-------
ap = 0 for qp <. qsp (dry plume)
(2.21)
qp = qsp (tp) f°r S * qsp (wet plume)
where q is the plume saturation specific humidity.
sp
Equation (2.21) implies that when the plume is unsaturated, no
liquid phase moisture due to condensation need be considered and when
the plume is saturated, the plume humidity is equal to the plume satura-
tion specific humidity. To calculate the saturated specific humidity,
thermodynamic equilibrium between liquid and vapor is assumed. The
Clausius-Clapeyron equation (or tabulated values) can then be used to
calculate the saturated humidity. The equation used in the model to
calculate the saturated specific humidity q is (Linsley et al.,
S
t
1975):
0.622e (t) 0.622 e(t)
/ \ ^ —.
Vt>p' = P.. - 0.378 e (t) " P,(z) + e (t) - 0.378 e (t)
t S Q S S
(2.22)
where t and p are absolute temperature and pressure, respectively; P
is the total pressure which is the sum of the dry air pressure Pd(z)
and the saturated vapor pressure e (t).
S
Since the variation of pressure is small (for instance, AP = 1% of P
corresponding to Az = 100M), the absolute pressure at sea level (i.e.,
Pd = 1013.25 mb) is used in equation (2.22), which becomes:
0.622 eg(t)
qs(t) = 1013.25 + 0.622 e (t) (2.23)
S
An approximate expression of e (t) was developed by Richards (1971)
S
as
11
-------
e (t) = 1013.25 x exp(13.3185 t -1.9760 t 2-0.6445 t 3-0.1299 t A)
S V V v v
where
pa
' V'o - 'ao - c-
pa
F =H +W =fD2U (q
o o o 4 o o Mo
= Qo
z = 0
o
(2.24)
pa
L,
12
-------
where the subscripts o and ao are associated with the values at tower
exit (or initial values) and the ambient at the same level, and
Ly(t) = [597.31 - 0.57 x to(°C)] x 4.1868 Jg'1, and C a = 1.005 Jg~loK~
2.2 Entrainment
The entrainment of ambient fluid into the plume is a function of
plume geometry, local mean velocity, buoyancy, and ambient turbulence.
The entrainment function first proposed by Morton et al. (1956) is:
E, = a 2rrb U (2.25)
Ir p
where a is entrainment coefficient determined from experiments; b is the
round jet radius; and U is the'jet centerline velocity.
Based on the integral conservation equations of mass, momentum,
energy, and mechanical energy, and assuming similar profiles, Fox (1970)
and Hirst (1971) derived an entrainment function for round jets which
includes the effect of buoyancy to the entrainment. It reads as follows:
a2
Elr = (al + Fr~ Sin9) 2lTb Up (2'26)
Li
where a, and a2 are entrainment coefficients, and Fr. is the local
2
densimetric Froude number defined as Fr = U /[(p_ - p ) b g/P0] =
LI p a p o
2
U A[(t - t ) t bg/t t ], and g is gravitational acceleration. Based
p p a o pa
on experimental results, a, was determined to be 0.057 for pure round
jet with Gaussian profile distribution (i.e., Fr, -»• ~). Hirst (1971)
suggested the value of a~ = 0.97. This appears to be too large when his
results are compared with experiments. A better estimate of the value of
13
-------
a» can be made from the work of List and Imberger (1973), who, based on
dimensional analysis and experimental data, derived a similar expression
for E.. for round jets (Koh and Brooks, 1975)
Elr = (0.057 + ^P) 2*b Up (2.27)
9 c / o
where F = m /y26 with m being the kinematic momentum flux
r\
- /. U dA, y the volume flux =.J. U dA, and 3 the buoyancy flux
A 6 p p
* a
Comparing equations (2.26) and (2.27) in a quiescent ambient
2
(i.e. sine = 1) and calculating F by using the Gaussian similarity
2
profiles for U and p , one finds a2 = 0.083 Fr /F = 0.4775. Hence
equation (2.26) becomes
E, = (0.057 + °;4775 sine) 2irb U (2.28)
Ir FrL p
The entrainment coefficient a in equation (2.25) has the extreme
values for pure jet (i.e., FrL -* ») a = 0.057 and pure plume (i.e.,
FrT •»• 0) a = 0.082 in a quiescent ambient. A critical value of FrT
L p L
may be determined from
0.082 = 0.057 + ^
which gives
FrLC - 19'X
For Gaussian similarity profiles of plume properties it will be
assumed that
(2.29)
Elr = (0.057 -1- sine) 2*b U for FrL > 19.1
0.082 • 27rb U for Fr. < 19.1
H Lt
14
-------
which implies that Fr = 19.1 was considered a small number below which
LI
the entrainment of a buoyant jet is similar to that of a pure plume.
Experimental results for two-dimensional slot jet are not sufficiently
comprehensive to obtain a similar entrainment expression [i.e., equation
(2.29)] (Koh and Brooks, 1975). Therefore, based on the experimentally
determined entrainment coefficient, the following form will be used for
the slot jet with Gaussian profile distribution, viz.,
Els = 0.14 • 2A • U (2.30)
where A is the length of the slot jet.
The entrainment functions embodied in equations (2.29) and (2.30)
are based on Gaussian profiles of plume properties. In this study,
top-hat similarity profiles are' assumed. The difference in the resulting
entrainment functions [equations (2.29) and (2.30)] due to this is a
factor of /2~. Therefore, equations (2.29) and (2.30) can be rewritten
as follows:
E, = (0.0806 + °16753 sine) 2irb U for FrT > 19.1
ir rr. p L*
L (2.31)
= 0.1160 2ub U for FrT $ 19.1
P L
Els = 0.198 • 2AUp (2.32)
As the plume bends over towards the direction of the ambient wind,
the plume velocity is about equal to the wind velocity. Then the entrain-
ment should be nearly as if the plume were a two-dimensional thermal in
a stagnant atmosphere. This entrainment is proportional to the jet
periphery and the velocity of the thermal. Abraham (1970) proposed the
15
-------
following form
E, = a» P U sine cos6 (2.33)
£ J Si
where P is the jet periphery, cos6 is arbitrarily chosen to diminish the
thermal type of entrainment closed to the initial stage of the vertical
jet, and a., is the entrainment coefficient for a line thermal. For
large Reynolds number, the experimentally determined value of a- is
0.5 (Richards, 1963). But a better value suggested by Koh and Chang (1973)
from their plume measurements and numerical model is 0.3536, which will
be used in this present model. Thus
E0 = 0.3536 P U sine cos6 (2.34)
2 a
Another type of entrainment is associated with ambient turbulence,
and expressed as
E3 = a4 P IT (2.35)
where a, and U' are the entrainment coefficient and a measure of turbulent
f 3
velocity fluctuations. Based on dimensional analysis, Briggs (1969)
found that U' is associated with eddy energy dissipation in the inertial
cl
subrange and gave an estimate of a^ = 1. In practice, the root-mean-
square value of the ambient wind velocity fluctuation may be used to
approximate IK, which is equal to a few percent of the mean wind velocity
under normal atmospheric conditions.
Finally, we may combine equations (2.31), (2.32), (2.34) and (2.35)
to construct a complete entrainment function as
E = P {a|u|+0.3536 Ujsin9 |cos6+1.0 ITJ (2.36)
16
-------
where for a round jet,
P = 2ub
a = 0.0806 + °'p'"-J|sine| for FrT > 19.1
f i _ \_i
0.1160 for Fr. $ 19.1
Li
and for a slot jet,
P = 2A
a = 0.198
Here U is the net velocity in the plume relative to the ambient velocity;
the absolute value is used here to account for both the ascending and
descending parts of the plume.
In the literature on buoyant jets, various investigators employing
the integral approach have devised differing entrainment functions. A
recent survey for the round jet can be found in Wright (1977). The
entrainment function expressed in equation (2.36) and incorporated in
the present model is but one possible expression. Should a different
form be shown to be superior in the future, the model can readily be
modified.
2.3 Merging Process
The individual plumes from the multiple cells of a cooling tower
typically merge within a relatively short distance from the exits.
Before the plumes merge, equations for individual round buoyant jets
are applied in this model to calculate the plume behavior. When several
individual plumes are merged, the resulting plume cross-section is no
longer round, but rather tends to be elliptical In shape. In this model,
17
-------
this merged plume is approximated by a slot jet in the central part and
two half round jets at the two ends of the merged plume as shown by the
solid lines in Figure 2.3. The nonuniform size of the plume is due to
the effect of the wind direction with respect to the tower configuration.
In general, it is necessary to consider all types of plume merging
including all the possible combinations between individual round plumes
and modified merged plumes as shown in Figure 2.4. The basic merging
criterion considered here is that the plume cross-sections are in con-
tact with each other. An additional criterion is incorporated for the
merging between two individual round plumes: the area of the trapezoid
should be equal to the sum of the areas of the two half round plumes
as circled by the dashed lines in Figure 2.3. When the plumes satisfy
these merging criteria, they are merged. The fluxes of the merged plumes
are summed to maintain the conservation of fluxes. Moreover, the new
shape and the new centroids of the merged plumes are determined,
and the integration of the equations is continued. Upon merging, the
entrainment and drag functions are altered due to the change in plume
shape. The merged plume shape is characterized by the radii Bl and B2 of
the two half round plumes, length of the slot jet A, and the angle <|»
(shown in Figure 2.3) between the centerline of the (inclined) plume
cross-section and the horizontal line parallel to the y-axis. As the
plumes merge a new set of Bl, B2, A and the plumes are
classified into two categories: one will be called horizontal for which
the total width (WD) of the new merged plume is larger than the total
18
-------
Figure 2.3 Merged Plume Shape
19
-------
L
(a)
Figure 2.4 Definition Sketch
20
-------
(g)
(h)
Figure 2.4 Definition Sketch
21
-------
height (HT), otherwise, it will be called vertical. Both types are
illustrated by Figures 2.4(a), (c) and (e); and (b), (d) and (f),
respectively. These two categories are not different in substance
and the distinction is made primarily for coding convenience in the
computer program. Bl and B2 are chosen to be the radii of the left end
(or lowest end) and the right end (or highest end) of the horizontal (or
vertical) plumes, respectively. The left end of the plume is the end
closer to the x-axis. For the cases of merging among individual round
plumes as shown by Figure 2.A(a) and (b), $ is the angle between the
horizontal line and the line connecting the two centers of the merged
ending plumes. For the cases of merging between merged plumes, is the
average of angles $. and $2 of the merging plumes 1 and 2, respectively,
as shown in Figures 2.4(c) and (d). For the cases of individual round
plume 2 joining the merged plume 1 as shown in Figures 2.4(e), (f), (g)
and (h), $ is assumed to maintain the original value of the merged plume
2 since the resulting merged plume is envisioned to be dominated by the
merged plume 2. After Bl, B2 and are determined, A can be calculated
by the following equations.
For horizontal plumes:
A = (WD-Bl-B2)/cos<|> for cos * 0
A = HT-B1-B2 for cos for sin^, V 0
A = WD-B1-B2 for sin<|> = 0 (2.37)
When the new shape of the merged plume is determined, then the calcula-
tion can be performed forward one integration step for the round jets at
22
-------
the ends and the slot jet (with unit fluxes found by dividing the total
fluxes of the slot jet by the finite length A) in the central part.
This will result in new values for the radii of the round jets at the
ends of the merged plumes, b , and b 2 and the half width and length of
the central part slot jet b and a. Because of the different entrain-
s
ment rates for round and slot jets, the calculated plume cross-section
determined by b , , b ~ » b and a n^Y not be smooth enough to represent a
realistic shape. The discontinuities occurring at the junctions of the
round and slot jets are demonstrated by the dashed line curve in Figure
2.5. In order to eliminate the discontinuity and to obtain a modified
smooth plume cross-section described by Bl, B2, and A, the following set
of equations is proposed:
0.5* (brl2 Url + br22 Ur2) + 2bsaUs=
[O.Sir (Bl2 + B22) + A (Bl + B2)] • U (2.38)
a + brl + br2 = A + Bl + B2 (2.39)
B1/B2 = brl/br2 (2.40)
where U , , U 2, U and u are the plume velocities corresponding to the
half round jets with radii brl and br2, the slot jet with half width bg,
and the overall merged plume defined by Bl, B2 and A, respectively.
Equation (2.38) describes the redistribution of the volume flux
from the calculated merged plume to the proposed modified plume. Equa-
tion (2.39) maintains the same plume length between the calculated and
modified plumes. Equation (2.40) keeps the same ratios of the radii of
the two half round plumes between calculated and modified plumes.
23
-------
Figure 2.5 Modified Merged Plume Shape
24
-------
After the modified plume shape is determined, the half width, BY
and the half height, BXZ of the merged plume, indicated in Figure 2.3,
can be determined by the following equations for the purpose of checking
plume merging at the next step:
BY = 0.5x (A • cos<{> + Bl + B2) for cos<{> H 0
= Bl for cos* = 0 and Bl £ B2
= B2 for cos4> = 0 and B2 > Bl
BXZ = 0.5x (A • sin<|> + Bl + B2) for sin * 0
= Bl for sin<(> = 0 and Bl i B2
= B2 for sin<)> = 0 and B2 > Bl
(2.41)
Due to the uneven change of Bl, B2 and A for each integration step,
the y-coordinate of the plume centroid also needs to be readjusted.
The amount of adjustment Ay noted in Figure 2.6 is
T
= [
A+B1+B2 A A +B1 +B2
Ay= -1 •] J x - + B2j+1 - 1+1 J*1 -1 i
= 0.5x|cos<)>|x (Bl. - B2.)x -^— + B2 - I
L J 1 A.J J+1
where j and j+1 refer to the calculation steps.
With the modified merged plume cross-sectional shape, the entrain-
ment and drag force can be determined and the conservation equations
integrated. During the calculation, barring further merging, the length
of the slot jet A generally will be reduced and the radii of the two
ending round plumes will be increased. Finally, when A diminishes to
zero, the shape of the merged plume cross-section becomes practically
25
-------
Aj+l +B2j + l
j + l
Aj+l H
0.5X(Aj+Blj-B2j)X— —
0.5X(Aj+Blj+B2j)-B2j
= 0.5X(Aj+Blj-B2j)
Figure 2.6 Correction of Ay for the Merged Plume
26
-------
round. At that point, a round plume is again adopted to carry through
the final stage of plume calculation.
27
-------
CHAPTER 3
COMPUTER PROGRAM
The governing equations for predicting the dynamic behavior of
multiple cooling tower plumes were presented in Chapter 2. No analytical
solution can be obtained due to their complexity as well as the arbitrary
ambient conditions in the governing equations. Therefore, a computer
program written in Fortran IV language was developed to solve these
equations. A standard fourth order Runge-Kutta method was employed in
the solution. The inputs to the program include tower exit conditions,
ambient conditions, tower configuration, entrainment and drag coeffi-
cients, and some control parameters. The basic routine of the computer
program begins with inputting data, setting initial conditions (sub-
routine SETIC) and calculating the first plume (from the tower with the
smallest value of x) by setting an indicator IND(I) = 1 for i
individual round plume (subroutines RUNGS and DERIVR). As the calcula-
tion continues, the subroutines CHKNWP, ALIGN and PLMERG are called to
check for the appearance of any new plumes, to align the existing plumes
at approximately the same x-coordinate, and to check for the merging
among the existing plumes, respectively, along the direction of the
plume trajectory. If new plumes appear (whenever x exceeds the x-
location of downstream tower exits), the results for such new plumes are
calculated stepwise until the stage is reached to necessitate the
checking of the merging criterion. If the plumes merge, the indicator
of the i and the j plumes are changed to IND(I) = 2 and IND(J) = 0
(J>I). In the subroutine RESETI, the fluxes of the merged plumes are
added together, and the initial conditions for the merged plumes are
28
-------
reset. The subroutines DERIVR and DERIVS are called to calculate the
plume half widths and velocities of the round and slot jets in order
to determine the shape of the modified merged plume. Then, subroutine
DERIVE is used to calculate the dynamic properties of the modified merged
plume. The calculation stops when the integration step number is equal
to the desired (input) step number. The outputs include the input
information, and the calculated plume properties such as temperature,
excess temperature, moisture, excess moisture, half width and trajectory
at visible, merging and final stages of the plumes. The detailed list-
ings and examples of the input and output are presented in Appendix A.
The general structure of the computer program is described by the flow
chart shown in Figure 3.1. Some important variables in the text and
«
program are compiled and listed in Appendix B. The complete computer
program is presented in Appendix C.
29
-------
Input
Call BLANK to initialize some storages
Calculate gradients of ambient profiles
I
Call SETIC to set initial conditions |
I
Call RUNGS and DERIVR to calculate the. results
of individual round plumes
Call CHKNWP to check if any new plume appears
Call ALIGN to align the existing plumes at approximately
the same x-coordinate
Call PLMERG to check if any plumes merged
I
Call RESETI (including call RUNGS, DERIVR, DERIVS and DERIVE)
to reset the initial conditions and calculate
the shape and results of the modified merged plume
1
{ yes
Printout minimum amount of results
1
•* Further output needed?
I yes
Call OUTPUT for detailed printout and contou
1
r plots
» END
Figure 3.1 Flow Chart of the Computer Program
30
-------
CHAPTER 4
RESULTS, COMPARISONS AND DISCUSSIONS
In this chapter, four example cases are presented. The results of
the present theory are also compared with the laboratory results of Fan
(1967), Chan et al. (1974), and field data from TVA (Carpenter et al., 1968).
In the example runs, a line array of four cooling towers and a round
array of five cooling towers are considered. For the cases with the line
array, three wind directions (i.e. 0°, 90°, and 135° with respect to the
tower array) are chosen. The input data cards are shown in Table 4.1,
which include the number of towers, the desired number of calculation
steps, control parameters, tower, configuration, ambient levels, temperature
profile, humidity profile, wind velocity profile, tower exit conditions,
coefficients of contour plots and heading of plots. Normally, the outputs
consist only of the input information, the results at the merging points,
and those at the beginning and ending points of the visible phases of plumes.
However, detailed printouts and/or contour plots can also be provided by the
program upon request. The contour plots of excess temperature, humidity
and liquid phase moisture for these examples are shown in Figures 4.1
through 4.12. The plots represent the distribution of the highest values
projected onto the X-Z plane. Detailed explanations of the input and
output parameters are presented in Appendix A.
Three sets of data from Fan (1967) for a single jet, one set from Chan
et al. (1974) for six towers and two sets from Carpenter et al. (1968) for
a single tower and multiple towers are chosen for comparison with the model.
31
-------
EXCS TEMP H TWRS 1 flRRflYS 0 OEG TO WIND
I2h
10
8
0
1 I I I i I I I I I I I I I I I I I I I I
TTTTTI
i i i i
i i i i i i i i i
i i i i i r
o
6
x/o
8
10
12
Figure 4.1 Excess Temperature Distribution for the Case of 4 Towers in
Linear Array and 0° to Wind Direction
32
-------
EXCS HUMI 4 TWRS 1 flRRflYS 0 DEO TO WIND
I I I I I I I I I I I I I I I I I I I I
12
10
8
o
\
rvi
_r. I I I I I I I I I I I I I I I I I I I I I I I I I I
0 2 4 6 8 10 12
X/0
Figure 4.2 Excess Humidity Distribution for the Case of 4 Towers in
Linear Array and 0° to Wind Direction
-------
EXCS LIQM U TWRS 1 flRRflYS 0 OEG TO WIND
I I I I I I I I I I I I I I I I I I I I I I I I I I I l_
-2
I I I I I I I i I i i i i I i i i i i i i i i i i i i i
6
X/D
8
10 12
Figure 4.3 Excess Liquid Phase Moisture Distribution for the Case of
4 Towers in Linear Array and 0° to Wind Direction
34
-------
EXCS TEMP 4 TWRS 1 flRRflYS 90 OG TO WIND
i i I I I I I l l l l I l I I I I I I I l I l l I I I i
12
Figure 4.4 Excess Temperature Distribution for the Case of 4 Towers in
Linear Array and 90° to Wind Direction
35
-------
I2h
10 h
8
a
\
M4
EXCS HUM I »A THRS 1 flRRRYS 90 DG TO HIND
I I I I I I I I I I I I I I I I I I I I I I I I l/T
0
2< I I I I I I i l I l l I I I I I I l I I l I I I I I l I
0 2 4 6 8 10 12
X/0
Figure 4.5 Excess Humidity Distribution for the Case of 4 Towers in
Linear Array and 90° to Wind Direction
36
-------
EXCS LIQM 14 THRS 1 RRRRYS 90 DG TO WIND
I I I I I I I I I I I I I I I I I I I I I I I I I I I
12
10
8
a
\
rvi
0
-2
'l I I I I I I I I I I I I I I I I I I I I I I I I I I I
0
6
X/D
8
10
Figure 4.6 Excess Liquid Phssa Moisture Distribution for the Case of A
Towers in Linear Array and 90° to Wind Direction
37
-------
EXCS TEMP 4 TWRS 1 RRRflY 135 DEG TO WIND
I I I I I I I I I I I I I I I I I I I I I M I I I I I
I i I i i i i i i i i
12
Figure 4.7 Excess Temperature Distribution for the Case of 4 Towers in
Linear Array and 135° to Wind Direction
38
-------
EXCS HUMI 4 TWRS 1 flRRRY 135 OEG TO WIND
12
10
8
o
X.
rvj
0
-2
I I I I I I I I I I I I
II I I I
I I I I I I I I | | i I I I I I I I I I I I I I I I I
02468
X/0
10 12
Figure 4.8 Excess Humidity Distribution for the Case of 4 Towers in
Linear Array and 135° to Wind Direction
39
-------
EXCS LIQM 4 THRS 1 flRRflY 135 DEG TO WIND
I I I I I I I I I I I I I I I I I I I I I I I I I I I II
o
fvl
-2
I I I I I I I I I 1 I I I I I I I I I_L I 1 I I I I I I
6 8
X/0
10 12
Figure 4.9 Excess Liquid Phase Moisture Distribution for the Case of 4
Towers in Linear Array and 135° to Wind Direction
40
-------
EXCS TEMP 5 TWRS IN ROUND flRRflY
I I I I I I I I I I I I I I I
o
\
ivl
I I I I I I I I I I I
i i ......
0
12
Figure A.10 Excess Temperature Distribution for the Case of 5 Towers
in Round Array
41
-------
EXCS HUMI 5 TWRS IN ROUND RRRflY
' ' ' ' I I I I i i i l l l i » t i i i i
0246 8 10 12
X/0
Figure 4.11 Excess Humidity Distribution for the Case of 5 Towers in Round
Array
42
-------
EXCS LIQM 5 TWRS IN ROUND flRRflY
12
10
8
I I I I I I I I I I I I I I I I I I T I I I I I I I
o
x
rvi
-2
0
I I I I I | | | | I I I I I I I I I I I I I I I I
24 6 8 10 12
X/0
Figure 4.12 Excess Liquid Phase Moisture Distribution for the Case of
5 Towers in Round Array
43
-------
The input data cards for these cases are shown in Tables 4.2 through 4.5.
The ambient conditions for the data from Fan and Chan et al. are
uniform. The velocity and temperature at the tower exit and ambient
are chosen to satisfy the given values of densimetric Froude number F
and velocity ratio K. The predicted results of dilution, plume trajectory
and width for Fan's cases are shown in Figures 4.13, 4.14 and 4.15, and
are compared with his experimental results. The comparisons are
generally good. The predicted excess temperature distribution
for the six tower case from Chan et al. is shown in Figure 4.16, together
with the experimental results. In this case the six towers are in one
line array and the ambient flow to it is normal. The contour plot is for
the distribution of values in the central x-z plane. It seems that the
present model tends to overpredict the excess temperature. The main
reason might be because of the neglect of the effect of the mixing in
the plume wake zone in the present model. However it should also be
noted that the experimental results of Chan et al. may have been influ-
enced by the blockage of the flow by the model towers due to the finite
width of the experimental flume.
The field results from TVA at the Paradise power plant include two
cases. One is for a single tower in a stable ambient (TVA-11, potential
3fl 3A
temperature gradient •£ = 0.59 °k/100m, 0 < ~ * 1.0 °k/m). The other
0Z 9Z
is for two towers in an ambient with a temperature inversion (TVA-14,
96
"fa* 1-42 °k/100m > 1.0 °k/m). Since only the average temperature
gradient and average wind velocities at a few levels were
available only rough estimates of ambient temperature and wind
velocity profiles were constructed based on the limited data.
-------
200
150
D
100
50
= 50
•TRACE OF JET BOUNDARY
(0.51cm ORIFICE, PHOTO N0.7650.l)~|
_• _ PRESENT THEORY
o EXPERIMENT (FAN,1967)
FAN'S THEORY
I 1 I I
I i i
50
y
D
100
F=20 k=8
60 (d)
100
80
60
40
20
0
• PRESENT THEORY
o EXPERIMENT (FAN, 1967)
0
20
40
8°
100
120
140
Figure 4.13 Comparisons of Plume Trajectory, Width and Dilution Between the
Figure P Theory and Fan's (1967) Experiments for F = 20 and K = 8
45
-------
250 200
I I I i | ' r
x
D
150
100
50
=50
= 100
= 150
TRACES OF JET BOUNDARIES (0.51cm ORIFICE)
_•_ PRESENT THEORY ~-*~ STATIONARY JET EXPERIMENT (PHOTO NO. 7646.4)
O EXPERIMENT (FAN ISST)**'^ TOWED JET EXPERIMENT (PHOTO NO. 7656.4)
FAN'S THEORY
I I I I I I i I I I I i I I I i I I i I i i i
50
100
100
80
60
40
20
F=40 k=8 60(g)
• PRESENT THEORY
o EXPERIMENT (B\N, 1967)
20
40
•
o
60 80
S/D
100
120
140
Figure 4.14 Comparisons of Plume Trajectory, Width and Dilution Between the
Present Theory and Fan's (1967) Experiments for F - 40 and K - 8
46
-------
250
x
D
200
150
100
50
I i i I
- PRESENT THEORY
O EXPERIMENT (FAN,1967)
FAN'S THEORY
= 50
= 100
= 200
= 150 TRACES OF JET BOUND ARIES (0.51cm ORIFICE)
/—/STATIONARY JET EXPERIMENT(PHOTON0.7646.li
X..ATOWED JET EXPERIMENT (PHOTO NO. 7657.4)
I
50
100
F=80 k = !6 60(j)
100
80
60
Q
QO
40
20
0
• PRESENT THEORY
O EXPERIMENT (FAN, 1967)
•
o
•
o
•
o
20
40
60S/D 8°
100
120
140
Figure 4.15 Comparisons of Plume Trajectory, Width and Dilution Between the
Present Theory and Fan's (1967) Experiments for F = 80 and k = 16
47
-------
*«
00
0
-2
1 I T
I I I I I I I I I I T
EXPERIMENT
PRESENT THEORY
PLANE
MEASURED
I I I I I I I I I I 1 I I
0
8
Figure 4.16 Comparisons of Plume Excess Temperature Between the Present Theory and Chan et al.'s
(1974) Experiments for F = 4 and K = 1.02
-------
Three ambient relative humidity profiles (100%, 70%, 0%) associated with
the relative temperature profiles were generated and tested. The exit
plume humidities were assumed 100% (saturated) except for one dry plume
case which is 0% for ambient and exit humidities. The input data cards
are presented in Tables 4.4 and 4.5. The predicted results and the compari-
sons are shown in Figures 4.17 and 4.18. From the variations of plume
trajectory for different ambient humidity conditions, the effect of the
ambient humidity can be seen to be quite significant. Similar conclusions
could be drawn for the effect of ambient temperature and wind velocity.
The present model overpredicts the plume trajectories for TVA's cases.
This could be due to the incomplete information of the ambient conditions
and the neglect of drift in the tower initial conditions. Adequate
ambient and source conditions are mandatory for proper model validation.
49
-------
01
o
600
500
400
300
200
100
o EXPERIMENT(TVA-II,I968)
PRESENT THEORY
A
•
V
D
EXIT HUMI
100%
100%
100%
0%
AMB HUMI
100%
70%
0%
0%
200
400
600
x(m)
800
1000
Figure 4.17
Comparisons of Plume Trajectories Between the Present Theory and TVA (1968, TVA-11, single tower)
Field Data in a Stable Atmospheric Condition (39/3z-0.59°K/100 m)
-------
500
400
300
200
100
0
o EXPERIMENT (TVA-14,1968)
PRESENT THEORY EXITHUMI AMB HUMI
A 100%
• 100%
100%
v
G
100%
70%
0%
0%
0%
0
200
400
x(m)
600
800
1000
Figure ^.18 Comparisons of Plume Trajectories Between the Present Theory and TVA (1968, TVA, two towers)
Field Data in an Atmosphere with an Inversion (36/^z=l.42°K/100 m)
-------
Table 4.1 Input Data Cards for Example Cases (Different Wind Directions to a Line
Array (3 cases) and Round Array (one case) of Towers)
"CASE (1) * TOWERS IN ONE ARRAY 0 DEGREES TO WIND
4 120 30 30 11
— -0-" 003 10 011111-
.00000 11. 45000 2?. 90000 34.35000
• .00000 .oonoo .00000 .00000
.00000 100.00000 200.00000
10.50000 10.30000 10.10000
70.00000 70.00000 70.00000
4.10000 5.22504 5.76969 4.10000 5.22504
5.76969 4.10000 5.22504 5.769f>9
9.44880 10.26800 31.90000 .02821 .00000
5.00000 5.00000 n 0 0 0
EXCS TEMP 4 TWRS 1 ARRAYS 0 OFG TO WIND 2/0
tXCS HUMI 4 TWRS 1 ARRAYS 0 DEG TO WIND Z/D
EXCS LIQM 4 TWPS 1 ARRAYS 0 DEG TO WIND Z/D
"CASE (2)" 4 TOWERS IN ONE ARRAY ' 90 DEGREES TO WIND
4 120 30 30 11
0 0 0 3 10 0 1 111 1
.00000 .00000 .00000 .00000
.00000 11.45000 2?. 90000 34.35000
.00000 loo.ooooo 200.00000
lO.bOOOO 10.30000 10.10000 ~ "" '"
70.00000 70.00000 70.00000
4.10000 5.22504 5.76969 4.10000 5.22504
5.76969 4.10000 5.22504 5.76969
9.44880 10.26800 31.90000 .02821 .00000
b. 00000 5.00000 0000
~F"X<~S TEMP 4 TWRS 1 ARRAYS 90 OG TO WIND 7/0
EXCS HUMI 4 TWRS 1 ARPAYS 90 OG TO WIND Z/D
EXCS LIDM 4 TWRS 1 ARPAYS 90 DG TO WIND Z/0
CASE (3) 4 TOWERS IN ONE ARRAY 135 DEGREFS TO WIND
4 120 30 30 11
0 0 " 0 3 10 0 •• — 1 1 111
.00000 8.10000 If). 19000 24.29000
'-" "".00000 fl. 10000 1ft. 19000 24.29000
.00000 100.00000 200.00000
lO.bOOOO 10.30000 10.10000
70.00000 70.00000 70.00000
' 4V10000 5.22504 5.76969 4.10000 5.22504
5.76969 4.10000 5.22504 5.76969
-9.44880 10.26800 31.900CO .02821 .00000
5.00000 5.00000 0000
EXCS TTMP 4 TWRS 1 ARRAY 135 DEG TO WINDZ/D
tXCS *JMI 4 TWRS 1 ARPAY 135 DEG TO WINr,Z/D
"EXCS'LIQM 4 TWRS 1 AROAY 135 DEG TO WINDZ/D
CASE (4) 5 TOWERS IN ROUND ARRAY
- - 5 100 30 30 11
0 0 0 3 10 0 0 1 1 1 1
.00000 5.00000 10.00000 15.00000 20.00000
10.00000 .00000 20.00000 2.00000 12.00000
'.ooooo 100.00000 200. ooooo - - — •-•-
10.50000 10.30000 10.10000
70.00000 70.00000 70.00000
4.10000 5.22504 c. 76969 4.10000 5.22504
5.76969 4.10000 5.22504 5.76969 4.10000
9.44880 10.26800 31.90000 .02821 .00000
5.00000 5.00000 0 0 00
EXCS TEMP 5 TWRS IN ROUND ARRAY Z/D
EXCS HUMI 5 TWRS IN ROUND ARRAY Z/D
EXCS LIOM 5 TWRS IN ROUND ARRAY Z/D
5.76969 4.10000
X/D
X/D
X/D
5.76969 4.10000
X/D
X/D
X/D
5.76969 4.10000
X/D
X/D
X/D
5.76969 4.10000
5.22504 5.76969
X/D
X/D
X/D
5.22504
5.22504
5.22504
5.22504
52
-------
Table 4.2 Input Data Cards for Three Cases of Fan's (1967) Experiments with
F = 20, K = 8; F = 40, K = 8; and F = 80, K - 16
CASE (1) 60(0) F=20 K=8
~ 1 350 1 1 1
000210
.0
"~ Y00000~-50.00000
31.87000 31.87000
.00000 .00000
.13700 .13700
'V00760" -1.10000 "20.00000 700000.00000
CASEJ2] 60
-------
Table 4.3 Input Data Cards for Chan et al.'s (1974) Experiment
with F = 4, K = 1.02
Case (1) 6 Towers in One Array 90 Degrees to Wind F=4, K=1.02
6 100 21 17 11
00 120
0
1 1
0 1
25
6
EXCS
.00000
.00000
.00000
.00000
.00000
.37621
.37621
.05690
.50000
.31250
TEMP 6
.
,
900.
25.
.
.
.
.
.
5.
TWRS
00000
06501
00000
00000
00000
37621
37621
38374
50000
06250
.00000
.13003
.37621
.37621
30.00000
1.00000
0 0
1 ARRAY 90 DEC
.00000
.19504
.37621
.37621
.00000
3.00000
0 0
TO WIND Z/D
.00000
.26006
.37621
.00000
.00000
.32507
.37621
X/D
.37621 .37621 .37621
X/D A3=0.3536 CD=1.5
54
-------
Table 4.4 Input Data Cards for TVA (1968, TVA-11, single tower) Field Data in
a-Stable-Atmospheric Oondlt:ion-<^e/9z-fr;»9J>K/1^0 m)
CASE. (1) rOO* EXIT HUMI~8T100« "AMB'HUMI
1 300
1
8
0
1
000
~~ .00000 . - -
.00000
rOOOOO~I00700000"150.00000 200.00000 250.00000 300.00000 350.00000 400.00000
20.00000 20.16000 20.24000 20.32000 20.40000 20.48000 20.56000 20.64000
100.00000 100.00000 100.00000 lOO.OOOnn 100.00000 100.00000 100.00000 100.00000
4.10000 4.10000 4.10000 4.70000 5.30000 5.90000 6.50000 7.10000
"7.90000 17.10000 139.00000 .67883 .00000
;ASE
HUMI 5-
1 300 1 1 1
-•- — Q--- o~ 0 8~~~1 ~"
-------
Tnput Data Cards for- TVA (1968, TVA-1&, two towers) .Elfild_Dat«. Iti an
Atmosphere with an Inversion (39/3z-1.42°K/100 m)
CASE" (1) "10095 EXIT HUMI & 100% AHB HUMI~
~2 300"~ 1 "1"~"1 " ""
00061010000
-.00000 29.06000 ' "
•OOOOO 54.65000
—;ooooo 50.00000 100.00000 iso.ooooo 200.00000 250.00000
7.00000 7.43000 7.86000 8.29000 8.72000 9.15000
LOO.OOOOO 100.00000 100.00000 100.00000 100.00000 100.00000
8.60000 8.80000 9.10000 10.50000 11.60000 J2.60000 8.60000 8.80000
"^9.10000 10.50000 11.60000 12.60000 ~""
7.90000 20.20000 149.00000 .73951 .00000
EXIT HUMI"
HUMI
2
0
•
•
*
7.
70.
8.
9.
7.
300 1
0 0
T)0000 "
ooooo
ooooo*
ooooo
ooooo
60000
10000~~
90000
1 1
6 1
29.06000
54.65000
50.00000
7.22000
70.00000
8.80000
10.50000
20.20000
0
100.
7.
70.
9.
11.
149.
1 0
OOOOO ]
44000
OOOOO
10000
60000 ~
OOOOO
0 0
[50.DOOOO
7.67000
70.00000
10.50000
12.60000
.73951
0
200
7
70
11
.00000
.89000
.00000
.60000
.00000
250.00000
8.11000
70.00000
12.60006
8.60000
8.80000
CASE (3) 100* EXIT HUMI & 0% A"B
2"300 —
0 0
.00000
.00000
" .00000
7.00000
~.ooooo
8.60000
9.10000
7.90000
1 1" "1
061
29.06000
54.65000
50.00000
7.22000
.00000
8.80000
"10.50000
100.00000
7.44000
—.ooooo
9.10000
"11.60000
150.00000 200.00000 250.00000
20.20000 149.00000
7.67000
iOOOOO
10.5000ft
12.60000
.73951
7.89000
.00000
11.60000
.00000
8.11000
.00000
12.60000
8.60000 8.80000
"0* EXIT HUMI I 0% AMB "HUMI
2 JOO ]
0 0 (
.00000
.ooooo
.uoooo
7.00000
.00000
8.60000
9.10000
L 1 1
) 6 1
29.06000
54.65000
'50.00000
7.22000
.00000
8.80000
10.50000
0 1
100.00000
7.44000
.00000 ~
9.10000
11.60000
0 0
150^00000"
7.67000
.OOnno
10.500QO
12.60000
0
200.00000
7.89000
.00000
11.60000
250.00000
8.11000
.00000
12.60000
7.90000 20.20000 149.00000
.00000
.00000
8.60000 8.80000
56
-------
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
In this study, a mathematical model and corresponding computer
program have been developed for the prediction of plume behavior from
multiple cooling towers. Some comparisons between the predictions
based on the present model and the measured results from laboratories
and the field are made in order to test the model. The following
conclusions and recommendations are made based on this study.
(1) The model is developed for arbitrary vertical profiles of
ambient temperature, humidity, wind velocity, and arbitrary tower
arrangement. The velocity defect for the downstream towers due to the
effect of the upstream towers and plumes can be included by specifying
different ambient velocity profiles for each plume. A general expression
for the velocity defect of the downstream towers might be developed in
the future.
(2) The temperature range for which this model is valid is -50°C
to 140°C, because of the accuracy associated with the calculation of
the saturation humidity.
(3) A set of suggested values of entrainment and drag coefficients
have been incorporated in the computer program. Because of the rapid
merging and usually rapid bending over of the plumes, the coefficients
a~ a and C. are the most important ones. Better estimates of their
3s a
values are needed such as by further experimental study or field program.
(4) The merging criteria and processes (defined in this model by
equations (2.38) (2.39) and (2.40)) could also be improved when further
57
-------
research results on plume interaction are available.
(5) The blockage and recirculation effects in the wake zone of the
towers and plumes have not been incorporated in the present model.
Future effort could be made to include these effects.
(6) Based on comparisons between model and laboratory results
(Fan, and Chan et al.), good predictions of dry plume behavior can be
obtained. In order to verify the model for actual cooling tower plumes,
a more complete set of experimental data (including the plume width,
trajectory, dilution and detailed ambient profiles of temperature,
humidity and wind velocity)are required. Therefore, a complete set of
field measurement are strongly recommended for validation of the model.
58
-------
REFERENCES
Abraham, G. (1970), "The Flow of Round Buoyant Jets Issuing Vertically
into Ambient Fluid Flowing in a Horizontal Direction," Advan. Water
Poll. Res. Proc. Int. Conf. Water Poll. Res. 5th Paper 111-15.
Briggs, G. A. (1969), "Plume Rise," AEC Critical Review Series Report.
Report number TID-25075.
Briggs, G. A. (1974), "Plume Rise from Multiple Sources," Cooling Tower
Environment-74. CONF-74032, ERDA Symposium Series. National
Technical Exchange Service. U.S. Dept. of Commerce, Springhill, VA.,
pp. 161-179.
Carpenter, S. R., F. W. Thomas, and R. E. Gartrell (1968), "Full-Scale
Study of Plume Rise at Large Electric Generating Stations," TVA,
Muscle Shoals. Alabama.
Chan, T. L., S.-T. Hsu, J.-T. Lin, K.-H. Hsu, N.-S. Huang, S. C. Jain, C. E.
Tsai, T. E. Croley II, H. Fordyce and J. F. Kennedy, "Plume Recirculation
and Interference in Mechanical Draft Cooling Towers," Iowa Inst. Hyd. Res.
Rep. No. 160, 41 pp.
Csanady, G. T. (1971), "Bent-Over Vapor Plume," J. Appl. Meteor., 10,
34-42.
Davis, L. R. (1975), "Analysis of Multiple Cell Mechanical Draft Cooling
Towers," Environ. Prot. Agency Rep. Office of Research and Develop-
ment, Ecological Research Series, EPA-66013-75-039.
Fan, L. N. (1967), "Turbulent Buoyant Jets into Stratified or Flowing
Ambient Fluid," California Institute of Technology, W. M. Keck
Laboratory of Hydraulics and Water Resources, Rep. No. KH-R-15.
Fox, D. G. (1970), "Forced Plume in a Stratified Fluid," J. Geophys.
Res., 75 (33), 6818-35.
Hanna, S. R. (1972), "Rise and Condensation of Large Cooling Tower Plumes,"
J. Appl. Meteor., 11, 793-799.
Hirst, E. A. (1971), "Analysis of Round, Turbulent, Buoyant Jets Dis-
charged to Flowing Stratified Ambients," Oak Ridge National
Laboratory, Report Number ORNL-4685.
Hoult, D. P., J. A. Fay, and L. J. Forney (1969), "A Theory of Plume
Rise Compared with Field Observations," J. Air Pollut. Contr.
Assoc. 19(9), 585-90.
Jirka, G. and D.R.F. Harleman (1974), "The Mechanics of Submerged Multi-
port Diffusers for Buoyant Discharges in Shallow Water," MIT Ralph
M. Parsons Lab. for Water Resources and Hydraulics, Report Number 169.
59
-------
Koh, R.C.Y. and N. H. Brooks (1975), "Fluid Mechanics of Waste-Water
Disposal in the Ocean," Ann. Rev. Fluid Mech., 7:187-211.
Koh, R.C.Y. and Y. C. Chang (1973), "Mathematical Model for Barged Ocean
Disposal of Wastes," Environ. Prot. Agency, Office of Research and
Development, Environ. Prot. Tech. Series, EPA-660/2-73-029.
Koh, R.C.Y. and L. N. Fan (1970), "Mathematical Models for the Predic-
tion of Temperature Distributions Resulting from the Discharge of
Heated Water into Large Bodies of Water," Environ. Prot. Agency
Rep. 16130 DWO 10/70, 219 pp. (Also Tetra Tech, Inc., Rep. TC-170).
Linsley, Jr., R. K., M. A. Kohler, and J.L.H. Paulhus (1975), Hydrology for
Engineers , McGraw-Hill Book Company, Inc., New York, NY.
List, E. J. and J. Imberger (1973), "Turbulent Entrainment in Buoyant
Jets and Plumes," J. Hydraul. Div., Proc. ASCE, 99:1461-74.
Meyer, J. H., T. W. Eagles, L. C. Kohlenstein, J. A. Kagan, and W. D.
Stanbro (1974), "Mechanical Draft Cooling Tower Visible Plume
Behavior: Measurements, Models, Predictions," Cooling Tower
Environment-74. CONF-74032, ERDA Symposium Series. National
Technical Exchange Service, U.S. Dept. of Commerce, Springhill, VA,
pp. 307-352.
Morton, B. R. (1957), "Buoyant Plumes in a Moist Atmosphere," J. Fluid
Mech., 2, 127-144.
Morton, B. R., G. I. Taylor and J. S. Turner (1956), "Turbulent Gravita-
tional Convection from Maintained and Instanteous Sources," Proc.
Roy. Soc. London, Ser. A 234:1-23.
Richards, J. M. (1963), "Experiments on the Motion of Isolated Cylin-
drical Thermals through Unstratified Surroundings," Intern. J. of
Air and Water Pollut., 7, pp. 17-34.
Richards, J. M. (1971), "Simple Expression for the Saturation Vapor
Pressure of Water in the Range -50° to 140°C," Brit. J. Appl. Phys.,
4, L15-L18.
Schatzmann, M. (1977), "A Mathematical Model for the Prediction of Plume
Rise in Stratified Flows," Sonderforschungsbereich 80, University
of Karlsruhe, W. Germany.
Slawson, P. R. and G. T. Csanady (1967), "On the Mean Path of Buoyant,
Bent-Over Chimney Plumes," J. Fluid Mech., 28, 311-322.
Slawson, P. R. and G. T. Csanady (1971), "The Effect of Atmospheric
Conditions on Plume Rise," J. Fluid Mech., 47, 33-39.
60
-------
Slawson, P. R., J. H. Coleman, and J. W. Frey (1975), "Some Observations
on Cooling-Tower Plume Behavior at the Paradise Steam Plant,"
Cooling Tower Environment—1974 (ERDA Symp. Series: CONF-740302),
147-160.
Weil, J. C. (1974), "The Rise of Moist, Buoyant Plumes," J. Appl. Meteor.,
13, 435-443.
Wigley, T. M. L. (1974), Comments on "A Simple but Accurate Formula for
the Saturation Vapor Pressure over Liquid Water," J. Appl. Meteor.,
13, 608.
Wigley, T. M. L. (1975), "A Numerical Analysis of the Effect of Condensation
en Plume Rise," J. Appl. Meteor., 14, 1105-1109.
Wigley, T. M. L. (1975), "Condensation in Jets, Industrial Plumes and Cooling
Tower Plumes," J. Appl. Meteor., 14, 78-86.
Wigley, T. M. L. and P. R. Salwson (1971), "On the Condensation of Buoyant,
Moist Bent-Over Plumes," J. Appl. Meteor., 10, 253-259.
Wigley, T. M. L. and P. R. Salwson (1972), "A Comparison of Wet and Dry
Bent-Over Plumes," J. Appl. Meteor., 11, 335-340.
Wright, S. J. (1977), "Effects of Ambient Crossflows and Density Strati-
fication of the Characteristic Behavior of Round, Turbulent Buoyant
Jets," California Institute of Technology, W. M. Keck Laboratory of
Hydraulics and Water Resources, Report No. KH-R-36, 254 pp.
61
-------
APPENDIX A
COMPUTER PROGRAM
The computer program based on the model and listed in Appendix C
was tested on an IBM 370/158. The detailed input and output information
are listed in this Appendix. The input ambient wind velocity profiles
(AU(NP,MG)) for each tower are designed to allow consideration of the
velocity defect in the wake of upstream towers (i.e., the tower array
parallel to the ambient wind direction). In addition, some suggested
input values are listed below for reference:
NS = 300
»
NX = 40
NY = AO
NCONT =11
IX(3) = IX(6) = IX(ll) =0
In this Appendix, the input sequence as well as the input and output
variables are tabulated, explained and related to the symbols used in the
text of this report.
A-l
63
-------
INPUT SEQUENCE
Symbol
NP,NS,NX,NY,NCONT
(IX(I),1=1,11)
(CX(I),I=1,NP)
(CY(I),I=1,NP)
(AZ(I),I=1,MG)
(AT(I),I=1,MG)
(AH(I),I=1,MG)
((AU(I,J),J=1,MG),I=1,NP)
DI(l),UO(l)f TO(1),HO(1),WO(1)
(DI(I),1=1,NP)
(JO(I),I=1,NP)
(TO(I),I=1,NP)
(HO(I),I=1,NP)
(WO(I),I=1,NP)
A1,A2,A3,A4,CD,TURBF
DX,DZ,XO,ZO
WIDTH, !IITE,MORE,NOMAP,ICENT
NOTICK
(HEDN(!.),k=l,10),(LABY(L),L=l,5),(LABX(M),M=l,5)
(HEDN(k),k=l,10),(LABY(L),L=l,5),(LABX(M),M=l,5)
(HEDN(k),k=l,10),(LABY(L),L=l,5),(LABX(M),M=l,5)
Parameter Format Subroutine
IX(1)=0+
IX(1)=1*
IX(1)=1*
IX(1)=1*
IX(1)=1*
IXdH*
IX(2)=1*
IX(3)=1*
IX(11)=1*
*
IX(8)=1*
IX(9)=1*
IX(10)=1*
514
1114
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
8F10.5
4F10.5
2F10.5
414
20A4
20A4
20A4
CTPS
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
MTP
OUTPUT
OUTPUT
OUTPUT
OUTPUT
OUTPUT
+ Skip card if IX(1)=1
* Skip card if the corresponding IX(I)=0, (1=1,2,3,11,8,9,10)
A-2
64
-------
In Program
NP
NS
NX, NY
[CONTA(NX,NY)]
NCONT
[CONTB(NCONT)]
EXPLANATION OF THE INPUT SYMBOLS
In Text Remarks
Total number of towers
Desired number of calculation steps
Horizontal and vertical grid sizes, respec-
tively (for contour plot)
Desired contour levels for plotting
IX(2)
IX(3)
IX (4)
IX(5)
IX(6)
IX(7)
IX(8)
IX(9)
IX(ll)
IX(1)=0
IX(2)=0
IX(2)=1
IX(3)=0
IX(3)=1
IX(3)=-1
MG
INRPR
IPNT=0
LC=0
LC=1
IX(8)=0
IX(8)=1
IX(9)=0
IX(9)=1
IX(10)=0
IX(10)=1
IX(11)=0
A- 3
65
Same exit conditions of all the
plumes (Input one card only)
Different exit conditions of the
plumes
No input card of entrainment and
drag coefficients is needed
Input the desired entrainment and
drag coefficients
No input card of DX, DZ, XO and ZO
is needed
Input the desired values of DX, DZ,
XO and ZO
No plot needed
Number of vertical levels for
ambient conditions
Interval of detailed printout for
plume 1
For contour plot (always use IPNT=0)
For cluster array (round array) of
towers
For line or random array of towers
No contour map plotted for plume
excess temperature
Contour map plotted for plume
excess temperature
No contour map plotted for plume
excess humidity
Contour map plotted for plume excess
humidity
No contour map plotted for plume
excess liquid moisture
Contour map plotted for plume excess
liquid moisture
No input card of WIDTH, HITE, MORE,
NOMAP, ICENT, and NOTICK is needed
Input the desired values of WIDTH,
HITE, MORE, NOMAP, ICE1TT and NOTICK
-------
In Program
CX(NP)
CY(NP)
AZ(MG)
AT(MG)
AH(MG)
AU(N'P.MG)
DI(NP)
UO(NP)
TO(NP)
HO(NP)
WO(NP)
DX.DZ
XO,ZO
WIDTH,HITE
MORE
NOMAP
ICENT
NOTICK
In Text
x
y
z
ta
Dc
U
A1,A2,A3
and A4
CD
TURBF
al»a2»a3
and a i«
Cd
U'
Remarks
x-coordinates of towers (in m)
y-coordinates of towers (in m)
Ambient levels (in m)
Ambient temperature profile corresponding to
AZ(I) (in °C) "
Ambient relative humidty profile correspond-
ing to AZ(I) (in percentage of the saturation
humidity)
Ambient wind velocity profile corresponding
to AZ(I) for each tower (in m/sec)
Diameter of each tower (in m)
Exit velocity of each plume (in m/sec)
Exit temperature of each plume (in °C)
Exit specific humidity of each plume (in
kg/kg)
Exit liquid phase moisture of each plume
(in kg/kg)
Entrainment coefficients (Default: Al=0.0806,
A2=0.4775, A3=0.3536, A4=0.)
Drag coefficient (Default: CD=1.5)
Intensity of ambient turbulent fluctuations
(in percentage, decimal; Default: TURBF=6.)
Increments of grid size in x and z directions,
respectively (Normalized by the diameter of
the first tower; Default:DX=0.5, DZ=0.5)
Location of the center of the top of the
first tower in the grid (Normalized by the
diameter of the first tower; Default:XO=1,
Z0=2.)
Width and height of contour map, respectively
(Inches; Default: 8", 8")
MORE=1 Do not finish off the map (Default:
'MORE=0)
NOMAP=1 Do not force grid to be square
(Default:NOMAP=0)
ICENT=1 Do not center the title (Default:
ICENT=0)
NOCITK=1 Do not draw tick marks (Default:
NOTICK-0)
A-4
66
-------
In Program In Text Remarks
HEDN(IO) 40 characters to plot as title on top
(Default: Blank)
LABY(5) 20 characters to plot as label on vertical
left (Default: Blank)
LABX(5) 20 characters to plot as label on horizontal
bottom (Default: Blank)
A-5
67
-------
EXPLANATIONS OF THE OUTPUT SYMBOLS
In Text
Cd« Ua
In Program
EXIT,COEF,TWLC,AMBL,
INPR,IPNT,LC,ETPL,
EHPL.EMPL.COPL
A1,A2,A3,A4,CD,
TURBF
NTHP
CX.CY
[(CX(I).CY(I)]
DIA,VELO,TEMP,HUMI,
LPMO [DI(I),UO(I),
HO(I)WO(I)]
NSTEP*
X.Y.Z x,y,z
[PX(NP,NS),PY(NP,NS),
PZ(NP.NS)]
PTEMP,PHUMI,PLQDMOIST tp,qp,ap
[PT(NP,NS),PH(NP,NS),
PW(NP.NS)]
Remarks
Correspond to IX(i) to IX(ll)
respectively
,32,33 ,a«t , Same as input symbols
EXCEST, EXCESH
[PET(NP,NS),PEH
(NP.NS)]
PCROSEC
[BXZ(I)]
SLOTLEN[A(I)]
PANGLE[PCOS(NP,NS)
PSIN(NP.NS)]
DILUTN
[PDIL(NP.NS)]
PVELO [PU(NP,NS)]
At, Aq
HT/2
A
e
Q/QO
u
The Nth plume
Same as input symbols
Tower diameter, exit values of
plume velocity, temperature,
specific humidity and liquid phase
moisture, respectively
The Ntn step of calculation referred
to each tower
The horizontal, lateral and vertical
coordinates of plume center
Plume temperature, specific humidity
and liquid phase moisture respectively
Excess plume temperature and specific
humidity
Half height of plume cross-section
Finite length of slot jet of the
merged plume
The angle between the tangent of
plume trajectory and the horizontal
line
Plume dilution
Plume velocity
NSTEP refers to the number of calculation step of plume 1 when each
plume first appeared
A-6
68
-------
APPENDIX B
EXPLANATION OF THE IMPORTANT SYMBOLS IN THE PROGRAM MTP
In Program
PX(NP,NS)
PY(NP.NS)
PZ(NP,NS)
PS(NP,NS)
PCOS(NP.NS)
PSIN(NP.NS)
PQ(NP.NS)
PMX(NP.NS)
PMZ(NP.NS)
PF(NP.NS)
PG(NP,NS)
PH(NP,NS)
PW(NP.NS)
PT(NP,NS)
PET(NP.NS)
PEH(NP,NS)
PAN
sin
2-BY
TI
g
al
a2
a3
aA
Excess temperature
Excess humidity
*
Net plume velocity
Average plume width
*
Plume dilution
Normalized PET.PEH & PW (or PEW)
Contour levels
Indication of the status of each plume
Plume which has not been started
Single plume
Merged plume
All plumes are merged
Beginning step number for each plume
Merged plume pair
Merged plume step numbers associated
with MP(I)
*
Beginning step number for visible plume
Ending step number for visible plume
3.1415926
*
*
*
*
B-l
69
-------
In Program
In Text
Remarks
CD
TURBF
UC
B
TP
HP
WP
ET
EH
MG
CFRL
ALV
CPA
ANG
ITHP
ENTRAN
IQ
IL
IK
KE(I)
UT
Fr
LC
-pa
6
E
<3
=3
>3
YP(I)
YR1(I),YR2(I),
& YS(I)
YR1P(I),YR2P(I),
& YSP(I)
YCD-Q
Y(2)=Mcos8
Y(3)=Msin6
Y(4)=G
Y(5)=F
Y(6)=x
Y(7)=z
it
*
*
Plume width
*
*
*
Excess temperature
Excess humidity
Elevation level
*
*
*
*
ith plume
*
All the plumes have not been
completely merged
All the plumes have merged
All the plumes have merged and
become a round plume again
Number of merged pairs
Plume step number
Ending step number of each plume
*
*
Derivatives of Y(I) with respect to s
Y(I) associated with the two half
round plumes and the central slot
plume for the merged plume
YP(I) associated with the two half
round plumes and the central slot
plume for the merged plume
* Refer to "List of Symbols"
B-2
70
-------
APPENDIX C
LISTING OF PROGRAM
C-l
71
-------
FORTRAN IV G LEVEL 20.7 VS
PAIN
DATE
6/07/77
l
-------
FORTRAN IV G LEVEL 20.7 VS
0001
MTP
DATE =
6/07/77
14:32
0002
0003
0004
A
----- 3
4
5
6
SUBROUTINE MTP( PX , PZ ,PO, PKX, FMZ, PG, PF, PCOS, PS IN, PENT, PU.PS.PB.P A,
lPI*P^IjP-t*£E±UP-i(*£Atlj£DU.,PY,PiL,CCNTA,CCNT6,CONTC,NP, NS ,NX ,NY ,
2NCONT.N4)
EXTERNAL DERIVE, DERI VS.DERIVF
DOUBLE PRECISION AQ, BO, CO, DO
COKMCK ySTCR£l/lND130),INDT(30),NOVlKl30),IS<30)
1 /STORE2/KP(30),MS(30),IIP(30)
,AU13Q.3Q1 ,
AUGC30.30)
-^TflR£4/AL30),B_ll30),B2l30),BXZl30),BYI30)fPMCOS(30),
PMSINC30),DW<30) ,NBV< 3d) ,NE V(30) tNCV(30)
-^OLNSIl/PAl.GRA.Al,A2,A3,A4.CD,TURaF,UC,B,TP,ET,HP,EH,WP,
MG,MGl,CFRLtALV,CPA,ANG,IQ,ITHP,ENTRAN
fNi itTn
8
/CCNST3/AQ,BQ,CC,DQ
V£CmTiJU/WIOTH,HITE,MOR£,NJMAP,ICENT,NOTICKtHEDNI10),
LABY(5),LABX(5)
0005
DIMENSION PXCNP,NS),PZ«NP,NS),PQ(NP,NS),PMX(NP,NS) ,PMZ(NP,NS),
2PENT(NP,NS),PHINP,NS),PWINP,NSJ ,PEH ( NP.NS ) ,CX<301 ,CY( 30 ) , KE<30) ,
4Y(6),YP(8) ,YS(81,YSPC8I,YR1(8),YR1PI8),YR2(8),YR2P{8»,PDIHNP,NS
. -5CONTAlNX,AlYJJ.CONTfllNaiNT).a;NTClN4J,JX112J,MGPA2(30),MGSTll30J.
6 PC (NP , NS ) t LCHK ( 301 , AHP ( 30)
X _ IMTIAII7F
0006
0007
__
CALL BLANKtPX,PZ,PGtPMX,PMZ,PB,PU,PFfPGPCOS,PSIN,PENT,PT,PS,PA7
lP£T«P-£H,PAN,PYfPOILtP-H,PW,PCfNP,NS,NX.NY,NCONT,N4,CONTA,CONTB,
2CONTCfMGPA2«MGSTl,DX,DZ,XOtZC,IPNT,KE,LCHKtAHP)
-4NPUT -CCNTAOL -P
GO TO -35
34 READC5.1I (DI( I),1=1,NP)
C-3
73
-------
FORTRAN IV G LEVEL 20.7 VS
MTP
DATE -
6/07/77
14:32
0029
_QO30
0031
0032
0033
READ<5,1J (TO(I),I*1,NP)
READIS.ll (HOU!,1*1.NP!
35 JF1IXI2) ^LE. -0) GO 10 32
C INPUT COEFFICIENTS OF ENTRAINMENT AND DRAG ;TURBF»TURB. FLUCT.
£ TURBF=X(IN-DECIMAL) CF AMBIENT JUNO VELOCITY
READ(5.1)A1,A2,A3»A4«CD,TURBF
0035
-0036 _
0037
-OO38
0039
1 FORMATJ8F10.51
-2 FORMATJ1214J —
32 t,RlTE<£,555)
5£5 FORMAT11H1J
MRITE(6.3)
np TUP WAR i ABIES«j
0041
-0042
-0043-
0044
-00.45.
0046
-0047
WRITEC6.4)
-4 FORMAT-IIX^ lt£NGTJUJ!, _T£MP^C, -M01STUREJKG/XG, VELO:M/SEC, -ANG1
1:DEG«)
^IStNXtNYtNCPNT _. .
WRITE(6t49)
if.a\ TCI (•t
WRITE(6.48I IIX(J).J'1,11)
_50 FORMATiiJUtN£U_CF-XO*ERS«i-,44,f—NO.-OF-CALCULAT10N STEPS-*.14.
1* GRID SIZE «X,Yf=',I4,- X',I4,« CCNTOUR LEVELS**.I*//)
-0043 49 fORMATiUC.lCONTKOL-P-ARAMETERS'J-
0049 36 FORMAT*1 EXIT COEF TMLC AHBL INPR IPNT LC ETPL EHPL '
I'PMPt rnpi • i
0050
-0051-
0052
-0053
0054
48 FORMAT UX, 11114, 2X)//)
5 FORMATUX, 'COEFFICIENTS OF ENTRAINNENT AND DRAG* I
—WRITE U».AJAl-.A2«A3.*«,CDfTURBF ----- --
6 FCRMAT(1X,'A1»' ,F8.5,5X,'A2-',F8.5,5X,1A3«i,F8.5,5X,'A4-t,F8.5t5
0055
-0056
0057
-0058
0059
hRITE«6,7»
7 FORMATiUC.iAMBJiliT _P-RCFJ-L£S'_I
WRITEI6.8)
B FORMAT-i3X,LH£JGHT-!_,7J(,«J-EMP^12X, 'tlUMJOlTy • ,9X, 'VELOC ITV J
00 556 I-1,MG
0061
-O062-
0063
-0X344-
0065
T»1.-373.16/TK
ES-0. 622*1013. 25*EST
AH(1I>AHP( II*0.01*FSH
pn o im\tv.rr
0067
-0068
0069
-0070
0071
nmy
9 WR1TE(6,10)AZ(I),AT(II,AH(I),AHP(I),AUI1,I)
•OO-EORMAI41JUJ
HRITE(6.11I
Jl -FORMATi/J
HRITE(6.12)
i? PHRMATIi«t«Tnupp
0073
-007*
-0075 -
0076
nn77
WRITEI6,18)
1*HUMI',9X,*LPMO*I
___ DO 47 J-.UNP ------- .-....-..
17 WRITE(6,13)I,CX(I).CY(I),DI(II,UO(I),TO(I),HO(II.MO(II
C-4
74
-------
FORTRAK IV G LEVEL 20.7 VS
FTP
DATE
6/07/77
14:32
-007d _. .. __.
(
0079
0080
0081
0032
-0083
0084
0085
0086
0087
0086
-DO 8 9
0090
1F12.8)
-WRITE(6, 242)
CALCULATION OF TEMPERATURE,HUMIDITY
MG1=MG-1
DO 14 1=1,MG1
11=1+1
DV=AZ(II)-AZ(I)
AND VELOCITY GRADIENTS
14
AhG(I>«(AH(II)-AH(I))/DV
DO 47 J=1,NP
00 47 1=1, FG1
11=1+1
DV=AZ( II I-AZ(I)
0092
0093
0094
-COS5
0096
0097
0098
OC99
-0100
DO 148 I»1,NP
-D02=01(IJ/2.
BXZ(I»=DC2
BYU)=002
B1(I)=C02
WRITE<6,15)
15 FORMATUX, 'P-LUME 1 APPEARS AT NSTEP
C SET INITIAL CCNDITICNS,
-IS//)
ALV=FALV(TP»
CALL _S£LLf
INTEGRATION BY RUNGE-KUTTA METHOD
0101
0102
0103
0104
-QIC 5 ....
1=0 ...
S=0.
DS=DI(ITHP)/20.
fin rn «;««
0106
0107
01C8
-0109-
0110
-0111
0112
-0113
0114
-0115-
0116
86 IF(NIP1 .GT. NP) GO TO 19
-CHECK IF -ANY-NE* PUJKE APPEARS __
CALL CHKNk.Pt PX.PZ,PQ,PMX,PMZ,PG,PF.PCCS.PS IN, PENT, PU, PS,P 8,P A,PT,
—lPET.PH.PEh.PWtPAN,PY,POU_.PC,CX,NP,NS,DERlVR,CY,KE)
19 IF(NII-1)16.105,105
ITHP=1
... — ALV-FALVtTPJ
DS=0.1*PBt 1,
_59fl-XALL RUNGS IS.
B1(1)=B
yP-, L.DERI VR)
BXZ(1)*B
-0118 —
-0119
-0120
0121
SOLUTIONS FOR SINGLE PLUME
-CALL SCLUTN(PXtPY.Pi.PQ.PMX,PMZ,PG,PF,PU,PENT,PS,PA,PB,PCOS,PSIN
lPT,PET,PHtPEH,PW,PAN,PDIL,PC,CY,Y,YP,S,ITHP,IKT,NP,NS)
r.n Tn -ju .
CHECK IF ANY NEK PLUPE MERGING CCCURS
105 CALL ALIGN(PJ(.PY.PX.PiJ,PKXtPMZ,PG,PF,PU.PENT.PS,PA,PB.PC.PCOSt
lPSIN,PT,PET,PH,PEH,PW,PAN,PDIL,CY,Y,YP,YS,VSP,YRl,YRlPfYR2,YR2P,
2DERIVE.DERIVS.DERIVR.S.LC.NP,NS,KE)
CALL PLMERG(PX,PY,PZ,PT,PET,Ph,PEH,PH,PA,PB,PAN,POIL,PCCS,PSIN,
C-5
75
-------
FORTRAN IV G LEVEL 20.7 VS
MTP
DATE =
6/07/77
14:32:
0122
.-0123
0124
0125
0126
16 00 23 1=1, NI
1THP=1
C
C
IKT= IK+NCV IM I I-ISI I )»1
IFIINOm ^LT.U GO TO 23
DS«0.1*P3( I.IKT-1)
RESET INITIAL CONDITIONS AND CALCULATE PLUME PROPERTIES FOR SINGLE]
AND MERGED PLUMES
0128
lCERIVE.DEPIVS,DERlVRfPX,PZ,PQ,PMX, PMZ,PG,PF,PCOS,PSINtPENT,PUtPB,
2PA.PT.PET.PEH.PUtLCl
SOLUTICNS OF PLUMES INCLUDING SINGLE 6 MERGED PLUMES
CALL SCLUTNlPX,PY,PZ,Pg.P«X,PMZ,PGf PF, PU.PENT.PS, PA, PB.PCOS.PSIN,
lPT,PET,PH,PEHtPH,PAN,PDILtPCiCYtY,YPfSfIt IKT.NP.NSJ
23— CCWIJNUE
0130
0131
0132
0133
0134
nj 3*
0136
0137
0138
4139
0140
0142
0143
0144
0145
0146
0147
0148
O149
0150
0151
0152
01*?
0154
-0155
0156
0157
0158
0159
0160
-0161
0162
4163
0164
0166
0167
0163
0169
0170
01 71
IL-0
78 DO 77 1=1, NP
IFUIK*NOVIKmj .LT. NSI GO TO 77
-INDUJ-0 -
77 CONTINUE
nr 7«; T=i,Kp
IFIIND(I) .GT. Oi GO TO 79
J5 CONTINUE -
GC TO 80
75 JK=JK*1 - _
IF(IO-2)86, 16,397
nr. nr HI 1 = 1, Np
IF(KE( I) .LE. 0) GO TO 82
-4FILCHK(I)^.LI-. -IJaO-I^J 81
KEU )=KEl I )•*•!
K=HGPA2(! )
PX( I,J)=PX(K,LI
PBCI !J)=PB
PC(I«JJ=PC1K,LJ
FCOS(I,J)=PCOS(K,LJ
PET(I,JI»PET(K,L)
Pf-H I ,JI«PEH(K,IJ
PH(ItJ)*PM(K,L)
GO TO 91
62 KEUI-NS
MRITE(6f808)
808 FODMAT( ix , 'BfSULTS OF THE VISIBLE 1
HRITEC6.225)
DO 807 I-1,NP
DO 803 J=1,KEN
IF IPHl 1 1 J) .GT.O.IGO TO 802
IF(NCV(II.EO.O)GO TO 803
NCVI IJ-0
CH«2. - ......
C-6
76
-------
FORTRAN
0172
0173
0174
0175
0176
IV G LEVEL 20.7 VS
PTP
DATE =
6/07/77
14:32:
0178
4179
-0195
0196
-0197
0198
—0199
0200
f.r U( 11J J
-B09 «RMAT(lX.2(I5,lXJ,3(i=8.2.1XJ,2(F7.2.1X),3(F8.5,lX),6(F7.2,lx),/l
B02 JFINCVUJ..NE.OJGO TO B03
NBVU)*J
-J.
CH=1
,''',,
I,J|,PW(I,j),pBtIfJlfPCCI,J),PAU,J),PANU,J),PDlLU,J),
— -2PUI 1 1 J )
0180 241 FORMAT|1X,2( I5.1X) ,3(F8.2,1X) ,2 IF7.2,1X) 3IFB 5 IX) fe(F7 7 x 1
^?18J 803 CONTINUE ' * ' '-«fl*ll
0182
O183
0184
-0185 -
0186
.0187 .
0188
-0189
0193
-0191 —
0192
-0193
0154
IF(CH-1.) 804,805,807
-804 -WRITE 4 6, 233) I
233 FORMATUX, 'NO VISIBLE PART OF PLUME FOR PLUME*, I4/)
GC TJ3-807
8C5 HRITE(t.243)I,J
241 FflRMATJlXT IPI lIMft , J^ 1 CTli | VISIRIP AT T^JC Tea u I M« T t nm <-Tr«. ...
8C7 CONTINUE TIRMlNATJON ST£P',IW.
242 FORMAT*//)
224 FORMAT (IX, -RESULTS AT THE LAST STEP OF CALCULATION')
22£ FORMAT (IX.'NSTEP NTHP X Z Y PTEMP EXCEST
-!,• PHUMI ---- EXCESH JU.QOMOIST-PAWHFWO PCROSEC SLOTLEN PANGLE .
2'DILUTK PVELO'I
NTHP=i
wRITE(6,226INS,NTHP,PX(l,NS),PZll,NSI,PYIl,NS»,PT(l,NS),PET(l,NS)
2PDIL(1,NS),PU(1,NS»
-226 FORMAT41X.2(J5*lXJ,3
-------
FORTRAN
0001
IV G LEVEL 20.7 VS
BLANK
CATE
6/07/77
14:32:
SUBROUTINE BLANK IPXtPZ,PQfPMX,PMZ,PB,PUtPFtPGtPCOSfPS IN,PENT,
]PTrPS,PAtPPTtPPH,PAktPYfPnil tPH.PH.PC.NP.NS.NX. NY.NCQNT.N4.CQNTA.
0002
0003
OOU4
0005
0006
0007
OOC8
.0009 .
0010
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
00^
0034
•0035
0036
0037
0038
0039
2CONTBtCONTC»HGPA2,MGSTl,DX,rt,XO,ZC,IPNTtKE,LCHK,AHP)
.DOUBLE PRECISION Ab, BO, CO, DO
CGPMON /STCRE1/IND(30),INCT(30>.NOVIM30),IS(30)
J. /STORE2/MP13QJ.MSC30I .I1PC30)
2 /STORE3/AH(30),ATI30»,A2<30I,AHG<30I,ATG(30),AU(30,30I,
A Aiirr(-»nf -*o^
3 /STORE4/A(30) ,B1 ( 30) ,62 ( 30) ,BXZ(30) , BY (30 J ,PMCOSt30» ,
4 - -J>MSJNL30J«OM(30J,NBV(30ltNEV(30) tNCVOO)
5 /CONSTi/PAI ,GRA,A1,A2,A3 , A4 .CD.TURBF ,UC, B,TP,ET, HP, EH, HP,
J> JlGtM£l*CFRL*ALV«CPAfANG,IQ,ITHP«ENTRAN
7 /CGNST2/IL.NIJ,IK.NI,NIP1
9 /CONST3/£Q,BO,CQ.CQ
IPB(NP.NS) ,PU(NP^NS»'pF(NP*NS/tPG0.
P01 I • Jt "0
PMX(I,J)*0.
PF-0.
PC(I,Ji«0.
PCOS(1,J)*0.
PUll ,JI-0.
P£T(I,J»«0.
DPMI 1 1 j) «n_
C-8
78
-------
FORTRAN IV G LEVEL 20.7 VS
BLANK
CATE
6/07/77
14:32
0040
-OO41
0042
0043
0044
0045
0046
-0047-
0048
.£049-
0050
0051
0052
£053-
0054
0055
0056
-0057-
0058
PTU.JI-0.
PA(I,J)»0.
-PHCI,JJ*0.
PY(I,J)=0.
PANU,J)=0. .._
PDIL(IfJ)-C.
DO 2 1*1,NX
- £0 2 J=1,NY
2 CCNTA(I,JI=0.
DO 3 J=1,NCONT
3 CONTB(I)=0.
DO S Ial,M&
5 CONTC(I)*0.
-00-6 1«=U30
DC 6 J-1,30
6 AU(ItJ)=0.
DO_7_l=i*2
0060
0061
0062
£063
0064
_G£65.
0066
OC67-
0068
0069
0070
--OOZ1-
0072
0073
0074
-OC75
0076
_007_7_
0078
-OOJ^-
0080
KE( I)=0
AT(!)=0.
Ah(I)=0.
•fi(j >=n.
7 AhG(IJ-0.
AC=0.000009153132
80=0.0002112502
-00=0.003660244
00=0.009494118
PAI-3.14159265
--GRA =9. 3066
Al=0.0806
A2=0.6753
A3=0.3536
CD=1.5
ItRBFsO.
DX=0.5
0082
X0=l.
20=?.
0084
IPNT=0
_CfBL=A2/l O.116-AU.
0086
nnai
0088
000°
0090
nnol
0092
flC93
0094
-0095
IL>0
MTIsQ
IK = 1
NIjl>2
ITHP=1
IKO(1)S1 - - ----
IS(U = 1
0096
END
C-9
79
-------
FORTRAN IV G LEVEL 20.7 VS
FALV
DATE
6/07/77
0001
0002
0003
OOOt
0005
0006
-0007
FUNCTION FALV(TC)
. JO DETERMlNE_LAT£M-h£AT. ALV
IF(TC .LT. 0.) GO TO 1
FALV*(597.31-0.57*TC)**.1868
GO TO 2
1 FALV-1677.01*0.622*TCJ*4.1868
2 RETURN
C-10
80
-------
FORTRAN IV G LEVEL 20.7 VS
SETIC
DATE -
6/07/77
0001
0003
_0004.
0005
0006
0007
.0008
O009
.-D010-
0011
-0012
SUBROUTINE SETIC(Y,I,CX)
—COMMON -yr£aMSJl/J>AIJGRA,Al.A2,A3,A4,CD,TUftBF,UC,B,TP,ET,HP,£H,WP,
1 MG,MGltCFRL,ALV,CPA,ANGtIO,ITHP,ENTftAN
2 y~STaRE3/AH(30)tATi30).A£(30),At-G(301,ATGl30)tAU(30,301 ,
* AUG(3C,30)
3 /STOR£5/DI(30),U013C),TO(30),HO(30),WO(30)
OIKENSICN Y(8),CXI30)
YI2)-0. " " ~
iii*nniT >
1I-WO(IJ»ALV/CPA)
Y(6)=CX(I)
RETURN
-END ,-
C-ll
81
-------
FORTRAN IV G LEVEL 20.7 VS
RUNGS
DATE -
6/07/77
1*532
0001
0002.
0003
SUBROUTI ME RUNGS(X,H,H,Y,V PR I ME.INDEX. DERIV)
__DJMENSJOK JOBJ .YPRJME18) ,ZI8),hlI8)jW2(8)tW3C8).M4(8)
C RUNGS-RUNGE-KUTTA SOLUTION OF SET OF FIRST ORDER O.D.E. FORTRAN I
C DIMENSIONS *UST -BE SET FCR EACH PROGRAM
C X INDEPENDENT VARIABLE
C H INCREMENT DELTA X.MAY BE CHANGED IN VALUE
C N NUMBER OF ECUATICNS
__£ Y _P£P£NPFNT VARJARIF R1DCK OKE DIMENSIONAL ARRAY
C YPRIME DERIVATIVE CLOCK ONE DIMENSIONAL ARRAY
£ THE PROGRAMMER KUST SUPPLY INITIAL VALUES OF Yd) TO YCN)
C INDEX IS A VARIABLE WHICH SHOULD BE SET TO ZERO BEFORE EACH
_C INITIAL ENTRY TD THE SUBROUTINE. I.E.. TO SOLVE A DIFFERENT
C SET OF EQUATIONS OR TO START fclTH NEW INITIAL CONDITIONS.
_C __LH£_PECGKAMK£R J4USI_WLJJ£ -A -SUBROUTINE CALLED .DERIVE WHICH
c COMPUTES THE DERIVATIVES AND STORES Tt-EM
_C Th£ .ARGUMENT^1_LST -IS SUBROLTINE DERIVE(X.N.Y,YPRIME 1
IF(INDEX) 5.5,1
1-DO 2-J=l.N -
0005
OOP^
OOC7
0008
0009
0010
0011
001?
0013
0015
0016
0017
00 IS
0019
O020
0021
0022 — -
0023
n<)2^
0025
-0026
0027
O028
wl(I)=H»YPRIME(I)
y 71 TlsV I I I*lhi1 ( I I*.SI
A=X*0. 5*H
-CALL OERIV.UU*UZ,YPaiME)
DO 3 I=1,N
3 Z(I>=Y(I)*.5*W2(I)
CALL CERIV(A,N.Z, YPRIME)
-CO 4 1*1, N
V.3
-------
FORTRAN IV G LEVEL 20.7 VS
OERIVR
DATE
6/07/77
15:27:
0001
0002
0003
000*
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
0046
0047
SUBROUTINE OERIVR(S,N,Y,YP)
DOUBLE PPECISICK *Q,BC,CC,CQ
COMMON /STOREl/IKCt30),INDT<30»,NOVIM30»,IS<30l
1 /STOftE3/AK30),AT(30),*Z(30},AHG(30),ATG<30),AJ(3C, 30J t
A ALG(30,30)
3 /CONSTl/PMtGR*,Al,A2,A3,A4fCO,TURBF,UC,B,TP,ETt-IP,EH,*Pt
4 KG, MGl tCFPL t ALV.CPA, ANG, 1C, ITHP.ENTRAN
5 /CCNST3/ACtBQtCQtDQ
6 /STORE5/CI(30I,UO(30),TO(30),HO(30),WO(30)
DIMENSION Y(8),YP<8)
DETERMINE AMBIENT CONDITIONS
TPK«TP+273.16
TOK»TO( ITHP)*273.16
DO 88 1-2, MG
IFIY<7) .GT. AZ(I)I GC TO 88
11=1-1
DZZ=Y(7)-«ZtII)
TA=AT( II )*ATG(II )*CZZ
HA=AH
-------
FORTRAN IV G LEVEL 20.7 VS
OERIVR
DATE
6/07/77
15:27:
0048
0049
0050
0051
0052
0053
0054
0055
0056
0057
005S
0059
0060
0061
0062
0063
0064
0065
0066
0067
0068
0069
0070
0071
0072
0073
0074
0075
0076
0077
0078
0079
HUMIDITY AND TEMPERATURE
CALL ITEP«TPK,hP,EST,Cl,C2l
TO DETERMINE THE PLUME LIQUID PHASE MOISTURE
WP«C3-HP
IFCfcP .GT. O.I GC TO 79
DRY PLUME
MP«0.
HP-C3
TP»TA*Y4
TPK-TP»273.16
GO TO 178
MET PLUME
79 TP-TPK-273.16
178 ET-TP-TA
TO DETERMINE ACIABATIC LAPSE RATE
GAMA*FGAMA(TAK«t-At
DETERMINE PLUME EKTRAINPENT
RT-TPK/TAK
PER-2.*PAI*B
IFIPT .EC. 1.) CC TO 99
FRL*UC*UC*TPK/(GRA*TCK*ABS(RT-1.)»B)
IFIFRL .GT. CFRL) GO TO 9
A12*0.116
GO TO 10
9 A12«A1*A2*APSIN/FRL
GO TO 10
99 A12-A1
10 ENTPAN«PER*IA12**BS«U)*»3*UA»APSIN*PCOS*A4*UP|
EQUATICNS CF 'CCNSERVATICN OF VOLUME, MCM. ,ENERGE AND MOIST. FLUXES
YP(1»«ENTRAN*RT
YP(2)-(UA*ENTRAN*PMC»/FSIN)*RT
YP|3I-«RT-1.-HP|«GRA*LSL/UC-SIGN*FMC*PCOS*RT
YP|4»«-fTG»GAMA»*9Y
YPC5I— HG*SY
YP(6)*PCOS
YP(7)-PSIK
RETURN
END
C-1A
84
-------
FORTRAN IV G LEVEL 20.7 VS
DErUVS
DATE -
6/07/77
15:213
0001
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
C
C
SUBROUTINE DERIVS«StN,V,YP»
DOUBLE PRECISION AQ.BCrCCtOO
COMMON /STOREl/INCf30).INDT(30),NOVIM30),IS(30)
1 /STORE3/AH(30l,AT(30«,«Z(3Cl,AHG(30l,ATG1301,AUJi0.30J,
A ALG(30,30)
3 'CCNSTl/PAI,GR*,Al,A2,A3,A4,CD,TUReFtUC,B,TP,ET,rll>, BH.WF,
* PGtMGltCFRL,ALV,CPA,ANG,ICtITHP,ENTRA*
5 /CCNST3/ACtBCtCQ,CQ
6 /STORE5/DI(30>,UC(30«,TO{20»,HO(30»,WO(30)
DIMENSION YIB).YP(B)
TPK=TP*273.16
DETERMINE AMBIENT CONDITIONS
TOK«TO(ITHP)»273.16
DO 68 I=2tMG
IF(Y(7» .GT. AZ(IM GC TO 88
88
90
65
YJ7)-AZ< Hi
TA=ATUI»**TG(II»*CZZ
HA=AHCII)*AHGim*DZZ
UA=AU(ITHPt II)*AUG(ITHP,II )*CZZ
TG=6TG(II»
HG*AhG(II)
GO TO 90
CONTINUE
DZl»Y«7)-AZCD*UA*UA*PSIN»PSIN*C.5
Y4=Y(4)/LSU
V5«Y(5I/LSU
C1*ALV/CPA
C3=Y5*HA
TO ASSUME THE PLUME IS SATURATED AND CALCULATE THE SATURATED PLUPE
HUMIDITY AND TEMPERATURE
CALL ITER(TPKtKPtEST,CltC2)
TO CETERMNE THE PLUME LIQUID PHASE MOISTURE
WP-C3-HP
JFCKP -GT. O.t GO TO 79
C-15
85
-------
FORTRAN IV G LEVEL 20.7 VS
OERIVS
DATE
6/07/77
0046
00*7
00*6
00*9
0050
0051
0052
0053
005*
0055
0056
0057
0058
0059
0060
0061
0062
0063
006*
0065
0066
DRY PLUME
MP-0.
HP«C3
TP-TAtV*
TPK«TP*273.16
GO TO 178
WET PLUME
79 TP-TPK-273.16
178 ET-TP-TA
EH-HP-HA
TO DETERMINE ACIA6ATIC LAPSE RATE
GAMA*FGAPAITAKtPM
DETERMINE PLUME ENTRAPMENT
TPK-TP+273.16
RT-TPK/TAK
ENTRAN»2.*J0.198»ABS(UMA3*UA*APSIN*PCOS»A**UP»
EQUATIONS OF CONSERVATION OF VOLUKE,MOM..ENERGE AND HOIS 1. FLUXES
YP(1)*ENTRAN*RT
YP(2»»-(TG«GAMA)*SV
YP<5l«-HG»SV
YP(6>«PCCS
YP(7)-PS1N
RETURN
END
C-16
86
-------
FORTRAN IV G LEVEL 20.7 VS
DERIVE
DATE
6/07/77
15:27:
0001
0002
0003
000*
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
SUBROUTINE DEPIVE(S,N,Y,YPI
DOUBLE PRECISION AQ.BCtCOtCO
COMMON /STORE1/INC130),INDTJ30I,NOVIM30I,ISC30I
1 /STORE3/AH30«.AT(30»,AZ(30),AHG(30>,ATG(30),AU(30»30),
A AUC00.3C)
2 /STCRE4/A(30),B1(30),B2(3C),BXZ(30),BY(30I,P*CJS( 30»,
3 PrSIN<30)tDU(30),NeV(30),NEv(30l,NCV(JC»
4 /CONSTl/PAI,GR*,Al.A2,A3,A4,CDfTUReFtUC,B,TP,ET,rt*.EH.WF,
5 MGtMGl,CFRL,ALV,CPA,ANG,IC,ITHP,ENTRAN
6 /CCKST3/AC,eQ,CO,CO
7 /STORE5/OI<30ltUC<30)fTO<30l,HOI30),WC(30l
DIMENSION Y(8I»YP<8»
TPK-TP+273.16
DETERMINE AMBIENT CONDITIONS
TOK»TO(ITHP|*273.16
DO 88 1*2,MG
IF(V(7) .GT. AZdM GC TO 88
11=1-1
DZZ = Y<7|-AZUI)
TA=ATUI MATGUI »*DZZ
HA=AH(II)«AHG(II)*DZZ
UA=AU(ITHP,II)+AUG(ITt-P,IIJ*CZZ
TG=ATG(II»
HG=AHG(II)
GO TO 90
88 CONTINUE
DZ1=Y(7)-*ZIMGII
TA=AT(MG1)+ATG(KG1)*021
HA=AH(MG1*»AHG(KG1»*CZ1
UA=AU(ITHP,MG1)*«UG(ITHF.MG1I*DZ1
TG=ATG(HG1)
HG=AHG(MG1»
90 TAK»TA*273.16
UP=CA*TURBF
DETERMINE MOMENTUM,TRAJECTORY ANC VELOCITY OF PLUME
PM=SORT(Y(2)*Y(2)«Y<3)**(3))
PCOS»YI2)/FM
PS1N»Y«3I/PM
IFCPCOS .NE. O.I €0 TC 86
ANG=90.
GO TO 65
66 ANG=ATAMPSIN/PCCS)*180./PAI
85 SIGN=1.
IFtPSIN .LT. 0.) SIGK»-1.
APSIN=ABS(PSIN)
SY=PSIN*Y(1»
UC«PM/YC11
U=UC-UA*PCCS
USU=UC*(A«ITHP»*(ei(ITHP)*B2(ITHPII*0.5*PAI*
-------
FORTRAN IV C LEVEL 20.7 VS
DERIVE
DATE
6/07/77
15:27.
0046
0047
0048
0049
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060
0061
0062
0063
0064
0065
0066
0067
0068
0069
0070
0071
0072
0073
0074
0075
0076
0077
0078
0079
0080
0081
0082
0083
0084
0085
0086
0087
C TO ASSUME THE PLUNE IS SATURATED AND CALCULATE THE SATURATED PLUPI
C HUMIDITY AND TEMPERATURE
CALL ITEDITPKfHP,EST,CltC2t
C TO DETERMINE THE PLUME LIQUID PHASE MOISTURE
WP-C3-HP
IFChP .GT. 0.) GC TO 79
C DRY PLUME
WP'O.
HP«C3
TP-TA+Y4
TPK-TP+273.16
GO tO 178
C MET PLUME
79 TP-TPK-273.16
178 ET-TP-TA
EH=HP-HA
C TO DETERMINE ADIABATIC LAPSE PATE
GAMA*FGAPAITAK,I-A)
C DETERMINE PLUME ENTRAINPENT
TPK«TP+273.16
RT-TPK/TAK
PER=2.*A(ITHP»
A12-0.196
IFCPT .EG. l.J GO TO S9
FRC-UC*UC»TPK/IUA*ENTRAN*PHC*«PSIN)*RT
YP(3»-«RT-l.-WP»*GRA*tSL/UC-SIGN»PMC*PCOS*RT
YPC4J —(TG*GAMA)*SY
YPt5l— HG*SV
YP(6)«PCOS
YP«7)»PSIK
RETURN
END
C-18
88
-------
FORTRAN IV G LEVEL 20.7 VS
PHI
DATE -
6/07/77
14:32
0001
-O002
0003
SUBROUTINE PHI(I,JR,H,CY,PZ,NP,NSiIKQ,IKP)
—CCMMCN /5TflR£l/JWflL3.0JJJNDT(30J,NOVlK(30),IS(30)
1 /STORE4/A<30),61(30), 62(301,6X2(30),BY(30J.PMCOS130J,
-2. J>MSINI30J,OM(30itNBV(30J.NEV(30) .NCVI30)
DIMENSION PZINP,NSI,CY<30)
TO CALCULATE _THE ANGLE OF THE INCLINATION OF MERGED PLUME «PHI)
0004
_0fl£5_
0006
-0007 .
0008
.0009
0010
0011
0012
-0013 -
IJR*INDT(JR)
1P-1NDT1MJ
IFdJR .NE. IM) GO TO 1
JFIIJR -.££• J. _jAND _1M EO
IFCJR .EG. M) GC TO 6
Iff I IB -PC. ? AND IM FO
2 DY*ABS(CY(JRJ-CY(MI)
DS=SQRTIOY»DY*DZ*DZJ
FMCOSU)=BY/OS_ __
1) GO TO
2) GO TO
1
-0015
0016
_OO17
0018
-0019
0020
.0021
0022
PMSIN(I)=DZ/DS
_____ GO TO -5 __ . ___
1 IFIIJR .NE. 1) GC TO 6
7 pjur.nst n»pw nsiMi
PMSIN( I)=PMSIN«M)
----- GC TO 5
e PMCOSC I)=PMCOS(JR)
GO TO 5
0024
0025-
0026
0027—
PMCOSi I)=SQRT(0.5*I1.*COSS)J
---- PMSINUJ
£ RETURN
__ END
C-19
89
-------
FORTRAN IV G LEVEL 20.7 VS
ITER
DATE
6/07/77
14:3.
0001
.-0002
0003
0004
0005
0006 ._
OOC7
_DOOB
0009
D010 _
0011
D012
0013
SUBROUTINE ITEP tTPK.HP.EST ,C1,C2»
T-l.-TS
£ST-1013.25*EXPU13.3185-C1. 976* (0.6445*0. 1299*T)*T>*T)*T I
ES«0.622*EST
HP*ES/(1013.25*ES1
FTPK=C2-C1*HP*273.16-TPK
.-ifiABS-iFipju— ^.L.n.r.n KFUJKN.
DST«(13.3185-(3. 952* (1. 9335+0. 5196*T I*TI*TI*TS/TPK
FTPKD*-1.*C1*>1P*OST*JHP-1.J
TPK*TPK-FTPK/FTPKD
GO TO 1
END
-G-20
90
-------
FORTRAN IV G LEVEL 20.7 VS
FGAHA
DATE
6/07/77
0001
0002
0003
0004
0005
0006
0007
0008
0009
0010
.0011.
0012
FUNCTION FGAMA(TAK.HA)
— 10 J)£TERHJNE_AOJAaAUC J.APSE RATE
T=1.-373.16/TAK
EST-EXPi{ 13. 3185-11. 976* (0. 6445+0. 1229*T|*T )*T ) *T )
£5-0.622*1013. 25*EST
HAS=0.99*ES/ (1013.25+ES)
IFIHA .GE. HAS) GO TC 1
FGAMA=O.OOS76
GO TO 2
1 RESP=EST/TAK
SATURATED AOIABATIC LAPSE FATE
FGAMA=O.OC976*(1.*5^20.*RESP)/(1.*839COOO.*RESP/TAK»
2-A£TURN ____ _____
END
C-21
91
-------
FORTRAN IV G LEVEL 20.7 VS
SOLUTN
DATE -
6/07/77
14:32:
0001
0002
-0003 —
SUBROUTINE SOLUTNJPX,PY,PZ,PGtPMX,FMZ,PGtPFtPU,PENT,PStPA,PB,PCOSi
lPSJN.PJ,P.ET..P.tUPEa.P.*fPAN.PDlL,PCtCYjYiYPtStl.JtNPtNSI
CCHMON /STORE4/A(30)fBl(30)tB2(3Cl,BXZ(30)fBY(30ltPMCOS(30)i
1 FMSINI30)(OMI30J,NBV<30),NEV(30)tNCV(30)
2 /CONST1/PAIfGRA,Al,A2.A3tA4,COtTURBFfUCtBtTP.ETtHP.EH.MPt
3 MG.MGl.CFRL.ALV.CPA.ANGfIQ.ITHP.ENTRAN
4 /STOREI/IN0(30)11NOTI30)iNOVIK (30)tIS(30)
. PMXI
IPPZ(NPtNS),PG(NP,NS)fPF(NP,NS),PU(NP,NS),PENT(NPtNS),PS(NP,NS),
2PAINP.NSJ.PBJNP.NS).PCOS(NP.NS),PS1NlNP,NS)tPT(NP.NS),PET(NP.NS)f
3PH(NP,NS),PEH(NP,NS),PH(NP,NS),PAN(NPfNS),PD1L(NP,NS),CYC30),Yt8),
0004
0005
OOOb
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
PX(ItJ)*Y(6>
P7I TTnn = Vl 71
pY'
PUU tJ)*UC
PENTU,J4s£NTAAN ..-
PS(I,J)-S
PA (I tJ)«A( I)
PC(ItJl=EXZ( I)
PPII ,.ll=R
PCOSd ,J)*YP(6I
J»SIN(I,JJ»YP47J^
PT(ItJ)-TP
-PEHI,J)»ET
PH(I,J)*HP
ppm 1 1 ii =FW
PHII t J)«UP
PAN! It J)ZANC
PDIL(I,J)*Y(l>/Pti(Itl>
-RETURN . -
END
C-22
92
-------
FORTRAN IV G LEVEL 20.7 VS
CHKNWP
DATE -
6/07/77
14:32:
0001
0002
0003
SUBROUTINE CHKNWP(PX,PZ,Pg,PMX,PMZ,PG,PF,PCOS,PSIN,PENT.PU.PS,PB,
!PA,PT,P£T,PiL.P.£h,Pjl,F.Ak,PY,PClL,PC,CX,NP,NS,DERlVR,CY,KE)
EXTERNAL DERIVR
COMMON /STOP.E1/IND(30),INDT(30J,NOVIK(30),IS(30)
1 /STORE4/A(301 ,81(30), 62(30), BXZ(30),BY(30).PMCOS(30),
2 PMSIN(30),DW(30),NBVI30),NEVI30),NCV(30)
3 /CONST1/PAI,GRA,A1,A2,A3,A4,CD,TURBF,UC,B,TP,ET,HP,EH,HP,
4* M/i u/~ i r* c ni A i tt ^ n * * ±< r< * ** • *.. n ^ ».*«*..
0004
-C -
5 /CONST2/IL,NII,IK,NI,NIP1
6 /STQR£5/DH30).UO(30),TO{30),HC(30I,WO(30)
DIMENSION PX(NP,NS),PZ(NP,NS),PO(NP,NSI,PMX(NP,NSI,PMZ(NP,NS),
1PB(NP,NS),PU(NP,NS),PF(NP,NSJ,PG(NP,NS),PCOS(NP,NS),PSIN(NP,NS)
2PENT(NP,NS»,PA(NP,NS»,PT(NF,NS),CX(30),Ym,YP(8),PS(NP,NSJ,
_3PHJNPjNSX,R»LLNP_,aSJj.E£LiJtf-,NSJjB£HiNPjNSJ ,PAN (NP , NS ) , PY (NP ,NS )1
4PCIL(NP,NS),CY(301,K E(30),PC INP,NSI
CHECK JF ANY NEk -PLUfE APPEARS
0005
0006
OOC7
onna
0009
0010
0011
D012
0013
0015
0016 __.
0017
0018
0019
r
0020
0021
0022
0023
0024
no?s
0026
Q0?7
IKK=IK*NOVIM1)-IS(1)
NIPP=NIP1
DP 77 -I = NIPP,NP
OS=DI(J)/20.
- 4F4ABS(CX4NIPP_)^CX(JJJ -GE. -CSJ -GO
40 FORMATdX, 'PLUME1, 2X,I3,'« APPEARS
N ! I =1 ._ j
IS( J)=IKK
-NOVIK(JJ=NOVJK(1J
MP1=J*1
IND«J)=1 . -
IKS-1
TP-TO(J)
CALL SETIC(Y,J,CXI
S=0.
JTHP*-i
3C CALL RUNGS(S,DS,7,Y,YP,L,DERIVR)
.9 .
Jfl
AT
-
NSTEP='f I 5//)
w SCLUTICNS FOR UNMERGED SINGLE ROUND PLUME
0028 CAU._SQLUTN(P-X.PJL,Pi-.PQ,PMX,FM2,PG,PF, PU.PENT.PS, PA, PB, PCOS.PSIN,
!PT,PET,P»-,PEH,PWfPAN.POIL,PC,CY,V,YP.S,J,IKS,NP,NS)
jHf TRTTPBlrN FHC STrPJ>-IMG-ThE_CALCULATJQN OF THE MEM
0029
0030
O031
0032
4033
0034
0035
0036
0037
0038
C
23
22
19
ISSUED SINGLE PLUME
Jf-CP2IJ.JKS> »r.F- P*«l, IKKJJ^CD JD-23
IFdKS .GE. NS) GO TC 22
DS«B*0.1
_ALV=FAl V(TP) - - --
GO TO 30
KE(J)*1KS
CONTINUE
AETURN — -
END
C-23
93
-------
FORTRAN IV 6 LEVEL 20.7 VS
ALIGN
DATE
6/07/77
14:32:
0001 SUBROUTINE ALIGNJPX.PY.PZ,POfPKX.PMZ,PG.PF,PU,PENT,PStPA,PB.PC,
lPCOS,PSl/iL.P:i-.P£T*P.hUf£H.PHtPAN,PCJL.CY,YtYP,YS. YSPtYRl,VRlP,YR2,
2YR2PtDERIVE,DERIVS,DERIVR,S.LC,NF.NS.KE)
0002 EXTERNAL OERIVEtOERIVS.DERIVR
0003 COMMON /STORE1/INDI301,INDTI30I.NOVIK(301.ISC 301
J. ycCNST_l/PAI,GRAtAl.A2fA3tA4tCD,TURBF,UC.B,TP,ET,HP,EH.WP,
2 MG,MGl,CFRLtALV,CPA,ANG,IO,ITHP,ENTRAN
3 aiC\ST2/ IL .NII .IX.NJ^AJPl _
0004
4 /STORE4/A(30)fBl(301,B2(30)tBXZ(30>rBY(30),PMCQS(30),
5 PM51N(30),DH(30J.NBV(30JtNEV(30> ,NCV(30i
DIMENSION PX(NP,NS).PYINP.NS)tPZ(NP.NS).PQ(NP.NSItPMX(NP,NS),
aPM2(NPtNSJ«PG(NP,NSJ-tPFlNP,NS),PU
0\15
4)016
0017
-0018
O019
On?n
0021
_0022
0023
-0024
0025
p^MAx-pxu'ii!'1
DC 1 I=ltNI
1MzIK«MnilIKI I I-Itf 1 1
IFCPXMAX .LT. PX(I,If)) PXMAX=PX(I,IM)
-J -CCNTINbE
00 2 1=1, NI
JMINDUJ —LT-._H GO TO 2
IM=IK+NOVIK«I)-IS(I )
DS"=P8(I,IM)*0.1
JFUPJIMAX-PJU1.JMJ--OSJ ^.LT- O.J GO TO 2
IM=IM+1
IFUNOUJ^.GT. 41 -GO JO 8
IFIIM .GT. KEII1) GO TO 8
Rl 1 T)sPR( I TIM1
B2(I»=PBII tIM)
J>CU«IM)=PBU.1NJ -
GO TO 9
R ITHP=[
0027
IKT=IM
CALL A£SET_U_UJXlL,DS^S,NPtNS,CY.Y,YP,YS,YSP.YRl,YRlP,YR2.YR2P, -
1DERIVE,OEPIVS,OERIVR,PX,PZ,PC,PMX,FMZ,PG,PF, PCOS,PSIN,PENT,PU,PBf
0029
CALL SOLUTN(PX,PY,PZ,PJ,PMX,PMZ,PG,PF.PU,PENT,PS,PA»PB,PCOS,PSIN,
0030
0031
0032
0033
0034
9 NOVIK1 I)=NOVIK(I)*1
GC TO 11
2 CONTINUE
PETURN
END
C-24
94
-------
FORTRAN IV G LEVEL 20.7 VS
FLHERG
DATE
6/07/77
14:32:
0001
0002
SUBROUTINE PLMERG«PX,PY, PZ,PT,PET,PH, PEH,PW,PA,PB,PAN,PDI L , PCOS ,
lPSJN.CY,NP.,NS*Kfc.MGPA2JMGSTl.PC»LChK,PU)
COMMON /STCRE1/INDI30) , I NOTC30) ,NOVIM30) ,15(30)
1 /STORE2/MP(301,MS(3C1,IIP130»
2 /STCRE4/A(30),BU30),e2<30l,BXZ«30l,BV(30),PMCOS»30),
3 PHSIN130) ,OW(30) ,NBV t 30) tNEV ( 30) ,NCV(30)
4 /CONST1/PA1,GRA,A1,A2,A3.A4,CO,TURBF,UC,B.TP,ET,HP,EH,HP,
5 ________ M
OO03
6 /CCNST2/IL,NI I ,IK,NI,NIP1
-DIMENSION PJUNP,NSJ,PZ(NP,NS),PB{NP.NS),PCOS7
0008
0009
0010
0011
0012
Opi i
0014
0015
0016
-0017
0018
001°
0020
0021
O022
0023
nnyL.
0025
0026
0027
0020
0029
OfMft
0031
^)032
0033
0034
0035
QlMfr
0037
0038
0039
0040
—0041
5LCHKC30) ,PU(NP,NS)
-C JIEARRAJUGE JHE-JTJIAJECTORIES OF -J HE EXISTING PLUMES
NJ*0
00 101-1=1, NI_ __
IFUND(I)-1)101,102,102
10? I^r-= IK *Nnu TM I )-I S1I >
NJ=NJ*1
PXI(NJ)=PX
IRE(NJ)=I
101 CONT INUE
C CHECK PLUME MERGING
— IL=0
NI1 = NJ-1
nn i n3 i «] ,N| i
J 1*1*1
J3C 103 J=J1,KJ
PYD*ABSIPYI(I)-PYHJ)I
. P_iO=ABSlPiIiI J--=P-24U J J
PYZ=SORT
-------
FORTRAN IV G LEVEL 20.7 VS
FLMERG
DATE
6/07/77
14:32
0042
-00.43
0044
0045
0046
0047
-0048.
0049
0050
0051
0032
0053
II-IRE(I)
111
113
103
205
INDTtJJI-INDCJJJ
JNDTdlJ'INOdl)
RESET IND(III*2.INDfJJ)«0 FOR JJ>II MHEN PLUMES II AND JJ MERGED
JND(JJ)*0
IIPHDI t 1
LS*MSd)
HT-IIP1LP1
NT>IIP(LS)
MGSTHLS)-MT
IFIKPIICI .r.T _ MTI r.p JO 116
LCHMLS)»1
116 WRITE(6.110)MT,LP.PX(LP,MTJ,PZ(LP»MT),PYILP,MT) ,PT(
1«>ET(LP,^T) (PHiLP.MT) fPFHItP.MT) tPyUP,MT)tPp((,P|MT>
2PAILP,MT),PAN(LPfMT).PDILILPtMT),PU(LP.MT)
i in FORMAT (ix.?it<:riyi T^IF«-?T I * I r ?'F7-7. lX)»3IF6i-$r 1^1
117 INDX*2
LP-LS
MT»NT . . .
GO TO 116
LP.MTI,
.PC(LP.MT),
.6IF7.2.1XJJ
C-26
96
-------
urv • n>H
0091
D092 .
0093
0094
0095
0096
OCS7
009S .
0099
0100
0101
0102
0103
0104
0105
0106
n i» o ICVCL iu«/ va PLHERG
119 FORMATC/I "
- - ICS-COWTJNUE
00 777 1=2, NI
IF(INO(I)-1J 777,779,779
777 CONTINUE
- - MI=0
ITHP«1
779 DO 400 _JsL?rMP
IF(INO(I))16,400,16
-. -40C CONTINUE
C ALL THE PLUMES ARE MERGED KHEN INOJ
_j ^Q ( i J *3
10=3
N 1=1
ITHP=l
16 -RETURN _^ .
ENC
DATE * 6/07/77
~~
II=C FOR KKNPfrl
14:32:
C-27
97
-------
FORTRAN IV G LEVEL 20.7 VS
RESETI
DATE
6/07/77
19:42:
0001
SUBROUTINE RESfTI 4 I, IKT ,OS.S,NP,NS,CV, Y, YP, VS, VSP, VR1. VitiP ,VR2,
1VR2P,DERIVE,OEJUVStOEPlVR,PX,PZ.PQtPM)
0002
0003
2PU,PB,PA,PT,PET,PEH,Ph,LC)
-EXTERNAL -OE«IV4^,4J€«IVS»0€«IVR --
COMMON /STCREl/INCt30),lNDT430l,NOVIK430)tlS(30)
/STCRE4/A430»,BIC30),B2I30I,BXZ<30I,BYI30),PMCJSI 301,
4
_5
/CONSTl/PAI,GRAtAl,A2,43,A4,CD,TUReF,UC,B,TP,ET,f,IRP(30).COdl33J,Ylft),
0005
OO06
0007
-0008
0009
-0010
0011
O012
0013
-001-4
0015
0016
O017
0018
-OOI*
0020
O021 ——
0022
0023
0024
-0025
0026
0027
0028
-0029
0030
-0031
0032
-0033
0034
0035
0036
3PA(NP,NS>tPCaS(NP,NSI,PSIN»PPX
-------
FORTRAN IV G LEVEL 20.7 VS
RESETI
DATE
6/07/77
19:42:
0042
-0043
0045
0046
0047
0048
-0049
0050
0051
0052
0053
0054
-0055
0056
0057
0058
O059
0060
-0061
0062
0063
0064
0065
0066
0068
O069
00/0
0071
0072
0074
0075
4)076
OOJ7
-9O7-8
0079
-0080
0081
-0082
0083
Ann*.
0085
fin at.
Y(5)*YI5)»PF(JJ,IKPI
APT = APT»PTUJ,IKP)
IJK«!JK+1 -
IRP< 1JK|=JJ
CYMANC=CY-fiY(JJ»
D 7UAkl<- - 07/11 luni.nw......
-400
404
401
244
-28
26
- — 34
gf ft
en
859
C
575
572
PZMINC=PZ(JJ,IKP)-BXZJJJ)
IFUNOTANC)-6C TO 26
JRZ-JJ
IF(PZMIN .LE. PZKINC) 60 TC 34
P7MT NT P 7 MI MT
CONTINUE -
IF(MM-IJK) 58,59,59
GO TO 60
APT=APT/FLCAT(IJK)
LC=C M?ANS CLUSTER OF TCWERS; LC-1 MEANS LIKE TOWER AitKA Y
CY( II=0.5*«CYMAK*CYMIN)
IKO«IK*NCVIK(M)-IS(M|
DCYAI=CYKAK-CYKIN
HJPZAI-PZMAN-PZ^ll.
IFiCCYAI .LT. CPZAI) GC TO 402
i fit rVMAU^ »•«"«"• «T f P 7HAN— rf H INI 1 CO TD 40?
IF(CY(M) .EO. CY(JR)) GC TO 407
0088
TO CALCULATE THE ANGLE CF THE INCLINATION OF MERGED PLUXE «PHI)
-------
FORTRAN IV G LEVEL 20.7 VS
RESETI
DATE
6/07/77
0096
0097
0098
0099
0100
0101
0102
Al A**
0104
0105
0106
0107
fti fto
0109
0110
0111
0112
0113
/ii n £
0115
0116
0117
0118
0119
•0120
0/21
0122
0123
0124 •--
0125
fil 3t*
0127
O128
0129
0130
0131
ni T"
0133
0135
ni ift
0137
Q13B
GO TO 573
GO TO 573
402 JR=JRZ
M=MZ
1KQ=IK+NOVIKIMI-IS«M>
IKP=IK*NCVIK(JR|-IS( JP|
C
PZY=ABS(CYIJR)-CY(MI 1
TO CALCULATE THE -ANGLE -CF THE INCLINATION OF MERGED PLU-4E (PHI)
CALL PHI
-VB1U*-BBB
0144
-0145
0146
O147
0148
YRlf2I*BBB*PU(M,IKQ)*PCCS-PZ
-------
FORTRAN IV G LEVEL 20.7 VS RESETI
C RESET I.C. FOR THE HALF ROUND PLUME
DATE
6/07/77
19:42:
-0150-
0151
0152
0153
0154
0155
-015*-
0157
0158
0159
0160
-04*1-
0162
€163
0164
0165
-01**-
0167
-01*8
0169
-0170
0171
0172
O173
0174
-0175 —-
0176
-0177
0178
0179
0180
0181
-01-82-
0183
VP2m5»-0.5*(VPl(;*»VR2l5Hi/A(I»
YS(7|*Y<7>
CALCULATE -NEW -HAL^-W!CT«- AND -VELO, -OF THE -HALF ftCUNO
L»0
AL-V-AtVl --- ---------------
CALL RUNCS -AKO ^ELO. OF
L = 0
-- ALV-FALVUPT^ ----
CALL RUNGS(S,DS,5tYS,VSF,ltOERIVSJ
-rO^F S t VS , VST , L
SLCT JET
BS=P
0185
C-
c
-01-86
0187
0188
S=S-DS
— CALCULATE -MERGEC -PLUME
THE PREVIOUS STEP
^THE -KOOIFI EO PLUME SHAPE dETe^MINED C
CALL PUNGS(S.DS,7,Y,YP,LiOERIVEI
0189
-0190
0191
0192
0193
0194
0195
-6196-
DETERMINE 81,82 AND A CF THE MODIFIED PLUME SHAPE FCK OLiULATINC
-EWTfAINKENT^NO-CRAG-FOP-NEXT
UU-UC
C61=BR2/eRl
*U 5*07963* (eRl*BRl*URl»BR2*BR2*UR2»»2.*BS*M*US»/JU
~APllil5707963*«U*CBl*CEl)-CB4*CB4
C-31
101
-------
FORTRAN IV G LEVEL 20.7 VS
0197 CP1=-CB3
RESETI
DATE
6/07/77
19X42:
0199
0200
0201
0202
.n?n^
0204
0205
0206
0207
0208
Ji?AQ
0210
0211
0212
0213
0214
0215
0216
0217
0218
0219
u??n
0221
0222
0223
02.24
0225
-A?? A
0227
O228
0229
0230
flyn
0232
0234
./loac
0236
n ? T 7 .
0238
— n?ao —
62P = B2(U
-AP=MII
C THE DETERMINED B1,B2 *NC A
-BlU»=<-BPl*SQRTALC
fi V 7 < IkmAAlAVl 1 A I i I
GO TO 416
BY(I)=AMAX1(B1(I)
GO TO 31
Cr AI rni ATC r T ur i c
29 L-0
AL V* FALV ( PT ( I IK1
I| 1
,B2(I))
ROUND -HAH> E - ... _ .
» •
CALL RUNGS(StDS,1,Y,YF,LtOERIVR)
B1(II=B
BXZtll-B
31 RETURN
ciun
C-32
102
-------
FORTRAN IV G LEVEL 20.7 VS
OUTPUT
DATE
6/07/77
0001
O002
19:42:
IX. I
-0003-
COMMON VSTORE1/INC<30»,INDT<30»-,4IOVIK<30»,IS<30*
1 'CCNTUU/WICTH,HITE,MOPE,NCMAP,ICENT,KOTICK,HEONUOJ•
-2 LABY<5»,IABX<5>
3 /STORE5/DI<30»,UOC30l,TO(30l,HOC30»tWOI30)
0005
-0006-
0007
0008
0009
-001O-
0011
lPmNP,NSl,PEH,PY-
42 IFCFEWC .GT. O.I GO TC 47
tX
-------
CORTRAN
DATE «
6/07/77
19:42:
0041
nnt?
0043
0044
0045
0046
0047
nn&n
0049
0050
0051
0052
0053
nn*i±
0055
0056
0057
0058
0059
flf\4*f\
0061
OO6Z '
0063
006.4 -
0065
ftnx-A
0067
UUOO
0069
11
31
a
32
— •-•*
a?
37
JU
7
5
1ft
17
--15
PZ(ItJ»«PZU,Jl/OI(U
PC(I,J)=PC(I,J)/OI(1)
PSII,J)'PSU,J)/OI<1)
PW(I,J)-PMI,J)/PEWO
PET«I,J)=PETII,J»/PETC
IF( IX(I» .LE. 0» GO TC 5
CALL ^P02(CONTA,OXYOZ,PX,PZ,PC,PET,PCOS,PSIN,NP,NS,KE.XJ ,ZO,NX.N'Vi
WRITE(6,31)
FORMATi IX, 'EXCESS TEMPERATURE PLOTS//*
GO TO 37
WRITE16.22*
-FOR^ATIlXi^-exCESS'-SPECIHC-ftUMIOITV PLOT',//)
GO TO 37
HRITE(t,33)
RE API 5, 30 1 (hEOMK),K*l,10)t(LABY(L) ,L»1 ,5 ) , CLABXC M),M«1 ,3)
CALL CCNTU(CCNTA,CCNTE,CONTC,NX,KY,NCONB,IFM)
IF(I-10)1C,17,15
IF( IX( I))5,5,9
END
C-34
104
-------
FORTRAN IV G LEVEL 20.7 VS
FMAX
DATE -
6/07/77
14:32
0001
.4002 —
0003
0004
0005
0006
0007
-flOQB _
0009
0010
FUNCTION PKAX«PT,NP,f*S,KE)
DIMENSION PUNP...NSL.KEOO)
PMAX«PTU,1)
DO 1 I*1,NP
K=KE«I)
DC 1 J=1,K
IF(PT(I,J) .GT. PMAX) PMAX-PT(I,JJ
_l_CONTOJUU£ ._
RETURN
-END
C-35
105
-------
FORTRAN IV G LEVEL 20.7 VS
GRD2
DATE
6/07/77
14:32-
0001
0002
0003
0004
0005
.0006
0007
0008
0009
0010
0011
_0012_
0013
0014
0015
0016
0017
-0018-
0019
0020
0021
0022
0023
.0024.
0025
0026
0027
-0028
0029
-0030-
0021
-0032
0033
0034
0035
-0036.
0037
0038
0039
-0040-
0041
-004-2-
0043
0044
0045
O046
0047
0048.
0049
4050
0051
0052
0053
-0054.
SUBROUTINE GRD2JA,DX,OZ,PX,PZ.PB,PG,PCOS,PS1N,NP.NS.KE,XO,ZO,10,
1JD) _....
COMMON /STORE1/INO(3C).INOT(3C) tNOVIKOOl tISI30l
DIMENSION JUlD,JD)tRM(5JiC(5i,lC(4J,PX(NPfNS)tPZINPtNS)fPG(NPtNS)
1PB/nX» 1.0005 ______
PB2C-PB{N,K*U*PCOS(K,K*1)
PB1S=PBIN,K)*PSIN(N,K)
DZZ-PZ«N,K*14-P2tN,X)
DXX=PX(N,K+1»-PX(N,K)
DPBS-PB2S-PB1S
OS«SO.RHOZZ*XZ
CB=PB(N,K»1)-PB(N,KI
OG=PGJN,KJ-PmN^K*J,J ____
IF(PSIN(N,K*1) .LT. C.I GO TO 101
105 IL*IC(3)+1
GO TOJ.12
104 IL=ICI3>+1
GO JO -113
103 lL
C(3»-PZtN,K+l)*PB2C-(PX(N,K+l)-PB2S)*RM<3)
IFiDXPB .EQ. 0.) GO TO 20
C(4)«PZ(N,K»1»-PB2C-
-------
FORTRAN IV G LEVEL 2C.7 VS
GR02
GATE
6/07/77
0055
.0056
0057
0058
OC59
0060
0061
-00£2-
0063
O064
0065
O066
0067
-OO43.
0069
O070
0071
O072
-0013-
0074
OC75
0076
-0077-
0078
-0079-
0080
0081
0082
OC83
0084
1FCI ILL 1) GO TO 12
_X=OX*f LCATL1-1)
IFII .GT. ICI3)> GO TO 7
GO TO 8
7 -ZU=RMI2)*X»CI2)
8 JU=ZU/DZ*1.0001
IFU—GT. -1CL2JJ_GO_LO-10
IFII .GT. Kill) GO TO 115
2L-RMI3)*X»C13)
GO TO 11
115 ZL=RM11J*X4C11J
GO TO 11
1C _ZL=AW4) «J(*£X4)
11 IFUZL-OZ*FLOATIJU-1)J .GT. O.J GO TO 12
1FIJU .LT. JL) GO TO 12
10XX,DZZ,I,K, ID.JDI
0086
0087
0088
O089
0090
nnci
GO TO 99
101 1FUC<2)-IC<4J) 121,122,123
122 IL=IC(2)*1
GC TO 124
122 IL=IC(4I+1
_GC JDJ.25 _________
121 IL=1CI2I+1
125 KMJ4)=(DZZ-OPBCJV10XX*OPBSJ
C«4)=PZ(N,K+1I-PB2C-(PX(N,K+11*PB2S)*RMC4J
12« OXOP«OXX-OP8S- —
IFIDXOP .EC. 0.) GO TO 21
RJU3 J *1 DZ Z *JP-BC jy-DXDK- __ ______ .
C ( 3 ) =P Z I N t K* 1 » * PB2C -(PX(N,K+1)-PB2S)*P.M(3)
21 RM(2J=-PCOSiN,K*l)/J>SlN{N,K*H
C(2)=PZUtK+ll-PX(N,K+l)*RM(2)
. .— JR-ICI3I --- --------
• IFUL ,GT. IR) GO TO 99
DO _L2fl_LaiL»Jfi ________ ______
0092
-0093
CO 9 4
4)095
0096
-CC5J-
0098
0099
0100
-0101.
0102
-0103.
0104
IFII .GT. IDJ GC TO 128
. JFI1—U.. -1J-GO-TO 1?H
X=DX*FLOAT(I-1)
-JFtl ,GT. 1C1J.JJJJO 10 130
IFCI .GT. IC12H GC TO 132
GO TO 133
-J.32 -ZU=RMI1)*J
GO TO 133
130-21
132 JO-ZU/DZ4-1.0001
0106
0107-
01C8
...0109 .
GC TO 136
135 ZL=RMI2)*X*CI2)
136 IF(IZL-OZ*FLOATUU-1I) .GT. 0.) GO TO 128
JL=ZL/DZ*1.9999
C-37
107
-------
FORTRAN IV G LEVEL 20.7 VS
GR02
CATE -
6/07/77
14:32:
0110
CALL PC2*in
CH=0.
172 MRITEC6.178J
176 FORMATI1H1I
DO 662 J=1.JO
L=JD*1-J
bt2 bRJT£16.3) < Al I , LJ*J *J P» J" »
3 FORMAT(lXt20(F5.2tlX)l
IF1CH -.EC- 0«J GO TO 173
IP-IP+20
GC TO 171
17' DO 310 N»l t^P . . ,
CO 310 I«l tNS
PX(NtI)=PX
-------
FORTRAN IV G LEVEL 20.7 VS
FD2
GATE
6/07/77
14:32
0001
0002
0003
.0004.
0005
-OOO6-
0007
0008
0009
0010
0011
nni 7
SUBROUTINE PD2(A,PX,PZ,PB,PG,PCOS,PSIN,RM,C,NP, NS.N,JL,JU,08,OG,
_1£Z-,JL. DXX ,U£Z-, J^K, la, -JO J
DIMENSION AUD,JDI,PX«NP,NS»,FZCNP,NS),PB»NP,NS),PG
-------
FORTRAN IV G LEVEL 20.7 VS
CONTL
DATE
8/03/77
10:1*:
0001
OOC2
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
0035
0036
0037
0038
0039
0040
0041
0042
0043
0044
0045
0046
0047
0048
0049
0050
0051
0052
0053
0054
0055
SUBROUTINE CONTUISET
YMAX«LIM
YNAX-YKAX
YNIN-YKIN
XNAX~XNAX
XNIN-XNIN
IF(KEV(2I.EQ.1I GOTO 10
DX*XMAX-XMIN
DY-YMAX-YMIN
IFIDX.GT.OYI GOTO 11
DUM'XSIZE
XSIZE-YSIZE
YSIZE-DUM
11 YSIZE«ANIN1IYSIZE.26.)
OX-AHIM C XSI ZE/OXtYSI ZE/ CY I
XSIZE-DX*XMIN)
C-40
110
-------
FORTRAN IV G LEVEL 20.7 VS
CONTU
DATE
8/03/77
10:14
0056
OC57
0058
0059
006C
0061
0062
0063
0064
0065
0066
0067
0068
0069
0070
0071
0072
0073
0074
0075
0076
0077
0078
0079
0080
0081
0082
0083
0084
0085
0086
0087
0088
0089
0090
0091
0092
0093
0094
0095
0096
0097
0098
0099
0100
0101
0102
0103
0104
0105
0106
0107
0108
0109
0110
0111
0112
0113
0114
0115
VD-YSIZE/X
-------
FORTRAN IV G LEVEL 20.7 VS
TOPO
DATE
8/03/77
10X14S
0056
0057
0058
0059
0060
0061
0062
0063
0064
0065
0066
0067
0068
0069
0070
0071
0072
0073
0074
0075
0076
0077
0078
0079
0080
0081
0082
0083
0084
0085
0086
0087
0088
0089
0090
0091
0092
00 S3
0094
0095
0096
0097
0098
0099
0100
0101
0102
0103
0104
0105
0106
0107
0108
0109
0110
0111
RS-RBIJ)
XS=X (J)
YS-Y CM
RM-RR
XM»XX
YM-YY
IF
-------
FORTRAN IV G LEVEL 20.7 VS
TOPO
DATE
8/03/77
0112
0113
0115
0116
0117
0118
0119
0120
0121
0122
0123
0124
0125
0126
0127
0128
0129
0130
0131
0132
0133
10116 IFUBS (XPA-XPB)-.00115003,5004,5004
5003 IFUBS (YPA-YPB)-.OOIUOC,5004, 5004
5004 CALL PLOTZUPAtVPA.XPBfYPB)
100 RC-CNTRINC+1)
NC»NC*1
60 TQ 80
103 XPA • XCL
YPA « YCL
GO TO 99
106 0-(RC-RM)/tRL-RM»
XPA«XCH-0*»XCH-XCLI
YPA»YCH-QMYCH-YCL»
GO TO 99
110 GO TO L,(112,118)
112 ASSIGN 118 TO L
RR -RB(J-l)
XX -X (J-l)
YY »Y (K)
GO TO 37
118 CONTINUE
RETURN
END
C-45
115
-------
FORTRAN IV 6 LEVEL 20.7 VS PLOT2 DATE - 8/03/77 1
0001 SUBROUTINE PLOTZ1X1.Vl*X2fY2I
0002 INTEGER EC
0003 LOGICAL*! LXS
0004 DIMENSION X(2>,Y(2),LXS<1)
0005 COMMON/CONTUU/SKIUPI26),
* XMINtXMAXt VMINtYMAXtXOFFtYOFFtXSIZEtYSIZEtNCOMT
0006 XUI-XSIZE *X1+XOFF
OOC7 X(2)*XSIZE *X2+XOFF
0008 Y(1)»YSIZE *Y1*YOFF
0009 Y(2)-YSIZE *V2*YOFF
0010 CALL SYSPLT(X(UtVll),3)
0011 CALL SYSf>LT(X(2),Y(2lt2l
0012 RETURN
0013 ENTRY FINDMTCLXS.HT,NBTI
0014 MT-NBT
0015 00 44 J-l.NBT
0016 IF(EC(LXS(MTI.* *).EQ.O) RETURN
0017 44 MT-HT-1
0018 RETURN
0019 END
C-46
116
-------
FDYN
SUPPORT FOP FORTRAN DYNAMIC BIT AND FULL WORD ARRAYS.
PAG;
LOG OBJECT CODE , ADOR1 ADDR2 STKT SOURCE STATEMENT
OCOOOO
OCOOOO 47FO FOOC
000004 06
000005 C7C5E3ESC5C3
OOOOOB 00
COOOOC 90E4 DOOC
000010 184F
000012 1821
000014 5830 2000
000018 5800 3004
00001C 8800 0002
000020 5000 3000
000024 4510 4028
000028 OAOA
OC002A 5010 3004
00002E 4130 3000
000032 1B13
000034 8A10 0002
00003B 4110 1001
00028
00004
00000
00002
00001
00003C 5010 3008
000040 98E4 OOOC
000044 92FF OOOC
000048 41FO 0000
00004C 07FE
00004E 47FO FOOC
000052 06
OC0053 C609C5C5E4D7
000059 00
00005A 90E4 DOOC
OC005E 184F
000060 1821
000062 5830 2000
OC0066 9801 3000
OC006A 4111 0000
00006E OAOA
OOOOF
00000
00001
00002
00003
00004
OOOOC
ooooc
00000
00000
00000
00004
00002
00000
00028
00004
00000
00002
00001
ooooa
ooooc
ooooc
00000
ooooc
ooooc
0004E
00000
00000
00000
00000
2 X15
3 XO
4 XI
5 X2
6 X3
7 X4
8
9 GETVEC
10
11*
12*
13*
14*
15
16
17
IB
19
20
21
22
23
24*
25*
26
27
28
29
30
31
32
33
34*
35*
36*
37*
38 FREEUP
39*FREEUP
40*
41*
42*
43
44
45
46
47
48
49
50
51*
52*
53
EOU IS
EOU 0
EOU 1
EQU 2
EQU 3
EQU 4
ENTRY FREEUP
CSECT
SAVE (14, 4),, «
6 12IOil5>
DC AL1I6)
DC CL61 GETVEC1
STM 14,4,12(131
LR X4.X15
USING GETVEC, X4
LR X2tXl
L X3,0(,X2)
USING ANCHOR, X3
L XOtOIMEN
SLA X0,2
ST XO, LENGTH
GETMAIN R.LV-COI
BAL 1,**4
SVC 10
ST XltLENGTH*4
LA X3,0(.X3)
SR XI, X3
SRA XI. 2
LA Xl.l(tXl)
ST XI. INDEX
DROP X3
RETURN (14.4I.T.RC-0
LM 14.4.12(13)
HVI 12(13), X'FF1
LA 15.0(0,0)
BR 14
SAVE (14,4),,*
B 12(0.15)
DC ALK6)
CC CL6' FREEUP*
STH 14,4,12(131
LR X4.X15
USING FREEUP, X4
LR X2,X1
L X3.0(.X2l
USING ANCHOR. X3
LM XO, XI, LENGTH
CROP X3
FREEMAIN R.LV-IO) ,A-( 1 )
LA 1,0(11
SVC 10
RETURN I14.4),T,RC-0
•X4
•X3
• X3
• X4
*X3
«X3
ASM 0200 10.13 08/03/77
11
12
13
14
15
16
23
FREE A DYNAMIC ARRAY.
SAVE REGISTERS.
BRANCH AROUND ID
IDENTIFIER
SAVE REGISTERS
SET UP A BASE REGISTER.
1X21- AIPARANETER LIST I.
1X31- AIARRAY ANCHOR!.
1X0)- DIMENSION OF ARRAY.
(XO)- LENGTH OF ARRAY IN BYTES.
(XII- A(ARRAV).
INDICATE GETMAIN
ISSUE GETMAIN SVC
1X31- AIANCHORIDI.
(XII- AIARRAYIDI - A( ANCHOR (1).
CONVEPT TO ARRAY INDEX MI TH
RESPECT TO THE ANCHOR I
ARRAY III - ANCHORIINDEX).
PLANT INDEX IN ARRAY ANCHOR.
RETURN TO CALLER.
RESTORE THE REGISTERS
SET RETURN INDICATION
LOAD RETURN CODE
RETURN
SAVE REGISTERS.
BRANCH AROUND ID
IDENTIFIER
SAVE REGISTERS
SET UP A BASE REGISTER.
(X2I- AIPARANETER LISTI.
(X3>> MARRAV ANCHOR*.
(XO,X1)» FREEMAIN PARAMETERS.
RELEASE THE CORE.
CLEAR THE HIGH ORDER BYTE
ISSUE FREEMAIN SVC
RETURN TO CALLER.
00860000
00880000
00900000
01180000
55
56
57
59
60
61
62
68800001
69000001
6 i
* 68
69
70
71
00260000
00640000
00700000
00800000
124
00860000
00880000
00900000
01180000
125
126
127
129
130
131
132
03130018
03140018
-------
FDVN
SUPPORT FOR FORTRAN DYNAMIC BIT AND FULLKORO ARRAYS.
PAGE
LOG OBJECT CODE
000070 9BE4 DOOC
000074 92FF OOOC
OC007B 41FO 0000
00007C 07FE
000000
CCOOOO
000004
000008
CCOOOO
00000B
AODR1 ADDR2 STNT SOURCE STATEMENT
OOOOC
000 OC
00000
ASM 0200 10.13 08/03/77
00000
00008
54»
55»
56 »
57»
58 ANCHOR
59
60 DIMEN
61
62 LENCTt
63 I NCR
64 INDEX
69
LN
XVI
LA
BR
DSECT
CS
OS
ORG
CS
OS
EQU
END
14,4,121131
12(13), X*
15,010,01
14
F
F
ANCHOR
Zf
F
1NCR
FF«
RESTCRE THE REGISTERS
SET RETURN INDICATION
LOAD RETURN CODE
RETURN
UNUSED MORO.
BITS/ROM OR • OF FULLWORDS.
LENGTH OF THE ARRAY, BYTES.
BYTES BETWEEN ROMS IN A BIT
ARRAY.
INDEX FROM START OF ANCHOR TO
START OF ARRAY FOR FULLHORD
ARRAYS.
00260000
00640000
00700000
OOBOOOOO
465
469
470
479
476
* 480
481
* 482
* 483
484
486
M?
H« *•
00 00
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-78-102
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
"MATHEMATICAL MODEL FOR MULTIPLE COOLING TOWER PLUMES"
REPORT DATE
June 1978
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
Frank H. Y. Wu & Robert C. Y. Koh
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
W. M. Keck Laboratory of Hydraulics & Water Resources
California Institute of Technology
1201 E. California Blvd.
Pasadena, CA 91125
10. PROGRAM ELEMENT NO.
EHA540
11. CONTRACT/GRANT NO.
EPA (5) R803989-01-1
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
U.S. Environmental Protection Agency Corvallis, OR
Corvallis Environmental Research Center
200 SW 35th Street
Corvallis, OR 97330
14
. SPONSORING AGENCY CODE
FPA/600/02
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A mathematical model is developed for the prediction of plume properties such as
excess plume temperature, humidity and liquid phase moisture (water droplet), plume
trajectory, width, and dilution at the merging locations and the beginning and ending
points of the visible part of the plumes. Detailed printout and contour plots of
excess temperature and moisture distribution can also be obtained if desired.
Based on comparison with laboratory data this model gives good predictions for the
case of dry plumes (no moisture involved). It should be noted that several empirical
coefficients are as yet not accurately known. Verification of this model for the wet
plume (such as for prototype cooling tower plumes) and the determination of the value:
for these empirical coefficients to be used in prototype applications must await
detailed comparison with field data.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Cooling Towers
Plumes
Mechanical Draft
Merging
Thermal Pollution
Cooling Water
18. DISTRIBUTION STATEMENT
Release to Public
EPA Form 2220-1 (R.v. 4-77)PREV.OUS EO.T.ON .s OBSOLETE
b.lDENTIFIERS/OPEN ENDED TERMS
Mathematical Model
19. SECURITY CLASS (This Report/
20. SECURITY CLASS (Thii page)
Unclassified
13B
21. NO. OF PAGES
134
22. PRICE
119
U S GOVERNMENT POINTING OFFICE: 1978—797-35*'195 REGION 10
-------