;LEAI
,OCT 28 1971
WATER POLLUTION CONTROL ItSSEARCH SERIES • 16130 DNH 01/71
POTENTIAL ENVIRONMENTAL MODIFICATIONS
PRODUCED BY
LARGE EVAPORATIVE COOLING TOWERS
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the
results and progress in the control and abatement of pollu-
tion of our Nation's waters. They provide a central source
of information on the research, development, and demon-
stration activities of the Water Quality Office, Environ-
mental Protection Agency, through inhouse research and grants
and contracts with Federal, State, and local agencies, re-
search institutions, and industrial organizations.
Inquiries pertaining to the Water Pollution Control Research
Reports should be directed to the Head, Project Reports
System, Office of Research and Development, Water Quality
Office, Environmental Protection Agency, Washington, B.C. 20242.
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POTENTIAL ENVIRONMENTAL MODIFICATIONS
PRODUCED BY LARGE EVAPORATIVE COOLING TOWERS
by
E G & G, Inc.
Environmental Services Operation
Boulder, Colorado
for the
WATER QUALITY OFFICE
ENVIRONMENTAL PROTECTION AGENCY
Program #16130 DNH 01/71
Contract 14-12-542
January 1971
Por sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price 75 cents
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EPA Review Notice
This report has been reviewed by the Water Quality Office,
EPA, and approved for publication. Approval does not signi-
fy that the contents necessarily reflect the views and poli-
cies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement
or recommendation for use.
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ABSTRACT
The objective of the study was to develop techniques for evaluating the
extent of plumes from large evaporative cooling towers. Analytical tech-
niques were used to describe the dynamics of the wet cooling tower plume
and its interaction with the environment. Primary emphasis was placed on
predicting the height of the plume. Classical atmosphere diffusion theory
was used to determine the downwind spread.
The study showed that the saturation deficit of the atmosphere clearly
controls the downwind spread of the ejected liquid water. Except for
cases where the relative humidity approaches 100%, downwind propagation
is limited to periods when the air temperature falls below the freezing
point. For a given set of atmospheric conditions, increases in the tower
radius, the saturation temperature, and the initial vertical velocity of
the plume contribute to increasing the final plume height.
The potential for adverse atmospheric effects due to cooling towers was
analyzed on a national basis and is presented in the form of a map of
the United States.
A computer program was developed to perform the necessary calculations.
The Appendix contains a description of the program, including input speci-
fications.
This report was submitted in fulfillment of contract number 14-12-542
under the sponsorship of the Water Quality Office of the Environmental
Protection Agency.
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TABLE OF CONTENTS
Section Page
1. 0 INTRODUCTION 1
1. 1 Tower Characteristics 2
1. 2 Scope of the Study 2
2. 0 TOWER PLUME AND DIFFUSION MODEL 5
2. 1 Plume Dynamics 5
2. 2 Downwind Diffusion 9
2. 3 Summary of Numerical Model 10
3. 0 SATURATION REQUIREMENTS 15
3. 1 Properties of Natural Fogs 16
3. 2 Dropsize Characteristics of Cooling Towers 17
3. 3 Parameterized Cloud Physics 17
4.0 CALCULATIONS 21
4. 1 Tower Parameters 21
4. 2 Penetration Height of the Plume 24
4. 3 Moisture Effects 24
4. 4 Case Studies 24
4. 5 Topographical Effects 27
4. 6 Summary of Calculations 33
4. 7 Prevention of Adverse Conditions by Seeding 34
5. 0 REGIONAL CHARACTERISTICS 36
5. 1 Site Evaluation 37
5. 2 Specific Criteria 37
REFERENCES 41
LIST OF FIGURES 43
LIST OF SYMBOLS 45
APPENDIX A - Computer Program 4 8
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SECTION 1. 0
INTRODUCTION
Recent studies indicate that the electrical power needs in the United States
are doubling every 6 or 7 years. To meet this need an increasing number
of steam electric generating facilities are required. One of the salient
features of these plants is that they require large quantities of cooling water.
This increased demand for cooling water has brought forth an environmental
problem called "thermal pollution", which is caused by the discharges of
large quantities of waste heat from the electrical power plants into various
natural waterways. Due to the likely adverse consequences of increased
temperatures from the discharged effluent on aquatic life, there has been
an increasing demand for alternative methods of cooling which would dissipate
the waste heat in a more preferable manner.
One of the more favored means of solving the thermal pollution problem is
the use of large evaporative cooling towers, which dissipate the waste heat
directly into the atmosphere. With the recent application of large cooling
towers in the United States, some concern has been expressed about the
possible adverse environmental consequences of the effluent discharges to the
atmosphere from the towers. In certain climates, the evaporation of water at
rates of several thousands of gallons per minute may create modifications
to the local environment through formation of fog, icing on nearby structures,
and "flashing" of transmission lines downwind of the tower. Other possible
adverse conditions such as haze formation, icing of bridges, and destruction
of crops have also been suggested.
The probability of a cooling tower causing adverse environmental modifications
is a function of the characteristics of the tower (height, exhaust velocities,
temperature, etc.) as well as the characteristics of the local climate near
the tower site. Certain areas have wind, stability, and humidity conditions
necessary for occurrence of adverse effects whereas many areas have condi-
tions where the tower effluent is dispersed effectively with insignificant environ-
mental modification resulting.
It is important to the orderly development of our national economy that a
rational delineation of the potential of inadvertent environmental modification
by cooling towers be obtained as soon as possible. Thus, this study was
initiated to analyze the physical consequences of the ejections of cooling tower
effluents and their subsequent dispersal into the environment. The prime
objective of the study has been to develop a predictive model from which the
general behavior of the cooling tower plume can be assessed in terms of
various meteorological conditions and local terrain features. In addition,.
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geographical regions throughout the United States have been classified as
to the potential for adverse effects occurring from the application of cooling
towers.
1. 1 Tower Characteristics
Cooling towers may be classified as wet type where water and air come in
direct contact or dry type where cooling is through indirect contact of heat
exchangers. The movement of air for both types may be created either by
mechanical draft with fans or by natural draft through a chimney.
In the dry type cooling tower, indirect heat transfer is by conduction and
convection through finned tube cooler sections, instead of evaporation. There
is no evaporative loss with subsequent water makeup requirements, but greater
air movement is necessary to reject the heat. Cooled water from the tower
is introduced into a direct contact jet condenser where it picks up heat and
then is returned to the tower for cooling. The dry type has poorer efficiency
than the wet type, and hence is less economical. Since no water is lost in
the dry type, it does not represent as clear a potential for inadvertent
environment modification as does the wet type, and it will not be considered
in this study.
In the wet type cooling tower, water is sprayed onto a lattice network (packing)
through which air is moved resulting in evaporative heat transfer. One type
of tower currently favored, the hyperbolic natural draft unit, is shown in
Figure 1.
The evaporation process in a tower such as shown in Figure 1 results in
cooling of the water by about 20°F. The cooled water is collected in a basin
under the fill. Solids in the water accumulate in the basin, and the wastes
are periodically removed by blow-down. Make-up water in the order of 3% of
the flow circulated is necessary to replenish evaporation and blow-down losses.
The make-up water may be chemically treated to protect the fill from deterior-
ation and the spray nozzles from plugging.
Typical large evaporative towers discharge 10,000 gpm and several towers may
be utilized at a given site. The subsequent interaction with the atmosphere
of these large fluxes of water is the primary concern in terms of possible
adverse effects.
1. 2 Scope of the Study
The main objective of this study has been the development of techniques to
model and predict the behavior of cooling-tower effluents when discharged into
the atmosphere under various meteorological conditions. The study is limited
to numerical calculations of the general characteristics of plume behavior.
Parameters used in the numerical model are those for typical wet-type natural
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Hot Water
Distribution
Asbestos Cement
Fill
DIMENSIONS OF
KEYSTONE GENERATING
STATION TOWERS
Height - 325 Ft.
Base Dia.-247Ft.
Top Did.- IA2 Ft.
Air Inlet - 26Ft.
Cold Water Bavin
Depth -6Ft.
Design Capacity-
56O.OOO gpm
II8»F to 9O°F
Cold Water Basin
FIGURE I. NATURAL DRAFT WET (Evaporative) COUNTERFLOW
TOWER FROM FWPCA
(1968)
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draft (hyperbolic) towers such as those at the Keystone Site in Pennsylvania.
Some consideration is also given to the behavior of plumes from mechanical
draft towers.
Due to the complexity of the problem, a considerable number of empirical
and parameterized concepts have been employed to develop a practical model.
The overall aim has been to develop a model that is readily useable rather
than one of rigor and complexity. Definition of important parameters and
their sensitivity to local variations has been a part of the study.
Various climatic regions throughout, the United States have been classified in
terms of the frequency of meteorological conditions favorable to adverse effects
from cooling tower plumes.
Clearly, a firm understanding of environmental modification by cooling towers
will have to be established by proper measurements in the vicinity of operation-
al towers, in order to validate and refine the theoretical concepts. However,
field measurements are beyond the scope of the present study. Besides proper
meteorological measurements, ecological monitoring will also be necessary
to evaluate the total influence of the tower effluent on the environment.
In summary, this study is regarded as one step in what necessarily must be
a broad program to properly evaluate the general application of large evap-
orative cooling towers throughout the United States.
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SECTION 2. 0
TOWER PLUME AND DIFFUSION MODEL
Study of the ejection of cooling tower effluents into the atmosphere
and subsequent dispersal into the environment involves knowledge of
several complex processes. In this study we have considered the
problem in the following phases:
(a) Dynamics of the wet effluent plume and its immediate
interaction with environment through entrainment. Primary emphasis
has been placed on predicting the height to which the plume penetrates.
(b) Horizontal diffusion of the ejected water vapor and its
contribution to the local saturation deficit.
A. subdivision of the problem into conditions in the immediate vicinity
of the tower (vertical plume) and those downwind (diffused plume) is
of obvious use in clarifying the important meteorological parameters.
2. 1 Plume Dynamics
The phenomena controlling the vertical growth of the wet plumes
from cooling towers are different from those controlling the movement
of dry particulate smoke, due to the energies involved in evaporation
and condensation in the wet plume and the buoyancy accelerations
produced. In this situation, the buoyancy forces are produced locally
rather than being a function of the initial temperature of the effluent
alone. Thus, the dynamics of the cooling tower is more closely
related to that of an isolated cumulus cloud, where condensation warms
the core of the plume while evaporation and chilling occur near the
edges.
Clearly the buoyancy of the wet plume will significantly influence the
vertical penetration. In fact, it is known that the observed plume
rise of cooling tower effluents is considerably greater than the values
calculated on the basis of initial effluent temperature alone. This
additional penetration is obviously important in assessing the close-in
characteristics.
Most previous studies of the behavior of effluent from stacks have
been based on the concept that the horizontal diffusion is equivalent
to that from a source at an "effective" stack height in place of the
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actual source, where the effective stack height is defined as the
height at which the plume becomes nearly horizontal. Methods for
determining effective stack height have produced varying results.
A summary of the present status has been prepared recently by
Briggs (1968). In this study we will assume that the plume grows
in a vertical column (tilted due to wind shear) and that the maximum
height of penetration of the column is of importance for prediction of
local modification (subsequently horizontal diffusion will be used to
spread the column downwind).
Over the past several years considerable progress has been achieved
in the application of numerical models to cumulus clouds (alikened
to moist buoyant plumes). One of the more widely used cumulus
models is the one -dimensional dynamic model with parameterized
entrainment and microphysical relationships. In this study, we
proceeded by modifying the cumulus model (Davis, 1967, Weinstein
and Davis, 1968) such as to make it more applicable to wet effluent
plumes.
The approach used in the model is to apply the vertical equation
of motion and the first law of thermodynamics with parameterized
relations for plume mixing, water particle growth, fallout, and
evaporation. Numerical calculations are carried out by lifting
incremental portions of the plume adiabatically through successive
vertical steps, and at each interval allowing mixing or entrainment
to occur with the environment.
The mathematical form of the model will be outlined here with emphasis
on those features unique to the cooling tower plume. For a detailed
derivation of the basic cumulus model equations, see Weinstein and
Davis (1968).
The vertical equation of motion can be written as (see list of symbols):
2
i dw dw 1
where the drag forces will be provided by the weight of liquid water in
the air and by mixing with entrained air. Thus,
Assuming that the plume environment is in hydrostatic equilibrium, and
that there is no horizontal pressure gradient between the plume and
outside air,
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- Peg'
.
and so
1 dw
2 dz
_
" g
T - T
v ve
T
ve
- gQ -
(1)
Equation (1) is the energy equation for our plume model. The first term
on the right is the buoyancy term, the second the drag due to the liquid
water, and the third the loss due to mixing with the slow-moving or station-
ary environmental air.
The temperature distribution with height in the ascending plume can be derived
using the first law of thermodynamics and the Clapeyron equation for variation
of saturation vapor pressure with temperature. The result is:
dT
dz
-g
e |- u(T-T ) -
~ O
=
C • •t*' J-
P »
i e
c
P
vq~v
c dz
P
c dz
P
(2)
c RT2
P
The terms on the right represent (from left to right) the moist adiabatic
temperature decrease, (the change in temperature resulting from adiabatic
expansion, with latent heat of condensation released by the condensation of
all vapor over saturation) the loss of heat to warm the entrained air, the
loss of heat to resaturate the entrained air, the heat released by freezing
liquid water, and the heat realized by the sublimation of the excess vapor
after freezing. The last two terms are applicable only to the height incre-
ment, dz, during which the phase change is occurring. After the glaciation
procedure has been completed, the moist adiabatic process is assumed to
be ice saturated and L replaces L in the first part of equation (2).
S 6
In this model, it is hypothesized that mixing or entrainment occurs through
a continuous incorporation of environmental air around the edges of the upward
moving plume. Several theoretical and observational studies have suggested
that the entrainment rate is inversely related to the plume radius,
i dM
M dz
R
(3)
"
where the entrainment ^ has dimensions (length) , R is the plume radius and
the dimensionless constant A depends upon the specific character of the plume
and thus must be determined experimentally.
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Laboratory studies suggest that the value of A should be .15 to . 22. In
this study we have used A = . 20. The variation of R with height along
the plume has been taken to be:
R = R + z sin a (4)
s
where Rs is the stack radius, z is height, and a is the half-angle of the
plume spread.
The correction to the computed vertical velocity due to the shear of the
horizontal wind follows the concepts outlined by Malkus (1952). The slope
of the plume as a result of a vertical shear of the horizontal wind is given
by:
tan 9 -^-
P
where the vertical velocity is w and the horizontal speed of the air in the
updraft is Up. If the vertical velocity (wp) calculated from equation (1)
is taken as the hypotenuse of the triangle given by the above relationship,
the true vertical velocity can be calculated.
2 2 /TT \2
w = w - (U )
P P
Up is obtained by considering the horizontal momentum in the cloud mass
before and after entrainment of environmental air.
(Momentum) 0 = (Momentum), + (dM)U
2 1 e or
U0 (M + dM) = MUn + (dM)U
2 1 e
with the definition of fi, u = — -j^~ , the above relationship can be stated as:
U + ydzlT
U =
.
2 1 + jidz
Substituting the above into the solution for w given earlier yields the final
form of the relationship:
2
w
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Utilizing the above set of equations, along with specifications of the initial
conditions (tower radius, initial plume velocity, effluent temperature) and
the environmental conditions (vertical distributions of temperature, humidity,
and wind) calculations of plume updraft velocities, change in plume radius,
liquid-water content, and maximum plume height can be obtained. These
vertical profiles of plume parameters are used in the next sections as inputs
for the second phase of the model which covers the diffusion and downwind
spread of the plume.
2. 2 Downwind Diffusion
The common practice for the analysis of diffusion of stack effluents is to
use an "effective" stack height in conjunction with relationships derived for
horizontal and vertical diffusion. The most widely used formulas are slight
modifications of those first proposed by Sutton.(1953). The relationships selected
for use in the cooling tower problem are of the form
X = 2TT a u exp
2
v z 2a "~ fia
17 y
2
y
(6)
*
where X is the concentration of the effluent, Q is the rate of release of the
effluent, u is the wind velocity, and ci and az are the standard deviations
of the horizontal and vertical concentration distributions. The standard
deviations, a and az, are functions of the distance downwind from the
source and must be specified in equation (6).
Clearly the most important part of using equation (6) for the downwind spread
of the effluent relies in obtaining ze, az, and a We assume that the
dynamics of the plume can be adequately handled as previously described
in order to obtain ae (defined as the altitude where w -» 0). The dependence
of a and QZ on the downwind distance and on local meteorological and
terrain factors is much more difficult. In fact, it is unlikely that a single
functional relationship can be found to describe the dependence of a and az
on the downwind distance for all values of the downwind distance. During
the early phase of the plume propagation the primary mechanism of dispersal
is the self-generated turbulence of the plume, or is due to turbulence generated
by local structures such as buildings and other towers. On the other hand,
at sufficiently large times the dispersal is primarily controlled by the ambient
turbulence of the atmosphere. The dispersion at intermediate times would
presumably depend on both the self-induced and ambient turbulence.
Csanady (1968) proposes that during the initial phase (within about 2 km from the
source) the standard deviations can be assumed to grow linearly with distance
from the source. That is, one can let
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CTy = pyx and °z = pzx
where py and p are constant. Equation (7) implies that the concentration
profiles are self-preserving with increasing distances from the source. It
can also be easily demonstrated that equation (7) is equivalent to assuming
that the entrainment parameter, A, is a constant, since equation (7) essent-
ially implies a linear rate of growth of the plume. In practice, we have
chosen p and pz empirically to give observed rates of plume spread con-
sistent with the angle a. introduced in equation (4).
At sufficiently large distances from the source the influence of the ambient
turbulence on the dispersion is of primary importance. Sutton (1953) gives
the following expressions:
0 = .JL x V* • * / (8)
z /2
where c and cz are appropriate constants (depending on the atmospheric
conditions) and the quantity p is the index corresponding to a power-law fit
for the atmospheric wind profile. That is, the wind profile is approximated as
/ u. . z v p
* ux z/ (9)
where Uj and Zj, are convenient reference values.
Pasquill(1961) and Turner (1967) have conveniently reduced these relation-
ships and observations of plume spread to a simple set of graphs which
express ay and a as functions of distance and stability class. Turner's
curves are given in Figures 2 and 3.
In the present study, equation (7) has been used for distances less than 2 km
from the source, and for distances greater than 2 km values of av and az
were obtained from Figures 2 and 3 with proper selection of stability class.
2. 3 Summary of Numerical Model
The model developed to simulate the behavior of the cooling tower effluent
can be divided into two phases; (a) the immediate stack region (less than
2 km from the source), and (b) the downwind region where ambient dispersal
10
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1,000
500
200
100
ISI
b
0.1
I 2 5
DISTANCE DOWNWIND, km
10 20
50 100
FIGURE 2. VERTICAL DISPERSION COEFFICIENT AS A FUNCTION OF DOWNWIND DISTANCE
FROM THE SOURCE. FROM TURNER (1969)
11
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10,000!
5,000
O.I
12 9 10
DISTANCE DOWNWIND, km
20
50 100
FIGURE 3. HORIZONTAL DISPERSION COEFFICIENT AS A FUNCTION OF DOWNWIND DISTANCE
FROM THE SOURCE. FROM TURNER
(1969)
12
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is predominent. In the immediate stack region the internal dynamics and
the vertical penetration of the plume is of prime importance.
Here we assume the cooling tower effluent to behave as a moist jet similar
to isolated cumulus clouds. We compute the temperature and buoyancy
changes in the plume using equation (2) which accounts for moist adiabatic
ascent, the losses due to mixing and evaporation, and the possible additional
heat derived from freezing of the effluent water. The computations are
accomplished using vertical steps of 50m intervals. Next, vertical velocities
of the plume are obtained from equation (1). The local buoyancy is used to
accelerate the plume while the weight of the water material and the entrain-
ment of environmental air drag the plume and cause it to decelerate.
The most critical relation in this phase of the plume growth is the para-
meterization used to simulate the self-induced turbulence and hence entrain -
ment. Our best information at this time is that the relations in equation
(3) and (4) appear to be adequate. However, further field measurements
will be necessary to confirm these relations.
Utilization of initial conditions (tower parameters), the atmospheric sound-
ings, and equations (1-4) allow the computation of the vertical profile of the
plume core and yield distributions of plume temperature, vertical velocity,
liquid water content, and spread of plume radius. The horizontal tilt of
the vertical plume due to wind drag is obtained using equation (5).
In the immediate vicinity of the tower (<2km) the diffusion of material from
the edges of the plume is obtained using relations for az and ay given in
equation (7), where pz and py are related to the half-angle spread, a, which
has been determined empirically. Due to the high internal vertical velocities
of the plume, local erosion near the height of the stack is small except
for atmospheric conditions in which the winds are gusty and the environment
is unstable. The emphasis on this portion of the model is the adequate
determination of plume penetration heights as a function of the tower para-
meters, and the local meteorological conditions.
In the second phase of the model the distributions of effluent are dispersed
downwind utilizing diffusion parameters which are related to the ambient
turbulence. The main result is to diffuse the effluent near the maximum
height of the plume (where the plume vertical velocity approaches zero and
the horizontal tilt is large) in the downwind direction. This is equivalent
to the standard stack-diffusion procedures which utilize equation (6) and
Figure 2 and 3.
Thus, the model simulates in numerical form the buoyant rise of the plume,
which is dragged by the weight of the material and depleted .by the local
entrain ment of environmental air. The height at which the plume's acceler-
ations are depleted and it is bent over by the horizontal wind is critical to
the subsequent downwind spread of the material by ambient diffusion. The
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immediate or local diffusion is obtained by linear expansion of the local
entrainment.
Throughout this portion of the model we have not discussed the effluent
water particle distribution or microphysical processes influencing the
plume. These relations will be discussed subsequently. Thus far, we
view the effluent as small water droplets moving through the plume area
and evaporating at the edges. The evaporated water mass is then diffused
outward and contributes to raising the ambient water vapor content.
14
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SECTION 3.0
SATURATION REQUIREMENTS
The major emphasis of this study is the concern over the modifications to
the local and downwind environment as the result of the ejection and diffusion
of the cooling tower vapor effluent. Specifically, the concern is to determine
what conditions are necessary for the additional water from the tower to be
of sufficient quantity to raise the local humidity to saturation, and hence
lead to formation of fog and haze. In addition, the relative distances and
volumes of the modification are of concern.
In order to properly define this aspect of the problem it is important to point
out how the water vapor content necessary to saturate the atmosphere varies
with temperature in the following manner:
_3
Temperature - °C Saturation Vapor Content - g m
-20° 0. 894
-10° 2.158
0° 4. 847
+10° 9.401
+20° 17.300
Next, we will define the saturation deficit, q^ as the difference between the
saturation mixing ratio at a given temperature, qg, and the local ambient
mixing ratio, q . Since the cooling tower effluent merely adds an incremental
amount of water vapor, Aq, to the local atmosphere, the relation of import -
ance for non-fogging is:
qs ' qe = qd > Aq
The importance of ambient temperature can now be seen since Aq. several
kilometers downwind for typical cooling towers is the order of 0. 1 to 0. 5 g
m~3. If the ambient temperature is 10°C and the local humidity is 50%
(qe = 4. 7 g m"3) then qd = 4. 7 g m"3. The addition of Aq = 0. 2 g m~3
from a cooling tower would only change the humidity 3%. On the other hand,
at -10°C and 90% humidity the addition of Aq = 0. 2 g m~3 would lead to
saturation. Thus, clearly the ambient temperature is of prime importance
in determining the saturation deficit and thus the conditions for the tower
effluent to contribute enough water vapor to cause fog development.
15
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3. 1 Properties of Natural Fogs
The formation of natural fog occurs through local cooling of the atmosphere
by radiation losses, or through advective changes in temperature or moisture,
with subsequent mixing leading to saturation. Table 1 summarizes the
properties of "tyPical" fogs classified as radiation (inland) and advection _3
(coastal). It can be seen that the typical water contents are . 1 to . 2 g m ,
the droplet diameters average 10/j to 20u, and particle concentrations vary
from 40 cm~3 to 200 cm"3. Around industrial areas where sources of
pollution are prevalent droplet concentrations will tend to be higher.
The visual range or horizontal visibility in a fog is related to the average
size of the fog droplets and the liquid water content by the following equation
which was derived by Trabert in 1901.
V- .
V " Q ) 2 Q
c L, n r
c
where Q = liquid water content, nr = number of droplets of radius r,
C = constant, and K = constant. Clearly the visibility decreases with
increasing liquid water content and with smaller average droplet diameters.
Visibility reduction can begin at humidity values well below 100% due to water
TABLE 1
PHYSICAL FOG MODELS
Fog Parameters Radiation (Inland) Advection (Coastal)
at the Surface Fog Fog
1. Average Drop Diameter 10 u 20 |U
2. Typical Drop Size Range 5-35 ,u 7-65 \i
3 3
3. Liquid Water Content 110 mg/m 170 mg/m
-3 -3
4. Droplet Concentration 200 cm 40 cm
5. Vertical Depth of Fog
a. Typical 100 m 200 m
b. Severe 300 m 600 m
6. Horizontal Visibility 100 m 300 m
16
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absorption by hygroscopic nuclei. Thus, the characteristics of the plume
chemicals and other nearby industrial pollutants become important as inter-
mixture with the water vapor plume may occasionally enhance the reduction
in visibility.
3. 2 Dropsize Characteristics of Cooling Towers
Very little observational data are available as to the dropsize characteristics
of the cooling tower effluent. Ledbetter, (1969) has recently completed
a laboratory study in which he attempted to simulate the cooling tower and
subsequently measure the dropsize distributions generated.
Figure 4 is an example of the results obtained by Ledbetter. The distribution
was found to be bi-modal with the first peak <5)u diameter (probably 2-3|i) and
the second in the range 20-40^. These experiments suggest that the water
droplet size distribution of cooling tower effluents is similar to that of
natural fogs. The reason for the distinct bi-modal distribution is not clear,
however.
3. 3 Parameterized Cloud Physics
To simulate the microphysical processes which occur in the moist ascent of
the plume we have used the parameterized representation given by Kessler
(1962, 1963, 1964). It is assumed that the development of water droplets
can be divided into three phases: condensation (vapor to liquid), auto con-
version (bulk process for changing the small condensed droplets to larger
drops), and coalescence (the collection of droplets by the larger drizzle-size
drops).
It is further assumed that the liquid water content of the plume can be
represented by two groupings called cloud water (droplets with no appreciable
fall velocity) and hydrometeor water (larger drops with fall speeds).
The change in cloud water is expressed as:
In addition, the change in hydrometeor water is:
d«h K! «. -> + •S^cS.0'876
"S" " (w - VJ (w - VJ U2)
17
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9-10
10-20 20-40 40-60 60-80
DROPLET DIAMETER (ft)
•0-100
FIGURE 4. DROPLET SIZE DISTRIBUTION FROM LABORATORY EXPERIMENTS
(LEDBETTER, •*«!, 1969)
18
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where Kj, K2, and (a) are coefficients relating to the microphysical con-
version rates. The terminal fall velocity is expressed as:
V, = 4. 5Q °' 125 (13)
t n
assuming the drop size distribution given by Marshall and Palmer (1948).
The model computes the total rainfall from the plume assuming that the
fallout is developed (conversion to hydrometeor water) during the vertical
ascent in the plume, and all converted hydrometeor water subsequently falls
out of the plume somewhere downwind. The computed rainfall is the max-
imum possible, since evaporation below the plume is not included here.
Thus, total rainfall is given by:
R = I oQ, dz (14a)
which is approximated by:
R = ) pR .
o £ ^ 01
(Q,9 + Qh1) dz
where R . = ™ 0 ni (14b)
Ol ^
This computation of "total rainfall" is useful in the original cumulus cloud
model, as it gives an estimate of total precipitation during the lifetime of
an isolated convective cloud. However, total rainfall is not really relevant to
a continuing convective plume, as from cooling towers, except as a relative
measure of precipitation potential. But it is also possible to convert the
computed water content into rainfall rate and radar reflectivity. With the
assumption that the hydrometeors are formed into a Mar shall-Palmer drop
size distribution, the following well-known relations are obtained:
Qh = 72 x 10"3 Rj0'88 (15)
where Q^ is in g/kg and R , the rainfall rate, is in mm/hr; thus,
19
-------
R, = 14 Q *'136 (16)
i n
fi q
and radar reflectivity Z, in units of mm /m is
Z = 200
At temperatures below 0°C, freezing is allowed to occur and release additional
latent heat. The microphysical conditions are handled in a similar manner
as above, but with different values for Kj, K^. a, and V^.. Experience has
shown that natural freezing of moist plumes in the atmosphere is unlikely
until the ambient temperatures approach -20°C.
20
-------
SECTION 4. 0
CALCULATIONS
The computerized version of the model that has been presented was used
to analyze the behavior and subsequent downwind spread of cooling tower
plumes. The input data used were the tower parameters and the vertical
distributions of ambient temperature, wind and relative humidity. A
number of model runs were obtained to analyze the effects of various
parameters on the general plume behavior.
4. 1 Tower Parameters
Most computer runs were conducted using the following tower characteristics:
Height = 50m, Velocity = 5.0 m/sec, Radius = 30m, and Saturated Temp-
erature of 90°F. However, variations of these parameters were also studied.
Figure 5 shows a typical profile of vertical velocity, and plume temperature
along with the variation of plume radius as derived by the model. The
effect of tower radius is shown in Figure 6. It can be readily seen that
the penetration height is significantly greater for increasing tower radii.
This is due to the fact that local entrainment and erosion is inversely
proportional to the radius of the local updraft.
The height of the tower above ground was found to have a negligible effect
on the penetration of the plume. This is due to the large buoyancy of the
initial updraft, which overshadows any reasonable changes in tower height.
The height of the tower must be considered when other structures are
placed in the vicinity, however, because local turbulence generated by
additional structures can change the above results.
Increases in tower temperature (saturation) and in the initial vertical velocity
clearly increase the penetration height of the tower plume. Thus, in the
design of towers, factors which promote greater penetration are first the
tower radius, and secondly the effluent temperature and draft velocity.
The preceding results are directly relevant to natural draft cooling towers.
The model is equally applicable to mechanical draft towers, since the only
tower parameters that need to be specified are height, radius, velocity, and
temperature. Since individual mechanical draft towers are limited in
radius to approximately 10 meters or less, it can be seen from Figure 6
that mechanical draft towers generally have limited penetration height
compared to the larger natural draft towers.
21
-------
2000
1800
1600
1400
1200
1000
800
o 600
Cu
400
200
VERTICAL VELOCITY
TEMPERATURE EXCESS
RADIUS
-2
I 1
6 8 10 12 14
VERTICAL VELOCITY -m/sec
4 6 8 10 12
TEMPERATURE EXCESS - 0°C
16 18 20
14 16
20 40 60
80 100 120
RADIUS -m
18
140 160 180 200
FIGURE 5. EXAMPLE OF NUMERICAL MODEL RESULT FOR A COOLING TOWER PLUME,
22
-------
2000
1800
I
oc
UJ
1600
1400
s
CD
X
(9
<
UJ
UJ
Q.
1200
1000
800
600
400
200
10 15 20 25 30 35 40
STACK RADIUS - m«ter«
45
50 55
60
FIGURE 6. EFFECT OF STACK RADIUS ON PENETRATION HEIGHT
23
-------
Several mechanical draft towers are usually used to provide a capacity equal
to a single large natural draft tower. In general, the combined plume from
the mechanical towers will have less vertical penetration than would a plume
from a single hyperbolic tower having equal volume. The discrete small
plumes may merge, but they do so with a large initial increase in entrain-
ment, because of the dry environmental air from between individual towers.
The modeling results indicate that mechanical draft towers as currently
used will always result in less penetration and greater potential for adverse
environmental effects than typical large natural draft towers.
4. 2 Penetration Height of the Plume
Figure 7 shows the effects of atmospheric stability on the penetration height.
Distributions are given for isothermal conditions, for a 5°C inversion and
a 10°C inversion (up to 300m, then isothermal above, all for surface T-0°C).
These curves clearly show that the initial buoyancy of the cooling tower
plume is sufficient to penetrate many low-level inversions if the wind is not
strong.
Wind and wind shear tend to accentuate the effects of stability and bend the
plume over, reducing the total penetration height. This is due to the increased
momentum exchange and the overall drag, causing the plume to yield to the
horizontal momentum of the atmosphere. Calculations show that the plume
core has vertical velocities in excess of 10 m/sec for the first few ten's of
meters and then decelerates very rapidly to the plume top (see Figure 7).
The large decelerations when coupled with horizontal wind drag result in
decreasing the effective plume height and lead to increases of water vapor
downwind, which under proper saturation deficit can yield fog formation.
4.3. Moisture Effects
As pointed out in Section 3. 0, the moisture deficit in the atmospheric layer
penetrated by the plume is of most significance in evaluating the adverse
conditions caused by fogging downwind from cooling towers. Figure 8 shows
a set of computations for a situation with a 10°C inversion and relative
humidity in the plume layer varying from 50% to 100%. It is clear that
the atmosphere's capacity to receive water fluxes typically generated by
cooling towers is generally good for these temperatures and normal humidities.
Thus, it can be clearly established that conditions suitable for fogging and
downwind visibility effects from cooling towers are related to moisture
deficits, which are controlled by the local relative humidity and temperature.
4. 4 Case Studies
Several couMivcer runs using actual atmospheric data have been made. These
will be use .-ore to further indicate the behavior of the cooling tower plunv.-
24
-------
iSOOr
1600 -
• 0°C ISOTHERMAL
— 0°C 5° INVERSION TO 300m
— 0°C 10° INVERSION TO 300m
WIND IS CALM
46 8 10 12 14
VERTICAL VELOCITY -m/*ec
16 IB
FIGURE 7. EFFECT OF STABILITY ON PENETRATION HEIGHT
25
-------
2200}
2000-
!300<-
iSOO
E
I
a
U!
O
CO
-.(
X
O
x
•100
100
.02
.04 .06
1.0
2.0
3.0
DOWNWIND DISTANCE —km
FIGURE 6. DOWNWiNO SPREAD OF LIQUID-WATER CONTENT, O.O5 g/m3 CONTOURS FOR VARIOUS
VALUES OF RELATIVE HUMiDITY EXPRESSED IN %
-------
The first case is for the Pittsburgh, Pennsylvania, sounding of 1200Z on
February 28, 1968 (Figure 9). Conditions for the Keystone Site were
utilized; Figure 10 shows the vertical profile of the plume parameters
while Figure 11 shows the results of the downwind dispersion of the
plume. Verification for this case was obtained through personal communications
with Dr. Charles Hosier*, who observed that the height of the plume was
at about 7000 ft. MSL and that the plume spread downwind for a considerable
distance with very light snow flurries falling from the plume. Photographic
measurements of the width of the individual tower plumes indicated a
radius of about 300 meters near the top, which is in close agreement with
the computed radius in Figure 10.
Another example is the Salem, Oregon, sounding for 1200Z on November 11,
1969 (Figure 12). This case is used to demonstrate the effects of a deep
layer of atmospheric moisture which is capped by an inversion and dry
air aloft. Figure 13 shows the distribution of liquid water downwind from
a typical hyperbolic tower.
Many additional runs have been completed which contribute to the general
under standing of the movement of moisture downwind from typical towers.
They will not be presented here but the overall results are given in Section 4. 7.
4. 5 Topographical Effects
Since it is desirable to extrapolate the results of dispersion of cooling-tower
effluents at one location to other locations, one of the necessary assessments
that has to be made is the influence of topographical variations on plume
dispersal. The influence of topography on the plume dispersal may occur
in three ways; firstly, through an effect on the local wind speed and direction,
secondly, through an effect on the characteristics of the atmospheric
turbulence, and thirdly, through the distribution of local moisture sources.
Most of the analyses mentioned above apply to an idealized "infinite-plane1'
ground for which the roughness characteristics are assumed to be
statistically uniform. Moreover, all ambient conditions are assumed to
be uniform and parallel to the ground. Such conditions are seldom realized
in the atmosphere and even over "gently rolling terrain influences can
occasionally be significant. A wind blowing more or less parallel to a
valley may be "channeled" in a direction parallel to the sides of the valley.
*Dean, College of Earth and Mineral Sciences, Pennsylvania State University,
University Park, Pennsylvania.
27
-------
to
OS
a
£
LJ
K
.0
Vi
if}
UJ
1C
Q.
500-
600-
700h
800-
345-08
355-02
900 -,
1000-
MOIST
ADIABATS \
DRY.
Q
UJ
LU
CL
CO
O
h-
o
IU
K
O
O
100-08
100-08
105-06
110-06
FIGURE 9. PITTSBURGH SOUNDING, FEBRUARY 28,1968 1200?
O TEMPERATURE ADEWPOINT
-------
2400
2200
—— VERTICAL VELOCITY
RADIUS
lit
1000
UJ
o
m 800
\
\
•*
•»
^
\
r
a
600
400
200
20
40
8 10 12 14
VERTICAL VELOCITY -m/sec
60
80 100 120
RADIUS - m
140
160
180
200 220
FIGURE 10. VERTICAL PROFILES FOR PITTSBURGH CASE
29
-------
CO
o
2000 -
1800 -
M
ec.
ui
X
—
lil
X
PLUME CENTERLINE CONCENTRATIONS - gm'3
2.0
3.0
DISTANCE - km.
FIGURE 11. Predicted Downwind Liquid Water Content for
Pittsburgh Sounding
-------
500
260-40
MOIST ' -15 \
AOIABATS / \
DRY / \
1000^-
295-10
285-06
200-05
180-08
FIGURE 12. SALEM SOUNDING, NOVEMBER 11,1969, I200E
O TEMPERATURE,
-------
co
to
PLUME CENTERLINE CONCENTRATIONS Qm
-3
1.0
2.0
DISTANCE — km.
3.0
FIGURE 13. Pr»cJif!.ecl Downwind Liquid Water Content for
SI.K '''og Sounding - 11 Nov. 196M
-------
Moreover, when a strong geostrophic wind is blowing parallel to the
valley there may be a funnel effect, and this may influence the cooling-
tower plume. When the geostrophic wind is blowing nearly normal to
the axis of the valley, complex downwash and upwash effects may occur
along the slopes of the valley. The effects of aerodynamic downwash on
chimney plumes have been studied in laboratory wind tunnels. The
cooling-tower plumes from sources located in valleys may also be in-
fluenced significantly by the katabatic and anabatic winds due to differential
cooling or heating.
Topographical features may also influence the dispersion of cooling-tower
effluents through their effect on the characteristics of the ambient
atmospheric turbulence. Topograhical features may cause different rates
of heating at different places, and thus create convective turbulence.
Local sources of water vapor such as rivers, lakes, ponds, etc. will
influence the local saturation deficit and hence be of importance in deter-
mining the cooling tower effects.
4. 6 Summary of Calculations
From the series of model runs the following results were obtained:
(a) For a given set of atmospheric conditions, increases in the
radius of the tower, the saturation temperature, and the stack velocity
contribute to increasing the penetration height of the tower plume. The height
of the tower above ground has a negligble influence on penetration height.
(b) For a given set of tower parameters, stability influences the
penetration height as does the bending-over effect of wind and wind shear.
The most significant parameter in determining the vertical plume dynamics
is the entrainment relation, which is determined by the stack radius and the
angular spread of the plume. Environmental relative humidity is important
in controlling the evaporative cooling at the plume edges and hence the rate
of depletion of thermal buoyancy.
For most cases of light winds ( < 3 msec ), penetration heights of
300-1000 meters are obtained but for stable air with strong wind, the
penetration heights are reduced to a few hundred meters.
(c) The saturation deficit of the atmosphere clearly controls the
downwind spread of the ejected liquid water. Except for cases where the
relative humidity approaches 100%, downwind propagation is limited to
the colder temperature periods typical of fall and winter (< 0°C).
Under calmer winds, penetration is sufficient and little problem is to be
expected near the tower. However, stability can limit penetration such
that strong winds can cause looping. On the other hand, typical moisture
33
-------
deficits occurring with windy conditions may be sufficient to completely
eliminate the appearance of the plume in a very short distance.
In summary, moderate winds with stable lapse rates and low moisture
deficits (high humidity and generally temperatures colder than about 0°C)
provide proper conditions for possible fogging and adverse modifications
downwind of typical cooling towers.
4.7 Prevention of Adverse Conditions by Seeding
It is well known that seeding of stable liquid-water clouds with properly
sized particles of sodium chloride or other hygroscopic materials can
modify the drop-size distribution in the clouds and, under certain conditions,
lead to an improvement in visibility. The physical process is one of
producing an initial small population of relatively large droplets. The
hygroscopic particles grow faster and have a larger equilibrium size than
natural droplets which have formed on less hygroscopic condensation nuclei.
Given the artificially broadened drop-size distribtuion, the large droplets
continue to grow to precipitation-particle size.
In terms of our cooling-tower model, the affect of seeding would be to change
the conversion constants, K and K in eqns. (11) and (12). The end result
would be a more rapid conversion from cloud water to hydrometeor water.
(Conversely, seeding with very large numbers of uniformly small hygroscopic
particles will produce a cloud of large numbers of small droplets with no
large droplets. Such a cloud, similar to many natural fogs, is extremely
stable with very slow conversion to precipitation. )
The beneficial affects on visibility to be obtained by broadening the drop-size
distribution can readily be seen from Trabert's equation for visibility given
previously. An increase in the mean droplet radius, for constant liquid water
content, leads directly to an increase in horizontal visibility. Any subsequent
decrease in water content due to precipitation further improves the visual range.
Results of the model calculations and limited observations from cooling towers
suggest that where tower plumes have large vertical penetration, natural
conversion will take place, leading to formation of precipitation particles.
With more limited vertical rise, less liquid water is condensed, and a
narrower drop-size distribution such as shown in Figure 4 would be expected.
When persistent stable plumes form downwind of cooling towers, there is
little question that the visibility in the plume could be improved by seeding with
properly sized hygroscopic particles. It is less clear that routine seeding
in a wide range of meteorological conditions would be advantageous. Certainly
34
-------
the production of fallout (precipitation) downwind of the tower would not
ordinarily be regarded as a beneficial effect. Further, an increase in
the number of large droplets will usually lead to longer travel times
and distances before the plume completely dissipates.
In the case of serious fogging episodes from towers, seeding offers a
technique for reducing the adverse effects. For optimum results the
seeding should probably be done downwind of the tower where the effects
are most serious, rather than at the tower itself. The most efficient
practical methods for performing the seeding would have to be determined
by experiment. Such experiments at a tower location where adverse effects
are relatively frequent are recommended.
The above discussion has been directed toward warm (above 0°C) plumes.
Supercooled tower fogs could be effectively dissipated by seeding with
freezing nuclei such as silver iodide, or with dry ice. In tower locations
where fogs are occasionally formed at temperatures lower than about -5°C,
silver iodide seeding of the plume at the tower could be utilized in problem
situations to change the fog into ice crystals which would fall out in a
relatively short travel distance.
35
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SECTION 5. 0
REGIONAL CHARACTERISTICS
Based on the results obtained from the model computations, it is now
possible to investigate various geographical regions of the United States
in order to rate these areas in terms of the potential for adverse effects
downwind of cooling towers. The model results show that typical summer
conditions with warm temperatures (high moisture deficit) and unstable
lapse rates generally will not lead to downwind propagation of a cooling
tower plume. The prime season of interest is the late fall and winter
where stable air and colder temperatures are prevalent.
Statistical data necessary for proper definition of low-level moisture deficit,
stability, and general dispersion is typically difficult to obtain on a regional
basis. For the purposes of this study we have used the following three
sources as a means of evaluating the geographical potential for cooling
tower production of fog:
(a) "Fog Frequency in the United States", A. Court, and R.
Gerston, The Geographical Review, p. 545.
(b) "Low-Level Inversion Frequency in the Contiguous United
States", C. R. Hosier, Monthly Weather Review, Vol. 89,
No. 9, September 1961, p. 319-339.
(c) "Estimates of Mean Maximum Mixing Depths in the Contiguous
United States", G. C. Holzworth, Monthly Weather Review,
Vol. 92, No. 5, May 1964, p. 235-242.
A qualitative classification for the potential for adverse cooling tower affects
has been made based on the following criteria:
(a) High Potential; Regions where heavy fog is observed over
45 days per year, where during October through March the
maximum mixing depths are low (400-600m), and the frequency
of low-level inversions is at least 20-30%.
(b) Moderate Potential; Regions where heavy fog is observed over
20 days per year, where during October through March the
maximum mixing depths are less than 600m, and the frequency
of low-level inversions is at least 20-30%.
(c) Low Potential: Regions where heavy fog is observed less than
20 days per year, and where October through March the max-
imum mixing depths are moderate to high (generally >600m).
36
-------
Figure 14 is a depiction of the results of this evaluation for the United
States. The main areas of high potential are the West Coast, Pacific
Northwest, the Appalachian Valleys, and the far Northeast Coast. The
areas of moderate potential are the Gulf and Atlantic Coasts, the Great
Lakes region, and leeward of the Continental Divide.
From the data obtained with the model calculations, these areas have the
most suitable climatic conditions for producing adverse effects downwind from
cooling towers. However, since the local microclimate of a given region
can vary considerably from the larger-scale features, each site will have
to be evaluated on the basis of the local parameters. As pointed out in
Section 4. 6, local topographic influences can be significant and will have
to be included in any site evaluation. Valleys with local moisture sources
(ponds, rivers, lakes) will obviously increase the fogging potential. On
the other hand, tops of hills or raised areas with greater roughness will
disperse the effluent more efficiently.
5. 1 Site Evaluation
To facilitate further evaluation of the cooling tower modifications it will be
necessary to derive certain data as statistics for given sites. From the
modeling concepts, the following meteorological parameters are needed for
site evaluation:
(1) Temperature measurements from the surface to heights several
hundred meters in excess of the expected plume penetration.
(2) Relative humidity as a function of height.
(3) Wind speed and direction as a function of height.
These data which provide input conditions for use of the numerical model,
are generally only available from standard radiosonde stations, and are only
taken every 12 hours. Thus, the standard U. S. Weather Bureau data are
not totally adequate for proper evaluation. In addition, observations on local
terrain effects such as valley winds, sea breeze, lake effects, etc. , will
have to be obtained.
5. 2 Specific Criteria
It would clearly be advantageous to have a quantitative set of criteria that
could be utilized in evaluating potential cooling tower sites. Unfortunately,
such criteria could not be derived within the scope of the present study.
Because the behavior of a tower plume depends on the interaction of several
tower characteristics (radius, updraft, velocity, and temperature) and the
ambient meteorological conditions through a depth of atmosphere, no simple
37
-------
GO
00
HIGH POTENTIAL
MODERATE POTENTIAL
SLIGHT POTENTIAL
FIGURE 14. GEOGRAPHICAL DISTRIBUTION OF POTENTIAL ADVERSE EFFECTS FROM COOLING TOWERS
BASED ON FOG, LOW-LEVEL INVERSION AND LOW MIXING DEPTH FREQUENCY.
-------
direct parameter could be determined which effectively measured these
complex interactions. Such a parameter could be derived empirically by
making a large number of model runs. However, far more runs would
be needed than could be done in this preliminary study.
General geographic criteria more quantitative than those represented by
Figure 14 could be derived by processing historical weather data from
existing radiosonde stations. Such an evaluation should determine, from
actual atmospheric soundings:
(a) mean moisture deficit, surface to 2000 feet
(b) mean wind speed, surface to 2000 feet
(c) potential temperature gradient, surface to 2000 feet
The 2000 feet height is somewhat arbitrary, but is selected on the basis that
if the plume penetrates to at least that height, and small moisture deficits
do not exist below that height, there can be reasonable assurance that no
serious adverse plume effects will occur at the ground.
Given a sizeable statistical sample of soundings from a given radiosonde
station, the frequency of occurrence of unfavorable values of these three
quantities could be determined.
The recommended evaluation procedure for a specific planned tower site is
as follows:
(a) From local surface data and upper-air soundings, determine
the frequency of occurrence of low-level inversions and lower
atmosphere stability (potential temperature gradients).
(b) Determine the frequency distribution of wind speed and direction.
(c) Utilize the numerical plume model to calculate penetration
heights for the most common (and for potentially troublesome)
wind and stability conditions. Actual tower characteristics,
or a range of planned characteristics should be used as input.
(d) Evaluate the climatological frequency of moisture deficits through
the computed plume rise intervals.
(e) The magnitude and relative frequency of moisture deficits in the
plume layer will be direct measures of the potential for per-
sistent plume fogs.
39
-------
(f) The model should be further utilized to predict log extent
and density in the most unfavorable situations.
(g) Finally, consideration should be given to any purely local
small-scale factors due to topography, moisture sources, etc.
which would modify the fog potential indicated by the model.
40
-------
REFERENCES
Briggs, G. A. , 1968: Momentum and Buoyancy Effects. Meteorology
and Atomic Energy, 1968, D. H. Slade, ed. , U. S. Atomic Energy
Commission, July, 1968. pg. 189-202.
Csanady, G. J. , 1968: Research on Buoyant Plumes. Annual Report,
1967, Department of Mechanical Engineering, University of Waterloo.
NYO-3685-13, 120 pgs.
Davis, L. G. , 1967: Alteration of Buoyancy in cumulus: An investigation
of dynamics and microphysics of clouds. Report No. 10 and Final
Report to National Science Foundation, NSF GP-4743, Dept. of Met-
eorology, The Pennsylvania State University, University Park, Pa.
Federal Water Pollution Control Administration, 1968: Industrial Waste
Guide on Thermal Pollution. U. S. Department of the Interior, FWPCA,
Northwest Region, Pacific Northwest Water Laboratory., Corvallis,
Oregon, 112 pgs.
Kessler, E. A. , Newburg, P. J. Feteris, and G. C. Wickham, 1962, 1963
1964: Relationship between tropical circulations and kinematic cloud
models. Prog. Repts. 1-5, Travelers Research Center, Inc. , Hartford,
Conn. , Cont. DA 36-039 SC-89099.
Ledbetter, 1969: Droplet size distributions from model cooling tower fogs.
Paper presented at National Meeting of Air Pollution Control Association,
New York, June 24-26, 1969.
Malkus, J. , 1952: Quarterly Journal of the Royal Meteorological Society,
7£, 530
Marshall, J. S. , and W. McK. Palmer, 1948: The distribution of raindrops
with size. J. Meteor. , 5, 165.
41
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Pasquill, F. , 1961: The estimation of the dispersion of windborne material.
Meteor. Mag. , 90, 1063, 33-49.
Sutton, O. G. , 1953: Micrometeorology, New York, McGraw-Hill. 333 pgs.
Turner, D. B. , 1967, 1969 (revised): Workbook of Atmospheric Dispersion
Estimates. U. S. Department of Health, Education, and Welfare.
Public Health Service, National Air Pollution Control Administration.
84 pgs.
Weinstein, A. I. , and L. G. Davis, 1968: A Parameterized numerical
model of cumulus convection. NSF Kept. No. 11, NSF GA-777, Dept.
of Meteorology, The Pennsylvania State Univ. , University Park, Pa.
42
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LIST OF FIGURES
Figure Title Page
1 Natural Draft Wet (Evaporative) Counterflow
Tower From FWPCA (1968) 3
2 Vertical Dispersion Coefficient as a Function of
Downwind Distance from the Source. From Turner
(1969) 11
3 Horizontal Dispersion Coefficient as a Function of
Downwind Distance From the Source. From Turner
(1969) 12
4 Droplet Size Distribution from Laboratory Experiments
(Ledbetter, et al, 1969) 18
5 Example of Numerical Model Result for a Cooling
Tower Plume. 22
6 Effect of Stack Radius on Penetration Height 23
7 Effect of Stability on Penetration Height 25
3
8 Downwind Spread of Liquid-Water Content, 0. 05 g/m
Contours for Various Values of Relative Humidity
Expressed in % 26
9 Pittsburgh Sounding, February 28, 1968, 1200Z,
° Temperature, ADewpoint 28
10 Vertical Profiles for Pittsburgh Case 29
11 Downwind Liquid-Water Content for Pittsburgh Case
Study, in g/m3 30
12 Salem Sounding, November 11, 1969, 1200Z,
°Temperature, ADewpoint 31
13 Downwind Liquid-Water Content for Sale n Case
Study, in g/m3 32
43
-------
LIST OF FIGURES (CONTINUED)
Figure Title Page
14 Geographical Distribution of Potential Adverse Effects
from Cooling Towers, Based on Fog, Low-Level
Inversion and Low Mixing Depth Frequency. 38
44
-------
LIST OF SYMBOLS
c specific heat of air at constant pressure (cal g deg )
c , c Sutton dispersion parameters in the horizontal and vertical
directions (mn , where n is a dimensionless constant)
(n = 2p/l+p)
dz (equation 2) height increment where freezing occurs (m)
_2
g acceleration of gravity (m sec )
K , K Conversion coefficients in parameterized cloud physics
equations (sec )
L Latent heat (cal g ), L evaporation, L freezing,
L sublimation
s
M Mass of cloud (plume) air (g)
N Number of cloud droplets of radius r per unit volume
r
_2
P Atmospheric pressure (dynes cm )
p Power-law wind profile exponent (dimensionless)
Proportionality constants in horizontal and vertical directions
for linear (shor
(dimensionless)
V Z
for linear (short-range) growth of plume standard deviations
Q* Source strength (release rate) of effluent from tower (g sec )
Q Liquid water content of cloud (plume) (g of water per g of air),
Q cloud liquid water, Q, hydrometeor water. (See equations
if and 12.)
q Mixing ratio (total water, vapor and liquid, per unit mass of
air) (g water per g air). In the text, q is sometimes used
interchangeably with the absolute humidity, qp , the mass of
water per unit volume of air.
q mixing ratio in environment
q saturation mixing ratio (a function of temperature)
S
45
-------
qd qs - qe
A q additional mixing ratio at a given point due to effect of
cooling tower.
R Gas constant for air (erg g deg ) (eq. 2)
R Radius of plume (m)
R Radius of plume at top of cooling tower (m)
s
_2
R Total rainfall (g m )
R Rainfall rate (mm hr )
r Radius of cloud droplet (microns -u)
T Absolute temperature (deg K)
T Air temperature in environment of plume
T Virtual temperature T = T (1 + g/e)/(l + g), a ficticious
temperature at which dry air would have the density of actual
moist air
T Environmental virtual temperature
ve
t Time (sec)
U, u Horizontal wind speed (m sec )
U Horizontal wind speed in tower plume
U Horizontal wind speed in environment
U1 Horizontal wind speed in plume before mixing with environment
U = U , Horizontal wind speed in plume after mixing
i P
u1 Horizontal wind speed at a reference height
V Terminal fall speed of cloud droplets or precipitation particles
(m sec )
w Vertical velocity of air in plume (m sec )
46
-------
w Calculated vertical velocity before wind shear is taken into
account (value obtained from eqn 1)
x, y, z Cortesian space coordinates
X Concentration of material in plume (from diffusion equation)
(g m-3)
f\ — *^
Z Radar reflectivity (mm m )
z Maximum height of penetration of plume
G
a Angle between plume axis and the outer edge of rising,
spreading plume (half-angle of plume spread)
0 Angle between the vertical and the center-line (axis) of rising
plume. (Tilt of plume due to horizontal wind)
e Ratio of the molecular weights of water and dry air
_3
p Density of air (g m )
p Density of air in plume environment
U Entrainment parameter (eqn 3) (m )
T , T Standard deviations of the spatial distribution of material in
v z
the plume in horizontal (y) and vertical (z) directions. (m)
47
-------
APPENDIX A
COMPUTER PROGRAM
48
-------
MANUAL FOR EG &G COOLING TOWER MODEL
(Adapted From Penn State Cloud Dynamics Model MOD 2)
I. Introduction
The Steady State Cumulus Dynamics model was developed to provide an
on-site evaluation of the seedability of cumulus clouds in the field. The
model has steadily evolved to its present state where it is now being used
by several organizations involved in cloud physics research. The mod-
ification for cooling tower plumes was developed by EG &G under the
present contract.
The computer program is written in Fortran IV. A listing of the program
and subroutines is given at the end.
II. Model Structure
The model can be subdivided into four sections: interpolation, calculation,
diffusion, and output.
In the interpolation section, a standard radiosonde sounding is broken down
into a sounding at constant height increments.
The calculation section of the program carries out the model calculations
producing profiles of vertical velocity, cloud temperature, temperature
excess, cloud mixing ratio, cloud and hydrometeor liquid water content,
radar reflectivity factor, and updraft radius.
The diffusion subroutine takes the calculated plume properties and computes
the spread of water in three dimensions due to atmospheric diffusion.
The last section outputs the profiles in tabular form and prints a summary
table of total rainfall, duration, cloud top height, and cloud top temperature
and updraft area for all boundary conditions put into the model.
III. Input Parameters
The model requires, as input data, the following:
1) A standard radiosonde sounding of pressure (mb), temperature
(°C), relative humidity (%), and, if desired, wind speed (m/sec)
starting at the top of the cooling tower.
49
-------
2) The vertical grid interval desired. (Meters)
3) The cooling tower height (cloud base). (KM)
4) The entrainment rate parameter (A in the relationship
H = A/updraft radius)
5) The conversion and collection rates for temperatures above
and below the ice nucleation temperature.
6) The initial updraft radius. (KM) (diameter of top of cooling tower)
7) The ice nucleation temperature. (°A)
Several other input parameters are also required as keys to the options of
the program.
IV. Options
The model was originally constructed with maximum versatility in mind.
For this reason there are some extra input parameters and several extra
steps in the program that allow utilization of model options. Several of these
are not relevant to the cooling tower application, but they will be briefly
described so that the complete program can be understood.
In the interpolation section, either only the initial sounding, or both the
initial and interpolated soundings may be printed out. The key for this
option is a paramete r, JN. If JN = 0, only the input sounding is printed.
In the model calculation section there are four options.
If desired, the model can be run with or without a correction of the vertical
velocity due to shear of the horizontal wind. The parameter NS is the key
for this option. If the calculations are desired without the wind shear
correction (as would be the case when wind data are not available) the
parameter NS is set to the wore1 "No". If the wind shear correction is
desired, the parameter NS is lefl blank.
The original model calculation could be run with the updraft radius varying
with height as dictated by continuity considerations (as the vertical velocity
increases with height, the updraft decreases) or with the updraft radius
constant with height. The parameter for this option is NCR (positive for
constant radius, zero for variable radius). For the cooling tower program,
a linear increase of radius with height is specified in the program, and the
variable radius option should always be used.
50
-------
In the energy equation used to determine the vertical velocity, the source
term is, of course, the cloud buoyancy. This buoyancy, however, must
be reduced by the weight of the liquid water being carried aloft. It is
still unclear how much liquid water should be carried aloft. An option is
allowed here. If the parameter, LWC, is set to zero, the total liquid
water (cloud water and hydrometeor water) is used to retard the buoyancy.
If the parameter, LWC, is set to 1, the buoyancy is retarded by the weight
of the cloud water only, whenever the terminal velocity of the median volume
drop diameter of the hydrometeor water (assumed distributed in a Marshall-
Palmer distribution) exceeds the vertical velocity in the cloud. If the
terminal velocity does not exceed the vertical velocity, the total water is
again used to retard the buoyancy.
The model was originally constructed to be run with a series of different
updraft radii and ice nucleation temperatures, to simulate natural and
artificially stimulated clouds of different sizes. Under these conditions it
is unnecessary to carry out the calculations starting from cloud base each
time. If the program is run with two successive initial conditions, differ-
ing only in the ice nucleation temperature (to see the difference between
a seeded and non-seeded cloud of the same size), it is only necessary to
start the calculations from cloud base for the seeded case (higher nucleation
temperature). When the non-seeded case is run, the calculations need only
start from the level of ice nucleation in the seeded case. The profiles
below this level are the same for seeded and non-seeded cases. For the
cooling tower application, where tower parameters or environment conditions
may be changed, it is necessary to start the calculations from cloud base
on every calculation
The model handles this choice of cloud base or ice nucleation level with
the parameter NBS. If NBS is set to 1, the calculations will start at
cloud base. If NBS is set to zero, the calculations start at the first level
below the ice nucleation level of the previous run. The profiles below this
level are taken from the previous run.
V. Input Formats
For every run, the following input cards are needed:
1) A Sounding Identifier card
2) A Ground Level Sounding Card
3) One card for each level of the input sounding
4) A blank card
51
-------
5) A boundary conditions card for each different boundary
condition
6) A run termination card
The formats for these cards are given below:
1) Sounding Identifier Card
Columns 1-78 Any identifying information (alphabetic or
numeric.
Columns 79-80 Key JN (0 or blank - only input sounding
printed. 1 or -1 - input and interpolated sounding
printed)
2) Ground Level Sounding Card (conditions at tower exit level)
Columns 1-10 Pressure (mb)
Columns 11-20 Temperature (°C)
Columns 21-30 Effluent Temperature (°C), EFT
Columns 31-40 Relative Humidity (100%)
Columns 41-50 Height (meters)
Columns 51-60 Wind Speed at Cloud Base (m/sec)
Columns 71-80 Vertical grid increment (meters)
3) Input Sounding Cards (one for each level)
Columns 1-10 Pressure (mb)
Columns 11-20 Temperature (°C)
Columns 21-30 Blank
Columns 31-40 Relative Humidity (%)
Columns 41-50 Wind Speed (m/sec)
-------
4) Blank card to separate input sounding from Boundary Condition
Card.
5) Boundary Condition Cards (up to 30)
Column 1 Updraft Radius option (NCR)
Blank - variable updraft radius
1 - Constant Updraft radius
Column 2 Cloud Base Option (NBS)
Blank - Calculations start from ice nuclea-
tion level
1 - Calculations start from cloud base
Column 3 Buoyancy Option (LWC)
Blank - Buoyancy decreased by weight of
total water (cloud water and hydrometeor
water) throughout cloud
1 - Buoyancy decreased by weight of cloud
water only when terminal velocity s vertical
velocity
Columns 4-7 Entrainment Rate parameter - (Al)
Entrainment Rate (u) = Al/Radius
Columns 8-17 Conversion Rate below Ice Nucleation Level (AK1)
Cloud water is converted to hydrometeor
water at a rate AK1 below ice nucleation
level
Columns 18-27 Conversion Rate above Ice Nucleation level (AKFl)
Cloud water is converted to hydrometeor
water at a rate AKFl above ice nucleation
level
Columns 28-37 Collection Rate below Ice Nucleation level (AK2)
Hydrometeors collect cloud water at a rate
AKF2 above ice nucleation level
Columns 38-47 Collection Rate above Ice Nucleation level (AKF2)
Hydrometeors collect cloud water at a rate
AKF2 above ice nucleation level
Columns 48-57 Cooling tower (Initial Updraft) Radius (CRAD)
Radius in km.
Columns 58-67 Ice Nucleation Temperature (TF)
Temperature in °A
53
-------
Columns 68-69 Vertical Wind Shear option (NS)
NO - No correction due to vertical shear of
horizontal wind
Blank - Invoke correction due to vertical
shear of horizontal wind
Columns 70-73 Vertical Plume Velocity (W)
Velocity in meters/sec.
6) Run Termination Card
Column 2-1
54
-------
A Sample set of input cards is given below:
1) Sounding Identifier Card
Hypothetical Sounding
1
0 1
787980
2) Ground Level Sounding Card
800.0 5.0 70.0 100.0 5.0 50.0
1 10 20 30 40 50 60 70
55
-------
3) Input Sounding Cards
608.0 -13.0 70.0 7.1 \
10 20 30 40 50 60 70 80
554.0 70.0 7.8
10 20 30 40 50 60 70 80
200.0 -67.0 10.0 15.0 \
10 20 30 40 50 60 70 80^
100.0 -67.0 10.0 20.0 \
10 20 30 40 50 60 70 80>
56
-------
4) Blank Card
5) Boundary Conditions Cards
III .2 0.001 0.001 0.0052 0.0052 1.000 267.0 NO 05.0
I 23 45 667
23 7 7 7 7 77 793
I I
I 2 3
.2 0.001
0.001
2
7
0.0052
3
7
0.0052
4
7
1.000
5
7
248.0
6
7
NO
6
9
05.0
7
3
\
.2
0.001
I
7
0.001
2
7
0.0052
3
7
0.0052
4
7
1.000
5
7
248.0
6
7
NO
6
9
05.0
7
3
.2 0.001
I 2 3
0.001
2
7
0.0052
3
7
0.0052
4
7
1.000
5
7
248.0
6
7
NO
6
9
05.0
7
3
57
-------
The four boundary conditions cards represent the common conditions of:
1) Cloud Buoyancy decreased by weight of cloud water only when
terminal velocity of hydrometeor is s vertical velocity.
2) u = • 2/R
3) AK1 = AKF1 = 0. 001
4) AK2 = AKF2 = 0. 0052
5) CRAD = 1.0 km (example is for a cumulus cloud; for cooling
tower CRAD is tower radius)
6) No correction due to vertical shear of the horizontal wind.
7) Initial vertical velocity (W) = 05. 0 mps
In addition, the options exercised on each card are as follows:
Card 1 - 1) Constant updraft radius
2) Calculations start from cloud base
3) The ice nucleation temperature is -6°C (267°A)
Card 2 - 1) Constant Updraft Radius
2) Calculations start at first level below -6°C level.
Profiles below this level are taken from previous runs.
3) Ice nucleation temperature is -25°C (248°A)
Card 3 - 1) Variable Updraft radius
2) Calculations start from cloud base
3) Ice nucleation temperature is -6°C (267°A)
Card 4 - 1) Variable Updraft radius
2) Calculations start at first level below -6°C level
3) Ice nucleation temperature is -25°C (248°A)
58
-------
VI. Listing
A listing of the program follows Table Al.
Table Al contains a complete description of the notation used in the listing.
Figures Al and A2 show flow diagrams for the interpolation and calculation
portions of the program.
TABLE Al
DESCRIPTION OF PROGRAM SYMBOLS
SYMBOL
AK1
AKF1
AK2
AKF2
AO.A1
AREA
CONG
DA
DEFX
DEN
DUR
DZ, NDZ
IDENT
ILEVL
INDOC
IT
ITOP
JN
LWC
DESCRIPTION
Conversion coefficient before freezing.
Conversion coefficient after freezing.
Collection coefficient before freezing.
Collection coefficient after freezing
Entrainment parameter (it = Al/Radius).
Updraft area.
Concentration of liquid water ( g m ) from diffusion equation
Heat realized from freezing of liquid water.
Difference between saturation and environmental moisture
concentration
Density of cloud air.
Duration of precipitation.
Vertical grid interval.
Characters on Sounding Identifier Card.
Key indicating if new input sounding level has been read in.
Grid interval desired in print out.
Key to indicate ice nucleation level has been reached.
Cloud top height (height at which vertical velocity goes to zero).
Key to indicate if listing of interpolated sounding is desired.
Key indicating if buoyancy should be decreased by weight of
total water or only cloud water.
59
-------
TABLE Al (Cont'd)
NBS
NCR
NFRZ
NTF,TF
NS
NUM
P
PE
PRAD
Q
QCL, AQC
QH, AQH
RA, RO
RH
RHE
RHO
DBS
SIZE, CRAD
SIGY, SIGZ
T, TC
TE
TEMPT
TH
THE, TTHE
TVE
U
UE
Key indicating if calculations should proceed from cloud base
or from previous ice nucleation level.
Key for variable or constant updraft radius.
Key to indicate freezing level has been reached.
Ice Nucleation temperature.
Key for correction due to shear of horizontal wind.
Initial condition card number.
Pressure of initial input sounding.
Pressure of interpolated sounding.
Normalized updraft radius (UPRAD/CRAD).
Total liquid water content.
Cloud liquid water content.
Hydrometeor liquid water content.
Total rainfall.
Relative humidity of initial sounding.
Relative humidity of interpolated sounding (environment R. H. ).
Density of environment air
Difference between saturated vapor pressure over water and
ice
Initial updraft radius.
Standard deviations of plume width in y and z directions.
1) Temperature of initial input sounding in interpolation
section.
2) Cloud temperature in calculation and output sections.
Temperature of interpolated sounding (environment temperature).
Cloud top temperature
Wind direction in initial sounding.
Wind direction in interpolated sounding (environment wind
direction)
Environment virtual temperature
Horizontal wind speed in initial sounding.
Horizontal wind speed in interpolated sounding (environment
wind speed).
60
-------
TABLE Al (Cont'd)
UPRAD
W, AW
X, AX
XE
XK1.XK2,
XK3.XK4
XL
XMU.XMU1
XS
Z
ZE
ZFZC
Updraft radius.
Cloud vertical velocity.
1) Mixing ratio in initial input sounding in interpolated
section.
2) Cloud mixing ratio in calculation and output sections.
Mixing ratio in interpolated sounding (environment mixing
ratio.
Constants in equation to determine XS.
Latent Heat
Entrainment parameter.
Saturated mixing ratio.
Height in initial sounding.
Height in interpolated sounding.
Radar Reflectivity factor.
61
-------
PR33RAM COOLTrf3( INPUT ,01'TH JT , TAPE 5^ I MP JT , TAPE6=OUTPUT )
COOLING TDWER MODEL ADAPTED FROM PENN STATE CUMULUS MfDrL
E^TRAINMENT WIND SPEED SOURCE .STREMGTH 4 DCT 70
DI^E^SION P(2),T(2),X(2),Z(2),3<2),QCL(2),QH(2),T\/E{2),*«2),U(?),
lTH(2),RH(2),DENm,PE(100).TEUOO),XE(100),ZE(lQO) ,UE(103),
2THE(100')»RHE(100), AW( 100 ) , AQH ( 100 ) * AQC( 1 00 ) , TC< 103 ) , A X( I 00 ) ,
3UP*AD(100) ,AO(30) ,RA(30) ,L>UR(30) ,ITOP(30),MTF(30),SIZE(33),
4AREM30) , TEMPT130) , DES < 30) , 10ENIT( 78 > ,NS ( 2 ) , XS t 100 ) ,C DM: I 50, 7 , 50 ) , S
5ISY(5D),SIGZ<50),DEFX(100),TTME(100),CDMC2< 50) , QE2L ( 1 03 )
OAT A (OE S = 0.5 5, 1.02, 1. 41 , 1. 73, 2. 00, 2. 21, 2. 39, 2.5 1, 2.63 , ?. 66, 2 . 68 ,
12.69,2.68,2.64,2.60,2.54,2.48,2.40,2.31,2.22,2. 13, 2. 04, 1 . 94, 1 .84,
2 1.75, .1.65.1.5S, 1.47,1.38,1.29)
100 READ (5,110) (IDENTU )t 1 = 1,78), JN
110 FORMAT (7RA1.I2 >
NSR=14N
*****
WRITE (6,120) UDENT( I),I=1,
FORMAT (1H1.79A1)
***** PAUT i INTERPOLATI0^4
WRITE (6,130)
FORMAT (1H , 40X , 16HIN IT I AL SOUNDING)
H-2
WRITE (6,140)
FORMAT (* PRESSURE*, 3X, *HEIGHT*, 3X,*TEHPE^AT JRE*, 3X,
l,3X,*WIND SPEEO*,3X,*WINO DI RECT IOM*// )
READ 15,150) P( 1),T( 1 > , RH( 1 ) , Z( 1 ) ,U( l),TH(l),OZ
150 FORMAT (2F10.0, 10X , 4F10.0, F 10.0 )
NOZ=DZ
INDOC=50/NDZ
TE(l), = T(l)+273,3
PE(1)=.P(1)/10.0
120
130
140
E. 4 TI VE HUM*
RHE(1)=RH(1)/100
ZE(1)=Z(1 )
160
170
190
200
THE(l)=TH(l)
ILEVL=0
READ (5,170) P( Z ) ,T (2 ) , RH( 2 ) , U( 2 ) ,TH< 2 )
FORMAT (2F10.0, IOX,3F10.0)
WRITE (6,180) P(l),Z(l)TT(ntRH(l).UE< J-l )*EXP(-9.87*DZ/(287.04*TE( J-l) ) »
CJPa*LO&(PE(J)/PE(J-l))
T£(J1=TE( J-1)«-(DTDP*DP)
RHE(J)=RHE( J-l)*(DRHDP*DP)
UE(J).=UE( J-1)+(OUDP*DP)
THE( J)=THE(J-1)+(OTHDP*DP>
GO TO 220
P(1) = P( D/10.0
PE( J) =P(l)*eX?{-9.87*
-------
220
>30
240
260
270
280
290
300
310
ZE(2)=.ZE( 1J + DZ
IF (ZE(2)-Z(2)) 230,230,250
ZE(1)=ZE(2)
CONTINUE
Z(1)=Z(2)
P(1)=P(2>
T(l)»T(2)
UMMLH2)
TH(l)=TH(2)
RH(1)=RH( 2)
N=J
ILEVL=1
GO TO 160
IF
FORMAT(*1MU=*,F5.3,*/RUP*,2X,*^UP = *,F6.3,* KM*, 4X , *K I =* , F !>. 3 , 2X
320
999
330
340
350
10
360
14.1.2A1,* SHEAR CORRECTION*)
RAD1=1000.0*C3AD
XMU1=AO(MUM) /RA01
WRITE (6,370)
370 FORMAT ( *0*, 2X, *HEI C,HT*, 4X, *HE I GHT*, 3X, *PXESSURE*, 2X
13X,.*CtOUD*,6X,*TEMP.*.4X,*MIXING*,4X,*CLOJn*,'5X,*H'.r
28X,*UPDRAFT*)
WRITE (6,380)
380 FORMAT(* *,31X, *VELOC ITY*, 3X, *T EMP. *, 5X, *5XCESS*, 4X,
l*WATEH*,5X,*WATKR*,1JX,*FACTOR*,5Xt*RAni JS*)
mirr (6,390*
>90 FORMAT (* *. IX, *(Mr.TKKS) *,3X, *( f K I: F ) * , 5 X , >( M3)*,ryX,*
i«-«n». :'. A >*,4 x ,<•( HFC. r.)*,?x,*i ,>VKr, )*, ^,\, *•( v-i/\r, > *, 3X,
.-'*( "1M6/M .1 ) *,4X, * ( METFRS ) * »
WlUTt (6,400)
400 FORMAT (1HO)
***** [-JJ TI ALI / ATI UN *****
IF (NBS) 420,420,410 63
, >
r)*,
^ T!
7X,
CAL* ,
*Z*,
* *\ T 1 0*, 5X,
, 3 x
00067
00058
00069
00070
00071
0007?
00073
00074
00075
000/7
00078
00079
OOOHO
00081
00082
00083
00084
00065
00086
00087
OOOK8
00389
00090
00093
00094
00098
OOD99
00100
00101
00108
00109
001 10'
00111
001 12
00113
00114
00115
00116
00117
00118
00119
OOK'O
00 I?. I
001??
001?4
-------
410 J=l
NFRZ=0
TH(1)=THE(1)
U(1)=UE(1)
TU)=305.0
TC< L)=305.0
XU)=XE(l)/RHE(1)
QH(1)=0.0
AQH(l)=0.0
QCL(1)=0.0
AW(1)=W(1>
IHT=IHT1
RO^O.P
RAD=RAD1
UPRADI1 ) = 1.0
DTMAX=0.0
SDTMX=0.0
JOTMX=0
JSOTM=0
GO TO 440
***** INITIALIZATION AT PREVIOUS FRFFZIN3 LEVEL ***** 00145
420 J=ITOB O01'f6
OTMAX = SOTMX 001^.7
JDTMX = JSOTM OOl'trt
T(1)=TC(ITOB) 00149
xm^Axuros) ooiso
OCL{1)=AQC(ITDB) 00151
QH(1)=AQH(IT03)/1000.0 001S2
W«l)=AW(I FOB) 00153
RAO=UPRAO(IT03)*RAD1 00154
RO=ROD 00155
TH(1)=THTH 00156
U<1)=UU 00157
IHT=IHT1 00158
IST=I^DUO1 00159
DO 430 I=ISTtITll8tINDOC 00160
IHT=IHT-»-NDZ*INDOC 00161
IHTT='IHT*325/100 OOU,?
A=TC(I)-TE(U 00163
PRAD=UP^AD(I)*RAD1 00164
BQH=AQH(11/1000.0 00165
C=.U4000.0*RGH>**1.136 00166
ZFZC=200.0*(C**1.6) 00167
430 WRITE (6,790)IHTt IHTT,PE( M tAW( I ),TCII) t A,AX( I ) ,A3r,( I )t 33H.ZFZC, 0016«
1PRAD 00169
440 TVE(l)=T(l)*(1.0*.6l*X(l)) 00170
Q(1)-QCL<1)+QH{1) 00171
0&N(l)=PE(J)/(2«7.04*TF(J)) 00172
INDIC=0 30173
XL=2500000.0 00174
DA=0.0 00175
XK1=22.5518 00176
XK2=2937.4 00177
XK3=4.93 00178
XK4=15.39 001 t'i
AKA=AK2 00160
AK = AK1 001 PI
UBASE=UE(1) 0018?
THBSE=THE(l) 00183
IT=0 00184
450 J=J+1 001^5
IF (N-J) 330,460,460 OOU'6
460 IHT=.HT + NDZ
RAnU(0- 12* ( IHT-IHT1 ) )
-------
470
480
VIOIST OR ICE ADIABATIC ASCENT *****
A=-0.009H3*DZ
B=l.O+( (X( 1)*XL )/( 287.0't*T ( 1 ) ) )
C=1.0+.622*XL*XL*X< 1 ) / I 1 004, 0*2 B7 . 04 *T ( 1 ) *T ( 1 ) )
T(2)=*T( 1 )+(A*B+UA)/C
***** MIXING AT CONSTANT PRESSURE *****
ES=,(10.0**( (XK1*T(2)-XK2)/T(2)))/(T(2)**X<3)
X(2) = < .622*ES)/ (PE( J)-ES)
A={XMU*DZ*XL/1004.0 )*(X(2)-XE(JM
8=(XMJ*D7 )*(T(2)-TE(J) )
C=1.0«-(.622*XL*XL*X(2))/( I 004 . 0*2 87 . 04* T ( ?)*T(2) )
T(2)=T(2)-(A+B)/C
ESM10.0**((XK1*T(2>-XK2)/T<2)))/(T(2)**X<3)
X(2)=(.622*ES)/ -XK4*QH( 1 ) **0. 1 2 5 ) ) *DZ
QCL(2)=QCLm-(X<2)-X(l) )-A
IF (QCH2M 500,510,510
QCL(2)=0.0
GH12)=QH< 1)
GO TO 550
QECH J) = (X(2)-Xt(J)+QCL( 1) )*UZ*XMU
QCL(2)=QCL(2 ) -XMU*D7.* (X ( 2 ) -XF ! J ) +QCL ( I) )
IF (QCL<21) 520,530,530
QCL(2)=0.0
OH(2)=QH(1 )*A
IF (QH( 2) ) 540, 550,550
QH<2)=0.0
IF (LWC) 5f>0,560,570
a{2)=QCL(2)+QH(2 )
500
510
520
530
540
550
560
GO TO 590
570 IF (W<1)-4.5*3H(I)**.125) 580,580,560
WATER=QCL(2)
590 ES=.T(2)*( UQ + .61*X(2) )
TVE(2)=TE< J)*(1.0+.61*XE< JM
***** VERTICAL VELOCITY COMPUTATION *****
A=ES-TVE(2)
D=,(TVE(2)*-TVE(1 ) )*.5
B=,9.87*DZ*( (A/U)-WATER)
A=(l.3-2.0*XMU*DZ)*W( I ) *H ( 1 ) +2. 0*8
***** CORRECTION DUE TO SHEAR OF THE HORIZONTAL WTO *****
IF(NSR.EQ.NS(1)) GO TO 600
ALPHA=U<1)/(1.0+XMU*DZ)
BETA=((XMU*DZ)/(1.0+XMU*DZ))*UE(J)
GAM=2.0*ALPHA*BETA*(COS(THE(J))*COS(TH(1))*SIN(THE(J))
l*SIN(TH(1) ))
EPSLN = 2.0*ALPHA*UBASE*(CGSUH<1) )*COSUHBSF)*-SIN(TH(l))*
ISIN(THBSE))
ZETA=.2.0*BETA*UBASE*(COS(THt'( J) ) *COS ( THBSF: ) +!>! n ( THE( J ) )«
1SIN)
OVEL = ALPHA*AL?)HA4UE T A*BE T A* JO AS E *UB ASE + 3 A^- bHSL N-/ F T A
A=A-OVEL
ALPHA=(1.0/(1.0+XMU*OZ))**2.
BETA=XMU*OZ
GAM = :nS(TH(l))*COS(THE(J))4-SIN(TH(U)*SIN(THl;IJ))
U( 1 ) = I\LI'H A*( BET A'-^ETA*UE ( J ) ^iJEt J )-H.H 1 )* J ( I ) *-2.0*BETA*(i7 ( J ) - J ( 1 ) *
1C.AM) 65
00190
00191
00192
00193
001 94
00195
00196
00197
00 199
00200
OOP.O?
00203
00206
00?07
00208
002^9
00210
00213
00214
00216
0021 T
00218
00219
00220
00222
00223
00224
00225
00276
00227
0022H
00229
00230
002 51
00232
00233
00234
00235
00236
00237
00238
C0239
00240
00241
0024?
00? 43
00244
00245
00246
0024 1
0024U
00249
00250
no 2 SI
002 52
OOP53
00254
00255
O025'>
1
-------
U(1)='J( U**.5
TTH=(U( l)*SIN(TH(l) )+BETA*UE( J)*SIM(THE( J) ) )/UJ< 1 ) *C J S( T H < 1 ) )
1+BETA*UE(J)*CDS(THE(J)))
TH(1)=ATAN(TTH)
600 IF (A) 610,670,.670
610 IF (T<2)-TF) 630,630,620
620 NFRZ=*1
GO TO 810
630 IF (IT) 640,640,810
640 DEN(2)=PE(J)/(287.04*TE( J»
*00=RO+(QH(2)+QH(1) )*(DEN(2)*DEM(1))*.25*DZ
IT08=J-l
IF (JDTKX-IT03) 650,650,660
650 SDTMX-DTMAX
JSDTM=JDTHX
660 UU=.UU)
THTH=TH(1)
GO TO 810
670 H(2)=*A**.5
Q ***** FREEZING *****
IF (IT) 680,680,720
680 IF (H2)-TF1 690,690,720
690 ITaIT+1
XL=2800000.0
XK1=9.5553
XK2=2667.0
XK3=0.0
XK4=11.58
AK=AKF1
DA = 330.0*m2)<-(UES(MT)*0.622*2.8E6/(PE( J ) *1 004 . OE2 ) )
ITOB=J-1
IF (JDTMX-ITOB) 700,700,710
700 SDTMX=DTMAX
JSDTM=JOTMX
710 UU=U(1)
THTH=TH(I)
ROD=RO
GO TO 460
720 DA=0.0
C ***** UP3RAFT RADIUS *****
DEN(2)=PE(J)/(287.04*TE( J) )
IF (NCR) 730,730,740
730 RAD=RAD1+(0.11*(IHT-IHTl))
C ***** TOTAL PRECIPITATION *****
740 RO = *OMQH(2)«-QH( 1 ) ) *(DEN<2) +DE^( 1) )*.25*DZ
Q ***** RADAR REFLECTIVITY FACTOR *****
C=(14000.0*QH(2))**(!.136)
ZFZC=200.0*(C**1.6)
C ***** UPDRAFT AREA *****
IF (T(2)-TE(J)-T(1)*TE(J-l)) 750,770,770
750 IF (DTMAX-TI l) + TE(J-l) ) 760,770,770
760 HT*IHT-IHT1-NDZ
DTMAX=T(1)-TE4
OOL'66
00267
00? 68
002f>9
00?7C
00271
00? 72
00273
00274
00? 75
00276
002 77
00?78
0027?
00280
00? HI
002H2
00283
002P4
00285
00?«6
00287
00288
002 a 9
D0290
002^)1
00292
00293
00294
00275
00296
00297
00 9
00300
00302
00.304
00305
00306
003T7
00308
00309
00310
00311
00312
00313
00314
0031r>
00316
00317
1°
66
00319
00320
00321
-------
800
***** STOKE PKuf-lLbS FOR GRAPHICAL OUTPUT *****
ITAB*J
AW( ITAB)=W(2)
TCUTAB)=T(2)
AQH(ITAfl)=QH(2)*1000.0
AX(ITA8)=X<2)
AQCUTAB)=QCL(2)
UPRAD(ITAB)=RAD/RAD1
***** PREPARE FOR NEXT
Q(l)=Q(2?
TVE(1)=TVE<2)
Ttl)=T<2)
X(1)*X<2)
QCL(1)=QCL(2)
QH(1)=QH( 2)
GRID STEP *****
*****
W<1)=W(2)
GO TO 450
C ***** TOTAL PRECIPITATION *****
BIO RA(NUM)=RO*39.37
***** DURATION OF PRECIPITATION
A=IHT-IHTl
WRirE(6,40) QH(2),XK4
40 FORMAT(* *,5X,*wH2 = *,E15.5,5X,*XK4 = *.El 5.5)
IF(QH(21) 35,45,35
35 CONTINUE
OUR(NUM)=2*(A/(XK4*QH(2)**.125))/60.0
GO TO 55
45 DUR(NUM)=0.0
55 CONTINUE
***** CLOUD TOP HEIGHT *****
ITOP(NUM)=IHT
c ***** FREEZING TEMPERATURE (OEG C) *****
NTF(NUM)=-NT
WRITE(6,30) NTF(NUM)
FORMAT(* *,5X,*NTF=*,E15.5)
***** CLOUD TOP TEMPERATURE (DEG C) *****
TEMPT(NUM)=T(2)-273.3
WRITE (6,820) RA ( NUM ) ,DUR( NUM ) , I TOP ( NUM ) , <\REA { NUM )
FORMAT(* TOTAL RAIN =*,F10.4,* INCHES PER CLOUD*,5X,* ^AIN
l,F10.2f* MINUTES*,5X,*CLOUO TOP = *,I5,*METEKS*,3X,*UPOrU-T t
2F6.4//)
INDX5=1
IF
-------
824 CONTINUE
832 CONTINUE
833 FORMATdH .17F7.4)
835 FORMATdH ,16F7.4!
INDX5=INDX5+1
IF(INDX5.LE.0)821,830
IF TOP DOES NOT REACH WARMEST FREEZING LEVEL, ***** 00355
PROCEED TO NEXT BOUNDARY CONDITION CARD ***** 00356
830 READ (5,340) NCR,NBS,LWC,A 1,AK1,AKF1,AK2,\) 00383
IF(NSR.EQ.NSd) ) GO TO 930 00384
NUM=.l 003 R5
IF (CRAD) 330,940,330 003"6
930 IF (CRAD) 100,940,100 003«7
40 GO TO 100
END 00389
SUBROUTINE DIFFZ(XS,XE,TE,W,PE,GCL,RAO,JE,.),IHT,CT^C,rFHE,DEFX,OEC
1L, IHT1)
DIMENSION DFFX( 100) ,TTH£(100) ,C3:NC( 5 0, 7, 50 ) , UE ( I 0^ ) , JC. ( ? ) , P r ( 1 00 )
l,W(2),TEdOO),XE(100),XS(100),SIGY(bO),SI3Z(-iO),X(100),:3r>j:2(50)fG
2ECH100)
nT=50.0/W(2)
= 3480.0*( (PE( J-1)+PE( J-2) 1/2.0) /( ( TE( J-l ) «• T E ( J - 2 ) ) /?.3)
= 50.0*UE( J)*OT*RAl/*2.0
WGT=RHO*VOL
Q=WGT*OECL(J)/OT
IF(Q.LE.O.O)GO TU 60
12
13
14
16
I r
DX=0.2
DO 15 1=2,50
XU)=X( I-1
SIGYl I ) =0.010*1 ALOG10(X( I ) ) )+1.839
SIGY( I »=10.0**SIGY( I )
I F ( X I I) . L E . 1 . 0 ) 1 3 , 1 4
SIGZU )=n
SIGZI I )=10.0**SIGZ( I )
GO TO 15
IF(X(M.LF.10.0)U>,17
SIGZ(I)=0.(>37*( .\LUG10(X( I ) )
Sir,/( I ) =10.0**S !G/ ( I )
r.n vo i '-
\ ic- / ( i ) - r1- s.'.i*( u i;r. ioi x ( i ) ) ) •»- 1. 62
sl>;/ ( ! ) --i c>.o**s 1 1,/ i i )
68
-------
15 CONTINUE
HT=IHT+50.C-IHT1
UAVG=UE< J)
DO 30 1=2,50
A=Q/(6.28*SIGY( I )*S IGZ ( I )*UAVG)
Z = 0.0
DO 20 K=l,50
B=-(0.5*< «Z-HT)/SIGZ(I ) »*( (Z-HT)/SIGZ( I )) ) )
C=-(0.5*< ( (Z*HT)/S!&Z( I ) )*( (Z+HT)/SIGZ( MM)
CONC1=A*< EXP(B)^FXP(C) )
CONCt I, 1,K)=CONC( I, 1,K)>COMC1
COMC2(K)=CONCL
Z=Z-i-50.0
20 CONTINUF
DY=0. 0
00 25 M=2,2
D=-( 0.5*1 (DY*34.95*X( I ) ) /S IGY( I ) )*( ( DY* 54.95*X ( I ) ) /S I '1Y ( [ ) ) )
DO 25 K = l ,50
CONC(l,M,K) = CONC( I,M,K M-CONC2
-------
START
Compute
Height of
L2 Data
(Z2)
/Print
Headings
Read Soundings at
Cloud Base (L2),
Cloud Base Ht. (Z2),
Grid Interval (DZ)
Initialize
(First Level
Interpolated (11) =
Cloud Base (LI))
Read
Sounding
Next Level
(L2)
Compute
Vertical
Gradient
(L2-L1)/(Z2-Z1)
Interpolate
Sounding
at DZ
Intervals
No
Yes
Drop LI Data
Replace by
L2 Data
List
Inter.
ounding
Print
Inter.
Sounding
Compute
Interpolated
Mixing
Ratio
TO MODEL
CALCULATIONS
SECTION
Figure Al. Flow diagram for interpolation section of steady-state cumulus model.
-------
Collection
From
Interpolation
Section
GO TO
More
Soundings
Summary
Table
START
Vertical
Velocity (W)
Conversion
More
Boundary
Conditions
Read Boundary
Conditions
(K , K , etc.)
J.
Correction
Plot
Profiles
Adjust
Vertical
Velocity
Initialization
W=W
Mixing
Ratio
Precipitation
Duration
Area
Compute
Heat released
by freezing
Lift Parcel
One Grid Int.
(Include heat
of freezing if
appropriate)
Mix Parcel
at
Constant
I Print
Drofile
this
level
Pressure
Figure A2. Flow diagram for calculation section of steady-state cumulus model.
-------
VII. Output
Examples of the output from the program follow. The first portion of the
output gives the input atmospheric sounding and the interpolated sounding.
These are clearly labeled and self-explanatory. Units are pressure-mb, ,
height-m, temperature-deg C, relative humidity-%, and wind speed-m sec
The second portion of the output lists parameters of the cooling tower plume
itself as computed by the cloud physics and dynamics portion of the model.
These parameters are also clearly labeled and show the cloud properties
at 200m vertical intervals. Above the table are given the values of input
parameters and constants used in the run. The conversion factors (A)K1,
K1F, K2, and K2F, and the ice nucleation temperature (TF) are always
given the values shown in the example. These have proven to be appropriate
in our computer runs both for natural clouds and cooling tower plumes. The
initial updraft radius (RUP) and updraft velocity (Wl) should be taken to
match the characteristics of the tower being modeled. The entrainment
rate ii(MU) has been taken as 0. 2/ updraft radiiis, and this relationship has
proven to be appropriate for cooling tower plumes as well as can be judged
from presently available data. As shown in the program, we have used
R = R0 + 0. 12Z for the variation of updraft radius with height (R = Radius,
Ro = initial radius, Z - height). Further experience may indicate a modifi-
cation of the factor 0. 12, or a variation of the proportionality parameter
with meteorological conditions, but for the present the program is written
for the value 0. 12, and the relationship ^ - 0. 2/R is recommended.
The final portion of the output gives the concentration of cloud water (excess
of available plume water over that required to saturate the atmosphere) in
g m~^ as a function of height, downwind distance from the tower, and hori-
zontal angle measured from the mean wind direction. Azimuth Angle 1
refers to the centerline of the plume, i. e. , the mean, wind direction. Angle
2 is a direction 2 deg on either side of the wind direction.
The example shown includes only a portion of the output cloud water field.
The horizontal axis is height; columns are for height s at 59m. intervals.
The vertical axis is downwind distance; each row is for a separate distance
and in this example the grid spacing is lOOrn in the horizontal. The com-
plete output continues this table to include heights arid distances beyond those
shown in the sample. Then similar tables are given for Azimuth Angle 2.
Normally, the model computes water concentration directly from, downwind
transport of plume water only at 50m vertical increments (the same heights
for which plume properties are computed). Concentrations at intermediate
heights are obtained by assuming all material to be released at .the 200n.i
g..'-ui points.
72
-------
and letting diffusion spread it vertically thereafter. Thus for example,
the sample shown indicates a water concentration of 41. 78 g m at a
height of 900m (above sea level) and a distance of 0. 3km downwind (entry
in 3rd row, 5th column from the right). At this height, the concentration
decreases to a value of 0. 08 g m~ at a distance of 1. 5km (15th row).
The adjacent columns (for 850 and 950m height) show lower concentrations
resulting from vertical diffusion. A more realistic vertical distribution of
water is obtained if the tabular values are averaged or smoothed in the
vertical.
Note also that the origin of the vertical scale is arbitrary, depending on the
choice of sounding and tower heights. The first primary cloud water column
in the output corresponds to the first height in the plume properties table for
which a value of cloud water is obtained, in this case 900m.
73
-------
PIT 290CT69 1 L
PRESSURE HEIGHT
KEYSTONE COOLING TOWER CASE
INITIAL SOUNDING
TEMPERATURE RELATIVE HUM WIND SPEED
WIND DIRECTION
969.00
962.00
V05.00
850.00
777.00
700.00
500. 00
PPESSIRE
989.00
964.25
940.54
917.21
8S4.25
B71.94
850.19
828.97
808. 3J
788.24
768.75
749.68
731.02
712.76
694.78
677.30
060.19
643.43
027.01
610.94
595.20
5/9.79
564.70
t>49.93
535.48
521.32
b07.48
493.92
500.00
719.77
1205.44
1701.70
2*14.92
3241.H8
5b03.01
HEIGHT
500.00
700.00
900.00
1100.00
1300.00
IbOO.OO
1700.00
1900.00
2100.00
2300.00
2bOO.OO
2700.00
2VQO.OO
3100. 00
3300.00
3bOO.OO
3^00.00
3900.00
4100.00
4300.00
4SOO.OO
4700. 00
4900.00
5100.00
5300.00
5500.00
5700.00
5900.00
-1.90
1.40
-1.10
-1.10
.80
-2.90
-20.00
TEMPERATURE
271.40
274.42
273.78
272. 7b
272.20
272. 2U
272, 2u
272.73
273.20
273.80
273.72
272.83
271.94
271.04
270.02
268.72
267.42
266.12
264.80
263. 4b
262.10
260.82
259.48
258.14
256.78
255.42
254. Ob
252.68
86.0
73.0
60.0
?2.0
20.0
21. n
10.0
INTERPOLATED -
RELATIVE HUM WliMD
86.000
74.009
68.198
62.852
52.766
37.448
22.135
21.442
20.880
20.320
20.102
20.343
20.585
20.827
20.755
19.922
19.086
18.245
17.400
16.551
15.698
14.840
13.978
13.112
12.24]
11.365
1«.485
9.600
6.00
11.00
9.00
11.00
13.00
20.00
30.00
'OUNDU
SPEED
6.00
10.58
10.26
9.44
9.38
10.19
10.99
11.56
12.12
12.68
13.72
15.40
17.09
18.79
20,22
2o.98
21.74
22.50
23. ?7
24.Q4
24.82
25.60
26. 3H
27.17
27.96
28.76
29,56
30.36
-0
-0
-0
-0
-0
-0
-0
WIND DIRECTION
-0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
n
0
n
o
o
o
0
74
-------
MU= ,200/RUP RUF=
HEIGHT
(METERS)
700
900
1100
1300
1500
HEIGHT
(FEET)
2275
2925
3575
42c5
4875
.030 KM
PRESSURE
(MB)
9b4.?543
940.54Q2
V17,?087
8V*. ,537
B71.9435
Kl= .001
VEHTICAL
VELOCITY
IMPS)
IS. 12982
11.26220
10.15187
0.59639
5.98962
KlFa .001 K2= .0052 K2Fo .
CLOUD
TEMP.
(REG A)
29n.384n
28?. 7493
27R.0140
274.73ln
272.2292
TEMP.
EXCESS
(UEO C)
15.9631
8.9727
5.2655
2.5310
.0292
MIXTMG
RATIO
(GM/KG)
I2.95m97
8.010377
5.920146
4.B05571
4.107319
0052 TF
0
2
?
1
1
CLOUD
WATER
(3M/KG)
.000000
.323961
.148326
.673263
.160076
* 24H.O Wl* 5. own SHEAR CORRECTTON
HYDRO
W&TER
(GM/KG)
0.000000
O.OoOoOO
.032391
.0*3676
.K.2880
7
FACTOR
(MM6/M3)
0.
0.
4.75F. + 01
2.A7E*02
8.95E*n2
UPDRAFT
RADIUS
(METERS)
52.no
74.no
96.00
118.00
140.00
TOTAL RAIN
XK4
-o.
= .0018 IMCHES PER CLOUD
1«53900F_*01
RAIN LASTS
6.74 MINUTES
CI.OUD TOP= 1700MFTERS UPORAFT AREA-il .000
AZIMUTH ANGLE = i
0.0000
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-------
BIBLIOGRAPHIC: E G § G, Inc., Environmental Services
Operation, "Potential Environmental Modifications
Produced by Large Evaporative Cooling Towers," FWQA
Publication No. 16130—-01/71.
ABSTRACT: The objective of the study was to develop
techniques for evaluating the extent of plumes from
large evaporative cooling towers. Analytical techniques
were used to describe the dynamics of the wet cooling
tower plume and its interaction with the environment.
Primary emphasis was placed on predicting the height
of the plume. Classical atmosphere diffusion theory
was used to determine the downwind spread.
The study showed that the saturation deficit of the
atmosphere clearly controls the downwind spread of
the ejected liquid water. Except for cases where the
relative humidity approaches 100%, downwind propagation
is limited to periods when the air temperature falls
below the freezing point. For a given set of atmos-
pheric conditions, increases in the tower radius, the
saturation temperature, and the intial vertical velocity
of the plume contribute to increasing the final plume
height.
The potential for adverse atmospheric effects due to
cooling towers was analyzed on a national basis and is
presented in the form of a map of the United States.
A computer program was developed to perform the neces-
sary calculations. The Appendix contains a description
of the program, including input specifications.
This report was submitted in fulfillment of contract
number 14-12-542 under the sponsorship of the Water
Quality Office of the Environmental Protection Agency.
(Tichenor-EPA)
ACCESSION NO.
KEY WORDS
Cooling Tower Plumes
Atmospheric Diffusion
Cooling Towers
Meteorology
Weather Modification
Fog
-------
1
5
Acce.ss/on Number
n Subject Field & Group
05C
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Title
"Potential Environmental Modifications Produced by Large Evaporative Cooling
Towers"
1Q Authors)
E G & G, Inc.
Environmental
Services Operation
16
21
Project Designation
FWQA Contract No.
14-12-542
Note
22
Citation
Report No. 16130 DNIQ1/71, Water Pollution Control Research Series, Water Quality
Office, EPA, 1971, 75 p.
23
Descriptors (Starred First)
*Cooling towers, *Meteorology, *Weather modification, *Fog, Cloud physics,
Thermal pollution, thermal power plants, air pollution, evaporation, mathematical
models, computer programs, cloud seeding
25
Identifiers (Starred First)
*Cooling tower plumes, *Atmospheric diffusion
27
Abstract The objective of the study was to develop techniques for evaluating the extent of
plumes from large evaporative cooling towers. Analytical techniques were used to
describe the dynamics of the wet cooling tower plume and its interaction with the environment.
Primary emphasis was placed on predicting the height of the plume. Classical atmosphere
diffusion theory was used to determine the downwind spread.
The study showed that the saturation deficit of the atmosphere clearly controls the down-
wind spread of the ejected liquid water. Except for cases where the relative humidity
approaches 100%, downwind propagation is limited to periods when the air temperature falls
below the freezing point. For a given set of atmospheric conditions, increases in the tower
radius, the saturation temperature, and the initial vertical velocity of the plume contribute
to increasing the final plume height.
The potential for adverse atmospheric effects due to cooling towers was analyzed on a
national basis and is presented in the form of a map of the United States.
A computer program was developed to perform the necessary calculations. The Appendix
contains a description of the program, including input specifications.
This report was submitted in fulfillment of contract number 14-12-542 under the sponsor-
snip of the Water Quality Office of the Environmental Protection Agency. (Tichenor-EPA)
Abstractor
Jruce A. Tichenor
'A'-"wffiJ-PNWL-Nationa1 Thermal Pollution Research Program
WR;102 (REV JULY 1969)
WRSIC
SEND TO: WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C. 20240
* GPO: 1969-359-339
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