154 177
24 0 16 29 50 76 96 111 122 139 145
25 0 13 26 47 62 70 85 93 105 135
26 0 26 43 63 78 93 110 106
27 0 25 43 62 67 89 107 103 108
28 0 34 50 61 64 77 86 94
29 0 27 41 54 60 69 88 102 109 98
30 0 44 74 119 166 194 227 260 289 308 tV
'-J
Page 1 of 5
-------
Table 2 (continued)
Obs. Plume Rise (meters) at Distance Downwind, x (meters)
Steam Plant No. x = 0 76 152 305 457 610 762 914 1.J?.~ 1,219
-~-
Paradise 31 0 59 94 117 132 154 152 160 171 178
(cont'd) 32 4 60 101 150 181 213 239 258
33 15 74 113 163 207 250 279 297 303 328
34 1 49 9Lf 152 205 254 229 307 370 306
35 0 34 55 98 140 174 204 232 257 279
36 1 52 84 138 174 205 227 250 267 283
37 0 40 69 124 173 206 238 268 285 305
38 0 16 30 43 62 77 91 104 114 12Lf
39 0 18 34 55 74 95 112 125 139 150
40 0 14 26 52 84 102 116 134 158 165
41 0 27 40 51 66 86 113 131 143 154
42 0 37 62 88 106 133 154 175 191
43 0 53 87 121 137 141 165 182
44 0 43 81 143 180 204 220 230 238 245
45 2 66 115 191 244 283 308 332 350 364
46 0 46 85 144 198 245 296 343 384 414
47 0 21 36 60 78 93 107 120 135 143
48 0 19 34 66 90 115 136 152 167 185
49 0 27 50 87 116 142 169 193 213 233
50 0 16 34 66 83 100 111 119 124 125
Gallatin 1 1,025
2 488
3 0 20 41 81 121 162 202 239 276 312
4 0 22 43 87 130 173 216 248 276 303
5 777
6 0 13 26 52 78 104 130 144 155 165
7 0 16 32 63 95 127 159 178 192 207
8 0 16 31 62 94 125 156 183 199 215
9 0 17 34 69 103 138 172 189 198 208
10 0 16 31 62 93 124 155 167 173 180
N
.y::,
Page 2 of 5
-------
Table 2 (continued)
Obs. Plume Rise (meters) at Distance Downwind, x (meters)
Steam Plant No. x = 0 76 152 305 457 610 762 914 1, 06 Z. 1,219
Gallatin 11 0 9 119 37 55 74 93 111 130
(cont'd) 12 13 64 93 127 160 176 214
13 56 12Lf 192 322 382 414 444 417 460 450
14 27 72 117 171 224 285 335 386 464 555
15 476 451 430
16 21 49 76 132 175 184 194 208 215 226
17 32 70 109 185 238 248 259 266 317 300
18 14 37 62 109 157 196 220 251 276 314
19 19 43 68 118 161 168 181 194 210 220
20 16 46 76 135 194 251 286 321 330 354
21 25 46 67 109 142 156 163 166 168 171
22 66 95 124 182 234 249 251 243 235 228
23 73 112 150 228 300 341 347 322 287 270
24 5 81 127 183 220 250 274 310 335 359
25 0 43 66 90 128 171 192 227 247 259
26 0 24 45 63 81 99 98 109 109 137
27 0 26 46 72 91 103 109 143 165
28 1 47 63 83 112 135 166 196 220 250
29 0 59 74 111 142 171 198 228 251 263
30 0 48 59 81 81 101 120
31 21 77 104 136 163 173
32 0 23 37 57 68 77 86 90 91 96
33 345 440 529 511 466
34 9 62 131 226 240
35 0 25 45 69 92 112 128 138 137 129
36 0 9 15 21 35 52
37 0 15 25 51 81 99 105 122
38 0 16 24 38 52 77 128
N
\0
Page 3 of 5
-------
Table 2 (continued)
Obs, Plume Rise (meters) at Distance Downwind, x (meters)
Steam Plant No. x = 0 76 152 305 457 610 762 914 1,067 1,219
Shawnee 1 14 70 127 234 330 407 457 495 546 526
2 27 81 134 203 242 258 266 266 260 240
3 0 20 40 87 136 160 186 200 220 236
4 0 58 113 195 265 318 365 460 446 493
5 0 9 13 15 16 18 22
6 0 18 28 39 43 45 48
7 0 15 26 44 58 68 88
8 0 11 22 35 42 47 53 45 31 24
9 0 6 13 20 29 29 26 21 16
10 0 11 20 39 60 80 99 126 120
11 0 16 32 52 67 78 79
12 0 13 25 41 50 53 54 57 61 68
Johnsonvi11e 1 58 118 156 198 212 210 208 201
2 107 143 179 251 323 363 375
3 720
4 69 193 294 424 474 480 492
5 81 186 268 368 393 375 357
6 46 245 366 466 453 418 400 400
7 58 171 258 357 434 501 556 586 627 661
8 7 38 59 77 91 101 105 119 112 97
9 22 72 112 166 203 211 206 224 225 293
10 324 320 316 453 498
11 22 62 81 108 126 142 156 167 176 185
12 32 100 137 187 221 232 241 244 242 249
13 46 116 166 246 320 368 414 405 379 347
w
o
Page 4 of 5
-------
Table 2 (continued)
Obs. Plume Rise (meters) at Distance Downwind, x (meters)
Steam Plant No. x = 0 76 152 305 457 610 762 914 1,067 1,219
Colbert 1 302 365 389 401 403 388
2 297 405 430 429
3 36 87 121 148 162 171 178 192 219
4 10 75 122 176 212 255 280 290 311
5 2 41 81 150 205 241 272 293 315 340
6 12 58 95 122 136 144 149 152 143 164
7 17 72 118 154 172 182 195 199 219 233
8 48 123 190 269 314 333 344 354 362 365
9 2 49 89 122 140 148 151 151 149 148
10 15 66 146 220 253 268 277 301
Widows Creek 1 0 21 42 61 77 93 103 117 117 136
2 0 23 44 63 77 99 103 125 119
3 5 37 57 80 103 130 155 155 149
4 72 190 262 323 356 345 377
5 56 120 163 208 243 304
6 130 258 314 331 333
7 1 55 71 73
8 18 63 86 126 129 134 138
9 18 81 111 154 190 214 238 301
10 22 101 136 205 286 316 278
W
I-'
Page 5 of 5
-------
Table 3
AVERAGE PLUME RISE WITH DISTANCE FROM SOURCE BY STABILITY CLASSES
SINGLE STACK OPERATION
Obs. QH Stability Stability Vs u Plume Rise (meters) at Distance Downwind, x (me ters)
Steam Plant ~ (ca1./sec. x 107) ( "1
-------
Tab Ie 3 (continued)
Obs. QH Stability Stability Vs u Plume Rise (meters) at Distance Downwind, x (meters)
Steam Plant No. (ca1./sec. x 107.2 (OK/100 m.) C1ass* (m. /sec.) (m./sec.) x = 0 76 152 305 457 610 762 914 1,067 1,219
-.--
Gallatin 15 1. 70 0.30 2 15.3 2.1 476 451 430
(cont'd) 13 1.70 0.09 2 15.3 2.2 56 124 192 322 382 414 444 417 460 450
4 1. 76 0.41 2 15.4 2.5 0 22 43 87 130 173 216 248 276 303
23 1. 77 0.36 2 15.3 2.5 73 112 150 228 300 341 347 322 287 270
3 1. 76 0.63 L 15.4 2.8 0 20 41 81 121 161 202 239 276 312
17 1.71 0.44 2 15.6 2.9 32 70 109 185 238 248 259 266 317 300
28 1.52 0.06 2 15.2 3.1 1 47 63 83 112 135 166 196 220 250
14 1. 70 0.23 2 15.3 2.1 27 72 117 171 224 285 335 386 464 555
22 1. 77 0.97 2 15.3 3.2 66 95 124 182 234 249 251 243 235 228
Avg. 1.71 0.39 15.3 2.6 104 113 141 167 218 251 278 290 317 334
25 1.50 0.10 2 14.8 4.6 0 43 66 90 128 171 192 227 247 259
7 1. 74 0.22 2 16.1 5.0 0 16 32 63 95 127 159 178 192 207
19 1.65 0.68 2 15.5 5.0 19 43 68 118 161 168 181 194 210 220
16 1.71 0.74 2 15.6 5.1 21 49 76 132 175 184 194 208 215 226
24 1.50 0.61 2 14.8 5.2 5 81 187 183 220 250 274 310 335 359
9 1. 75 0.39 2 16.4 5.4 0 17 34 69 103 138 172 189 198 208
8 1. 74 0.11 2 16.1 5.8 0 16 31 62 94 125 156 183 199 215
6 1. 74 0.72 2 16.1 5.9 0 13 26 52 78 104 130 144 155 165
Avg. 1.67 0.45 15.7 5.3 6 35 58 96 132 158 182 204 219 232
10 1. 73 0.30 2 15.4 6.9 0 16 31 62 93 124 155 167 173 180
27 1.50 0.13 2 14.8 10.4 0 26 46 72 91 103 109 143 165
Widows Creek 6 1. 79 0.04 2 22.9 2.2 130 258 314 331 333
10 1.57 0.09 2 22.9 2.4 22 101 136 205 286 316 278
5 1. 79 0.49 2 22.9 3.4 56 120 163 208 243 304
Avg. 1.72 0.21 22.9 2.7 69 160 204 248 287 310 278
9 1.57 0.25 2 22.9 4.1 18 81 III 154 190 214 238 301
3 1. 77 0.02 2 22.9 4.8 5 37 57 80 103 130 155 155 149
8 1.57 0.22 2 22.9 5.2 18 63 86 126 129 134 138
Avg. 1.64 0.16 22.9 4.7 14 60 85 120 141 159 177 228 149
1 1.77 0.19 2 22.9 6.5 0 21 42 61 77 93 103 117 117 136
Paradise 6 1.86 0 3 16.4 2.6 1 97 160 228 269 304 327 340 354 375
3 1. 70 -0.09 3 15.6 4.9 0 59 93 109 110 147 184 221 256
31 2.00 -0.02 3 16.4 5.7 0 59 94 117 132 154 152 160 171 178
Avg. 1.85 -0.06 16.0 5.3 0 59 94 113 121 151 168 191 214 178
2 1. 70 -0.05 3 15.6 6.8 0 31 50 67 71 95 119 143 167 179
24 1.84 -0.13 3 15.6 7.2 0 16 29 50 76 96 III 122 139 145
21 1. 78 -0.17 3 15.3 7.3 0 34 54 78 102 126 148 167 188 242 L0
Avg. 1.77 -0.12 15.5 7.1 0 27 44 65 83 106 126 144 165 189 10
23 1.84 -0.04 3 15.6 10.9 0 25 44 65 84 112 115 133 154 177
Page 2 of 3
-------
Table 3 (continued)
Obs. QH Stability Stab ili ty Vs u Plume Rise (meters)' at Distance Downwind , x (meters)
Steam Plant No; (cal./sec. x 10~ (OK/IOO m.) Class* (m./sec.) (m./sec.) x = . 0 76 152 305 457 610 762 914 1,067 1,219
Gallatin 12 1. 70 -0.03 3 15.3 3.8 13 64 93 127 160 176 214
29 1.52 -0.00 3 15.2 4.4 0 59 74 III 142 171 198 2.28 251 263
Avg. 1.61 -0.02 15.3 4.1 7 62 84 119 151 174 206 228 251 263
20 1.65 -0.04 3 15.5 5.8 16 46 76 135 194 251 286 321 330 354
18 1.71 -0.02 3 15.6 6.1 14 37 62 109 157 196 22 10 K/100 m.
2 O
-------
Table 4
~ AND ~ VALUES - INITIAL PLUME RISE PHASE
R, R,
Paradise Steam Plant
1* 1 2 2 2 2 2
x z x z x z x z x z x z x z
R, R, R, R, R, R, R, R, R, R, R, R, R, R,
43.1 14.7 245.8 51,6 2,1 3,3 6.8 4,8 24.6 14,8 29,3 12.3 73,3 21.2
86.1 21.5 491.6 96.8 4,3 4,7 13,6 8,0 49.2 22,9 58,6 19,6 146,5 34.6
172,2 31.6 983,3 154,8 8.5 6.7 27,2 12.4 98,3 32,9 117.2 26,9 293,1 53,8
258.3 36,2 1475,0 200,0 12.8 7,7 40,8 15.5 147,5 40,6 175,8 33,1 439,6 69.2
344.4 41,2 1967.0 248,4 17.1 8,4 54.4 17.4 196,7 47.4 234,5 42.3 586.2 82.7
430,5 45,8 2458.0 293,6 21,3 9,2 68.0 19,5 245.8 52,3 293,1 51.5 732,7 95,2
516.6 48,6 2950.0 335,5 25.6 9,6 81. 7 21.1 295,0 57.4 351. 7 58,9 879,6 102,9
602,7 53.7 3441. 0 367.8 29,9 10.1 95,3 23.6 344.1 61,6 410,3 64,2 1026,0 127,0
688,8 57,6 3933.0 400.0 34,2 10,4 108.9 24,9 393.3 65,5 468.9 59.2 1172.0 144.2
2 3 3 3 3 3
x z x z x ~ x z x z ~ z
R, R, R, R, R, R, R, R, R, R, R, R,
143.8 34.0 1,4 1.7 10.5 8.1 29.2 10,3 39.5 13,5 100,3 32.9
287,6 64,2 2.7 2,9 21,0 13,0 58.4 16,9 79.0 21. 8 200.6 57.9
575,2 103,8 5.5 4.1 42,0 15.6 116.7 24.9 157.9 30.1 401.1 85.5
862.7 139,6 8.2 4.8 63.0 16,7 175.1 31. 8 236.9 33.2 601.7 110.5
1150.3 179.3 10.9 5.4 84,1 20.8 233.5 40.6 315.8 40.9 802.2 147.4
1438.0 211.3 13.7 5,9 105.1 23.2 291.9 48.3 309.8 50.8 1003.0 151,3
1726,2 235.9 16.4 6,1 126,2 26.3 350.5 55.2 474.0 53.4 1203.9 175.0
2013.1 262.3 19.1 6.3 147.1 29.5 408.7 63.2 552.7 56.5 1404.0 202.7
2300.0 283.1 21. 8 6.7 168.1 24.6 467,1 72.4 631.7 50.8 1604,5 232,9
w
*Stabi1ity classification data group. 111
Page 1 of 2
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Table 4 (continued)
Gallatin Steam Plant
1* 2 2 2 2 3 3 3
x z x z x z x z x z x z x z x z
.Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, .Q, ,Q, ,Q, ,Q,
- - -
8.8 5.3 1.8 2.7 12.9 5.9 30.5 6.4 94.1 32.1 5.8 4.7 24.6 10.0 87.6 27.6
17.6 7.7 3.6 3.3 25.8 9.8 61.0 12.4 188.2 56.8 11.5 6.4 49.2 16.8 175.2 51. 7
35.1 12.6 7.2 3.9 51. 7 16.3 121. 9 24.8 376.4 88.9 23.1 9.0 98.3 30.3 350.3 72.4
52.7 16.4 10.8 5.1 77.5 22.4 182.9 37.2 564.6 112.3 34.6 11.4 147.5 43.6 525.3 93.1
70.2 18.0 14.4 5.9 103.3 26.8 243.8 49.6 752.9 127.2 46.2 13.2 196.7 56.1 700.4 103.4
87.8 18.8 18.0 6.6 129.2 30.8 304.8 62.0 941.1 134.6 57.7 15.6 245.8 64.5 875.5 112.6
105.4 19.1 21. 6 6.8 155.1 34.6 365.9 66.8 1130.0 176.6 69.3 17.3 295.1 72.9 1051.1 125.2
122.9 19.4 25.2 7.5 180.8 37.1 426.7 69.2 1317.5 203.8 80.8 19.0 344.1 79.7 1226.0 125.2
140.5 19.7 28.8 7.9 206.7 39.3 487.7 72.0 92.4 19.9 1401.0 157.4
Widows Creek Steam Plant
1* 2 2 2 3
x z x ~ x z x z x z
,Q, ,Q, .Q, ,Q, ,Q, ,Q, ,Q, ,Q, ,Q, .Q,
1.2 3.1 1.7 3.5 8.2 6.4 22.2 6.1 18.0 5.7
2.5 4.2 3.3 4.4 16.3 9.1 44.4 12.2 35.9 13.7
4.9 5.2 6.6 5.4 32.7 12.9 88.9 17.8 71. 9 16.0
7.3 5.7 9.9 6.2 49.0 15.1 133.3 22.4 107.8 18.2
9.8 5.5 13.2 6.7 65.3 17.0 177.7 27.1 143.7 23.3
12.2 6.1 16.5 6.0 81. 7 19.0 222.1 30.0 179.7 24.3
98.1 24.4 266.7 34.1 215.7 29.5
114.4 16.0 311.0 39.7 251.6 28.1
*Stabi1ity classification data group.
LV
C)\
Page 2 of 2
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Table 5
PRINCIPAL METEOROLOGICAL PARAMETERS AND MAXIMUM PLUME RISE
68 Per Stack
Obs. No. of VS U. u3 u2 Ul U 7fZ 6T T QH Q llli 8
Steam Plant ~ ~ (m./sec.) (m./sec.) (ro./sec.) (m. /sec.) (m./sec.) (ro. /sec.) (OK/100 m.) i..:!2. i.:!Sl (ca1./sec. x 107) (m. 3/sec. x 102) ~ ~
Paraaise 1 1 15.6 4.8 6.4 12.4 9.4 8.5 1.73 120 291 1. 70 5.46 89
2 5.5 4.6 7.6 6.0 6.8 -0.05 113 298 1. 70 5.59 179
3 4.7 4.6 5.5 5.0 4.9 -0.09 111 300 1. 70 5.63 256
4 16.4 7.9 8.8 9.3 9.2 8.1 1.37 121 291 1.86 5.70 115
5 4.8 6.0 7.3 6.7 6.0 0.85 120 293 1. 86 5.73 188
6 2.3 2.2 3.4 2.8 2.6 0.00 116 297 1.86 5.81 375
7 5.3 5.0 3.9 4.5 4.7 0.01 114 298 1.86 5.84 195
8 17.8 5.4 4.4 2.6 3.5 4.1 0.44 119 293 2.02 6.25 295
9 2.7 2.9 3.5 3.2 3.3 0.17 117 295 2.02 6.30 363
10 3.5 1.5 2.5 2.0 1.9 0.01 113 299 2.02 6.38 331
11 17.1 4.3 3.5 4.7 4.1 4.5 0.59 119 293 1.87 6.02 329
12 2.7 3.7 4.2 3.9 3.7 0.65 120 292 1.87 5.99 363
13 1.6 2.7 5.2 3.9 3.4 0.30 116 295 1.87 6.06 457
14 2 20.2 8.6 7.7 10.5 9.1 8.8 1.42 142 280 2.24 6.61 201 61. 9
15 4.3 5.5 11. 9 8.7 7.7 0.55 141 281 2.24 6.63 226 56.9
16 17.0 8.1 7.3 6.4 6.8 7.2 0.05 126 288 1.89 5.83 251 30.1
17 17.7 6.6 7.5 9.3 8.5 7.8 0.56 128 287 1. 97 6.04 127 5.6
18 9.5 7.8 6.7 7.3 8.6 0.08 125 291 1. 97 6.11 183 14.7
19 8.6 8.4 7.8 8.2 7.7 -0.01 121 294 1. 97 6.19 237 16.1
20 9.8 8.8 9.8 9.3 9.5 0.06 121 295 1. 97 6.20 176 25.5
21 1 .15.3 5.1 7.6 8.7 8.1 7.3 -0.17 120 297 1. 78 5.36 242
22 15.6 4.8 6.0 9.2 7.5 7.7 0.28 124 292 1.84 5.40 219
23 9.9 8.8 11.6 10.3 10.9 -0.04 121 294 1.84 5.44 177
24 6.9 7.7 7.0 7.3 7.2 -0.13 118 297 1.84 5.50 145
25 11.3 10.9 10.0 10.5 11.4 0.18 125 291 1.84 5.37 135
26 18.0 10.3 10.4 9.8 10.2 10.8 0.01 137 275 2.18 5.93 110
27 10.2 10.0 9.8 10.0 9.5 0.00 137 275 2.18 5.94 108
28 9.8 7.3 10.1 8.8 10.0 0.02 136 277 2.18 5.97 94
29 7.4 8.0 7.3 7.6 8.3 -0.02 136 277 2.18 5.97 109
30 16.4 6.9 4.5 5.1 4.8 5.2 0.08 137 279 2.00 5.44 308
31 5.9 5.8 5.0 5.4 5.7 -0.02 135 281 2.00 5.48 178
32 2 18.1 2.4 3.8 6.4 5.2 4.8 0.63 139 281 2.22 5.96 258 62.9
33 3.7 3.5 5.3 4.4 4.4 0.11 136 284 2.22 6.02 328 69.3
34 3.8 5.3 5.8 5.7 5.5 0.02 133 287 2.22 6.09 370 62.0
35 19.0 4.5 6.3 5.7 6.0 6.8 0.65 137 283 2.43 6.30 279 8./
36 6.9 6.0 8.0 7.0 6.6 0.46 135 285 2.43 6.34 283 20.2
37 5.5 5.6 6.2 5.8 5.8 0.03 131 289 2.43 6.44 305 31.6
38 1 19.1 10.7 13.3 21.9 17.9 16.8 1.12 140 283 2.44 6.30 124
39 9.6 11.3 19.1 15.3 13.8 0.37 137 286 2.44 6.35 150
40 8.2 8.2 14.2 10.7 10.6 0.02 135 288 2.44 6.40 165
Page 1 of 4
.~~
-...J
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Table 5 (continued)
118 Per Stack
Obs. No. of Vs 'U~ u3 ~ ul U E fiT T QH Q fih e
Steam Plant B2..:.- ~ (m./sec.) (m. /sec.) (m. /sec..) (m./sec.) (}n. / sec.) (m. /sec. ~ (oK/100 m.~ J:!l k.!2 (ca1./sec. x 107) (m. 3/sec. x 102) ~ ~
Paradise 41 1 19.1 8.2 7.5 8.2 7.8 8.4 0.09 132 291 2.44 6.47 154
(cont'd) 42 19.2 5.2 5.7 9.1 7.3 8.0 0.27 145 279 2.46 6.23 191
43 4.6 4.6 6.8 5.8 5.2 0.11 144 280 2.46 6.25 182
44 2 19.5 3.6 5.2 9.0 7.2 5.9 1.54 142 275 2.33 6.35 245 42.1
45 3.7 5.0 6.4 5.7 4.2 0.53 138 279 2.33 6.44 364 38.0
46 4.6 3.9 4.5 4.2 3.7 0.03 131 286 2.33 6.59 414 26.2
47 18.4 7.5 9.7 12.2 10.9 10.3 1.25 138 281 2.22 6.09 143 10.3
48 5.3 5.9 10.5 8.3 8.6 0.51 135 284 2.22 6.14 185 11.8
49 9.4 7.5 9.5 8.5 8.6 0.27 133 286 2.22 6.20 233 12.3
50 7.7 8.5 11.0 9.7 8.5 0.03 130 289 2.22 6.26 125 8.2
Gallatin 1 1 15.4 1.0 1.8 1.5 1.7 1.0 0.35 112 297 1.76 5.08 1,025
2 1.0 1.5 1.9 1.7 1.3 0.09 109 300 1. 76 5.13 488
3 3.7 6.1 1.8 4.0 2.8 0.63 III 299 1. 76 5.11 312
4 2.9 2.6 2.2 2.4 2.5 0.41 114 296 1. 76 5.07 303
5 1.4 0.8 2.7 1.8 1.3 0.35 113 297 1. 76 5.10 777
6 16.1 3.8 4.9 8.2 6.5 5.9 0.72 116 294 1. 74 5.26 165
7 4.8 3.2 6.6 4.9 5.0 0.22 114 296 1. 74 5.29 207
8 5.2 5.8 4.8 5.3 5.8 0.11 III 299 1. 74 5.34 215
9 16.4 2.5 5.2 8.6 6.8 5.4 0.39 113 297 1. 75 5.41 208
10 15.4 5.8 6.8 9.4 8.2 6.9 0.30 112 298 1.73 5.11 180
11 6.5 6.4 7.4 7.0 6.9 -0.16 109 301 1.73 5.16 130
12 15.3 3.8 2.9 4.1 3.5 3.8 -0.03 110 300 1. 70 5.09 214
13 2.4 1.8 2.1 1.9 2.2 0.09 109 301 1.70 5.11 460
14 2.6 2.2 1.7 1.8 2.1 0.23 110 300 1. 70 5.09 555
15 2.8 1.4 2.1 0.30 110 300 1. 70 5.10 476
16 15.6 2.8 4.6 6.5 5.5 5.1 0.74 114 296 1.71 5.15 226
17 1.8 3.8 3.7 3.7 2.9 0.44 112 298 1. 71 5.18 317
18 5.3 4.6 8.7 6.7 6.1 -0.02 107 303 1.71 5.26 314
19 15.5 3.3 3.6 8.6 6.2 5.0 0.68 113 297 1.65 5.13 220
20 4.6 5.2 6.1 5.7 5.8 -0.04 106 304 1.65 5.25 354
21 15.3 1.7 4.8 4.3 4.6 4.6 1.06 115 295 1.77 5.03 171
22 1.6 4.2 3.0 3.6 3.2 0.97 113 297 1.77 5.06 251
23 2.7 2.6 1.9 2.3 2.5 0.36 111 299 1.77 5.09 347
24 14.8 2.8 4.0 5.3 4.7 5.2 0.61 124 282 1.50 4.67 359
25 4.1 6.0 3.6 4.8 4.6 0.10 121 286 1.50 4.73 259
26 8.2 7.9 11.3 9.8 9.9 0.00 117 289 1.50 4.78 137
27 6.7 11.6 11.7 11. 7 10.4 0.13 117 290 1.50 4.79 165
28 15.2 2.7 3.3 5.1 4.3 3.1 0.06 133 273 1.52 4.66 250
29 4.8 4.2 5.7 4.9 4.4 0.00 131 275 1.52 4.69 263
30 3.3 3.6 4.0 3.7 3.7 -0.15 125 281 1.52 4.79 120
Page 2 of 4
w
CO
-------
Table 5 (continued)
lie Per Stack
Obs. No. of VS U4 u3 u2 Ul U KZ 6T T QH Q 6h e
Steam Plant ~ ~ (m. /sec.) (m./sec.) (m./sec.) (m./sec.) (m./sec.) (m./sec.) l:K/100 m.) 1:!l i:!2 (ca1./sec. x 107) (m.3 /sec. x 102) i!!!.J. ~
Gallatin 31 1 15.2 1.3 1.5 2.1 1.8 1.7 -0.08 125 281 1.52 4.80 173
(cont'd) 32 2 7.9 6.9 6.6 7.7 7.1 7..4 0.01 133 285 0.870 2.46 96 82.3
33 7.7 1.0 1.3 1.1 1.2 1.2 0.70 136 277 0.834 2.37 529 69.8
34 1.6 1.6 1.6 1.6 1.5 0.23 132 281 0.834 2.40 240 3.9
35 4.6 4.7 5.7 5.1 5.1 -0.05 128 286 0.834 2.44 138 41.0
36 8.9 9.9 13.1 11.7 10.8 1.51 135 281 0.861 2.38 52 15.4
37 9.5 9.2 12.7 10.8 10.5 0.93 133 283 0.861: 2.40 122 17.5
38 10.0 9.5 13.3 11.4 11.8 0.11 128 288 0.861 2.44 128 12.6
Shawnee 1 9 14.2 4.6 2.8 2.5 2.7 3.1 0.04 129 290 0.557 1.40 546 54.6
2 13.8 1.6 2.4 4.7 3.5 2.5 0.27 130 289 0.531 1.36 266 34.2
3 3.5 3.4 3.5 3.4 3.8 0.07 129 291 0.531 1.37 236 38.0
4 2.3 '3.0 3.8 3.5 2.4 -0.08 124 296 0.531 1.39 493 55.8
5 8 14.4 5.8 0.7 6.8 3.7 6.3 3.70 134 289 0.553 1.41 22 79.5
6 4.3 7.4 5.9 1.64 132 191 0.553 1.42 48 89.7
7 4.5 9.0 7.0 0.17 130 294 0.553 1.43 88 80.5
8 9.0 8.1 8.5 -0.03 126 298 0.553 1.45 53 75.3
9 8.0 8.8 8.7 -0.49 124 299 0.553 1.46 29 79.2
10 14.0 5.4 3.5 7.1 5.3 6.3 0.'09 129 296 0.528 1.40 126 68.2
11 6.4 5.6 6.4 -0.35 122 302 0.528 1.43 79 88.0
12 14.4 5.4 10.1 8.8 0.38 130 294 0.558 1.43 68 52.2
Johnsonvi11e 1 2 28.4 1.0 3.5 2.8 3.2 2.7 1.59 131 293 1.17 2.80 212 5.5
2 2.2 2.3 1.6 2.0 2.3 0.34 126 298 1.17 2.80 375 16.0
3 1.0 0.7 1.0 0.00 123 301 1.17 2.88 720 13.0
4 29.2 1.0 1.2 1.0 1.1 1.2 1.33 137 289 1. 25 2.83 492 19.5
5 1.5 1.2 1.4 1.3 1.3 1.42 133 293 1. 25 2.87 393 25.3
6 1.0 1.2 0.9 1.1 1.1 0.53 128 297 1. 25 2.92 466 15.4
7 1.9 1.7 2.1 1.8 2.2 0.07 124 301 1. 25 2.95 661 13.9
8 28.9 4.1 6.6 9.9 8.3 6.8 1. 98 135 290 1.22 2.82 119 21.5
9 2 28.9 5.2 5.5 5.1 5.3 6.1 0.62 129 295 1. 22 2.87 293 20.3
10 26.8 1.8 2.3 1.5 1.8 1.9 0.07 131 294 1.10 2.65 498 30.0
11 23.0 2.5 5.7 5.5 5.5 5.1 1.57 138 288 0.98 2.23 185 87.1
12 2.9 2.7 7.3 5.0 5.2 0.48 135 291 0.98 2.25 249 86.1
13 1.8 2.4 3.7 3.0 1.9 0.02 133 293 0.98 2.27 414 81.8
Colbert 1 3 13.9 1.0 1.5 3.7 2.5 1.4 1.43 141 273 0.844 1.82 403 8.6
2 1.3 1.4 4.3 2.9 1.9 0.76 137 278 0.844 1.85 430 10.4
3 1.3 4.3 7.0 5.7 4.8 1.73 131 284 0.703 1.88 219 31.6
4 3.0 4.8 6.0 5.5 3.8 0.13 125 290 0.703 1.92 311 19.7
5 3.5 3.9 6.3 5.1 4.8 -0.04 122 293 0.703 1. 94 340 17.1
6 11.6 1.6 4.6 10.1 7.8 5.3 2.99 131 284 0.612 1.57 164 35.4
7 2.0 5.1 7.1 6.1 4.2 1.86 127 287 0.612 1.59 233 34.7
8 2.7 4.2 4.3 4.3 3.2 0.19 121 293 0.612 1.62 365 34.7
9 12.4 2.6 4.0 5.9 5.0 4.0 2.12 131 284 0.674 1.69 151 79.3
10 4 10.9 3.0 4.3 6.9 5.5 4.5 1.01 119 295 0.539 1.54 301 22.8
Page 3 of 4 W
\.0
-------
Table 5 (continued)
tie Per Stack
Obs. No. of Vs U u3 Uz Uj U y:;;; tiT T QH 1 Q till e
Steam Plant ' (m.3 /sec. x 1(2)
~ ~ (m. / sec.) (m./sec.) (m. / sec.) (m. /sec.) (m./sec.) (m./sec.) (OK/100 m.) i:!9. i.:JS2. (ca1./sec. x 10) ~ ~
Widows Creek 1 22.9 4.7 5.1 5.7 5.4 6.5 0.19 119 283 1.77 5.08 136
2 6.6 6.4 5.3 5.8. 6.0 ~0.17 116 286 1.77 5.14 125
3 6.0 6.8 4.1 5.5 4.8 0.02 115 287 1.77 5.16 155
4 1.5 3.3 4.3 3.8 2.5 1.32 121 279 1. 79 5.04 377
5 1.9 3.5 4.1 3.8 3.4 0.49 117 283 1. 79 5.12 304
6 3.5 1.6 2.2 1.8 2.2 0.04 110 290 1. 79 5.24 333
7 24.5 5.9 6.0 6.2 6.1 6.2 -0.18 118 280 1.59 5.44 73
8 22.9 5.7 6.1 4.8 5.5 5.2 0.22 125 275 1.57 4.97 138
9 3.3 3.2 5.7 4.4 4.1 0.25 122 278 1.57 5.03 301
10 2.0 2.9 2.7 2.8 2.4 0.09 118 281 1.57 5.09 316
Page 4 of 4
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a
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Table 6
OBSERVED AND CALCULATED PLUME RISE - SINGLE STACK OPERATION
Calculated Plume Rise (meters)
Wind Observed Lucas,
Obs, Stability Speed Plume Rise Moore, & Davidson-
Steam Plant Noo Class (mo/sec.) (meters) Holland Spurr Bryant CONCAWE Bosanquet Csanady
Paradise 4 1 8,1 115 116 147 27 157 142 310
1 1 8.5 89 102 132 24 145 121 245
38 1 16,8 124 72 115 13 104 47 59
10 2 1.9 331 536 1,058 231 486 6,000 23,382
9 2 3.3 363 309 395 107 321 1,061 4,768
13 2 3,4 457 280 332 97 302 831 4,471
12 2 307 363 257 262 87 284 589 3,656
8 2 4.1 295 249 280 80 273 580 2,581
11 2 4,5 329 211 243 66 245 456 1,998
7 2 4,7 195 200 659 58 236 898 1,401
30 2 5,2 308 191 379 52 227 602 1,661
43 2 502 182 233 369 66 252 643 2,241
5 2 6.0 188 156 192 42 197 257 734
22 2 7,7 219 120 223 28 162 198 348
42 2 8.0 191 151 238 36 183 237 624
41 2 8,4 154 143 305 33 175 234 423
28 2 10.0 94 109 395 24 145 188 284
40 2 10.6 165 113 395 24 147 170 218
26 2 10,8 110 100 452 22 137 170 230
25 2 11.4 135 81 205 16 121 95 109
39 2 13.8 150 87 167 16 121 75 102
6 3 2,6 375 361 584 133 369 2,256 8 , 4 34
3 3 4,9 256 177 303 51 219 111 1,081
31 3 5.7 178 174 271 46 212 381 1,233
2 3 608 179 127 218 32 171 194 451
24 3 7.2 145 128 210 30 171 273 391 .j::-.
I-'
Page 1 of 3
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Table 6 (continued)
Calculated Plume Rise (meters)
Wind Observed Lucas,
Obs. Stability Speed Plume Rise Moore, & Davids on-
Steam Plant No. Class (m./sec.) (meters) Holland Spurr Bryant CONCAWE Bosanquet Csanady
Paradise 21 3 7.3 242 122 206 29 166 167 393
(cont'd) 29 3 8.3 109 131 190 31 167 144 497
27 3 9.5 108 114 166 26 151 103 338
23 3 10.9 177 84 139 17 125 18 118
Gallatin 21 1 4.6 171 192 205 52 234 331 1,207
1 2 1.0 1,025 880 579 445 734 1,820 112,393
2 2 1,3 488 677 714 307 603 3,627 47,849
5 2 1,3 777 677 508 309 603 1,735 51,157
14 2 2.1 555 407 440 155 414 1,503 10,827
15 2 2.1 476 407 412 155 414 1,339 10,827
13 2 2.2 460 388 544 145 399 2,033 9,310
4 2 2.5 303 352 352 124 369 1,007 7,358
23 2 2.5 347 353 364 122 370 1,037 6,977
3 2 2.8 312 314 299 105 339 730 4,902
17 2 2,9 317 297 319 102 326 814 4,393
28 2 3,1 250 252 493 93 292 1,573 6,509
22 2 3,2 251 276 251 87 308 540 3,473
25 2 4.6 259 167 355 51 216 598 1,319
7 2 5.0 207 176 290 50 218 430 1,007
19 2 5,0 220 167 216 47 213 324 905
16 2 5.1 226 169 211 46 213 311 845
24 2 5.2 359 148 212 43 197 327 977
9 2 5,4 208 164 242 46 207 333 826
8 2 5.8 215 152 320 40 195 360 605
6 2 5.9 165 149 199 40 193 253 632
10 2 6.9 180 126 228 30 171 212 368
27 2 10.4 165 74 221 16 117 103 105
~
N
Page 2 of 3
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Table 6 (continued)
Calculated Plume Rise (meters)
Wind Observed Lucas,
Obs. Stability Speed Plume Rise Moore, & Davidson-
Steam Plant ~ Class (m./sec.) (meters) Holland Spurr Bryant CONCAWE Bosanquet Csanady
Gallatin 12 3 3.8 214 225 391 68 265 600 1,827
(cont'd) 29 3 4.4 263 178 328 57 225 658 2,039
20 3 5.8 354 144 254 38 190 252 500
18 3 6.1 314 141 244 36 186 225 424
11 3 6.9 130 126 216 30 171 156 349
26 3 9.9 137 78 145 17 121 69 125
Widows Creek 4 1 2.5 377 373 264 182 372 565 11,471
6 2 2.2 333 424 675 213 410 2,492 14,186
10 2 2.4 316 352 510 192 360 1,772 13,734
5 2 3.4 304 274 290 118 296 614 4,304
9 2 4.1 301 206 303 91 241 595 2,864
3 2 4.8 155 196 542 78 227 706 1,495
8 2 5.2 138 162 277 66 201 418 1,458
1 2 6.5 136 142 265 48 181 274 638
2 3 6.0 125 154 250 53 192 217 778
~
LV
Page 3 of 3
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44
Table 7
OBSERVED AND CALCULATED PLUME RISE - SINGLE STACK OPERATION
Calculated Plume Rise (meters)
Wind Observed Optimized Formulas
Obs. Stability Speed Plume Rise Lucas, Moore,
Steam Plant No. Class (m./sec.) (meters) CONCAWE & Spurr Csanady
Paradise 4 1 8.1 115 164 127 141
1 1 8.5 89 152 115 128
38 1 16.8 124 111 94 88
10 2 1.9 331 465 860 523
9 2 3.3 363 317 339 333
13 2 3.4 457 300 289 317
12 2 3.7 363 283 232 289
8 2 4.1 295 273 243 274
11 2 4.5 329 247 213 248
7 2 4.7 195 239 509 246
30 2 5.2 308 230 309 241
43 2 5.2 182 252 302 254
5 2 6.0 188 202 167 189
22 2 7.7 219 169 185 163
42 2 8.0 191 187 195 177
41 2 8.4 154 180 241 167
28 2 10.0 94 152 296 146
40 2 10.6 165 153 294 140
26 2 10.8 110 144 331 138
25 2 11.4 135 129 164 120
39 2 13.8 150 128 133 110
6 3 2.6 375 360 470 400
3 3 4.9 256 223 245 235
31 3 5.7 178 216 217 225
2 3 6.8 179 178 176 181
24 3 7.2 145 177 169 176
21 3 7.3 242 173 166 175
29 3 8.3 109 173 152 171
27 3 9.5 108 157 133 154
23 3 10.9 177 133 112 126
Gal1atin 21 1 4.6 171 237 183 218
1 2 1.0 1025 682 547 800
2 2 1.3 488 569 637 657
Page 1 of 2
-------
45
Table 7 (Continued)
Calculated Plume Rise (meters)
Wind Observed Optimized Formulas
Obs. Stability Speed Plume Rise Lucas, Moore,
Steam Plant No. Class (ro./sec.) (meters) CONCAWE & Spurr Csanady
Gallatin 5 2 1.3 777 569 472 649
(cont'd) 14 2 2.1 555 402 393 440
15 2 2.1 476 402 371 437
13 2 2.2 460 389 471 428
4 2 2.5 303 361 316 381
23 2 2.5 347 362 326 378
3 2 2.8 312 334 270 336
17 2 2.9 317 322 285 336
28 2 3.1 250 292 414 352
22 2 3.2 251 305 228 293
25 2 4.6 259 220 296 243
7 2 5.0 207 222 245 224
19 2 5.0 220 217 189 211
16 2 5.1 226 218 185 208
24 2 5.2 359 202 186 211
9 2 5.4 208 211 207 207
8 2 5.8 215 200 263 199
6 2 5.9 165 198 172 188
10 2 6.9 180 177 191 168
27 2 10.4 165 125 177 124
12 3 3.8 214 267 316 279
29 3 4.4 263 229 267 265
20 3 5.8 354 196 206 196
18 3 6.1 314 192 197 189
11 3 6.9 130 177 174 174
26 3 9.9 137 130 118 130
Widows Creek 4 1 2.5 377 364 245 360
6 2 2.2 333 398 569 439
10 2 2.4 316 353 440 418
5 2 3.4 304 294 257 302
9 2 4.1 301 247 261 270
3 2 4.8 155 230 427 237
8 2 5.2 138 207 235 226
1 2 6.5 136 187 220 185
2 3 6.0 125 197 202 202
Page 2 of 2
-------
Table 8
SUMMARY - CALCULATED AND OBSERVED PLUME RISE VALUES
BY WIND SPEED AND STABILITY CLASSIFICATION
Wind Percent of Observed Rise
Stability Speed Observations > 100% Observations 7 100% Total
Formula Class (mo/sec.) No. Max. Avg. No, Mino Avg. Avg.
CONCAWE 1 > 3 3 171 151 1 90 90 136
'< 3 0 1 97 97 97
2 > 3 14 162 127 20 56 85 103
<:3 8 140 115 5 67 76 100
3 > 3 7 159 138 8 55 79 107
<3 0 1 96 96 96
Total 32 171 129 36 55 83 105
Csanady 1 > 3 3 144 131 1 71 71 116
<:3 0 1 95 95 95
2 > 3 13 164 130 21 59 85 102
<: 3 8 158 126 5 78 85 110
3 > 3 9 162 131 6 55 74 108
<" 3 1 107 107 0 107
Total 34 164 129 34 55 84 106
Lucas, Moore, and Spurr 1 > 3 3 129 115 1 76 76 106
< 3 0 1 65 65 65
2 > 3 18 315 169 16 52 83 128
<:3 6 260 151 1 53 76 III
3 > 3 8 162 130 7 58 76 105
<3 1 125 125 0 125
Total 36 315 149 32 53 79 117
~
0\
-------
Table 9
OBSERVED AND CALCULATED PLUME RISE - MULTISTACK OPERATION
Calculated Plume
Wind No. of Degrees Observed Rise (meters)
Obs. Stability Speed Stacks Off Line Plume Rise Optimized Formulas
Steam Plant No. Class (m./ sec.) Operating of Stacks (meters) CONCAWE Csanady
Paradise 44 1 5.9 2 42.1 245 238 210
14 1 8.8 2 61.9 201 174 151
47 1 10.3 2 10.3 143 161 136
46 2 3.7 2 26.2 414 333 350
45 2 4.2 2 38.0 364 302 305
33 2 4.4 2 69.3 328 278 288
32 2 4.8 2 62.9 258 263 259
34 2 5.5 2 62.0 370 240 243
37 2 5.8 2 31. 6 305 247 240
36 2 6.6 2 20.2 283 228 211
35 2 6.8 2 8.7 279 224 204
16 2 7.2 2 30.1 251 191 194
15 2 7.7 2 56.9 226 192 185
17 2 7.8 2 5.6 127 185 177
50 2 8.5 2 8.2 125 184 176
18 2 8.6 2 14.7 183 173 169
48 2 8.6 2 11. 8 185 182 169
49 2 8.6 2 12.3 233 182 172
20 2 9.5 2 25.5 176 161 154
19 3 7.7 2 16.1 237 187 184
Page 1 of 3
~
-...J
-------
Table 9 (continued)
Calculated Plume
Wind No. of Degrees Observed Rise (meters)
Obs. Stability Speed Stacks Off Line Plume Rise Optimized Formulas
Steam Plant No. Class (m./sec.) Operating of Stacks (meters) CONCAWE Csanady
Gallatin 33 2 1.2 2 69.8 529 442 60]
32 2 7.4 2 82.3 96 126 146
37 2 10.5 2 17.5 122 104 105
38 2 11.8 2 12.6 128 96 103
35 3 5.1 2 41.0 138 166 203
Shawnee 2 2 2.5 9 34.2 266 351 476
1 2 2.7 9 54.6 546 300 405
3 2 3.8 9 38.0 236 258 338
10 2 6.3 8 68.2 126 140 173
7 2 7.0 8 80.5 88 118 142
12 2 8.8 8 52.2 68 129 147
4 3 2.4 9 55.8 493 316 436
11 3 6.4 8 88.0 79 113 142
8 3 8.5 8 75.3 53 109 129
Page 2 of 3
~
00
-------
Table 9 (continued)
Calculated Plume
Wind No. of Degrees Observed Rise (meters)
Obs. Stability Speed Stacks Off Line Plume Rise Optimized Formulas
Steam Plant No. Class (m. /sec.) Operating of Stacks (meters) CONCAWE Csanady
Johnsonvi11e 4 1 1.2 2 19.5 492 556 624
5 1 1.3 2 25.3 393 525 570
1 1 2.7 2 5.5 212 309 308
11 1 5.1 2 87.1 185 171 165
8 1 6.8 2 21. 5 119 165 141
6 2 1.1 2 15.4 466 592 711
7 2 1.8 2 13.9 661 421 493
10 2 1.9 2 30.0 498 380 468
13 2 1.9 2 81. 8 414 341 428
2 2 2.3 2 16.0 375 344 394
12 2 5.2 2 86.1 249 169 181
9 2 6.1 2 20.3 293 178 176
3 3 1.0 2 13.0 720 614 792
Colbert 1 1 1.4 3 8.6 403 461 543
9 1 4.0 3 79.3 151 176 176
7 1 4.2 3 34.7 233 182 189
10 1 4.5 4 22.8 301 178 205
3 1 4.8 3 31. 6 219 177 184
6 1 5.3 3 35.4 164 154 137
2 2 1.9 3 10.4 430 373 450
8 2 3.2 3 34.7 365 219 276
4 2 3.8 3 19.7 311 211 262
~
1.0
5 3 4.8 3 17.1 340 180 219
Page 3 of 3
-------
TENNESSEE VALLEY AUTHOPITY
Division of Health and Safety
APPENDIX B
FIGURES
Muscle Shoals, Alabama
September 1968
-------
V1
t-'
Figure 1.
INSTRUMENTATION. PRIMARY PIBAL STATION
-------
52
.-
- ';.~~1
Figure 2. CAMERA WITH SPECIAL TRANSIT MOUNT
-------
53
I
I
I
10-- PLUME PATH
, I 1 I
I I 1 I I
I I I , /
I I 1 1 I
I I 1 1 I
I , 1 , I
I I 1 1 /
I I II I, I
I I /
I I J / I
I , ,I I /
I , 1 ' /
I' , /
I I 1 I /
I I / I /
I , 1 II /
I I /
I I 1 I I
I I J I /
I 1 I
I 1 I I
I I I I
I I 1 I
I/,I /
I I 1 I I
I I I I I
'/,I I /
I I 1/
, ,1/
liP OBSERVATION POINT
A. PLAN VIEW
OBSERVED POINTS
VERTICAL ANGLE
TO TOP OF STACK
o
o
00
VERTICAL ANGLE TO BOTTOM OF PLUME
VERTICAL ANGLE TO TOP OF PLUME
B. PROFILE VIEW
SCALE 1"=1500'.!
Figure 3. PLUME OBSERVATIONAL PLAN BY MODIFIED TRANSIT
-------
240
200
o
o
C"I
o
CD
......
o
"""
o
00
o
C"I
......
o
CD
......
o
o
C"I
o
C"I
......
o
o
o
00
o
"""
160
120
80
40
00
40
80
120
o
o
C"I
o
CD
......
o
C"I
......
o
C"I
......
o
o
C"I
o
"""
o
o
o
"""
o
CD
......
o
00
o
00
Figure 4.
TEMPLATE ON PLUME PHOTOGRAPH
240
200
160
120
80
40
00
40
80
120
VI
~
-------
..
!loo
40 60 6!1 10 TEIIPERATURE of
0
0 !I 10 I!I 20 2!1 30 3!1 WIND SPEED - FT ISH
o !l0 100 I!IO 200 2!1O 300 3!10 WIND DIRECTION DEGREES
4!1oo
4000
... 3!10D
...
...
...
I 3000
o
z
::>
~ 2!l00
<:I
...
~ 2000
GI
C
~ I!lOD
!2
...
:I:
1000
PLUME PHOTOGRAPH - 0715
4!1OO
I I
EVALUATION OF PLUME RISE DATA
PARADISE STEAM PLANT 4 -1-65 PHOTOS
TIME' 0715 STACK HEIGHT - 600'
TOP - -
-- -- --It
~ --:::::: --- ---
-=-=-=- --
~--.:= 80 TO..I
WIND SPEED AND DIRECTION PROFILE - 0716
TEMPERATURE PROFILE - 0720
PARADISE STEAM PLANT
APRIL I, 1965
4000
... 3!100
...
...
...
I 3000
o
z
::>
~ 2!1oo
<:I
...
1) 2000
III
C
EIIP.:.
,.
I
i
!loo
I
I
I
I
,
,
,
,
,
I
~ 1!l00
!2
...
:z:
\
,
I
,
1000
o
o
!loo
2000 2!1oo 3000 3500 4000
DISTANCE IN FEET
4500 !IOoo 5500 6000
1000 I !loa
DIR. a TEMP. PROFILE
PLUME
PROFILE - 0715
WIND SPEED,
0716-0720
V1
V1
Figure 5.
DATA FROM TYPICAL DAY OF FIELD OPERATION, APRIL 1, 1965 PARADISE STEAM PLANT
-------
10
/
/
/
/
/
/
/
,,~
«::~7
/
,~
&
:7
/
/
/
/
/
/
/
/
~
100
NI~
LEGEND
.6.. INVERSION
o STABLE
X NEUTRAL & UNSTABLE
Figure 6.
1010
X
L
INITIAL PLUME RISE PHASE i vs 1
1000
10
\J1
C)'\
-------
100
Nlc:..l
10
LEGEND
/:;. INVERSION
o STABLE
X NEUTRAL & UNSTABLE
1
1
10
100
x
1,
Figure 7. INITIAL PLUME RISE PHASE I vs 1-
L L
VI
"
-------
1000
58
o
x
100
le(l)%
.2, 'J.,
NI~
.
o
10
LEGEND
. -INVERSION
O-STABLE
X-NEUTRAL & UNSTABLE
1
10
100
1000
. Figure 8.
~
i X
END OF INITIAL PLUME RISE PHASE - i VS +
10000
-------
,..
a
.....
)(
<..>
~ 2.0
......
co
~
z:
o
V>
V>
~ 1.5
Lo.J
~
pI> .
a ..~
~~
~
.r
LEGEND
>1 STACK
OPERATING
.
o
y
...
ED
.
STEAM
PLANT
PARADISE
GALLATIN
SHA WN EE
JOHNSONVILLE
COLBERT
WIDOWS CREEK
1.0
M.
m
1 STACK
OPERATING
o
x
V
A
+
a-
.5
(I
d~
.,
o
a
8
9
1
2
3
7
456
VOLUME EMISSION (M3/Sec x 102)
Figure 9. HEAT EMISSION VS VOLUME EMISSION
-------
-0
C
o
u
~ 30
....
CI)
a..
II)
....
«
o
o
5
~o
\x
V 0 ~ ~V.,
1 STACK STEAM
OPERATING OPERATING PLANT
o . PARADISE
X 0 GALLATIN
V ... SHAWNEE
~ A. JOHNSONVILLE
~ 0 + e COLBERT
. D . WIDOWS CREEK
. 0
0
..
.~ T
.. $ e
E9X EB $
X
A
1.0
1.5
2.0
2.5
3.0
3.5
POTENTIAL TEMPERATURE GRADIENT MIt.Z ("KIlOO m)
Figure 10. WIND SPEED VS POTENTIAL TEMPERATURE GRADIENT
4.0
0"\
o
-------
"1:)
c:
o
u
~ 12
~
-------
VI 103
...
Q)
+-'
Q)
~
~
-.J
a..
o
LLI
>
0::
LLI
en
~ 102
)(
)(
)(
x
o )( X
c 'tP 0 ~l9xcr ~ 0
X X'ix XXX!
X X X 80
o Bg x°c9
<99
o 0
o
LEGEND
o PARADISE STEAM PLANT
X GALLATIN " "
o WIDOWS CREEK " "
62
100 10 I
AVERAGE WIND SPEED AT STACK TOP - (Meters Per Second)
Figure 12. OBSERVED PLUME RISE VS AVERAGE WIND SPEED AT STACK TOP
-------
UJ 103
...
Q)
+-
Q)
:2
.r::
'....J
a..
o
UJ
>
c::
UJ
en
~ 102
63
x
)(
'X
x
Xx 0
Or@..MOO~)(X
~'[J 0 ~
xx 0
XJf~O
X~(S 0 >8
9:3#0 XOO 0
800
0°
o
LEGEND
o PARADISE
X GALLATIN
o WIDOWS CREEK"
STEAM PLANT
"
10° 101
AVERAGE WIND SPEED BETWEEN STACK TOP AND PLUME TOP - (Meters Per Second)
Figure 13. OBSERVED PLUME RISE VS AVERAGE WIND SPEED BETWEEN
STACK TOP AND PLUME TOP
-------
100
700
600
HOLLAND FORMULA
-5
t.h:1.5'{d+4xIO ~
iI
100
,
~/'/
~«;/
~«),/
~~;r ,
c ~/
CI ~'<3'
~q,«i"
,/
'" to. cp"
,.6
.6. CCt'
A 4A A ~/ 8
'" ~ ,.4~
4 -4,'
~ ~«; '"
2f1.,tr~
/
~,//
CI
~. 500
"
~
~ 400
'"
....
'"
cc:
....
::E
:3 300
"-
c
....
>
'"
~ 200
OJ
o
&
[]
[]
600
CI
~ 500
"
~
.<:
<1400
....
'"
cc:
....
::E
:3 300
"-
o
....
>
'"
~ 200
OJ
o
LEGEND
'" - =: 3.0 m/sec
[] - < 3.0 m/sec
100
100
200
1000
800
900
Figure 1~. RELATION - OBSERVED AND CALCULATED PLUME RISE
BOSANQUET FORMULA
~
t.h= 4.77(QYs2 +
(I +0.43 v.)u:
s2
6.37gQD(AJi-J -2)
[3 1;
~/'
~<,;/
~
4-
'"
A
[]
4-
LEGEND
4>- '=: 3.0 m/sec
[] - < 3.0 m/sec
1000
Figure 15. RELATION - OBSERVED AND CALCULATED PLUME RISE
100
600
DAVIDSON-BRYANT FORMULA
6h=d(~t(l+tT)
300 400 500 600 100
CAlCULATED PlUME RISE dh (Meters)
;;; 500
~
!
~ 400
....
'"
cc:
....
::E
:3 300
"-
c
....
>
'"
~ 200
OJ
o
,
,
,
~/
~«;/
~~/
~~,
c :'\~'
£\ c ~CJ/
a #:/
:.,~ .... ///'/
~& ////
/'
,/
,,,,,,
c
100
LEGEND
"'-'=:30m/sec
[] - < 3.0 m/sec
1000
0"\
-!»
-------
65
700 700
CSANADY FORMULA OPTIMIZED CSANADY FORMULA
I1h=2SO~ ~
600 ~<;f/ 600 I1haC({ry27
Iff" ~"'~
~ ~~V i 500 0
~ ,,'i''/
£ 500 r..~/ ht},."'-'; 0
<{<-qy ~ o/.f'
4
~ 400 / ~ 400
ii: / .. .. .." .. ,,"/0
'" /
:!; "" .. / 0 a a
:: 300 / .. 2 .. .. '" Iff! a a
/ ~ 300
11. / /'
c I ~~:
'" / '" ..
> .. ..
ffi 200 / " ..
UJ t" /.. " " " " 200 t.. e""
III A
0 ,,/ A .. A A 0 A~ Af
A
100 / A A.. A LEGEND LEGEND
A A 100 /" A
/ .. - '" 3.0 m/sec / A - '" 3.0 m/sec
/ 0-< 3.0 m/sec / 0- < 3.0 m/sec
~ ~ ~ ~ ~ 600 ~ ~ ~ ~
CALCULATED PlUME RISE I1h (Meters)
Figure 17. RELATION - OBSERVED AND CALCULATED PLUME RISE
~ ~ ~ ~ ~ 600 ~ ~ ~ ~
CALCULATED PlUME RISE 11 h (Meters)
Figure 20. RELATION - OBSERVED AND CALCULATED PLUME RISE
700
700
600
CONCAWE FORMULA
I1h=0.175 [*]
OPTIMIZED CONCAWE FORMULA
~
!
! 500
4
~400
ii:
'"
:!;
~ 300
c
~ 200
gj
o
4:-/'
~«;/
Iff"
r:f'/
,,'i'/
00 r.."'C:/
A: A
t ~....A
)~?f..~A A
"",
600
ro...m]
t.h=.414l["Ji4
a
a
I~
4:-"
~~/
!If/
a 1\.~',' D
a~~"/
«<1,/
. ... a 1','
It. ,'D D
A ~ A"Dtt'l.
A AAA,/" 46
A "A.' ..
14,1'.."":A
.J,,~A
,/" "t"
/
"
A
o
A
a
ii: A}' 300 #,'/'b a
1l','''''1t. A IC 6 A+"" A
c A C A
"' ?;t A" A ""
> m ~/ AA A
0: 200 200 A
~ A ,.6. A A A A A A
,A. .. A A A t A A
0 4,4 .. AI1/>. 0 A ~"AA
" .6.64 A LEGEND 100 A A LEGEND
100 A A A - '" 3.0 m/sec /A A A - '" 3.0 m/sec
/
, a - < 3.0 m/sec / a - < 3.0 m/sec
,
~ ~ ~ ~ ~ 600 m ~ ~ ~
CALCULATED PlUME RISE 11 h (Meters)
Figure 19. RELATION - OBSERVED AND CALCULATED PLUME RISE
~ ~ ~ ~ ~ 600 ~ ~ B ~
CALCULATED PlUME RISE I1h (Meters)
Figure 22. RELATION - OBSERVED AND CALCULATED PLUME RISE
-------
~ 500
Qj
~
.c
it 300
...J
<
Z
S
~ 200
600
rP
o
700
700
100
/
/
/
/
/
//
/
/
/
/
/
/
/
/
/
/
~
/0
/
600
~ 500
Qj
:IE
/
/
/
0/
/
/
l'
~/~
/
/
/
00
o
00
Q-
o
~
o
o
00
o
.c
it 300
...J
<
Z
co
~ 200
100
600 700
Ah (Meters)
1000
800
900
1000
100
Figoa.., 23. RELATION - CALCULATED PLOME RISE FROM THE ORIGINAL AND
OPTIMIZED CSANADY FORMULAS
~ 500
Qj
~
.c
/
#//
tP /
~/
0/
/
/
/
(j\
(j\
100
1000
Figure 25. RELATION - CALCULATED PLUME RISE FROM THE ORIGINAL AND
OPTIMIZED LUCAS, MOORE, AND SPURR FORMULAS
-------
I
m
I
1.0
.8
(j\
---.J
.6
.4
.2
o
1
10
11D.1D
1000
STACK SPACING (Fe-et)
Figure 26. VARIATION OF THE VALUE OF B WITH STACK SPACING
-------
5" 500
;:
~
""
~ 300
Q
....
>
a:
....
~ 200
0-
'700
~/
~o/
<:.>~'<-'Y 0
Ca~ C
W
~<.,;/
~~;rC
IA ~
.t.::
AIAIA /C
A A /
A A6 /
As. /
46/)1 IA
6 / CI
6~
Ar'66
tV6~
// J,
/
600
C
C
C
m
ao
100
LEGEND
IA - a!: 3.0 m/sec
a - < 3.0 mIse<:
100
200
300 400 500 600 700
CALCULATED PlUME RISE dh (Meters)
Figure 27. RELATION - OBSERVED AND CALCULATED PLUME RISE
CSANADY FORMULA - MULTISTACK.
~ 500
;:
~
.<:
~ 300
Q
....
>
a:
....
~ 200
o
~ 500
~
~
.... 400
~ 300
Q
....
>
. a:
....
~ 200
o
1000
700
x
x 0
o
x
a
600
100
~
a ~'9
~7
~~ a
cY
~
Aa aq.~
/ CI
A6 6 a/
IA 6 /
A 6 6 /
~ /
tt /.-f
A/ a
~
~6b.&
//~
/ 6
LEGEND
A - a!: 3.0 m/sec
a - < 3.0 m/sec
CI
a
a
a
a
a
Figure 28. RELATION - OBSERVED AND CALCULATED PLUME RISE
CONCA WE FORMULA - MULTISTACK
700
~/
~O/
~"!, x
~~7
x x,?,
00/
C}/"
x ~'Yx
q.~
00 x '0 x 0 ~ >0
x 0 ( ~ 0 0
xOxo'loa'600
~x:OJ/O.. xO
)(0 00 0 x
&ox <9 0
?..u 0
0~7&S.o ~ 0
/01l0
/ x
/ x
x 0
x x
LEGEND
o SINGLE STACK OPERATION
x MULTISTACK OPERATION
600
o
100
1000
Figure 29. RELATION - OBSERVED AND CALCULATED PLUME RISE
. CSANADY FORMULAS-SINGLE AND MULTISTACK
1000
(j"\
00
-------
TENNESSEE VALLEY AUTHORITY
Division of Health and Safety
APPENDIX C
FORMULAS
Muscle Shoals, Alabama
September 1968
-------
where:
70
HOLLAND PLUME RISE FORMULA
1.5 Vsd ~ 4 x 10-5 QH
6h =
"IT
6h = predicted ri~e of the plume above the ~tack top (meters)
Vs = stack gas exit velocity (meters per second)
d
= stack exit diamete~ (meters)
QH = heat emi~sion (calories per second)
u
= mean horizontal wind speed (meters per second)
-------
where:
71
BOSANQUET. ET AL, PLUME RISE FOP,MULA
IF G > 0
4.77 (QV)1/2
s
6h = +
(1 + 0.43 ~s)U
QD 0n J 2
_3
u T1
+.? 2)
J -
6.37 g
6h = predicted rise of the plume above the stack top (feet)
Q
= stack gas emission rate converted to temperature T1
(cubic feet per second)
Vs = stack gas exit velocity (feet per second)
u
= mean horizontal wind speed (feet per second)
g
= acceleration due to gravity (feet per second2)
D
= difference between ambient temperature and stack gas
temperature at stack top (OK)
J
_2
u
(Q VS)1/2
[ (T )1/2
0,43 g~
+ 1
V T J
- 0, 28 2...2
gD
G
= change of potential temperature with height from stack
top to plume top (OK per foot)
T1 = temperature at which density of flue gases is equal to
that of the atmosphere (OK)
-------
where:
72
BOSANQlJET. ET AL, PLUME RISE FORMULA
IF G <' 0
z = 6.37 g ~ Z
U Tl
/ovs
x = 3.57 - X
u
x
= distance downwind from stack (feet)
Q
= stack gas emission rate converted to temperature Tl (cubic
feet per second)
Vs = stack gas exit velocity (feet per second)
u
= mean horizontal wind speed (feet per second)
z
= predicted rise of the plume above the stack top (feet)
g
= acceleration due to gravity (feet per second2)
D
= difference between ambient temperature and stack gas
temperature at stack top (OK)
Tl = temperature at which density of flue gases is equal to
that of the atmosphere (OK)
G
= change of potential temperature with height from stack top
to plume top (OK per foot)
8
-
".- --
---
./ V
/'
/
/
/
I
7
6
IS
Z4
3
2
o
o
10 20 30 40 ISO 60 70 80 90 100
x
THERMAL RISE OF A PLUME SHOWING
RELATIONSHIP BETWEEN x AND Z
-------
73
DAVIDSON-BRYANT PLUME RISE FORMULA
lIh =
dC)" (1 + ~:)
where:
lIh = predicted rise of the plume above the stack top (meters)
d
= stack e~it diameter (meters)
Vs ~ stack gas exit veloc~ty (meters per second)
'IT
=
mean horizontal wind speed (meters per second)
liT = temperature difference between exit stack gas and ambient air (OK)
~ = absQlute temperature of stack gas (OK)
~
-------
where:
74
CSANADY PLUME RISE FORMULA
6h = 250 1-
_3
u
6h = predicted rise of the plume above the stack top (feet)
F
= flux due to buoyancy and momentum = Vsr2b (feet4 per second3)
Vs = stack gas exit velocity (feet per second)
r
= stack exit radius (feet)
b
Pa - P
= buoyant acceleration at top of stack = g
(feet per second2)
P
where:
P
= density of effluent (pounds per cubic foot)
Pa = density of atmospheric air (pounds per cubic foot)
= acceleration due tQ gravity (feet per second2)
g
u
= mean horizontal wind speed (feet per second)
-------
where:
75
CONCAWE PLUME RISE FORMULA
6h = 0.175
[QH 1/2J
-3/4
u
6h = predicted rise of the plume above the stack top (meters)
u
= mean horizontal wind speed (meters per second)
QH = heat emission (calories per second)
-------
76
LUCAS. MOORE. AND SPURR PLUME RISE FORMULA
IF ~~ > 0
0.7 aN
[::t'
6h =
u
IF de < 0
dz -
r 1/'+]
6h = ~ L QN u
where:
6h = predicted rise of the plume above the stack top (feet)
~ = stack height factor (dimensionless)
aN = 4.500
for Hs = 200 feet
5.000
= 300 feet
5.500
~ 400 feet
-
u
= mean horizontal wind speed (feet per second)
QN = heat
emission
(megawatts)
GN = stability parameter =
108 de
dz
_2
U
(dimensionless)
de
-=
dz
change of potential temperature with height (OK per 1.000 feet)
-------
77
OPTIMIZED LUCAS, MOORE, AND SPURR PLUME RISE FORMULA
IF de > 0
dz
~h ' (0. 7) ~55DD) [~: l"
IF ~ < 0
dz -
(5500) QN,20
6h =
u
where:
6h = predicted rise of the plume above the stack top (feet)
QN = heat emission (megawatts)
108 de
dz
_2 (dimensionless)
u
GN = stability parameter ~
u
= mean horizontal wind speed (feet per second)
~~ = change of potential temperature with height (OK per 1,000 feet)
-------
where:
78
OPTIMIZED CONCAWE PLUME RISE FORMULA
[QH' 444]
6h = 0.414 u.694
6h = predicted rise of the plume above the stack top (meters)
QH = heat emission (calories per second)
-
u
= mean horizontal wind speed (meters per second)
-------
79
OPTIMIZED CSANADY PLUME RISE FORMULA
(F ),27
6h = C U3
where:
6h = predicted rise of the plume above the stack top (meters)
C
= stability coefficient (dimensionless)
g
= acceleration due to gravity (meters
g Vsr2 (~:)
per second 2)
(meters4 per second3)
F
= flux due to buoyancy and momentum =
Vs = stack gas exit velocity (meters per second)
r
= stack exit radius (meters)
6T = temperature difference between exit stack gas and ambient air (OK)
Ta = ambient air temperature (OK)
u
mean horizontal wind speed (meters per second)
C VALUES FOR OPTIMIZED CSANADY FORMULA
150
(/) 140
I.LJ
:::>
...J
<:
>
c..> 130
120
110
-.002
o .002 .004 .006 .008 .01 .012
POTENTIAL TEMPERATURE GRADIENT Ae/tJ.Z (oK/M)
.014
-------
Symbol
B
b
C
d
D
e
F
g
G
GN
H
s
t.h
J
R,
In
n
Q
QH
NOMENCLATURE
A value ranging from 1 at zero stack spacing
to 0 at approximately 3,000-foot stack
spacing
Pa - P
Buoyant acceleration at top of stack = g
P
Stability coefficient
Stack exit diameter
Difference between ambient temperature and
stack gas temperature at stack top
Napierian base = 2,71828
Flux due
g Vsr2
to buoyancy
t.T or Vsr2b
T
and momentum =
Acceleration due to gravity
Change of potential temperature with height
from stack top to plume top
Stability parameter =
108 ~
dz
_2
u
Height of stack
Ris e 0 f the plume above the stack top
[ T 1/' V T]
-z - 0 . 43 ( g~ ) -
u 0.28 s 1 + 1
(Q Vs) 1/2 gD
F
-3
U
Logarithm to the base e
Number of stacks
Stack gas emission rate converted to
temperature T1
Heat emission
80
System of Units
dimensionless
ft./sec2
dimensionless
m.
OK
dimensionless
m, 4/sec.:3 or
ft. 4/sec. 3
m./sec.2 or ft./sec.2
OK/ ft.
dimensionless
ft.
m, or ft.
dimensionless
ft.
dimensionless
dimensionless
m.3/sec. or
ft. 3/sec.
cal./sec.
Page 1 of 2
-------
Symbol
QN
r
T
Ta
T1
Ts
6T
U4
U3
U2
Ul
u
Vs
x
Xl
z
~
e
p
Pa
de 1'::.8
- or -,;-
dz oZ
NOMENCLATURE (continued)
Heat emission
Stack exit radius
Ambient air temperature
Ambient air temperature
Temperature at which density of flue gases
is equal to that of the atmosphere
Absolute temperature of stack gas
Temperature difference between exit stack
gas and ambient air
Mean horizontal wind speed at stack top
Mean horizontal wind speed at plume bottom
Mean horizontal wind speed at plume top
Mean horizontal wind speed at plume centerline
Mean horizontal wind speed between stack top
and plume top
Stack gas exit velocity
Distance downwind from stack
Distance downwind from stack where the plume
levels off
Predicted rise of the plume above the stack
top for a given x
Stack height factor
Plume angle off the line of stacks
Density of effluent
Density of atmospheric air
Change of potential temperature with height
81
System of Units
mw
m. or ft.
OK
OK
OK
OK
OK
m./sec.
m. /sec.
m./sec.
m./sec.
m./sec. or ft./sec.
m./sec. or ft./sec.
ft.
ft.
m. or ft.
dimensionless
degrees
lbs./ft.3
lbs./ft.3
°K/lOO m. or
°K/l,OOO ft.
Page 2 of 2
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