WATER POLLUTION CONTROL RESEARCH SERIES • 16130GKF12/70
A METHOD FOR PREDICTING
THE PERFORMANCE OF
NATURAL DRAFT COOLING TOWERS
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE
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WATER POLLUTION CONTROL RESEARCH SERIES
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the results and progress 1n the control and abatement
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Office, Environmental Protection Agency, Room 1108,
Washington, D.C. 20242.
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A METHOD FOR PREDICTING THE PERFORMANCE
OF
NATURAL DRAFT COOLING TOWERS
BY
Environmental Protection Agency
Water Quality Office
Pacific Northwest Water Laboratory
Corvallis, Oregon 97330
Project #16130 GKF
December 1970
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 • Price 75 cents
Stock Number 5501-0122
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ABSTRACT
A method is developed for analyzing the performance of counterflow
and crossflow natural draft cooling towers that does not assume
saturated air at the top of the packing. Types of cooling towers
and the principles of operation are considered. Simplified differen-
tial equations for the heat and mass transfer relations and the
methods of integrating them for both counterflow and crossflow towers
are given. A large number of integration steps is shown to be unneces-
sary. ^Equations for estimating the pressure losses in the tower are
also given. Simplified flow charts using these Integration schemes show
how the computer program is used to evaluate tower performance. The
computed performance of towers of various heights operating in moist
and in dry conditions is shown. The effect of inlet water temperature
is shown to be significant. Finally, the computed performance of a
given tower with fixed inlet water temperature is shown as a function
of relative humidity and dry bulb air temperature.
111
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CONTENTS
Page
ABSTRACT 111
LIST OF FIGURES vi1
LIST OF TABLES v11i
CONCLUSIONS 1x
COOLING TOWER TYPES 1
PRINCIPLES OF TOWER OPERATION 5
MATHEMATICAL MODEL 11
Simplified Derivations 11
Counterflow 12
Crossflow . 16
Tower Height 18
Estimating Coefficients 20
Mass Transfer Coefficient 21
Heat Transfer Coefficient 21
Rish's Method 21
Standard Heat Transfer Correlation 22
Friction Coefficient 22
Rish's Method ..... 22
Standard Friction Correlation 23
Estimating Pressure Loss 23
Form Drag 23
Skin Friction 24
Contraction Loss 24
Spray Loss 24
EXAMPLE COMPUTATIONS 25
REFERENCES 33
SYMBOLS 35
APPENDIX - COMPUTER PROGRAM 37
RUNNING THE PROGRAM 39
Input Options and Variables 39
Demonstration Case ....... 39
Required Variables 39
Parallel Plate Packing 39
Default Values 39
Other Sizes 39
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CONTENTS (Cont.)
Page
Other Packings 40
Pressure Loss Due to Tower Structure
and Geometry 40
Input Variables 42
Output Options 48
Listing Initial Values 48
Listing Results of Integrations 48
Listing Results of Each Integration Step. ... 48
Listing Format 48
Card Deck Set-Ups 50
BLOCK FLOW CHART 51
EXPLANATION OF PROGRAM VARIABLES 53
PROGRAM LISTING 59
SAMPLE OUTPUT 67
vi
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LIST OF FIGURES
Figure Page
1 Counterflow Tower 2
2 Crossflow Tower 3
3 Temperature - Total Heat Psychrometric Chart ... 6
4 Changing Air Conditions 7
5 Two Examples of Changing Air Conditions 8
6 Counterflow Schematic 13
7 Simplified Flowchart of Counterflow
Computer Program 15
8 Crossflow Schematic 17
9 Simplified Flowchart for Crossflow Method 19
10 Performance of Towers - Hot, Dry Conditions . , . . 30
11 Performance of Towers - Moist Conditions 31
12 Peformance of a Typical Tower 32
13 Types of Packing 47
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LIST OF TABLES
Table
1 Effect of Changing Integration Intervals 27
Z Counterflow Example • 28
3 Packing Data • • 45
vlii
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CONCLUSIONS
The mathematical model is capable of yielding reliable predictions
of cooling tower performance at relatively low cost. Inasmuch as
the state of the air leaving the packing is actually determined
and not merely assumed to be saturated, the program results will
be of value in studying the effect of a tower on local atmospheric
conditions.
When the atmospheric conditions are such that the air becomes
saturated before it reaches the top of the packing, the integration
scheme is modified slightly so that the program will not predict
a supersaturated condition. This condition might arise when the
bulk air becomes saturated and its total heat is less than the
total heat of the thin layer of saturated air next to the water
and at the water temperature. Water vapor can still be transferred
to the bulk air by virtue of this driving potential, but the program
assumes that the bulk air cannot be supersaturated. Therefore, the
program forces part of the excess water vapor to condense into
droplets and the temperature of the mixture of saturated air and
water droplets to increase until the total energy of the mixture
is the same as the bulk air is at 100 percent saturation.
Tower performance is very sensitive, to the values of the heat transfer
and friction coefficients. An option in the program makes it
relatively easy to change the equations predicting these coefficients
to conform to different types of packings. Because the program
computes the actual velocities at different sections in the tower,
these relationships can be based on the local velocity. Therefore,
the coefficients can be varied in the mathematical model just as
they vary in the actual tower.
The degree to which the performance predicted by the model conforms
to that of an actual tower depends on how well the input data used
in the program match those of the actual tower. Therefore, final
verification of the model awaits the acquisition of reliable test
data on actual towers for which the inlet and packing geometry
is known. These data are especially needed to estimate heat
transfer and friction coefficients.
1x
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SECTION I
COOLING TOWER TYPES
Cooling towers are merely heat exchangers that transfer heat from
water to air. Dry towers perform this function without direct
air-water contact and rely solely upon heat transfer by convection.
Wet towers use direct air-water contact, with energy transfer by
evaporation being the predominant exchange mechanism, and convection
playing a minor role. To promote evaporative and convective cooling,
wet towers require large water surface areas and high airflow rates.
Large water surface areas are produced by distributing the warm water
over packing that either breaks the water into small droplets (splash
packing) or allows the water to flow downward in thin films (film
packing). Airflow can be produced with fans or natural drafts. In
either case, the tower and packing can be designed to operate with
the air flowing upward through the packing (counterflow) or horizontally
across the packing (crossflow). This paper is concerned only with
the wet, natural draft cooling tower.
A natural draft cooling tower is basically a large chimney that
provides a draft to pull air over a large surface of water. Either
heating the air or increasing its vapor content will decrease its
density, and it will rise. Thus, airflow is established without
the expenditure of external power. This is an important advantage
for natural draft towers, because the mass rate of airflow required
is of the same order as the mass rate of waterflow which, for large
heat sources like nuclear power plants, may be equivalent to a small
river, e.g., 1000 cfs.
Natural draft towers are usually constructed from reinforced concrete
and because of their large height are hyperbolic in profile for
greater structural strength. Figures 1 and 2 show the basic components
of counterflow and crossflow towers.
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. DRIfT '• .
• ELIMINATOR-)/
HOT WATER
DISTRIBUTION
^ _ K . . I .-,
COLD WATER
BASIN
FIG. 1 COUNTERFLOW TOWER
2
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CO
DRIFT
ELIMINATOR '
FILL
'COLD WATER
BASIN
FIG. 2 CRQSSFLOW TOWER
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SECTION II
PRINCIPLES OF TOWER OPERATION
Figure 3 provides information leading to a basic understanding of
how a natural draft cooling tower operates. This psychrometric
chart contains the same information as the Carrier psychrometric
chart that is frequently employed in the United States, but presents
the data in a form that can be used more directly in cooling tower
calculations. The left vertical scale is the total heat of the
moist air, which is the quantity that governs energy exchange for the
combined sensible and latent heat transfer. Inasmuch as the total
heat depends almost entirely on the wet-bulb temperature, the total
heat scale may also be interpreted as a suitably graduated scale of
wet-bulb temperatures, as is illustrated by the right-hand vertical
scale. The abscissa is the dry-bulb temperature. The state of moist
air can be found on the diagram by any two of the following three
quantities: wet-bulb temperature, dry-bulb temperature, and relative
humidity. The specific volume lines refer to the true specific
volume of the mixture (reciprocal of the density) in ft3/lb of mixture,
This is useful in calculating the difference in density between two
points in the tower and thus determining the draft through the
tower.
Even though the variables are related through the heat and mass
transfer relations in a rather intricate manner, inspection of
Figure 3 can yield a qualitative picture of the effect of some of
the variables on tower performance. For example, Figures 4 and 5
which are similar to Figure 3, but with much of the psychrometric
data removed for clarity, show how the state of the air and the
temperature of the water change as they move through the packing
in a counterflow tower.
Although the type of psychrometric chart (Figure 3) used in this
paper has been suggested by others, Wood and Betts (6,7) appear
to be the first to publish it. Also, Figures 4 and 5 are based
upon similar curves by Wood and Betts.
If one assumes that the water is at the same temperature as the
layer of saturated air next to it, the locus of points indicating
the change in water temperature as it flows down through the packing
is represented in Figure 4 by the saturation line T-S-R-Q. Thus
the water is cooled from 62 to 9]. The line A-B-C-D-E shows the
character of the air as it flows up through the packing, where
point A represents the state of the incoming air. The state of the
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CD
f
O
120
110
100
90
80
70
60
50
40
30
AT ATMOSPHERIC PRESSURE OF
1000 MILLIBARS
40
32 40 50 60 70 80 90 100 110 120
DRY BULB TEMPERATURE (°F)
FIG. 3 TEMPERATURE - TOTAL HEAT PSYCHROMETRIC CHART
6
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INLET WATER
SATURATION LINE
OUTLET WATER
CHANGING AIR
CONDITION
e
i
AIR TEMPERATURE t, (°F)
FIG. 4 CHANGING AIR CONDITION
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60
INLET WATER
50
SATURATION LINE
OQ
40
30
20
INLET AIR
(MOIST)
INLET AIR
(HOT, DRY)
70
80 90
TEMPERATURE t (°F)
TOO
FIG. 5 TWO EXAMPLES OF CHANGING AIR CONDITIONS
8
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air is striving to reach the state of the saturated air with which
it is locally in contact across the packing. Initially, the inlet
air (point A) "sees" the saturated air across the bottom element
of packing surface at the outlet water temperature (point Q), thus,
the state of the air will try to reach point Q by traveling along
the path AQ. After a small exchange of energy has taken place, the
air has reached state B and has moved along the packing to a point
where it is in contact with the saturated air at a different water
temperature (point R). The state of the moist air then begins to
change by moving along the path BR. Continuation of this process
yields the locus of states of the air flowing through the packing
as a kind of "pursuit" curve (line A-B-C-D-E).
Figure 5 shows pursuit curves for two different atmospheric conditions,
one cool and moist (the curve on the left), the other hot and dry
(the curve on the right). The difficulty in using a natural draft
cooling tower in hot dry climates is illustrated by the pursuit
curve on the right. If the atmospheric condition were hotter and
dryer (further to the right) the inlet air would "aim" toward the
outlet water at a shallow angle, initially, and the state of the
air would tend to cross the lines of constant specific volume in'
the wrong direction. Under such conditions, the air density would
increase, and it would be difficult to get the tower "started."
Towers constructed in hot-dry climates often require somewhat larger
chimney heights to provide the necessary draft, since the density
differences between the incoming and exiting air are so small.
Additionally, increasing the inlet water temperature will promote
a higher cooling efficiency.
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SECTION III
MATHEMATICAL MODEL
Simplified Derivations
The total heat approximation for heat and mass transfer, developed
by Merkel around 1925 (see Reference 4), states that the energy
transferred equals the energy lost by water which must equal the
change in the total heat of the air (i.e., the gain in energy of
the air). Using this approximation, and neglecting the small changes
in water and air flow rates due to evaporation:
hr
(i - 1) dA - L C do - G di (1)
where,
-p - 'PL
hr = Convection coefficient of heat transfer for air,
BTU/hr ft2 °F
C = Specific heat of the air vapor mixture, BTU/lb °F
p- = Coefficient of mass transfer, Ib/hr ft2
S
6 = Water temperature, °F
ifl = The total heat of saturated air and water vapor
at 9, BTU/lb
i = Total heat of the air at the air temperature,
BTU/lb
dA = Increment of heat transfer surface area, ft2/ft2
of cross-section
L = Water flow rate per ft2 of cross -section, Ib/hr ft2
ll
-------
CpL = Specific heat of water, * 1 BTU/lb °F
de = Differential change in the temperature of
the water as it flows over the surface dA, °F
G = Airflow rate per ft2 of cross-section, Ib/hr ft2
di = Differential change in the total heat of the air
as it passes over dA, BTU/lb.
Therefore,
de =
L C
di =
PL uf
1« -Oh,
dA
(2)
(3)
Also, the change in air temperature due to sensible heating equals
the sensible heat transferred from the water to the air:
where,
Therefore,
G C dt = hQ (9 - t) dA
t = Air temperature, °F
dt = Differential change in the temperature of
the air as it flows over the surface dA, °F.
(4)
(5)
Counterflow
Film flow packing in a counterflow tower is shown schematically in
Figure 6. Starting at the bottom of the packing with values for 9,
12
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UNIT CROSS SECTION
FLOWING WATER LAYER
AIR
FIG. 6 COUNTERFLOW SCHEMATIC
13
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i, and t equal to outlet water temperature, and inlet air total
heat and temperature, respectively, Equations 2, 3, and 5 are used
to calculate the changes in these quantities, i.e., de, di , and dt,
as the air and water flow across the differential packing areas (dA)
The design magnitude of the water flow rate (L) and estimates for
the air flow rate (G) and heat transfer coefficient (he) are also
required for the computations. New values for water temperature (e),
air total heat (i), and air temperature (t) are obtained by stepwise
integration until the top of the packing is reached:
9A + dA - 6A + de
dA ' 1A + dt
dA • 1A + d1
where the subscript A identifies the element of packing surface area
where the differential changes are evaluated and A + dA represents
the next element of surface, as shown in Figure 6. When A + dA
equals the total area available, the integration is complete and
the inlet water temperature and the condition of the exit air are
presented for the initial conditions. Since outlet water temperature
is usually desired, it must be 'assumed initially and adjusted by
trial and error until the given inlet water temperature results.
This is done within the computer program, which also adjusts the
airflow rate so that it corresponds to the quantity determined by
the friction loss, air density and tower height. A simplified flow
chart of the computer program which outlines the logic is given in
Figure 7. A complete description of the program is presented in
Appendix III.
The method of integration used here is similar to the arithmetic
method developed by Wood and Betts and illustrated graphically in
Figure 4. If dt in Figure 4 were calculated for each step by
Equation 5, the method becomes essentially the same integration
procedure that is presented in this paper. One advantage in using
dA instead of dt as the variable of integration is that it is easier
to evaluate the performance of a given tower. Another advantage is
that it is possible to extend the method to crossflow towers.
14
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Input data Including:
atmospheric conditions
packing characteristics
desired tower height (H)
desired inlet water temperature (
water loading (L)
Estimate air flow rate (G)
Calculate friction coefficient
Calculate heat transfer coefficient (hQ)
I
Estimate outlet water temperature (o )
Counterflow Integration scheme
No
Is Inlet water (0.) = desired value?
Yes
Calculate pressure losses
Is calculated H - desired value? |
lYes
Resulting output describes tower performance
i
END
FIGURE 7. SIMPLIFIED FLOWCHART OF COUNTERFLOW COMPUTER SYSTEM
15
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Crossflow
As shown schematically in Figure 8, the crossflow packing 1s divided
up into rows and columns designated by the indices I and J, with
water flowing down the columns and air flowing across the rows.
(Parallel plate packing is used in this schematic for illustrative
purposes, not to indicate an actual crossflow packing arrangement.
Although the authors do not know of a crossflow tower using parallel
plate packing, such an arrangement may be practical.) The rows and
columns delineate rectangular elements of surface area dAj j.
By using the appropriate subscripts denoting rows and columns,
one can rewrite Equations 2, 3, and 5 to describe the differential
changes in water temperature (9), air total heat (i), and air
temperature (t) within crossflow packing:
(i6
LJ LPL
V'0T ! " nl,j' hr
di = I"3 ' Gl
dA, .......... (9)
dt =
(el,j - tl,j>
cp
/^
The integration scheme is similar to the one used for the counter-
flow case, except the differential changes in water temperature
apply down a column and the differential changes in air temperature
and air total heat apply along a row:
de ................ 02)
d1 ................
=tI,J*dt
Water temperature for all elements of the top row are equal to the
inlet water temperature, and air temperature and total heat for all
elements of the first column are equal to that of the incoming air.
16
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UNIT COLUMN
FLOWING WATER LAYER
UNIT ROW
FIG. 8 CROSSFLOW SCHEMATIC
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Starting with the element (1,1), one solves for water temperature
in each successive area element of the first column as the
water flows down until the outlet water temperature for that column
is evaluated. The water temperature in the next column is evaluated
in a similar manner starting with the inlet water temperature at
the top of the column. However, the air that the water contacts
in each of the elements of this column is changed, since the air
has passed across the first column of water. The new magnitudes
of air temperature and total heat computed for each row are used
in the integration as the water flows down the column. This
process is continued until the final column has been evaluated.
In this way it is possible to compute a temperature distribution
throughout the packing grid. A mixed outlet water temperature is
then calculated for the water flow out of all the columns, and
mixed air temperature and total heat are similarly computed for
the outlet air
A flow chart for the crossflow method is shown in Figure 9. In
the crossflow calculations it is not necessary initially to estimate
the outlet water temperature, since it can be solved for directly.
As previously stated, a computer program for crossflow towers is
not yet available.
Tower Height
For a natural draft tower, the basic design objective is to achieve
a sufficiently high airflow rate. This rate is a function of the
difference in pressure across the packing and the friction loss.
For a given airflow rate, the driving force acting on the air must
equal the friction loss through the tower. A simplified expression
for this concept which is used by several investigators (1) is:
H Ap = N|^ + iL (15)
where,
H = Tower height, ft
Ap = Difference in moist air density between the inlet
and the top of the packing, lb/ft3
N = Number of velocity heads lost
p = Average moist air density, lb/ft3
V = Average air velocity, ft/sec
18
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Input data Including:
atmospheric conditions
packing characteristics
desired tower height (H)
inlet water temperature (Ch)
water loading (L)
I Estimate air flow rate (G)
Calculate friction coefficient (Cp)
[ Calculate heat transfer coefficient (hfi) |
Crossflow Integration scheme
Calculate pressure losses
Is calculated H - desired value
E
Resulting output describes tower performance |
END
FIGURE 9. SIMPLIFIED FLOWCHART OF CROSSFLOW COMPUTER PROGRAM
19
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g = Acceleration of gravity, ft/sec2
T * A friction factor whtch accounts for the drag
of the falling water, hr
In general, as long as a density difference (Ap) exists, a tower
height (H) can be selected to obtain the required driving force,
however, there is a practical economic limit on tower height.
Some investigators assume that the resistance of the tower to
airflow is primarily due to inertia losses caused by the packing
and supports, as distinct from friction losses and the drag of falling
water. Therefore, in order to simplify their calculations they
take the number of velocity heads lost (N) as a constant for a
given tower and neglect the friction factor (T). Actually, the idea
that packing resistance is primarily due to inertia losses is some-
what debatable for a film flow packing consisting of parallel plates
where skin friction losses predominate. Analytical relationships have
been developed which correlate skin friction with heat transfer, and
they should apply directly to the simple geometry of parallel plates.
Also, expressions for the resistance should realistically include a
term due to the shell friction which would involve the shell surface
area and hence the height of the tower. In addition, there will be
some drag from supports and water distribution pipes, but this can
probably be minimized by careful design. In the computer program
the resistance is determined by computing the pressure drop at four
different sections in the tower (inlet, packing, shell, and
obstructions such as drift eliminators) based on the local velocity
and configuration through each section.
The direct correlation between skin friction and heat transfer in
parallel plate film packing should lead to a more accurate
calculation of the heat transfer and friction coefficients. How-
ever, the computational technique is not restricted to parallel
plate packing. If an effective value of the product hQ A is known
or can be determined for other types of packing, effective values
for the heat transfer coefficient ((13) and dA can be determined
for use in the computer program.
Estimating Coefficients
The performance of a cooling tower is strongly dependent on the
heat and mass transfer, and friction coefficients. Methods of
approximating these coefficients are given following
20
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Mass Transfer Coefficient
The mass transfer coefficient KQ, in Ib/hr ft2, based on the difference
between the concentration of water vapor in the saturated air in
contact with the water and the concentration of water vapor in the
main air stream is given approximately by:
06)
Another method used in cooling tower work is to relate KG directly
to the type of packing (3):
IT - A ^> ~n (17)
where,
a = Mean area of water-air interface per cubic
foot of packed volume, ft2/ft3
A = Empirical constant, ft
n = Empirical constant.
Values of n and A for different types of packing are given in Reference
3.
Heat Transfer Coefficient
Two methods are used to estimate the heat transfer coefficient. These
are the methods presented by Rish (5) and the heat transfer
relations based on a modified Reynolds analogy.
Rish's Method - Rish presents a semi-empirical equation developed
for plate type packing which, rearranged, yields:
Cn C, G
fc - P ' -ar (18)
2 + 7.16 Cf (|
where ,
C = Friction coefficient.
21
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Standard Heat Transfer Correlation - A common heat transfer relation-
ship used in tube, duct and annul us work is the modified form of
the Reynolds analogy (2). In the Reynolds analogy, heat and
momentum are assumed to be transferred by analogous processes in
turbulent flow. For Reynolds numbers from 10,000 to 120,000
and Prandtl numbers in the range 0.5 to 100, the Reynolds analogy
is modified sitghtlyon the basts of experimental data to yield
the following equation:
Nusselt No. = 0.023 (Reynolds No.)°'8(Prandtl No.)0'33
or
0'33
'•° (Prr-30 (19)
K K
where,
D = Hydraulic diameter, ft (the hydraulic diameter
is 4 times the flow cross-section divided by
wetted perimeter, thus for an annul us or large,
closely spaced plates, the hydraulic diameter
is 2 times the distance between the annul us
walls, or 2 times the distance between the plates)
v = Air velocity, ft/hr (for a water film having
appreciable velocity, v should be the relative
velocity between the air and the water)
k = Conductivity of the moist air, BTU/hr ft °F
U = Coefficient of viscosity, Ib/hr ft.
The Prandtl number is defined as the ratio of the kinematic viscosity
(a measure of the rate of momentum transfer between molecules) to
the thermal diffusivity (a measure of the ratio of the heat transmission
to the energy storage capacity of the molecules). The Prandtl number
for air varies with temperature around 0.7.
Friction Coefficient
Two methods are used to estimate the friction coefficients.
Rish's Method - For flat asbestos-cement sheets, 1-inch on centers,
under counterflow conditions, Rish (5) gives the following expression:
22
-------
Cf = 0,0192 (|jr)0'5 (20)
Standard Fricti.on Correlation - For Reynolds numbers from 10,000
to 120,000 Cf is given by the empirical relation:
Cf * 0.046 (Reynolds no.)"0'2 (21)
Presently, the counterflow program can use either Rish's expressions
to calculate heat transfer and friction coefficients for parallel
plate packing or it can use Equation 17 and Lowe and Christie's data
(3) for other types of packing. The program can be readily modified
to use other relations for computing the coefficients for different
types of packing.
Estimating Pressure Loss
The total pressure drop in a tower is due to the cumulative effect
of form drag, skin friction of the packing, and an effective pressure
loss due to the contraction of the incoming air.
Form Drag
The drag force, in Ib, is given by:
Drag = CD AD
where ,
Cp = Drag coefficient for obstructions based on the
dimension or drag area (Ap).
This is converted to the pressure drop by dividing by the appropriate
area, A ef, of the airflow over which this force acts. Therefore,
pressure drop due to form drag, APf (lb/ft2) is:
_ ............ .... (23)
Aref
23
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Skin Friction
The formula for the pressure loss due to skin friction of the
packing, APs (lb/ft2), is similar to that for form drag:
(24)
D A
The quantities Cn -r^— or Cf-~- are often referred to as N, the number
D Aref f Aref
of velocity heads lost.
Contraction Loss
In addition to the pressure drop due to the packing or obstructions,
there may also be a pressure drop to the contraction of the air stream
within the tower. When this air stream does not expand to fill the
tower, Lowe and Christie (3) show that N for this loss can be estimated
by:
Contraction = °'167
where ,
d = Tower diameter at the lower edge of the shell, ft
•
b = Height of the air opening, ft
Spray Loss
Rish (5) indicates that the pressure drop in velocity heads due to
water falling from a sheet of packing may be estimated by:
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SECTION IV
EXAMPLE COMPUTATIONS
To "test" the program, a set of example computations were performed
using the counterflow model.
Initially, the program was tested to determine the proper number of
integration steps. By setting a fixed value for the product hJ\,
it was possible to compare the results computed by the
program using various numbers of integration steps with results
obtained from the "Integral" solution presented in a paper by Wood
and Betts (6). The following data are given by Wood and Betts (6):
hQA/L C = 0.816 ft2
Outlet water temp. = 85°F
Air dry-bulb temp. = 90°F
Relative humidity = 37%
C = 0.24 BTU/lb °F
L =1200 lb/ft?hr
G = 800 lb/ft2 hr
Therefore, the magnitude of h-A is computed as:
hGA = (0.816 ft2) (L.C )
hGA = (0.816 ft2) (1200 lb/ft2 hr) (0.24 BTU/lb °F)
hfiA = 235 BTU/hr °F
The area required can be evaluated by dividing hgA by an assumed value
for hQ. For example, if an hQ of one BTU/hr ft2°F is assumed, then A »
235 ft2 per unit of cross-section. Therefore, for 10 integration steps,
dA = 235/10 = 23.5; 20 integration steps, dA = 235/20 = 11.75; 100
integration steps, dA = 235/100 = 2.35; etc.
Parallel plate packing constructed of 1/4-inch thick asbestos cement
sheets spaced 1-inch on centers provides a total of 24-square feet of
wetted surface in each cubic foot of packing.
25
-------
Therefore, the total packing height can be calculated as:
Packing height = ^235 ft-2 )-
(24 ft2/ft)
Packing height = 9.8 ft
Thus, for 10 integration steps, the program will calculate changes
in air and water parameters at 0.98 foot vertical intervals; for
20 integration steps, 0.49 foot intervals; etc,
Table 1 gives the results obtained with various numbers of
integration steps. Wood and Betts results are shown for comparison.
This table shows that a large number of integration steps are not
necessary for reasonable results. Computations with cooler, moister
air show the same effect. In applying the program to various situations
it was found that 20 integration steps are reasonable, both in terms
of accuracy and computer time.
The first test checked only that portion of the program dealing with
heat and mass transfer (Equations 2, 3, 5, 6, 7, and 8). To test
the total program, the Wood and Betts data were used with two sets
of air conditions. Rish's expressions for heat transfer and friction
coefficients, Equations 18 and 20, respectively, were employed.
Inlet pressure losses (i.e., form drag) were neglected. A counterflow
tower with a diameter of 300 feet and an air inlet height of 20 feet
were assumed.
Skin friction losses in the packing were computed using Equation 24,
where for the stated packing size and spacing, A/A f = 235 = 314.
775"
This ratio refers to the area for surface friction divided by the
amount of open space in a one square foot horizontal section of
packing. For this case, the packing itself takes up 1/4-inch of
every inch, so 75 percent of the space is vacant.
Table 2 gives the results of the computer runs for two sets of
air conditions. A tower height of 350 ± 10 ft. and an inlet water
temperature of 97 ± 0.1°F were assumed.
Comparing the results in Table 2 with those in Table 1 is not
advisable, since Table 2 gives answers based on different values
of the heat transfer coefficient (he) and air flow rate (6).
The most significant difference between the results for the'two
inlet air conditions is the effect on cooling range. It is easily
seen that the air at 77°F and 70 percent relative humidity gave
26
-------
IV3
TABLE 1
EFFECT OF CHANGING INTEGRATION INTERVALS
No. of Integration Steps
dA, ft2
Vertical intervals, ft
Inlet 6, °F
Outlet t, °F
Outlet i, BTU/lb
Outlet relative humidity, %
10
23.5
0.98
96.88
91.21
44.57
83.93
20
11.75
0.49
96.86
91.36
44.55
83.33
100
2.35
o.io
96.85
91.49
44.54
82.87
200
1.18
0.05
96.85
91.50
44.53
82.82
Wood & Betts
—
—
97
91.6
44.6
83.5
-------
fO
CO
TABLE 2
COUNTERFLOW EXAMPLE
Item
Inlet water temperature
Outlet water temperature
Cooling range (°F)
Outlet air temperature
Outlet air total heat
(BTU/lb)
Outlet relative humidity
(*)
Heat transfer coefficient,
he (BTU/hr ft2 °F)
Friction coefficient, C^
Air Flow (Ib/hr ft2)
Tower height (ft)
Air at 90° F - 37% Rel. Hum.
97.0
85.5
11.5
92.6
48.9
91.4
1.088
0.02691
611
353
Air at 77° F - 70% Rel. Hum.
97.0
82.8
14.2
88.3
45.6
98.0
1.363
0.02236
885
353
-------
better cooling than the air at 90°F and 37 percent relative
humidity, i.e., a cooling range of 14.2 °F versus a cooling range
of 11.5 °F.
The effect of different values of inlet water temperature and heat
transfer coefficient (hg) can be noted by comparing the intermediate
results of the computer runs. Figures 10 and 11 show the combined
effect of various values for inlet water temperature, hG, and tower
height on tower performance for hot, dry air and cool, moist air,
respectively. The vertical lines illustrate the cooling range for
a given tower height, as shown on the abscissa, for the inlet water
temperature indicated by the location of the top of the line. The
heat transfer coefficient, he, corresponding to the conditions 1n
the tower is given at the top of each line. The towers characterized
in Table 2 are tower A (Figure 10) and tower 6 (Figure 11). All of
the other towers represented are theoretically feasible, but were
rejected by the program because their height was not within 10 feet
of 350 feet as prescribed.
Note the significance of operating a tower with a higher inlet water
temperature, particularly under hot-dry conditions, Figure 10.
The cooling range can be increased without significantly increasing
the outlet water temperature, e.g., for towers C and D compare the
difference between inlet water temperatures to the difference between
outlet water temperatures. A similar comparison can be made for
towers H and I, Figure 11. The cooling range might also be increased
by increasing the tower height, but the height required may be
uneconomical, e.g., tower F. The fact that the moist temperate
condition is more favorable can be seen by comparing the two plots
and in particular, towers A and G.
The performance of a typical counterflow natural draft tower 400 feet
high is shown in Figure 12. Note that the tower performance (i.e.,
its cooling range) falls off more rapidly with Increasing relative
humidity at high air temperatures.
29
-------
98
2
LU
O.
97
96
95
94
86
85
84
uu
_l
»—
o
83
1.088 ]
-
*
1
*
>
i
A-
f
.088
1.0<
4
'
I
\
(
38
i
hfi= 1.373
.179 T K
«
i
i
• i
: D
ASSUMPTIONS:
Water loading « 1200 Ib/hr ft2
Inlet Air at 90°F, 37%
m Packing 1/4" plates, 1" on centers, 9.8' high
i
' '
E
— 1 — 1 L- 1 | i i
373
f
t
F
300 400 500 600 700 800 900 TOOO
FIGURE 10: PERFORMANCE OF TOWERS - HOT, DRY CONDITIONS
30
-------
2
UJ
Q.
OC
UJ
UJ
a:
UJ
104
102
100
98
96
94
ASSUMPTIONS:
Water loading - 1200 Ib/hr ft'
Inlet air at 77 F, 70%, R. H.
Packing 1/4" plates, 1" on centers, 9.8' high
86
84
82
80
300
1.363
1.420
T 1.420
1.363
T
r '
H I J
TOWER HEIGHT (FT)
i i
1.639
400
500
600
FIGURE 11: PERFORMANCE OF TOWERS - MOIST CONDITIONS
31
-------
120
110
100
90
80
70
60
ASSUMPTIONS:
Height: 400'
Diameter: 300*
Height Air Inlet: 20'
_ Packing
1/4" plates, 1" on centers, 9.8
Water loading 1700 Ib/hr ft*
Inlet water temperature: 120°F
Atmospheric Pressure « 14.493 Ps1
high
J
c
_L
50
AIR TEMPERATURE (DRY BULB) °F
FIGURE 12: PERFORMANCE OF A TYPICAL TOWER
10
20
30
40
50
Too
32
-------
REFERENCES
1. Chilton, H., "Performance of Natural-Draught Water-Cooling Towers,"
Proceedings of the Institution of Electrical Engineers> London,
Part II, 99, No. 71, 1952. pp. 440-456.
2. Kreith, F., "Forced Convection Inside Tubes and Ducts," Principles
of Heat Transfer, E. F. Obert, ed., 6th edition, International
Textbook Co., Scranton, 1962, pp. 343-346.
3. Lowe, H. J., and Christie, D. G., "Heat Transfer and Pressure Drop
Data on Cooling Tower Packings and Model Studies of the Resistance
of Natural Draft Towers to Airflow," International Heat Transfer
Conference, Denver, 1962, pp. 933-950.
4. McKelvey, K. K. and Brooke, M., The Industrial Cooling Tower,
Elsevier Company, Amsterdam, 1958.
5. R1sh, R. F., "The Design of a Natural Draught Cooling Tower,"
London, International Heat Transfer Conference, Denver, 1962,
pp. 951-958.
6. Wood, B. and Betts, P., "A Temperature Total Heat Diagram for
Cooling Tower Calculations," The Engineer. 189, 1950, pp. 337-349.
7. Wood, B. and Betts, P., "A Contribution to the Theory of Natural
Draught Cooling Towers," Proceedings Institution of Mechanical
Engineers. London, (War Emergency Proceedings, 56), 1963, 1950,
pp. 54-64.
33
-------
SYMBOLS
The following symbols are used in this paper:
A = Area of contact surface at the air-water interface,
ft2/ft2 of cross-section
Ac = Cross-sectional area, ft2
AD = Drag area, ft2 (See Equation 22)
Aref = Reference area f°r computing pressure drop, ft2
a = Mean area of water-air interface per cubic foot of
packed volume, ft2/ft3
b = Height of the air entrance at the tower base, ft
CD = Drag coefficient
Cf = Skin friction coefficient
Cp = Specific heat of the air, BTU/lb °F
CpL = Specific heat of the water, BTU/lb °F
D = Hydraulic diameter, ft
d = Tower diameter, ft
G = Airflow rate per square foot of cross-section, Ib/hr ft2
g = Acceleration of gravity, ft/sec2
H - Tower height, ft
hQ = Heat transfer coefficient, BTU/hr °F ft2
I = Index coordinate for unit row in crossflow case
i = Total heat of moist air, BTU/lb
35
-------
i' = Total heat of saturated air at temperature 6, BTLJ/lb
6
j = Index coordinate for unit column in crossflow case
KG = Mass transfer coefficient, Ib/hr ft2 (See Equation 16)
k = Thermal conductivity, BTU/hr ft °F
L * Water flow rate per square foot of cross-section, Ib/hr ft2
N = Number of velocity heads lost
n = Empirical constant (See Equation 17)
t = Air temperature, dry-bulb, °F
V = Velocity of the air, ft/sec
v = Air velocity, ft/hr
8 = Water temperature, °F
X = Empirical constant, ft"1 (See Equation 17)
u = Coefficient of viscosity, Ib/hr ft
p = Density of the moist air, lb/ft3
T = Friction factor to account for the drag of falling water,
hr (See Equation 15)
APf = Pressure drop due to form drag, lb/ft2
AP = Pressure drop due to skin friction, lb/ft2
36
-------
APPENDIX - COMPUTER PROGRAM
The main body of the paper dealt with the basic integration scheme,
along with the pressure loss, and heat and mass transfer relations.
This appendix deals primarily with the details of the computer
program.
The program was developed on the Control Data 3300 computer at
Oregon State University, and then modified to operate on FWPCA's
IBM System/360 computer facility. All references herein are to
the System 360 version of the program, which is written in Fortran
IV and compiled on the G level compiler.
37
-------
RUNNING THE PROGRAM
Input Options and Variables
The program is written so that only those variables which have
significance for the case being run need be input.
Demonstration Case
If the user wishes to run the program without any input variables,
the program may be called with no cards in the input stream.
The program then assumes a test case, and runs with preassigned
values. Output options of printing the initial assumptions,
and of printing the results of iterations, are assumed. A sample
output is shown later in this appendix.
Required Variables
If the user does not want a test case, he must input tower geometry
(HTOWER, DTOWER, and HAIRIN), a local meteorology (AIRTI and HUM)
and inlet water parameters (WTRTI and WTRF or WTRFT), If some, but
not all of those are input, the program will terminate after
listing the input variables.
Parallel Plate Packing
Default values - If no packing related variables are input, the
program assumes parallel plate packing of 1/4-inch plates on 1-
inch centers, 9.8 feet high.
Other sizes - The user may alternatively input THICK, SPACE, and
HPACK.Tfie" pressure loss in the packing is then computed:
with
V =
Aflowp
39
-------
These formulae, however, make certain assumptions with which the
user may not agree. They are:
. _ SPACE-THICK
"flow " SPACE
A - 24 x HPACK
"total" SPACE
^-i... — ~" T*QT*u I
drag T
flow
The values of ATOTAL, AFPK, and ADPK may be input in lieu of SPACE,
etc., to access the program beyond the above assumptions.
In any case, when using parallel plate packing, the program
computes Cf and hG from the empirical formula of Rish (5), equations
20 and 18.
Other Packings
The program allows for use of the experimental data of Lowe and
Christie (3) for different types of packing. There are two
possibilities:
1. If LAMBDA, N, ADPK, AFPK, and HPACK are input, the program
computes !IG with Lowe and Christie's data (equation 17), but Cf
to be used in the packing pressure loss equation is computed
from Rish (equation 20).
2. If LAMBDA, N, HPACK, PI3, P23, PI6, and P26 are input, the
packing pressure loss is interpolated from the velocity head
experimental data of Lowe and Christie.
Pressure Loss Due to Tower Structure and Geometry
If the user wishes to include form drag in the pressure loss
computations, he has the option of inserting the variables, AFIN,
ADIN, COIN to compute inlet pressure losses; AFOT, ADOT, and CDOT
to compute outlet losses; and AFSL, ADSL, and CDSL to compute losses
due to the shell.
40
-------
The program uses the variables AF— to compute the velocity using
airflow and density. It then applies this velocity to equation
23 using AD-- and CD— to compute a pressure loss with a simple
"form drag" scheme. If a more sophisticated method, such as
accounting for several rows of structural columns, is desired,
AF--, AD—, and CD-- may be adjusted to achieve the desired results
without reprogramming.
41
-------
Variable
Name
ADIN
ADOT
ADPK
ADSL
AFIN
AFPK
AFOT
AFSL
AIRF
Input Variables
Default Value* Units
ftVft2
0.
0.
314.
0.
1.
.75
WTRF
ft2/ft2
ftVft5
ft2/ft2
ft2/ft2
ft2/ft2
ft2/ft2
ft2/ft2
Ibs/hr ft2
Meaning
Normalized cross-sectional
drag area at the air inlet.
Normalized cross-sectional
drag area at the air
outlet.
Surface area per unit
flow through area to be
used with Cf in computing
pressure loss in packing
due to skin friction
coefficient.
Normalized cross-sectional
drag area in the shell.
Normalized cross-sectional
flow through area at the
air inlet.
Portion of tower cross-
section which is unobstructed
by packing.
Normalized cross-sectional
flow through area at the
outlet of the packing.
Normalized cross-sectional
flow through area in the
shell.
An initial guess for the
normalized air flow rate.
The program modifies this
as execution proceeds.
* A default value is the value assumed by the computer if the
variable has not been input. If the user inputs a variable, it
will be used in place of the default value.
42
-------
Variable
Name
AIRTI
ATMOS
ATOTAL
COIN
CDOT
CDSL
CP
DTOWER
HAIRIN
HPACK
HTOWER
HUM
Default Value
90
14.493
235.
0.
0.
0.
.24
300
30
9.8
350
.37
Units
°F
lb/in2
ft2
BTU/lb °F
ft
ft
ft
ft
LAMBDA
N
P13
None
None
None
vel/hds/
ft
Meaning
Inlet air temperature,
dry bulb.
Atmospheric pressure.
Total packing surface
area in one square foot
of tower cross-section.
Drag coefficient for
the inlet structures.
Drag coefficient for
the outlet structures.
Drag coefficient for
the shell.
Specific heat of moist air.
Tower diameter at
packing.
Height of the air inlet.
Height of the packing.
Tower height.
Relative humidity of the
inlet air.
Lowe & Christie's
empirical A(See equation
17 and Table 3).
Lowe & Christie's
empirical N (See equation
17 and Table 3).
Lowe & Christie's
pressure drop data
(See Table 3).
43
-------
Variable
Name __
P16
P23
P26
SPACE
STEPS
THICK
TOLERH
TOLERT
WTRF
WTRFT
WTRTI
WTRTO
Default Value Units
None vel.hds/ft
None
None
1.
20
.25
10.
.1
1200
8.5 x 107
97
WTRTI - 25
vel.hds/ft
vel.hds/ft
inches
inches
ft
Ibs/hr ft2
Ibs/hr
Meaning
Lowe & Christie's
pressure drop data
(See Table 3).
Lowe & Christie's
pressure drop data
(See Table 3).
Lowe & Christie's
pressure drop data
(See Table 3).
Center to center
spacing of parallel
plates.
Number of integration
steps.
Thickness of a single
parallel packing plate.
If the computed
tower height is within
±TOLERH of the specified
value, the program ends.
If the computed inlet
water temperature is
within ±TOLERT of the
specified value, the
program accepts the
computation.
Normalized water flow
rate.
Total water flow rate
through tower.
Inlet water temperature.
An initial guess for
the outlet water
temperature.
44
-------
PACKING DATA - TABLE 3*
lOMft
Christie
No.
Description of
Packing
Figure
No.
DIM
nslons in Fie. 13
ht vfc H U S
Jlnchesl (Inches) (Inches) (Inches) (Inches)
Transfer
x n
••••••Id.' '. !!'!» •l.Tr~VfTinV^^^ii4IBIBBHHri
Hater
1000 Ib/hr ft*
P13 *IR PW
3 ft/sec C ft/sec
*t»r
2000 It/hr ft*
WM JK •^btf
Pit
3 ft/sec 6 ft/tec
cn
8
9
10
11
14
15
16
17
19
21
Triangular
Splash Bar
13 (a)
0.09
0.50
Flat Asbestos
Sheets
Corrugated
Asbestos Sheets
22
23
24
25
26 Trlanj
Splas
27
28
29
30
31
32
37
(ular
> Bar
13 (c)
AS
13 (a)
13 (d)
13 (e)
13 (f)
13 (b)
tilth 8ars
Upside Down
2% 5%
2li cs/
/• 3 A
•2% vk*5%
' 2*A 5 A
6
6
6
a
11A
1 I/
1 /V
1
6
1%
IV,
2VS»
1%
1
4
5
2
6
5 ft 13
Alter-
nately
12
18
9
8
8
10
10
7Vi
6
8
6
3
3
3
2%
3
0
2
2
0
2
2
2V*
1
0.094
0.096
0.07S
0.072
0.088
0.11
0.12
0.14
0.084
0.21
0.22
0.18
0.11
0.17
0.074
0.087
0.079
0.072
0.095
0.098
0.093
0.187
0.50
0.45
0.42
0.47
0.70
0.72
0.76
0.73
0.49
0.69
0.61
0.68
0.66
0.58
0.52
0.55
0.58
0.54
0.53
0.54
0.46
0.65
2.7
3.7
2.0
1.7
1.9
0.7
0.8
0.9
0.9
3.4
3.2
4.3
3.1
1.0
4.4
1.2
1.2
0.9
0.9
1.3
1.7
1.3
4.8
2.0
3.3
1.7
1.3
1.6
0.5S
0.6
0.7
0.7
2.7
2.7
3.1
2.7
0.5
4.1
0.9
0.9
0.75
0.7
0.9
1.3
0.8
4.1
3.S
4.8
2.6
2.4
2.8
1.0
1.1
1.1
1.2
5.1
3.8
5.1
3.5
1.6
5.1
2.0
2.1
1.7
1.6
2.2
2.6
2.0
6.4
3.9
2.1
1.7
2.1
0.7
0.8
0.9
1.0
3.6
3.1
3.6
3.1
0.8
4.6
1.3
1.3
1.2
1.1
1.3
1.8
1.3
5.4
•Taken fron Reference 3
-------
TABLE 3 (CONT.)
Lowe ft
Christie
Packing
No.
38
39
40
41
42
43
45
47
48
49
50
51
55
57
58
59
61
62
Description of
Packing
Asbestos Louvres
M
H
11
Triangular
Splash Bar
N
Asbestos Louvres
w
N
M
Rectangular
Splash Bar
H
Corrugated
Asbestos Sheets
Figure
No.
13 (g)
13"
H
M
13 (b)
H
13 (g)
13 (g)
N *
M
13 (h)
M
" (1)
h.
(Inches)
1
1
1
1
iVi
1 1/2
l'/2
1V2
Dimensions In Fig. 13 Trar
va
(Inches)
5%
5'A
ty
5'A
5'A
5'A
5V,
Corrugations
HoHz.
ha
2V,
• /I 6
1 V
2V,
?5.
ya
5JA
2V,
Yh
5JA
2V,
H W S
(Inches) (Inches) (Inches) X
1 10% 0.203
1 6% 0.287
1 20% 0.118
1 15% 0.154
5 7'/2 2Vz 0.095
6 7 )/2 3 0.089
1 6% 0.351
I'A 6V. 0.247
11A 151A 0.169
1V2 201A 0.101
8 92 0.086
8 12 2 0.08
Corrugations
Vert.
hb yb
2V, 53A 0.186
iVi, fh 0.308
2Vi 5% 0.207
iVis 2V. 0.248
2V. 7 0.163
83A 2'ft s 0.133
isfer Pressure Drop (vely. heads/ft)
1000 Ib/hr ft*
P13 AIR P16
n 3 ft/sec 6 ft/sec
0.70 2.7 2.5
0.68 4.8 4.2
0.69 1.7 1.5
0.67 2.1 1.8
0.49 1.3 0.8
0.47 1.2 0.7
0.66 10.5 9.5
0.66 6.8 6.1
0.65 4.7 4.0
0.63 2.9 2.3
0.52 2.5 1.9
0.53 1.7 1.4
0.73 3.8 3.3
0.80 9.0 8.0
0.79 3.2 2.8
0.79 10.8 10.0
0.7V 4.3 3.8
0.72 2.4 1.6
2000 Ib/hr
P23 *»
3 ft/sec
3.1
5.8
2.1
2.6
2.3
2.2
12.0
8.4
5.5
3.6
3.1
2.5
4.4
9.0
3.9
11.5
5.4
3.1
ft'
P26
6 ft/sec
3.0
4.9
1.8
2.2
1.4
1.2
10.5
7.2
4.7
2.6
2.7
1.8
3.8
9.0
3.2
11.0
4.3
2.1
-------
(a)
H — »j w
t t t
(b)
w
1 t t
t t t
t t t
-*( K-H
0)
ALTERNATE LAYERS OF
UOUVRES TURNED THRO* 90* I
t
t t I
w
"tea
era
CTZD
t t t
AIR FLOW
SHEETS
TIGHTLY
PACKED
t t t
AIR FLOW
FIGURE 13: TYPES OF PACKING (from Lowe and Christie (3))
-------
Output Options
Listing Initial Values
The user has control over whether the initial (input or calculated)
values of the variables will be listed.
Listing Results of Iterations
Results of each iteration are listed after an adjustment to WTRTO
or AIRF is made. A message is also written whenever the program
makes an iteration to modify either of the above.
Listing Results of each Integration Step
Information about the status of the integration may be printed
after each step. This is essentially a diagnostic mode, since it
generates volumninous output. As used here, each iteration
encompasses one or more integrations. Thus, each time a line of
iterative data is printed, STEPS lines of integration step results
would be printed.
Listing Format
Column Title
ITER NO
WATER LOSS
OUTLET
AIR
DENSITY
AIR
VELOCITY
IN PACKING
CALC
HEAT
TRANS
COEFF
Units
Ib/hr ft2
lb/ft3
ft/sec
BTU/hr ft2°F
Meaning
Iteration number.
Water evaporated per square
foot of tower cross-section.
Density of the air above the
packing.
Air velocity in packing
(equals nominal velocity if
Lowe & Christie's data are
used).
Calculated heat transfer
coefficient (0 if Lowe &
Christie's data are used)
48
-------
Column Title
Units
Meaning
TOWER
CHARACTERISTIC
(K*A/L.)
SKIN
FRICTION
COEFF
RELATIVE
HUMID
INLET
WATER
TEMP
OUTLET
AIR
TEMP
OUTLET
AIR
ENTHALPY
PROFILE
PRESSURE
LOSS
PACKING
PRESSURE
LOSS
SPRAY
PRESSURE
LOSS
VENA CON
PRESSURE
LOSS
SHELL
PRESSURE
LOSS
TOWER
HEIGHT
(decimal
fraction)
BTU/lb
lb/ft-
lb/ft5
lb/ft'
Ib/ft'
lb/ft5
ft
Tower characteristic or
number of transfer units.
Skin friction coefficient
(0 if Lowe & Christie's
data are used).
Relative humidity.
Inlet water temperature.
Air temperature above the
packing.
Air enthalpy above the
packing.
Sum of the pressure losses
at the inlet, outlet and shell.
Pressure loss due to packing.
Pressure loss due to water
falling from the bottom of
the packing.
Pressure loss due to the
Vena-Contracta.
Pressure loss due to the
shell.
Total tower height.
49
-------
Card Deck Set-ups
The program described herein is stored as a load module on a disk
pack at U. S. Time Sharing, Inc., to which most FWPCA System/360
terminals have access. To invoke the program, use the following
JCL and data cards:
//JOBLIB DD DSN=KENBYRAM, DISP=(OLD,KEEP),UNIT=2314
// VOL=(PRIVATE, RETAIN, SER=FWPCH)
//STEP1 EXEC P6M=COOLTOWR, REGION=200K
//FT06F001 DD SYSOUT=A,DCB=(RECFM=FBSA,LRECL=133,BLKSIZE=1330)
//FT05F001 DD *
/*
consists of
1. An "output options" card, with a "T" in
column 1 if results of iterations,
column 2 if all steps of each integration,
column 3 if input variables and assumptions,
are to be printed. Columns are blank otherwise,
2. Any number of "input variable cards" with
columns 1-8: variable name, left justified,
and spelled correctly.
columns 9-18: variable value, anywhere in
field, with decimal point punched.
One variable fits on each card, with the cards in any order.
Not all variables need be input (see page 49),
To run the demonstration case, are omitted.
50
-------
BLOCK FLOW CHART
INPUT
Check that appropriate com-
binations of variables are
Input. Print variables.
Initialize airflow related
variables
Initialize outlet water tem-
perature related variables
•[ Compute one integration step]
4-
Adjust for saturation
no
no
^through integrating?>
yes
^Extrapolating water tempera tureT^>-*--^-—H Compute new tempera tur&t-
Ino
[Compute pressure losses
[and tower heights
yes
Compute new airflow-!
no
Tower height within V
tolerance?
lyes
no
Extrapolate on airflow for
new tower height '
Alterations been printedT>
lyes
Print final tower height
and outlet water temperature
no
->.[SetEND flag |
51
-------
EXPLANATION OF PROGRAM VARIABLES
Variable Name
A
AIRFL
AIRT
C
CF
CONWTR
DA
DAIRT
DENT
DNSARI
DNSARO
DNSAVG
DTODTI
DWTRT
ENDFLG
ENT
ENTI
ENTSA
Definition
The area integrated over as the integration
proceeds.
The last air flow rate used by the program.
The air temperature as the integration
proceeds.
A temporary variable.
Friction coefficient.
The weight of water which has been
condensed out as the integration proceeds.
A portion of the total area, = ATOTAL/STEPS,
The change in air temperature during one
integration step.
The change in enthalpy of the air during one
integration step.
Density of the inlet air.
Density of the outlet air.
Average of the outlet and inlet air densities,
The rate of outlet water temperature change
versus inlet water temperature change.
The change in water temperature during one
integration step.
Logical: true, if the program has reached a
normal termination.
The air enthalpy as the integration proceeds.
The enthalpy of the inlet air.
The enthalpy of the air during the saturation
adjustment loop.
53
-------
Variable Name
Definition
ENTSAT
EXTAFL
EXTWTO
FND
H
HI
H2
HENT
HG
HUM I
INHIB
IPG
JD
JM
JULDAT
JY
LBW
The enthalpy of a pound of saturated air-water
mixture.
Logical: true, if this iteration is being
made to extrapolate airflow.
Logical: true, if an iteration is being
made to extrapolate outlet water temperature.
A variable which is either "*" or blank,
indicating whether an initial value has
been read in, or assumed, respectively.
Calculated tower height.
*
Holds the last calculated value of tower
height while a new value is being extrapolated.
Holds the calculated value of tower height.
HI and H2 are then used in an extrapolation
for airflow.
The adjusted enthalpy of the air-water
droplet mixture as its temperature is
raised in the saturation adjustment loop.
Heat transfer coefficient.
The relative humidity of the air as the
integration proceeds.
Logical: true, if program execution is to
be terminated before starting the iterations
(if input data are in error, for example).
Counts the pages printed out.
Integer value of day of month.
Integer value of month.
The subroutine which fetches month, day and
year from the operating system.
Integer value of last two digits of year.
Pounds of water (droplets) per pound of air
at any point in the packing, according to
the status of the integration.
54
-------
Variable Name
Definition
LBVI
LBVLBA
LBVLBS
LITER
LSTEP
NB
NE
NOITER
PI
P2
PPP
PRIN
PRINP
PRITER
Pounds of vapor per pound of air, in the
inlet air.
Pounds of vapor per pound of air at any
point in the packing, according to the
integration.
Pounds of vapor per pound of air at
saturation.
Counts the lines printed on a page with
results of iterations, and controls heading
printing.
Counts the lines printed on a page with the
step by step results of iterations and
controls heading printing.
Controls which of the packing related
initial variables will be printed. The
first 26 values of VALS() are printed,
and then the NBth through NEth values are
printed.
See above.
The number of iterations, or the number of
times the program has completed an
integration.
Temporary variable.
Temporary variable.
Logical; true, if the tower has parallel
plate packing.
Logical: true, if Lowe & Christie's
pressure loss constants have been input
(P13, P16, P23, P26).
Logical: true, if the input data and
initial assumptions are to be printed.
Logical: true, if the results of each
iteration are to be printed.
55
-------
Variable Name
Definition
PRLIN
PRLPK
PRLPR
PRLOT
PRLSL
PRLSP
PRSTEP
PSA
PSAH
PSAT()
PSW
READINO
Tl
vv
VALSC)
Pressure loss at the inlet.
Pressure loss in the packing.
Pressure loss due to profile (=PRLIN+PRLOT).
Pressure loss at the outlet.
Pressure loss in the shell.
Pressure loss due to spray.
Logical: true, if each step in the
integration is to be printed.
Saturation vapor pressure at the air
temperature.
Saturation vapor pressure in the loop
which adjusts super-saturated air to
saturated air at constant enthalpy.
Function which obtains the saturation
vapor pressure from a temperature used as
the function argument. It is looked up in
a table.
Saturation vapor pressure at the water
temperature.
Logical: true, if a particular initial
variable has appeared in the input stream.
Example: If READIN(2)=TRUE, AIRTI has been
input, AIRTI=VALS(2)=value, VNAMES(2)='AIRTI.'
Temporary variable used to hold air temperature
in the saturation adjustment loop.
Temporary variable.
The value of an input variable, read from
the card. It is later placed in VALS().
The value of the initial variables, which
may be changed by input.
56
-------
Variable Name
Definition
VHSP
VHVC
VIN
VN
VNAMESO
VNOM
VPEN
VPENT
VPRES
VPRESI
VPK
VOT
VSL
WTRLT
WTRT1
WTRT2
Velocity heads lost to spray interference
with airflow.
Velocity heads lost due to Vena-Contracta
in the tower.
Air velocity at the inlet.
The input variable name read from the
input card, used in searching through the
table of VNAMESO.
Alphameric, holds the character representation
of the input variable names, for interpreting
the input cards.
The nominal velocity in the packing, feet/
second.
The enthalpy of the moisture in the air
and used in the saturation adjustment loop.
The enthalpy of the vapor in a pound of
air.
The vapor pressure of the air at any point
in the packing.
The vapor pressure of the inlet air.
Air velocity in the packing.
Air velocity at the outlet.
Air velocity in the shell.
The water which condenses out during an
integration step.
Holds the last calculated value of inlet
water temperature while a new value is
being calculated.
Holds the second calculated value of inlet
water temperature for extrapolation. WTRT1
and WTRT2 are combined in making an extra-
polation.
57
-------
PROGRAM LISTING
rf»LAMBOA.N»L6VLBS,ieVI. ) t
CrtrO, VALS<4»* (HAT»IN. VALS (S) ) » HUM.VALS (6) ) . («T«FT, VALS (7) ) t
» «
(D'»SAPT»vALt>«2SM,(TwICK»VALSt?6) >« (SPACF f >/ALSI«'7) ) *
, (AFPK,VALSI2<»»»
CP13.VALS<3 ) « f Plb, »/Al S (36) ) • (P<»b« VA|> (37) )
DATA VALS/06.9t90.,357..300.«33.4i.37*8.5E7«l2t)2.3t2«0.»?0.»
*,lH / t IPG.L lTr.B,L*TfiP/Ui5? .
IMMIH.CMOFL'i/2'.F'ALSF./
.bHAFCT tSHAFSL tSHADlN »5HADCT .SHAOSL .5HCOIN .
6Hn>JSAPI
»5H-(PACK
• 5HP13 tSHPifi .SHPl*. »5HP26 /
Ł»«»•*•••«**»••*••«»»*«»»*»»«««»»*••»««••«••*««»«««<>«»»<>*«*•«**»*«•«««
c TME PAT^E' LC<"' I^P'^ SECTION is DF.MGNFO TC I^OHF THAT
C APP*CpPIAT- CSM«1'-ATIC'JS ^F VALUES AWE TMPUT. aLL VrtHIABLtS
C HAVE OFFA ILT WALi"E» AMI. rNLV THOSE WHICH >IEED T.O «fc CHANfifcO
C MUST ap POJT
•»»«•»«•«»***•»••»•« ••«««•••»««*»•••»«•*«**••••
104 F
CALL JJL">*T(jv,.j^,jn)
70 *E4DTN(I)«.FAL*F,
101
»^ Tr, 7?
)PWJ
71 FS
77
7?
00001
00002
00003
00004
oooos
00006
00007
00008
00009
00010
00011
00012
00013
0001*
00015
00016
00017
00018
00019
00020
00021
00022
00023
0002*
00025
00026
00027
*»•
•**
00029
00030
00031
00032
00033
0003*
00035
0003*
00037
00038
00039
OOOfcO
00046
00047
00048
00049
OOD'JO
OOOS1
00052
00053
00055
71 Ia»."i7
OOOS7
0005H
59
-------
FIVN.EI.VNAMESllMGC TC 74
7*
76 FORMATIONS VARIABLE NAMED **A8)
60 TO 77
RFADINtI»».TRUE.
65 T5 77
79 00 7» 1-1.7
IF(READITSu(EM*UTuWER*«785398
IF I. NOT.
IFJ.MCT.
AlRT«ApTI
)AIPF«WTRF
VPRES«H'J*«PSAT (AIPT)
LBVLPA«.ft??*VPRES/,AT
VPENT»1 561 . * .4»* PARF*,I3/*OVARIARLE NAME -'"
no 89 I»l«25
IFUWCT.'EAOINIII)FND«*TAR
M ««01TE<%{90)VNAMF.S(1)»VALS(I) «FNO
C OCTfRMlwE PACK IW TYPE
000*1
000*2
00043
OOO**
00045
000**
000*7
000*8
000*9
00070
00071
00072
00071
00074
OOOTS
00076
00077
00076
00079
00080
OOOdl
00082
00083
00084
00085
00086
00087
00088
00089
00090
00091
00092
00093
00094
0009*
00096
)97
'98
00099
00100
00101
00102
00103
0010*
00105
00106
00107
00108
00109
00110
00111
00112
00113
0011*
60
-------
1F«B€ADIVH?8))6C TC 11
lFl.NCT.*EADIN(?6).ANn..MCT.REAr>IN(27»ftC T
GC TC 5
* ir(PEADIM(?T»6C TS 8
WRITE I*»*3)VNAMES»?7>
ATCTAL»?*.*HPACK/SPAC(r
SC TC 2
3 IFt.NCT.<)EADI'lO?).AMn..NCT.REAOTN(33»<'C TC
PPP«. FALSE.
• .AND..*5T.REAOIN<37))6C TC
"RIN..TBJE.
NE»37
11 00 9 I*M3*r>iE
C TC 9
1NHIR-.T9JE.
IF(INHI«)STCP
1? FCRMAT «*0 (PARALLEL PLATE PACKING NCT ASSUMED)*/)
? IF|PPP)^ITF(f .13)
13 FCRMAT «0 (PARALLEL PLATE PACKING ASSIJ4EO) */)
1F«.MCT.»»INP)6C TC 93
OC 14 I*Nfl»NE
CH CTHEH INPUT CR
14 WRITE (6*93) VNA<4ES (I) tVALS(I)*FNO
91 FCRMAT(*0*,20X»*«VAL«»E CALCuLATEn
93 OA«ATCTAL/STEPS
C END INPJT AND IMITIAL17ATICK,
C START ITERATICK
€••»••••••••••••*•»••••*•»»•••••••••*•••*••••***••••••**»••••*•»•••»«•
9* VN5M«AI7F/«ONSAR1»3600.»
IF«PPP)3C TC 16
KAL«MPAC<»LAMBUA* (AIRF/WTRF ) »»N
00116
00119
OUl?o
001?1
001?3
Ool?<»
001P5
001?6
001?7
001?y
00111
oni 1?
00139
OCl3«»
00115
U0136
oo nr
00118
OoUg
oouo
001*1
OOU3
00 U4
OOU5
00 U6
001*7
OOU?
00150
00151
0015?
00153
0015*
00155
00156
00157
00158
00159
001*0
00161
00162
00 * 6 J
00lt>*
00165
00166
00167
00168
00169
OOl 70
HGCUT«0.
61
-------
Kt.NOT.rftlNI
•9NCV3.-1.
TC
- 1 000. » /1000.
cr.o.
03 T
irUNOT.W»P)6C TC
ENT.ENTl
CCSWTR-0.
C INTE6RAT1CN LOCP BEGINS WITH STATEMENT A
Ł•••••••••••»•»••«»**•••*«»••••••»••••••«•••••••••••••••••••••••••••••
IF(PSw«E3«0.)63 T3 llO
/Cp
ir«.NCT.»RSTEP.C«.EXTwTC.C«.EXTAFL)OS TC 3*
iritSTEP.LT.*7)GC TC 3ft
JMtJD«JY»IPG
37 fSRMATttlCCCLlMe TOWER PROGRAM - STEP BY STEP RESULTS
ATR SATUR ACTUAL REL PNDS «TR/ VAPC«*/
« APR* TEHP TEMP ENTHAL ENTHAL HUM PNOS AIR
L5TEP-0
LITER-5?
LSTEP-LSTEP*!
MRlTE(6«38)A*toTRT»AIRTtENTSAT«ENT«HUMltLBVUBA«VPRtS
OATRT»H3»OA»<*TRT-AIRT)/(AIRF«CP)
1F«P3A.f3,Q.)OC TC 110
(ATMCS-PSA)
ULC.DGC TC 99
Ł•••••••••••••••»»••••••»•*•*«••*•••«****•••»»*•••»••»*•*•*•»••«•**•*•
ttlH
OMtl
ooi
ootn
coin
Miff
001 TO
Miff
00100
00101
001*4
OOlff
OOlOf
OOIM
00100
OOlfO
001*1
00192
OOUJ
00104
OOlfS
00106
OOIOT
OOIM
00200
00201
00202
00203
0020*
00205
00206
00207
00206
00209
00210
00211
00212
00213
002 U
002 IS
00216
00217
00218
00Z'9
00220
00221
00222
00223
62
-------
c ir MIXTURE is SUPER-SATURATED t RAISE TEMPERATURE TO
C A POINT WHERE MIXTURE IS JUST SATURATED* KEEPING THE TOTAL
C ENTHALPY CONSTANT
€+•••••••••••••••••••••*•••••••+••••••••••••••••••••*•••••••••••••••••
T-AIRT
•7 T»T».l
PSAHvPSAT(T)
IF80 TC
LBW».622*PSAH/ UTMCS-PSAH)
ENTSA«CP» 6C TO 2*
LBVLBA* ( ENT-CP* C AIRT-32. ) I /VPENT
tf TRLT«A I QF* GO TO 30
LSTCP*50
LITER-0
WRITE (6*31 )JM» JO* JVtIPQ
11 FORMAT (01CCCLINQ TOWER PROGRAM - RpSULTS OF ITEt*ATlONS**53x«
• 12, 2(1-1/12).* PAOE**T3/*0«22X,*AIR CALC TCWE»*/
0022*
00227
00228
0022*
00230
00231
00232
00233
0023*
00235
0023*
00237
0023S
00239
00240
00241
00242
00243
00244
00245
002*6
00247
00248
002*9
00250
00251
00252
00253
00254
00255
00256
00257
00258
00259
00260
00261
00262
*••
00263
00264
00265
00266
00267
00266
00269
00270
00271
00272
00273
00274
00275
00276
00283
00284
63
-------
•* HER HATER AIR IN WANS TfRISTlC FRICTION MfLAT MATC*«
•* AIR AIR PRESSURE PRESSURE PRESSURE PRESSURE TOMCR*/ 002M
•* MC LOSS DENSITY PAKINO COEFF (K*A/L> COEFF HUMID TEMP «• OOIM
•* TEMP ENTHAL LOSS LOSS LOSS LOSS MCI«MT*> OO290
JO WRITE t**3?)NCJTEf»tWTRLT,DN$ARG.VPK.HaOUT»KAL«CF.HUMl»WTRT»AlRT. 00291
• CNT»P»LP»»P«LPK,PkLSP.PRLVC.H 00291
39 rORMAT6C TO 39 00296
WRITE <6i98> 0029T
9* FORMAT U.HCRC THAN 100 ITERATIONS* EXECUTION TERMINATED*) 0029S
STOP 00299
C*»«»»»»*»*»»»»««*»»»»»««*»«»»»«»»»«»»««*««»»»«»»»»»««»*»»»«««»«»»»««« 00300
C NC* FIND IF SPECIFICED TOLERANCES ARE MET, AMD IF NSTt WHICH 00>01
C OF AlRF SP WTWTO SHCULO BE ADJUSTED 00302
c PRINT A MESSAGE *«F6. 1 «*) *) 00310
LITEP«LITE«*1 00311
OS TO «6 00312
4A «RITF(6«43>WT*TC 00313
LITER»LTTFO*2 0031*
41 FCPMAT«0«ŁXTRAPCLATI*r, FROM WTRTO«*fF6. 1 .*> 0) 00315
4A WTRTl««(TPT 00316
WTRTO«*T:»TS«.OOI 00317
F00 TO ?9 003?1
TO *4 00322
00323
LITE»«LITE«»*? 0032*
41 F3QMAT|*3(EXTHAPCLATlMr, FROM AI»F«*»F7.1 «*) *) 00325
44 *IBFL*AI4F 00326
Hl.H 0032?
AIPF«AI9F«10, 00328
riTAFL-.T^'JE. OOJ29
65 TC 9^ 003^0
Ł•••••••••••••••»••»•»•»•»*•»••*»•••••*•»••••«••••••«•»•••**«»»•••*«•« 00331
C A SAMPLE TTfwATIC^ HA« HECN MADE TC ADJUST AJQF OH rtTHTS 00332
C PRINT v«EJ?AOE» AND f>C ANCTHER ITfKATfSN 00333
0033*
00335
00336
64
-------
TO 95
'
LITER-LITER*!
55 FORMATS iMOOlFylNG AIRF TO *tF7.1t*>*>
•8 TO 9S
t4 WTRT2.WTRT
DTGDTI-.001/
33
9« FORMAT »#-E^O COOLING TOWER PROGRAM*/
• *OFIMAL CUTLET WATER TEMPERATURE IS*,F6.1/
• *OFI« 00351
LITER-LITER*!
68 TC l5
•2 WRITE <6t60)WTRTC
LITER-LITEB*2 .
60 FORMAT (« *> 00371
jt» «•• at UUJ't
003T3
65
-------
FUNCTION PSAT(T) 00001
DIMENSION V(181) 00002
DATA M/0/ 00003
OATAV/.OB854,.09223,.09603..09995,.10401,.10821,.11256,.11705..121 00004
•70,.12652,.13150..13665,,14199,.14752..15323,.15914,.16*25,.17157, 00005
••17811,.18486*.19182*.19900,.20642*,2141,.2220*.2302*.2386,.2473,. 00006
•2563,.265%..2751,.2fl5Q..29&1..3056,.3164,.3276,.3390,.3*09..3*31,. 00007
•3756,.3896,.4019,.4156..4298..4443,,4593,.4747,.49Q6,.5069,,5237,, 00008
•5410,.559R..5771,.5959..6152..6351,.6556,.6766,.6982,.7204,.7432,. 00009
•7666,.7906,.8153..8407,.8668..8935..9210..9492..9781,1.0078,1.0382 00010
••1.0695.1.1016*1.1345,1.1683.1,2029,1.2384,1.2748,1,3121,1.3504*1, 00011
•3896,1.4298,1.4709,1.5130,1.5563,1*6006,1.6459,1.6924,1*7400,1.788 00012
•8,l*«3H7,l,flft97,1.9420,1•9955*2*0503,2.1064,2*163S.2.2225,2*2826,2 00013
••3440,2.4069,2.4712,2.5370,2.604?,2.6729,2*7432,2*8151,2.8886*2*96 00014
•37,3.0434,3*1188,3.1990,3,281,3*365,3,450,3*537,3*627,3,718*3*811* 00015
•3.906,4.303,4.102,4*201,4.306,4.411,4,519,4.629,4*741,4*855*4*971, 00016
•5.090,5.212,5*335,5.461,5.590,5.721,5,855,5.992,6*131,6*273*6*417, 00017
•6.565*6.715,6.868,7.024,7.183,7.345,7*510,7*678,7*850,8*024*8*202* 00018
•*.383,8.567,8.755,8.946,9.Ul,9.339,9.541,9.746,9.955,10.168,10.38 00019
•5,10.605.10.A30*11.058,11.290,11.526.11.769,12*011*12.262*12.512,1 00020
•?.771,13.031.13.300,13.568.13.P45,14.123,14,410,14.696/ 00021
"JT«T 00022
P5AT«0. 00023
IF(NT.8T.31)(*C TO 5 00024
PSAT»V<1) 00025
00026
C« IN PSATI TABLE EXCEEOE3. T«**F8.2) 00027
OOOcB
ii»N 00029
wqiTM 00030
FCUMATJ*-) 'C^t THftN 5j FKrtCRS IN PSAT — EXEcUTlC'i TE«MlNATEo*> 00031
5TcP 00032
IF(NT.5?.212)^3 1C 4 00033
PSflT«V(MT-31 )» 00036
66
-------
SAMPLE OUTPUT
COOLING TOMER PROGRAM - LISTING OF INITIAL VARIABLES
VARIABLE NAME VALUE
MTRTI 97.000000
AIM I 9O.OOOOOO
HTONEft 350.000000
OTOMEM 300.000000
HAIRIN 20.000000
en NUN 0.370000
•^ WTRFT 94,822960.000000
MTRF 1199.999756
A1RF 1199.999756
MTRTO 72.000000
STEPS 20.000000
TOLERT O.IOOOOO
TOLERH 10.000000
AFIN 1.000000
AFOT 1.OOOOOO
AFSL 1.000000
AOIN O.O
AOOT 0.0
AOSL 0.0
COIN 0.0
COOT 0.0
CDSL O.O
CP 0.240000
ATHOS 14.492999
ONSAR1 O.070712
{PARALLEL PLATE PACKING ASSUMED)
t/ I/ t PAGE 1
ATUTAL
AFPK
AOPK
235.000000 *
O.79OOOO *
314.000000 *
WALUE CALCULATED FROM UTHER INPUT OR ASSUMED
-------
- RESULTS W ITERATIONS
I/ I/ 1 FACE *
co
AIR CALC TONER
OMfLET VCLCTV NEAT CMARAC- SKIN INLET OUTLET OUTLET PROFILE PACKING SPRAY VENA CON
ITEM MATER AIR IN TRANS TERISTIC FRICTION RELAT MATER AIR AIR PRESSURE PRESSURE PRESSURE PRESSURE TOMER
NB LOSS OENSITV FAKING COEFF IK*A/L1 COEFF HUMIO TEMP TEMP ENTHAL LOSS LOSS LOSS LOSS HEIGHT
1 6*07 0.072124 6.223 1.639 1.3370 0.0192O 0.791 74.5 77.6 28.9 0.0 0.268895 O.O81065 0.952113 -988.
(EXTRAPOLATING FROM MTRTO- 72.0)
IMODIFYINC MTRTO TO 82.4)
2 22.33 0.049609 6.335 1.639 1.3370 0.01920 0.874 103.6 92.8 47.5 0.0 0.273714 0.081085 O.952113 1185.
(EXTRAPOLATING FROM MTRTO* 82.4)
(MODIFYING MTRTO TO 8O.7)
3 10.31 O.O7O1O6 6.312 1.639 1.3370 O.O1920 0.853 97.4 89.9 43.1 0.0 0.272749 O.O81085 O.952113 2155.
(EXTRAPOLATING FRUM MTRTO* 8O.7)
(MODIFYING MTRTO TO 8O.5)
4 18.04 O.O70141 6.311 1.639 1.3370 0.01920 0.851 97.0 89.7 42.8 0.0 0.272681 O.081O85 0.952113 2288.
(EXTRAPOLATING FRUM A1RF* 12OO.O)
(EXTRAPOLATING FROM MTRTO* 8O.5)
IMOP1FV1NC MTRTO TO 8O.5)
IMUOIFVINC A1RF TO 885.8)
7 12.14 O.07O459 4.648 1.364 1.1129 0.02235 0.865 91.2 87.6 40.8 0.0 0.172538 O.065959 0.518761 2991.
(EXTRAPOLATING FRUM MTRTU* 8O.5)
MTRTO TO 83.0)
8 15.49 O.069846 4.666 1.364 1.1129 0.02235 0.883 97.4 91.2 45.9 0.0 0.173291 0.0659*9 O. 518761 875.
IEXTRAPOLATINC FR4JN MTRTU* 83.0)
IMUOIFVINC MTRTU TU 82*6)
9 15.27 O.O69884 4.667 1.364 1.1129 0.02235 0.882 97.0 91.0 45.6 0.0 0.173243 O.O65959 o. 518761 916.
fexTMAPOLATtNC FRUM AIRF* 845.6)
ItXTRAPOLATINC FROM MTRTO* 82.8)
INUUlHriNC MTRTU TO 82.7)
AIRF TO 686.4)
12 11.01 O.070145 3.61O 1.168 0.9530 0.02539 0.892 92.7 89.3 43.8 0.0 0.117965 O.O5546O 0.311533 Sbb.
ItXlRAPOLATlNC FRUM MTRTU* 82.7)
WTRTU TU 84*9)
1) 13.26 O.O69633 3.623 1.168 0.9530 0.02539 0.905 97.4 92.3 48.2 0.0 0.118396 0.055*60 0.^11^,33 <>:>o
ItalRAPULAllNC FRUM MTRTU* 84.9)
MTRTO TO 84.7)
-------
COOLING TOMER PROGRAM - RESULTS OF ITERATIONS
AIR CALC TOWER
OUTLET VELCTV HEAT CHARAC- SKIN INLET OUTLET OUTLET
ITER MATER AIR IN TRANS TERISTIC FRICTION RELAT WATER AIR AIR
NO LOSS DENSITY PARING COEFF U*A/L) COEFF HUMID TEMP TEMP ENTHAL
I/ i/ | PAGE )
PROFILE PACKING SPRAY VENA CON
PRESSURE PRESSURE PRESSURE PRESSURE TOMER
LOSS LOSS LOSS LOSS HEIGHT
14 ll.Ot 0.0*9*7* 3.622 1.168 0.9530 0.02539 0.904 97.0 92.1 47.9 0.0 0.118360 0.05546O 0.311533 4*8.
(EXTRAPOLATING FROM AIRF* *86.4)
(EXTRAPOLATING FROM WTRTO- 84.7)
(MODIFYING WTRTO TO 84.6)
(MODIFYING AIRF TU 617.7)
17 11.37 O.O698OO 3.256 1.095 0.8935 0.02676 0.9O8 95.2 91.3 46.9 0.0 0.10O948 O.051621 0.252275 444.
(EXTRAPOLATING FROM WTRTU- 84.6)
(MODIFYING WTRTO TO 85.5)
!• 12.21 0.0*9593 3.261 1.095 0.8935 0.02676 0.913 97.O 92.5 48.8 0.0 0.101O97 O.05I621 0.252275 362.
(EXTRAPOLATING FROM AIRF- 617.7)
(EXTRAPOLATING FROM MTRTO- 85.5)
(MODIFYING WTRTU TO 85.3)
(MODIFYING AIRF TO 609.3)
21 11*89 O.069634 3.216 1.086 0.8860 0.02695 0.913 96.6 92.3 48.4 O.O 0.099O06 O.O5114O 0.245437 367.
(EXTRAPOLATING FROM WTRTU- 85.3)
(MODIFYING WTRTO TO 85.6)
22 12.11 0.069581 3.217 1.086 0.8860 0.02695 0.914 97.0 92.6 48.9 0.0 0.099043 0.051140 0.245437 350.
CUOLlNG TOMfcR PROGRAM
UOlLtT WATER TEMPERATURE IS 85.6
TUMcR HEIGHT IS 350.
-------
BIBLIOGRAPHIC!Winiarski, L.D., Tichenor, B. A., Byram, K.V., "A
Method for Predicting the Performance of Natural Draft Cooling Towers,"
Environmental Protection Agency, National Thermal Pollution
Research Program, Report No. 16130 GKF 12/70, December 1970.
ABSTRACT: A method is developed for analyzing the performance of count-
erflow and crossflow natural draft cooling towers that does not assume
saturated air at the top of the packing. Types of cooling towers and
the principles of operation are considered. Simplified differential
equations for the heat and mass transfer relations and the methods of
integrating them for both counterflow and crossflow towers are given.
A large number of integration steps is shown to be unnecessary.
Equations for estimating the pressure losses in the tower are also
given. Simplified flow charts using these integration schemes show how
the computer program is used to evaluate tower performance. The com-
puted performance of towers of various heights operating in moist and
in dry conditions is shown. The effect of inlet water temperature is
shown to be significant. Finally, the computed performance of a given
tower with fixed inlet water temperature is shown as a function of
relative humidity and dry bulb air temperature.
ACCESSION NO.
KEY WORDS:
Cooling towers,
Water cooling
Thermal pollution
Thermal powerplants
Energy dissipation
Evaporation
BIBLIOGRAPHIC: Winiarski, L.D., Tichenor, B. A., Byram, K.V., "A
Method for Predicting the Performance of Natural Draft Cooling Towers,"
Environmental Protection Agency, National Thermal Pollution
Research Program, Report No. 16130 GKF 12/70, December 1970.
ABSTRACT: A method is developed for analyzing the performance of count-
erflow and crossflow natural draft cooling towers that does not assume
saturated air at the top of the packing. Types of cooling towers and
the principles of operation are considered. Simplified differential
equations for the heat and mass transfer relations and the methods of
integrating them for both counterflow and crossflow towers are given.
A large number of integration steps is shown to be unnecessary.
Equations for estimating the pressure losses in the tower are also
given. Simplified flow charts using these integration schemes show how
the computer program is used to evaluate tower performance. The com-
puted performance of towers of various heights operating in moist and
in dry conditions is shown. The effect of inlet water temperature is
shown to be significant. Finally, the computed performance of a given
tower with fixed inlet water temperature is shown as a function of
relative humidity and dry bulb air temperature.
ACCESSION NO.
KEY WORDS:
Cooling towers,
Water cooling
Thermal pollution
Thermal powerplants
Energy dissipation
Evaporation
BIBLIOGRAPHIC: Winiarski, L.D., Tichenor, B. A., Byram, K.V., "A
Method for Predicting the Performance of Natural Draft Cooling Towers,"
Environmental Protection Agency, National Thermal Pollution
Research Program, Report No. 16130 GKF 12/70, December 1970.
ABSTRACT: A method is developed for analyzing the performance of count-
erflow and crossflow natural draft cooling towers that does not assume
saturated air at the top of the packing. Types of cooling towers and
the principles of operation are considered. Simplified differential
equations for the heat and mass transfer relations and the methods of
integrating them for both counterflow and crossflow towers are given.
A large number of integration steps is shown to be unnecessary.
Equations for estimating the pressure losses in the tower are also
given. Simplified flow charts using these integration schemes show how
the computer program is used to evaluate tower performance. The com-
puted performance of towers of various heights operating in moist and
in dry conditions is shown. The effect of inlet water temperature is
shown to be significant. Finally, the computed performance of a given
tower with fixed inlet water temperature is shown as a function of
relative humidity and dry bulb air temperature.
ACCESSION NO.
-------
Accession ATumbor
Subject Field & Group
013E
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Water Quality Office, Environmental Protection Agency, Pacific Northwest Water
Laboratory, Corvallis, Oregon
Title
A METHOD FOR PREDICTING THE PERFORMANCE OF NATURAL DRAFT COOLING TOWERS
10
Authors)
Winiarski, Lawrence D.
Tlchenor, Bruce A.
Bvram. Kenneth V.
16
21
Project Designation
16130 GKF 12/70
Note
22
citation Environmental Protection Agency, National Thermal Pollution Research Program
Report No. 16130 GKF 12/70, December 1970. 69 p., 13 fig, 3 tab, 8 ref.
23
Descriptors (Starred First)
*Cooling towers, *Water cooling *Thermal pollution, thermal power plants
Energy dissipation, evaporation
25
Identifiers (Starred First)
*Natural draft
27
Abstract
A method is developed for analyzing the performance of counterflow and
crossflow natural draft cooling towers that does not assume saturated air at the
top of the packing. Types of cooling towers and the principles of operation are
considered. Simplified differential equations for the heat and mass transfer
relations and the methods of integrating them for both counterflow and crossflow
towers are given. A large number of integration steps 1s shown to be unnecessary.
Equations for estimating the pressure losses in the tower are also given. Simpli-
fied flow charts using these integration schemes show how the computer program is
used to evaluate tower performance. The computed performance of towers of various
heights operating in moist and in dry conditions is shown. The effect of inlet
water temperature is shown to be significant. Finally, the computed performance
of a given tower with fixed inlet water temperature is shown as a function of
relative humidity and dry bulb air temperature.
Abstractor
, ... .
L. Wimarski
Institution
WQQ/FPfl Pacific Northwpgt- Water
Cnrvallis.Oregon
(FORMATION CENTEIT
WR:I02
WRSIC
mi v losa>
- JU1-Y 1B091
WATER RE SOUR C ES SC 1 EN f 1 F
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
« GPO: 1989-359-339
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