United States Industrial Environmental Research EPA-6OO/7-80-034
Environmental Protection Laboratory February 1980
Agency Research Triangle Park NC 27711
A Mathematical Model
of Electrostatic
Precipitation (Revision 2)
Interagency
Energy/Environment
R&D Program Report
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/7-80-034
February 1980
A Mathematical Model of
Electrostatic Precipitation (Revision 2)
by
R.B. Mosley, M.H. Anderson,
and J.R. McDonald
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
Contract No. 68-02-2193
Program Element No. EHE624
EPA Project Officer: Leslie E, Sparks
Industrial Environmental Research Laboratory
Office of Environmental Engineering and Technology
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
-------
DISCLAIMER
This report was prepared as an account of work sponsored by
the United States Government. The report has been reviewed by the
Industrial Environmental Research Laboratory, U.S. Environmental
Protection Agency, and approved for publication. Approval does
not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorse-
ment or recommendation for use. Neither the United States nor
the U.S. Environmental Protection Agency, nor any of their employees,
nor any of their contractors, subcontractors, or their employees,
makes any warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness or
usefulness of any information, apparatus, product, process or
computer program disclosed, or represents that its use would not
infringe privately owned rights.
111
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ABSTRACT
The objectives of this project were to develop analytic
approximations for describing the electrical conditions in a
wire-plate precipitator and to reduce the execution time required
by the computer program which represents the model of electro-
static precipitation developed under the sponsorship of the
Environmental Protection Agency.
In this report, a new semi-empirical, approximate theory
for predicting electrical conditions is described. In the approx-
imate theory, analytical expressions are derived for calculating
voltage-current characteristics and electric potential, electric
field, and space charge density distributions. Comparisons of
numerical and approximate solutions over a wide range of possible
precipitator geometries and electrical operating points indicate
that for practical purposes the approximate theory can be used in
lieu of the more rigorous numerical theory. This saves large
amounts of computer time and makes possible hand calculator usage.
Recent modifications to a previously described theory for numeri-
cally determining electrical conditions in wire-plate electrostatic
precipitators are also discussed.
The numerical technique for performing the integration over
the particle surface in the charging rate equation has been changed
in order to decrease the computer time required. A Gaussian
quadrature method which replaces a Simpson's rule method is pre-
sented. This modification results in a factor of 10 decrease in
computer time required to perform the particle charging calcu-
lations while preserving essentially the same degree of accuracy.
The new and modified subroutines in the computer program are
discussed. Detailed flow charts for each of these subroutines are
provided. A listing of the computer code for each of these sub-
routines as well as for the entire program is given. Examples of
various applications of the model are described and demonstrated
in detail.
This report was submitted in partial fulfillment of Task 5
of Contract No. 68-02-2193 by Southern Research Institute under
the sponsorship of the U.S. Environmental Protection Agency. This
report covers a contract period from October 1, 1976 to December
31, 1978 and work was completed as of December 31, 1978.
iv
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CONTENTS
Disclaimer
Abstract iv
Figures vii
Tables ix
Nomenclature x
Metric Conversion Factors xiii
1. Introduction 1
2. Conclusion 3
3. Recommendations 4
4. Approximate Solution for Space Charge Limited Currents
in Wire-Duct Precipitators 6
Background 6
Development of equations 6
Comparisons of approximate model with numercially
integrated solutions and experimental observa-
tions 17
Subroutine EFLD3 23
Subroutine CMAN 26
5. A Generalization of the Integration Scheme used in the
Mathematical Model to Compute the Electrical Con-
ditions in a Wire-Duct Precipitator 43
Background 43
Development of equations 44
Boundary conditions 48
Subroutine ELFD4 49
Subroutine output 53
6. Gaussian Quadratures Integration for Computing
Particle Charging Rates 67
7. Effects of the New Modifications on the Predictions
of the Model 75
Discussion 75
Input data 83
Machine-dependent aspects of the computer
program 83
Example cases and comparisons of the analytic
approximations with predictions of the previous
model 88
References 101
v
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Appendices,
A. Listing of EFLD3
B. Listing of CMAN ,
C. Listing of EFLD4 ,
D. Listing of OUTPUT
E . Listing of RATE ,
F. Complete Listing of the Computer Program.
G. Output Data for Example 1 (Revision 2)
H. Output Data for Example 1
I. Output Data for Example 2
J. Output Data for Example 2
K. Output Data for Example 3
L. Output Data for Example 3
M. Output Data for Example 4
N. Output Data for Example 4
O.
(Revision 1)
(Revision 2)
(Revision 1)
(Revision 2)
(Revision 1)
(Revision 2)
(Revision 1)
Definition of Variables Used in the Program.
103
103
109
112
120
122
124
179
194
209
225
241
257
273
290
307
vi
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FIGURES
Number Page
1 Schematic showing a cross section of the wires and
plates in an electrostatic precipitator 8
2 Schematic representing a cylindrical distribution
of space charge and its associated images 10
3 Schematic illustrating a planar distribution of
space charge and its associated surface charge 11
4 Current-voltage curves showing a comparison of the
approximate model with the numerically integrated
solution for geometrical parameters corresponding
to the experimental conditions of Penney and
Matick 20
5 Comparison of theoretical potential profiles
between a wire and plate with experiments of Penney
and Matick 21
6 Comparison of theoretical potential profiles midway
between wires with experiments of Penney and
Matick 22
7 Flow chart for subroutine EFLD3 27-37
8 Flow chart for subroutine CMAN 38-40
9 Schematic illustrating positions of integration
grid points in the new integration scheme 46
10 Flow chart for subroutine EFLD4 54-61
11 Flow chart for subroutine OUTPUT 64-66
12 Flow chart for function subprogram RATE 71-73
13 Flow chart for simplified logic of the entire
program 76-82
14 Comparison of fractional collection efficiencies
computed from Revision 1 of the model using elec-
trical conditions measured in a laboratory precipi-
tator with those computed from Revision 2 of the
model using the approximations 90
vii
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Number pag£
15 Comparison of fractional collection efficiencies
computed from Revision 1 of the model using theore-
tical current-voltage calculations with those
computed from Revision 2 using the approximate
electrical calculations 92
16 Comparison of fractional collection efficiencies
computed from Revision 1 of the model using the
estimation procedures and the parameters in
Example 2 with the corresponding calculations
in Revision 2 using the approximations 97
17 Comparison of fractional collection efficiencies
computed from Revision 1 of the model using measured
electrical conditions from a full-scale, cold-side
precipitator with those computed from Revision 2
of the model using the approximations 99
Vlll
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TABLES
Number Page
1 Comparison of Approximation and Numerically
Integrated Solution 18
2 Charge on Particles Computed by Different
Integration Methods 68
3 Core Requirements for Various Segements of the
Computer Program 85
4 Input Data Cards for Example 1 91
5 Input Data Cards for Example 2 93
6 Input Data Cards for Example 3 (Revision 2).... 95
7 Input Data Cards for Example 3 (Revision 1).... 96
8 Input Data Cards for Example 4 98
IX
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NOMENCLATURE
V (x,y) The electrostatic potential at a point (x,y) (V)
s
V A constant determined by the amount of charge on a
st wire (V)
x Coordinate position measured toward the plate with
the corona wire as origin (m)
y Coordinate position measured parallel to the plate
with the corona wire as origin (m)
S Wire-to-plate spacing (m)
J\.
S Half wire-to-wire spacing (m)
Eo The electric field at the surface of the wires (V/m)
ao Radius of the discharge wires (m)
V Potential (V)
J Current density (A/m2)
b Ion mobility (m2/V-sec)
e0 Permittivity of vacuum (A sec/Vm)
R Distance from the wire at which the solutions are to
be matched (m)
Vi A constant determined by the amount of space charge in
a cylinder (V)
V(x,y) Potential at the point (x,y)(V)
V0 Constant used for matching the potentials at x=R (V)
£ Constant occurring in the potential expression
5 Constant occurring in the potential expression
Y Constant occurring in the potential expression
x
-------
p(x,y) Charge density at point (x,y)(C/m3)
KI A constant used to match the charge density profiles
at X=R
fi Empirical factor used in charge density calculation
fa Empirical factor used in charge density calculation
fa Empirical factor used in charge density calculation
F Factor which corrects for overlapping of space charge
cylinders
E Electric field (V/m)
E x-component of the electric field (V/m)
X
E y-component of the electric field (V/m)
ax Spacing of integration points along the x-direction
(m)
ay Spacing of integration points along the y-direction
(m)
a Parameter in the equation for charge density (C/m3)
$ Parameter in the equation for charge density (C2/m6)
AV Potential drop across the corona region (V)
VW Potential at the surface of the wire (V)
ECOR Average field required to drive the corona (V/m)
RC Radius of the corona (m)
AC Radius of the wire (m)
q Instantaneous charge on a particle (C)
t Time (sec)
NO Free ion density (m~3)
e Electronic charge (C)
q_ Saturation charge due to field charging (C)
S
a Particle radius (m)
'Vi
v Mean thermal speed of ions (m/sec)
xi
-------
60 Arccos (q/qc)
s
ro Radial distance along 9 at which the radial component
of the total electric field is zero (m)
k Boltzmann's constant (J/°K)
T Absolute temperature (°K)
K Dielectric constant of the particle
E Average electric field between the electrodes (V/m)
Si
9 Azimuthal angle in a spherical coordinate system with
origin at the center of the particle (radians)
f (6) Function to be integrated
F(t) Function to be integrated
A, (k=0,1,...,n)Gaussian weights
t, (k=0/l,...,n)Roots of Legendre polynomials
XII
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To Convert From
grams/ft3
ft
ft2
in
ftVmin
ft/sec
METRIC CONVERSION FACTORS
To
kg/m3
m
m2
m
m3/sec
m/sec
°K
Multiply by
0.00229
0.3048
0.0929
0.0254
0.000472
0.3048
(°F+459) x
1.8
Xlll
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SECTION 1
INTRODUCTION
The EPA/SoRI computer model of electrostatic precipitation
was firstipublished in 1975.l Revision 1 of the model2'3 was
published in 1978. This computer model has been used by many
individuals involved in electrostatic precipitation technology.
In general, the various users have found the model useful. How-
ever, many users have commented that the time required to run
the model was excessive.
This report describes revisions to the model that greatly
reduce the computer time required with only a slight loss in
accuracy. The revisions described in this report consist of:
1. A new procedure for calculating electric fields and
V-I curves using an approximate analytic solution and,
2. A new procedure for calculating particle charge.
The revisions affect the internal workings of the program, but
do not affect the model-user interface. The data input require-
ments and the format for the data are the same in this revised
model as the data in the original model.
The revisions may be implemented either by adding the new
procedures to an existing version of the model or by obtaining
a tape copy of the complete revised model from NTIS*.
This report does not replace the previous model reports but
is intended to supplement them. The user is urged to obtain and
read references 2 and 3 before using Revision 2 of the model.
This report provides a complete description of the new procedures
including their effect on execution time and accuracy.
A second, new procedure for calculating electric fields and
V-I curves is also described in this report. This procedure has
not been incorporated into the working version of the model
because the slight increase in accuracy gained by its use does
*National Technical Information Service, Springfield, Virginia
22161.
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not justify the long computing time required to use it.
The report contains sample problems showing how to use the
new procedures. Complete FORTRAN listings for all new pro-
cedures and the revised model are included in appendices of this
report. This revised model is described as Revision II Aug. 1979
Please note that this computer program is distributed on
an "As Is" basis without warranty by either the United States
Environmental Protection agency or Southern Research Institute.
We are, however, interested in your comments—especially those
that will allow us to improve the model. If you have comments
or suggestions, please contact either the authors or the EPA
project officer.
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SECTION 2
CONCLUSIONS
The version of the mathematical model of electrostatic pre-
cipitation presented in this report offers an option which requires
significantly less time to perform a calculation than does the
previous version because of two factors. First, the time required
to perform the charge calculation has been decreased through the
use of Gaussian quadratures instead of the Simpson's rule inte-
gration. There is little loss in accuracy (on the order of 2%
maximum) due to the faster charge calculation. Second, the time
required to run the program has been further decreased by the use
of analytic approximations to the solutions of the electrical
equations. For practical ranges of operating parameters, the
inaccuracies introduced by these approximations are within accept-
able limits. The combination of these two modifications to the
program decreases the computation time by about a factor of 10
from that required by the previous version of the model.
The numerical method used to compute the electrical solutions
in the previous version of the model has been modified to accept
variable step sizes in the discretization scheme. This new
numerical method gives rise to improved accuracy in some cases,
but requires more execution time than is justified by its use.
Consequently, this new numerical scheme has not been incorporated
into the computer program.
For current users of the model, this new version can be used
in exactly the same manner and with the same input data as before
with the only difference being that the particle charging will
be done using the Gaussian quadratures rather than the Simpson's
rule integration. In order to convert a working version of the
program to the new revised form, it is necessary to replace sub-
programs CMAN and RATE by the new versions listed in Appendices
B and E, respectively. The new subprogram EFLD3 listed in
Appendix A must also be added. In addition to these subprograms,
a few statements must be added to the main program. These modi-
fications may be seen in the listing of the program in Appendix
F. The data block subprogram used to initialize certain variable
arrays may not be necessary with some computers. A tape copy of
the complete program is available from NTIS (see footnote in the
Introduction). Detailed instructions for using the model must
still be obtained from Revision 1 of the model report.
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SECTION 3
RECOMMENDATIONS
Although the mathematical model of electrostatic precipitation
presented in this report represents a significant improvement over
the previous version, more work still needs to be performed in
order to improve the fundamental basis and user oriented aspects
of the model.
With respect to the fundamental basis of the model, it is
recommended that the following research be pursued:
1. Theoretical and experimental studies of the effects of
particles on the electrical conditions should be continued in order
to better describe the effect on the electric field distribution.
2. Theoretical and experimental studies of electrical break-
down mechanisms in the collected particulate layer should be given
greater emphasis in an attempt to acquire the capability of theo-
retical prediction of when electrical breakdown will ensue for a
given value of dust resistivity.
3. Since the model underpredicts field-measured collection
efficiencies for fine particles without the use of empirical
correction factors, theoretical and experimental studies should
be continued in order to remove the empiricism or to explain the
discrepancy. These studies should include a reevaluation of the
theories presently used in the model and an examination of those
effects which are presently neglected such as particle charging
near corona wires and phenomena due to the gas flow field. There
is evidence1* that free electrons may play a role in particle
charging in negative coronas for temperatures of 150°C to 350°C.
A charging theory which accounts for this effect is needed.
4. The mathematical model should be restructured to take
into account time-dependent effects. The effects due to the
growth of the particulate layer and the rapping schedule should
be included as a function of time. Although the empirical pro-
cedure employed in the present version of the model represents
a useful interim technique for estimating the effects due to
rapping reentrainment in precipitators, it does not describe the
temporal and dynamic aspects of the rapping process. The inclusion
of time-dependent effects is necessary in order to optimize the
electrical operating conditions and the rapping schedule and
intensity.
-------
The above research is needed in order to make the model indepen-
dent of empiricism and of the experience and judgment of the user.
With respect to the user oriented aspects of the model, it
is recommended that the following work be performed:
1. Alternative numerical techniques need to be investigated
and implemented in order to make the computer program run signif-
icantly faster.
2. Although the charging calculation has been speeded up
considerably by the Gaussian quadratures, the speed could be in-
creased even more. As can be seen from Figure 2 of Reference 4,
the particle charge distribution could be represented to a con-
siderable degree of accuracy by two simple power laws in the two
regions separated by a particle radius of about one micrometer.
To determine the two power relationships it would only be necessary
to compute the charge for three particle sizes. The charge on the
remaining particles would be computed from the appropriate rela-
tionship. For a calculation with 15 particle sizes, this approxi-
mation should decrease the time for computing the charge on the
particles by about a factor of 5.
3. Procedures which edit the input data should be implemented.
4. Documentation of the computer program needs to be included
in abbreviated form in the computer card deck.
The above work is needed in order to continue the transition in
which the model is transformed from a research tool to one which
is more practical to use.
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SECTION 4
APPROXIMATE SOLUTION FOR SPACE CHARGE
LIMITED CURRENTS IN WIRE-DUCT PRECIPITATORS
BACKGROUND
In order to model the behavior of an electrostatic precipita-
tor, it is necessary to compute the electric field and potential
in the interelectrode space. In the mathematical model of pre-
cipitation developed by Southern Research Institute under the
direction of the Environmental Protection Agency's Particulate
Technology Branch of the Industrial Research Laboratory at Research
Triangle Park, a relaxation method is used to solve Poisson's
equation coupled with the charge transport equation. This numer-
ical procedure requires a great deal of computer time. The computer
time required could be greatly reduced if an analytic solution to
this system of equations were available. Since an exact solution
does not seem probable, an approximate solution is appropriate.
An analytic solution is further desirable because it would signi-
ficantly simplify some of the difficulties of incorporating the
space-charge effects of particles into the mathematical model.
DEVELOPMENT OF EQUATIONS
Using a conformal mapping technique, Cooperman5 demonstrated
that the electrostatic potential V (x,y) in the interelectrode
s
space of a wire-duct precipitator with 2N+1 corona wires can be
written as
Vfl(x,y) =
N
£
m=-N
In
coshfr (y-2ms )/2s - cos (Trx/2s ]
\* J^ Jt
coshfr (y-2ms )/2sv + cos
(1)
with
s
Eo
st
IT Sin(Trao/2s)
X
N
m=-N
cosh (nnrs /s )
cosh2 (nnrs /s ) - cosMirao/2s )
jf J* «»
-1
(2)
-------
where
Eo = the electric field at the surface of the wires (V/m),
ao = radius of the wires (m),
s - wire-to-plate spacing (m),
X
s = half wire-to-wire spacing (m),
x = the displacement from a wire toward the plate (m),
y = the displacement from a wire in the direction parallel
to the plate (m),
2N+1 = the number of corona wires.
Figure 1 shows the region of the precipitator that is of interest.
The origin is taken at the wire, while x is measured toward the
plate and y is measured toward an adjacent wire. When a current
flows in the presence of space charge, equation (1) does not
apply. Equation 1 can be used to advantage, however, in obtaining
an approximate solution for the dynamic case in which the current
is space charge limited. Suppose a steady current flows under
the action of an applied potential for the case illustrated in
Figure 1. The electrical configuration will be simplified by
using the principle of superposition. Each of the contributions
to the potential will be separated and described below.
First consider just the electrodes. For a negative corona,
the wire will be charged negatively while the plate will be
charged positively. The charge on the plate will exceed the magni-
tude of the charge on the wire by an amount equal to the quantity
of negative space charge in the interelectrode space. The negative
charge on the wires coupled with an equal amount of positive charge
on the two plates constitutes a situation similar to the static
case of Cooperman. Mathematically, the solution for this case is
identical in form to the electrostatic case, but the amount of
charge on the wires is not necessarily the same as when the cur-
rent is zero. Suppose that a small increase in the electric
field at the surface of the wire gives rise to a large increase
in the number of electrons emitted from the wire during the corona
discharge. The field at the surface of the wire when a current
flows, then would be nearly the same as Peek's value of the field
required for corona start. In this case, the charge on the wire
will be computed in terms of Peek's condition6 on the field at
the wire. The static-like solution would then be completely
determined. It remains to specify the contributions to the po-
tential from the negative space charge coupled with an equal
amount of positive charge on the plates and from the corona dis-
charge process itself. These last contributions must be approxi-
mated since closed-form solutions are not available.
-------
PLATES.
WIRE
j
•\\
i
,\l = O ON
THE PLATES
V = V0 = APPLIED POTENTIAL ON THE WIRES
Figure 1. Schematic showing across section of
the wires and plates in an electro-
static precipitator.
8
-------
The primary considerations to be used in obtaining approximate
solutions will be the apparent symmetry of the arrangement. For
example, the equipotential lines near the discharge wires look
very much like those for a wire-cylinder geometry, 5 while the
equipotential lines near the plates look very much like those for
a parallel plate geometry.7'8 Using these observations, it will
be assumed that the space charge near the wire is distributed in
the same manner as that in a wire cylinder geometry, and that the
space charge near the plate is distributed in the same manner as
that in a parallel plate geometry. These two space charge dis-
tributions along with their associated surface charges are illus-
trated in Figures 2 and 3, respectively. Potentials computed
from these two geometries will be matched at some point (x=R,
where R is the radius of the cylinder of charge) in the inter-
electrode space to yield continuity of potential. The electric
field is also required to be continuous at the matching point.
The contributions to the potential by the corona region will
be assumed to be small. According to Loeb, 9 the potential drop
across the ionization region of a corona is essentially independent
of the current. The effect of the corona on the field at the sur-
face of the wire at corona start is included in the measurement of
Peek's field since the measurement is made with a minimum steady
current. Based on the above considerations, it is assumed that
the only role which the corona plays is to supply ions to carry
the current in the interelectrode space.
Negative charge distributed uniformly in planes parallel to
the plate which has an equal amount of positive charge, as shown
in Figure 3, will yield a potential V given by
") OT h 3/2 3/2
V" ' I(8- R) - (X~ R) ]'
where
J = current density (A/m2) ,
b = ion mobility (mz/V-sec) ,
EO = permittivity of gas (approximately 8.85 x 10~12 A sec/Vm) ,
and
R = point at which the solutions are to be matched.
In this same region, near the plate, the potential produced by
the cylinder of negative charge coupled to an equal amount of
positive charge on the plates must be taken into account. For
points which lie outside the cylinder of charge shown in Figure 2,
the solution will be the same as for a line of charge at the
center with the same quantity of charge as contained in the cyl-
inder. This problem has a solution similar to the electrostatic
-------
^l-x
IMAGE
= R
SPACE-CHARGE
SURFACE-CHARGE'
\
4 i
***** + /
+ X
*•• — ^
IMAGE
Figure 2. Schematic representing a cylindrical
distribution of space charge and its
associated images.
10
-------
SURFACE CHARGE
_ \
t
_--_-_,_ ^
SPACE CHARGE
x = R
. ___p ^
f
x = Sv
-PLATE
Figure 3. Schematic illustrating a planar dis-
tribution of space charge and its
associated surface charge.
11
-------
case mentioned before. When all 2N+1 wires are considered, the
contribution to the potential for x greater than R will be
N
(y-2ms )/2s - cos (Trx/2s )
~j
'
J
V = V! 2-r ln ' (4)
Lcoshir(y-2ms )/2s + cos(irx/2s )J
ni"~ N y x x
where Vi depends on the amount of charge in the cylinder.
At points inside the cylinder of charge, the potential due
to the other wires is given by
coshiT(y-2ms )/2s - cos(irx/2s
V =
m=1 ( [coshTr(y-2msy)/2sx + cos (7rx/2s
rcoshir(y+2ms )/2s - cos(frx/2s
I y _ x
)"]
-
x)J
+ 1 __,
In
[coshTr(y+2ms )/2sx + cos (7rx/2sx)J
To this we must add the potential due to the charge inside the
cylinder as well as that due to the two images shown in Figure 2.
To obtain the potential due to the negative space charge in the
cylindrical distribution, we subtract the electrostatic solution
for a wire and cylinder with no space charge from the solution
of the same wire and cylinder with space charge.10 The two images
are used to account for the coupling of the space charge in the
cylinder with the associated charge on the plates. The potential
at a point inside the cylinder due to space charge and the two
images is given by
V(x,y) = V0 - a0E0 J (-£±) In (*"$') + (l+6(x2+y2- ao2))"5 - Y
,!»[<
* 1C
r^'1)
( 4 )
+ Y
[ /x2 + y2 + 4s (s - x
1 n 1 xx
(6).
)\ /x2 + y2 4- 4s (s +
1 j 1 _ 1 XX
1 1 D2 J. Aa If, D\ / \ T>2 i A ~ 1- i r.\
x)
where
6 = 2Js /Tre0bao2E02,
Y = (1 + MR'-ao2)),
12
-------
Eo = electric field at the wire,
ac = radius of the wire.
The constant V0 is to be chosen to match the solutions at the
point x=R.
In the event that the cylindrical symmetry extends all the
way to the plate, the condition that the potential be zero on the
plate will be met rigorously only for y=0. This limitation can
be removed in an empirical manner by adding y2 to a few terms.
This would have little effect near the wire, but allows the
boundary conditions to be met by a slight modification to the
cylindrical solution. The potential at a point inside the cyl-
inder (x%
-d+6(R2+y2-a02))
(1+5(x2+y2-a02))
C+d+6(R2+y2-a02))!5
13
-------
x2+y2+4sv(sx-x) x2+y2+4sv(sv+x)
-. =rr-) + In
(s
XX
Z( rcoshTr(y-2ms )/2sx - cos(irx/2sx)
j ln coshTT(y-2ms )/2s + cos(irx/2s )
m=l v L y x *
("cosh7r(y+2ms )/2sx - cos(7rx/2sx)
+ ln coshir(y+2ms^)/2s" + cos{irx/2s )
L y x x.
. rcoshTr(y-2ras )/2s - cos (7rx/2s ) 1
_ ^ ^ « i y x x i
st / ^ n [coshTr(y-2ms')/2s + cos(7rx/2s )|
m=-N (8)
Ev(x,y) = a0E0 --? d+6 (x2+y2-a02)
X -
. ,1=1
2 |x2+yz+4s (s -x) ' x2+y2+4s (s
XX x ^
_ coshTr(y-2msy)/2sx _
Sin(7rx/2sx) ^ cosh2Tr(y-2ms )/2sv - coS2 Crrx/2s V
y x x
coshir (y+2ms ) /2s
N
Sin(Trx/2s)
m=-N
cosh2Tr(y+2ms )/2s - cos2 (Trx/2s )
^ X X
coshTr(y-2ms )/2s
cosh27r(y-2ms )/2s - cosz(Trx/2s
*••
(9)
By(x,y) =
14
-------
2 ' x2+y2+4s (s -x) xz+yz+4s (s +x) R2+y2+4s (s -R)
I X x XX XX
(g
1!
-H. ( Sinhir(y-2ms )/2s
ViTT ^k I V X
— cos(7tx/2sx) 2^ jcosh2TT(y-2ms,J/2s - cosz (ux/2s )
x -, ^ y x x
SinhTr(y+2ms )/2s
y
cosh2 it (y+2ms )/2s - cos2 (iTX/2s )
y x x
N
SinhTr(y-2ms
s cos(irx/2sx) ^ ) cosh2ir(y-2ms )/2s - cos2 Ux/2s ,
x m=-N l Y x x
(10)
for x < R, and
1/2
3/2 3/2
- R where
fi = {[1+0.16 y/Sy] [1+2.2 (y/Sy)9]}'1 , (19)
f2 = 0.45 e0a0Eo [ (1+6 (x2+y2-a02) ) ** - 1]
f R2-y2+4s (s -R) R2-y2+4s (s +R) 1
l___^ _ x x _ . xx _ (20}
(R2+y2+4sv(s -R))2"'"(Rz+y2+4sv(s +R))2 ' V '
L A A A A J
and
fa = (U+0.75 y/sy] [1+2.2 (y/Sy)9]}" . (21)
Equations (8) through (21) completely characterize the approximate
model. Although the charge profiles have not been optimized from
an empirical standpoint, they are adequate for most purposes. It
16
-------
should be pointed out that the charge density profiles are the
least important of all the functions described in this model. The
electrical behavior of precipitators is characterized primarily
by the potential and the electric field. As will be shown in the
next section, the potential and electric field expressions of this
approximate model predict the operating conditions of wire-duct
precipitators quite well.
COMPARISONS OF APPROXIMATE MODEL WITH NUMERICALLY INTEGRATED
SOLUTIONS AND EXPERIMENTAL OBSERVATIONS
In general, the agreement of the approximate model with the
numerically integrated solution is found to be quite good. In all
the cases described here, the approximate model was compared with
the results of the numerical integration scheme described in Section
5 of this report. Table 1 summarizes the comparison between the
approximate model and the numerical solution for a wide range of
geometrical parameters and current densities. Columns 1, 2, and
3 list the corona wire radius, the wire-to-plate spacing, and the
half wire-to-wire spacing, respectively. While more combinations
of geometrical parameters in this table are typical of industrial
electrostatic precipitators, examples of both close and wide wire
spacing are shown. Both large and small corona wires are repre-
sented and a considerable range of plate spacings is given. Column
4 lists the current densities that were used. The values of cur-
rent density were chosen to represent both moderate and relatively
high space charge situations. Column 5 gives the percent difference
in applied voltage for the approximate and numerically integrated
solutions. Column 6 gives the percent difference in the average
electric field at the plate. Column 7 gives the maximum percent
difference in the potential profiles. Columns 8 and 9 give the
maximum percent differences in the x-component and the y-component
respectively of the electric field profiles. Column 10 gives the
maximum percent difference in the charge density profiles. For a
comparison with average errors, consider the parameters shown in
row 3 of Table 1. For these parameters, which are typical of
electrostatic precipitators in the United States, the average
difference in the approximate and integrated potential profiles
is 1 percent. The average difference in the x-component of the
electric fields is 2 percent while the average difference in the
y-components is 24 percent. The average difference in the charge
density profiles is 8 percent. It can be observed that the
average differences in the approximate and integrated solutions
are appreciably smaller than the corresponding maximum values
listed in Table 1. The average errors stated for this particular
set of parameters are representative of those occurring throughout
the table.
In the approximate model, one is free to choose the position
(x=R) at which to match the functions derived from the two dif-
ferent symmetries. For the calculations shown in Table 1, R was
chosen to be 0.975s . This corresponds to using only a few
J\,
17
-------
Table 1. COMPARISON OF APPROXIMATION AND NUMERICALLY INTEGRATED SOLUTION
oo
Wire
Radius
(10~3 m)
1.1906
1.1906
1.1906
1.1906
1.1906
1.1906
1.1906
1.1906
1.1906
1.1906
3.00
3.00
0.500
1.016
1.016
0.1524
0.1524
Wire
Plate
Distance
(m)
0.127
0.127
0.1'27
0.127
0.127
0.127
0.127
0.127
0.200
0.200
0.127
0.127
0.127
0.1143
0.1143
0.1143
0.1143
Half Wire-
to-wire
Distance
(m)
0.03175
0.03175
0.0635
0.0635
0.127
0.127
0.15875
0.15875
0.0635
0.0635
0.0635
0.0635
0.0635
0.07348
0.07348
0.07348
0.07348
Current
Density
(nA/cm5)
10
100
10
100
10
100
20
100
20
80
20
100
10
20
200
5
180
Percent
Difference
In Applied
Voltage
1
3
0
2
3
1
2-
2
3
4
2
2
3
1
2
22
9
Percent
Difference
In Field At
The Plate
6
12
8
9
1
0.1
5
6
1
6
4
2
9
3
1
6
10
Max. %
Difference
In Potential
Profiles
2
5
3
8
8
11
12
13
7
2
2
4
4
3
6
22
9
Max. %
Difference
In
x-component
of field1
12
12
12
11
12
5
10
16
15
7
7
9
15
9
10
18
16
Max. Z
Difference
In
y-component
of field2
400
400
100
320
53
118
30
40
60
50
50
50
300
40
80
300
213
Max. %
Difference
In Charge
Density
Profiles3
23
32
18
12
8
10
19
22
24
10
10
12
14
9
15
6
13
1Points closer than two diameters to the wire and points near the plane connecting the centers of the wires with the
plates have been neglected.
2Even though the percent difference in the y-components of the electric field seems quite large in some cases, the
absolute error is relatively unimportant because the y-component is much smaller than the total field for nearly all
such cases.
3Some points very near the plates and some near the centers of the wires have been neglected.
-------
millimeters near the plate in which the space charge is distri-
buted according to the rectangular geometry of a parallel plate
arrangement. The reason for using such a small volume with
rectangular symmetry is that in general the parallel plate
solution predicts too large an effect due to space charge. The
fact that rectangular symmetry plays such a small role in the
space charge contribution to the profiles does not necessarily
contradict the observations made earlier that the equipotential
lines near the plate reflect a strong influence of planar geometry.
The planar character of the equipotential lines is largely pro-
vided by the static-like solution which accounts rigorously for
much of the charge on the plates. For cases in which the radius
(R) of the cylinder of space charge is larger than the half
wire-to-wire spacing, adjacent cylinders of space charge will
overlap. In this situation the effects of space charge would
be overestimated. To correct for that error in this simple
model we reduce the contribution to the potential and electric
field components from space charge associated with wires other
than the central one by the fraction of the volume of the cyl-
inder that does not extend beyond s . This fraction is given by
1 - | ArcCos(s /R) - $ (R2-s 2)** , s < R
F = \ L ^ yjy
' sy * R ' (22)
This factor would multiply Vi in the space charge terms arising
from wires other than the central one (m=0). Surprisingly, this
simplistic correction yields rather good agreement between the
approximate model and the numerically integrated solution. In
all cases the approximate model agrees well with the numerically
integrated solution for zero current. This case, of course, cor-
responds to the electrostatic solution at conditions for corona
start, the limit in which the approximate model becomes exact.
Predictions of the approximate model as well as those of the
numerical solution are compared with some experimental results of
Penney and Matick8 in Figures 4, 5, and 6. An effective ion mobility
of 1.8 x 10" "* m2/V'sec in the approximate model yields voltage-
current curves which predict the experimental operating conditions
to within one percent. These voltage-current curves along with
the numerically integrated ones are shown in Figure 4. Figure
5 shows a comparison of the potential profiles along a line con-
necting the wire with the plate. The approximate model agrees
with this measured potential profile to within 3 percent. A
comparison of the potential profiles along a line connecting a
point midway between two wires with the plate is shown in Figure
6. The approximate potential is as much as 15 percent larger
than the measured potential along this line. The approximate
potential is 10 percent larger than the numerically integrated
19
-------
S - 0.1143m
x
S » 0.07348m
18
16
14
y
b =
f =
o -
1.8xlO~" m2/V-s
1.0
Integrated
A- Approximation
B- Penney and
Matick's
Operating
Conditions
12
(X
(U
10
03
c
01
Q
0)
0)
00
CO
0
I
10
20
30 40 50
Applied Voltage, kV
60
Figure 4. Current-voltage curves showing a
comparison of the approximate model
with the numerically integrated
solution for geometrical parameters
corresponding to the experimental
conditions of Penney and Matick.
20
-------
40
30
20
4-1
e
0)
4-1
O
P*
10
S = 0.1143m
x
S = 0.07348m
y
b = 1.8x10 4 m2/V-s
f = 1.0
• • - Integrated
A - Approximation
• - Experimental
O - Integrated
A - Approximation
D - Experimental
I
= 1.524xlO~'*
a =
m
1.016xlO-3m
o
A
O
D
A
p
1
1
1
Plate
468
Displacement (10~2 Meters)
i
10 * 12
Wire
Figure 5. Comparison of theoretical potential
profiles between a wire and plate
with experiments of Penney and Matick.
21
-------
30
5 20
AJ
O
PL.
10
y
b
f
0.1143m
0.07348m
1.8x10""
m
2/V-s
1.0
Integrated
Approximation
Experimental
Integrated i
A - Approximation \ a
D - Experimental I
O -
AD
O
a =
1.524xlO~*m
1.016xlO~3m
A O
O
D
OD
Plate
Displacement (10~2 Meters)
o 1
0
•5
*
:°A
i
2
1
1 1 1 1 ' 1
4 6 8 10/12
Wire
Figure 6. Comparison of theoretical potential
profiles midway between wires with
experiments of Penney and Matick.
22
-------
potential along this same line. The apparent reason for this
disagreement lies in the large current density used. A large
current density corresponds to the large space charge limit
where the approximation is expected to be less accurate. Also,
the region between the wires is where the approximate model
is expected to be least accurate. It should be noted that
moderate errors in the potential profile in the regions between
the wires have little influence on the predicted electrical
operating conditions of the electrostatic precipitator. The
value of 1.8 x 10"1* m2/V*sec used for effective mobility is con-
sistent with measured values of ion mobility in negative corona
discharges in ambient air. It may be concluded that the pre-
dictions of the approximate model agree quite well both with
the numerically integrated solutions and with experimentally
measured electrical properties of electrostatic precipitators.
SUBROUTINE EFLD3
This subroutine calculates the electrical conditions in a
wire-plate precipitator under conditions corresponding to those
in both EFLDl and EFLD2. The particular calculation to be done
is determined by the value of the parameter NVII which in turn
is determined by the input parameter NVI. When NVI has the
value 3, NVII is set to 1 (NVI is then, also, set to 1) and a
calculation analogous to the one in EFLDl is performed. Under
these conditions, either equation (9) or (12) is used to compute
the average electric field at the plate. This calculation is
based on known or measured values of current and voltage.
When NVI has the value 4, NVII is set to 2 (NVI is set to
2) and a calculation analogous to that in EFLD2 is performed.
In this case, the subroutine calculates a voltage-current curve
up to a specified value of operating voltage and calculates the
average electric field at the plate for the operating applied
voltage. The voltage-current curve is generated by (1) specifying
a starting value of average current density at the plate, (2)
incrementing upward on the average current density, and (3) de-
termining the applied voltage at each value of current density.
When a value of current density results in an applied voltage
which exceeds the specified operating applied voltage, an inter-
polation is performed to obtain the operating voltage and current
density. At this operating applied voltage, calculations can
also be made to give the average current density, average electric
field, and average electric field at the plate in subincremental
lengths. The potential, electric field, and charge density are
computed using equations (8)-(22).
The following is a sequential list of the calling arguments
and their descriptions.
UEQ - Effective charge carrier mobility (m*/V'sec).
23
-------
AC - Radius of discharge electrode (m).
VO - Chosen operating applied voltage (m).
SX - Wire-to-plate spacing (m).
SY - One-half wire-to-wire spacing (m).
NX - Number of grid points in the x-direction.
NY - Number of grid points in the y-direction.
AEPLT - Average electric field at the plate (V/m).
TDK - Temperature of the gas (°K).
P - Pressure of the gas (atm).
RF - Roughness factor for the discharge wire
(0.5 £ RF <_ 1.0) .
START - Chosen initial current density at which the
voltage-current curve calculations starts (A/m2).
Current density increments in units of START
until a change is specified.
DSTART - Chosen increment in current density which is
used in place of START when specified (A/m2).
CSTART - Chosen increment in current density which is
used in place of DSTART when specified (A/m2).
IFINAL - Indicator which terminates the loop over average
current densities at the plate after IFINAL
times.
VSTART - Initial estimate of applied voltage corresponding
to the first value of average current density at
the plate on the voltage-current curve (V).
VSTART is not actually used in EFLD3.
VW - Operating applied voltage corresponding to a
given current density (V).
ACDNTY - Average current density at the plate (A/m2).
NWIRE - Number of wires per gas passage per electrical
section.
NEC - Indicator which governs the calculations of
average current density, average electric field,
and average electric field at the plate in sub-
incremental lengths. The calculations are
24
-------
performed when NEC = 0 and are not performed
when NEC = 1.
EBD - Electrical breakdown strength of the gas (V/m).
JIl - Indicator which governs the change in the incre-
ment on average current density at the plate from
START to DSTART. The change occurs on the Jll-th
value of current density.
JI2 - Indicator which governs the change in the incre-
ment on average current density at the plate
from DSTART to CSTART. The change occurs on the
Jl2-th value of current density.
The following is a list of the variables which are in common
with the main program.
EAVG(M) - Average electric field in a given subincrement
of length (V/m).
CHFID(M) - Average ion density in the absence of particles
in a given increment of length (#/m3).
ECOLL(M) - Average electric field at the plate in a given
subincrement of length (V/m).
VCOOP(I,J) - The static-like contribution to the potential
at a grid point (V).
NPRNT - Indicator which specifies the logical unit
number of the printer.
NVII - A parameter which determines whether a voltage-
current curve is generated. If NVII is 1 known
values of current and voltage are used. If NVII
is 2 a voltage-current curve is generated.
The vollowing variables are in common with EFLD4, and CMAN.
ECX(I,J) - The x-component of the static electric field
at a grid point (V/m).
ECY(I,J) - The y-component of the static electric field
at a grid point (V/m).
AX(I) - The distance between the I-th and I+l-st grid
points in the x-direction (m). This is used
only with EFLD4.
AY(J) - The distance between the J-th and the J+l-st
grid points in the y-direction (m). This is
used only with EFLD4.
25
-------
XI(I) - The x-position of the I-th grid point (m).
This is used only with EFLD4.
Yl(J) - The y-position of the J-th grid point (m).
This is used only with EFLD4.
LTEST - A logical variable which determines whether a
variable or fixed grid spacing is used. When
LTEST is .FALSE, a fixed spacing is used. When
LTEST is .TRUE, a variable spacing is used. This
variable is initialized to .FALSE, by a Block
Data subprogram.
Of the above variables, the values of the following must be
provided by the main program: UEQ, AC, VO, SX, SY, NX, NY, TDK,
P, RF, START, DSTART, CSTART, IFINAL, VSTART, NWIRE, NEC, EBD,
JI1, JI2, NVII, and NPRNT. Values of AEPLT, VW, ACDNTY, EAVG,
CHFID, ECOLL, VCOOP, ECX, and ECY are determined in the subroutine.
This subroutine calls subroutine CMAN to compute the static-like
solutions. It also calls subroutine ARCCOS to evaluate equation
(22). Since the subroutine ARCCOS has not been changed from the
version described in the previous model report, it will not be
described here.
There are three conditions which will terminate the calculation
of the voltage-current curve in EFLD3. The calculation is termi-
nated if (1) the specified, operating, applied voltage is reached,
or (2) the number of points on the curve is equal to the value of
IFINAL, or (3) the specified value of the electrical breakdown
strength near the collection electrode is exceeded. If the break-
down strength is exceeded, a message to this effect is printed.
Figure 7 shows a detailed flow chart of this subroutine. A listing
of this subroutine is given in Appendix A.
SUBROUTINE CMAN
This subroutine calculates the static-like solution for
potential and the components of electric field at each point in
a grid which is established in EFLDl, EFLD2, EFLD3, or EFLD4.
The calculation is based on an electrostatic solution for a
wire-plate geometry. It uses equations (1), (2), (4), and (14)
to compute the potential. The components of the electric field
are computed from the derivatives of these equations. These
expressions can be recognized in equations (12) and (13). This
subroutine differs from CMAN in the previous model report pri-
marily by the addition of the electric field component calculations.
Figure 8 shows a detailed flow chart for this subroutine.
Information is transmitted between this subroutine, the main pro-
gram, and other subroutines through calling arguments and common
statements. The following is a sequential list of the calling
arguments and their descriptions.
26
-------
START SUBROUTINE"")
REAL: MOBILT,
NWIRE, MAXS
LOGICAL LTEST
1
DIMENSION: RHO, EX, OLDRO, OLDV,
CDNSTY, V, EY, EAVGS, CHFIDS, ECOLLS
B
BL
1
C
LOCK COMMON. EAVG, CHFID
/
L.
BLOCK COMMON: ECOLL
CALC. PRODUCT (EORO) OF ELECTRIC FIELD AND
RADIAL DISTANCE AT IONIZATION BOUNDARY
DEFINE GRID OF
MOBILITY VALUES
SSTART = START
:*
DEFINE CONSTANTS
IN CALCULATIONS
BLOCK COMMON: VCOOP, NVII
(START LOOP OVER "\
CURRENT DENSITIES )
OCK COMMON: NREAD, NPRINT
BLOCK COMMON: ECX, ECY,
XI, Y1, AX, AY
BLOCK COMMON:
LTEST, RHO, V, EX, EY
I
NITIALIZE TO ZERO
LDRO, OLDV, CDNSTY, MOBILT
I
01 =
NO
YES/
START = CSTART (
\YES
= jm • » •
1 START = DSTART
1 A
NO
DEFINE STATEMENT ESTABLISH DESIRED
FUNCTIONS COSH (Z) CURRENT DENSITY
AND SINH (2) .
1
vo = -vo
VW = -VST ART ^
CALC. RELATIVE
AIR DENSITY (RELD)
^
Figure 7. Flow chart for subroutine EFLD3 (sheet 1 of 11).
27
-------
TRUE
CLACULATE PARAMETERS:
A1, 81. B1R, C1, R1
SET TO ZERO: VWIR, EXWIR,
El, E2, E3, F1, F2, SUM1, SIG1
YES
FALSE
i
NO
ACDNTY = MAXS
START LOOP OVER THE
WIRES TO COMPUTE
STARTING VOLTAGE
COMPUTE THE SUM IN THE
STARTING POTENTIAL DUE
TO THE WIRES
C
END LOOP OVER THE WIRES
FOR STARTING VOLTAGE
Figure 7. Flow chart for subroutine EFLD3 (sheet 2 of 11).
28
-------
CALCULATE PARAMETERS:
SOON, SQOP, RNN, RNP, ARGR
YES
CALL ARCCOS
CALCULATE FAC1
ICOUNT =
"
CLACULATE PARAMETERS: EO
RLAM, RAD, RASX, RAR1, RONSP,
CLAM, WLAM, VNAUT, VT
EVALUATE FUNCTION
(F) FOR METHOD OF
FALSE POSITION
NO
E3 = EORO + 0.1 • EORO • F/|F|
^
Figure 7. Flow chart for subroutine EFLD3 (sheet 3 of 11).
29
-------
START LOOP OVERGRID
POINTS IN X-DIRECTION
«F2-
E2»F1)/(F2-F1)
START LOOP OVER GRID
POINTS IN Y-DIRECTION
PRINT: APPLIED VOLTAGE
COULD NOT BE MATCHED
IN 100 ITERATIONS
Figure 7. Flow chart for subroutine EFLD3 (sheet 4 of 11).
30
-------
COMPUTE PARAMETERS:
B1, B1R, C1
YES
NO
NO
{S
X
X = AC
£
COMPUTE PARAMETERS:
SQRN, SQRP, SQXN, SQXP, ARGX.
ARGY, RAXY, RASXY, RAR1Y, COSHY,
SINHY, CX
YES
NO
COMPUTE FUNCTIONS:
VXYJ, EXJ. EYJ. RHOJ
FOR XR1
SUMV = 0., SUMEX = 0.
SUMEY = 0.
COMPUTE: COSX, SINX
Figure 7. Flow chart for subroutine EFLD3 (sheet 5 of 11).
31
-------
START LOOP TO SUM SPACE CHARGE
CONTRIBUTIONS FROM OUTSIDE SY
CALCULATE: COSHN, COSHP, SINHN,
SINHP, DENON, DENOP, TERMV, SUMV,
TEREX, SUMEX, TEREX, SUMEY
c
END LOOP TO SUM SPACE CHARGE
CONTRIBUTIONS FROM OUTSIDE SY
CALCULATE: VWIR. EXWIR,
EYWIR, VXYJ, EXJ, V(I11, 112),
EXII11, 112), EY(I11, 112),
RHO (111, 112)
C
END LOOP OVER GRID
POINT IN Y-DIRECTION
INCREMENT X
C
END LOOP OVER GRID
POINTS IN X-DIRECTION
YES
EPLT - 0.
Figure 7. Flow chart for subroutine EFLD3 (sheet 6 of 11).
32
-------
c
START LOOP TO AVERAGE FIELD
AT THE PLATE
TRUE
COMPUTE EPLT USING
VARIABLE INCREMENT
SIZES FROM EFLD4
COMPUTE EPLT USING
UNIFORM INCREMENT
SIZE
C
END LOOP TO AVERAGE FIELD
AT THE PLATE
COMPUTE AVERAGE
FIELD AT PLATE
(AEPLT)
NO
WRITE: VW.
ACDNTY,AEPLT
Figure 7. Flow chart for subroutine EFLD3 (sheet 7 of 11).
33
-------
YES
YES
OLDVW = VW
OLDCD = ACDNTY
c
END LOOP OVER
CURRENT DENSITIES
/PRINT: BREAKDOWN FIELD 7"
/ IS EXCEEDED, VW, ACDNTY/
INTERPOLATE TO FIND
CURRENT DENSITY AT VO
VW = OLDVW
IVCK = 1
Figure 7. Flow chart for subroutine EFLD3 (sheet 8 of 11).
34
-------
YES
NO
K = 1
c
START LOOP OVER SUB
INCREMENTAL LENGTHS
START LOOP OVER GRID VALUES
IN SUB INCREMENTAL LENGTHS
YES
CALC. CONTRIBUTION TO
AVG. ELECTRIC FIELD
IN SUB INCREMENT
CALC. CONTRIBUTION TO
AVG. ELECTRIC FIELD IN
SUB INCREMENT
YES
CALC. AVG. ELECTRIC FIELD
IN SUB INCREMENT
CALC. CONTRIBUTION TO
AVG. ION DENSITY IN
SUB INCREMENT
C
END LOOP OVER GRID VALUES
IN SUB INCREMENTAL LENGTHS
Figure 7. Flow chart for subroutine EFLD3 (sheet 9 of 11).
35
-------
STORE VALUES OF AVG. ELECTRIC
FIELD AND ION DENSITY FOR
SUB INCREMENT
K = K+ 1
(
END LOOP OVER SUB
INCREMENTAL LENGTHS
A
J
NYY
= NY1
(
START FIRST LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
>w
)
y
CALC. EAVG(L)
AND CHFID (L)
NYY = NYY - 1
END FIRST LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
KK = 1
M1 - NY1 + 1
M2 = 2(NY1)
(
START SECOND LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
CALC. EAVG(M)
AND CHFID(M)
KK = KK + 1
A
^ END SECOND LOOP TO PUT SUB^\
INCREMENTAL QUANTITIES J
^IN CORRECT ORDER J
t_
1
\
r]
( START LOOP OVER SUB "\
\^ INCREMENTAL LENGTHS J
\
CALC. AVG. E
FIELD AT PLA
1
J LL - LL
LECTRIC
TE
+ 1
(END LOOP OVER SUB A
INCREMENTAL LENGTHS J
LI = N\
n
: START FIRST LOOP TO PUT SUB^N
INCREMENTAL QUANTITIES )
IN CORRECT ORDER J
n *r^^
CALC. ECO I
LI = LI -
-L(L)
1
^END FIRST LOOP TO PUT SUB^\
INCREMENTAL QUANTITIES J
^ IN CORRECT ORDER ^/
L2 = 1
11 = NY1 -t
12 - 2INY1
1
)
Figure 7. Flow chart for subroutine EFLD3 (sheet 10 of 11).
36
-------
START SECOND LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
CALC. ECOLL(I)
L2
= L2
+ 1
END SECOND LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
V = - VO
START
= SSTART
END SUBROUTINE
Figure 7. Flow chart for subroutine EFLD3 (sheet 11 of 11).
37
-------
START SUBROUTINE
REAL: NUM. M. NWIRE
LOGICAL LTEST
BLOCK COMMON
VCOOP, NVII
BLOCK COMMON
ECX, ECY, X1, Y1, AX, AY
BLOCK COMMON
LTEST, RHO, V,
EX, EY
DETERMINE #OF GRID STRIPS
IN EACH DIRECTION (NXI AND NYI)
c
START LOOP OVER
X-DIRECTION
START LOOP
Y-DIRECTION
CALC. X AND Y
POSITIONS (X AND Y)
YES
[VCOOP (i. j) • vw
NO
Figure 8. Flow chart for subroutine OMAN (sheet 1 of 3).
38
-------
M = NWIRE
NUM = 0.0
DENOM = 0.0
EXO - 0.
EYO = 0.
EXSUM = 0.
EYSUM = 0.
CALC. ARGUMENTS FOR COS
AND COSH FUNCTIONS IN STATIC
SOLUTION [El. F1. G1. AND H1]
CALC. COS AND COSH FUNCTIONS
[E2. F2, G2, AND H2]
CALC. ARGUMENTS FOR LN
FUNCTIONS IN STATIC POTENTIAL
[TT AND TB]
CALC. LN FUNCTIONS
[F AND G]
CALC. SUM IN NUMERATOR OF
STATIC POTENTIAL [NUMJ
CALC. SUM IN DENOMINATOR OF
STATIC POTENTIAL [DENOM]
CALCULATE SIN AND SINH
FUNCTIONS IN THE STATIC FIELD
[H3, F3, E3. G3]
CALCULATE THE SUMS IN
THE STATIC FIELDS
[EXSUM,EYSUM]
YES
M - M + 1.
NO
CALC. POTENTIAL AT
POINT (X.Y) [V COOP (I, J)l
Figure 8. Flow chart for subroutine OMAN (sheet 2 of 3).
39
-------
CALC. XANDY COMPONENTS OF
FIELD AT POINT (X, Y) [ECX(U),
ECY(I,J)]
c
END LOOP OVER
Y-DIRECTION
c
END LOOP OVER
X-DIRECTION
CALC. FIELD AT THE
WIRE [ECX(1,D. ECY(I.I)]
C
END SUBROUTINE
J>
Figure 8. Flow chart for subroutine OMAN (sheet 3 of 3).
40
-------
VW - Electric potential at the wire (V).
NX - Number of grid points in the x-direction. It
cannot exceed a value of 15.
NY - Number of grid points in the y-direction. It
cannot exceed a value of 15.
SX - Wire-to-plate spacing (m).
SY - One half wire-to-wire spacing (m).
PI - Value of the constant pi.
AC - Radius of the discharge electrode (m).
NWIRE - Number of wires per gas passage per electrical
section.
The following variables are in common with the main program,
subroutine EFLD2, subroutine EFLD3, and subroutine EFLD4.
VCOOP(I,J) - The static potential at a point in the grid (V).
NVII - A parameter which determines whether a voltage-
current curve is generated. When NVII is 1
known values of current and voltage are used.
When NVII is 2 a voltage-current curve is pro-
duced.
The following variables are in common with EFLD3 and EFLD4.
ECX(I,J) - The x-component of the static electric field at
a grid point (V/m).
ECY(I,J) - The y-component of the static electric field at
a grid point (V/m).
AX(I) - The distance between the I-th and the I+l-st
grid points in the x-direction (m). This is
used only with EFLD4.
AY(J) - The distance between the J-th and the J+l-st
grid points in the y-direction (m). This is
used only with EFLD4.
X1(I) - The x-position of the I-th grid point (m). It
is used only with EFLD4.
Y1(J) - The y-position of the J-th grid point (m). It
is used only with ELFD4.
41
-------
LTEST - A logical variable which distinguishes between
fixed and variable grid spacing. When LTEST is
TRUE the variable grid spacing of EFLD4 is used,
Of the above variables, the values of the following must be
provided by the main program: VW, NX, NY, SX, SY, PI7 AC, NVII,
and NWIRE. Values of VCOOP, ECX, and ECY are determined in the
subroutine.
42
-------
SECTION 5
A GENERALIZATION OF THE INTEGRATION SCHEME USED IN
THE MATHEMATICAL MODEL TO COMPUTE THE ELECTRICAL
CONDITIONS IN A WIRE-DUCT PRECIPITATOR
BACKGROUND
A mathematical procedure for calculating electrical conditions
in wire-duct electrostatic precipitation devices has been presented
by McDonald, et al.l1 This procedure is based on a technique to
numerically solve Poisson's equation and the current transport
equation simultaneously under appropriate boundary conditions.
Values are computed for the electric potential, electric field,
and space charge density. The method of solving the transport
equations is based on a numerical technique suggested by Leutert
and Bohlen.12 This technique uses equally spaced increments in
approximating the derivatives by difference ratios. The use of
equal increments can work well when the increments are suffi-
ciently small. In the case of electrostatic precipitation devices,
for which a typical wire-to-plate spacing is 12.7 cm (5 in.), a
large number of increments are required to obtain the desired
accuracy in the numerical calculation. An integration which re-
quires a large number of increments requires both a large computer
and a large amount of computing time. In addition, the use of
equal increments does not allow one to account for the finite
size of the corona wire unless the increments are equal to the
radius of the wire. In some cases, treating the wire as if it
were infinitesimally small might give rise to significant in-
accuracies.
The limitations imposed on the numerical solution by using
equal increments can be removed by generalizing the procedure
to include variable sized increments. It has been demonstrat-
ed 13 / i u, i s, i e, 17, i e that improvecj accuracy can be obtained with
fewer integration increments if increments are adjusted to the
characteristics of the particular solution. For instance, if
one chooses small increments in the region where the solution
varies rapidly and larger increments where the solution changes
more slowly, improved overall accuracy can be obtained for a given
number of integration steps. Since the wire-duct geometry repre-
sents a case in which the potential and the electric field change
more rapidly near the wire than near the plate, a choice of small
increments near the wire and larger increments near the plate
should yield improved accuracy for a fixed number of integration
steps.
43
-------
DEVELOPMENT OF EQUATIONS
In the steady-state the equations which describe the elec-
trical conditions in an electrostatic precipitator are
V • E = p/e0 (23)
V • J = 0 (24)
J = pbE (25)
E = -$V (26)
where
E = electric field (V/m) ,
p = space-charge density (A sec/in2),
£o = permittivity of the gas (A sec/Vm) ,
J = current density (A/m2),
V = electric potential (V) ,
b = mobility of charge carrier (m2/V'sec),
x = coordinate position measured toward the plate with the
corona wire as origin (m) ,
y = coordinate position measured parallel to the plate with
the corona wire as origin (m) .
In terms of potential equation (23), Poisson's equation, becomes
lv=_p/eo (27)
Substitution of (25) and (26) into (24) yields
V • J = pb(p/e0) + b(-VV) • (Vp)
+ p(-VV) • (Vb)
= °' (28)
or after rearrangement
B« *
-------
Equations (27) and (29) must be solved simultaneously for the
potential and charge density. To obtain approximations for the
derivatives in (27), first make a Taylor series expansion about
the point labeled (2,2) in Figure 9. The potential at a point
displaced by a small amount in the x-direction from point (2,2)
can be written as
V(x,y2) = V2,2 +
2 / 2
(X-X2)
92V
21
(x-x2)2 + ir
? , 2 J .
33V
2 , 2
(x-x2)
(30)
For points displaced in the y-direction, the potential would be
V(x2,y) = V2,2
9V
21
2,2 (y-ya)
92V
1_ 93V
31 8^"
2 , 2
2 , 2
(y-ya)
(y-ya)
(31)
First consider the x-direction. If terms of greater than second
order are neglected, the potential at adjacent grid points can
be written as
Vi , 2 =
9V
, 2
2 , 2
2,2
(32)
and
V3,2 =
where
(aX2) + 2 9
= x2 - Xj
ax2 = x3 - x2
, 2
(ax2)
(33)
(34)
To eliminate the first derivative, multiply (32) by ax2/axi, and
add the result to (33). After some rearrangement, the second
derivative becomes
ax2Vi,2 -
3 V, = --
2/2 axiax2(axi + ax2;
Similar considerations for the y-direction yield
ax2)]
(35)
45
-------
PLATES
WIRES
3,2
I
Sv
Figure 9. Schematic illustrating positions of
integration grid points in the new
integration scheme.
46
-------
32V
ay2V2,
2 i 2
ay i ay 2
+ ay2)
ay2) ]
(36)
Equations (35) and (36) can be used in Poisson's equation to
compute
ax2 Vlf 2
V
2,2 - \:
) t
V
3, 2
axiax2
ax2)
V2, 3 + ay2 V2,
p 2 , 2
ayiay2
ay2)
(37)
The components of the electric field can be obtained from the
partial derivatives of the potential. If the second derivatives
are eliminated from (32) and (33), one obtains
E = -
x
ax
V3,2 - ax2
2 / 2
axiax2(axi + ax2)
- ax22)
(38)
and
2 / 2
ayi2 V2/3 - ay?2 V2,i - V2,2 (ayt2 - ay22)
ayiay2(ayj+ ay2)
(39)
While equation (37) generalizes the potential calculation to allow
for an arbitrary choice of grid spacings, equations (38) and (39)
should yield more accurate values of the field components since
these equations depend on the potential at three points instead of
only two.
The electric field and potential are computed at the boundaries
of the integration cells, while the charge density is associated
with the centers of the cells. To be consistent with these assump-
tions, and avoid using two interlacing grids of computational
points, we use a different discretization scheme for the charge
density and carrier mobility. The derivatives of these two func-
tions are approximated by difference ratios based on the spacing
of the cell boundaries.
ia
ax
_ P2r2 ~ Plr2
2,2 axi
IP
3y
2 1 2
_ P2 , 2 ~ P2f 1
47
-------
3b _ ba/2 ~ bi/2
3x 2/2 axi
8b _ ba, 2 - bz/i ,.
W 2/2 iTI (40)
The charge density can then be interpreted as the average value
within the cell. Since the charge density varies more slowly
than the field and potential, the accuracy of the discretization
equation is not critical. Substitution of (40) into (29) leads to
L
Pz,2 = -a + (a2 - 3) / (41)
where
™ - ~u FTP (*•»*> 2 " bi, 2x . p /2b2, 2 - b2, ix •, . .
a - 2b2,2 LEx ( 1x1 ) + Ey ( ^ ) J (42)
and
E p E p
6 • -e° lJL^r + -^wr* • »«3>
Both EX and E are evaluated at point (2,2). In effect, the charge
density is based on a two point approximation. These equations
have the advantage that the charge density in a cell can be up-
dated immediately using the new value of the field at the cell
boundary. This iterative scheme has the advantage over the old
scheme that new values of all the functions (potential, field,
and charge density) are computed each time through the grid of
points. In the old scheme, two sweeps through the grid points
were required to update all the functions. As implied above,
equations (37), (38), (39), and (41) can be solved simultaneously
for the potential, field and charge density at point (2,2). Point
(2,2) will then be moved successively to all points in the grid
producing values of potential, field and charge density at each
point.
BOUNDARY CONDITIONS
The solutions for the potential, electric field and charge
density must be obtained subject to a certain set of boundary
conditions. The current set of boundary conditions is given by
(1) p = p , the charge density at the surface of the corona,
s
(2) E = 0 along aline AB of Figure 9,
X
(3) E =0 along lines BC, CD, and AD in Figure 9,
(4) p = J/Exb near the plate.
48
-------
SUBROUTINE EFLD4
This subroutine calculates a voltage-current curve up to a
specified value of operating voltage and calculates the average
electric field at the plate for the operating applied voltage.
The voltage-current curve is generaged by (1) specifying a starting
value of average current density at the plate, (2) incrementing
upward on the average current density, and (3) determining the
applied voltage at each value of current density. When a value
of current density results in an applied voltage which exceeds the
specified operating applied voltage, an interpolation is performed
to obtain the operating voltage and current density. At this
operating applied voltage, calculations can also be made to give
the average current density, average electric field, and average
electric field at the plate in subincremental lengths. As pointed
out earlier, this subroutine was used for the comparisons with the
approximate solutions shown in Table 1.
The potential, electric field, and charge density are com-
puted by solving equations (37), (38), (39), and (41) simultaneous-
ly using a relaxation technique. In solving the equations, the
corona region near the wire is treated as a source of ions. It
is assumed that the change in potential across the corona region
can be described by
AV = VW - V(2,l) = ECOR (RC - AC), (44)
where
VW = potential at the surface of the wire (V),
V(2,l) = V(l,2) = potential at the surface of the corona (V),
ECOR = average field required to drive the corona (V/m),
RC = radius of corona (m),
AC = radius of the wire.
Note that the potential drop across the corona region will be
small when the two radii are nearly equal. The case in which
RC = AC corresponds to the conditions used in the model previously.
It is assumed that the corona is cylindrical.
Numerical Algorithm
(1) Calculate the potential, electric fields, and charge
density at the grid points using the approximate solution pre-
sented earlier.
(2) Hold the potential at the wire fixed, recalculate the
potential, the fields, and the charge density at the grid points
using equations (37), (38), (39), and (41) - (43).
49
-------
(3) Repeat step 2 iteratively until the potential profile
changes negligibly in successive interations.
(4) Check to see if the average current density at the
plate is the desired value. If the average current density
agrees with the specified value, a solution has been obtained.
If the average current density at the plate does not agree with
the specified value, adjust the potential at the wire and repeat
steps 3 and 4.
The primary differences between this subroutine and EFLD2
of the mathematical model are:
(1) EFLD4 uses variable sized integration increments.
(2) EFLD4 can account for the potential drop across the
corona.
(3) EFLD4 accounts for the finite size of the corona region
by specifying the potential there.
(4) EFLD4 computes the average current density at the plate
by integrating over the plate rather than computing the
mean value from several points.
(5) EFLD4 also computes the average field at the plate by
integrating over the plate.
(6) EFLD4 calls EFLD3 to obtain an approximate starting
solution.
(7) EFLD4 uses the method of false position to obtain the
correct current density.
(8) EFLD4 does not require a value of VSTART.
(9) EFLD4 uses more stringent conditions for convergence of
potential and current density than does EFLD2.
The following is a sequential list of the calling arguments
and their descriptions.
UEQ - Effective charge carrier mobility (m2/V»sec).
AC - Radius of discharge electrode (m).
VO - Chosen operating applied voltage (m).
SX - Wire-to-plate spacing (m).
SY - One-half wire-to-wire spacing (m).
50
-------
NX - Number of grid points in x-diraction.
NY - Number of grid points in y-direction.
AEPLT - Average electric field at the plate (V/m).
TDK - Temperature of the gas (°K).
P - Pressure of the gas (atm).
RF - Roughness factor for the discharge wire (0.5 <_
RF <_ 1.0) .
START - Chosen initial current density at which the voltage
current curve calculation starts (A/m2). Current
density increments in units of START until a change
is specified.
DSTART - Chosen increment in current density which is
used in place of START when specified (A/m2).
CSTART - Chosen increment in current density which is
used in place of DSTART when specified (A/m2).
IFINAL - Indicator which terminates the loop over average
current densities at the plate after IFINAL times.
VSTART - Initial estimate of applied voltage corresponding
to the first value of average current density at
the plate on the voltage-current curve (V).
VSTART is not actually used in EFLD4 to start
the integration.
VW - Operating applied voltage corresponding to a
given current density (V).
ACDNTY - Average current density at the plate (A/m2).
NWIRE - Number of wires per gas passage per electrical
section.
NEC - Indicator which governs the calculations of
average current density, average electric field,
and average electric field at the plate in sub-
incremental lengths. The calculations are per-
formed when NEC = 0 and are not performed when
NEC = 1.
EBD - Electrical breakdown strength of the gas (V/m).
51
-------
JIl - Indicator which governs the change in the in-
crement on average current density at the plate
from START to DSTART. The change occurs on the
Jll-th value of current density.
JI2 - Indicator which governs the change in the in-
crement on average current density at the plate
from DSTART to CSTART. The change occurs on the
Jl2-th value of current density.
The following is a list of the variables which are in common
with the main program.
EAVG(M) - Average electric field in a given subincrement
of length (V/m).
CHFID(M) - Average ion density in the absence of particles
in a given subincrement of length (#/nr).
ECOLL(M) - Average electric field at the plate in a given
subincrement of length (V/m).
NPRNT - Indicator which specifies the logical unit number
of the printer.
The following is a list of variables which are in common with
subroutines EFLD3 and CMAN.
ECX(I,J) - The x-component of the static electric field
at a grid point (V/m).
ECY(I,J) - The y-component of the static electric field
at a grid point (V/m).
AX(I) - The distance between the I-th and the I+l-st
grid points in the x-direction (m).
AY(J) - The distance between the J-th and the J+l-st
grid points in the y-direction (m).
XI(I) - The length of the I-th increment in the x-direc-
tion (m). This is used only with EFLD4.
Yl(J) - The length of the J-th increment in the y-direc-
tion (m). This is used only with EPLD4.
LTEST - A logical variable which distinguishes between
fixed and variable grid spacings. When LTEST is
TRUE the variable grid spacing of EFLD4 is used.
VCOOP - The static-like contribution to the potential
(V).
52
-------
NVII - A parameter which determines whether a voltage-
current curve is generated.
Of the above variables, the values of the following must be
provided by the main program: UEQ, AC, VO, SX, SY, NX, NY, TDK,
P, RF, START, DSTART, CSTART, IFINAL, VSTART, NWIRE, NEC, EBD, JI1,
JI2, NVII, and NPRNT. Values of AEPLT, VW, ACDNTY, EAVG, CHFID,
ECOLL, VCOOP, ECX, ECY, XI, Yl, AX, AY, and LTEST are determined
in the subroutine. The subroutine calls subroutine EFLD3 to obtain
initial approximations for the potential, electric field, and
charge density at the grid points.
If, for a given current density, convergence on the potential
grid can not be obtained in 4000 iterations, a message stating
that convergence can not be obtained is printed and those values
which were calculated in the last iteration are used for that
particular point on the voltage-current curve. If convergence
on a given average current density at the plate can not be ob-
tained in 25 iterations, a message stating that convergence can
not be obtained is printed and those values which were calculated
in the last iteration are used for that particular point on the
voltage-current curve.
There are three conditions which will terminate the calculation
of the voltage-current curve. The calculation is terminated if
(1) the specified operating applied voltage is reached, or (2) the
number of points on the curve is equal to the value of IFINAL, or
(3) the specified value of the electrical breakdown strength near
the collection electrode is exceeded. If the breakdown strength
is exceeded, a message to this effect is printed. Figure 10 shows
a detailed flow chart of this subroutine. A listing of this sub-
routine is given in Appendix C.
This subroutine calls subroutine EFLD3 which was described
earlier. The arrays containing the variable grid spacings are
transmitted through a common statement. The logical variable
LTEST is used to distinguish the variable spacing of EFLD4 from the
fixed spacings used in the previous model. The variable, LTEST, is
initialized to FALSE in both CMAN and EFLD3 by a data block sub-
program.
SUBROUTINE OUTPUT
This subroutine prints the arrays computed in EFLD4. It
prints all rows corresponding to the NX grid points in the x-
direction. If NY is greater than 18, only selected columns
corresponding to certain values of Y are printed. The first 9
columns are printed,•then 9 columns chosen by a multiple which
spans the remaining columns are printed. The values of Y are
printed above the columns, and the values of X are printed beside
the rows. For each point in the array which is printed, the
potential is printed under the charge density, the x-component
53
-------
c
START SUBROUTINE
REAL: MOBILT, NWIRE, MAXS
LOGICAL LTEST
DIMENSION. RHO, EX, OLDRO,
OLDV, CDNSTY, V, EY, EAVGS,
CHFIDS, ECOLLS
BLOCK COMMON: EAVG, CHFID
BLOCK COMMON: ECOLL
BLOCK COMMON: VCOOP, NVII
BLOCK COMMON: NREAD, NPRNT
BLOCK COMMON:
ECX, ECY, XI, Yl, AX, AY
BLOCK COMMON:
LTEST, RHO, V, EX, EY
INITALIZE TO ZERO:
OLDRO, OLDV, CDNSTY, MOBILT
VO = -VO
VW = -VSTART
J
CALCULATE RELATIVE
AIR DENSITY (RELD)
CALCULATE EORO
DEFINE GRID OF MOBILITY
VALUES
SSTART - START
DEFINE CONSTANTS
ESTABLISH GRID SPACING
LTEST - TRUE
CALL EFLD 3
PRINT ELECTROSTATIC SOLUTION
'/
START LOOP OVER
CURRENT DENSITIES
YES
Figure 10. Flow chart for subroutine EFLD4 (sheet 1 of 8).
54
-------
ESTABLISH DESIRED
CURRENT DENSITY
CALCULATE SPACE-CHARGE
DENSITY AT THE WIRE (QZERO)
CALL EFLD3
PRINT APPROXIMATE SOLUTION
WITH NON-ZERO CURRENT
7
Z = 0
INITIALIZE INDEPENDENT AND
DEPENDENT VARIABLES FOR
FALSE POSITION SCHEME:
F1=0, F2=0, V1=0. V2=0, V3=0
YES
PRINT: CONVERGENCE
CAN NOT BE OBTAINED
IN 25 ITERATIONS
ON CURRENT DENSITY
STORE CURRENT
VALUES OF V AND p
(JT)
1
Figure 10. Flow chart for subroutine EFLD4 (sheet 2 of 8).
55
-------
SET p(1,1) = p(1,2) = p(2,1) = QZERO
SET EX(1,1) = EX(2,1) = EY(1,1) = EY(1,2) = EO
(PEEK'S FIELD AT THE SURFACE OF
THE WIRE)
c
START LOOP OVER
GRID POINTS
CALCULATE V(IMX,J),
EX(NX,J), EY(NX,J), p(NX,J)
YES
CALCULATE Vd.NY),
EXI1.NY), EY(1,NY),/9(1,NY)
CALCULATE V(1,J),
EX(1,J), EY(1.J),p(1,J)
CALCULATE V(I,NY),
EX
-------
END LOOP OVER
GRID POINTS
YES
PRINT: CONVERGENCE CAN
NOT BE OBTAINED IN 4000
ITERATIONS ON THE
POTENTIAL GRID
/START LOOP OVER GRID \
[ POINTS FOR CONVERGENCE I
VTKT y
X
IV-OLDVI
-------
PRINT: F, V(2,1), ACDNTY,
LL. Z
V3
^ I V2 • V1 I
ARG - |"(V2+V1/2|
ACDLST
FUN* |1— ACDNSTY
VW = V(2,1)+EO*(RC-AC)
V(1,1) = VW
CALCULATE THE AVERAGE
ELECTRIC FIELD AT THE
PLATE (AEPLT)
PRINT: LL, Z
PRINT: P, V, EX, EY FOR ALL
GRID POINTS
PRINT: VW, ACDNTY, AEPLT
NO
PRINT: BREAKDOWN
FIELD IS EXCEEDED
VW, ACDNTY
INTERPOLATE TO
FIND CURRENT
DENSITY FOR VO
VW = OLDVW
IVCK = 1
Figure 10. Flow chart for subroutine EFLD4 (sheet 5 of 8).
58
-------
OLDVW = VW
OLDCD = ACDNTY
END LOOP OVER
CURRENT DENSITIES
RSUM = 0
ESUM = 0
START LOOP OVER GRID\
VALUES IN SUB '
INCREMENTAL LENGTHS
START LOOP OVER
SUB INCREMENTAL LENGTHS
Hsy
NO
YES
CALCULATE CONTRIBUTIONS
TO AVG ELECTRIC FIELD
IN SUB INCREMENT
CALCULATE CONTRIBUTIONS
TO AVG ELECTRIC FIELD
IN SUB INCREMENT
CALCULATE AVG
ELECTRIC FIELD IN
SUB INCREMENTS
Figure 10. Flow chart for subroutine EFLD4 (sheet 6 of 8).
59
-------
CALCULATE CONTRIBUTIONS
TO AVG ION DENSITY IN
SUB INCREMENT
END LOOP OVER GRID
VALUES IN SUB
INCREMENTAL LENGTHS
I
/£TART SECOND LOOP TO PUT su
(INCREMENTAL QUANTITIES IN
VCORRECT ORDER
UB\
CALCULATE EAVG(M)
AND CHFID(M)
STORE VALUES OF AVG.
ELECTRIC FIELD AND ION
DENSITY FOR SUB INCREMENT
| KK
= KK-H 1
END SECOND LOOP TO PUT SUB
INCREMENTAL QUANTITIES IN
CORRECT ORDER
END LOOP OVER SUB
INCREMENTAL LENGTHS
NYY = NY1
START LOOP OVER SUB
INCREMENTAL LENGTHS
START FIRST LOOP TO PUT
SUB INCREMENTAL QUANTITIES
IN CORRECT ORDER
CALCULATE EAVG(L)
AND CHFID(L)
s J
CALCULATE AVG
ELECTRIC FIELD AT
PLATE
LL =
LL + 1
NYY = NYY - 1
END FIRST LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
I
END LOOP OVER SUB
INCREMENTAL LENGTHS
KK = 1
M1 = NY1+1
M2 - 2(NY1)
L1 = NY1
START FIRST LOOP TO PUT
SUB INCREMENTAL QUANTITIES
IN CORRECT ORDER
CALCULATE ECOLL(L)
L1 - L1+1
Figure 10. Flow chart for subroutine EFLD4 (sheet 7 of 8).
60
-------
1
END FIRST LOOP TO PUT
SUB INCREMENTAL QUANTITIES
IN CORRECT ORDER
L2 = 1
II = NY1+1
12 = 2(NY1)
START SECOND LOOP TO PUT
SUB INCREMENTAL QUANTITIES
IN CORRECT ORDER
CALCULATE ECOLLID
L2 = L2-M
END SECOND LOOP TO PUT SUB
INCREMENTAL QUANTITIES
IN CORRECT ORDER
V = -VO
START = SSTART
c
END SUBROUTINE
Figure 10. Flow chart for subroutine EFLD4 (sheet 8 of 8).
61
-------
of electric field is printed under the potential, and the y-
component of the electric field is printed under the x-component.
The only exception to this order is for the static (zero current)
case in which the charge density is not printed. For the static
case, this subroutine is called by ENTER2 which is a different
entry point. When the subroutine is entered at ENTRY ENTER2 it
behaves as described above except that the charge density is
not printed.
The following is a sequential list of the calling arguments
and their description.
NX - Number of grid points in the x-direction.
NY - Number of grid points in the y-direction.
The following is a list of the variables which are in common
with EFLD4.
RHO(I,J) - Charge density at a grid point (c/m3) .
V(I,J) - Potential at a grid point (V).
EX(I,J) - x-component of the electric field at a grid
point (V/m) .
EY(I,J) - y-component of the electric field at a grid
point (V/m) .
CDNSTY(NX,J) - Current density at a point on the plate (A/m2) .
XI (I) - x-position of a grid point (m) .
Yl(J) - y-position of a grid point (m) .
NPRINT - Indicator which specifies the logical unit number
of the printer.
EAVG(M) - Average electric field in a given subincrement
of length (V/m) .
CHFID(M) - Average ion density in the absence of particles
in a given subincrement of length *
ECOLL(M) - Average electric field at the plate in a given
subincrement of length (V/m) .
VCOOPd/J) - The static-like contribution to the potential at
a grid point (V) .
ECX(I,J) - The x-component of the static electric field at
a grid point (V/m) .
62
-------
ECY(I/J) - The y-component of the static electric field at
a grid point (V/m).
AX(I) - The distance between the I-th and I+l-st grid
points in the x-direction (m). This is used
only with EFLD4.
AY(J) - The distance between the J-th and the J+l-st
grid points in the y-direction (m). This is
used only with EFLD4.
Figure 11 shows a detailed flow chart of this subroutine. A
listing of this subroutine is given in Appendix D.
63
-------
c
START SUBROUTINE
)
LOGICAL LTEST
DIMENSION: RHO, EX, OLDRO
OLDV, CDNSTY, V, EY, EAVGS,
CHFIDS, ECOLLS
BLOCK COMMON: EAVG, CHFID
BLOCK COMMON: ECOLL
BLOCK COMMON:
VCOOP, NVII
BLOCK COMMON: NREAD. NPRNT
BLOCK COMMON: ECX,
ECY, XI, Y1, AX, AY
BLOCK COMMON:
LTEST, RHO, V, EX, EY
N2 = (NY-D/9
N1 = NY -8 «N2
/
I
PRINT: J, J=1,9
/
PRINT: YKJ), J=1,9
(
START LOOP OVER
ROWS FOR 1ST 9 COLUMNS
PRINT: RHO(I,J), J-1.9;
V(I,J), J=1,9); XKl); EX(I,J),
J=1,9; EY
-------
START LOOP OVER ROWS
FOR LAST 9 COLUMNS
TO BE PRINTED
PRINT: RHO(I,J), J=N1,NY, N2;
V(I,J) J=N1,NY, N2; X1(l)
EX(I,J), J=N1, NY. N2; EY(I,J),
J-N1, NY, N2
C
END LOOP OVER ROWS
c
c
RETURN
ENTRY ENTER 2
N2= (NY-D/9
N1 = NY -8 »N2
PRINT: J, J=1,9
7
PRINT: Y1(J),J=1,9
C
START LOOP OVER ROWS
FOR 1ST 9 COLUMNS
PRINT: VCOOP(I,J), J=1,9;
ECXU.J), J=1,9; XI(I);
ECY(I.J), J=1,9
C
END LOOP OVER ROWS
FOR 1ST 9 COLUMNS
Figure 11. Flow chart for subroutine OUTPUT (sheet 2 of 3).
65
-------
PRINT: J, J=N1,NY, N2
7
PRINT: YKJ), J-N1, NY, N2
START LOOP OVER ROWS FOR
LAST 9 COLUMNS TO BE PRINTED
PRINT: VCOOP(U), J=N1, NY, N2;
ECX(I,J), J=N1,NY,N2, X1(l);
ECY(IJ), J=N1, NY. N2
c
RETURN
c
END SUBROUTINE
Figure 11. Flow chart for subroutine OUTPUT (sheet 3 of 3).
66
-------
SECTION 6
GAUSSIAN QUADRATURE INTEGRATION FOR
COMPUTING PARTICLE CHARGING RATES
Previously, the RATE function subprogram has used Simpson's
rule to perform the numerical integration over the angle 0 . RATE
has been rewritten using the Gaussian quadrature method to perform
this integration since the same accuracy can be obtained using
fewer increments than would be required by Simpson's rule. This
reduction in the number of integration increments results in a
significant saving of computer time. Also, by reducing the number
of increments used in the Runga-Kutta integration which is used
to integrate the charging rate over time a further reduction in
the amount of time required to compute particle charge is accom-
plished.
Previously, 10 increments in the Runga-Kutta integration
and 20 increments in Simpson's rule were recommended in order to
obtain sufficient accuracy in the model projections. Comparable
accuracy can be obtained using five increments in the Runga-Kutta
integration and three increments in the new Gaussian integration.
A detailed comparison of the two integration schemes using dif-
ferent numbers of integration increments is shown in Table 2 .
The charges computed by the different schemes are given for
several particle diameters as well as for several positions
within the precipitator . The difference in the charge computed
by the two methods for various particle diameters is negligible
for smaller particle diameters (.1 - 5 micrometers) and increases
to the order of 2% for larger particle diameters (20 - 30 micro-
meters) . These differences in accumulated charge have a neg-
ligible effect on such quantities as efficiency, effluent MMD,
and particle standard deviation since the major differences
occur at particle diameters which are easily collected by the
precipitation process. In the next section a description of
the new RATE function is given.
FUNCTION SUBPROGRAM RATE
This function subprogram calculates the right hand side of
Nebq
_g_2
4eo
)
67
-------
TABLE 2. CHARGE ON PARTICLES COMPUTED BY DIFFERENT INTEGRATION METHODS
Particle Charge (10"
Coul)
CTl
00
Particle Length
Radius Increment of
(10~'m) Precipitator
\ 1
(• 10
°'2 { 20
) 27
0.7
1.6
3.5
1
10
20
27
1
10
20
27
1
10
20
27
|
. >
«-» (
) 27
!1
10
20
27
10 Inc. Runga-Kutta
20 Inc. Simpson's
Time/Loop = 5.5 sec
0.017469
0.035541
0.041324
0.043734
0.14605
0.26117
0.28877
0.29881
0.69225
1.0918
1.1742
1.1857
3.1898
4.5682
4.7153
4.7153
18.618
26.097
26.506
26.506
102.97
144.39
146.65
146.65
20 Inc. Runga-Kutta
40 Inc. Simpson's
Time/Loop = 22 sec
0.017447
0.035536
0.041322
0.043733
0.14574
0.26112
0.28876
0.29880
0.69001
1.0912
1.1740
1.1856
3.1756
4.5534
4.7266
4.7266
18.518
25.920
26.399
26.399
102.40
143.36
146.04
146.04
10 Inc. Runga-Kutta
5 Pt. Gaussian
Time/Loop = 1.4 sec
0.017428
0.035531
0.041320
0.043732
0.14563
0.26107
0.28873
0.29878
0.68934
1.0911
1.1745
1.1862
-3.1701
4.5282
4.7183
4.7183
18.474
25.363
25.832
25.832
102.15
140.25
142.84
142.84
5 Inc. Runga-Kutta
5 Pt. Gaussian
Time/Loop = 0.7 sec
0.017452
0.035533
0.041321
0.043733
0.14633
0.26109
0.28874
0.29879
0.69215
1.0912
1.1745
1.1862
3.1822
4.5284
4.7184
4.7184
18.548
25.364
25.832
25.832
102.56
140.26
142.84
142.84
5 Inc . Runga-Kutta
3 Pt. Gaussian
Time/Loop » 0.4 sec
0.017459
0.035534
0.041309
0.043715
0.14636
0.25923
0.28661
0.29658
0.69278
1.0838
1.1682
1.1801
3.1816
4.5578
4.7528
4.7528
18.547
25.358
25.827
25.827
102.59
140.26
142.84
142.84
-------
exp
[(
4ire kTar
o -oo
(K + 2) /sin 8d8
r3ar 2 - r 3(K + 2) + a3(K - IKeE-CosO \~]
. L o o J a \
r-=—-2 rr—: —I ij
ira vN e
^ exP (-qe/47reoakT) , (45)
where qg = 4TreoEaa (1 + 2 ) , (46)
Qn = arccos (q/qc) , (47)
O o
and q = instantaneous charge on the particle (C) ,
q = saturation charge due to field charging (C) ,
o
0 = azimuthal angle in a spherical coordinate system with
origin at the center of the particle (radians) ,
0 = maximum azimuthal angle for which electric field
0 lines enter the particle (radians) ,
N = free ion density (m~3)f
e = permittivity of free space (C2/N-m2) ,
e = electronic charge (C),
= permittivity of free s
2_ = average electric field between the electrodes (V/m),
Cl
b = ion mobility (m2/V-sec),
r\,
v = mean thermal speed of ions (m/sec)/
a = particle radius (m),
k = Boltzmann's constant (J/°K),
T = absolute temperature (°K),
t = time (sec),
69
-------
K = dielectric constant of the particle, and
r = radial distance along 0 at which the radial component
0 of the total electric field is zero (m).
The above equation is used in subroutine CHARGN. In order to use
this function subprogram, subroutines ARCCOS and ZERO must be sup-
plied.
The first and third terms on the right hand side of equation
(45) are calculated in a straight forward manner. However, the
third term involves an integration over the angle 9 which must
be performed numerically. The integration is performed by using
the Gaussian guadrature 9 which is given by
1
F(t)dt f (48)
f
where
6 = *s(TT/2 - 60)t + h(QQ + ir/2) , (49)
and the integral
1
f
F(t)dt = AQF(t0) + AiF(ti) + ..... AnF(tn) (50)
is evaluated using tabulated values of A(k = 0,1 ..... n) and
t (k = 0,1 ..... n) . The subprogram performs the operations indi
cated in equations (48) and (50) for a fixed number of points,
n = 3.
If the charge on the particle is equal to or greater than
the saturation charge, the first term on the right hand side of
equation (45) is set equal to zero. Once the three terms on the
right hand side of equation (45) are calculated, then they are
added to give the total charging rate.
Figure 12 shows a detailed flow chart for this subprogram.
All information which is transmitted between subroutine CHARGN
and this function subprogram is transferred through calling argu-
ments. The following is a sequential list of the calling argu-
ments and their descriptions.
ECHARG - Value of an electronic charge unit (C) .
SCHARG - Value of saturation charge number from the field
charging equation (see equation 46) .
70
-------
c
START FUNCTION
SUBPROGRAM
)
REAL: INTGRL, NE,
NUMBER. NTIME
DIMENSION: T,A
DATA: T
DATA: A
CALC. CHARGE ON
PARTICLE (NE)
NUMBER - SCHARG20
YES
Figure 12. Flow chart for function subprogram RA TE (sheet 1 of 3).
71
-------
START LOOP OVER
GAUSSIAN TERMS
CALC. VALUE OF
0 (THETA)
CALC. PARAMETERS DEPENDENT ON
6 (CTHETA. TCONST, ECOS)
CALC. COEFFICIENTS OF POLYNOMIAL IN
WHICH THE RADIAL COMPONENT OF ELECTRIC
FIELD IS ZERO (Cl AND CO)
CALL ZERO
CALC. ARGUMENT OF EXPONENTIAL FUNCTION
IN CHARGING RATE FOR REGION II (ARG1)
CALC. FUNCTION
VALUE (YVAL)
SUM GAUSSIAN
FUNCTION VALUES (YFUC)
c
END LOOP OVER GAUSSIAN
TERMS
YVAL - 0.
Figure 12. Flow chart for function subprogram RATE (sheet 2 of 3).
72
-------
CALC. CHARGING RATE FOR
REGION II {RATED
RATE1 = 0.
CALC. ARGUMENT OF EXPONENTIAL FUNCTION
IN CHARGING RATE FOR REGION III (ARG3)
YES
[NO
iING RATE IN
1ATE2)
1
RATE2 = 0.
YES
NO
CALC. CHARGING RATE IN
REGION III ( RATE 3 )
RATE3 - 0.
CALC. TOTAL CHARGWG
RATE (RATE)
c
END FUNCTION
SUBPROGRAM
Figure 12. Flow chart for function subprogram RATE (sheet 3 of 3).
73
-------
CONST - Value of the quantity [2 j*"*j a3E0] found in
equation (46) [V-m2]. (K+<2)
EZERO - Applied electric field strength for particle
charging (V/m) .
2
V - Value of the quantity C4TreoakTJ found in equation
\ ** D ) •
RSIZE - Radius of the particle (m) .
ECONST - Value of the quantity [i.m/£+o\ ] found in -equation
(45). KUJVI-Z;
CMKS - Value of the quantity [4ire0] found in equation (45)
(C2/nt-m2) .
RR - Value of the quantity E^fr-] found in equation (45)
[1 1 *» *
m-1 ] .
FCONST - Value of the quantity [ iyToi'S08 J found in equation
(45) [m2]. IK+^JCI
. 2
FACTOR - Value of the quantity [ v^ ] found in equation (45)
[mVsec]. *
bqs
COEFF - Value of the quantity [7^— ] found in equation (45)
4E
°
AFID - Free ion density for particle charging (#/m3).
NTIME - Residence time for particle charging (sec) .
NUMBER - Particle charge number.
Of the above variables, the values of the following must be
provided by subroutine CHARGN: ECHARG, SCHARG, CONST, EZERO, V,
RSIZE, ECONST, RR, FCONST, FACTOR, COEFF, AFID, NTIME, and NUMBER.
The total charging rate given on the right hand side of equation
(45) is RATE and is determined in the function subprogram.
74
-------
SECTION 7
EFFECTS OF THE NEW MODIFICATIONS ON
THE PREDICTIONS OF THE MODEL
DISCUSSIONS
Two of the modifications described earlier in this report
have been incorporated into the working version of the computer
program which represents the mathematical model of electrostatic
precipitation. The analytic approximations to the electrical
solutions in a wire-plate geometry have been incorporated into a
subroutine called EFLD3. This subprogram has been included in
the program with several options. When EFLD3 is used, the calcu-
lation performed is completely analogous to that in either EFLDl
or EFLD2, except that the analytic approximations are used to
replace the numerical solutions. The subroutine CMAN along with
the modifications described earlier was substituted for its
original version. The Gaussian Quadratures integration scheme
for computing the charge on particles has also been included in
the program. This integration method has the effect of speeding
up the charge calculations but should not give rise to any notice-
able change in the results of the model predictions.
Although a new numerical integration scheme was described
in Section 5 and has been listed in Appendix C, it has not been
included in the computer program for modeling electrostatic
precipitators. This new numerical solution was used primarily
to test the previous numerical solution and the approximate
solution. The subprogram listed in Appendix C could be sub-
stituted for EFLD2 in the computer program if one so desired.
Such a step is not considered practical, since the program would
then require even more time than before to execute. The new
numerical method may prove valuable, however, in developing
further extensions to the mathematical model.
A complete listing of the new version of the computer pro-
gram for modeling wire-plate electrostatic precipitators is given
in Appendix F. A list giving the definitions of variables used
in the program is given in Appendix 0. This program differs
from the one listed in the previous model report mainly in that
it contains the new subroutine EFLD3 and has new versions of the
subroutine CMAN and the function subprogram RATE. A simplified
flow chart for the entire program is shown in Figure 13.
75
-------
(
START MAIN
PROGRAM
L
READ INPUT
DATA
NVII =0
YES
YES
NVII = 2
NVI =2
NVII = 1
NVI - 1
Figure 13. Simplified flow chart for logic of the entire program (sheet 1 of 7).
76
-------
©*<
START CONVERGENCE LOOP
ON OVERALL EFFICIENCY
ITER =
ITER+1
CALC. NO. OF PARTICLES
IN EACH SIZE BAND
CALL PRTINP
YES
NO
PRINT OUT ALL
INPUT DATA (IN PRTINP)
7
Figure 13. Simplified flow chart for logic of the entire program (sheet 2 of 7).
11
-------
START LOOP OVER
INCREMENTAL LENGTHS
VISAME = 1
ANDNSECT>1
VISAME = 1
AND NDSET>1
INO
ITER + 1
1
CALL SPCHG1
YES
c
START LOOP OVER SUB
INCREMENTAL LENGTHS
c
START LOOP OVER
PARTICLE SIZES
L
Figure 13. Simplified flow chart for logic of the entire program (sheet 3 of 7).
78
-------
YES
NO
CALL
CHARGN
CALC. PARTICLE
CHARGE, EQ. (15)
YES
CALC. IDEAL PARTICLE MIGRATION
VELOCITY AND EFFICIENCY
RETRIEVE NUMBER OF
PARTICLES ENTERING
FIRST INCREMENT
CALC. NO. OF
PARTICLES REMOVED
YES
CALC. SUM OF
WEIGHT REMOVED
YES
STORE NUMBER OF
PARTICLES ENTERING
FIRST INCREMENT
Figure 13. Simplified flow chart for logic of the entire program (sheet 4 of 7).
79
-------
CALC. NO. OF PARTICLES
ENTERING NEXT INCREMENT
c
END OF LOOP ON
PARTICLE SIZE
I NO
CALL SPCHG2
END OF LOOP ON SUB
INCREMENTAL LENGTHS
NO
I
YES
DETERMINE REDUCED CURRENT
AT WHICH TO START V-l CALC.
1
ESTIMATE REDUCED
CURRENT DENSITY
Figure 13. Simplified flow chart for logic of the entire program (sheet 5 of 7).
80
-------
CALL EFLD1
c
START LOOP OVER
PARTICLE SIZES
YES
CALL EFLD3
Figure 13. Simplified flow chart for logic of the entire program (sheet 6 of 7).
81
-------
CALC. IDEAL PARTICLE MIGRATION
VELOCITY AND EFFICIENCY
CALC. NO. OF PARTICLES REMOVED AND
SUM OF WEIGHT REMOVED
CALC. NO. OF PARTICLES ENTERING
NEXT INCREMENT
END OF LOOP OVER
PARTICLE SIZES
CALC. TOTAL WEIGHT
COLLECTED AND MMD
PRINT SECTIONALIZED
DATA ( IN PRTINC )
PRINT INCREMENTAL
DATA (IN PRTINC)
END OF LOOP OVER
INCREMENTAL LENGTHS
CALC. OVERALL MASS
COLLECTION EFFICIENCY
INO
lett-*
X
, J
CALL
PRTCHG
1
PRINT OUT RESULTS OF
CHARGE CALCS (IN PRTCHG)
7
PRINT OUT PARTICLE SIZE RANGE
STATISTICS (IN ADJUST)
PRINT OUT UNADJUSTED MIGRATION
VELOCITIES AND EFFICIENCIES, AND
DISCRETE OUTLET MASS LOADINGS
(IN ADJUST)
CALL PRTSUM
(IN ADJUST)
PRINT OUT SUMMARY
TABLE UN PRTSUM)
END OF MAIN
PROGRAM
Figure 13. Simplified flow chart for logic of the entire program (sheet 7 of 7).
82
-------
It is stressed that one who is not familiar with the model
should read both volumes of the previous report2'3 before trying
to use the program to model precipitators. Only the information
relevant to the present modifications is discussed in this report.
INPUT DATA
The formats for inputting data to the program are exactly the
same as for the previous version of the model. In fact, any set
of input data which would execute in the program listed in Revision
1 of the model will also execute in the program listed in this
report. The only difference will be that charging is computed
using Gaussian Quadratures rather than Simpson's rule.
There is one important extension to the options available
in the input parameters. In addition to the values of 1 and 2,
the parameter NVI can now have values of 3 and 4 as well. The
parameter NVI is an indicator which determines the technique used
to compute the electrical conditions. As before, when NVI = 1
the user must supply known or measured values of the operating
applied voltage and current. If NVI = 2, the program will con-
struct a voltage-current curve for a specified wire-plate geometry
up to a voltage which is specified by the user. Both of these
techniques for determining the electrical conditions are discussed
in Volume I2 of the previous report. When NVI has the new values
of either 3 or 4, a new parameter NVII is initialized by the pro-
gram. NVI is then set to either 1 or 2 so that the logic of the
program proceeds as before. If NVI = 3, NVII is set to 1 and
then NVI is also set to 1. If NVI = 4, NVII is set to 2 and then
NVI is also set to 1. If NVII = 1, EFLD3 rather than EFLDl is
called. A calculation completely analogous to that in EFLDl is
performed except that the analytic expressions from Section 4 are
used to compute the electrical properties. Under these conditions,
the electric field at the surface of the wire is chosen so as to
match the specified potential at the wire. In this case, Peek's
condition on the field is not used. If NVII = 2, EFLD3 rather
than EFLD2 is called. The resulting calculation is completely
analogous to that in EFLD2 except that the electrical properties
are computed from the analytic expressions described in Section 4.
In this case a current-voltage curve is generated up to the
operating voltage specified. The reader is referred to Volume
2 of the previous report for the details of constructing a com-
plete set of input data. Since the Simpson's rule integration
scheme has been replaced by Gaussian Quadratures, the parameter
NUMINC is no longer used in the program. It is still read in,
however. The output data will be identical to that described
in Volume 23 of the previous report.
MACHINE-DEPENDENT ASPECTS OF THE COMPUTER PROGRAM
The computer program, presented and discussed in this report,
has been developed on a Digital Equipment Corporation (DEC) PDP
83
-------
15/76 computer. Although the program should compile successfully
with only minor changes on most computers with a fortran compiler,
there are certain machine-dependent aspects of the program that
should be discussed. These machine-dependent properties can be
utilized to make the usage of the program more general and to ex-
tend the application of the program.
In order to use the program on most computers, the first two
executable statements in the program must be changed. These state-
ments define the input (read) and output (write) logical unit
numbers. The value of the variable NREAD specifies the input
logical unit number and the value of NPRNT specifies the output
logical unit number. These two changes should normally be the
only modifications which are necessary to allow successful com-
pilation of the program. The approximate time reguired to compile
the entire program on the DEC PDF 15/76 computer was 1716 seconds.
Once the program is compiled, it will execute provided that
enough core is available to store the program. The total core
requirements on the DEC PDF 15/76 are 131,221 octal words (45,713
decimal words) for the program plus 7,632 octal words (3,994 dec-
imal words) for system software necessary to implement the program.
Table 3 lists the various segments of the program and their core
requirements.
Due to the fact that the particular DEC POP 15/76 which has
been used to develop the program has only approximately 57,563
octal.words (24,435 decimal words) of core that can be accessed
at any given time, it was necessary to overlay subroutines in
order to fit the program into core. The main program (ESPM), the
data Block, and subroutine CMAN were kept in resident core and
the overlay was established by setting up the following six links:
LINK1 = SPCHG1, EFLD1
LINK2 = SPCHG2, EFLD2
LINK3 = ADJUST, WADJST, CFIT, LNFIT, QTFE, LNDIST, PRTSUM
LINK4 = CHARGN, RATE, ZERO/ARCCOS
LINKS = PRTINC, PRTCHG, PRTINP, CHGSUM
LINK6 = EFLD3/ARCCOS
With the above overlay, the required core is 56,275 octal words
(23,741 decimal words) including system software. The core re-
quirements were determined by the core utilized in resident core
and the largest link (LINK2). Also, the link table required an
additional 323 octal words (211 decimal words) of core.
In order to get the program to execute on computers with
small storage capacities, an overlay similar to the one discussed
84
-------
TABLE 3.
Octal
Words
LINK1
SPCHG1
EPLDl
LINK2
SPCHG2
EFLD2
CORE REQUIREMENTS FOR VARIOUS SEGMENTS
OF THE COMPUTER PROGRAM
407
13,664
732
15,775
Decimal
Words
RESIDENT
CODE
ESPM
CMAN
DATA
BLKl
BLK2
BLK3
BLK4
BLK5
BLK6
BLK7
BLK8
BLK9
BLK10
BLK11
BLKl 2
BLKl 3
BLKl 4
BLKl 5
BLKl 6
BLKl 7
BLK18
BLKl 9
BLK20
BLK21
System
Software
11,541
1,362
3,411
502
62
16
1
15
1,354
3,410
170
74
74
53
202
703
4
71
5
2
17
57
263
1,774
6,731
4,961
754
1,801
322
50
14
1
13
748
1,800
120
60
60
43
130
451
4
57
5
2
15
47
179
1,020
3,545
263
6,068
474
7,165
LINKS
LINK4
LINKS
LINK6
EFLD3
ARCCOS
Octal
Words
Decimal
Words
ADJUST
WADJST
CFIT
LNFIT
QTFE
LNDIST
PRTSUM
System
Software
7,200
610
372
624
160
1,567
1,635
393
3,712
392
250
404
112
887
925
267
CHARGN
RATE
ARCCOS
ZERO
System
Software
343
634
200
130
12
228
412
128
88
10
PRTINC
PRTCHG
PRTINP
CHGSUM
System
Software
1,747
1,563
5,352
1,156
110
999
883
2,794
622
72
14,046
200
6,182
128
85
-------
above may be possible. On computers with large memories such as
the IBM 370/158, UNIVAC 1100, or CDC 7600, no such action is
necessary. When an overlay is not used, a significant amount
of core could be gained by deleting subprograms EFLD1 and EFLD2.
This might provide additional core for expanding some of the
arrays.
Without changing the fundamental operations of the program,
the dimensions of certain arrays can be decreased or increased
if necessary. The dimensions of these arrays may be decreased
in order to fit the program on a small computer or they may be
increased to give greater flexibility on a large computer. In
the version of the program presented in this report, the following
quantities determine array sizes which may be changed:
• number of increments along the length of the precipitator
• number of particle size bands
• number of electrical sections in the direction of gas flow
• number of grid points used in the calculations of elec-
trical conditions
• number of rapping puff particle size distributions
• number of sets of nonideal conditions of nonuniform gas
velocity distribution and gas sneakage and/or particle
reentrainment without rapping.
The above quantities have maximum values of 45, 20, 10, 225, 10,
and 15, respectively.
The number of increments along the length of the precipitator
that can be utilized can be changed by changing the dimension of
DW and the dimension of the first subscript of XDC. DW appears in
COMMON/BLK6/ and XCD appears in COMMON/BLK7/. COMMON/BLK6/ appears
in the main program and subroutines PRTINP, CHGSUM, PRTINC, PRTCHG,
ADJUST, and PRTSUM. COMMON/BLK7/ appears in the main program and
subroutines SPCHG2 and PRTCHG. DW also appears in the dimension
statement in the subroutine SPCHGl. If the storage capacity of
the computer is large enough, the program should be modified to
handle more than 45 increments. Although 120 increments should
be sufficient to handle most cases, as many as 180 increments may
be necessary in certain cases.
The number of particle size bands that can be utilized can
be changed by changing the dimension of CHKSUM, DIAM, ONO, DXS,
XMV, PCNT, RAD, CCF, VOL, XNO, Q, WS, QSAT, OLDQ, OLDXNO, XDC,
OLDQF, OLDQT, SOLDQF, SOLDQT, YY, RPCNT, DMDLD, WUNCOR, RDMDLD,
CDMDLD, PCTOT, CPCTOT, WSL, PXS, EUNCOR, and AREA. In addition,
changes must be made to those variables which depend on the number
86
-------
of particle diameters in the particle size histogram. These vari-
ables must have a dimension which has a value of 1 greater than
those which depend on the number of size bands. These variables
include PRCU, ENDPT, PRCUNR, RPRCU, PRCUC, Z, and Y. CHKSUM
appears in the dimension statement in the main program. DIAM,
ONO, DXS, XMV, PCNT, RAD, CCF, and PRCU appear in COMMON/BLKl/.
VOL, XNO, Q, WS, QSAT, OLDQ, and OLDXNO appear in COMMON/BLK6/.
XDC appears in COMMON/BLK7/. ENDPT appears in COMMON/BLKlI/.
OLDQF, OLDQT, SOLDQF, and SOLDQT appear in COMMON/BLK20/. COMMON/
BLK1/ appears in the main program and subroutines PRTINP, PRTCHG,
and ADJUST. COMMON/BLK6/ and COMMON/BLK7/ appear in those locations
previously designated. COMMON/BLKll/ appears in the main program
and subroutines PRTINP, ADJUST, LNFIT, and LNDIST. COMMON/BLK20/
appears in the main program and subroutine CHGSUM. QSAT and XNO
appear in the dimension statement in subroutine SPCHG1. XNO, RAD,
CCF, OLDQ, and Q appear in the dimension statement in subroutine
SPCHG2. YY appears in the dimension statement in subroutine PRTCHG.
RPCNT, DMDLD, WUNCOR, RDMDLD, CDMDLD, PCTOT, CPCTOT, WSL, PXS,
PRCUNR, RPRCU, PRCUC, and EUNCOR appear in the dimension state-
ment in subroutine ADJUST. DIAM, ONO, and PXS appear in the di-
mension statement in subroutine WADJST. Z and Y appear in the
dimension statement in subroutine CFIT. Z, Y, and PRCU appear
in the dimension statement in subroutine LNFIT. AREA, PRCU, and
PCNT appear in the dimension statement in subroutine LNDIST. In
changing XDC, it is the second subscript which accounts for the
maximum number of size bands which can be considered.
The number of electrical sections in the direction of gas
flow that can be utilized can be changed by changing the dimension
Of LSECT, LINGS, PS, AS, VOS, TCS, WLS, ACS, BS, SYS, VGS, VGASS,
TEMPS, VISS, RFS, STARTl, START2, STARTS, VSTAR, and NWS. LSECT,
LINCS, and PS appear in COMMON/BLK2/. AS, VOS, TCS, WLS, ACS, BS,
SYS, VGS, VGASS, TEMPS, VISS, RFS, STARTl, START2, STARTS, and
VSTAR appear in COMMON/BLK6/. NWS appears in COMMON/BLK19.
COMMON/BLK2/ appears in the main program and in subroutine PRTINP
and ADJUST. COMMON/BLK6/ appears in those locations previously
designated. COMMON/BLK19/ appears in the main program and sub-
routines PRTINP, PRTCHG, and ADJUST. LSECT appears in the dimension
statement in subroutine SPCHG1.
The number of grid points that can be utilized in the calcu-
lation of electrical conditions can be changed by changing the
dimensions Of VCOOP, RHO, EX, OLDRO, OLDV, CDNSTY, V, EY, EAVGS,
CHFIDS, ECOLLS, EAVG, CHFID, ECX, ECY, XI, Yl, AX, AY, and ECOLL.
VCOOP appears in COMMON/BLK13. EAVG and CHFID appear in COMMON/
BLK8/. ECOLL appears in COMMON/BLK9/. ECX, ECY, XI, Yl, AX, and
AY appear in COMMON/BLK21/. COMMON/BLKl3/ appears in the main
program and subroutines CMAN, EFLD1, EFLD2, and EFLD3. COMMON/
BLK8/ appears in the main program and subroutines SPCHG2, EFLD2,
EFLD3, and PRTCHG. COMMON/BLK9/ appears in the main program, sub-
routine EFLD2, and EFLD3. COMMON/BLK21/ appears in EFLD3 and CMAN.
87
-------
RHO, EX, OLDRO, OLDV, CDNSTY, V, and EY appear in the dimension
Statement in subroutine EFLDl. RHO, EX, OLDRO, OLDV, CDNSTY, V,
EY, EAVGS, CHFIDS, and ECOLLS appear in the dimension statement
in subroutines EFLD2 and EFLD3. VCOOP, RHO, EX, OLDRO, OLDV, CDNSTY,
V, EY, ECX, and ECY are doubly subscripted variables with the first
subscript referring to the number of grid points in the direction
perpendicular to the gas flow and the second subscript referring to
the number of grid points in the direction parallel to the gas flow.
EAVG, CHFID, ECOLL, EAVGS, CHFIDS, and ECOLLS are singly subscripted
variables whose dimension must be a value of two less than twice
the dimension of the second subscript in the variables VCOOP, RHO,
EX, OLDRO, OLDV, CDNSTY, V, and EY.
The number of rapping puff particle size distributions that
can be utilized can be changed by changing the dimension of ARD50
and ARSIGM. ARD50 and ARSIGM appear in COMMON/BLK12/. COMMON/BLK12/
appears in the main program and in subroutines PRTINP and ADJUST.
The number of sets of nonideal conditions of nonuniform gas
velocity distribution and gas sneakage and/or particle reentrain-
ment without rapping that can be utilized can be changed by changing
the dimension of ASNUCK, AZIGGY, and AZNUMS. These variables appear
in COMMON/BLK12/. COMMON/BLK12/ appears in those locations pre-
viously designated.
If any changes are made that affect arrays, these changes
will also affect the limitations on the input data discussed in
the previous report. The limitations on the input data discussed
previously are only applicable to the version of the program pre-
sented in Appendix F of this report. If changes are made, then
new limitations on the input data must be established.
EXAMPLE CASES AND COMPARISONS OF THE ANALYTIC APPROXIMATIONS WITH
PREDICTIONS OF THE PREVIOUS MODEL
Example 1
In this example, the model calculations are performed using
geometrical parameters corresponding to a laboratory precipitator.
This device has a plate-to-plate spacing of 25.4 cm, a wire-to-wire
spacing of 12.7 cm, a wire radius of 0.1191 cm, a gas velocity of
0.976 m/sec, and a current density at the plate of 25.8 nA/citr.
These parameters are also typical of full-scale precipitators. The
inlet mass loading and particle size distribution, operating volt-
ages and currents, gas flow rate and velocity, and gas temperature
and pressure were measured and are used as input data for the model.
A reduced effective ion mobility of 1.65 x lO"1* m2/v-sec is used in*
the model since the use of this value results in good agreement
between theoretical and experimental current-voltage characteristics
for corona discharge in ambient air. Although the precipitator is
divided into four baffled and independent electrical sections, the
last two sections were connected together during the experiment and
this is reflected in the input data to the model.
88
-------
Figure 14 shows a comparison of fractional collection effi-
ciencies computed from Revision 1 of the model using electrical
conditions measured in a laboratory precipitator with those com-
puted from Revision 2 of the model using the approximate calculation
of the electrical properties. Since the predictions of Revision
1 of the model have been previously compared with the experimental
results, the experimental values will not be shown. Instead, a
comparison of the new calculations obtained using the approximations
described in Section 4 with the previous model predictions will be
stressed. Revision 2 of the model contains a new charge calculation
scheme as well as an approximate representation of the electrical
solutions. As can be seen in Figure 14, the fractional collection
efficiencies computed by the two versions of the model are in
excellent agreement. The maximum difference of three percent
occurs for a diameter of 0.25 micrometers. The input data card
set which was used in Revision 2 of the model is shown in Table
4. The output data corresponding to the input in Table 4 are
given in Appendix G. The corresponding set of output data from
Revision 1 of the model are shown in Appendix H. Comparison of
these two appendices will show that the overall agreement of the
two versions of the model is quite good. The calculations shown
in Appendix H required 2,801 seconds on the DEC PDF 15/76 computer
while the corresponding calculations shown in Appendix G required
only 334 seconds. These results represent a significant saving
in computer time without a significant loss in accuracy.
Example 2
In this example, the geometric parameters corresponding to
the laboratory precipitator were the same as in Example 1. In
this case, the gas velocity was 1.49 m/sec and the average current
density at the plate was 10.8 nA/cm2. The primary difference in
this example and the previous one lies in the manner in which the
electrical operating conditions were determined. For this case,
these quantities are predicted by the model by calculating clean-
gas, current-voltage curves for each electrical section and esti-
mating the reduction in current in each increment of length due to
charged particles. A reduced effective ion mobility of 1.65 x 10""*
m2/V-sec and a roughness factor of 0.90 were used.
Figure 15 shows a comparison of the fractional collection
efficiencies predicted by Revision 1 of the model using integrated
electrical solutions with those predicted by Revision 2 of the
model using the approximate electrical solutions discussed in
Section 4. A maximum difference between the two predictions of
three percent occurs at a diameter of 1.6 micrometers. Table 5
gives the input data card set used to obtain the model predictions.
The output data set is shown in Appendix I. The corresponding cal-
culations for Revision 1 of the model are shown in Appendix J.
The calculations in Appendix J required 47,886 seconds on the
DEC PDF 15/76 computer. The calculations in Appendix I required
only 5,175 seconds.
89
-------
99.9
99.5
99.0
98.0
-
THEORETICAL (REVISION I, USING EFLD1)
THEORETICAL (REVISION II, USING EFLD3)
10.0
GEOMETRIC MEAN DIAMETER,
Figure 14. Comparison of fractional collection efficiencies computed from
Revision I of the model using electrical conditions measured in a
laboratory precipitator with those computed from Revision II
of the model using the approximations.
90
-------
TABLE 4. INPUT DATA CARD SET FOR EXAMPLE 1
COLUMN NUMBER
CARD
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
1
L
0
0
0
0
0
2
o
3
0
+
+
+
+
+
•f
2
6
A
1
5
6
3
6
2
6
2
1
2
3456
0 1'
B _ E S
0103
0 3
0 1 5 _
000.
20
20 _
0
.000
0303
.250
.500
.250
.500
.250
.500
1
7890
P : _ S
1010
10
004.
0 .
3 .
o
2 _ 4 6
0 6
0 E + 0
0 E + 0
0 E + 0
0 E t 0
0 E + 0
0 E + 0
1
C
0
0
3
0
o
0
0
0
0
1
0
2345
A - 1 2
3000
0
00.1
0
0
002
6672
+ 4.6
+ 2.0
+ 4.5
+ 2.0
+ 4.4
+ 2.0
6 7
5 F
1 0
9
0 0
0
_ 4
Q
_ 5
0 0
Q 0
8 0
0 0
4 0
0 0
5
8901
T 2 / 1
1010
9 . 0 _
.104
. 4 0 _
. 0 0
400
7.33
0 E + 0
0 E + 0
0 E + 0
0 E + 0
0 E + 0
0 E + 0
234567
0 0 0 A C F
2
100
. 0 0
0 . S
6 . 0
2 10
4 2 _ 6 6 .
4 + 1.50
2 + 3.20
4*1.50
2 + 3.20
4 + 3.00
2 + 3.20
3
8901
M ,- J -
0 . 0 _
0
0
002
6672
0 0 E -
0 0 E +
0 0 E -
0 0 E +
0 0 E -
0 0 E +
3 5 5 1 ?
234567B901234567890123456789012345678901234567690
24 . OUA/FT2
5.1 1.03 0.0001651.0 1500000. l.OOE + 09
0 . 60 0. 8 0 1 . 00 1 . 20 1 . 40 1 . 80
10. 0 20 . 0
60.6672_100.0
04 + 6.2500E+00 + 4.6875E-02 + 5.0000E + 00 + 5.0000E*00
00 + 7.6800t+01 + 1.0CQOE + 00 + 1.8000E-05+8.3333E-01
04 + 6.2500E+00 + 4.6875E-02 + 5.0000E + 00 + 5.0000E + 00
00 + 7.68DOE+01 + 1.0000E + 00 + 1.8000E-05 + 8.3333E-01
04 + 1.2500E+01 + 4.6875E-02 + 5.0000E + 00 + 1.0000E + 01
00 + 7.6800E+01 + 1.0000E + 00 + 1.8000E-05 + 8.3333E-01
-------
J
.
-
Ill
-
-
.
..
-
THEORETICAL (REVISION I, USING EFLD2)
THEORETICAL (REVISION II, USING EFLD3) ,
10.0
GEOMETRIC MEAN DIAMETER,
Figure 15. Comparison of fractional collection efficiencies computed from
Revision I of the model using theoretical current-voltage calculations
with those computed from Revision II of the model using the
approximate electrical calculations.
-------
TABLE 5. INPUT DATA CARD SET FOR EXAMPLE 2
COLUMN NUMBER
CARD
NUMBER
1
2
3
4
5
6
7
8
9
10
12
13
15
16
18
20
21
1 6
L A
0 1
0 5
2 0
0 .
0 .
0 .
2 .
0 .
0 3
+ 6
+ 9
+ 6
+ 9
+ 2
+ 9
0 1
B _
0 1
0 3
0 2
0 6
0 0
2 0
2 0
0
0 6
. 2
. 0
. 2
. 0
. 5
. 0
E
0
2
5
0
0
5
0
5
0
0
0
•s
4
1
6
0
0
0
0
0
0
F
1
0
0
1
0
0
0
0
0
0
1
: _ S
515
102
1 0
0 4 .
_ 0 .
3 .
0 .
2
E + 0
E - 0
E + 0
E - 0
E + 0
E - 0
C
0
0
3
0
0
0
1
0
1
0
1
A - 8 2 F T
100010
0 9
00.100
0 0
4
076 0
+ 4.080
+ 6.000
+ 4 . 080
+ 6 . 000
+ 3.053
+ 6.000
2
2/1
101
9 . 0
. 1 0
. 4 0
. 0
. 0 5
0 E +
0 E -
0 E +
0 E -
3 E +
0 E -
0 0 0 A
0 2
4.00
6 3
04 + 6
05 + 2
04+6
05 + 2
02 + 4
05 + 2
3 4 5 6 7 B
CFM;CALCULATED V-I FOR_EACH_EIECTRICAL_SECTION
1000.0 5.1 1.03 0.0001651.0 1500000. l.OOE+09
0.50_ 0.60 _0.80 1.00 1.20 1.40 _ 1.80
6.0 10.0 20.0
0.2682 0.8652 2.9845 5.9695 9.5515 12.835 19.7004
.2500E-05 + 6.2500E+00 + 4.6875E-02 + 5.0000E + 00 + 5.0000E+00
.OOOOE-05+2. OOOOE-05 + 3. 8000E+04
.2500E-05 + 6.2500E + 00 + 4.6875E-02 + 5.0000E + 00 + 5.0000E+00
.OOOOE-05 + 2. OOOOE-05 + 3 .8000E + 04
.8853E + 00+7.6000E+01 + 1.0000E+00 + 1.8000E-05 + 4.1667E-01
.OOOOE-05 + 2. OOOOE-05 + 3. 8000E+04
-------
Example 3
This example used the same input data as Example 2 except
that the estimation procedure described in Volume I* of Revision
1 of the model report was employed. In this application of the
estimation procedure, an I-V curve is generated to yield the oper-
ating values of current and voltage. The input data card set used
in Revision 2 of the model is given in Table 6. The output data
from the calculation is given in Appendix K. Since the results
of the calculation using the estimation with this set of parameters
was not presented in Revision 1 of the model report, the input data
card set for this case is shown in Table 7. The corresponding
output data are shown in Appendix L. Figure 16 shows a comparison
of the fractional collection efficiencies from the two calculations
Once again there is good agreement between the two model calcula-
tions. A maximum difference in collection efficiency of three
percent occurs at a diameter of about 1.3 micrometers. The time
required by the DEC PDF 15/76 computer to perform the calculations
shown in Appendix K was 2,568 seconds. The corresponding time
required for the calculations shown in Appendix L was 10,019
seconds. These two times can be contrasted with those in Example
2 for which the more rigorous calculations took 5,175 seconds and
47,886 seconds, respectively. For a comparison of the estimation
procedure with the more rigorous calculation, one should use
Appendices L and J. However, it can be seen from Appendices K
and I that the approximations contained in Revision 2 of the
model give an adequate representation of the theory with a sub-
stantial savings in time of computation.
Example 4
In this example, the two versions of the model are compared
using parameters measured at a full-scale, cold-side precipitator
Predictions of the model were compared with the experimental mea-*
surements in the previous model report. The input data card set
is shown in Table 8. The output data for this calculation using
the approximate electrical solutions are shown in Appendix M.
The output data for the corresponding calculations using inte-
grated electrical solutions are shown in Appendix N. in these
two calculations measured values of current and voltage are used.
Figure 17 shows a comparison of the fractional collection effici-
encies for these two computations. The maximum difference in
computed efficiencies of 1.3 percent occurs for a diameter of
0.2 micrometers. The calculations shown in Appendix N required
6,181 seconds of computer time on the DEC POP 15/76 system. The
calculations shown in Appendix M required only 789 seconds on the
same system.
All the comparisons of collection efficiency made here used
the ideal cases. In the case of full-scale precipitators, these
predictions would not be expected to agree well with measurements.
For such cases, nonideal effects described in Revision 1 of the
model report would need to be taken into account. Some examples
were described in detail in Volume II3 of the previous model
94
-------
TABLE 6. INPUT DATA CARD SET FOR EXAMPLE 3 (REVISION 2)
COLUMN NUMBER
12345678901234567890123456789012345678901234567890123456789012345678901234567190
CADD
NUMBER
1 1601
2 LAB_ESPl_SCA-«2rT2/1000ACrH;CALCULATED_V-I_FOR_EACH_ELBCTRICAL_S*CTIO«
3 0201041515010001010102
4 0503
52002210102
« 0.065 10.0 »».0 1000.0 5.1 1.03 0.0001651.0 1500000. 1 . 0 0 E + 0 9
7 0.000.004.000.100.104.00
vo
y, 8 0.20 0.30 0.40 0.50 0.60 O.»0 1.00 1.20 1.40 1 . • A
9 2.20 3.0 4.0 6.0 10.0 20.0
10 0.0 0.0076 O.OS63__O.Z«82__0.86S2__2.984S__S.»693 9.5S13__12.835 19.7004
11 26.8643)_38.8042_4».2S16_64.1765_7».1014_100.0
12 03060612
11
14
15
16
17
It
1*
20
21
5 3 3 E 02
4 . 8 8 5 3 E 00 7.6000E 1 1
-------
(Ti
TABLE 7. INPUT DATA CARD SET FOR EXAMPLE 3 (REVISION 1!
COLUMN NUMBER
1 3 1 3 ' 5 5 7 T
12345676901234567890123456769012345676901234567890123456789012345678901234567890
CARE
NUMBER
1 1601
2 LAB_ESI>:_SCA-82FT2/1000ACFM;CALCUI,ATED_V-I_rOR_EACH_ELECTRICAI,_SECTION
3 0201021515010001010102
4 1020
5 2002210102
6 0.065__ * ° • ° _ „ 99. 0 1000.0__5.1 1.03____0. 0001651. 0_ 1500000. l.OOE+09
7 0.000.004.000.100.104.00
8 0.20 0.30 0.40 0.50 0.60 O.BC 1.00 1.20 1.40 l.BO
9 2.20 3.0 4.0 6.0 10.0 20.0
10 0.0 0.0076 0.0563 0.2662 0.8652 2.9845 5.9695 9.5515 12.B35 19.7004
11 26.8643_38.8042_49.2516_64.1765_79.1014_100.0
12 03060612
13 +6.2500E-*-00-t-4.0BOOE-t'04 + 6.2500E-05+6.2500E + 00 + 4.6875E-02 + 5.0000E + 00 + 5.0000E-t-00
14 + 2.SOOOE+00 + 3.0533E+02+4.8853E + 00+7.6000E + 01 + 1.0000E+00 + 1.8000E — 05 + 4 1667F n 1
15 + 9.0000E-01 + 6.000CE-05<-2.0000E-05+i.OOOOE-05<-3. BOOOE + 04
16 + 6.2500E+00-*-4.0800E + 04 + 6.2500E-05-*6.250CE + 00 + 4.6875£-02 + 5.0000E-+00*5.000GE-+00
17 + 2.SOOOE + 00 + 3.0533E + 02+4.8B53E + 00 + 7.6000E + 01 + 1.0000E + 00 + 1.8000E-05 + 4.1667E — 01
IB *9.0000E-01 + 6.0000E-05»2.0000E-05 + 2.0000E-05»3.8000E+04
19 +1.2500E + 01 + 3,9600E+04 + 1,2500E-04 + 1.2500E+01 + 4.6875E— 02 + 5.0000E + 00 + 1.0000E+01
20 +2.5000E+00+3.0533E+02+4,B853E+00+7.6000E+01+1.0000E*00+1.8000E—05+4.1667E-01
21 »9.0000E-01 + 6.QOOOE-OS»2.0000E-05»2.0000E-OS->3.BOOOE«04
-------
99.9
IEORETICAL (REVISION I, USING EFLD1)
THEORETICAL (REVISION II, USING EFL03)
50.0
10.0
GEOMETRIC MEAN DIAMETER,
Figure 16. Comparison of fractional collection efficiencies computed from
Revision I of the model using the estimation procedure and the
parameters in example 2 with the corresponding calculations in
Revision II using the approximations.
97
-------
TABLE 8. INPUT DATA CARD SET FOR EXAMPLE 4
00
CARD
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
1
0
0
1
0
0
1
0
1
0
+
+
+
+
+
+
2 3
4 0
1 0
S 0
. 9
. 0
. 1
0 .
. 0
5 .
3 1
2 .
3 .
2 .
3 -
2 .
3 .
456789
1
103101
3
6 6 2
00.003
0 0
1 0 1
0
6 38 2
01010
6 4 6 0 E +
6 2 5 0 E *
6 4 6 0 E +
6 2 5 0 E +
6 4 6 0 E +
6 2 5 0 E +
I
01234
00300
7 . 0
.000.
. 3 0
4 . 9 0
. 0 3 3
0.484
044-4.
00+3.
04 + 4.
00 + 3.
04 + 4.
00+3.
567
D ~ S
010
9
100
0
2
0
3
060
272
2 1 0
272
245
272
j 5 4 5 5 T— r
B90123456789012345678901234567890123456789012345678901234567890
IDE ESP: PLANT Aj SCA3243FT2/10QOACFM;J"15»°UA/tT^
10102
9.6 2270.0 100.0 1.2 0.00022 1.0 1500000. 5. OOE+10
.253.00
.50 0.90 1.30 1.90 3.10 3.90 5.10 6.90
5.10 29.90
.286 1.189 2.004 3.524 7.048 8.70 10.352 12.334
2. 599 100. 0
OE + 04 + 2.7300E-01+1.5720E + 04 + 8.2500E-02 + 5.5000E + 00 + 1.2000E+01
4E+05 + 4.1000E+00+3.1500E + 02 + 1.0000E+00 + 2.290'OE-05 + 9.0000E-01
Q E + 0 4 + 4 .3300E—Q1 + 1. 572QE + 04 + 8. 2500E—02 + 5 .5 OOOE + 00 + 1 .2000E + 01
4E+05 + 4. 1000E+DO+3. 1500E+02 + 1 . OOOOE + 00 + 2 .2900E-05+9 . OOOOE-01
OE+04+5.5800E-01+1.5'720E + 04 + 8.2500E-02 + 5.5000E+00 + 1.2000E + 01
4E+05 + 4.1000E+00+3.1500E + 02 + 1.0000E + 00 + 2.2900E-05 + 9. OOOOE-01
-------
-
THEORETICAL (REVISION I, USING EFLD 2)1
THEORETICAL (REVISION II, USING EFLD3)
10.0
GEOMETRIC MEAN DIAMETER, /im
Figure 17. Comparison of fractional collection efficiencies computed from
Revision I of the model using measured electrical conditions from
a full-scale, cold-side precipitator with those computed from
Revision II of the model using the approximations.
-------
report. The purpose of the comparisons made here is to establish
that the modifications to the model described in this report do
not significantly alter the predictions made by 'the model. Since
the modifications lead to significant savings in computer time
without changing the final results appreciably their use is
justified.
100
-------
REFERENCES
1. Gooch, J. P., J. R. McDonald, and S. Oglesby, Jr. A Mathe-
matical Model of Electrostatic Precipitation. EPA-650/2-75-
037, U.S. Environmental Protection Agency, Raleigh Durham,
North Carolina, 1975.
2. McDonald, J. R. A Mathematical Model of Electrostatic Pre-
cipitation (Revision 1): Volume I. Modeling and Programming,
EPA-600/7-78-llla, NTIS No. PB284-614, June 1978.
3. McDonald, J. R. A Mathematical Model of Electrostatic Pre-
cipitation (Revision 1): Volume II. User Manual, EPA-600/
7-78-lllb, NTIS No. PB284-615, June 1978.
4. McDonald, J. R., M. H. Anderson, R. B. Mosley, and L. E.
Sparks. Charge Measurements on Individual Particles Exiting
Laboratory Precipitators. Presented at the EPA Symposium on
the Transfer and Utilization of Particulate Control Technology,
Denver, Colorado, Paper A7-1, July 23-26, 1979.
5. Cooperman, P. The Dependence of the Electrical Characteristics
of Duct Precipitators on Their Geometry. Unpublished Report,
Research Corp., 1952.
6. Peek, F., Jr. Dielectric Phenomena in High Voltage Engineering
(University Microfilms International, Ann Arbor, Michigan,
1959), p. 73.
7. White, H. J. Industrial Electrostatic Precipitation. Addison-
Wesley, Reading, Massachusetts, 1963. p. 73.
8. Penney, G. W., and R. E. Matick. Potentials in D-C Corona
Fields. Trans. AIEE, 79:91-99, 1960.
9. Loeb, L. B. Electrical Coronas: Their Basic Physical Mechanism.
University of California Press, Berkeley, California, 1965.
p. 46.
10. White, H. J. Reference 7, p. 91.
11. McDonald, J. R., W. B. Smith, H. W. Spencer, and L. E. Sparks.
A Mathematical Model for Calculating Electrical Conditions in
Wire-Duct Electrostatic Precipitation Devices. J. Appl. Phys.,
48(6):2231-2246, 1977.
101
-------
12. Leutert, G., and B. B8hlen. The Spatial Trend of Electric
Field Strength and Space Charge Density in Plate-Type
Electrostatic Precipitators. Staub, 32(7):27, 1972.
13. Joslin, T., and D. Fletcher. The Digital Simulation of
Electrode Processes: Procedures for Conserving Computer
Time. J. Electroanal. Chem., 49:171-186, 1974.
14. DeMari, A. An Accurate Numerical One-Dimensional Solution
of the P-N Junction Under Arbitrary Transient Conditions.
Solid-State Electronics, 11:1021-1053, 1968.
15. Brumleve, T. R., and R. P. Buck. Numerical Solution of the
Nernst-Planck and Poisson Equation System with Applications
to Membrane Electrochemistry and Solid State Physics. J.
Electroanal. Chem., 90:1-31, 1978.
16. McAfee, L. C., Jr. Optimized Numerical Models for Semi-
conductor Devices: Part I. IEEE Trans. Electron Devices,
ED-23(4):442-446, 1976.
17. McAfee, L. C., Jr. Optimized Numerical Models for Semi-
conductor Devices: Part II. IEEE Trans. Electron Devices,
ED-23(4):447-452, 1976.
18. Franceschetti, D. R. and J. R. Macdonald. Numerical Analysis
of Electrical Response: Statics and Dynamics of Space-
Charge Regions at Blocking Electrodes. J. Appl. Phys.,
50(1):291-302, 1978.
19. Conte, S. D. Elementary Numerical Analysis. McGraw-Hill
Book Company, New York, New York, 1965. p. 138.
102
-------
APPENDIX A
LISTING OF EFLD3
103
-------
001 SUBROUTINE EFL03 (UEO.«C. VO.SK.8r,MX,NV.*EPLT.TOK.P.«r.
002 l5T»PT.D3T*«T.C3T*RT.lFlN*L.V9T«l»T,VH,ACONTY,Ml«rRE.NECtEBO,JM.JI?>
ooi r EVALUATION nr FIELDS, SPACE CMA»GF DENSITY, POTENT^! , AMD
004 C CUftBENT flFNSlTY FOR A WIPE-PLATE PRECIPITATOR
DOS PEAL M*lRE.MAXS,Mn8ILT(15,15)
006 LOGICAL LTE3T
007 DIMENSION »HOn5.15).EXM5.15).OLDRO(lS,|3>,OLDV(l5,15).
OOfl lCr>NSTYnS,15),V(}5.15).EY(!5.1S).EAVG3(30),CNFIDS(SO).ecOUSC30)
004 COMMON/BlK»/EAVGf30).eHFIOf30)
010 COM'10N/9LK«»/ECOIL(30)
Olt COMMON /BU'*0>./,OLOV/225*0./,CONSTy/a?5*0./.»S«F-12
030 SSTARTitSTART
031 '
032
031
035 TVCKen
036 PC«AT
037 rn 100! 1I«1.1FINAL
03« IFf IT.FO.JTl)
039 IFni.Cf.JI2) STAPT«C8TART
0«0
o«i
0«2
043
044
04«5 Pl» = SQRTf ABSfBI))
046 C1»B)*SV/P1
oar PI«R*SX
049
050
051 Fist'.
052 F2»0'.
053 FJ»0.
054 FJ»0'.
055 F2«0'.
056
057
059 ^0 3*01
060
104
-------
06? SIGl«STCl+CH/(CH*CM-COSf*l*»C)*C08(*l**C))
063
060 3601 CONTINUE
06S '
066
067 SU»M«2.*SUv»l*AlOeCABS(Cl.-COSfAl*AC)>/fr.+COS(Al*ACn))
06* IMR1.GT'.SX)R1«3X
060 8QON«Ri*Rl»4.*8X*(SX-«l)
07» SQOP*Rl*RIt4.*8X*(8X+Pl)
OTt
07S ARGPiPT«Rl/SX/2.
074 FACl«l'.
075 IF(R1'.LE.5Y) CO TO 60
076 CAIL APCCnS(SY.R1,ACOS)
077
078
07» ICOU'JTBO
oeo o(i CONTINUE
061
088
06S
060
005
066
OR7
088 Cl AM«FPRn*SX*STN(Pl#Rl/?'./8X)*r?.+Rl*(2.*JX.Rn/(Rl*Rt
'
090 2 »f*»AP|-l.)
091 WLA1»CI A**FAM
09? VMAUTsCUAM*ALOG(AB8C(l.-C08fAl*Rl))/(l'.*C08(Al*Rl)l))
09) 1 •2.*Rt»*(SX-R1)*SaRT(AB*(8x»R1))/3.
09A VT = VW4HT-tORO*fPARl«l . + f R*D»1 . 1 * A|.OC(R t /AC ) 4»AO*ALOG f (RADtt . ) /
099 1
096
097 IF(MViT.Ftv'.l)GO Tn 10
09fl BO TO ^n
090 jo COMTTS"E
100 rsVT-VO
101 ir(F'.F.O.O.)GO TO 30
10? ir(AHSfP).LT.r.OE-0«*»»S(VO)) so TO 30
105
10« IF(F'.LT.O.)Ft«F
105 '
107 IFfF'.r,T.0.5E2sFORn
108
110 ICOUHTaICOUNT+1
111 IFdCOUNT.rO.lOOlWRITEl-NPRNT. 51)
112 5! FpPMATf lOX.'THF 4PPUUO POTENTIAL COOUD NOT HE MATCHED IN
115 1 '100 ITERATIONS'/)
114 irntouNT.r,T.ioo)Go TO 30
115 CO TO 60
116 5
117 V(1,1
11» CALU
120 DO 310A 111»1,NX
105
-------
121
122 Y»0.
125 DO 3800 TI2el,NY
12H IFft.TE8T)X«Ximi)
125 TFeLTE3T)YsYl(tl?)
126 IFfNVIt'.CQ'.nXMX
127 XKIHJsX
12S Yi(I12lBY
12Q 81»2.*ACONTY/EP80/M09lLT(Ill.n2>
UO R1PaSORT(ABS(Hi M
131 Clsfll*SY/PI
132 IF((IH.FQ'.11.ANn.(I12'.EQ.l))X«tC
133
13a
135
136
13T *PGX«PI*X/8X/2l
13« *R6Y»PT*V/8X/2.
139 P*XV«Snt?T(»BS(l .
100 PA9XYaS(?RT(Aasn,
141 RAPlYaSOBTf AflSfl.*C1 *(R1«P1+V*Y-AC*AC)/EORO/EORO))
COSHYaro9H{Al*Y)
SINHYaSINH(Al*V)
CX»C"S(A1*X)
IFfX.GT. 1,00001 *R1) 60 TO 3*6"
U6 VxYJ«.FoRO*(RARlY.RAXY*(R*n.l.)**L06(SORT(AB8((Rl*B|+Y*Yl/
108 ?
1«» f XJ».Enpn*((RAXY.|'.)»X/(X«XtV*V)-(RARl -.!.)*( (X.2'.*SX)/80XM
150 1 +fX»2.*9X)/SOXP>/2.)
151 FVJs.pnPO*f (R»XY «l.)*Y/CX*X*Y*Y)-(RAim-f.J*Y/(«»l*Rl+Y*Y)
152 1 -(PAP1 -l.)»tY/SOXN+Y/80XP-Y/SQ«»N.Y/80RP)/2.)
153 RHnjs.FP80*CJ/EORO/RAXY
'
155 > .FPSO*En«0*(RAXV-t.)/2.«(fSOON.Y*Y)/80RN/80RN*(800l»-Y»V)/
156 3 80t»P/SORP)*0.9
157 GO TO 3B61
15A 38feC CnwTlMHF
159 VXYJ«ri AH*ALOG(AR8f (f.OSHY-CX) /(f COSHYtCX) ) )
161 FXJs-Cl »^*pI*8TNtAl*X)«C08Hy/3x/(COSMV*cr8HY-CX*CX)
162 1 -Bl"*SnPTf A«S(X-R1 ))
161 FvJ=.riA**PI*CX*3INHY/SX/(CoSHY*C03HY.CX*CX)
'
165 1 *./fl
166 3*61 CONTINUE
167 SUMVBO'.
16* SUMEX»o.
169
170
171
172
173
17« C08HNaCCi3HfP!*fY-2i*Rl*8YJ/2' /8X)
175
176
177
i ?«
179
180
106
-------
181
162
163
184
IBS
166 SU^EYsSUMEY+TEREY
167 100 CONTINUE
168
189
190
191 VXYJavXYJ + VWTP.
192 FxJaFxJJFXWIR
193 FYjaFYJ+CYWIR
195
196
197 RHOf Tll.t 12)aRHOJ
198
199
20fl
201
202 3100
203 5150 CONTTNMF
20« VrteVCl.l
205 PPLTsfl'.
aob no
207
TFf .^nT.LTFSTj EPLT
210 1200 CONTTNi'F
211
212 IFfNVlI.FQ.ai».RITEfNPRNT.B88l>) V«, ACONTY, »EPLT
211 flan* FORM»Tf3«X,»V« a '.1PFH .U.?X»'*CONTY • '. 1P€1 1 .a. 2X. '»FP|.T • ',JP
21 « IF t !.«//)
215 IF(APSfFX(MX,l))'.LT.EHDj GH TO 1«80
216 wRTTV(MPBNT,laftn VW,*CnNTY
217 t«*i Fop^ATt* THE R»EAKDOWM FIELD NMH THE PLATE is r.xcEF-oEn AT VN «»,E
^IP iii'.y.ix.'AMo ACPNTY «».FU'.«)
219 UP TO 1«??S
220 i"«o rnMTM'ip.
?21 IF{IVC".f1J.ll 60 TO 1S2S
222 TFf ARSfVW),EO,AB8(VQ)) GO Tn IS25
22! IF(A"SfVW).CT.*P3CVO)) GO TO H23
2?U PL
225 P(
227 1523
228
229
230 IVCKr|
231 f,o TO 1526
232 152« rONTIHUf
235 1101
235 IFCM»'C'.NF.O) GO TO 300"
336 K«l
237 no 3001 J«»,NYI
238 PSHH»O'.
239 tSllnao'.
240 no 3«0? I
107
-------
241 IF(J.FO.I) GO TO 3005
242
243 lEY(l.J+n**2))/(2.*NX)
244 GO TO 3006
?45 3005
246
?47 IFd'.FO.NX)
248 3006
249
250 3002
251
252
253
25« 3001
255
256 00 3003 L"1,NY1
257 fcAVGCLUFAVGSfNYY)
258 CHFIO(L)=CHFIDS{NYY)
259 NYY«NYV«I
260 3^03 CONTINUE
261
262
263
264 DO 3004
265
266
267
268 S000 3007 NN«1,.MY1
272 ECHLLSr
273 U«U+1
?74 3"o7
275
276 r»0 3008 L«1,NY1
277
27*
279
280 L?=l
281
282
283 DO 3009 1=11.12
284 ECOLl m
285 L2«L2+1
286 3009 CONTINUE
287
28ft STARTeSSTART
289
290
PROG > 4K
108
-------
APPENDIX B
LISTING OF CMAN
109
-------
001 SUBROUTINE CHAN fVW.NX,NY.SX.3V,PI.AC,NHIRE)
002 C COOPERHAN SERIES OETFRMfNATION FOR VOLTAGE MIRE TO PLATE
003 C FOR SUBROUTINE lflU.fi
004 REAL NIIM.M.NWIRE
OOS LOGICAL LTE6T
006 COMMON /8LK13/VCOOPM!I»15).NVIT
00? COM*ON/BLK21/ECXfl5.1S),eCYfl5.15),Xl(15l,Yl(l5>.AX<15).AYM5)
000 COMMON /BLK22/ LTEST.RHOfIS,151. V(15,15) .CXCIS.15) .EY(is. 151
004 NX1»NX-1
010 NY1«NV-1
Oil DO 402 t«l.NX
012 IFfNVII.l)301,300,301
013 300 I»NX
01« 301 CONTINUF
015 00 430 J«1.NY
OU X«FLOAT(I-l)*SX/FLOAT(NXl)
01T IFfLTF9T)X«Xl(I)
018 Y«FLOAT(J-1)*SY/FLOAT(NY1)
01«» IFfLTEST)Y«Yl(j»)
020 IF(X'.EO.O.'.AND.Y.EO.O.)CO TO 440
021 SO TO flSO
022 440 VCOOP(I,J)"VH
023 60 TO 030
024 450 CONTINUE
025 M..NWJRE
026 NUHcO.O
027 DENOMsO.O
026 EXO«0.
02« EYO«0.
030 EXSUM.o,.
031 EYSUM.C.
032 4«»0 El«Pt*(Y-»(2.*M*8Y))/(».*3X)
033 Fl«Pl*X/f2.*3X)
034 Gl»PI*H*SY/SX
035
036
03T
038 C2«(EXP(Gl)+EXP(.GlJ)/2.
039 H?«COS(H1)
040 TT«(E2-F2)/(E2*F?)
041
0(12 F«ALOr,(TT)
043 6vAL06(TB)
044
045
046
047
048
049 G3«tfXP(Gn»EXP(.6t))/2.
050
051
052
053
05tt
055
056 EXO*ExO+Sl
057 EYO«EYO+32
058 IFTM.LT.NWIRE) GO TO a08
059 GO TO 410
060 408 M«M»!.0
110
-------
061 GO TO 090
062 410 VCOOP(I,
063 ECX(I,J)«-(PI*VW/2',/SX/DENOM)*FXSUM
064 PCY(I.J)
065 430 CONTINUE
066 40a CONTINUE:
067 «0« CONTINUE
068 ECXU(i)
060 ECY(1.1)«-(PI*VW/2./8X/OENOM)*FYO
070 RETURN
071 END
111
-------
APPENDIX C
LISTING OF EFLD4
112
-------
SUBROUTINE EFL04 [UtO, AC.VO, SX.SY, NX.NY.AEPLT.TDK.P.RF.
lSTART,OST*RT.C8TART,IFlNAL.VSTART.V»l,MtDNTY,NKIRe,NEC,EBD.JIl,,Il2)
C EVALUATION OF FIELDS, SPACE CHARGE DENSITY. POTENTIAL . AND
C CURRENT DENSITY FOR A HIRE-PLATE PRSCIPITATOH
REAL NWIRE.MAXS.MOBILTfU.lS)
LOGICAL LTEST
DIMENSION RHO,OLOVflSf15).
ieDN8TYet5.i51.V{lS,l5).EYllS,iS).EAVG3C30).CHFIDS(30),EeOLLSC30)
COMMON/BLK8/EAVG(30),CHFID,YH15).AX(l5),AY(15)
COMMON /BL*22/ LTEST, RHO,V. EX. fY
DATA OLDRO/22S*0./.OLDV/225*0./.CDN3TY/22S*0./.MQBILT/ /FLOAT (NXS)
AY1»(SY-RC1/FLOAT(NY2)
113
-------
BX»2J*(SX-2.*RC)/RC/FIOAT(NX3)/FLOAT(NX2)
BY«2.*(SV-RC)/RC/FLOAT(NY2)/FLOAT(NYn
00 2000 I«!.NX
AX(I)"RI*BX*RC
AX(1)»RC
AXU)«AC
AX{NX)»AX(NXl)
IF(I.EQ,»SO TO 2000
2000 CONTINUE
DO 2001 J«1,NY
AY(J)»RJ*BY*RC
AYU)"RC
AY(1)»AC
AY(NX)«AY(NX1)
ipcj.eo.noo TO 2001
Yl(J)»Yl(J»lUAVfJ"l)
2001 CONTINUE
VAsABS(VO)
VliABS(VlK)
IFINA1«1
.,
18TART,D8TART.CiTART,IFiNAl.V»TART,Vl.AeDNTY,NWIRE,MCC,CBO.JIl,Jl2)
3555 FoiJAT(lHl!lOX?'ELECTR08TATlC SOLUTION AT CURRENT ONSET*//)
CALL ENTER2(NX.MY)
DO 1001 JXMiXFiNAL ^mmtmw
XF(Xi;toJjXl> 8TART-D8TART
IF(Il'6E.JI2) START-C8TART
MAXS"HAX848TART
ACDNTV'HAXS
152* CONTINUE
1/ROC)))
VA»AB3(VO)
Vl'ABS(VW)
.
CALL EFLD3(UEQ.AC»VA,8X,8Y.NX,NY.ArpLT.TDK.(»,RF,
18TART,D8TART.CSTART,IFINA1,V8TART,V1,ACONTY,NWIRE,NEC,EBD,JI1,JI2)
W*ITE(NPRNT,!560) ACDNTY
3560 FORMATdHJ.lOX.^ApPROXIMATE SOLUTION FOR CURRENT DENSITY OF •
1 l'El2t3,2X,'AMP8 PER SQUARE METERV/)
CALL OUTPUT(NX.NY)
WRITE (NPRNT, 8888) V(|, 1) .ACDNTY,
60 TO 1001
Z>0
2 CONTINUE
Fl»0.
F2«0.
Vl«0,
V2»0.
V3»0.
114
-------
1 Z»Z+l
IZ»Z
IF(IZ.EQ.NITER) WRlTECNPRNT,1865) NITER
1865 FORMATflX,' CONVERGENCE ON CURRENT DENSITY CAN NOT BE OBTAINED IN'
1 , 16,' ITERATIONS')
IPCIZ.EQ.NITER) 60 TO 700
300 LL»LL+1
00 315 I«l.NXl
00 315 JBI.NY
OLOV(I,J)sV(ItJ)
OLORO(I, J)«RHOfI,J)
S15 CONTINUE
RHO(1,2)«OZERO
00 301 I«1.NX
DO 301 JM.NV
IF(I.EO.l) GO TO »00
IFfI.EQ.NX3 60 TO 006
AXS«AX(I»})*AX(I)
AXS2«AX(I)*4X(I}
60 TO 801
606 CONTINUE
AXS«AX(I-l)*AXtI-n
AXSUMBAxn-l)+AX(I-l>
AXSl*AXS
AXS2«AXS
60 TO 801
800 CONTINUE
AXSMAX(I)*AX(I)
AXSUM«AXri)+AXri)
AXSl«AX(l)*AX(l)
AX82«AX(l)*AX(n
801 CONTINUE
!F(J,EQ.l) 60 TO 802
IF(J.EO.Ny) 00 TO 803
AYS«AY(J-n*Ay(J>
AYSUMKAY(J«1)^AY(J)
AY81«AYtJ-l)*AY(J-l)
AYS2«AY(J)*AY(J)
60 TO 60tt
002 CONTINUE
AYS«AY(J)*AY(J)
AYSUM«AYtJ)+Ay(J)
AY91«AY(l)*AYj;i)
AYS2«AY(l)*AY(n
GO TO SOU
803 CONTINUE
AYSi«AY{NY-n*»Y(NY»l)
AY82sAY(NY-l)«AY(NY«l)
804 CONTINUE
ASPm(AXS*AYS)/EP80
ASSal./(2.*(AX3+AY8))
IFCd.EQ.l'.AND'.j'.LE.Zj'.OR.fj'.rO.l.ANO.I.LE.Z)) 60 TO 301
115
-------
IF(I,EO.l'.AND'.J.N*.l) 00 TO S04
iriI.E9.NX) 60 TO 140
IFCi;Ni;r.«ND'.J.CQ.I) 60 TO SOS
IF(J.EO.NY) 60 TO 600
00 TO 506
600 V(X,NY>«A88*/AXSU»H
12.*AX8*Vei,NY.U*A8P*RMOtItNY))
EX(I,NY)«-(VfJtl»NY)*AX(I«n*AXn»l>.VfI.l.NY)*AX*EXAV«AX(l)*FYfI,J)*
2M08XLT(I.J«l))/2./AX(l)/AYtJ»l)/MOBILT(rifJ)
BETA«»Cl»80*(AY(J-l)*EX(I.J)*RHO(l,J)+AXfl)*EY(I,J)*RHO(I.J-n)
1 /AX(l)/AY(J.l)
60 TO 302
350 vei,NV)BAS8*(2.«AVS*VC2,NY)*2.*AXS*Vfl.NY-l)+ASPftRHOCl(MY))
EK(l,NY)«0,
60 TO 301
SOS VCI,l}«A88*«2.*AY8*UX*V(I-l,l))>/»XSUM*2.*
1 < AX(J- J >«AX(I-1)»AX(I)*AX (!)))/( AX CI-n+AXCJ)>/AX(I«l)/AX< I)
, .
ALPHA*EP80*(2.*AYCl)*EX(!,J)«MOB!I.T(!|lJ)+2.*AX(I.»l)*EY(I.,n*
lM08!LT(IiJ)-AV(l)*eX(I.J)*MOBXLT(I»l«J)»AX(I«l)*EY(I»J)*
{HOBILTdf i))/2'v/AX(I»n/AV(i)/HOBILT)[I.J)
60 TO '02
506
ltAX(I-l)*AX{I.lJ-AX(I)*AX(I)))/fAX(I«l)*AX(I))/AX(I«l)/AXfl)
EY(I.J)*«(V(!.J*l)tkAY(Ji>l)«AY(J-l)*V(l.J«i)*AY(J)«AY(J).V(IfJ)*
l(AY(J-t)«AY(J..l)»AY(J>*AY(J)))/CAY(J»lJ*AY(J))/AY(J-i)/AY(J)
ALPHA«EP80*(2'.*AY(J»l)*EX(I(J)*MOBILT(t»J)«2.*AX(l»l)*EY(l.J)*
JM08ILT(I,J)-AY(J-n*EX(I,J)*M0BILT(I.l.J).AX(I.l)*IY(I,J).
60 TO S02
340 CONTINUE
V(NX«J)«0.,
EX (NX, J)«VfNXl.J)/AX(NXn
ALPHABCP80*(2'.«AY(J«!)*EX(I,J)»AY(J.1)*EX(X|J)»HOBXLT(I.1(J)/
116
-------
I HOBILT8Y
C ****************************************************
IF(ACDNTY.LT'.1.0E-08) GO TO 980
C ****************************************************
1000 CONTINUE
FBACDNTY-MAXS
IF(TEST.LT.TFSTl) GO TO 9«0
V3BV(2»n«COEF*V(2.l)*F/ABS(n
IF(F'.EO.O.)GO TO 980
IF(F'.GT.O,)F2«F
IFfF.GT.O.)V2»V(2,n
IF(Fl*F2.LT.O.)V3»(Vl*f2»V2*Fl)/(F2-Fl)
WRITE (NPRNT, 3710) F, V(2, 1) . ACDNTY.fLL.IT
3710 FORMAT(10X<'F«ifEll.3,5X.»V(2,n»,EH.3
I EU.3.5X.»U«',I5.5X,*IZn',I5)
V(2.1)«V3
ARG«AB8(2.*(V2»V1)/(V2*V1))
FUNBAB8(1,«ACDLST/ACDNTY)
IF(ARG.LT.1.0E-0«.ANO.FUN.LT.5.0r»02)GQ TO 2
ACDLST»ACDNTY
GO TO 1
960 CONTINUE
V(l,2)*V(2il)
VH>V(2.1)+EO*(RC»AC)
EPLT«0.
DO 1200 J*2,NY
1200 CONTINUE
AEPLT.EPLT/SY
700 CONTINUE
WRITE (NPRNT.3S65) ACDNTY
117
-------
3565 FORMATUHl.lOX. 'NUMERICALLY INTEGRATED SOLUTION FOR CURRENT DEN8IT
iY 0FMPE12.3.2X.'AMP8 PER SQUARE METER'//)
CALL OUTPUT(NX.NY)
WRITE (NPRNT. 8888), V«, ACDNTY, AEPLT
6866 FORMAT(36X,'VW • MPEt l'.4»2X, 'ACONTY • ', IPEll ,4,2X, 'AgPLT * • IP
IEU.4//)
WRITE(NPRNTf3720) LL,IZ
3720 FORMAT (1 OX. 'LL"', I5,5X. »IZ«', 15)
IF
-------
KKBKK+1
3004 CONTINUE
3000 CONTINUE
DO 3007 NN«t.NYl
. LL-U + 1
3007 CONTINUE
L1»NY1
DO 3008 1*1. NY1
ECOLl(t)«ECOLLSan
LlsUl-1
3006 CONTINUE
I2*2*NYl
DO 3009 Isll.i?
ECOLLfI)«ECOLL8(L2)
3009 CONTINUE
VO«»1.*VO
STARTsSSTART
END
119
-------
APPENDIX D
LISTING OF OUTPUT
120
-------
SUBROUTINE OUTPUT(NX,NY»
DIMENSION RHO(t5*15),EX(15.15).OLOI)Ori5.15),OlDV(15,15),
ieDNSTY(l5,15).V{l5.15).EY(15.l5).EAVGSfJO).CHFIDS<3D),ECOU8C30)
CO*MON/RU*/EAVG(30),CHPID<30)
COMMON/BIK9/ECOU (30)
COMMON /BLK13/VCOOPC15.1S).NVII
COMMON /BUZ?/ LTEST.RMO.V.EX.EY
COMMON/BU17/NREAD.NPRNT
COMMON /BLK20X R jlVAR.UCMAN .EORO.EPSO.H.LINTE6,FACtNHALF,NVITER
I. NITER. VCK.IPOT,COEF.TEaCFtRELO,FAC2.VCOR,ECOR
NPRNT.6
NPRNT»3
N2«fNY«J)/9
10 FOBMATdttX, »(*Y(».iat*)*i»X))
it FORMAT(9X.9(|PE13,3)//>
DO 292 I«1.NX
WRITE(NPRNT,30)
1 I.(RHO(If J).
30 FORMATCaX.'Xf'.IZ.^'^ElS'.B^X^Fls'.S/SX.Fb.*. 9E13.5/9X.
1 9E13.5/J
292 CONTINUE
WRITF(NPRNT.850) (CONST Y (NX. J) . J«i.9)
SSO FOPMAT(3X,9E13.5)
15 FORMATf/HX, 9f *Y { •, 12. *J
WRITE (NPRNT, 11) (Yl (J) , J«NJ,NY.N2)
00 J93 I«1,NX
WR1TE(NPRNT,30)I.(RHO(I, J).J«Nl,NY.N2J.(V(I,J),J«Nl,NV.N2).XltI).
1 (EX(I,J).J«NliNY,M2).(EYtI.JJ,J»Nl.NY.N2)
293 CONTINUE
WRITE (NPRNT. 650) (CONSTY(NX,J)iJ»Nl,NY.N2)
RETURN
ENTRY CNTER2fNX,NY)
WRITE(NP»NT,15) CJ.J«1.9)
WRITE(NPRNT,11) (YHJ),J«1,9)
DO 3510 I«l, NX
3510 MRlTE(NPRNTl3550)I((VCOOP(I,J).jBl.9),fECX(I,J),J«l,«),XlrI)»
( J, J«N1.NY.N2)
WRITE (NPRMT.lt) (Y1(J),J«N1,NY.N2)
DO 3520 IBI.NX
3520 MRI TE(NPRNT, 3550)1 f(VCOOP (I. J).J»Nl,NY.N2>,(ECXU,J)(JaNl,NY,N?),
1 Xl(I).(ECY(l,J)(jBNltNY.N2)
3550 FORMAT(«X,'Xr.I8,')»,9F!3:0/9X,9Ei3'.3/3X,Ffc.*, 9E13.3/)
RETURN
END
121
-------
APPENDIX E
LISTING OF RATE
122
-------
001 FUNCTION RATE 7011.7011,7019
OH 7015 CONTINUE
014 60 TO 7007
015 7006 THZERO«O.
016 7007 YFUC«0*.0
017 DO 7002 I»l»3
Oil THETA«T(I)*(PI-2'.*THZERO)/4.«(l»I*2.*THZERO)/4.
019 CTHETA>C08(THETA)
020 TCON8T«CON8T*CTHeTA
021 ECOSBEZERO*CTHETA
022 Cl>-NE/(CHK8*CC08)
023 CO«TCON8T/(2.*ECOS)
024 CALL zfRO(ci>co,RZERO)
025 AR6lBr(NUMBER*V*(RZERO-R8IZC)/RZERO«(eCON8T-RR*RZeRO«FeoN8T/RZFRO*
026 1*2)»CTHETA1
027 IF(AB|'(AR6i).6T.30.0) 60 TO 7025
028 VVAL«EXP(ARG1)*3TN(THETA)
029 60 TO 7026
030 7025 VVAL«o'.
031 7026 CONTINUE
032 YFUC»YFUC*A(I)*YVAL
033 7002 CONTINUE
034 RATEl«e»»I-2.«THZfRO)/«.*VFUC*FACTOR*AFID
035 60 TO 7012
036 7011 RATE1«0'.
037 7018 CONTINUE
038 AR63»-V*NUMBER
039 !F(AB8(ARG3).6T.30.0) 60 TO 7031
040 RATE2»FiCTOB*EXPf»R63)*»FIO
041 GO TO 7032
042 7031 RATE2«0.
043 7032 CONTINUE
044 IF (NUMBER-8CHARO7008. 7009,7009
045 7008 A*TEl«COEPF*(l'.-NUMBER/8CHAR6)**2*AFID
046 60 TO 7010
047 7009 RATE3«0'.
040 7010 CONTINUE
049 DATEBRATE1+RATE2+RATE3
osb RETURN
OS1 END
123
-------
APPENDIX F
COMPLETE LISTING OP THE COMPUTER PROGRAM
124
-------
•ft****************************************************
E.P.A'.-SO.R.I. ESP NoofL
THIS PRnGRA* 18 RESIGNED TO CO*Pim PERFORMANCE
OF A WTRF-PLATE PRFCIPITATOR HSINC DESIGN AND
ooi c
002 r
003 r.
oo* c
oos c
006 C
DOT C
00* C
009 C
01« C
OH C
012 C
013 C »*«***»*»*»****••*•*•*******»••*****•**»*••••••••••••»»
01« C
015. C
016 "ML Nm»E,LTHICK.JP»»T.,)loN,l INC.N»S.LINGS
017 JHTECEP VISKIP.VISAMF
OPERATINR PARAMETERS. THE PROGRAM MAS DEVELOPED BY
PERSONNEI OF THE SOUTHERN RESEARCH INSTITUTE FOR
OR. LES SPARKS OF THE PARTICULATE TECHNOLOGY
BRANCH. INDUSTRIAL ENVIRONMENTAL RESEARCH LAB.
ENVIRONMFNTAL PROTFCTION AGENCY, PROJECT OFFICER,
REVISION 2. AtlG*., 1974
01" COMMfiN/Rl K(/DlAMf?0).nNn(20).CX8(20),XMVf20),PCNT(20),RAO(20),
020
822 COM>inN/ft|.KJ/VG.ATOT*|. ,r>fi.f T»r,PL.PL."HO
025 CQ*fnM/Hl K«/NS
02« rnMMnn/pLKS/ZMHOI.SIGMl.NnNlD.NRAPn.TOK.
02S CPMMOH/BI.Kh/VOL (?0) ,X»jn(201 ,0f?0) .WSI20) . ITL (40) .n><(«5) . AS( 1») .
026 lVn8(10).TCS(in),WLS(in).ACS(101,BS(10).SYS(10).VG$rtO).VSA8S(ln).
027 2TjMP5(lo),VISSno).Q8iTf2o5.ll»E.FP80.PI,rRAVG,ec.TEHP,FPS.V»VC.
028 JPLOn(2nj.OLO>NO(?0).PFS(10),8TARTl(10),START2{101.STARTl(101.
OJfl
OSl
032
033
03»
035
036 COMMON /BLK13/VCnOP(15.15J.NVIT
037
040 PWT.LTHIC^t JP*BT».TIOK'.I,ROVRI
Qttl COMMON/HI K\6/^CAI C.NT . VRATIO.NF
OOP n''MnN/RlKI7/NREAn.MPPWT
Oa? CHMMON/bt K1«/5CO«EF,CZMOL,CSIGMO.NRUN,SNUCK,Zir,GV.pMHO.l»8IGtA
044 COM«PN/i5LM<»/tK,rw.NN.Nll«INc,NX,NY.NDATA,
nas uri ,JT?.VISKTP.VT SAME. us, FPATH.EBO.NOSET.
0«*«
0«7
04A
0«9
0^0
0^1 C
052 r. CONSTANTS
050
OSS IFINAL»1
057
OS* PT • 3. 1« 15927
059 E » r.*E-19
060 '
125
-------
061 PPSO m B.B5E-1?
062 CMK8«a'.«PI*fc"»5n
063 0000 CON7TMHF
06« C
065 C
066 NPSET.O
067 PFAOCNPEAn.5) NENDPT.MOATA
068 s
069
070 «500 CONTINUE
071 rS»NE»|r»pT-l
072 P.EADfNREAO.7) ITl,
073 7 FORMATfflOA2)
07« CO Tn(9«
075 9400 CONTINUE
076 READfNREAD.«fl6«) NFST, NDIST.NVT ,NX.HY,NITFR.NCALC.NP.APD.NEFF .
077 INTEMP.NONin
078 fl»M FOP.MATM1I2)
07*
080
081
082
085
08a
085 IFfWVi;F.O.?) »EAnfNREAD,8530) TFINAL, JI 1 .
086 «S^O
087 PEAUfNPEAO,6) OL.PI. .FTAO.DO.FPS. VRATIO.US.FPATM.ERD.RHO
080 b FOBHATf9FB.O.f.6.?)
089 f
090 C
091 C
092 PL • PI *
093 r»t s ni * 2.29F-OJ
094 RHO » wnn/ion.o
095 ny « ni / nn
096 C
09T IF(NPAPD.RT.I) RFAnCNP.CAD.8S3n ( APDSOf I) , AB3IBH( p . I»2. MRAPD)
099 PEAnrii«»EAr>.8S3?) { ASNUCK (I) , A2TG6Y( I ) , AZNOMSd ) , T»1 .
100 «5^2 F'
lOt PEAIifNPE
102 « F(7»MATf J
103 f>(
105
106
107 9UOJ C
10« IF(NniST.t0.2) (MpfAn
111 IF(Mni8T.f.0.2) Gn TO «S21
112 no 3
HI
11« 3
115 CALL LMFlT(PRCU,n50,8lGHAP.6FIT)
116
117
11^ CO TO
119 »5?1 C
120 CALL LHnTST(05n,siGMAP.pPCU,PCNT)
126
-------
121
122
1Z5
120 IFfNPATA.GT.l) 60 TO 6530
125 PEAnfl"RtA0.770 11(13 NSFCT«1,WJH$EC
120 RFAP(HRE»D,762J *S tMECT) . V08 (N8ECT) . TCS f NSECT) ,
129
130
131 7*2 FnRMATf7ffcll.4))
132 IF(WVl'.EO.I) RO TO 11«3
133 RtAOfNREAO,7621 RF8(NsrcT),ST«RTl(N$ECT).START2(MP 1 I « I ,^S
Ib6 VOL f II a PCMT(I) * r.V
157 1 CfU'TlM'E
150 TFfNWT'.EO.l) ITERsO
160
161 iF(NVi'.ER.t) 1TER«ITE»+1
16?
165
16«;
166
167
16A
16"
170
171 C
172 C STAI-'T INCHF.HITMTAl. AM*L*SIS OF PRECIPITATO*
175 C
175
176 LKH
177 ZWTaft".
17"
17<»
180
127
-------
181
182
185 00 300" T«t,«F
18«
186 IFU'.EO.l) GO TO 761
187 IFaNOrx-LSECTfNSECTn 760.760.76l
18« 761 COWTTNUE
189
191 IFfl'.FO.l) KO T() 760
193
19fl 760
195 IF(^rnnP.NE.l) GO TO 76a
196
197
198
199
200
202
203 NHIWE«NWS(NSECT)
20tt
205
206
207
20R
?09 I TMCsl INCS(NSECT)*0.305
21" HF»RFSfNSECT)
?11
21?
213
SL^GTHsFinATfLSECT(NSfcCTn*Ll^r
217 C
21A C CALCMI ATF TPW *EAN FBEF PATH
219 C
220
221
222
223
22«
225
22*> VC«E**?/(«C*TDKJ
227
229 C COMPUTE ION MOBILITY CDRRfCTFD FOP TEMPERATURE A*D PRESSURE
230 C
231 "»
233
23«
235 IF(^IVI'.E0.1) GO TO
236 nTIt'r s TINC/FLnATfNT)
?37 «6/5 CONTINUE
23f« C
239 r COMPUTE WtlGHT OP OUST
c
128
-------
290
300
201 H • DL *
242 C
243 Do 699S
244 CC
245 60*3 CONTINUE
24ft IMNVl'.Fd.?) GO TO 4676
247 ERAVGmVn/SX
248 no <>°HP L«I»US
249 OSATfL)«(«.*Pl*EPSO*fRAOCL)+THFP)**2)*ERAVG*(l.+2'.*((EPS-r.)'
251 69«9 CONTINUE
25?
25? RRs(E*FHAVG)/(BC*TDK)
250
255 0676
256
257 IFfNVI.cn. 2) GO TO «677
258 IPfNrST.C0.2) GO TO 0678
C*IL
on TO ««>7e
262 1677
263
260
265 IFf (Vl«*ME'.EQ.l)^AND.(WSFCT.CT'l)) CO TO 5560
266 IF((VmME.EQ.1).*ND.(NOSFT.GT.l)) GO TO S560
267 wtllTF f MPPMT,71«0) NSECT
26* 7100 Fij»MATf//25X,'CLFAN G»S VOLTAGF-CUBRENT OENSITV-rjELO AT THE PLATE
269 1 PFLATTfWSHIP FOP SFCTIOM MO'. »,I2//)
270 rrfNVTI.FQ.2)CALL EFLnKUf 0, AC. V", 8X, 8V, MX. NY, AfPl.T, TOK.P.RF.
271 lSTART.r»STAKT.CSTA»T,irlNAl.VSTART,VW.ACOMTY,N»«IRF.NEC>FBO.JIl,.TI2)
275 »STAPT.i)$TAP.T.CSTART.IFINAL.VSTAPT,VW,AeDNTV.NWlRE.kJFC.F*O.JIl,JJt?)
27« rn 7919 NZ»J,MT
?75 >CI MNfNZ)«ECCULfNZ)
276 7919
277
27fl
279
280
281 TFf NVt'.EO.?) TC«tPCLN*A
2B? C
?ej c roMpurr ruRRFNT DFNSITV
280 CD » 1C / A
28S C
286 C
287 C rOMpllTP FLFCTRIC FIELD IN DEPOSIT
288 tT » CO * RHO
289 C
290 t
291 r COMPUTE CUWENT PEP.' H. OF
29? r
293 CL = TC / WL
290 C
29* HPWl'.fO.l) CO TO 0679
297
129
-------
334
301 GO TO 4600
30? «679 CONTTMUE
103 CALL 8PCHC1.FID.AFIO,AVeFt»>.XCO.U.UEn ?9oo j • i, NS
337 IFfNVj'.EO.n 6" TO 46H2
33ft nLOQ(Ji»'J(J)
339 TFfII>F.l) GO Tn Ugt,
340 *4f»P2 COMTlMl.lf
341 IFd'.Nf .1) C-n TO a?6
342 IFrJ.GT.l) GO TO «38
343 TIMEI.O.
344 XIPC«0'.
345 IFfMVi.f'0.2) Gn Tn U6A3
346 TjMf.F«TlNC
347 IFtNCALC.tl.O)
Sad r,o TO
349 U6*3
350
351 IF(NCALC.EO.O)
352 4h6<
353 GO TO
354 a2<> CONTTNDt
355 IFfWVi'.FO.l) r;0 TO 46Q5
356 IFfJ.GT.l) GO TO <»29
js? TIMFT«TIMEF
35B IFf (ITFR.GT.l)'.AND'. (TI.EO.n)
159
360
130
-------
361 «?•» CONTINUE
362 IFflT'.WE.l) SO TO 82*2
363 XtPe»Xr>e(I
364 GO TO 82.fv08fN8FCTl.GT'.VOS(NSErT-l))) GO TO
39"5 SfcflO CP'JTTr-JHF
396 TP(C.w>ifli CONTINUE
.
a 16 TrrfTTMFi.eu.n'. j'.ANO*. (CNUMBR'.GT.5CHA»G1) Qt J)«3CHAOG*1.6F-19
019 TFfNVl'.EO.I-) GO TO 2900
020 C
131
-------
421 c COMPUTF MJRRATION VEI ocity FOR EACH SIZE RANGE
a?? c
424 IMITER.FQ.J) fMV« 1. • FXPC X )
433 C
434 C CQWTF N'lMBFR OF PARTICLES REMOVED IN EACH 8JZE
435 C
436 JMITEB.EO'.l) GO TO 3761
437 IFdl.ME.n RO Tn *7M
430 XHO(j)«oi OXNOf J)
439 GO TO J7<>3
440 3761 CONTINUE
441 IF(II>F'.n GO TO 376?
44? OLnXNOf.Jl=XNO(J)
4«3 3T63 Cl^TTVUl
nXNOBXKipr J1*EFF
TFflTPB.ME.NTTERl f,0 TO 3T65
DXS(.t)«nXS(J)+OXNO
«5fl C
a51 r C*LC'!L»TF THF CURRENT OEMSITV »T THE PLATE DUE TO THf PARTICUL»TF
453 17*1 CD>JTT>Jl.'f-
(,54
455 C
457 IFfNVl'.FP.t) 0" TO 9131
asB f#(.L SPCHG2(NS.XMr),vi8,»AO.LINC,E,U,ERAVG,nNSION,
463
IFMT'.I.T.MI) GO TO 6337
441$
U66 BIOVPaPHOSUM/FLOATfHTl
IFf I.E".I ) G° TO 376
Tf tRTnVP.GT.0.09) GO TO 375
469 37* CWTTNdE
470 IFf(viSKrP.En.i)'.nR.(NC5T.Fo'.2n GO TO 31»7
471 V"«TTFfiiMRNT,71Ull I
47? 71«1 Frj»MATf//23X.»OIPTV GAS VOLTAGF-CURPEMT OENSITV. FIELD AT THE Pi ATF
«73 I PFLATIQNSHIP FOR INCREMFMT NO'. '.I2//J
47a Ner.«l
475 STARTaSTAnTl(MSECT)*(HEO/U)
476 !FruVTT.F'j'.2)CALL FFLOS(UEQ. AC. VO,SX,SV, MX.NV. AfPlT, TOK.P.RF,
477 !ST*PT.osTAPT,CSTABT,IFlNAL.V8TART,VW,ACr>WTV.NMlRF.NEC.FPn.JIl, JI?)
476 JFfMVIT.Nt'.aKALI EFin?(UEQ,AC.VO,SX.SV»MX.NV.ArPlT,TDK,P.RF.
479 1STABT.OSTART.C5TART,IFINAL,V8T*RT,VW,ACONTV,NKIRE.NEC,FRD.JI1,JI?)
4SO GO TO 11188
132
-------
oei 31 87
48?
08? 3188
484
485
486 ^75
• 87 IFnTEP.ME.mTFP.> GO TO 10*0
488 IF(P'hF.x',E<3.t) St.lMCD««.
489 TFflNDFX.LQ.l) SIHVO«0.
090 Sl)McnssiJMCP*ACONTY
1J91 8u*VO=8UMVO-Vw
49? IFflNnFX'.E^.LSECTtNSFc'')) TC$ (NSECT)«(5UMCn**) /FLOAT (LSFCTf NSECTJ)
495 IF( t^TPX.tO.L8PCT(NSECT)> VoS(N3ECT)«SHMVO/FtO»T (LSECT (NSECf) )
094 IPS" CnHTMUF
49S IFnTEP.LT.NITCR) 60 TO 764
«9h
497 60 TO
098 013
099 IFfUFO'.LT.I ,OE-4)UFQ»| .OE-«
500 TFflMOFX.EQ.l ) GO TO 377
501 IFtUFQ'.NF.l.OE-O) GO TO 9153
50? tFfir
SOX GH TO
504 9133 CnNTTriif
505 SIGH**PPOV»I-ROVPI
SO* 31G*AcAn3(SItt«A)
507 TFfSI&Md'.LT..01) GO Tn 9132
508 377 CO^TlNiif
509 IF(NFST.FO'.?) GO TO
510
51?
513 lF(HVlT.nt.l)CALl fFLnl (HER, CO. AC, V0.3X,5V,»JX,NY.TRK .? , »EPLT.
514 1VF.RUr.rVf »GE)
515 tPLTr.1 ,*AEPLT
Slfc Gfi TO «1%3
517 «18? '"nMTlriiF
518 EPI T»ERAVO/l .7<5
519
520
52? HO ?Pfe5 jslfNS
523 C
52« r CO«PMTf HJGRAT10M VFLOCITY FOR FACH SIZF RANGE
525 r
526
527
528
529 C
53P C COMPi'TF. FFFlClEMrv FOR EACH SIZE RANGE
531 C
532 X=f-**FMV)/(VG*FLOATaSECTfNSF.CT.m
533 C
53« EFf • 1. " FXPt X J
535 C
536 C CnhPUTF NUMBER OF PfcP-TlCLES PE^OVEO IN EACH SIZE
537 C
538
539 I-xS(J)
540 »8f Jl
133
-------
sat XMr EOAVG • SEPAVR
57« CAl I. PPTTNC
57fl 3000 rnMTTWE
590 C
581 FTC»rzi"T/UL)*100.
502 IFtNVj'.EQ.2) GO TO 16?0
583 riFT«ETC-ETAO
564 PlFFBiRSdlFF)
585 IFfOTFF-0. 05)60,^00, 300
566 300 FQt.Jim.tl
587 WRITEfMPP^T,M656) ETAP.FTC
58fl «*.5«> FOR»»T(f/' FST. EFFICIEMCV •' ,Ffc.2,5X, 'UNCORRECTEO COMPUTED FFFIC1F
58«» 1|UCV »'.F6,?J
590 TCflTfP.FQ.NITERl GO TO 60
501 ETAOsETC
592 Bn TO JO1*
593 hO CnHTtMUE
59« Gn TO 1621
595 1*?0 CONTINUE
596 WRiTFfMPRNT,i6?2^ FTAP.ETC
597 1622 FORHAT(,f' DE8IRK* EFFICIENCY ••.F6.2|5X, 'IINCORRECTEO COMPUTED EFFIC
?9« tUNCV m'.fh, 2)
599 1621
600
134
-------
601
602 DO
603
605
606
60T CALL
609 *n TO a 000
610 «K
135
-------
•01
002 REAL LINCS.NMS
001 INTEGER VISKIP.VISAWE
OOi DIMENSION IBLNK(2M
005 COMMpN/BLKl/DIAHf20).ONOC20).DXS(,20),XMV(20),PCNT(20),RAO(20).
00* 1CCF(20>.PRCUC21)
007 COMMON/BLK2/LSECT(10).I.INCS(10).P8<10)
OOB COMMON/BLK3/VG.ATOTAl,DD.KTAO,Dl,PL,RHO
009 eONMON/BLKS/*H«Dt,8lCMl.NONlO,NRAPO,TDKfNUM8EC.NEFF,NTEMP.CFIT
010 COMMON/BlK6/VOL(20),XNO(20)fO(20),NS(20).ITl(40).DM(45).AanO).
Oil lV08CtO).TCSnO),WL3nO).AC8(101.BS(10).SYS(10),VG8C10).VGASS<10).
012 2TEMP8(10),VI88(10),08AT<20>,U,r.EP80,PI,E»UVe.Be.TEMP.EP8.VAVC.
013 SOLDQ(20).OU>XNO<20),RFlMO),8TARTinO).START2clO).8TARTSflO),
014 4VSTARC10)
015 COHMON/BLK11/ENDPT(21),NENDPT
01* COMMON/BlK12/ARD50riO),A»»8IG»«(IO>,ASNUCKM5).4ZNUMS(15|.AZIGGYC15)
«l? COMMON/etKU/TMFP.NVI.NVl
OIB COMMON/BLK16/NCALC.NI.VRATIO.NF
019 COMMON/BLK17/NREAD.NPRNT
020 COMMON/§LK19XLK,OV.NN.NUMINC. NX. NY. NDATA. NEST, NOI8T, NITER,
021 lJIl.JI2.V18KIP,VIS*ME,U8.FP»TH.EBO.ND8ET.NW3(10).D50,SieMAP
022 DATA IBLNK/21*' '/
025 IFtLK) IJJ.lll.lfcO
024 111 CONTINUE
025 NRITE(NPRNT,5650)
026 5850 FORMAT(UOX, •***»*****»**•***********•**•*••»*»*«•»)
027 WRITE(NPRNT,585l)
02B 5851 FORMAT(40X,»«'.S5X,'«»)
029 MRITF(NPRNT«5B52)
030 5852 FORHATraox.'*'.9x, 'E.P'.A*. ESP MODEL*, tox.»*»)
031 MRITE, AND »0.«.1.',«X.'*M
034 WRITE(NPRNT,58SI)
035 WRITE fNPRNT,Se54)
036 5«54 FORMATf40X.'*'.TX, 'REVISION II. AUG., 1979', 5X. '*')
037 WRITE (NPRNT, 5851)
03B WRITE(NPRNT,S850)
039 N08ET«N08ET+1
040 OLB«OL/2^29E«03
041 PLB-PL/0.305
042 RHOC68»100.*«HO
04S NCARD»O
044 WRXTE(NPRNT,2000) NQSET
045 2000 FORMATf//* PRINTOUT OF INPUT DATA FOR DATA SET NUMBER »,I2//)
046 NCARD»NCARD+1
047 WRITE(NPRNT,200n NCARO
048 2001 FORMAT(//' DATA ON CARD NUMBER MS//)
049 WRITE(NPRNT,iOOO) NENDPT.NOATA
050 IflOO FORMAT^ NENDPT • '.I2.2X,* NDATA » ».I2)
052 NRITFJNPRNT,200|) NCARO
053 NRITE(NpRNT«iOOt) ITL
054 1001 FORMAf(2X,40A2)
055 60 T0(6000. 6001*6002, 6002)iNDATA
056 6000 CONTINUE
057 NCARDBNGARB+I
058 MRITF(NPRNT,2001) NCABD
059 WRITE (NPRNT, 1002) NEST, NDI8T.NV1, NX, NY, NITER, NCALC.NRAPD.NEFF,
060 INTIMP.NONID
136
-------
0*1 ioo2 FORMAT** NEIT • •.IZ.ZX.'NDIST • M2,2x.*NVx « *.X2,2x,*Nx • *
Q62 l.I2.2Xt'NV • %!2.2X.*NITEft • «.X2.2X,'NCAIC • *X*NPD •
Oft) 2X2.2X.»NEI'F • '«X2,eX,'NTEMp • •,X2,2X.'NONXO
064 IFfNCALC.NE.O) 00 TO 1003
065 NCARD«NCARO+1
0*4 KRITE
076 1005 CONTINUE
077 NCARD«NC*RO*I
070 HRXTEfNMNT»2001) NCARO
079 MRITE(NI»RNT(1007) 0(.8, (•(.«. ET»0. DO, EP8
0*0 1007 PORMATf* OL • '.F9.S.' CRN/fCr«.2X,'PL • *,'».«,• PT'.ZX.'ETAO •
081 1',FB'.5,' «',2X.*00 • >,F«.2,» K6/H**S'.2X,'E '
082 MRI7E(NPRNT, 1008) VR*TIO,U8,rf *TM,tBO,RHOC68
08S l«08 FORMATif* VRATIO • »,F8f«,2X.»U8 • »,F8,6,»
08« t« <>.F8'.4.2X,*EOO • '.F8.0.' V/M«.2X,'RHOeC8
085 IF(NRARO.Ea.l) CO TO 100*
086 NCAROiMCARD+1
087 MRXTE(NRRNT,tOOn NCARO
088 WRITE (NPRNT.10101 (X.ARD50(I),I,AR8X6MCI),X«2.NRARO)
08« 1010 FORMATt* AR050(',X2,*) • SF4.1,* UH».2X,'AMIfiM(
0*0 in
091 1009 CONTINUE
092 MC*RO«NC
09) MRXTE(NMNT,200t) NCARO
094 DO iOit I'l.NONIO
095 lF(l'.EOl7) NCARD«NCARD*1
096 1F(X'.EO>) NRITE(NRRNT,20C1) NCARO
097 iFtllEo'jJ) NC«RO*NCARO«I
098 IF(X.E0.13) NRITf(NPRNT, 20011 NCARD
099 HRITC(NPRNT,65TO) I. A8MUCK(I)(I. A2IG6V(X),X,AZNUM8(I)
too 6570 FORMAT;' ASNUCKC'.II •> • '.F4.2,2X,*AZX6GYC,I2.') • '.F4.2,zx.'
101 1AZNUMS(»,I2,«) • SF4.1/J
102 1011 CONTINUE
103 NC«RO?NC*ftD4l
104 HRITE(NPRNT,200n NCARO
105 NDCARDM2
106 IF(NENBPT.LE.IO) NOC»RO«1
107 IF(NENDPT,GT'.20) NDCARD>3
108 &0 TO(1012, 1013, 1014), NDCARD
109 1012 CONTINUE
110 WR!TE(NPRNT,!015> (IBLNKd) , I,ENOPT(I) ,X»1,NENDPT)
111 1015 FORMATf5(lX,Al.'ENOPT(',X2,n » *,F8.3.' UM'.lX)/)
112 CO TO 1016
113 1013 CONTINUE
114 WRITE(XPRNT,101») (XBLNK(l) ,I,ENOPT(I) ,X«1, lOj
US NCARBaNCARD*!
116 MRITE(NPRNT,200n NCARO
117 «RITe(NPRNT,l015) (IBtNKtI),X,ENOPT(I),X«ll,NENDRT)
118 CO TO 101*
119 1014 CONTINUE
120 WRITr'(NPRNT,1015) (XBLNKd) , X,ENOPT(I)
137
-------
121 MCAROMMCAROfl
122 MRITCjtMPRNTf200n NCARD
123 «RITE(NPRMT, 10151 (IBLNKfl J,lf ENOf T(I).1»11,«0)
124 NCARO«NCARD+!
125 KRITE(NPRNT,2001) NCARD
12* WRITE fNPRNT, 1015) JtlBLNKd ) , I,ENOPT (I).I«21,NENDPT)
127 1016 CONTINUE
121 6001 CONTINUE
12« IFCNDIST'.EQ.l) 60 TO 1017
iso NCARO«MCARD+I
1S1 *RITE
157 1020 CONTINUE
158 1019 CONTINUE
159 IPCNOAU.CT.l) GO TO 5000
160 NCARDvNCARDtl
161 NRITE(NPRNT,2001) NCARD
162 IF(NUM8ECi6T.S) 60 TO 1026
163 WRITE(NPRNT,102S) NUM3EC. (IBLNK(I) ,X.L8ECT(I), If 1 .NUH8EC)
164 10Z5 FORMATC NUM8EC « '. I2,2X.5f IX, At. »L8ECT( », la. •) • ',12))
165 60 TO 1027
166 1026 CONTINUE
|67 WRITEJMPRNT, 10251 NUMJEC. (I8LNK(I) . I,L8ECT(I) , I»1.5)
168 Wftire , I , VOS( 1) . I, TC3f I) , I ,HLS(1 )
175 1029 FORMATtf A8(».I2,') • •.lFEll'.4,' FT«*2;.2X, *V08(M2. *) •
176 Ilt4,» V*.2X,»TC8('.I2.') « »,JPCU.«.' A',2X, •WL8(',I2. •) • »,
177 21.«.'.FT*/)
178 WRITE(NPRNT, 103.0) I ,*C3(J ) . I.BS 1 1) . I.NW8 (I)
179 1030 FORMATS AC8(*,I2.*} • MPE11.4,' IN',2X, »B8< *. 12, *) • »,lPEll'.«
180 l.» IN'.2X,'NW8(».I2,») • '.1PE11.4)
138
-------
181 NCARO*NCARD«I
181 NRITE(NPRNT,2001) NCARO
183 *RITE(NPRNT,103l) I,$Y»(I).I. VC8(Ht I, V6AS8(I)
184 1031 FORWATf SY8(',I2,') • '.1PF11.4.' IN',2X, 'Vetf*. 19, ') • »,1PE11,
185 14.' FT**3/HIN'.2X,»VOA8SC».It.M • MPE11.4,' FT/SF.C».2X. 'TEMPSC
186 2.12.') • SlPEll'.A.' FV)
18T WRITE (NP*NT,10S2J I .PSU> ,1 .VISSU) ,I,LINCS(I)
188 10S2 FORMAT^ »»8('.IZ,*) • »tlfEU,4.' ATM»,2X,'V183(».I2,*)
190 IMNVl'.CQ.l) CO TO 10{8
192 MRITE(NPRNT»2001) NCAPD
»RITE(NPRNr,103.3) I ,RFStl). I.8TAR71 (I) ,l.STAftT2(I)
1033 FORMATt' RF8(',I2.»1 • •,1M1».4.2X.'8TARTH«. ».•) «
1 A/M**2'.2X,'8TART2(',I2.'1 • '.IPE11.4,' A/M**2»/)
WRlTE(NPRNT,103fl) I.STARTSf I) , I. V8TAR(I)
19T 103' FQRMATf* 8TART3f ».I2. •) • *.lPEll'.4.' A/M**2».2X. 'V8TAR( '.IZ, ') *
198 1 '.IPEli'.*.' V»)
199 1028 CONTINUE
200 00 TO 4000
201 6002 CONTINUE
202 NCARD«NCARO*I
203 MRITC(NPRNT,200t) NCARD
204 DO 163S I«1,NUM8EC
20S IFHfEO,«) NCARO«NCA»0*1
206 irdlEQ.fl) W»ITE(NPRNTi2001) NCARO
207 IF(I.EO.T) NCARDaNCARD+1
208 IF(I,E0.7) MRITE(NPRNTf200I) NCARO
209 iF(iuo.iO) MC*RO«NCARD»I
210 IF(I.EO.IO) WRITE(NPRNT,2001) NCARO
211 IFCNDATA'.EO.O) co TO tost,
212 HRITE(NpRNr,103?) I.VG8(I).I.VOA88(I)
213 1037 FQRMATf' V08(i,I2.') • '.tPfli.a,' FT««3/NIN»,2X. »V6A8S(».I2, ') «
21* 1 'ilPEJU."'' FT/SEC'/)
215 GO TO 1055
216 1036 CONTINUE
217 MRITE(NPRNT,1038) I . VoS(I ) . I .TC8CI)
218 1038 FORMATt' V03(',I2.') • *,lPfll.4,» V*,2X,«TCS(M2,«) «
21« l.» A'/)
220 1035 CONTINUE
221 5000 CONTINUE
222 WR!TE(NPRNT,1039)
223 1039 FORMATdHl)
224 160 CONTINUE
225 RETURN
226 END
139
-------
ooi SUBROUTINE SOCHGI (SH.ROVRI.OROVRI.XS. ETAPF. ON, QSAT.XNQ M LSECT
002 iTC.Ve.ETAO.riO.AriO.AVGFID.XCO.U.UeO.X.NSECT.LlNC.PL.CD^ERAVG,
003 2NSt XPI )
004 REAL LINC
005 DIMENSION DW(43).GSAT(20},XNO(20>,LSECT(!0)
00* IFfl.NE.l) 80 TO 1266
007 Sw • o.O
009 ROVRI«!0.
00* OROVRI»20,0
010 C
on c COMPUTE VALUE or EXPONENT IN DEUTSCH EQUATION FOR THE STATED iff'
012 c
Oil XS«ALOG(100./(100..ETAOn
014 C
015 128* CONTINUE
016 C
01? C COMPUTE EFFICIENCY PER LENfiTM INCREMENT
018 C
01* ETAPF • 1,»EXP(«LINC»XS/PL)
020 C
021 C COMPUTE AMOUNT OF MATERIAL RfMOVEO PER INCR.ON A TOTAL WEIGHT BASTS
022 C
02} DW(I) • (W • 8W) * ETAPF
020 SW • SW * DN(I)
02S FIO«Cp/(E«U*ERiVC)
026 ' SUM«0.0
027 00 1500 L«1,N8
020 1300 SUMBSUM«QSAT(L)*XNO(L)
oso
031 AFIO«FID/"OVRI
032
033 XCD»CD*100000.
034 C
03B C COMPUTE EFFECTIVE MOBILITY
036 C
037 UEQ«U/ROVRI
030 C
Q39 XPJ»ET*PF*100.
040 PETURW
041 END
140
-------
001 SUBROUTINE SF-CH62 (N8.XNO.VI8,ftAD,LINe.E.U.ERAVG.r>N8TOM.
002 IDELTNP.8UMHOB.PNUM.RHOP.TCMRG,F'MOB,TON&».RDN8I.AFIO,UEO.AVGF1D.
003 2RIOVR,!.X8.ETAO,Pl.ETARF.CCF.XH.OLDQ.O.II.NSECn
00« REAL LINC
008 DIMENSION XNO(10),RAD(20).CC*(»0),OU>Q(20).0(20)
006 COMMON/BLK7/XDC(45.20)
007 COMMON/BLK8/EAVG
-------
001 SUBROUTINE EFLD1 (UEO,CD.AC,VO.SX,8Y.NX,NY.TDK,P.AEPLT.VERGE,
002 1CVER6E)
003 C EVALUATION OF FIELDS, SPACE CHARGE DENSITY, POTENTIAL , *NO
004 C CURRENT DENSITY FOR A HIRE-PLATE PRECIPITATOR
oos REAL MAxj»MiNj.MOBiLT(i5.n>
00* DIMENSION RHO(1S.15).EX(15.15).OLDRO(15,15),OLDV(15.15),
007 ICDNSTV{H,15>»V(15.1S).EYC15,H>
000 COMMON /BLKl3/VCOOP(15.15).NVir
00* COMMON/BLK17/NREAD.NPRNT
OtO DATA RHO/22S*0'./.V/225«0./.EX/225tO./,EY/22S*0./.OLORO/28S*o./.
Oil 10LDV/223*0./.CDN3TV/223«0,/,NOBILT/225*0'./
012 VO«-1,*VO
013 PI'S.1«16
01« EP80M'.094EM2
019 RO • AC
016 RQC • 100.0*RO
01T RF • f.O
Oie »EIO • (2»5.0/TOKJ*(P/1.0J , .
019 EORO • ROC*RF*(30.0*RELD * 4.0*80RT(RELD/ROCn*1.0E03
020 C
021 C COMPUTE INITIAL ESTIMATE OF SPACE CHARGE DENSITY AT MIRE
023 VERGE«(.*.*CD*M'.OI * o.»»)*8Y>/(2'.*Pi«UEQoEORO)
024 C
02S OZERO-VERGE
026 00 550 I"1.NX
02? 00 550 J«1.NY
02S MOBILTfI.
029 550 CONTINUE
030 MAXJ«CD*1.01
031
032 NX1«NX«1
033 Nyt«Nr-l
034 AX'SX/NXl
035 AY«8Y/NV1
036 AX8»AX*AX
03T AY8«AY*AY
038
03« AS8*r./t2,*(AX8+AY8))
040 Z«0.
041 DO 4615 I'liNX
042 00 4615 J'liNV
043 «6}I V(I,J)«VCOOP(I.J)
044 1 Z.Z+1.
045 IZ*Z
OU6 IF(Z'.EO'.2S) NRITE(NPRNT,U65)
047 1865 FORMATdX,' CONVERGENCE ON CURRENT DENSITY CAN NOT BE OBTAINED IN
048 125 ITERATIONS'}
049 IF(Z'.E0.25.3 GO TO 700
050 LL»0
051 300 Ll»LUt
052 RHpn,l)"OZERO
053 CXfl.D»0,0
054 EvM.n»0.fl
055 DO 201 1*2.NX
056 fYfI'l'»0,
057 EX(I,l)«(Vn-l.n
058 Ol*2,*MOBlLT(I.l)
059 02BQUAX
060 01«OUAY
142
-------
061 B4»02*AY
0*2 9S»«fPSO»EXCI,l)*(03»AY*MOBlLm»l.l))
061 Q6«Q5*Q9
064 07«01*0«*EPSO*AY*EX(I,l)«RHO9
077 P7«Ri*»4*EPSO*AX*EY(t,J)«RHO( I.J.I)
078 P8«-30RTfP6+P7)
079 RHO(1,J)«(P9+P8)/P4
060 20S CONTINUE
081 DO 202 1«2,NK
082 EY(I.NY)«0.
085 E*(I.NV)«(VCI.t,NY).V(l,NYM/AX
084 P.1«2.«MOBIUT(I,NV)
089 R2IRUAX
086 »3«R1*AY
087 P.4*R2*AY
088 R5«-fPSO*EX(I,NYU(R5.AY«MOBILT(I«l,NYn
089 R6M9*RS
090 »7«Rl*Rfl*EP30**Y*eX(I.NY)*RHO(T-l,NY)
091 R8
09t RM
091 202 CONTINUE
090 DO 307 I«2«NX
099 DO 307 J«2.NY1
096 313 ExjtI,J)«f»l,)*(V(I.J).V(I.l,J)i/AX
097 fY(l,J)«t-l.)*CV(I.J}«V(I,J.l))/AY
098 Ol«2.*HOBIl.T(I,J)
099 02»01*»X
100 D3*D1*AY
101 D4«D2*«Y
102 DS*«EP90*(EX(I,J)*(D3«AY»MOBILT(I-liJ))tEY(IiJ)*(02-AX*MOBILT(I,J
103 11)))
104 Ofc«05*05
105 07«01*Oa*EPIO*<
106 Oe»-80RTCDfc+D7)
107 RHO(I.J)»(D5+06)/D«
108 307 CONTINUE
109 DO 301 I*1«NX1
110 00 30\ J«1»NY
111 OLDV(J,J)«V(I,J)
112 OlORO(I,J)"RHOfI,J?
113 ir(l'.CO,l.*ND.J.C0.1) 60 TO 301
114 lF(llEO,l,*NO.J.NE,n 00 TO 304
119 lF(I.NE,U*NO.J,EO,n 60 TO 309
116 IFU'.EQ.NY) CO TO 600
117 Op TO 106
118 600 V(I.NY)BASa*(AY8*eV(I-l,NV)+V(T«liNYn*2'.*AXS«V(I,NY«l)*A8P*RHO(I,
119 1NY))
120 GO TO 301
143
-------
s«4 ifd.eo.i.ANo.j.eo.NY) eo TO jso .
V(l*J)*A88*(2.*AY8«V(2>.HtAXl*rV(lfJ*n«V(l.J.m»A8»*RHOCl(J))
11} 60 TO SOI
124 350 VO,NY>*A88*C2.*AY»*Vf2,NV)#2,*AX8*Vei,Nv.l>«'A8P*RHOfl,NY))
12S 60 TO SOI
12ft SOS VCI,n»A8S*CAY8*(V(I*ltM*V N*ITE
|33 1000 ITERATION!')
134 irCLL.CQ.2000) 60 TO 700
133 00 320 I-1.NX1
13ft 00 320 J«1.NY1
1ST IP(AB8(V(X.J)»OLDV(I.J)).LT.1.1 00 TO 320
138 60 TO 300
13* 320 CONTINUE
140 CON8TV(NX,n«CX(NX.n*M08ILT(NX.l)*RHOfNX,J.)
1«1 ACDNTV«CON8TV(NX.l)
142 9SO DO 900 J'Z.NY
143 CDN8TYfNX,J)"EX(NX,J)*M08ILT(NX,J)*RHO(NX,J)
144 ACDNTV«ACONTVtCDNaTV(NX.J)
14S 900 CONTINUE
14ft ACDNTY«ACDNTY/NV
14T IFtACDNTY.OT.MAXJ) 60 TO 910
148 IP(ACDNTY.LT.MtNJ) 60 TO 920
149 60 TO 9AO
ISO 910 QZERO«MINJ/ACDNTY*QZeftO
1S1 60 TO 1
152 920 OZEROBMAXJ/ACDNTY*QZe*0
153 60 TO 1
134 980 EPLT«EX(NX.l)
153 00 1000 J«2,NY
15ft EPLT«EPLT+EX(NX,J)
137 1000 CONTINUE
138 AE^LT«C^LT/NY
139 700 CONTINUE
1*0 CVERGE'QZERO
141 VO«-1.*VO
Ift2 RETURN
165 END
> «K
144
-------
001 SUBROUTINE EFL02 (UEO.AC.VO,8X.SY.NX.NY,AEPLT,TQK.P.RF.
002 lSTART.DSTART,CSTART,mNAL.V8TART,VWtAeDNTY,NWlRE.NEe,EBO.JIl,JI2)
OOS C EVALUATION Of flELDS, SPACE CHARGE DENSITY, POTENTIAL * AND
004 C CURRENT DENSITY FOR A HlRE-RLATE MECIHTATOR
OOS REAL MAXJ.Mmj.HOBILT(15.l5).N«lRE.MAX8
006 DIMENSION RMO(i5.15).eXC15.l5).OLDROflS,lS),OLOVM5,15).
007 1CDNSTYU5,15),V(15.15),EYU5.1S),EAVB8{30),CMFID8(30),ECOLL8(30)
OOS COMMON/BLK8/EAVG(30).CHriD(30)
009 COMMON/BLK9/ECOLLC30)
010 COMMON /BLK13/VCOOP.*
046 18QRT(RELC7/ROC)))
047 CALL CMAMCVW.NX.NY.SX.SY.PI.AC.NWIRE)
048 Z«0
OA9 DO 46)5 I"1»NX
050 DO 4615 J«1»NY
051 4615 V(I,J)«VCOOP(1.J)
052 1 2*7*1
053 IZ«Z
054 IF(Z'.EQ'.25) MRITE(NRRNT.186S)
055 1865 FORMAT(IX,* CONVERGENCE ON CURRENT DENSITY CAN NOT BE OBTAINED IN
056 125 ITERATIONS')
057 IFtZ.EO.25) 60 TO TOO
058 LL«0
059 300
060
145
-------
0*1 VCMJ.VK
062 EX(l.n«0.0
0*« 00.201
0*5 EV(I.|)*0.
0** Ex(
0*7 Qi«
0*S 02*01*AX
0** Q3BQI*AV
070 04«Q2»AY
071 05..|rp80*EX(!,l)*(03.»V*MOBILTfI-l.l))
078 Q6'QS*03
073 07«OU04*EP80*AY«eX
07* RHO(I,1)««J5*08)/04
077 201 CONTINUE
078 DO 203 J-2.NY
07* exfl«JJ«Ot
080 EV(1,J)"(V(1,J«1)
OBt PI«8.*MOBILTC1,J)
083 P3«»»1**Y
080
089
08*
087
088 P7»AB3iTP7)
089
090 «HO(1,J)»(P5*P8)/P«
091 203 CONTINUE
092 00 202 I«2f
093 fY(I.NY)«0.
094 FXd.NYj-tV
095 R1«2.*MOBILT(I,NY)
096
097
098
099
100
102 R7"AB8(R7)
J03
10M RHO(I,NY)»(R5+»8)/R«
105 202 CONTINUE
106 DO 307 I«2.NX
107 00 307 J«2.NY1
108 313 EX(I.J)*(-t.>*(V(I.J).V(I-l,JM/AX
109 EY(I/J>«<-l.>*CVfI.J).VC!,J.in/AY
110 01«2.«MOBILT(I.J)
111 D2«0)*iX
112 03«D1*AY
113 D4«02*AY
114 OS".EP50*(EX(I.J)*(D3.AY«MOBILT(I-1,J))»FY(1,J)*(02-.*X*MOBILT(I,J,
115 i»n
117
118 D7«AB8(D7)
119 08«-8QRT(06*D7)
120
146
-------
121 SOT CONTINUE
122 00 301 I'l.NXi
123 DO 361 J«1,NV
124 OUDV(I.J)»V(I,J)
12S OLOROfI,J)»RHO(I.J)
126 lF(l,EO,l.*Nt).J.EO.n CO TO SOI
127 IF(I.EO,l.ANO,J.NE;i) CO TO 304
128 lF(I.NE.t.AND.J.EQ.n 60 TO 303
129 IFCJ'.EQ'.NYI 60 TO 600
139 CO TO SO*
til 600 V(l.NY>mA8S*»VCl,J»l))+A8P«RHO(l«J»
136 CO TO 301
137 350 V(1.NY)»A3S«(2'.*AY8*V(2,NY>*2.*AX8*V<1.NY"1)*A8P*RHO(1.NY))
138 60 TO 301
13* 305 V(I,n
140 GO TO SOt
141 306 V{I,,
142 10(1. J))
143 301 CONTINUE
144 IF(Ll'.EQ'.2000) WRITEtNPRNT. l«66J
145 1066 PORMATC1X,' CONVERGENCE ON POTENTIAL GRID CAN NOT BE OBTAINED IN
146 1000 ITERATIONS')
14T IFfLL'.EQ.aOOO) 60 TO 700
148 DO 320 1*1. NXi
14« 00 320 J«1,NY
150 IF(ARS(V(I,J)»OLDV(I.J)).LT,il1 GO TO 320
151 60 TO 300
152 320 CONTINUE
153 CDN8TY(NX,l)aeX(NX.l)»MOIILT(NX.l)*RHO(NX.n
154 ACONTY«CnN8TY(NX.l)
155 950 DO 900 J-2.NY
156 CONST Y(NX,J)»EX(NX,J)*M08ILT (NX. J)*RHOtNX.J)
IS? ACDNTYaACDNTY*CDN8TY(NX,J)
158 900 CONTINUE
159 *CDNTY«ACONTY/NY
160 IF(ACDNTY.GT.MAXJ) GO TQ
161 IF(ACONTY.LT.MTNJ) GO To
162 60 TO 480
163 910 VWBVM4>1.*VM*(MMJ»ACDNTY)/MAXJ
164 60 TO 1000
165 920 VW«VW+l.*VW«(Mltgj«ACONTY)/MlNJ
166 1000 CONTINUE
16T TESTBARSrACDNTY-(MAXJ+MINJ)/2.1
168 TESTHO.OUACDNTY
169 IFfTfST.LT'.TESTn GO TO 980
170 60 TO i
171 980 CONTINUE
172 E»LT«EX(NX.l)
173 00 1200 J*2fNY
174 EPLT«EPLT*EX(NX,J)
175 1800 CONTINUE
176 AfPLT«f»LT/NY
177 700 CONTINUE
178 WRITE(NPRNT,888BJ VW. ACDMTY, AEPLT
179 8888 FORMAT(38X.»VW • '. JPE1 1 ,4,*X, 'ACDNTV • •, 1PC11.4.2X.
180 1E11.4//)
147
-------
m iFirmfExcwium'.LT.EBD) 00 TO 1400
IB* WRITE(NI»**T,1481) VW.ACDNTY
IBS 1401 FORMATt'.THE BREAKDOWN HELD NtA» THE PLATE 18 EXCEEDED AT VW »• r
104 lit. 4. IX, 'AND ACDNTY •',€!».«) 'E
185 CO TO 1525
tat i«ao CONTINUE
10T IF(IVCK.EQ.I) 60 TO 1529
IBB :ru6s(v»o,ea,»8s«4CONTr
192 GO TO 1520
19S 152* CONTIMJF
195 VNiOLDVM
19* 1VCK«1
19T 60 TO 1526
198 152« CONTINUE
199 1001 CONTINUE
200 1525 CONTINUE
201 iritNEC.NE.O) 60 TO 3000
202 K«l
20S 00 5001 J«liNYl
204 »SUM»o.
205 E3UMBQ.
206 00 SOO? I«1.*X
207 IF(J'.EO.I) CO TO S005
208
209
210 60 TO 3006
211 soos CONTINUE
219 ESUM«ESUH+SQftT(EX(I,J+l)**2+FV(ItJ+l)**2)/(2.*NX)
21S IF(I.EO.NX) ESUMBE0UM.VO/(2.*8X)
214 3006 CONTINUE
215 R3UM«BSU
216 3002 CONTINUE
217 FAVGS(K)«ESUN
214 CHFID8(K)
219 K«K*1
220 3001 CONTINUE
221 NVY«NY1
222 DO 3003 L»1,NY1
221
224
225
226 3003 CONTINUE
227 KK.l
228
229
230 Do SOOi M*MI,M?
2S1
2S2
2SJ KKiKK+1
2S4 3004 CONTINUE
235 3000 CONTINUE
2^6 LL-1
1ST DO SOQ7 NN«1,NV1
259 LL«U»1
240 3007 CONTINUE
148
-------
241 Li«NYl
242 00 3006 1=1,NYt
243 ECOLt(U«ECOUSCLn
244 Ll»Lt-l
245 3000 CONTINUE
246 L2»i
247 Il-NYUl
24S 12«2*NY1
249 DO 3009 I»I1,I2
25$ ECOLL(I)»ECOLL8(L2)
251 L2«L2*1
252 3009 CONTINUE
253 VO«-1.*VO
254 3TART«SSTART
255 RETURN
25* END
PROG > 4K
149
-------
001 SUBROUTINE CHARBN CECMARB.SCHARC.NUNINC,CONST,EZERO.V.Rsm.ECONST
002 *.CMK8.RR.FCONST,FACTOR.COEPF.AFIO,RATE.H.XI,YI.NN.X.Y)
DOS H2»M/2'.
00« Y«YI
OOf X*XI
00* 00 2 Ivl.NN
007 Tl«H*RATCeECHARG.SeMAR6.NUMINC.CONST,EZERO,V,R8IZE,ECO»»ST,C*K3.I»R,
008 *FCONBT.rACTOR,COEFF.A«D.X.Y>
00«
OtO
Oil
012 *FCON8T.FACTOR.COEff,AFIO.X+M2,V*T2/2.1
OH T««H*RATE(ECHAR6.3CHAR6,NU)
-------
001 FUNCTION RATE (ECHAR6.8CHAR6.NUMINe,COM8T,EZERO,V.R8lZE.ECON8T.
002 *CMK8.RR.FCONST.FACTOR.COEFF.AFID.NTIME.NUMBER)
ooi REAL WGRL.NE.NUMBER.NTTME
OOA DIMENSION mj.Am
005 DATA T/«0,T7«59*67,O.O.O.T7«S9*67/
00* DATA A/fl'.55SS5SS*.0.8888B88«vO.S5S5S556/
007 NE««NgMB|R«ECHARG
008 M«3'.t4l39ZT
004 IF(NUMBER*8CHARS)7005.7006.700*
010 7005 CAU ARCCQ8(NUNBER.8CHARO.THZERO)
Oil IF(THZERO.LE.l.E-OS) 60 TO 700*
012 JFn'.S7.7HZEROJ 7011.7011,7019
013 7019 CONTINUE
014 60 TO 7007
01S 7006 THZERQiO.
016 7007 YFUC-o'.O
017 DO 7002 I
018
01« CTHETA»C08(TMETA)
020 TCON5T«eON8T*CTHFTA
021 EC08«EZERO*CTHCTA
022 C1«.NE/(CMK8*ECOS)
023 CO»TCON3T/(2.*EC05)
024 CALL zfRO(Ci.co.MZE
023 »RGl"«fNUWBER*V*(RZ
02* 1*2>*CTHETA)
027 IF(AB|(AR61).6T.30.0) 60 TO 709S
026 YVAL»EX»»tARGl)*S1N(THETA)
029 60 TO 7026
OSO 7025 W*L»0'.
031 7026 CONTINUE
032 YFUC«YFUC+A(1>*YVAL
033 7002 CONTINUE
034 BATEl«(PI-2
035 60 TO 7012
036 7011 RATElBO.
037 7012 CONTINUE
038
039 IF(ABa(ARG3).6T.SO.O) GO TO 7011
040 RATe2«(T*CTOfi»EXPf*BG5)**FIO
041 GO TO 7032
042 7031 RATE2«0.
Q43 7032 CONTINUE
044 IF(NUMBEP-SCHAAG)7006.7009.7004
045 7006 RATE3BCOEFF»(r..NUMBER/SCHARG)**2*AFID
046 60 TO 7010
047 7009 RATES«0'.
046 7010 CONTINUE
04?
oso RETURN
051 END
151
-------
001 SUBROUTINE ARCCOS CA.B,AC08)
002 RAT10«A/S
003 T«l.
ooa SUM.O.
005 TERM»RATIO
006 i U«2,*T-r.
007 V«2.*T
OOS
009
010 5UM.9UM+TERM
Oil TsTfl'.
012
015 S ACOS«r.5707963.8UM.RATIO
oio RETURN
015 END
152
-------
001 SUBROUTINE ZERO (Cl,CO.m»0)
002 BK9QRT(C£7.*CQ*CO)/(ei*Cl*Cn)
005 CALL APCCOS(8,1..C)
004 D«»2'.*SQRT(Ci/3.J
005 RZERO«
oo* RETURN
007 END
153
-------
001 SUBROUTINE CH68UM
002 WEAL LlNCtlTMICK.JPART.JIOW
OOS eONMON>8LK5/ZMMDIfai6MlfNONID.MRAPO,TDIC,NUMKC.NEFF,NTENP.eFIT
004 COMMON/BLK*/VOL(20),XNO(20)fO(?0)«Mt(20).ITL(40).OM(«S).AanO).
OOS lVOBC10>.TC8nO)fNL8(!0)fAC8(101fB8riO).8YSnO).V68(10).V6AS8(10).
006 2TeNP8C10)»VI8SOO).88ATe20).U»E,EPSO,PIfeRAVe.BeiTeNP.EP8.VAVC.
OOT 10LOOf?&).OLDXNO(20).RF8 60 TO SO
024 80LOOF(J)"OLDOF(J)
025 80LOOT(J)*OLDQT(J)
026 S3 CONTINUE .
027 IF((lTER.6T.H.ANO.(II.Ea.n) BO TO 54
028 60 TO SS
02* 54 CONTINUE
030 OLOQf(J)«80LOOF(J)
031 OLOOTfJ)«SOLOOT(J)
031 SS CONTINUE
033 50 CONTINUE
034 IFCNVI.fQ.2) 60 TO 56
oss iFtr.er.i) eo TO 56
036 OLOOF(J)«Or
037 OLOOT(J)«0.
038 56 CONTINUE
03« 8ATCH6»E*8CHAR6
040 IF(OLOQFtJ)tGEl8ATCN6) 60 TO 1
041 CFi«(jtCHRFID«U*E)/<4'.*EMOM*(TIHEF-TINEI>
042 CF2»1./(l.-OtOOF(J)/8ATCN6) .
043 OFB8ATCHC*((CF1«CF2-1.)/(CF14CF2))
044 IF(QF'.6T'.8ATCH6) QF«8ATCH6
045 CO TO 2
046 1 CONTINUE
047 OF'OLOOF(J)
048 2 CONTINUE
049 OLOOF(J)BQF
050 AR9«(v*OLOOT(J))/E
051 IFfARG.GT.30.) CO TO 10
052 QT«(E/y)*Al.OGC((E**2*R8IZE*VAVe*eHRF!D)/(4.*EP80*BC*TDK))*(TIHEFo
053 1TIMEI)*EXP(AR6))
054 OlDQT(J)*QT
OSS 00 TO 9
056 10 CONTINUE
057 QT-OLOOTfJ)
058 9 CONTINUE
059 CNUMBR»(OF+QT)/E
060 RETURN
154
-------
001 SUBROUTINE PUTINC
002 REAL LJNC.ITHJCK.JRART.JION
003 COMHON/BlKS/Ve.ATOTAL,DD.ETAO,DL.H»«HO
00« COMMflN/BLK5/rMMDl,8I6MI,NO»IID|NR*PO,TOK,»»UN8EC»NEFF,NTEKP.6FIT
OOS CONMON/BLK6/VOL(20),X»lOC20>,OC80>,WSf*.0).ITl(40)tOW(45).A8C10}.
00* |V08(10).TCS(10>.ML8<10),AC8(iO).ISnO).8VS(10)*V68(10).VOASS(10).
007 2TEMP8(10>.VI88np),OSAT<20),U,E.EPSO,PI,ERAV6,BC,TEMP,EPS.VAVC.
008 30LDQ(20),OLDXNO(20),ftF8(10).8TARTl(10).8TART2(10).8TART3(10).
00* 4V8TAR(t01
010 COHMON/BLK14/TMFP.NVI.NVI
Oil COMMON/BLK15/NPRINT,NSEeT,3LNGTM.A.VO,TC.B,AC.WL.CL.CD.ET.SY.
012 lVGAa.P,Vl3,W,LINe,XPI,RIOVR,EPlT,AFID,XCD,ZMO,
013 2WT.LTHieK»JF-ART,JION,I,ROVRI
014 COMMON/BLK1T/NREAD.NPRNT
015 iFtNPRJNT.NE.U 00 TO 8439
016 IFJNSECT'.GT.I) 60 TO 1585
017 WRITE{NPRNT,6S50)
018 6530 FORMAT*//' INCREMENTAL ANALYSIS OF PRECIPITATOR PERFORMANCE'//)
019 WRITEtNPRNT,30101 ITL
020 3010 PORMAT(»0',40A2/>
021 1585 CONTINUE
022 NPRlNTvO
023 WRITE(NPRNT,7820J N8ECT.SLNGTH
024 7820 FORMATC/* CALCULATION 18 IN SECTION NO'. «'.I2,' AND THF SECTION LE
028 1NGTH J8 ••.F8.«,' M*>
026 WRITE(NPRNT,T715) A,VO.TC
027 7715 FORMAT*/' COLLECTION AREA •'.1PE11.3.' M2*.T«1.'APPLIED VOLTAGE «'
028 1.EU.3,* VOLTS'.7X,*TOTAL CURRENT ««,Ell'.3,' AMF8*)
02* NRITE(NPRNT,7716) B.AC.WL
050 T7lfc FORMATt' WIRE TO PLATE "'.IPEll.S,' M'.Tai.*CO«ONA **IRE RADIUS •*,
031 ten.5,' M'.BX,'CORONA MJRE LENGTH ••,Ell'.3.» M»)
032 HRITE(NPRNT,T717) CL|CO,ET
033 77i7 FORMAT'C' CURRENT/M •'.IPEII.S,* AMP/M».T«I.'CURRENT OENSITV «'.EH
034 1.3.* AMP/M2',ex,'DEPOSIT E FIELD «',E1!.3.' VOLT/M')
035 «R1TE(NPRNT,7718) SV,VG,V6A8
036 7716 FpRMATf* 1/2 WIRE TO WIRE ••.IRE11.3,* M»,T«l.'6A8 FLOW RATE «'.tl
037 U.S.* M3/SeC',«X,'6A3 VELOCITY •SE11.3,* M/SEC*)
038 WRITF(NPRNT,773l) TDK.P,VIS
03* 7731 FQRMATC1 TEMPERATURE «'.F8.3,» K',T41,'PRESSURE •'.'8.3.' ATM'.19X
040 1,'VISCOSITY B'.lPEll.S.' K6/M«SEC')
001 WRITE(NPRNT.7732) U.VAVC.TMfP
042 7732 FORMATf* ION MOBILITY »•,1PE1l'.3,» M2/VOLT-8EC»,T41,'MEAN THERMAL
043 1SPEEO •'.Ell.3.' M/8EC'.4X. »PA«T. PATH PARAM. "'.EILS.' M»)
044 WRITE(NPRNT,7733) W.LINC.XPI
045 7735 FORMATf* OUST WEIGHT «'.1PE11.S,« KG/SEC*.T41,'LENGTH TNCR. «'.OPF
046 UO'.S.' MMSX, 'INPUT EFF./INCR*. «'.F6.2)
047 IF(NVl'.EO«l) GO TO 46B*
048 WRITE(NPRNT,4322)
04* 0322 FORMAT(//T2,'RIOVR»,5X.'ERAVG'.eX,'EPLT'.8X,«AFlO«.6X,»C»«CDS6X,'M
050 1MD*.8X,'WEIGHT',4X.'OUST LAYER',3X,'J(RART)',6X.'JCIONl',3X,'INCR.
OS1 2 NO.'/)
052 GO TO 0690
OS3 4689 CONTINUE
054 WRITE(NPRNT,4333)
055 4333 FQHMAT(//T2,»ROVRI',5X,»ERAVG*.8X,'EPLT',8X,tAFIp',6X,'CMCOf,6X,'M
056 lMO%ex.*WEI8HT«,4X,»DU8T LAYFR'.3X.'J(PART)',6X, • JdONi »,
057 2 NQ.'/I
058 4690 CONTINUE
059 R439 CONTINUE
060 IFCNVl'.EQ.n GO TO 4691
155
-------
RIOV*,£**V«,f«.T.AriD.XCD,ZMOfl«T.lTHTCK.
062 IJPART.JION.I
0*3 «3IS rORMAT
-------
001 SUBROUTINE PRTCH6
002 REAL N*8
003 INTEGER VISKIP.VISANE
004 DIMENSION YY(20)
005 eOMMON/BLKt/OIAM(ZO),ONO(20),DX8(20)«XMV(20)(PCMT(20),RAD(20)«
006 lCCF(20).P"CUC2t)
007 COMMON/BLK4/NS
008 COMMDN/BLK6/VOU20).XNO(20),0(20),M8(20).ITL(40).DN(45),A8(10).
00* lVOSO9),TCS(101,»IL8ClO),ACSnO>,B8UO),8Y3tlO),VGStlO).VGAS8(10>.
010 2TEMp3(10)«VI8S<10).Q8AT(20),U(E.EPSO(PI(ERAV«,aclTEMP.EP8,VAVC.
Oil 30LDO(20).OLt>XNO(20).RFS(10>,8TARTl(10).8TART2(10).aTARTSMO).
012 4VSTAR(10>
013 eOMMON/BL*T/XOe<45.20J
014 COMMON/BLK8/EAVG(30),CHFID(30)
015 COMMON/BLK14/TMFP,NVI,NV1
016 COMMON^BLK16/NCALC.NI.VRATIO.NF
OJT COMHON/BLK1T/NREAD.NPRNT
018 COMMON/8LK19/LK,OV.NN.NUMINC.NX.NY.NOATA.NE8T,NDI8T,NmR.IFINAL.
01* UIl,Jl2.VISKIP.Vl8AME.U8.FPATH.EBD.ND8ET.N»»8nO).B50.3lGMAP
020 C
021 C OUTPUT f»OH CHARfime ROUTINE
022 C
023 WRITE(NPRNT,«9«2)
01* 9992 FORMAT(1H1)
025 WRITE (NPRNT, 554)
026 356 rORMAT(/T3.'CHARGING RATE8 FOR PARTIttE 81TE8 FROM SUBROUTINE CHAR
027 1GN OR CH08UM'/)
028 irit(Nf*LC.EQ.l),OR'.(NE8T.E0.2)5 GO TO 1880
029 MRITE(NPRNT,1879)
030 1879 FORMATf/T3,»8RI THEORY USEO FOR PARTICLC CMAWING'J
OS1 GO TO 1881
032 1880 CONTINUE
033 WRITE (VIPRNT, 1881)
034 1882 FORMAT(/T3.'8UM OF CLAtSICAl FIELD AND DIFFU8IONAL CHARGES USED FO
oss IR PARTICLE CHARGING?)
036 1881 CONTINUE
037 WRITE(NPRNT,2500)
038 2SOO FORMATC//T2,'INCREMENT NO.',T20.'Q/0*ATF FOR INDICATED PARTICLE 81
039 1ZE8')
040 J3«l
041 KS«8
042 6S44 CONTINUE
043 IP(K*«N8) 6541.6942,6942
044 6542 CONTINUE
04S K8«NS
046 6541 CONTINUE
047 WRITE(NPRNT,357) (DIAM(J),J.JS.K8)
048 357 FORMAT(//T4,10(EI1.4*2X)//)
049 DO 360 IP1.NF
050 DO 3S9 J«J3,«8
051 IFCNVl'.EO.D GO TO 4692
052 N • NJ/2
053 Q8ATM«f«.*PI*EP30*tRAD(J)+TMFP>**2)*EAV6(N)*(l,+2'.*{(EPS-l.)/
054 l(EP9»2.»*(R*D(J)/(RAD(J)*TMF
055 VY(JJ«XOC(!.J)/Q8ATM
056 GO TO 359
057 4692 CONTINUE
058 YY(J)«XDCt!»J)/QSAT(J)
059 359 CONTINUE
060 WRITE(NPRNT,358) I,(YY(J).J-J8.K8)
157
-------
061 390 rORM«TtT3«I2.T6,10(r7.4,6X))
062 360 CONTINUE
061 If(M>g'.N0J 60 TO 69«3
064 J8U8+0
065 KSBK8+0
066 60 TO 69*4
067 65«S CONTINUE
060 NRJTE(MP*NT,9992)
069 NRITE'(NMNTf4S2)
070 432 FQRMATJI.K$)
000 «29 FORMATr//ta,IO(Ell.4,3X)//)
001 DO 43) I«1»NF
062 MRITE(NPRNT(«30) I,tHDC(T,J).J»J8,«3)
083 430 FOftHATfT3«I2»T6,10(E13.9ilX))
014 431 CONTINUE
089 ir(KS',EO'.NS) 60 TO 6968
006 J8-J8+8
067 KS»K8*«
000 60 TO 6969
009 6960 CONTINUE
090 RETURN
091 END
158
-------
001 SUBROUTINE ADJUST
002 C ft********************************************
003 C
RAPPING REENTRAINMENT PROCEDURE IN
oot c
oos c
THIS SUBROUTINE NA3 DCVfLOPED UNDER
00* C
007 C
000 C THE SPONSORSHIP OF E.P.R.I. BY SO.R.I.
009 C
010 C A********************************************
Oil DOUBLE PRECISION EFE8R.DL06,EFFNR
012 REAL LINCS
015 DIMENSION RPCNTC20).OMDLD(20),WUNCOR(20).RDMOLO(20),CDMDLO(20),
014 1PCTOT{20J.CPCTOT(20>,«L<*0).PX8<20),PRCUNR(21).RPRCU(21),
015 2PRCUC(2l>.EUNCORf20)
01* COMMON/BLK1/DIAM(20),ONO(20),0X8(20),XNVC20)fPCNT(20),RAO(20),
017 iccn2o>,p«cum>
016 COMMON/BLK2/L8ECT(10).LINC8(m.P8(10)
019 COMMON/8LK3/VG.ATOTAL.OD.ETAO,DL.PL.RHO
020 COMMONmK4/N8
021 COMNON/BLK5/ZHMDI,SIGMI,NONIO|NRAPO,TDK,NUMSEC.NEFrfNTENPfGFIT
022 COMttON/BLK6'VOL(20),XNO(20),0<20)fM»(20).ITLUO),DM(«Sl.AS<10).
023 lVOSnO)»TCSeiO),NL8nO),AC8(10).B3(10),8V8(10),V68(10).VGASS(10).
020 2TEMPSnO)*VI89(10).Q8AT(20),UfE.EP80,PX,ERAVC,BC*TEMP,EPS(VAVC.
025 SOLDG(20).OLDXNO(*0).RF8UO)f8TARTltlO>.START2eiO).8TART3(lO).
02* 4VSTARMO)
02T COMMON/BLK11/ENDPT(21).NENDPT
02» COMMON/BLK12/ARD50(lO).ARSieH(10)*A8NUCK(15)«AZNUH8(l5),AZI6CV(lS)
029 COMNON/6LK17/NREAD.NPRNT
030 COMMON/BLK 18/SCORCF,CZMDL.C8IOMO.N(»UN,8NUCK.ZlCeY.(»MMD.R8I6H*
031 COMMON/BLK19/LK,DV.NN.NUMINC.NX.NY.NDATA.NEST«NOI8T,NITER.IFINAL.
032 lJn.JI2.VI8KIP.VI8AMC.US.FPATH.ESO.NDSET,NWS(lO),D«0>8I6MAP
033 NRUN • 0
034 NSlaNS*!
035 NUMSlBNUMSEC-1
036 CONVF«3'.67E*03*(TDK/PS(NUMSEO)
03T NRAPOC«0
038 XiO.O
039 00 15SS 1"1»N8
040 EFE8RBl>X8(I)/ONO(I)
041 IFCEFESR.ST.0.999999) EFE8R»0.999999
0«2 X»X«EFESR*PCNT(I)
043 155» CONTINUE
044 1713 CONTINUE
045
04* IF(NRAPDC.EQ.l) CO TO 6078
047 60 TO 6080
049 6078 CONTINUE
049 ARD50(1)**.0
050 ARSIGM(1)*2.5
051 RMMD«*'.0,
052 R8I6MA>2,5
053 CO TO 6079
054 6080 CONTINUE
055
056 RSIGMA^ARSICM(NRAPOC)
057 6079 CONTINUE
058 CALL LND!ST(RMMD.RSICMA,RPRcU,RpeNT>
059 DO 7575 I»l,N8
0*0
159
-------
KRITE(NPRNT,19)
19 Po*MA7ir4X,'8m».sx,,'ccF>,2x.»iNiET *».ix,'ouTLET XMX.'COR. oun
tET I*.IX.'NO-RAP EFF.'.IX,»NO.RAP M'.2X.'NO»RAP P'^X.^COR. iff.*.
2ix.'coR'. w',sx,'eoR. PJ) '
0*1 TITS CONTINUE
062 MONCKsO
06S 1867 CONTINUE
0*4 NONCK«NONCK»1
06S SNUCKMASNUeKCNONCK)
066 Zl6«Y»AZI60Y(NONrK)
067 ZNUM8MAZNUM8(NONCK)
0*8 WRITE(NPUNT,18)
06t !• FORNATHHl.' PARTICUC «IZC R»N8t STATISTICS*/)
07fl KRITE(NPRNT,18fc«) NONCK
OTI i860 FORMAT*/* CORRECTIONS FOR NONIBEALITIES USINO SET NO; * i».« OF co
07« 1RRCCT10N FAR*MCTrR8'/>
on c
074 C PRINT DIAM., PERCENT, AND EFFICIENCY FOR EACH SIZE RANGE
07S C
07* NRITE(NPRNT,19)
077
07S
079
OSO C
OS1 C
082 ViO.O
OSS DO 2990 I"1|N8
084 EFESR«DXS(j)/ONOi!)
08f IF (EFE9R .6T..999999 ) EFE8R • .999999
096 XEP«EFE8R*100.nO
OS7 IF (XEP '.61. 99,9999 ) XEP • 99.9999
OS6 IF(EFEaR,CE,0.99999)WV«XMV(I)*!00.
089 IF(EFE8R.LT.0.99999)HVa(V6/ATOTAL)*100.*AL06OOO./(100..XEP))
090 IFCZieeyoO.0)4704.4704,4705
091 4704 Fl«l.
092 60 TO 4706
09S 4705 CONTINUE
094 Fl«i.*.7
095 4706 CONTINUE ,
096 IFONUCK-0.0)4701,4701,4702
097 4701 F2»l.
098 00 TO 4703
099 4702 F2»DlOG(l,«EPE8R)/(ZNUM8*DLOO(SNUCK»(l'.«SNUCK)*(!.0-EFESR)**(r /
100 1ZNUM8)))
101 «7Q3 CONTINUE
102 WY8-NY/FZ
ios WYV*WY/PI
104 ZNLFF • Fi*P2
105 WYSVaWY/ZNLFF
106 WUNCORjtpBNV
107 EUNCOR(D>EFE8R«100'.
108 CALi. WAOJSTCOIAM.I.MYaVtONOfPXS.ATOTAL.Vfi.EFESR)
109 IF (FFE8R ,CT..999999 ) EFESR • .999999
110 XeP«EFE8R*100.00
111 IF (XEP ,GE. 99.9999 ) XEP • 99.9999
112 IF(EFE9Rf6e.0.99999)NY«XMV(I)«100.
US IF(EFE8ft.LT.0.99999) wy«(V6/ATOYAL)*100'.*«LOO( 100'./(100'..XCP))
114 PXSmyCFESR*ONOtI>
115 Y • Y * EFESR • PCNT(I>
116 2990 CONTINUE
HT IDCiO
118 8PO«0'..
119 SCPOiO.
120 IX*0
160
-------
121 1141 CONTINUE
122 8COREF • O'.O
121 IDC»IDC+1
124 DO 5540 I»1,N8
125 XX«IX+1
12* EFF8*«PX8(p/ONO(I)
127 ir CEFESR .OT.'. 999999 > EFE8R • .999999
128 XEP«EFE8R*100.DO
12* IP (XEP ,6E. 99.9999 ) XEP • 99'.9999
ISO IF(EFE8R.6E.0.99999)WY«XHVm*100.
Ill IF(EFE8R.LT.O,9999«W«(VG/ATOTAL)*100.*ALOe<100./tlOO..XeP))
152 XYmPCNT(I)*lOO'.
153 PENTR«100.«XEP
1S4 PCTOT(I)*FENTR*PeNT(n*r.E»02
155 iritlx'.CT,!) 60 TO 7150
15* CLPTL5»0.
157 DO 1 I8-1.NUH81
158 CLPTL8«CLPTL8*FtOAT(L8ECT(I8))*LINCS(18)*0.50S
159 1 CONTINUE
140 NVX«0
141 1450 CONTINUE
142 NYX«NYX+I
145 IF(NYX'.EQ.a) 60 TO 1451
144 XEFF«y
1«5 IF(NFFF'.EQ'.2) XEFF«X
106 EXPONTBil06(l,/(l.-XEFF))
147 XMEL8«OL*exP(.CEXPONT«CLPTL»)/PL)
148 XHCL8BXMEL8«(i.-EXP(-(EXPONT*FLOAT(LIECT(NUM8CC))»LINC8(NUM8EC)*0.
149 150S)/PL))
ISO XMLL8»XHEtS>XHCL8
151 XMCL8«XMCL8*CONVF
152 IF(NTEMp'EO.l) KAPL08B0.1S5*XMCt8**0.905
155 IF(NTEMP.E0.2) P*PL08«0.618«XMCL8**0.894
154 60 TO 1452
155 1431 CONTINUE
156 CXPONT.ALOGCl./d.-Y))
157 YMEC9«0L*EXP(.(EXPONT*CLPTL81/PU
158 YHCLS«YHELS*(l.nEXP(»(EXPONT*FI.OAT(L8ECT(NUM8EC))*LINC8(NUM8EC)*0.
159 1505)/PU)
160 VMLL8«VMEU8-rMCL8
161 YMCL8«YMCLS*CONVF
161 14S2 CONTINUE
165 IF(NVX'.EO.I) GO TO 1450
164 7130 CONTINUE
165 PN8B((P.*PLOS/(DD*CONVP))*RPCNTim*l«E>02)/( (5. 14159*01 AM(I)«*3)/6.
166 1)
16T WY8V«wr
168 EFFWRB(ONO(n*(l.»EXP(*>(ATOTAL*WV8V)/(100,*V6)))«RN8)/ONO(I)
164 CRNP • ONO(I)»(1..EXP(.(ATOT*L*WY8V)/(100.*VO))). RN8
170 IF(fCRNP'.J.E'.0,0) EFFWR • EFE8R
171 IFtEFFWR.GT,.999999) EFFWR*.999999
172 COP.EFF«EFF«R*100'.00
173 IFfCOREFF.SE.99.9999) COREFF»99'.9999
17« IFfEFFWR',6E.0,99999) WYP«WY8V
175 IF (EFFWR.LT.0,99999) WYP«(V6/ATOTAL)*100'.*AL06( 100./(100'.«COREFF) )
176 8COREF • SpOREF t COREFF*PCNT(I)
177 CPENTR«100.»COREFF
178 CPCTOTjtI)«CPENTR*PCNT(I)*l.E«02
179 IFtIOC.NE.1) 60 TO 1543
180 8PO«SPn*PCTOT(I)
161
-------
181 SCPOMCPOtCPCTOT(I)
181 1343 CONTINUE
t83 at«u'.0*EFES*)»oNorz;
184 M3L(I)*8L«(1.3*333*3.14159MADJTI )*«3)*DD
18S IF(IOC'.EO.l) 60 TO 1344
IB* PCTOTei)«CPCTOT(I)/SPO)*iOO'. ,
187 Cf>CTOTm*(CPCTOT(I)/SCPO)*100.
188 DiDHALOGWENDPm*i»"ALoeiocENp
189 OMOLD«C'^CNT(I)*RAPL08*l.E.02)/DLO
19! CDMDLOm»DMOLDTS) V
20T 3*75 FORMAT(//SX,23MAOJU8TEO NOMAP EFP. • .F8.4)
208 WRITE(NPRNT,5802) ZMMDl
209 5602 FORMATfSX('MMD OF INLET SIZE DISTRIBUTION «',lPCU.3>
210 WRITE(NPRNTf5803) 8IGHI
211 5803 PORM»Tf5X,'8I6HAP OF INLET SIZE DISTRIBUTION ••,1PE11.3)
212 IF(NOI8T.E0.1) NRITE(NPRNT*«250) CFIT
213 9250 FORMAT(5X,'LOG-NORMAL GOODNESS OF FIT • *,P*.3>
214 C
215 C CALCULATE MMD OF EFFLUENT UNDER NO-RAP CONDITIONS
21* C
217 PRCUNR(1)»0.
218 SUMNR«PRCUNR(1)
219 DO 1750 !«t,N3
220 SUNNRiSUMNR^PCTOTd)
221 PRCUNRd + nMUMNR
222 1750 CONTINUE
223 CALL LNFIT(PRCUNR,ZMDL.8!GMO,ZQFIT)
224 2982 «RITE(NPRNT,2«»97) ZMOL
225 2997 FOPMAT(5X,'MMD OF EFFLUENT UNDER NO-RAP CONDITIONS •MPF11.3)
22* MR!TE(NPRNT,5601) 8ICMO
227 5*01 PORMATit5x,'SIGMAP OF EFfLUtNT UNDER NO-RAP CONDITIONS .'.lPril.5)
228 WRITE(NPRNT,9250) ZGFIT
229 COREFWf(VG/ATOTAL)*|00.*ALOG(100,/(100>SCOREF))
230 WZa(VG/ATOTAL)*100'.*ALOG(10o./(100.-Y))
231 HRITE(NPRNT,2996) MZ
232 2998 FORMATC5X,'PRECIPITATION RATE PARAMETER UNDER NO-RAP CONDITIONS •'
233 1.F7.3//)
234 PRCUC(1)«0.
235 SUMC»PRCUCm
23* DO 1751 I»l,N8
237 8UMC«aUMCtCFCTOT(I)
238 PRCUC(I+1)*SUMC
239 1751 CONTINUE
240 CALL LNFIT(PRCUC,CZMDL*C8IGMO,CGFIT)
162
-------
241 NRITE
296 HRITr(NPRNT««2SO) CQFIT
25T «RITP(NPRNT,5003) COREFH
256 5005 FORMAT (5X, 'CORRECTED PRECIPITATION RATE PARAMETER ••.F8.2)
25* WRITE(NPRNT,6565)
260 6565 FORMATMH1.' UNADJUSTED MI6RATIQN VELOCITIES AND EFFICIENCIES. AND
261 1 DISCRETE OUTLET MASS LOADINGS*//)
262 NRITF(NPRNT,19«0)
263 1*80 FORMAT(1X,I6HIDEAL UNADJUSTED, JX. 16HIDEAL UNADJUSTED, TX.6HNO-RAP, 1
264 10X.12HRAPPIN6 PUFF.6X, 15HNO.RAP+RAP PUPF.5X, 12HRAPP1NG PUFF.aX.8HP
265 2ARTICLC)
266 WRITE(NPRNT,198n
26? 1981 FORM*T(1X,17HMI6. VEL. (CM/SEC) ,4X. 1SHEFFICIENCV (*),4X, 17HDM/DLOGOC
260 1MG/DSCM) .2X, 17HDH/DLOGO(N6/DSCM) ,2X( 17HDM/DLOGO(Mfi/OSCM) .2X, 15HOI3
269 2TRIBUTION(X),ZX,8HOIAM.(M))
270 00 1082 M«1,NS
271 WRITF(NPRNT,1983) NUNCOR(M) , FUNCOR(M) ,DHDtO(H) ,ROMOLO(M) ,
272 lCOMOLOfM)i«PCNT(M).OlAN(M)
273 1983 FORHAT(lX,tPElO,3,4(10X.lPEl0..3),7X,lPEl0.3,6X.lPE10.3)
27« 1982 CONTINUE
275 NRUN • NRUN * J
27* CAUL PRT8UM
27T IFfNONCK'.LT.NQNlO) GO TO I«fc7
278 IFfNRAPDC.LT.NRAPD) GO TO 1713
279 RETURN
280 END
163
-------
001
002
003
004
OOS
00*
007
008
00*
010
Oil
01*
013
014
015
01*
OIT
Olfl
019
020
021
022
023
024
085
02*
027
020
02*
030
031
032
033
034
015
03*
SUBROUTINE MADJST fDlAM,I,MY.ONO.PXS.ATOT*L,VG.EFfSR)
A*************.*****)
CORRECTION FACTORS IN THIS SUBROUTINE
ARE BASED ON DATA TAKEN UNDER
C.P.R.I. SPONSORSHIP 8Y SO.R'.I.
ft******************************************
DOUBLE PRECISION IFE8R
DIMENSION DJAMf20).ONOt20).PX8f20).CFAeT<24),OCMfCK(24>
DA '*'" * — • " * ' '
IBS
200/
DATA c'AcT/2. 43,?. 329,2.24. 2. 17.2. 11.2.05, 2.00, 1.9*5.1.92,1.889,1.
BS, 1. 82, 1, 79, 1. 7*. 1. 74, 1. 71, 1 .80S, 1.5, 1.37.1. 27, 1'.te. 1.1 15.1.09,1.
00/ . . . .
DATA DCHeCK/.2E»0*,.25e-0*,.3E-0*,.35E-0*,.4E-0*,'.flSE-0*..SE-0*,.S
5E-0*. ,*r-0*. .fcSE-O*. .71.0*. .781-0*. ,BE»0*. .BSE.O*. ,»E-0*, .9SE-06,
r.E»0*.r.SE-0*.2.E»06,2,SE-0*,S.E«0*,3,Sr-0*,a.E»0*,4.SF»06/
15E
er.....,,,.,,.,.
ir((DIAH(n.LT.2.0E-07).OR.(DlAM(I).6E.4.SE»06)) CO TO 6
DO 3 L"lf23
tF((DIAM(I).6E.DCHECK(L)).AND.rDIAM(I).Le.DCHrCK(L»l)» GO TO «
60 70 3
4 CONTINUE
WFACTBCIrACT(L)-((OUM(I)«DCHECK(L))/(DeHeCK(L*l)*DCHECK(L)))*
1(CFACT(LJ-CFACT(L»1))
CO 70 S
3 CONTINUE
* CONTINUE
rFE8R«l.-eXP(.fATOTAL«WYJ/(100'.*VGl)
PXS(I)BEFESR*ONO(I)
S CONTINUE
RETURN
END
164
-------
001 SUBROUTINE LND1ST (D50.SIGMAP, PRCU.PCNT)
002 DIMENSION Y(lOO).mOO),ARFAC20),PRCU(2n,PCNT(20)
005 COMMON/8LK4/NS
OOa COMMON/8LKll/ENDPT(2n.NFNDPT
00? PI«»3'.1416
006 SIGMAZ«ALOG(SIGMAP)
007 N.NS+2
008 NINCsiOO
009 ASUMcO'.
010 K«0
Oil DO 240 J"1.N
012 IFU'.SQ'.IIGQ TO 230
013 IFfj'.EO.(N))CO TO 252
014 X2«ALQG(ENDPTU»
015 XlsALOG(CNDPT(J-l)J
016 GO TO 213
017 ?30 CONTINUE
016 XlsALOG(O.Ol)
019 X2*ALOG(ENDPT(Jn
020 GO TO 233
021 232 CONTINUE
022 X1«ALOG(ENOPT(J-1))
023 X2*ALOG(1000.)
02a 233 CONTINUE
02S
027 SGTl«r./(SlGMAZ*(2.*Pl)**.5)
02$ SGT2B2'.*S!GMAZ**2
029 DO 254 I«1«NINC
030 Y(I)«S6Tt*EXP(.(O.ALOG(050))**2/SGT2)
031 o«o*nx
032 234 CONTINUE
033 CALL OTFE(OX.Y.Z.NINC)
034 A3UM«ASUHtZ(NIKiC)
035 IF(j'.LT.N) PPCU(JJ«ASUM
03* IF((J.F0.1).OR'.(J.FQ.N))GO TO 246
037 K«K+1
038 *RFA(K)BZ(NJNC)
039 240 CONTINUE
040 DO 241 I>1,NS
041 PCNTdJeAREAdl/ASUM
042 241 CONTINUE
043 SUMsO.
044 DO 2 1=1. NS
045 SUMnSUM+PCNTCn
046 2 CONTINUE
047 CHECKi * 1.0 - SUM
048 PCNT(NS)«PCNT(NSUCHECK1
049 CHECK? t 1.0 • PRCU(NENDPT)
050 PRCU(NF.NOPT)»PRCU(NENOPT)+CHFCK2
051 RETURN
052 END
165
-------
001 SUBROUTINE QTFE
-------
001 SUBROUTINE LNFIT tPRCU.DSO.SJCKAP.CflT)
002 C THIS SUBROUTINE FITS COMPETENT. CURVE TO A lOfNORKAL DISTRIBUTION
oos DIMENSION z<2t),Y<2i),pRcu(2i)
00« COMHON/BLK 1 1 /ENOPT (21 ). NENOPT
005 N9TAOO
00* J»0
007 DO 1 !»}.NENDPT
OOa IF(PRCU(I).LE.O.O)GO TO 1
00* JBJ+1
010 r
-------
001 SUBROUTINE CFIT (A.B.R.N8TAC.Z.V)
002 C THIS SUBROUTINE FITS A STRAIGHT LINE, ViAfBX, USING LEAST SQUARES
003 DIMENSION ZC21),V(2n "
00« XN«0'.0,
OOS SUMX»0.0
00* SU*Y"0'.0
007 8UMXV.O.O
000 5UHXX»0.0
004 SUHVY»0.0
010 00 * I-1.NSTA6
Oil IUMX«3UMX*Z(I)
012 »UMy«sUMYfy(I)
Oil SUMXY«8UNXVfZ(I)*Ym
014 SUMXX«8UMXX«Z(T)**2
015 SUMVY«8UMVY«Y(I)**2
014 XN»XN+1.0
017 * CONTINUE
018 C CALCULATE A,B
019 B«(XN«8UMXY*SUMX«SU*V)/(XN»8UNXX-8UMX*«Z) .
020 A«(8UMXX*8UHV.SUMX*SUMXV)/(X»i*8UMXX«SUNX**2)
021
022 RETURN
023
168
-------
001 SUBROUTINE PRT3UM
002 REAL LINCS
001 CO«MONm*2/l.8ECTC10),L,INCS{10>.PStlO)
00* CONMON/BLKS/VC.ATOTAL.DO.ETAO,Ol..P|..*HO
OOS
006 COMMON/BLK6/VOU20),XNO(20),0(*0)»NS<20).XTU40),DN(4S),A8(10),
007 lVOS(tO).TCS(tO),Nt.S<10),AC8<10J.SSUOJ.SYSUO>,V«8(10>.V6A8S<10).
008 ?TE"PSMO).VI8SC10).08AT(?0).U,E.EP80.PI,ERAVG,BCtTeMP.EPS,VAVC.
009 30100(20). OLBXNO(20).I»FSOO),STAI»T1 MO). STA*T2(10).START3( 10).
010 4V8TARMO)
Oil CO"HON/BLKI7/NREAD.NPRNT
012 COMMON/BlK18/8COl»fr,CZMin..C8ieMO.NP.UN,8NUCK,Z!GCY.RMMO.R8IGMA
013 SCAaATOTAl/VG
01*
01* 00 6571 I«liNUM8EC
017 V08UH«VoSa>*rLOATtLSECTm)*LTNCSm*0.305+V08Ut«
018 Cp3UM«(TCSm/(A8m*9.3E-02n*i.E*OS*FLOAT(L8ECT*
01* 10.305»CDSUM
020 6971 CONTINUE
021 AVO»V08UM/Pl
022 ACD«CD8im/Pt
023 RHOCG8«RHO*100.
024 WRITE (NPRNT,1«94)
025 1999 roRHAT(iH
026 fRXTE(NPR
027 9520 FORMAT(9X,
028 1 A************************************************************')
029 WRITE (WPRNT, 1060)
050 WRITE (NPRNT,J060)
Oil 1060 roR«AT(9X,»»',ll«X.»*»)
052 HRITE(NPRNT,9SOO)
033 9500 roPMAT(9X,'*',3«»(,'8UMM»RY TABLE OF ESP OPERATIN6' ,«5X. •*')
03« WRITr(NPRNT,9501)
035 9501 PORHAT(9X«'*',aiX< 'PARAMETERS AND PERFORMANCE*, «7K, »*'J
036 MRITE(NPPNT,!060)
037 WRITE (NPRNT, 1060)
038 WRITF{NPRNT,10fcO)
039 WRITE (NPRNT, 1060)
040 WR!TE(NPP.NT,9502) NRUN
041 9502 roRMAT(9X,»*',46X,'OATA SET NUHBER '.I J.«9X,«*»)
042 *RtTE(NPRNT,1060)
043 WRITE(NPRNT,1060)
044 WRITE(NPRNT,9S03) 8COREF.8CA
045 9503 FORMAT(9X,««*,12X.»ISP PERFOPMANCEl'.SX, 'EFFICIENCY « '.FB.**' X',
046 15X,'SCA • *,1PE10.3,' M**z/(M**s/SEC) »,21X. »•')
047 fRITE(NPRNT,1060)
048 WRITE (NPRNT, 1060)
049 WRITE(NPRNT,9S04) AVO
050 9504 FORMAT(9X,'*',12X, 'ELECTRICAL CONOITIONSl ».SX, »AVc'. APPLIED VOLTA6
051 1C • '.VPE10.3,' V'.ftOX,'**)
052 WRITF(NPRNT, 1060)
053 WRITE(NPRMT,9505) ACD
054 9505 FORMAT(9X,**',39X,*AVG. CURRENT OEN8ITV • •,Ff.2.» NA/CM*«2'»36X. *
055 1*')
056 *RITEfNPRNT,1060)
057 WRITE (NPP.NT, 9506) RHOCC8
058 9506 FO«MAT(9X,«*»,39X, 'RESISTIVITY • '.IPEIO',3.' OHM«CM».««X. •*')
059 WRITE(MPRNT,1060)
060 WRITE(NPRNT,1060)
169
-------
0*1 KRITE(NPRNT,9S07) ZMHDI,8IOMI
0*2 9507 FORMATt9X,»*MZX,'3m DISTRIRUTXON8|',SX. 'INLET HMD .
063 i' UM',SX.MNLCT SXGMAP • '.1PE10.3.Z3X,'*')
06« WRITE(NPPNT,1060)
065 W*ITE(NPRNT,9SOI) CZMDL.CSIO»*0
046 4508 FORMAT(«X,'**»S*X, ^OUTLET HMO • MPE10.3,' UM'.SX, 'OUTLET 8I6PAF
06T I* ?.lPEiO,S,21X,'*»)
068 »*XTE(NPRNT,1060)
069 WRITE(NpRNTf1060)
070 MRITE(NPRNT,9509) 8NUCK.ZIOGV
071 9509 PORMAT(9X«'*',12X«'NONIDEAL PARAMETERIl'.SX, '6*3 SNEAK4GC PRACTIQN
orz i • *.r«.z,» /SECTION', sx,»e*8 VELOCITV SISMAG • '.ra.z.tx,'*')
073 WRITE(NPRNT,1060)
07« WRITE(NPRNT,9510) RMMD,R8I6MA
075 9510 FORMAT(9X,'*»,17X, 'RAPPING KNO • '.1PE10.3.' UM»,5X, 'RIPPJUO 8IQNA
076 IP • ',1PEIO,3,18X,'»')
077 WRITE (NPRNT« 1060)
078 HRITE(NPRNT,!060)
079 WRITE(NPRNT(9520)
oeo RETURN
081 END
170
-------
ooi BLOCK DATA
002 LOGICAL LTEST
003 COMMON /BL«2/ LTCST,RHO<15.1S1.V(15.l5).EX(15.l5),rr(l5fl5>
00* DATA LTE6T/.rAl8e./.RHO/?a5*0./.V/22S*0./feX/2a5*0./.CV/2ZS«0./
005 END
171
-------
001 SUBROUTINE CHAN f VW.NX,NV,3x.3Y,PI. AC,NNIRE)
002 C COOPERHAN SERIES DETERMINATION FOR VOLTAGE WIRE TO PLATE
003 C FOR SUBROUTINE EFIELfl
004 REAL Wlw.M.NNIRE
005 LOGICAL LTE8T
006 COMMON /8LK1S/VCOORC1S, H).NVIT
OOT COM*ON/BLK21/ECXri5.15).«yfl5.l5>,XIC15»,Vl(15),AX
008 COMMON XBLK22/ LTESTfRHBf IS, 1S>. V(15. 15).EX< IS. 15) .EY(1«», 15)
009 NXl«NX-t
010 NyiBNV-1
Oil 00 402 I«1.NX
012 IF(NVII-l)501,JOfl,301
on 3oo i«wx
01« J01 CONTINUE
015 DO «50 J-l.NV
01* X«fLOAT(I-l)*SX/rLOAT(NXl)
017 1F(LTE9T)X«X1(I)
018 V«FLOAT(J-1)*3V/FLOAT(MY1)
020 ir{X'.EO.O..AND.Y.EO.O.)CO TO 4AO
021 CO TO «50
02? a«o vcooP(l,J)»vw
021 60 TO 430
024 450 CONTINUE
02S M«»NMJRE
026 NUMcO.O
027 DENOMiO.O
028 EXO«0.
029 EYO«0.
030 EX8UM.O,
031 EYSUHiO.
032 490 El«PI*tY»(2.*M*8Y))/(2.*3X)
033 F!»PI*X/(2.*3X)
034 ei*PI*H*SY/8X
035 Hl»?I*AC/(2.*SX)
036 E2»(ExP(El)fEXP(-El))/2.
037 F2»COS^F!)
038 62>(EXP(ClUEXP(>Gl))/2.
039 H2»COS(H1)
040 TT«(E2-F2)/(E2*F?)
041 TB»(62-H2)/(G2*H2)
042
OttJ
044
045
046
047 F3*SIN(F1)
048
049 63*(EXP(Gl)«EXP(«6n)/2.
050 SU"X"F3/(E2-F2)+r3/fEt+r
051 8UMY»E3/CE2»F25-F.3/(E2*F
052 Sl»H3/ff,2-H2)+H3/(G2tH2)
053 S2*G3/(G2»H2)»G3/(G2+H2)
OStt EXSUHtEXSUHtSUMX
055 EYSUM.EY8UM+3UMY
056 f)fO«EKO+81
057 EYO«EYO+S2
05» IffM.LT.NWlRE) GO TO 408
059 CO TO 010
060 008
172
-------
061 60 TO 490
062 410 VCOOPfl,J)«VW*NUM/DENOM
063 ECX(l,J)«
064 ECY(I.J)«
06S 450 CONTINUE
066 40? CONTINUE
067 4Q4 CONTINUE
066 £CXU.n«
060 ECYM.M«"fPI*V*/a./SX/DENOM)*FVO
070 RETURN
071 END
173
-------
001 SUBROUTINE E?L03 (UEO.AC,VO,SX.SV«MXfNr,4EPLT,TDK.R,Rr.
002 ISTABT.OSTART.CSTART.lFlNAU.VSUBT.VN.ACDWTV.Nwip.e.NECtEBO.JIl.Jl?)
005 C FVALUATIOM nF FIELDS, SPACE CMA»Gf DENSITY, POTENTJAI ,
OOa C CURRENT DFNSITV FOR A Hm-PHTF PRECIPITATOR
005 REAL MWIRE.MAXS.MOBILTCIS, 151
006 LOGICAL LTEST
OOT DIMENSION RHO(15.15),F.X(IS.1S).OLDRO{15, tS).OLOV(t5,lS).
008
009
OtO
OH COMMON /RL"t
051 WVtBK'Y-1
035 TVCK«o
03fc »C«Ar
03T HO 1001
03« IFdt.FO'.JTn 5TART«OI»TABT
039 IFdI.6E.JI2) 8TART»CSTA«T
0<)0
0«1
0
-------
061
062
06) SUMlBSUMl+ALnC-fABS{CCH«COS(Al*AC))/(CH»COS(Al*Ae))))
060 5601 CONTINItf
065 '
066
067 .
06* 1M«1.GT.SX)R1«SX
06"
070
071
072
075
07«
07S lFCwr.LE.5Y) GO TO bO
076 CAIL APCC08(SY.R1,»COS>
077
079
oao on CONTINUE
061
062
085
0«5
066
08T l/(?.*HI*SY/PT/EO<»n/RAPU(RARl-t ,
066 '
069
090 2 *C»AP1-1.)
09J
092
09J 1 .2.*B1P«(SX"«l)*90RT(AR»J(8y«ptn/l,
095
096 2 +AL06fABS((AC*Ar*«.*3X*t8X*ACl)/8QO^nn+«LAH4tal.AM*8UHW
097 lFf'ivn.rr..l)QO TO 10
09fl 60 Tn in
090 jo CONTT'i'iF
100 FsVj-vn
101 IF rF.fO.p.jCO 70 50
10? 7rrARsm.LT.l'.OE.O«**BStVP)) r,o TO 30
10S
10« IF(F'.LT'.0.)F1»F
105
10* IFfF.fiT,0.)F2«F
107 lFfF'.fiT.O.)E2eFORO
10« TF(Fl*F?.LT.O.)f
109
110
111 Jf( ICOUM.FO.lOOJ^PITEfNPRNT, SI)
112 3) K?PMATnOX,*7HF APPtTEO POTEN7TAC COULD NOT BE MATCHED
HJ 1 MO" ITFPATTON5V)
110 IFflCDUMT.GT.lOOlGO TO 30
CO TH 60
117 V(1.1)BVT
11* CALL r"AN(BLA:4.NX,NY,SX.3Y.Pl,AC,NWIRC)
120 DO 51 nn 111*1,
175
-------
121 IFfNVH.ro'. J)I11«NX
122 Y»o.
123 DO 3800 T12'1,NY
124 lFfLTC«T)X«Xl(Hl)
125 !F(LTEST)Y«YHI1»
126 TFfNVn'.EQ'.l)X«8X
127 XKXlllsX
128 Y)(I12)«Y
12« 8l»2..ACONTY/EP80/M08lLTmi.I12>
130 R1R«30RT(AB3(B1M
131 Cl«Hl*«y/Pl
132 irniH.FO'.n
133 50RNeSQON+Y*Y
134 3QRP«SOOP+Y*Y
139 SOXN»x*X+Y*Y+4'*SX*(3X«X)
136 8(JXP»X*X«Y*Y + 4.
137 A»GX«PI*X/SX/2'
IS* AR6Y»PT*Y/SX/2.
130
141 RARlY«8RRTfAB8fl.*Cl*(Rl*RUv*Y-AC«AC)/EORO/CO<»0))
142 COSHYsC09H(*]*y)
143 8IMHY«3INH(A)*Y)
144 CX«C"SfAl*X)
149 IPfX'.GT. 1.00001 *R1) CO TO 3860
146
147
148
149 fXJ«-Ei5ftn*«RAXY-l.)*X/fX*X*Y*Y)-(«ARl -1 . )* ( ( X-?'.*SX) /8QXN
150 1 ifX+2.*8X)/80XP>/2.)
151 P.Yj*-EPPO*f (RAXY -l.)
152 1 -(RAR1 -l.)*(Y/8ClXN+Y/80XP.Y/SORN«Y/30RP)/2.)
153 RHnjm.fPSn*Cl/eORO/»AXY
154 1 *r./n.+ ((V + 1.r."001/3Y1**9*2'.20)/(l.i.l6?*Y/8Y)
15S ? -FPSO*En»0*(RAXY.l.}/2.«(f800N.Y*Y)/30RN/30RN*(300P"Y«Y)/
156 3 80RP/SORP)*0.9
157 CO TO 3861
15* 386C CONTlMiir
159 VXYJ»rt AM*4LnGrA«8<(C08HY«CX)/fCOSHYtCX)n
16" l+?'.*niP*C(X-on*gQflT(ABSn 100
173
174
175
176
177
178
179
180
176
-------
181 1 +»Lnc(*BS((COSHP.Co8X)XfCnsMP*C08X)))
182 SU*V»5UMV*TFI»MV
18S TtPfXmf OSHH/r»f
184 SUMf.XaSHMEX + TEBEX
IBS
186
187 100
IBB
190
191 VXYJsvXYJfVWIR
IPS FYJaFYJ+fY*!*
l9/» vmi.Ti?)«vxyj+vcnaPmi,ii2)
195 f xmi.H?)»EXJ*FCX(I11.112)
196 FVfIli.ll2J«FYJ+ECVrill.Tl?)
197
198
199
200
201 X«X+SX/FLO*TCNX1>
20? 3100
203 5150
205
206 no 12"n J=?,MY
207
20* TFf .
210 1200 CCNTTNi'F
215 IMAMSfMPJX.nj.LT.EHD) 6n TO 1«80
216 wRTTFfMP»NT,lu»n Vw.iCDNTY
217 1««1 FQPM4TC THE «»E»KDOWH F1EJ.D >JF»R THE PL*Tf 18 FUttF-OEn AT Vtt a'.E
SIP 111 '.a. IX, 'AMI) ACPNTV »'.F.tl.«l
219 (,.-> Tn i«!?S
320 1 Go
227 1523
228
229 VMBOI. ov«i
211 KO TO
232 l52«
233 MO)
23« 1526-
235 IP(nrc.NF.O) GO TO
236 Hat
237 no 3001
238 BS'iM.o'.
23<> tSU»«o'.
TO 5(»0? 1*1, »
177
-------
IF(J.FD.l) GO TO 3005
242
243
244 f,o TO 3006
24.5 3005 CONTINUE
246
247
248 3006
249 PSUHaPSilM-(FJHon.JU»Hfl(I,j4lM/(2.M.6E«19*Nxi
250 300? CONTIMllf
251
252
253
254 3001
255 WYYaNYl
256 DO 3003 L"1,NY1
257
258
259 NYYmMYY.l
260 3003 CONTINUE
261 Mil
262
263
264 00 3004
265
266
267
26ft 3004
269 3000 COfc'TTMUF
270 LL*\
271 r>0 3007
272 ECOLlSfl
273 U«U.+ 1
274 3007 CONTIMDf
275 I 1*NV1
276 no 3008 L«lfNYl
277 ECOLL(L)«ECOLL8(L1)
27* U«L1-1
279
280
281
282 I2«2*NYl
283 PO 3009 1*11,12
284 ECOLl(I
28? 12*1.2*1
286 3009 CDNTTM'lE
287 Vo«-i.*VO
288 STARTcSSTAPT
289 PFTUPN
290
PROC > 4K
178
-------
APPENDIX G
OUTPUT DATA FOR EXAMPLE 1 (REVISION 2)
179
-------
00
o
»****•**•*•*•**»**••»*•*•*•**••**»•*
E.P.A. FSP "OOFI
I.E.R.L.-R'.T'.P. AND SO.B'.T.
REVISION II, AUG., 197«
»•***«•*******»***** *****•*•**•****»*
PRINTOUT OF INPUT Pit* FOR DATA SfT
OATA ON CARD NUMBER i
NENDPT • u NOATA • t
0*Ti ON CARD NUMBER 3
LAB EIPl 8eA»t25FTJ/1000ACFt«|J«2fl.OUA/rT2
DATA ON CARD NUMBER s
NEST • t NDIST • i NVI • 3 NX • to NY • 10 NITER > 3 NCALC • o NRAPO • t *EFF « i NTE«P • i NOW ID • 2
01 TA ON CAM NUMBER 4
NN • 5 NU"I*C * 3
DATA ON CARD NUMftFR S
DL « 0.01500 CRN/ACF PL * 10.0000 FT FTAO • 99.00000 X DO « inoO.no KG/M**] EPS • S.iOOr*00
VRATIO « l.PJOO US * 0.000165 M**2/y.$FC FPATH • 1,0000 FRO • 1SOOOOO. V/M RHOC6S * 1.00F+09 OHM. CM
DATA ON CARD NU-8ER 6
ASNUCK( I) • 0.00 AZSGRV( 1) = O.OA A7NU*
-------
ENOPTt I) • ft,2on I.IH fcMOPTC 2) * 0.^00 111 fJDPT( }) : O.dftO UN MHPTC u; « 0.500 UM fNQPTf 5) t 0,*0« U"
ENDFT( 6) • e>01 U* ENDPTt 7) • 1,«00 UM ENQPTf ») • t.ZOO UM fNOPTt ») * 1,«0n UH fNOPT(lO) • 1,»00 \J»
DAT! ON CARD
• ?.ZO« "M tNpPTd?) c ^.oofl im EMOPT(Jl) • a.roft U« tinPTtiu) » ».oso U«« f-OPTdS) • 10.000 UH
EMOPT(1») » 20.000 U«
0*Ti ON c*PD NUHHFR 4
PRCUt 1) • . 0.0000 * P»CUC ?) * 0.0002 X P»CU( J) « O.aftfl? X PRCi'f a) • 1.1)002 X P»CU( S) • 2,«*72 X
P*CU( ») > T.6672 X P"CU( 7) • 12.6002 X P"C"( » « 17.4002 X P"CU( 9} > 21,1312 X P'CUUO) • 2«.^132 X
DAT* ON CARD MUMMER 10
PRCU(H) • 36.0002 X PPCUO2! « at. 6*72 X PRCUCIS) « «7.1I«2 X PRCU(ta) • 66.6672 X "»Cu(15) > 90.6672 X
(_i PRCU(16) • 100.0000 X
00
H
D4T* OM C*»0 NUHBfR 11
• I ISECT( 1) » J LSfCTf 2) • I LSfCT( J) • 6
DATA OM C«*0 NUMBER 12
*8( 1) • 6>2500E«00 FT**2 VOS( 1) » a(6000f»0a V TCS( )) • I.i000r»0« * «LS( I) • 6,»OOEtOO FT
*Cif i) • «.6«75E.o2 IN BS( i) * <<.ooonE«oo IN NW»( n • 5.?noar«on
DAT* ON CARD MUMAFR 's
SV8( I) • 2.5000f+00 IN VGSf I) > 2.noOOF*02 FT..J/MJN Ws»5»f !) • S.200«E»00 FT/SEC Tr-PS( H • 7.6»OOF>01 F
PS{ 1) « 1.000«a V TCSr ?) • 1.5000E«0« A «ISC 2) « 0,2^n1E»00 FT
ACSf ?) « «.6»75F-02 J" "*( ?^ « ?.fl«OPE»0« !•* «»S( 2) «
-------
DATA ON CARD NUMBER 15
•Yi( 2) • 2.IOOOE400 IN VQK 2) • 2.0000C+02 FT**3/HIN VGASS( 2) • 3,2000E«00 FT/8EC TEMPI ( 2) • T'.*800C*Ol P
2) • i.ooooe*oo ATM vm« 2) • I.BOOOE-O? KG/M.SCC LXNCSC 2) • 8.5333^-01 FT
DATA ON CARD NUMBER t*
Alt 3) • 1.2300C+01 rT**2 VOS( 1) • 4.4400E*0« V TC8C S) • 3.0000E-04 A MIS( 3) • 1.2500C+01 FT
°° ACS ( 3) • 4.*«TSE-02 IN BS( 3) • 5.0000E»00 IN NN8( 3) • l'.OOOOE*01
DATA ON CARD NUMBER 17
fVS( S) • 2.SOOOE+00 IN VC3< 3) • 2.0000C*02 FT**S/MXN V6A8S( S) • J.2000C*00 FT/8CC TEMP8C 3) • T.*»OOE«01 F
3) • i.oeooE«oe ATM vissc 3) • i.sooec-os KC/M-SEC LXNCSC 3) • 8.3issE-oi FT
-------
INCREMENTAL ANALYSIS 0' PRFCIPITATOR PERFORMANCE
LAB ESP| SCA«l25FT2/lflOOACFM|J*?2 MJ/SEC
PRfSSHRE « 1.000 ATM
fEAN THERMAL SPEED « na
5.76E.6*
2,!S8f-0(l
I,58f.«e«
2.58F.-Oa
APPLIEO VOLTAGE « «.580E«o« VOLTS
CORONA WIRE RADIUS • I.l91E-OJ M
CURRENT DENSITY * 2,581f-0« AMP/M2
GAS FLPM RATE « 9.«60E-C2 "J/SCC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEEO • a.«19E*02 -/SEC
LENGTH INCR. •0'.2S«1656S M
NO,
TOTAL CURRENT • 1.500F-««
CORONA WIRE LENGTH • 1.90*t»00 M
DEPOSIT It FICLO » 2.5*1E»OJ VOLT/M
GAS VELOCITY • 9,76«E-oi »/$EC
VISCOSITY • i,8ooc«os KG/*<.SFC
PART, PATH PARAK, • V,7oer«o« »
IN»UT EF'./INCR. • 31,87
ROVRI ERAVG EPLT AFID CMCD MHO WEIGHT
2.aa60Ft!3 25^8
?io73lE»13 25*8
CALCULATION IS IN SECTION NO. • 3 AND THF SECTION LENGTH IS • 1.5250 M
DUST LAYE» J(PART)
1,0169
1.0099
1,0058
I.606E+05
1.606E«05
J.b06E»05
2,5TJ7E*05
2.5TJTE+05
?.5TJTE»05
2.01E-06
2.10E«06
1.86C»06
2.833E-06
2.10ir-06
COLLECTION AREA • i'.|62E*00 H2
HIRE TO PLATE « r.zTOf-«i M
CURRENT/M • 7.869E.05 AHP/M
l/t WIRE TO WJRE • 6.150E-0? M
TEMPERATIIRf • 297.667 K
ION MOBILITY * ».T98E-0« "?/voLT.8Fe
DUST WflGHT • J.2SOF-fl6 KG/SEC
8.299E-05
(..I56E.05
«.731E»A5
4.50F.O*
1.93E-08
2,58E.O(I
INCR. NO,
a
5
6
APPLIFD VOLTAGE « «.««0r*n« VOLTS
C1ROHA «IRE RABIUS • 1.191E.03 M
CURRENT DENSITY • ?,5S1F-0<1 AMP/M2
GAS FLO*- RATE i 9.4«nf.n? HS/8EC
PPF8SURE • 1,000 ATM
MFAN THERMAL SPFED • «.»«
1».CR, Mi.
7
•
9
-------
1,0007 3.49fcEt05 2,5222Et05 J.Sb«lE»JJ 25. 8 l.J*E-f»6 b.h?7F-07
1.000* J.O«6E»05 2.5222E»05 2.56«PE*IJ 25.8 l.HE-06 S.«7)E-OT
1,0002 3.«9fcE*05 ?.5222E»05 2.5b52E«lJ 25.8 I.2«E-04 «.5«6F«07
EST. EFFICIENCY • 99'.00
UNCORRECTED COMPUTED EFFICIENCY « 92.59
1.*OSF-05
I.S12E-05
1.9bF-fl*
t.71F..08
I.S1E-08
Z.58E.04
2.58F«oa
t»
12
INCREMFNTAL ANALVSIS
PRECtPTTATOR
LAB f8P| 8CA«12SFT2/1000ACFM|J«Z«.OUA/FT2
CALCULATION IS JN SECTIO" NO. • 1 AMD THE SECTION LENGTH IS « 0.7*25
COLLECTION AREA • S.812E-01 Mj
HIRE TO PLATE • 1.2TOE-01 M
CURRFNT/H • 7.869E-0? AMP/M
1/2 HIRE TO HIRE • *.i5oE-o? M
T£MPE»ATU»I • 297,467 K
ION MOBILITY • >.798E-0« MJ/VOLT-SEC
DUST HEIGHT • 3.250E-06 KG/SEC
APPIIEO VOLTAGE • a.bOOF. + Ofl VPLTS
CORONA MIRE RADIUS • 1.1 l,5^nF-«« AMPS
«I«E IENGTH i 1,«06E*l)0 «
FIELD « ?,5«iF*os VOLT/M
GAS VELOCITY • 9,T*nE.oj «/SFC
VISCOSITY m i.soof-ns XG/M.^FC
PART, PATH PARAM. « s.70«t»flB M
INPUT EFF./INCR, • 19,«l
00
ROVRI
ERAVG
J,622E»05
EPLT
MMO
WEIGHT
2.5906E+05 2,J896F«1S
2.58«4E*05 ;
A.15E-0*
i .
6.159E-06
1.0524
I!0249
CALCULATION IS IN SECTION NO. • 2 AND THE SECTION LENGTH IS • 0.7*25 «
25.8
25,8
25.8
COLLECTION ARE* • 5.812E-01 M2
WIRE TO PL»TE « i'.270E-oi M
CURRENT/M • 7.869F.OS AHP/M
1/2 HIRE TO WIRE • 6.350E-02 M
TEMPERATURE • 297.667 K
ION MOBILITY • 1.T9BE-OB H2/VOLT-SFC
DUST HEIGHT • 3.250F-96 KG/SEC
APPLIED VOLTAGE « «.580E*0« VOLTS
CORONA WIRE RADIUS » 1.1»1F-01 M
CURRENT DENSITY • 2.58JE-Oa AMP/M?
GAS FLOW RATE • 9.«60E»02 "5/SEC
PRESSURE » 1,000 ATM
MEAN THERMAL SPEED • U.u39F»0?
LENGTH INCR. •0.25416565 M
OUST LAYER J(PART)
?.9a2E-0«
1,»63E-0«
U.80E-B6
5.77E-08
5.16F-OH
?,5BE-8U
?,S«F»0(1
?.5SF..O J.?«ioF.06 KS/SEt
OUST LAYER JfPARTJ
*,326E-05
*.1T1F-05
(J.TUlt.OS
U.51E-08
J.9«E-08
J(ION) I*CR. N-0,
?,58E.Oil
?,S8E.n«
?.58E«0«
APPLIED VOLTAGE * tt.aaOEtOll VOLTS
CORONA "IRE RADIUS « l.!«tr-M •»
CURRENT DENSITY x 2.581F-C« AHP/MJ
GAS FLO« RATE « 9.flbOE-(i? M1/SEC
PRESSURE • 1,808 ATM
MEAN THERMAL SPEED • a.«39F*o? M/SEC
LFNGTM INCR. «n.?5«J6565 H
CURRENT • J.OTOF-OU A«P«
A i"IRE LFNGTH *
FTFLD • ?
GAS VfL,f!CJTY • 9,7*OE»01
VISCOSITY « I.SOOF*^ KG/M»SFC
PART. PATH PARA*. > 5.7«8F.ns
ROVPI
EMAVG
fPLT
•if TRHT
LAYER .!fP»»T)
. '"O,
-------
.0055
.0039
.0027
.0019
.0013
.0009
S.496E+05
S.496E405
3.496E405
00
Ul
2.S235E405
2,4235E405
2.52S5E485
2,S235E405
2.5518E+13
2.S58«E«15
2.5610E*1S
25.8
25,8
25ja
25.8
as. a
25 '.a
1.66E-06
1.54E-0*
1.45E-0*
1.S8E-06
llJlE-06
1.24E-06
1.2«Tf-06
9.985E-OT
8.100F-07
6.6J6F-07
5.477E-07
«.5?OE-07
J.653E-05
2.925E-05
2.373E-05
l,9tt4E-05
1.A85E-05
1.3JSE-05
2.93E-08
2.56F-08
2.2ttF..O»
1.96E-08
1.72F-08
i. sir-os
2.SaE»04
2.9BE-04
2.5BE-04
2.58E-04
7
a
9
to
11
12
-------
CHARGING RATES FOR PARTICLE SIZES FROM SUBROUTINE CHARGN OR CHfiSUM
SRI THEORY USED FOR PARTICLE CHARGING
INCREMENT NO.
0/05ATF FOR INDICATED PARTICLE SIZES
0'.2500E«06 0.3500E»06
1 1.0360 T.0360
2 1.6777 1,6491
3 1.6671 1,6326
4 210124 1,9405
5 2.1020 2,0172
6 2.1715 2,0764
7 2,2249 2,1208
8 2.2703 2,1586
9 2.3096 2,1915
JO 2,3446 2,2205
11 2.3756 2.2466
12 2.4040 2.2701
0'.1600E<»05 A.2000E-05
1
2
3
4
5
6
7
8
9
10
11
12
.0360
.3251
,4022
.4454
.4758
,4992
,5134
.5257
.5366
,5464
,5553
.5634
,0360
.2889
.3571
,3949
,4215
.4419
,4536
,4638
.4729
,4«11
,4666
.4686
0.4500E-06 0,5500E»06 0.7000E-06 0.9000E-06
,0360 ,0360
.6048 .5613
.7664 ,7056
,8605 .7890
,9271 .6460
,9785 .8935
2,0161 .9262
2.0463 1.9541
2.0762 1,9784
2,1010 2.0000
2.1232 2,0194
2.1033 2.0370
.0360 1.0360
.5044 1.4447
.6295 1.5522
.7013 1.6134
.7520 1.6567
.7911 1.6901
.8163 1.7125
.6417 1,7318
.8622 1.7468
.6804 1.7639
.8967 1.7776
.9115 1.7899
0'.2600E-05 0.3500E-05 0'.50QOE-05 0.8000F-05
1.0360
1,2540
1.3129
1.3450
1.3675
l',38fl7
1.3939
1.4019
1.4091
1,4157
1.4157
1.4157
.0360
.2226
.2717
,2979
.3162
,3302
.3369
.3369
.3369
.3369
.3369
.3369
.0360 1.0360
.1918
.2303
.2504
.2644
.2752
.2796
.2796
.2796
.2796
.2796
.1569
.1604
.1982
.2060
.2155
.2178
.2176
.2178
.2178
.2176
.2796 1.2178
O.HOOC-05
1.0360
1.3993
1.49*7
1.5466
1.5870
1.6164
1.6356
1.6522
1.6666
1.6798
1.6915
1.7022
0.1500E-04
1.0360
1.1178
1.1352
1.1435
1.1494
1.1541
1.1541
1,1501
1.1541
i.1541
1.1541
1.1541
0.1300E-05
1.0360
1.3643
1.4509
1.4997
1.5342
1.S606
1.5776
1.5921
1.6050
1.6165
1,6269
1.6363
-------
CHARGE ACCUMULATED ON PARTICLE SIZES IN EACH INCREMENT
INCREMENT CHARGE FOR INDICATED PARTICLF SIZES
CO
-J
0.2500F-06
i 0.18895E-17
2 0.30598E-17
3 0.34410.E-17
4 0.36703E-17
S 0.38336E-J7
6 0.39*04E-17
7 0.40579E-17
8 0.4t407E-t7
9 0.42126E-17
10 0.42762E-17
It 0.43331E-17
12 0.4384SE-17
0.1600E-05
2 o[75592E-lt
3 0.799Q1E-16
4 0.82454E-16
5 O.S4191E-J6
7 o!e6334E«l*
8 0.87038E-16
9 0.87662E-16
10 0.8822IF-1*
11 0.88727F-16
12 I
0'.3SQOE<06
0.53183E-17
0,,59103E«17
0.65055E-17
0.66967E-17
0,6«398E-17
0.69617E-17
0.70477E-IT
O.T121JE-17
0.2000E-05
0.11407E-1S
0.12011E-15
0.1234SE-1S
0.12581E«15
OJ2761E-15
0.12865E-15
0.129S5E-15
0.13036E-15
8.13109E-15
8.13174E-15
0.13174E-1'5
0.52363E-17
0.81110E-17
0.89879E-17
0,9flOJ2E-17
0.99997E-17
0,10190E-U
0.10619E-K,
0.10731E-16
0.10835E-16
0.2600E.05
0.15399E-15
0.18639E-19
0.20325E-H
0.20717E-15
0.20837E-15
0.5500E-06
0.75764E-17
0.12473E-16
0.13083E-16
0.1SS14E-16
0.13B1TE-16
0.182<»OE-ie>
0.1U768E-lh
0.3500E-05
0.27760E-15
0.32759E-15
0.34076E-1S
0.34776E-1S
0.3S267E-15
0.35613E-15
0.35822E-15
0.35822E-15
0.35822C-15
0.35822E-15
0.35822E-15
0,35822E«15
P.7000F-0*
0,tl922f"16
0 19578E-16
0.30161E-16
0.20612F-1*
0.20925F-16
0.21639K.16
0.21827E-14
0.21997C-16
0.5flOOE-05
0.66989E-1S
0,68079F-15
0,69fl3lE-lS
0.69668E-15
0.69668E-1S
0.9000E-C6
0.19Z80F-16
0,26BB5f-lfe
0.30024E-16
0.30829E-16
0.31U50F-16
6.3186AE-16
0.32228F-16
0.32544F-J6
0.32825E-16
0.33078E-16
0.33309E.J6
O'.SOOOE-OS
0.143881*14
0.16067E-14
0.16777F-10
f»,l6881E-lU
0>9fc68E-tS
0.1t>9l3F-ia
0.16913F-18
0.l69J3E«ta
0.169J3E-10
0.1100E-05
0.38391E-16
0.41007F-J6
0.42490E«16
0.43S39E-16
0.4U872E-16
0.45327E-16
0.45727E»16
0.fl<»407E.U
0.l500E-Ofl
0.?527fcE-10
0.55677E-14
0,56193E«10
o!s<>193E-ia
O.Sbl93E»i4
0.56193E-10
0.56193E-14
0.1300E-OS
8.39355F-1*
9.55J13E-16
9.S8280F-16
O.S9289E.16
0.59926E.J6
0.60479F-1A
0.614Q3E-16
0.61798E-16
0.62158E-1*
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NQNlftEALITIES USING SET NO. t OF CORRECTION PARAMETERS
2,
s'
4,
s!
7.
9,
ll
1.
1.
2.
2,
3.
5,
8.
1.
00
00
SIZE CCF INLET X
500E-07 1.590 o'.OOO
500E-07
500E-07
500E-07
OOOE-07
OOOE-07
100E-06
300E-06
600E-06
OOOE-06
600E-06
500E-06
OOOE-06
OOOE-06
500E-05
.414 Q.400
.320 0,600
.261 1,667
.205 5,000
.159 4,933
,130 5,000
.110 3,733
.090 8,000
.072 6,667
.055 10,667
.041 10,667
.029 11,333
.018 12,000
.010 19.333
EFFICIENCY - STATED
OUTLET X
0'.0009
T.7859
2,5381
6.4831
17'. 2301
14'.2047
1211443
7,6527
13.0744
6.1804
8' 7944
5.4164
2,3183
0,1755
0.0007
• 92'. 50
COR. OUTLET X
0.0005
1.1202
1.6050
4,0240
10.7313
9.0357
7,9052
5.2837
9,4199
6,6204
8,7947
7,4037
8,1639
8,4692
11.4226
COMPUTED »
NO-RAP EFF.
87'. 25 18
87.3555
88', 0199
88.9860
90.2408
91.8451
93,1214
94,1943
95,3716
96.5251
97,6651
98.5620
99.4207
99.9586
99.9999
92.4959
NO-RAP W
,381
,414
634
976
.468
10.199
10,891
11,581
12,503
13.670
15,287
17,259
20,959
31,694
56.257
CONVERGENCE
NO-RAP P
12.7482
12.6445
11.9801
11.0140
,7592
.1549
.8786
.8057
.6284
.4749
2.3349
.4380
0.5793
0.0414
0.0001
COR. EFF.
87.2518
86.8819
87.4690
88.6923
89.9461
9!. 4197
92.5937
93.3696
94.4841
95.3483
96.1378
96.7487
96.6255
96.6939
97.2323
COR. W
8.381
8.264
8.451
8.869
9.347
9.992
10.590
11.041
11.790
12.483
13.240
13.940
13.789
13.672
14.595
COR. P
12.7462
13.1161
12.5310
11.3077
10.0539
615803
7.4063
6.6304
5.5159
4.6517
3.8622
3.2513
3.3745
3.3061
2.7677
OBTAINED
ADJUSTED NO-RAP EFF, • 97'. 1680
MMO OF INLET SIZE DISTRIBUTION « 3.300E*00
SI6MAP OF INLET SIZE DISTRIBUTION • 2'.164E*00
LOG-NORMAL GOODNESS OF FIT » 0.934
MHQ OF EFFLUENT UNDER NO-RAP CONDITIONS * l'.296E«00
SIGMAP OF EFFLUENT UNDER NO-PAP CONDITIONS • l.628E*00
LOG.NORMAL GOODNESS OF FIT « 0.961
PRECIPITATION RATE PARAMFTER UNDER NO.RAP CONDITIONS « 14.502
O'.OOO WITH 0.000 SNEAKAGf. OVER 4.000 STAGES
SIGMAG"
NTEMP • 1
RHMD • 6.00
RSIGMA • 2.50
CORR'. EFF. » 95*.3156
CORRECTED MMO OF EFFLUENT •
CORRECTED SI6M*p OF EFFLUENT
LOG-NORMAL GOODNESS OF FIT
2.354E+00
* 2.154E+00
0.915
CORRECTED PRECIPITATION RATE PARAMETER « 12.«5
-------
UNADJUSTED MIGRATION VELOCITJFS AND EFFICIENCIES, AND DISCRETE OUTLET *ASS LOADINGS
M
00
V£>
IDEAL UNADJUSTED IDEAL UNADJUSTED
"1C. VEU'.(CM/SEC) EFFICIENCY*)
3.605E+00
3,877E«flO
«.212E*flO
«.S68E+00
5.118E+00
5.861E+00
6.609E+00
7.J58E+00
e.assE+oo
9.978E*80
l.221f+01
t.5adE+ei
.877E+01
,10«E»01
.440C+01
,7a*E+01
. 157E+01
.612E+01
,029E»01
.361E+81
,757£»01
. 1J9E+81
.S03E401
.777E+01
5.»26E»01
DM/OLOGD(MG/DSCH)
CAPPING PUFF
«,70lE-01
l.«66E+00
l,558E+00
1,638E+08
1,215E+00
9,9T5E-01
0.607E-01
2.390E-OS
J.72?e-05
1.280E-02
2.S20E-02
fl.U27F-02
8.127F-82
1.2SIE-01
1.72»E-8t
2,fl«lE-01
3.378E-01
fl.539E.01
5.810e-01
6.T50E-01
6.62TE-0!
6.67QE-01
NO-P.AP4RAP PUFF
DM/DLOGDtMS/OSC«>
1.776E-03
2.911E-01
8.93SE-01
.SlOEtOO
.639E+00
.755E*88
,387t*00
.335E+00
.l«8EtOO
8.150E-01
A.7I1E-01
RAPPING PUFF
DISTRIBUTION(*J
«. J60E-0?
1.022E-81
l,78aE-8l
2.642E-01
7.953E.01
1.132E«00
1.661E+80
8.791E+00
1.709Et01
2.1 iaE»01
2.A87E+01
PARTICLE
D1AM.CM)
2.SOOE-OT
0.500E-07
5.580E.07
7.800E-07
9,OOOE«07
1.308E«0»
2.0001-06
2.600E-06
3,?OOE«0»
5.000E-0*
«,OOOE«Ot
t .SOOE-05
-------
**«****•*»*»***•**********»**********•********»*****»*»**************»»•»**<
SUMMARY TABLE OF FSP OPERATING
PARAMETERS AND PERFORMANCE
DATA SET NUMBER 1
ESP PCRFORMANCEl
EFFICIENCY « 95.3156 X
SCA
ELECTRICAL CONDITIONS!
SIZE OISTRIBUTIONSi
NONIOEAL PARAMETERS!
AVG. APPLIED VOLTAGE * fl.515F+0
-------
PARTICLE SIZE RANG? STATISTICS
CORRECTIONS FOR NONIDEALITIES USING SET NO'. 2 OF CORRECTION
SIZE CCF INLFT X
2,500E-07 1.590
3.500E-07 1.414
4,500E-OT 1.320
5.500E-07
7,OOOE-07
9.000E-07
1.100E.06
1.300E.06
1,600E-06
2,OOOE-06
2.600E-06
3,SOOE-06
5,OOOE-06
0,OOOE-06
1.500E.05
.261
.205
.159
.130
,110
,090
.072
.055
.041
,029
.018
.010
0.000
0,400
0.600
f.667
5' 000
0,933
5.000
3,733
6,000
6,667
10.667
10,667
11,333
12,000
19.333
OUTLET X COR. OUTLET X
010007
1.0492
2'. 08 18
5 '.3981
14'.6749
12.5106
11,0687
7.2247
12'. 9907
8.7171
10.4009
7'.5515
4 '.5396
1,0716
0.2721
o,noo5
1.0109
1,0625
3,7277
10,1593
e, ems
7.9308
5'.414A
10,0111
7.2589
9.9081
8,4919
8.6265
7,6040
9.5816
NO-R4P EFF,
83.5792
83.6036
80.3356
65.3804
86.7494
88,5465
90.0056
91.2624
92'. 6688
94' 0970
95.5793
96.6039
98.1916
99.5968
99.9364
NO-RAP M
7.351
7,367
7.503
7,824
8.224
8,817
9.371
9.918
10,632
11,514
12.690
14.010
16.327
22,434
29.951
NQ-RAP P
16.4208
16.3564
15.6600
14.6196
13.2506
11.4535
9,9944
8.7376
7.3312
5,9030
4.4207
3.1961
1,8084
0.4032
0.0636
COP. FFF.
83.5792
83.0869
83.6*81
85.0353
86.4029
88.0460
89.3853
90.2931
91.6256
92.7138
93.7800
94.6725
90.9061
95.7595
96.6633
COR, *
7.351
7.231
7.378
7.729
8.119
8.643
9.126
9.490
10.091
10.657
11.303
11.931
12.113
12.859
13.859
COR. P
16.4208
16.9131
16.3119
14,9647
13.5971
11.9536
10.6147
9.7069
8.3744
7.2862
6.2160
5.3275
5,0939
4.2405
3.3167
EFFICIENCY -
« 92'.50
COMPUTED • 92,0959
CONVERGENCE OBTAINED
ADJUSTED NO.RAP EFF, « 95.4853
MHO OF INLET SIZE DISTRIBUTION • 3.300E+00
SIGMA* OF INLET SIZE DISTRIBUTION • 2'.164E*00
LOC.NQRMAL GOODNESS OF FIT * 0.934
MHO OF EFFLUENT UNDER NQ-R4P CONDITIONS » 1.466E+00
SIUMAP OF EFFLUENT UNDER NO-RAP CONDITIONS • 1.719E+00
LOO.NORHAL GOODNESS OF FIT • 0.961
PRECIPITATION R»TE PARAMETER UNDER NO.RAP CONDITIONS 9 12.604
SIGHAG* O'.IOO KITH 0.100 SNEAKAGE OVER 4.000 STAGES
NTEHP • 1
RMMD « 6.00
RSIGMA » 2.50
CORR'. EFF, « 93.3079
CORRECTED HMD OF EFFLUENT • 2.315E+00
CORRECTED SIGMAP OF EFFLUENT « 2,099E«00
LOG-NORMAL GOODNESS OF FIT « 0.935
CORRECTED PRECIPITATION RATE PARAMETER • 11.00
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AMD DISCRETE OUTLET MASS LOADINGS
vo
to
IDEAL UNADJUSTED
MI6. VEL'. (CM/SEC)
J.605E+00
S,B7TE»00
4,212E*00
4.5*8EtOO
5.8*1E*00
fr.6C9Ei.00
7,S58E»00
e.46)E+00
9.97SE+00
i.22ie»ot
i,54B£*oi
2.094E+0!
3.U9E+01
5.62*E»Ol
IDEAL UNADJUSTED
EFFtCIENCVtX)
5>77E*01
7,157E+OJ
7.6J2E+61
,02<»E+01
,757E»01
.50SE»01
'.777E*01
,9»6E»01
.000f»02
WO-RAF
OM/DLOCOtMC/DSCM)
6.999E-OS
3,639E-01
1.990E+00
l,B?flE+00
2.016E+00
l.iiaf+oo
1.020E+00
U.5A8E-11
1.532E-02
RAPPINC PUFF
OM/DLOGO(M6/D8CM)
2.02«E>03
6.668E»03
1.50«E-02
2.727E-02
5.203E-02
9.552E-02
1.470E-01
2.ft2BF-01
2.869E-01
3.971E-OJ
5.335E-01
b.CJ'E-01
7.935E-01
7.789E-01
7.BOOE-01
NO.RAP+RAP PUFF
DM/OLOGD(HG/DSCM)
2',09UE-03
2.032E-01
3.790E-01
1.182E+00
2.042E+00
2.2«3E*00
Z.SlSEtOO
2.031E+00
2.303E400
2.092E*60
1.S47E400
1.707E+00
1.230E-+00
8.607C-01
T.993E-01
RAPPING PUFF PARTICLE
DISTRIBUTION^) DIAM'.(M)
S.360E-02
1.02?E»01
1.780E-01
l(64ZE»01
7t953E»0 t
l,tJ?E*00
1 |42AC*00
1,661E«00
3.BJJE+00
«,21UE»00
6,79JE»00
1,0»«E*01
1,769E*01
2,tl«E*OJ
2,««7E+01
,500E«07
.5001-07
.9001-07
.500E-07
.OOOE-07
.OOOE-07
. 100E.06
.300E-06
.600E-0*
.OOOf-0*
.600E-0*
.SOOE.06
.OOOE-06
,OOOE»0»
.500E-05
-------
V0
u>
A*******************************************************************************************************************
SUMMARY TABLE Of ESP OPE»ATING
PARAMETERS AND PERFORMANCE
ESP PERFORMANCE I
DATA SET NUMBER 2
EFFICIENCY • 93.307' « ic* • Z.«»»E»OI M*«I/(M«»S/SEC)
ELECTRICAL CONDITIONS!
SIZE OISTRIBUTIONSI
NONfDEAL PARAMETERS!
AV6. APPLIED VOLTAGE • «.515E*0« V
AVO. CURRENT DENSITY • ZS.81 NA/CM**2
RESISTIVITY • r.OOOE»0« OHN.CM
INLET HMO « !.300E«00 UM INLET SIGMAP • 2'.1*4E«00
OUTLET NMD • 2.J15E+00 UM OUTLET SIGMAP • 2.09*E*00
CAS SNCAKAGC FRACTION • O.Jfl /SECTION OAS VELOCITY SI6MAG • 0.10
RAPPING NMD • t.oOOE+00 UN RAPPING SIGMAP • {.900C+00
STOP 011111
-------
APPENDIX H
OUTPUT DATA FOR EXAMPLE 1 (REVISION 1)
194
-------
t************************************
E.P.A. E8P MODEL
t.E.H.L.-R.T.P, AND SO.R.I.
REVISION i,JAN, i, ma
A************************************
PRINTOUT OF INPUT OAT* FOR DATA SET NUMBER 1
DATA ON CARD NUMBER >
NENDPT • 16 NOATA • t
DATA ON CARD NUMBER 2
LAB EJP| SCA»12SFT2/tOOOACFM»J«24.0UA/FT2
DATA ON CARD NUMBER 3
J-1
vo
01 NUT • i NDIST • t NVI • i NX • 10 NY • 10 NITER • s NCALC • o NRAPD • t NEFF • i NTEHP • i NONZD • 2
DATA ON CARD NUMBER 4
MN • 10 NUMINC • 20
DATA ON CARD NUMBER 9
DL • 0.015*0 CRN/ACF PL • 10.0000 FT ETAO • 99.00000 X 00 » 1060.00 KG/***! EPS • S.lOOEtOO
VRATIO • 1.0300 US • 0.000165 M«*2/V«8EC FPtTM • 1.0000 EBO • 1500000. V/M RHOC6S • 1.00E*09 OHM.CM
DATA ON CARD NUMBER *
ASNUCKC 1) » 0.00 AZI66VC 1) • 0.00 AZNUMS( 1) • 4.0
ASNUCKC 2) • o.io AZICOVC ?) • o.to AZNUMSC 2) • «.o
DATA ON CARD NUMBER 7
-------
ENDPTf n • 0.200 UM ENOPTt 2) • 0.100 UN ENOPTf 3) • 0.000 UN ENDPTC 4) • 0.500 UM ENDPTt 5) • 0.600 UM
ENDPTf 6) • 0.800 UM ENDPTt 7) « 1.000 UM ENDPT( 8) • 1.200 UM ENDPTC 9) • 1.400 UM ENDPT(IO) • J.BOO UH
DATA ON CARD NUMBER 8
CND'TCH) • 2.200 UM ENDPT(12J a 3.000 UM ENOPT(lS) • a.000 UM FMOPTC14) • 6.000 UM CNDPT(IS) • 10,000 U*
ENOPT(16) • 20.000 UM
DATA ON CARD NUMBER «
i
PRCUt 1) • 0.0000 X PRCUt 2) • 0.0002 X P«CU( 3) • 0.0002 X PRCUC «) • 1.0002 X PRCUt S) • 2.6672 X
PRCUC 6) • 7.6672 X P»CU( 7) * 12.6002 t PRCU( 6) « 17.6002 X PRCUt 9) • 21.3332 X PftCU(lO) • 24.3332 X
DATA ON CARD NUMBER 10
£ PRCU(ll) • 36.0002 X PRCUU2) • 46.6672 X P«CU(13) « 57.3302 X PRCUU4) • 68.6672 X PRCUC15) • 80.6672 X
a*
PRCUU6) • 100.0000 X
DATA ON CARD NUMBER 11
NUM8EC • 3 LSECTC 11 • 3 L3ECTC 2) • 3 LSECTC 3) • 6
DATA ON CARD NUMBER 12
ASC 1) * 6.2500E+00 FT**2 Vn5( 1) « a.6000E+Ofl V TC3( 1) • 1.5000E-0« A ML8C 1) • 6.2500E+00 ft
ACSt 1) • 4.6875E-02 IN BSC 1) • S.OOQOEvOO IN NHS( 1) • S.QOOOE»00
DATA ON CARD NUMBER 13
SVS( 1) • 2.5000E*00 IN VCSC 1) • 2.0000Et02 FT**J/MJN VQASSC 1) • 3.2BOOF»00 FT/SEC T£MPS( 1) • T.6800E*Ol F
P8( 1) • l.OOOOE+OP ATM VISSC 1) s 1.8000E-05 KG/M.8EC LINCSt 1) • 8.3333E-01 FT
DATA ON CARD NUMHER 14
A8C 2) • 6.2500F+00 FT**2 V05C 2J * 4.5flOflC+0« V TCS( 2) • 1.5000E-04 A *LS( 2) * 6.2500E+00 FT
) * «,*«75f.o2 IN »»( 2) * s.»(»ooe*oo in
-------
DATA ON CARD NUMBER IS
8VS( 2) • 2.5000E+00 IN V68( 2) • 2.0000Et02 FT»*3/MIN VG*8S( 2) • 3,2000E»00 FT/8EC TEMPSC Z) • 7,*800E»Ol F
CSC 2) • 1.0000E*00 ATH VI3S( 2) • l.BOOOE-05 KG/M.8EC LINCSC 2) • 8.33J3E-01 FT
DATA ON CARD NUMBER 16
ASC 3) • 1,2500E*01 PT**2 V08( 3) • O.flOOOE+Oa V TC8( 3) • 3.0000E-04 A ML8( S) • 1.2500E+OJ PT
AC8( 3) • 4.6875E.02 IN B8( 3) • S.OOOOEtOO IN NW8( 3) • l.OOOOE+01
DATA ON CARD NUMBER 17
8V8( 3) • 2.5000E»00 IN VQ8( 3) • 2.0000E+02 FT**3/MIN VGA88C 3) • 3.2000E*00 FT/8EC TEMF${ j) • T,fc800E*01 F
P8( 3) • l.OOOOEtOO ATM VI88C 3) • 1.8000C-05 KG/M.8EC LINCS( 3) • 8.3313E-01 FT
VO
-J
-------
INCREMENTAL ANALYSIS Of PRECIPITATOR PERFORMANCE
LAB ESPl SCA«125FT2/1000ACFM|J«24.0UA/FT2
CALCULATION 18 IN SECTION NO. • 1 AND THE SECTION LENGTH IS • 0.7625 M
COLLECTION AREA • 5.812E-01 Hj
WIRE TO PLATE « I.JTOE-OI M
CURRENT/M • 7.869E-05 AMP/H
1/2 WIRE TO MIRE . 6.350E-02 M
TEMPERATURE « 297.667 K
ION MOBILITY • 1.798E-04 M2/VOLT-8EC
OUST WEIGHT • 3.2SOE-0* KG/SEC
APPLIED VOLTAGE • 4.600F+04 VOLTS
CORONA NIRE RADIUS • l.l'lE-03 M
CURRENT DENSITY • 2.SB1E-04 AMP/M2
GAS FLOW RATE • 9.460E-02 M3/8EC
PRESSURE > 1.000 ATM
MEAN THERMAL SPEED • 4.439E+02 M/8EC
LENGTH INCR. BO.29416565 M
TOTAL CURRENT • l.SOOE-04 AMPS
CORONA MIRE LENGTH • 1.906E+00 M
DEPOSIT E FIELD • 2.581E+03 VOLT/M
GAS VELOCITY • 9.760E-ot M/SEC
VISCOSITY • I.BOOE-OS KC/M.SEC
PART. PATH PARAM. • 5.708E-06 M
INPUT EFF./INCR. • 31.8T
ROVRI
ERAVG
ID
00
1,0860 3.622E+05
1.0501 3.622E+05
1.0288 3.622E+05
EPLT
2.7624E+05
2.74S5E+05
2.7356E40S
AFID
2.2B04E+13
2.3583E+13
2.«OT3E*13
CHCO
25.8
25,8
25.8
HMO
6.69E-06
a,07E-06
2.89E-06
HEIGHT
1.033E-05
6,5«5E-06
4.124E-06
DUST LAYER J(PAHT)
CALCULATION IS IN SECTION NO. • 2 AND THE SECTION LENGTH IS • 0.7625 M
COLLECTION AREA • 5.812E-01 M2
WIRE TO PLATE • i.27oE-oi M
CURRENT/M • 7.869E.05 AMP/M
1/2 NIRE TO MIRE • 6.J50E-02 M
TEMPERATURE • 297.667 K
ION MOBILITY • 1.798E-04 M2/VOLT-SEC
DUST WEIGHT • 3.250E-06 KG/SEC
3.027E-04
1.917E-04
1.208E-04
5.00E»OB
6.06E-08
5.3TE-08
J(ION)
2.58E-04
2.58E-04
2.586-04
APPLIED VOLTAGE • 4.580E+04 VOLTS
CORONA HIRE RADIUS • 1.191E-03 M
CURRENT DENSITY • 2.581E"04 AMP/M2
GAS FLOH RATE • 9.460E-02 MS/SEC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • 4.0J9E+02 M/SEC
LENGTH INCR. >0.25416565 M
. NO,
1
2
3
TOTAL CURRENT • l.SOOE-04 AMPS
CORONA HIRE LENGTH • 1.906E+00 M
DEPOSIT E FIELD • 2.581E403 VOLT/M
GAS VELOCITY • 9.760E-01 M/SEC
VISCOSITY • 1.800E-OS K6/M.8CC
PART. PATH PARAM. • 5.70BE-08 H
INPUT EFF./INCR. • 31.87
ROVRI
1.0165
1.0096
1.0056
ERAVG
EPLT
AFIO
3.606E+05 ?.7206E+05 2.4470Etl3
3.606E+05 2.7206E+05 2.4&38E+13
3.606E*05 2.7206E+05 2.4736E*13
CMCD
25.6
25.8
25.8
HMD
2.35E-06
2.04E-06
1.80E-06
HEIGHT
2.836E-06
2.085E-06
1.589E-06
CALCULATION IS IN SECTION NO. • 3 AND THF SECTION LENGTH IS • 1.5250 M
COLLECTION AREA • 1.162E+00 MS
HIRE TO PLATE • 1.270E-01 M
CURRENT/M * 7.869E-05 AMP/M
1/2 HIRE TO «IRE « 6.350E-02 »
TEMPERATURE « 297.667 K
ION MOBILITY * I.798E-04 M2/VOLT-SEC
OUST WEIGHT • j.?5or-o6 KG/SEC
OUST LAYER JtPART)
J(ION) INCR. NO.
8.J10E-05
6.107E-05
0.655E-05
4.64E-08
4.03E-08
3.49E-08
2.58E-00
2.58E-04
2.58E-04
4
S
6
APPLIED VOLTAGE • 4.440E+04 VOLTS
CORONA HIRE RADIUS • 1.191E-03 M
CURRENT DENSITY • 2.S81E-04 AHP/M2
GAS FLOH RATE « 9.460E-02 M3/8EC
PRESSURE • 1,000 ATM
MEAN THERMAL SPEED • 4.439E+02 M/SEC
LENGTH INCR. B0.2S41656S M
TOTAL CURRENT • 3.000E-04 AMPS
CORONA HIRE LENGTH • 3,812E+00 M
DEPOSIT f FIELD • 2.S81E+03 VOLT/M
GAS VELOCITY • 9,760E-oi I/SEC
VISCOSITY • 1.800E-05 KG/M.SEC
PART, PATH PARAM. • s.rosE-os M
INPUT EFF./INCR. « 31.87
ROVRI
ERAVG
1.0031 3.496E+05
1.0018 3.«»6E»05
I.0011 J.496Ff05
EPLT
?.6452E*05
2.6452E+05
AFID
2.5578E+I3
2.5611E+13
CMCD
25.8
25.8
25.8
HMD
1.60E-06
1.50E-06
1.42E-86
HEIGHT DUST LAYER J(PART)
1.206E-06
9.603E-07
7.745f«07
J.533E-05
2.813E-OS
2.269E-OS
2.9SE-08
2.54E-08
2.21E-08
2.58E-04
2.58e*04
2.58E-04
INCR. NO,
7
8
9
-------
1.000* 3.49H+05 2,*4S2E»05 2.3*A2Ctl3 2S.8 1.35E-0* *.30«E»
1.0004 3.49*E+05 2.*452Et05 2.5649E+13 25.6 1.27E-0* S.174E-
1.0002 3.496C+05 2.**S2E«OS 2.56S3C«13 25.8 l.JOE-86 4.272E-
EST. EFFICIENCY • 99,00 UNCORRtCTEO COMPUTED EFFICIENCY • 9J.24
1.8»TE»OS
1. SUE-OS
1.252E-05
1.92C»06
1.48E-08
1.46E-08
I.5BE>04
2.58E-04
2.98C.04
16
11
12
INCREMENTAL ANALYSIS OF PRECIPITATOR
LAB ESPl 8CA»12SFTZ/1000ACFM|J«24.0UA/FT2
CALCULATION 18 IN SECTION NO. • 1 AND THE SECTION LENGTH 18 • 0.7625 M
COLLECTION AREA • 5>12E-01 MJ
WIRE TO PLATE » 1.270E-01 M
CURRENT/M • 7.8A9E-05 AMP/H
1/2 WIRE .TO "IRE • 6.350E-02 M
TEMPERATURE • 297.6*7 K
ION MOBILITY • 1.798E-04 MJ/VOLT.
OUST WEIGHT • 3.2SOE-06 K6/BEC
SEC
APPLIED VOLTAGE • 4.*OOE*04 VOLTS
CORONA MIRE RADIUS • 1.191E-03 M
CURRENT DENSITY m 2.5B1E-04 AMP/M2
CAS FLOW RATE • 9.4*OE»02 M3/8EC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • 4.439E+02 H/SEC
LENGTH INCR. "0.2541*565 M
TOTAL CURRENT • 1.500E-04 AMPS
CORONA MIRE LENGTH • 1.906E»00 M
DEPOSIT E FIELD • 2.581E*03 VOLT/M
CAS VELOCITY • o.760E-oi H/SEC
VISCOSITY • 1.800E-05 KO/M-8EC
PA«TW. PATH PARAM. • 5.708E-OB M
INPUT EFF./INCR. • 20.11
vo
vo
ROVRI
ERAV6
EPLT
AFIO
1.0543 3.622Et05 2.7479E+05 2.3490E*IS
l.OSri 3.*22CtOS 2,7395E*05 2.3879(^13
1.0230 3.622Ef05 i - - .— .
CMCD
25. 8
2S.6
2S.8
MHO
6.71E-06
4,07E-0*
2.B9E-06
HEIGHT
1.032E-05
6.541E-06
4.130E-6*
CALCULATION IB IN SECTION NO'. • 2 AND THE SECTION LENGTH IS • 0.7*29 M
COLLECTION AREA • 5.812E-01 M2
HIRE TO PLATE • i.27oE«oi M
CURRENT/M • 7.86«C«05 AMP/M
1/2 HIRE TO HIRE • 6.350E-02 M
TEMPERATURE • 297.6k7 K
ION MOBILITY • 1.798E-04 MZ/VOLT-SEC
OUST HEIGHT • s.250E«06 KG/SEC
DUST LAYER J(PART)
3.822E-04
1.916E-04
1.210E-04
J(IOM) INCR. NO.
4.9M.08
4.06B-08
5.38E-OS
2.58E.04
2.58E-04
2.98E-0*
APPLIED VOLTAGE • 4.560E»04 VOLTS
CORONA HIRE RADIUS • 1.J91E-OS M
CURRENT DENSITY • 2.581C-04 AHP/M2
GAS FLOW RATE • T9.460E»02 MS/SEC
PRESSURE • 1,000 ATM
MEAN THERMAL SPEED • «,«39E«o2 H/SEC
LENGTH INCR. •0.25416565 M
TOTAL CURRENT • l.SOOE-04 AMPS
CORONA HIRE LENGTH • 1.906£*00 M
DEPOSIT E FIELD • 2.581E«03 VOLT/M
GAS VFLnCITY • 9.760C-01 M/BfC
VISCOSITY • l.BOOE-05 KO/M.SEC
PART, PATH PARAM. • 5.708E-OB M
INPUT EFF./INCR. • 20.11
ROVRI
ERAVG
EPLT
AFIO
1.01*8 3«*0*E*OS 2.720BE»09 2.4463E»13
1.0114 3.606E+C5 2.7208E»05 2,4593E*1J
l.OOTfl 3.*06E*05 2.720BE»05
CMCD
25.8
2S.B
25.8
MHO
2.3SE-06
2.04E-0*
1.80E-06
HEIGHT
2.842r>06
2.088f06
1.59U-06
DUST LAYER J(PART)
J(ION) INCR. NO.
8.326E-05
6.H7E-95
4.662E-45
4.65E-08
4.03E-08
3.49E«0»
2.58E.04
2.98E-04
2.58E-04
CALCULATION IS IN SECTION NO. • I AND THE SECTION LENGTH IS • 1.5250 M
4
5
t
COLLECTION AREA * l.t»2E+00
HIRE TO PLATE • i.2Toe-oi «
CURRENT/H • 7.8*9F»A5 AHP/M
1/2 HIRE TO WIRE • 6.3SOE-02
TEMPERATURE • 297.6*7 K
ION NOBILITY • 1.T98E-04
OUST WEIGHT • j.250E-o6 KG/SEC
APPLIED VOLTAGE • 4.440f*04 VOLTS
CORONA HIRE RADIUS • 1.191E-03 M
CURRENT DENSITY • 2.581E-04 AMP/M2
GAS FLOW RATE • 9,460E»o2 M3/8EC
PRESSURE • l.OOB ATM
MEAN THERMAL SPEED • 4.439E+02 H/SEC
LENGTH INCR. BO.294165*5 M
TOTAL CURRENT • S.OOOE-04 AMPS
CORONA HIRE LENGTH • 3,8|2f*00 M
DEPOSIT E FIELD • 2.581F+03 VOLT/M
GAS VELOCITY • 9.7*oE»oi M/SEC
VISCOSITY • I.800E-05 KG/H.SEC
PART. PATH PARAM. • 5.708F-OB M
INPUT EFF./INCR, • 20,tl
ROVRI
ERAVG
EPLT
AFIO
CMCD
MMD
HEIGHT
OUST LAYER J(PART)
J(ION) INCR. NO,
-------
1.0052
1.0036
1.0025
1.0017
1.0012
1.0008
3.496E+05
3.496E+05
3.4»6E+05
3.496E*05
3.496E*05
3.496F+05
2.b<>61E+05
2.ha61E+05
?|(S«61E*05
?.6461£+05
2.646IE+05
2.5568E+1J
2.5629E+13
2.5638E+13
25.8
25.6
25.8
25.8
25.8
25.8
.60E-06
.50E-06
.02E-06
.55E-06
.27E-06
.20E-0*
1.208E-06
'.6I5C-07
T.753E-07
h.J18E-07
5.178E-07
«.275E-07
J.538E-05
I, 8176-05
2.J71E-05
t.Sfl<»E-05
1.5176-05
l,253E«05
2.03E-08
2.5fle»0«
2.21C-OB
1.92E-08
1.68E-08
J.06E-OB
2.56E-04
2.58E-Oa
2.58E-Oa
2.58E-04
2.58E-Ofl
2.58E-04
7
8
9
10
11
12
10
o
O
-------
to
o
CHARGING RATES FOR PARTICLE SIZES FROM SUBROUTINE CHARGN OR CHG8UM
SRI THEORY USED FOR PARTICLE CHARGING
INCREMENT NO.
0/QSATF FOR INDICATED PARTICLE SIZES
o.
1
2
3
4
5
6
T
a
9
10
it
12
0.
1
<
s
«
5
*
T
a
*
10
it i
12 1
2500E-06 0.
1.0360
1.6765
1,6668
2.0127
2.1027
2.1726
2.2263
2.2719
2.3116
2.3466
2.JT79
J.4063
I600E»05 0.
.0360
.34J9
.4177
,4596
.4892
.5119
.5253
.9374
.5479
.5573
.5659
.3737
3500E-06 0.4500E-06 0.
1.0360 1.0360
1.6491 1.6069
1.6344 1.7709
1.9433 1.8663
2.0207 1.9336
2.0805 l.»659
.1253 2.0239
.1634 2.0564
.1966 2.0647
.2259 2.1097 j
.2521 2.1322 i
Z.27S9 2.1525 i
iOOOE-05 0.2600E-OS 0.:
.0360 1.0360 1
.3037 1.2*38 |
.3692 1.3109
.4052 1.3486
.4305 1.3699
.4499 1.3061
.4609 1.1946
.470* 1.4022
.4793 1.4069
.4670 1.4069
.4941 1.4089
.4941 1.4089
5500E-06 0.
.03*0
.5659
.7129
.7977
.8577
.9039
.9369
.9651
.9697
P.0116
J.0312
J.0489
ISOOE-05 0.!
1.0360
.224*
.2*99
.2942
.3113
.3245
.3307
,3307
.3307
.3307
.3307
.3307
TOOOE-06 0.
.0360
.5128
.6406
.7136
.7651
.8047
.«322
.6358
.87*5
,8948
.9113
.92*2
5000E-05 O.I
,03*0
.1652
.2210
,2399
.2533
.2*3*
.2*77
.2*77
.2*77
.2*77
.2*77
.2*77
9000E-0* 0.
,0360
.4572
.5667
.6267
,*724
.7060
,7285
.7478
.7*48
,7800
.7936
.6059
JOOOE-05 0.1
.03*0 (
.1440 1
.1704 1
,1639 |
.1935
.2009
,2032
.2032
.2032
.2032
.2032
.2032
1100F-05 0.
.03*0
,ai46
.5110
.5653
.6034
.6328
.6517
.6662
.662*
.6955
.7071
.7177
SOOt-04
1.9805
.0975
.1165
.1279
.1345
.139*
.139*
.139*
.139*
.139*
.139*
.139*
1300E-05
,03*0
.3809
.4676
.51*0
,5501
.57*2
,5926
.60*9
.6195
.6307
.6409
.6501
-------
to
o
to
CHARGE ACCUMULATEH ON PARTICLE SIZES IN EACH INCREMENT
INCREMENT CHARGE FOR INDICATED PARTICLE SIZES
1
2
3
a
5
6
7
.8
9
10
11
12
1
2
3
0
5
6
7
8
9
10
It
12
0.2500E-06
0.18B95E-17
0.30576E-17
0.34412E-17
0,367o8E»l7
0.3B350E-17
0.39624E-17
0.10603E-17
0.41436E-17
0.42159E-17
0.42797E-17
0.4S369E-17
0.4J686E-17
0.1600E-05
0.59103E-16
0.76553E-16
0.80874E-16
0.83269E-16
0.84954E.16
0.8624«E«16
0.870Z5E-16
0. 877021-16
0.88302E«lfc
0.888alE»l«
0.8932«E-16
0.89775E-16
0.3500E-06
0.33«13E-17
0.5318aE.t7
0.5915*E-17
0.62673E.17
0.65169E-17
0.67099E-17
0.66543E-17
0.69772E-17
0.70BfllE-17
0.71786E-17
0.726S3E-17
0.73399E.17
0.2000E-05
0.91693E-16
O.H538E-15
0.12118E-1S
0.12036E-15
0.12660E-15
0.12832E-15
0.12930E-15
0.13016E-15
0.13092E-15
0.13161E-15
0.13223E-15
0.13223E-15
o.asoor-06
0.52363E-17
0.8l21flF>17
0.89506E-17
0.9HJ25E-17
0.97737E-17
O.JOOJ7E-16
0.1022«r-16
0.10393E-16
0.10936E»16
0.10663E-16
0.10776E-16
0.10«T9E>U
0.2600E-05
0.15399E-15
0.187B3E-15
0.19602E-15
0.200a7E>15
0.20361E-1S
0.20602E-15
0.20728e«14
0.20841E-15
0.20941E-15
0.20901E-15
0.209«1E-15
0.20901E-15
0.5500E-06
0,7576«E-17
0.11451E-16
0.12526E-16
0.131S7E-16
0.1J58SE-1<>
0.13923E-16
O.iaifcOE-tfc
0.1U370E-16
O.luSStE-16
0.10710E-16
0.1K853E-16
0.1U983E-16
0.3500E-05
0.27760E-15
0.328UE-15
0,3a026E-15
0.34677E-15
0.3513fcE-15
0.35a90E-15
0.35A57E-1S
0.3S6S7E-15
0.35657E-15
0.3S6S7E-1S
0.356S7E-15
0.356S7E-15
0.7000E-06
0,11922C-16
0,17flO»E«16
0.18879E-16
0.19720E-16
0,20312F*16
0.20768E-16
0.21085E-1«>
0.21356E-16
0.21594E-16
0.21805E-16
0.2199aE-16
0.22166C-16
0.5000E-05
0.56009E-15
0.6«529E-J5
0.66482E-15
0.67509E.15
0,68237E«15
0.68798E-15
8.69025E-15
0,6902?E.J5
0.69025E-15
0.69025F-J5
0.69023E-15
0.69025E-15
0.9000E-06
0.192BOC-16
0,?7117E«1*
0.291SSE-16
0.30309E-16
0.31122E-16
0.31747E-1*
0.32165E-16
0.325Z6E-16
0.32842E-16
0.33123E-16
0.33376E»16
0.33607E-16
0.8000E-05
0.1430BE-14
0.15888E-14
0.16255E-14
0.16442E-14
0.16575E-14
0.16678E-14
O.U710E-J4
8.16710E-14
0.16710E-14
0.16710E-14
0.16710E-14
B.16710F.14
O.UOOE-05
0.28423E-U
0.38808E-16
0.41455E-16
0.02942E-U
0.43990E«1*
0.04795E«16
0.45315E-16
0.45766E.16
0.46162E-U
0.46516E»16
0.06635E-16
0.47125E-16
0.1500E-04
0.47743E-U
0.53438E-14
0.54458E-J4
0.54918E-14
0.55241E.14
0.55489E-1«
0.55««9E«1«
0.55489E.14
0.55489E-U
0.55089E-14
O.S5489E-14
0.55489E-14
0.1300E-05
0.39J53E-16
0.52455E-16
0.55747E-16
0.57586E-16
0.58880E.16
0.59875E-16
0.60498E-16
0. 610391-16
0.61S17C-16
0.fcl9«flE-16
C.62330E-16
0.62682E-16
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NONJOCALITIES USING SET NO. 1 OP CORRECTION PARAMETERS
SIZE CCF
,SOOE-07
.500E-07
.500E-07
.sooE-67
.OOOE-OT
.OOQE.07
.100E-06
.300E-06
.600E-06
,OOOE-06
.600E.06
.500E-06
.OOOC-06
.OOOE-06
.sooE-05
.590
.414
.520
.2*1
.205
.1*9
.ISO
.110
090
.072
loss
.041
.029
.010
.010
INLET X
0.000
0,400
0.600
1.6*7
5.000
4,933
5.000
3.733
8,000
6.667
10.667
10.667
11.333
12.000
I9.SSS
OUTLET X
0.0010
1.0004
2.6661
6.7516
17.7324
14,3956
12.1946
7,5*13
12.6201
7,9521
B.5246
5.197«
2.1022
0,1505
0.0000
COR. OUTLET X
0.0006
1.1360
1.6102
1,0195
10.5901
0.0090
7.65*8
5,0070
9.0344
6,3065
0.6306
7.4069
0.4664
0.9957
12.1675
NO-HAP EPP,
00.5607
00.7009
09.3651
90.3050
91.5119
93.0155
94.1010
95.1393
96.1645
97.1453
90.0073
90.0337
99.5391
99,9700
99.9999
NO-RAP N
0,024
0.072
9,110
9.495
10.036
10,029
11.572
12.104
13,260
14.469
16.099
10.112
21,090
33,002
50.252
MO-RAP P
11,4X13
11.2991
10.6349
9.6950
0.4001
6,9045
5.0102
4,0607
3.8355
2.S547
1.9127
1.1663
0.4609
0.0300
0.0001
COR. EPP.
00.5607
00.2556
00.0470
90.0200
91.2347
92.6155
93.6056
94.3630
95.3300
96.0306
96.6510
97.1205
96.9107
96,9000
97.3973
COR. H
0.024
0.715
0.925
9.381
9.905
10.602
11.239
11.702
12.467
13.137
13.020
14.446
14.140
14.134
14.046
COR. P
11.4313
It. 7444
11.1530
.9712
.7653
.3045
.3144
.6362
.6700
.9614
.3490
.8715
.0093
.1000
.6027
EFFICIENCY • STATED • 93.24
COMPUTED • 93,2425
CONVERGENCE OBTAINED
ADJUSTED NO.RAP EFF. • 97*. 6066
NMD OF INLET SIZE DISTRIBUTION • 3.3001*00
SI8NAP OF INLET SIZE DISTRIBUTION • 2.164E+00
LOO-NORMAL GOODNESS OF FIT • «.934
NMO OF EFFLUENT UNDER NO-RAP CONDITIONS • 1.2791*00
SICMAP OF EFFLUENT UNDER NO-RAP CONDITIONS • 1.626E*00
LOC-NORNAL 000ONESS OF FIT • 0.961
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS • 15,107
•ISNA6* 0.000 NITH 0.000 0MEAKA0E OVER 4.000 STA0ES
NTENP • I
•NMO • 6,00
RflfMA • {.50
COM. EFF. • 95.0647
CORRECTED NMD OF EFFLUENT • 2.407E+00
CORRECTED SI8NAP OF EFFLUENT • Z.t77E»00
LOS-NORMAL SOOONEM OF FIT • s.*is
CORIteCTED PRECIPITATION RATE PARAMETER • 12.**
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS LOADINGS
to
o
IDEAL UNADJUSTED
MIG. VCL.(CM/SEC)
3.795E+00
4.448EtOO
4.S32E+00
5.425E+00
b.224EtOO
7.022E*00
7.«17E»00
9.001E+00
1.056E»Oi
1.286E»pl
1.624E*>01
2.189£»B1
3.300E+01
5.825E»01
IDEAL UNADJUSTED
EFFICIENCV(X)
NO-B4P
RAPPING PUFF
,649Et01
,950E»01
.834E+01
,220E*01
,S36Et01
,905E*01
,25«E+01
,576Et01
.8JSE+01
,95«E*01
.997E+01
l.OOOE+02
1.3S7E-01
2.«71E-01
7.659E-01
1.275E+00
1.379E+00
1.017E+00
B.195E-01
5.684E-OJ
3.737E-01
1.U3E-01
6'.094E«03
2.390E-05
1.619E-03
5.350E-0?
1.204E-02
2.182E-02
a.!63E"02
T.642E-02
1.623E-01
2.2<»5E-01
3.177E-01
4.26SE-01
5.463E-01
6.3«8E-01
6.231E-01
6.272E-01
NO-RAP+RAP PUFF RAPPING PUFF
DM/OLOGDCMG/OSCH) DISTRIBUTION (t)
J.668E-03
1 141 1E«01
2.591E-01
7.876E.01
1.316E+00
1.411E+00
1.496E+00
1.179E+80
1.265E»00
1. 137E4.00
9.952E-01
9.200E-01
7.461E-01
.S60E-02
.022E-01
.764E-01
.642E-01
.953E-01
,132E*00
.424E+00
,661E*00
,83tE»00
,230E*00
,79lE*00
,044E*01
,709E*01
6.292E-01 2.114E+01
t.272E*01 2.887E*01
PARTICLE
OIAH.(M)
2.500E-07
3.500E-07
4.500E-07
5.500E-07
7.000E.OT
9.000E-07
1.100E-0*
1.300E-06
t .600E-06
2.000E-06
2.608E.O*
S.500E-06
5.00DE-06
8.000E.06
1.500E-05
-------
SUMMARY TABLE OF ESP OPERATING
PARAMETERS AND PERFORMANCE
10
o
en
ESP PERFORMANCEl
DATA SET NUMBER 1
EFFICIENCY • 95.0647 X SC* • 2.156E+01 M**2/(M**3/8EC)
ELECTRICAL CONOITIONSi
SIZE DISTRIBUTIONS!
NONIDEAL PARAMETERSi
AVG, APPLIED VOLTAGE • a,515E+0« V
AVG. CURRENT OCNSTTV • 25,81 NA/CM«*2
RESISTIVITY • l.OOOE+09 OHM.CM
INLET MMD • J,300E*00 UM INLET 8IGMAP • 2.16«EtOO
OUTLET MMD • 2.a07E+00 UM OUTLET SIGMAP • 2.177E+80
GAS SNEAKAGE FRACTION • 0.00 /SECTION GAS VELOCITY 8IGMAG • 0,00
RAPPING MMO • 6.000E*00 UM RAPPING 8I6MAP • 8.9001*00
-------
PARTICLE SIZE HANCE STATISTICS
CORRECTIONS FOR NONIDE»LimS USING SET No. 2 OF CORRECTION PARAMETERS
SIZE ccf INLET x
2.500E-07 1.590
J.500E.07 1.414
4.500E-07 1.320
5.500E-OT 1.261
T.OOOE-07 1.205
9.000E-07
1.100E-06
l.SOOE-06
1.600E-06
2.000E-06
2.600E»06
3.500E-06
5.000E-06
6.000E-06
1.500E-05
.159
.130
.110
.090
.072
.055
.oat
.029
.018
.010
0.000
0,
-------
UNADJUSTED MICAATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS LOADINGS
to
o
-J
DEAL UNADJUSTED IDEAL UNADJUSTED
16. VEL. (CM/SEC) FFFtCIENCVm
,79SE>00
,088E»00
.«48E*00
.832E+00
.fl2SE*«0
,22«E+00
,022E*00
.817E+00
.001ei.no
.056E+OJ
.286E+01
,62«E+OI
.1B9C+01
.SOOE+01
.066E+01
.3J9E+01
.6«9E*01
.9SOC+01
361E+01
,83flE»ni
.220E+01
.536E+OJ
,905E*01
.254E+01
.576E+01
.815E+01
.954E+01
997E+01
,82SE»01 l.OOOE+02
- RAP
r v^. ••%*!/ v--wr v
6.375E-05
1.7H5E-01
3.290E-01
1.037E+00
1,770E»00
2.064E+00
1.SA2E+00
1.73«E+00
1.129E+00
8.810E-01
3.771E-01
7,0?aE-02
1.187E-02
RAPPING PUFF
DH/DLOGO(M6/DSCH)
1.933E-03
6.386E-03
1.037E-02
2.60aE-02
"«969E"02
9.122E-02
l.aOOE-01
1.937C-01
2.740E-OI
3.7«2E-01
5. 0956-01
6.521E-01
7.577E-01
7,«38E-01
7.487E-01
NO-RAP+RAP PUFF
DM/DLOCD(MG/03CM)
1.996E-03
1.S49E-01
S.S33E-01
1.06JE+00
1.820E+00
2.015E»00
2.20flE*00
l.77fcE*00
2.008CfOO
1.831E+00
1.639E+00
1.533E+00
1.135E+00
8.iaoE-01
7.605E-01
RAPPING PUFF
DISTRIBUTION(S)
«.360E-Ol
J.022E-01
1.78aE-Ol
7.95IE-01
1.132E+00
l.«2«E»00
1.66tF»00
3.831E+00
«.23«E*00
8.79tE*00
t.709E*01
2.114E+01
2.867E»OJ
PARTICLE
DIAM.(N)
2.500E-07
3.500E-07
4.500E-07
3.500E.07
7.000E.07
9,OOOE«07
1.100E.06
1.300E-06
1.600E.06
2,OOOE»06
2.600E.06
3.500E-06
5,OOOE«06
8.000E.06
1,500£«05
-------
ft***************************************
to
o
CO
SUMMARY TABLE Of ESP OPERATING
PARAMETERS AND PERFORMANCE
OAT* SET NUMBER
ESP PERrORMANCFI EFFICIENCY « <»3.
-------
APPENDIX I
OUTPUT DATA FOR EXAMPLE 2 (REVISION 2)
209
-------
r.p'.»; ESP
T.F.B.l.-R'.T.P. AN9 SO.».J.
PFVISTON n, AUG.. 1979
**•••«*•»»»«*»*««••*«•«««»•*••»*«•«*•
PRINTOUT OF INPUT DAT* FOR DATA SET NUMBER 1
DAT*. ON CARD NUMBER t
NENOPT • 16 NDATA • t
DATA ON CARD NUM8FP 2
LAB ESPi 8CA«82FT8/1000AeFMfCAUCULATED V.I F0» fACH ELECTRICAL SECTION
DATA ON CARD NUMBFR 3
NCST • i NOIST • i NVI • a NX t is NV « is NITER * i NCALC • o NRAPD « i NF.FF • i NTE-P • i NONID * i
DATA ON CARD NUMBER a
NN • 5 NU"INC • 3
DATA ON CARD NUMBER 5
IFINAl • 20 JII • 2 JI2 a 21 VISKIP s 1 VISAME * 2
DATA ON CARD NUMBFR 6
DL • O.OiSno GRN/ACF Pt * 10. 0000 FT F.TAH • 94.00000 X DO * 100". "0 KC/«**J EPS • S.lOOFtOO
VRATIO * 1.0300 US « O.OOOIfrS ««*?/V-SFC FPATM • 1. 0000 FBI) • 150000C. V/M RHOCRS * I.OOF«0« OMM-C4*
DATA ON CARD
ASNUCK( 1) • 0.00
1) * 0.00 A7K'U"S( t) * 1.0
-------
ASNUCKC 2) » 0.10 AZISGY( 2) « 0.10 A7NUMSI 2) > 4.0
DATA ON CARD
ENDPTC 1) «
ENDPT( 6) •
0.20(1 UM
O.BOO UH
ENOPTJ 2) «
ENDPT( 7) •
0,100 IJM ENDPT( 1) *
1.000 UH FNOPT( 8) s
0.400 UM fNOPTt 4) • 0.500 UM EN(>PT( •>) » 0,600 UM
1.200 UM EMQPTC 9) • 1.400 U» ENpCTdO) • 1,800 UK
DATA ON CARD NUMBER 9
ENDPTUl) « 2.200 UK ENO»T(12) * 3.000 UM CNOOT(lJ) • a. 000 U" E*DPT • 1?.8150 X PRCUOO) • 19.7004 X
DATA ON CARD NUMHFR n
MCU(lt) • 2*.86«3 X PRCU(12) « 3A.8042 X PRCUC13) • 49'.25I6 X PRCIKld) * 64,1765 X MCU(15) « 79.1014 X
MCU(1*> • 100.0000 X
DATA ON CARD NUHBCR It
NUM8EC • 3 18FCT( 1) • * L8ECT( 2) • * LSECT( J) • 12
DATA ON CARD NU»BF* 13
A8( 1) * ».2500f»00 PT**2 V08( I) « 4.«800E»Oa V TC8( 1) • 6.2S09f-05 A «L8( 1) • *.2SOOE«00 FT
AC«( 1) • 4.*e75E.02 I1* BS( t) • 5.00nOE*00 IN NM$( i) • s.0000f»08
DATA ON CARD NUMBER 14
SV8( 1) » 2.500<>r»00 IN *T,8f I) « 3.0SS3F«02 FT**J/MlM VCA88( 1) • «,8X51f*nn FT/SEC TrMP$( 1) • T.hnoOF»OI F
Me D • i.oooflE+oo AT<« viss( i) • i.eooor-05 Kr,/M.src LINCS< n « u.jAhTF-oi FT
-------
DAT* ON CARD NUMBER 15
RFS( 1) • 9.DOOOF-01 3TARTK 1) • fc.OJOOE-fl? A/M**2 STiRTZf 1) • J.0008E-05 A/M**J
8TART3t 1) • 2'.0000e-05 A/H«*2 V8TAR( J) • 3l8900E*0« V
DATA ON CARD NUMBER 16
Al( 2) • *.2900E*00 FTo«2 VOS( ?) • H,08flOE+0« V TCK 2) « ».2500E"05 A ML3( 2) • 4.2SOOE+00 FT
AC8( 2) • 1.68TSE.02 IN B8( 2) • S'.OOOOE»00 IN NHS( 2) • 5.6000E+00
DATA ON CARD NUMBER 17
IV«t I) • 2.SOOOE+00 IN V08f 2) • S.O!33E*02 FT**S/MIN V6»88( 2) • «.8855E+00 FT/8EC TEMPS( 2) • T.»600E»C1 f
nt 2) • 1.0000E«00 ATM VtSS( 21 • I'.eOOOE-OS KG/M.SEC LINC8( 2) * «.U*TE-01 FT
DATA ON CARD NUMBER !•
ro
[^ RfBC 2) • •'.OOeOE-Oi STARTlit 2) • 6.0000E-03 A/M**2 START2( 2) • Z.OOOOE-05 A/M**2
BTARTK 2) • Z'.OOOOE-OS A/M*«2 V$TARf 2) • 3.8000E+Oa V
DATA ON CARD NUMBER 1*
Alt 1) • 1.2500E«01 FT**2 V08( 3) • S.«)680E*0« V TC8C 3) • 1.2SOOE-0* A NL8( 3) • 1.2500E+OI FT
ACB( 3) • «.*8T5E»02 IN B8( 3) • S'.OOOOE^eO IN NHS( 3) • l.0008E*01
DATA ON CARD NUMBER 20
8V8( 3) • 2.5000E+00 IN V6S( 3) • S.0533E+02 FT..J/MJN VS*SSC 3) • 0.88S3E+BO FT/8EC T£MP8( 3) • T.*OOOE*01 F
F8( 3) • l.OOOOEioO ATM VI8SC 3) • 1.8000E-05 KB/H>8EC UINCBC 3) • «.16«TE-OI FT
DATA ON CARD NUMBER 21
RFBC 3) • 9.0000E>01 STARTU 3) • 6.0000C-05 A/M*«{ |T»RTZf 3) • 2.0000E-05
• TARTS( 3) • 2'.OOOOE»OS */M*»2 V8TAR( 3) • 3'.8000E*0« V
-------
NJ
H
U)
CLEAN 048 VOLTAGE-CURWNT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO. t
VW • .Jr.76<»BE+0« ACONTV • 6'.OOOOE-05 AEPLT a .J.T77JE»05
VM • -j'.8J4Te+0« ACDMTV • 8.0800r-05 AEPLT • -l.ft*47E»09
VH • .3'.8«*9E*04 ACDNTV • t.OOOOE-04 AEPLT • •1,9«69E»09
VH • •S.«SSTE«0« ACOMTV • l'.20GBE-0* AEPLT • »t.«2<»C«OS
VM • .4'.0129E»04 ACDNTY • 1.4000E-0* AfPLT • .>,0*8BE»09
VH • .4.0*7SE«04 ACDNTY • l.*008E-0« AEPLT • •t,16*7E«09
VM • -4'.1204E+04 ACONTV • 1.BOOOE-04 AFPLT • -2.237kE«09
VM • .4'.OS»IE*04 ACONTV • l'.*478E-04 ACPLT • .I,1B*|E«09
INC««EMTAL ANALVill Of
PEMOPM4NCE
LAS ESPi ICA«S2PT2/1000AerM|CALCULATED V.J FOR EACH ELECTRICAL SECTION
CALCULATION IS IN SECTION NO*. • 1 AND THE SECTION LENGTH IS • 0.7419 M
COLLECTION AREA • 9.812E-01 M* APPLIED VOLTAGE • 4.080f»04 VOLTS
MIRE TO PLATE • i'.2Toe-oi M CORONA MIRE RADIUS • I.HIE-OJ H
CURRENT/N • 9.02«E>0« AMP/M CURRENT DENSITY • 1.44Bf«04 AMP/HI
1/2 HIRE TO MIRE • 4.190E-02 M GAS FLOH RATE • I.M«E-01 MS/SEC
fE«*CMTtfft« • 2*7.222 K PRESSURE • 1.000 ATM
ION MOBILITY • 1.799E-04 M2/VOLT-SEC MEAN THERMAL SPEED • 4.4S4E+02 N/SEC
OUST MEI9MT • |.190E»09 KG/SEC LENGTH tNCR. •0.1270B4S9 M
TOTAL CURRENT • *.STSE«OS AMPS
CORONA HIRE LENCTH I l.«0»f*00 M
DEPOSIT E PIELD • J.**8E»01 VOLT/M
OAI VELOCITY • J.4«OE400 M/SEC
VISC6IITV • 1.800E-09 KB/M.SEC
PART, PATH PARA*. • 5.700E-08 M
INPUT Err./IMC*. • IT.«*
RIOVR
O.BUG
ERAV6
EPLT
0.4684
0,4814
0.4804
0.4BM
APID
I,1BOBE«11
2ll84tE+05 1.1824E*!]
-••-•"— 1.1824EO3
2,ia«lE*09
1.1824Etl]
1.182TE»tS
CNCD
11,9
11,7
11,1
11,2
11,2
11.2
HMD
T.jor-o*
2128E-0*
1>2E-04
1.41E-04
HEIGHT DUST LAYER JCPART)
J(ION) INCH. NO.
i.oioe-os
8,»78E-04
8.21TE-0*
>4 i.sse-08
8.7S1E*04 8.7*E>OB
«.oioE-o4 i.ue-or
8.440E-04 1.2IE-8T
8.0IOE-04 I.24E-07
7.S90E-B4 1.29E-07
l.«9E.O«
1.65E-0*
1.69C»04
1.B9E-04
l.»9E«04
1.HE.04
-------
CLEAN 6AS VOLTA6E-CURRF.NT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO'. *
VM • -3.T648E+04 ACDNTV • ..OOOOC-OS AfPLT • .J.TT7SE«05
VN • -3r.8347E»o4 ACDNTV » B.OOOOE-OS AFPLT • .I,»*»TE»OS
VN • .3'.B*»SE*04 ACONTY • 1.0900C-0* AEPLT • .l.«4««E+OS
VH f -3'.«S37E*04 ACDNTV • l'.2000E-04 AEPLT • -2.024SE+«5
VN • -4'.0123E«04 ACDNTV m l.«900E-oa *ePLT • -2.0fBSEt09
VM p -4'.Ok73E*04 ACDNTV • l.»OOOE-04 AEPLT • -Z.1»«TE + 03
VH • -4.1204EO4 ACDNTV • r.SOOOE-0* AEPLT • -2.23TkE«Of
VN I «4.0802E«04 ACONTV • l.»«T8E-0« AEPLT • .J.l»»ie*05
to
CALCULATION IS IN SECTION NO'. • 2 AND THE SECTION LENGTH 18 • O.TkZS N
COLLECTION AftEA « 5.812E-81 M2
HIRE TO PLATE • I.JTOE-OI M
CURMENT/N • S'.02«E-05 AMP/N
i/> HIRE TO NIP.E • k.iseE-oz M
TEMPERATURE • 24T.222 K
ION MOBILITV • l.T«!E-Oa N2/VOLT.SEC
OUST HEI0HT • 2.1SOE»OS KG/SEC
APPLIEO VOLTAGE • •.080E»0« VOLTI
CORONA MIRE RADIUS • 1.1*IE>03 H
CURRENT DENSITY • i.*«8r-0a AMP/M2
OAS PLON RATE • l.«a«t-01 M3/8EC
PRESSURE • J.OOO ATM
MEAN THERMAL SPEED • «.«3*E*02 M/SEC
LENSTH INCR. •0.12708*35 M
TOTAL CURRENT • «.STIE-OS AMPS
CORON* MIRE LENGTH • l.*fl*E«00 M
DEPOSIT E FIELD • l.M8E«03 VOLT/M
GAS VELOCITY • i,««oe»oo «/SEC
VISCOSITY • 1.800E-05 KG/M.8EC
PART. PATH PARAM'. • S'.TOOE>«8 M
INPUT EF'./INCR. • IT.t*
RIOVR
ERAV6
,OSkE*OS
CMCO
MMD
MEIBMT DUST LAYER J(PART)
.T024
.7085
,T|4B
'.05»E«05
1.162TE*13
1.1827E*I3
1,1827E+13
!.fB*TE + U
1.1827E+13
1 . 1 827E+1 3
11,3
"r"
ills
11^7
11. 8
114SE-0*
1,32E-06
1,1»E-0»
l.OSE-0*
9,97E-07
».31E-OT
7.460E-0*
t.747E-Ok
k.O*3E-Ok
I.4«7E-0«
4,«*2F-Ot
4.48*C-0*
t.»73E-0«
k,033E-0*
S.4SOE-04
4,«17E-0«
4.43BE-04
4,013E-0«
.23E-07
.20E-07
.I7E-07
.13E-07
,0«E.07
.OSE-07
.»5E-BA
,*5E-04
.tSE-04
.»5E-0«
.kSE-04
.65E-04
7
B
«
10
11
12
EPLT
2'.18klE*05
2,lBktE»OS
2,l8klE*03
2,18611*05
2.18*1E*05
2.l8kiE*OS
CLEAN GAS VOLTAGE-CURRENT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR 8FCTION NO. 3
VN • .3.7701E+04 ACONTY • t.OOOOE-09 AEPLT • -1.7777F*05
VH • -3.83SOE«04 ACONTY • B.OOOOE-05 AFPLT • -1.8»?!E*05
VH • -3.8*»8E*04 ACONTV • 1.8000E-04 AfPLT • -l.»«7JE»05
JCION) INCR. NO.
-------
VM • -3'.9560E*04 ACDNTV • l'.2000E*04 AEPLT a -2.02SZE»05
VM » -4'.0128E»04 ACDNTY > 1.4000E-04 AFPLT • .2.0993E*05
VW • -J'.9601E*04 ACDNTV • l'.2l42E-04 AFPLT • .2.0S06E+05
CALCULATION IS IN SECTION NO*. • 3 AND THE SECTION LENGTH IS • 1.5250 H
N>
H"
Ul
COLLECTION AREA • l.l»2E*00 M2
MIKE TO PLATE • 1.270E-01 H
CURRENT/N • 3.702E-05 AMP/M
1/2 MIRE TO MIRE « 6.3SOE-02 M
TEMPERATURE • 297.222 K
K»N-MOBILITY « 1.795E-04 MI/VOLT-SEC
DUST MEIOHT • 2. HOE-OS KO/SEC
APPLIED VOLTAGE * 3.960E+04 VOLTS
CORONA MIRE RADIUS • 1.191E-03 M
CURRENT DENSITY • 1.214E-04 AHP/M2
GAS FLO* MATE • 1.444E-01 M3/8FC
PRESSURE • 1.000 ATM
MBAN THERMAL SPEED • 0.fl36E+02 M/SEC
LENGTH INCR. «0'.12T08035 M
RIOVR
0.475*
0.4*29
0.4902
ERAVG
'.963Et05
.7047
.7116
.7166
.7257
.7125
.7191
.7456
EPLT
2',0306EtOS
2,0306E*05
2.0306E*05
CMCO
HMD
2,030*EtOS
.963EfOS
l,963Ef05
2,030*Et05
2.0306E*05
2,030*E*OS
2,0306C+05
'.963E«OS 2.0J06E+05
,27«5E*12
.27«5E»12
,2745E*12
,2746Etl2
,27«6E»12
.27«6E»12
',\ BlSlE«07
,2 6,OSf-07
•;T
f^
.0
9.1
WEIGHT
3.764E-0*
7.31E-07
7,04E-07
6,78E-07
6,56E-07
6.S8E-07
6.22E-07
6.09E-07
m' j
2.884E-06
5.87E-07
2.445E-06
2.260r-06
2.095E-06
1.947E-06
1.8UE-06
1.693E-0*
l.S64F*06
DESIGN EFFICIENCY • 99.00
UNCORRECTED COMPUTED EFFICIENCY • 79.01
TOTAL CURRENT • 1.412E-00 AMPS
CORONA MIRE LENGTH • 3.S12E+00 M
DEPOSIT E FIELD • l'.21«E+03 VOLT/M
GAS VELOCITY • I.«*OE*OO M/SEC
VISCOSITY • i.spoE*es KG/M*SEC
PART. PATH PARAH. • 5.700E-08 M
INPUT EFP./INCR. • IT.46
DUST LAYER J(PART)
J(ION) INCH. NO.
3.38SE-04
3.0BSE-04
2.372E-04
2.167E»»4
2.022E-04
.742E-04
.622E-04
.S14E-04
.41AE-04
9.33E-06
8.93E-08
8.52E-08
8.14E-06
7,77E-OS
T,«Jf.08
7.10E-08
6.79E-08
6.50E-08
6.22E-08
.21E-04
.21E-04
5.71E-08
.21E-04
,?1E-C4
,21f-04
.21F.04
.21E-04
,21F»Oft
.21E-04
13
14
IS
1*
17
18
19
20
21
22
23
24
-------
to
CHARGING RATES FOR PARTICLE SIZES FRO" SUBRnilTINf CHARGE OR
SRI THEORY USED FOR PARTICLE CHARfilMR
INCREMENT NO. 0/OSATF FOR TMRICATFR PARTICLE SIZFS
0.250nE-06 0.3500E-06 0'.4500F»06 O.S500F-06 0.7000f-06 0.9000E-06 0.11POE-05 0.1300^-05
I
2
to
It
12
L.0663
1. 5532
1.5070
1.6119
.6-M3
.7551
.eoea
.8541
.8941
1*296
.9616
,9906
1J 2.0095
iu 2.0274
15 2.0443
16 2.0603
IT 2.0756
IS 2.0001
19 2,1040
20 2.1173
.0390 0.9995 0.9613 0.91J6 0.8615 O.M20 0.7916
.1082
.4468
'.5398
.6096
.6654
,Tlt«
.7515
".7861
,«168
.8444
,8694
,8853
.9003
>1«5
.9280
.9409
,9531
^9648
.9760
21 2.1300 1.0867
22 2,1423 1,9970
23 2.1540 2,0070
24 2.1654 2.0070
.2569
.3840
'.4680
.5305
.5802
,6214
.6566
.6871
.7142
',7385
.7605
.7742
.7872
.7995
.8111
.8222
'.8328
,8429
,8525
.86|8
^8618
,8618
.2112 1.1555 1
.3296 1.2644 1
.4068 1.3341 1
.4639 1.3852 1
.5090 l.«25« 1
.5463
.5780
.6056
,6300
,6518
.6716
.6637
.6951
.7059
.7162
.7260
'.7354
.7443
.7528
.7528
.7528
.7528
.8618 .7528
.11584 ]
.4865 \
.5108 1
.5322 1
.5514
.5688
.5792
.5890
.5983
.6072
.6156
.6236
,6236
.6236
.6236
.6236
.6236
.6236
.0976
.1990
.2625
.3085
.3443
,3737
.3986
.4201
.4390
.4559
,4711
.4800
.4884
1.4964
1.5039
1.5111
1.5111
1.5111
1.5111
.04A6
.1481
.2086
.2517
.2851
.3123
.3352
.3549
.3722
.3876
.4015
.4094
.1169
."240
.4240
.4240
.4240
.4240
.4240
1.5111 1.1240
1.5111 1.1200
.0102
.1093
.1680
.2092
.2410
.2666
.2882
.3067
,32?9
.3373
.3502
,3575
.1643
.3708
.3708
.3708
,370*
.3708
.3708
,3708
.3708
1.5111 1.4200 1.3708
1.5111 1.4240 1,370§
O.lfcOOE-flS 0.2000E»OS 0'.2600E>05 0.3500E-05 0.5000E-05 O.SOOOE-05 0.1500E-04
1 0.7564 0'7216 0,6866 0,6534 0.6227 0.5910 0.5508
2 0.9665 0.9233 0.8795 0.8392 0,8019 0.7571 0.6984
3
L.0651 1.0195 0.9729 n.93«2 0.8872 0.8368 0,769n
4 1.1226
m
6
7
g
9
10
11
12
13
14
15
16
IT
If
10
20
ei i
.1623
.1925
.21*8
.2S70
.2543
.2694
.2828
.2948
.59
.1624 1.1269
.0055 0.90117
.0316 n.9293
.0501 0.9537
.0646 0.9740
.0762 0.9912
.0859 1.0069
.0894 1.0160
.OB94 1.0?3">
.0894 1.1297
.189ii 1.3151
.0891 1.0397
.0894 1.0197
.0894 1.0397
.0894 1,0397
,0fl9« 1.0397
-------
22 1,5075
25 1.3075
24 1.3075
1.2505
1.2505
1.2505
l'.2029
l'.2029
1.1624
1.1621
1.1624
1.1269
1.1269
1.089(1
1,0894
1.089*1
1.0397
1.0397
1.0397
to
M
•O
-------
CH4RSE tCCUHUUTEB ON PARTICLE SIZES IN EACH INCREMENT
INC"EXENT CHARGE FOR INDICATED PARTICLE SIZES
to
»-•
CO
1
2
3
a
5
6
7
8
9
10
11
12
13
14
15
16
17
16
19
20
21
22
23
24
1
2
3
a
5
t
7
8
*
10
11
12
13
14
15
16
17
1»
19
20
21
22
23
24
0.2500E-06
0.1T422E-17
0.22111E-17
0.2U623E-17
0.26336E-17
0.27631E-17
fl.2S6T6E.17
0.29547EM7
0.30294E.17
,309«TE-17
.HS2Se-l7
.32050E-17
.32525E-17
.32838E-1T
.33126E-17
0.33402E>17
0.33664E»17
0,339l3E-l7
0.34150E>17
0.34377E-17
0.34594E-1T
0,3«602E-17
0.35982E-17
0.35195E-17
0.35380E-17
0'.1»OOE-05
8.386T5E-16
0.49«l8E»16
0.54462E«16
0.5TJ99E-1*
0.594J2E-1*
0.609T7E-16
0.62218E.16
0.63252E-1*
8.6013TE-16
0.6«9o9E-16
0. 65593E.lt
0.66207E-16
0.66540E>16
0.668<>5E.16
0.668S5E>16
8.66855E-16
0.6685SE-16
0.6685SE-16
0.66855E-16
0.66855E.J6
0.«6855E.16
0,*685SE-16
0.66B55E.16
0.*6S5SE-lfc
0.3500E-06
B'.30823E-17
0,3T803E-IT
8,41808E-17
8.44497E.17
9.4651«E-17
0.48126E-1T
9J«9067E-17
0.5061SE-17
0.5161«E-17
0'.52501E-17
8.53298E-17
O.S4820E-17
0.54481E-1T
»,54915E.1T
8.55325E-17
0.55T15E.1T
«,56086E-1T
0.56440E-IT
0,56T78E-1T
9.57101E-IT
0,57ai8E-17
0.5TT10E-1T
0,57996E-17
0.57996E-17
O'.ZOOOE'OS
0,S7246E-16
0.73240E-1*
8.80878E-16
0,85518E-lt
0.68652C-16
6.90996E-16
0'92857E.U
0,94396E>16
8,95703E-16
8.96837E>16
8.97837E-16
e,98730E.16
9.99200E>16
8.99280E-16
8.99200E-16
8.99208E.16
8.99200E-16
8.99200E-16
8.99200E.1A
0.99200E-16
8.99JOOE-16
8,99?08E-16
0.99JOOE-16
8.99200E-16
n.4500E*0«>
0.45269E-1T
0.5692TE-17
8.62682E-17
0.66487E>17
8.69389E-17
0.71572E-17
0,T343TE-17
0.75028E-17
0.764HE-1T
O.T7641E-17
0.787<|OE-1T
O.T9737E-17
0.80359E-17
8.809a6E»17
0,81501E-17
0.82029E-17
0.82538E-1T
0.83009E-17
0.83466E»17
0.8S904E-17
0,8«325E-17
0.84325E-17
0.8«325E-17
0.84325E>17
8.2608E-09
9.9ia*9e-16
O.MT1BE-15
8.12962E-15
0.13777E-15
0.14310E-H
6,la70?E-!5
0,15909E-15
0.15260E-15
0.1S471E-1S
0.1565SE-15
0.15813E-15
0.15954E-15
0.16825E-15
0,1682SE-1S
0.16025E'1S
0.16025E-I5
0.16025E-1S
0.16025F»15
0.16025E>15
0.16025F-1S
0.16825E-15
0.16025E-15
0.1602SE-IS
O.U025E-15
0.5500E'06
0.6390?E>17
O.T9S80E-17
0.87137E-1T
0.92196E.1T
0.95935E-1T
0.98893E-17
0.10!34E>16
0.10302E-16
9.10522E-16
0.10682E-16
0.10825E-16
0.1095SE-16
0.11034E>16
0.11109E-16
0.1H80E-16
O.I1247E-16
8.1131ZE-16
0.11373E-16
0.11431E>16
0.11487E-16
0.1148TE-16
0.1ia87E«16
0.11487E>16
0.11487E>16
0.3588E-85
8.15693E-15
0.20155E-15
0.22342E>15
8.Z3818E-15
0.2«886E«15
6.25683E-15
0.26158E-15
0.26604E-15
8.26975E-15
0.27291E-1S
0.275fc4E-15
0.2780aE-15
8.27919E-15
8.27919E-15
0.27919E-15
0.27919E-15
0.27919E-15
0.27919E-15
0.27919E-1S
0.27919E-15
0.27919E-15
0.27919E-15
0.279J9E-15
B.27919E-15
8.70BOF»06
0.9«017F-17
0'.11917E»16
0.13nanF«l6
0,13759E-16
0.ia286E»16
0'.1«700E-1*
Oll584JE«16
0,1533IF-16
0.15582F-1*
0.158B3F-16
0.16001E-1*
O.lblSOE-lfc
0.162B7E-16
0.163B8F-16
0,16480F-lfc
0.16575E-16
8,1666?E-16
B,167flSE"16
0,167«SE-lfc
0.1674SE-16
8.16745E-16
0.16745F-1*
0,167«5F-16
0.167aSE>16
8.5000E-05
0'3039tE.lS
0,39JS4E-15
0.43298E-15
0.46311F-11!
0,48530E-l5
0,50292F-lS
0.514B2E-H
0.52416F.15
0.53173E-15
8.53801E-15
9.S4336F-15
0.54T98E-15
0,5a99«E-l5
9,54998«-l5
0.54998E-1?
0.54998F-H
9.506
8.1«369E>16
0.18306F«16
8.19998F-16
0.21057F-16
0.21823E-16
0.22*22E-1*
B.229I2E-16
0.23326F-1*
8.23684E-1*
0.24000E»16
0.24282E»16
0.2«536F«lk
0.24fc84E>16
B.24824E-16
0.2«957E-16
0.250S3E-16
0.?5!03E-16
0.25283E-1*
9.25203E-16
0.252B3E-16
0.25203E-16
B.25203E-16
0.25203E-16
0.25203E-16
O'.eOOOE-OS
9.73569E-15
0.9a2SOE-15
B.10*17F-1«
B.11099E-14
8.11673E-H
0.121S8E-1"
B.12517E-ia
0.12802F-KI
B.13072E«14
8.13?52E-1«
B.13397E-1«
B.13517E-1*
0.13562F«I«
8.13%62E-1«
B.1356?E-1«
0.13562F-H
fl.!3562E-l«
0.13562E*1«
8.I3562F-1«
8.135«2E»ta
9.13562F.-1«
8.I3562E-1*
O.I3562F'ia
C.13S62E-ia
0.1190E'OS
0.29212E.16
0.2578«E-16
0.28232E>16
0.29718E-16
9.3B779E-16
0.31600E>16
0.32268E-16
0.32831F'|A
8.31316E-16
0.33742E-I6
0.316
0.350161-16
0.3S816E-lfc
6.35816E-16
0.350UE-16
0.35016E>16
0.35016E-1*
0.35016E-1*
0.35016E>16
0.35816E-U
B'.1500E»94
8.241018E-U
0.38481E-14
0.33561E-14
0.356T2E»14
0.37197E-14
0.38398E-10
0.39a8aE>14
0,40560E>ia
0.41625E-14
0.a2512E-ta
0.43261E-14
0.43947E-14
0.4a3«5E-14
0.«a6ToE-la
n.aa9«2e-l114
0.45376E-14
B.1300E>OS
0.26950E-16
0.34393E>16
0.37769E«16
0.39765E.16
9.4U71F-16
0.422ME-16
Q.«3125E>16
0.438S8F-16
0.ua«8HE-16
a.a58a8E«l*
0.4S530E«16
9.a59TlF-16
O.H62l7E«16
0.46«SOE'16
6.U6fc71F.16
0.16671F-16
0.46671E-16
0.86671E.16
fl.«667IE-16
B.a6»71E-16
0.a6671E-16
0.4t671E>16
0.46671E-16
0.466T1E-16
-------
PARTICLE SIZE RANG? STATISTICS
to
CORRECTIONS FOR NONIBEALITIE8 USING SET NO*. 1 OF CORRECTION PARAMETERS
.SIZE CCF INLET x
2.500E-07
3^500E*07
4,500E-07
5,500E-07
7.000E-07
9.000E-07
1,100E-06
1,300E-06
1,600E-06
2,OOOE-06
2,600E-06
3,500E-06
5,OOOE-06
0,OOOE»06
.589
.414
.320
.261
.205
,159
,130
.110
,090
,072
,055
,041
.029
,018
1.500E-05 1.010
0,000
0,049
0,212
0,597
21119
2,905
3,582
3^203
9,0*5
7,164
11,940
10,447
14,925
14,925
20.099
OUTLET t COR. OUTLET X
0.0201
O'. 1299
0.5586
1.5120
5'.2257
610981
7,7967
6,7014
12,8769
12,0500
17,1710
12,2611
12,0579
4,1302
0.5022
0,0235
0,1259
0,5037
1,3489
4,5857
6,065?
6,0762
5,9731
11,5702
10,9277
15,9605
11,9976
12,7053
6,5073
4.6609
NO-RAP EFF.
59' 1650
58.7095
59,1955
60,2813
61.0360
64,2328
66,3110
68,4115
70,9701
73,9489
77,7415
81,0356
07,4957
95,7169
99.5688
NO-RAP M
5'563
5,494
5,568
5,736
5.984
6.386
6,758
7,158
7,683
8,355
9,333
10,593
12,915
19,570
33.831
NO-
40,
4l!
40,
™r
30!
35,
33,
31.
29,
26
*if
18
IS,
4.
0.
RAP P
8350
2905
8045
7187
1640
7672
6890
5885
0299
0511
2585
1644
504S
2831
4312
COR. EFF.
4
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS LOADINGS
to
to
o
IDEAL UNADJUSTED
MIG, VEL'. (CM/SEC)
2.393E+00
2,532E*00
2.714E+00
2,919E«00
3.234E+00
3.*70E*00
1'.2»1E*01
1,957E*01
5.383E»Ol
IDEAL UNADJUSTED
EFFICIENCV(l)
.OS9Et01
.632E+81
.191E401
,679E+8t
,988E*81
.750E»0»
C572C+01
,957E»Ol
NO-RAP
DM/DLOGD(M6/DSCM1
2.662E-02
2.613E-81
l.aa9E*00
1.7H9E+01
2.5I6E*01
3,«77E+OJ
3.283E+01
1.721E+81
a.678E+CO
RAPPING PUFF
DM/DLOSDCMG/DSCM)
1.051E-82
S.a72E-02
T,809E-02
l.al6E-01
2.781E-81
7,638E-81
1.053E+00
l.a89E+00
3.5«5Et8fl
NO-RAP+RAP PUFF
OM/DLOGD(HG/08CM)
3.912E-02
1.527E+88
5.80aE*86
1.87eE*81
1,838E*81
2.62lEt01
3.11aE»81
2.82jE*fll
8.722C+80
4.556C+80
RAPPING PUFF
DISTRIBUTION^}
1.822E-8!
l,78aE-81
7.953E-81
1.132EOO
l.a2aE400
».«.6iE*oe
3,831E*80
1.80aE+81
1.T89E+01
2.I11E401
2.8B7E+01
PARTICLE
DIAM'. (M)
2.400E-07
3.500E.87
a.500E«07
5.580E-87
7.000E-07
9.000E-07
1.380E.86
J.680E-06
2.*80E«06
3.S80E-86
8.000E-06
i.5oee»85
-------
ft**********************************************************
SUMMARY TABLE OF ESP
PARAMETERS AND PERFORMANCE
ro
to
DATA SET NUMBER 1
PERFORMANCei EFFICIENCY • 81.0093 X SC* • l'.610C+01 M»*2/(M**]/8EC>
ELECTRICAL CONDITIONS!
SIZE DISTRIBUTIONS!
NONIDEAL
AVG. APPLIED VOLTAGE • 4.020E+04 V
AVC. CURRENT DENSITY • 10.11 NA/CM**2
RESISTIVITY • l.OOOf+09 OHM.CM
INLET MMD • 3.967E+00 UM INLET SI6MAP • 2.165EtOO
OUTLET HMD • Z.463E+00 UM OUTLET SICHAP • 1,962EtOO
GAS SNEAKAGE FRACTION a 0.00 /SECTION GAS VELOCITY SIGMAG « 0.00
HARPING MMD • 6.000E+00 UM RAPPING SIGMAP • 2,500E*00
A*************************
-------
PARTICLE SIZE RANGE STATISTICS
to
to
to
CORRECTIONS FOR NONIDEALITIES USING SET NO'. 2 OF CORRECTION PARAMETERS
SIZE (
2'.500E«07
3.500E-07
4'.500E-07
5,500E-07
7.000E-07
9,OOOE-07
1,100E-06
1.300E-06
1.600E-06
2,OOOE>06
2.600E-06
3' 500E-06
5.000E-06
6,OOOE-06
1.500E-05
:CF
.589
.414
.320
.261
,205
..159
.130
.110
.090
.07?
,055
.041
,029
,018
.010
INLFT X
o'.ooa
0>49
0,212
0^597
2 j J9
2,985
31582
3,283
6,865
7, 164
11.900
10J407
10,925
10,925
20.899
OUTLET X
O',0179
0.1157
0'.4986
113727
0,7090
6.2735
7'.1533
6'.2075
12'.0867
11^5199
16.8568
12'.S155
13,2853
5,7558
1.6318
COR. OUTLET X
0,0210
0,1101
0.0593
1.2364
4,2278
5.6010
6', 4488
5.6085
11,0716
10,6240
15,8651
12,2600
13,7535
7,6473
4.9811
NO-RAP EFF.
54.9130
50.0426
50.8886
55^9220
57,0000
59,7100
61.7165
63',7581
66.2502
69.1731
72.9351
77,0347
82.9356
92.6069
98.5031
NO-RAP w
0,908
0.884
4,945
5,089
5,301
5.647
5.964
6'.305
6.707
7,310
8.118
9 138
10,983
16,179
26.100
NO-RAP P
45.0870
45.5574
45'. 1114
44,0776
42.5960
40.2896
38'. 2835
36.2419
33.7098
30.6269
27.0609
22.9653
17,0604
7,3931
1.4969
COR. EFF.
39.0952
08.8017
52.6265
50.7332
56,3950
58.6907
60.6082
62.3985
60.7504
67.5849
70.9563
70.3497
79,8576
88.8003
94.7902
COR. *
3.121
4.158
0.601
0.923
5.156
5.092
5.793
6.076
6.477
6.998
7.680
8.452
9.953
13.599
18.353
COR. P
60'.5048
51.1983
47.3735
45.2668
43.6006
01.3093
39.3516
37.6015
35.2496
32.4151
29.0437
25.6503
20',1424
11,1 997
5.2098
EFFICIENCY - STATED • 99.00
COMPUTFO « 79.0050
CONVERGENCE OBTAINED
ADJUSTED NO-RAP EFF. • 80'.B296
HMD OF INLET SIZF DISTRIBUTION • 3.987E+00
8X6MAP OF INLET SIZE DISTRIBUTION • 2*.165E + 00
LOG-NORMAL GOODNESS OF FIT • 0.985
HMD OF EFFLUFNT UNDER Nfl-RAP CONDITIONS s 2.892E+00
SIGMAP OF EFFLUENT UNDER NQ-RAP CONDITIONS s 1.871E+00
LOG-NORMAL GOODNESS OF FIT • 0.995
PRECIPITATION RATE PARAMETER UNDER NO-PAP CONDITIONS » 10.2*0
SIGMAG"
NTEMP • 1
RMMD • 6.00
RSIGHA > 2.50
CORR'. EFF. •
CORRECTED
o'.ioo WITH o.ioo SNEAKAGE OVER
0.000 STAGES
78'. 1021
OF EFFLUENT • 2.579E+00
CORRECTED SIGMAP OF EFFLUENT » 1,971E*00
LOG-NORMAL GOODNESS OF FIT • 0.991
CORRECTED PRECIPITATION RATE PARAMETER a
9,45
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTIFT MASS LOADINGS
to
10
U>
IDEAL UNADJUSTED
MIG. VEL'. (CM/SEC)
2.393E*00
2,S3>E*00
S.234E*00
3,670E*00
4.101E*00
«,548E*00
7.434E+00
9,502E*00
l.291E*01
1>5TE*01
3.383E»01
IDEAL UNADJUSTED
J.197£*01
3.348E*01
3,542E*01
4.059E*01
4,462E*Ol
5^679E*01
8,790E*01
9,572E»01
NO-BAP
OM/oLOGOfMG/DSC*)
3.H9E-02
2,883E-01
J.602E+00
S,S9*E*00
1.1TSE»01
Z.019E+01
2,81~2E + 01
2,8«6E*01
3.447E*Ol
,
3.89SE*01
3,118E*Ot
2.348E*01
8.0761*00
1.6«7E*00
RAPPING PUFF
1.080E-02
5'.570E-02
8,n31E-02
2,7T8E»81
5.099E-01
7.847E-01
1.083E+00
1.532E+00
2.848E*00
3.64?E*00
4,236E*00
4.185E*00
NO>RAP*RAP PUFF
OM/DLOODCM6/D8CH)
4.240E-02
3.240E-01
1.682E*00
5.341E*00
1.201E*01
2.066E+01
2,««OE*01
2.99«E*01
3.600E*01
4.3268*01
4.180E*01
3.483E*01
2.7TZE*01
1.223E*01
5.872E*00
RAPPING PUFF
DISTRIBUTION(X)
4.J60E-02
1.022E-01
1.784E-01
2.642E-01
7.933E-61
i.is«e*oo
1.424E*08
1.66lE*flO
3.831E*00
4,234E*00
K,79]E*00
1.044E481
1.7096*01
2.nar*ei
2.887E*01
PARTICLE
DIAM.(M)
2.300E-07
3.SOOE.07
4.500E.07
5.500E.07
r.OOOE.OT
9.000E-07
1.100E-06
1.300E-06
1.600E-06
2.000E-0*
2.600E-06
3.500E-06
5.000E-0*
8.000E.06
l.fOOE.05
-------
****•»****»**•*»•*** *****************»****************»********************»*******t********************************
to
ESP PERFORMANCEl
SUMMARY TABLE OF FSP
PARAMETERS AND PFRFOR*»NCE
OAT* SET NUMBER 2
EFFICIENCY « 78.1021 X SC* • 1.610E»OJ M**2/(M*»3/SEC)
ELECTRICAL CONDITIONS!
SIZE OlSTRIBUTlONSi
NONIOEAL PARAMETERS!
AVG. APPLIED VOLTAGE • a.020E*04 V
AVG. CURRENT DENSITY • 10.11 NA/CM**2
RESISTIVITY • l.OOOE+09 OHM. CM
INLET HMD • J.9gTE»00 UM
OUTLET MMD • 2.570f4.QO UM
INLET SIGMAP • 2.I65E+00
OUTLET SIGMAP • 1.971E»00
GAS 3NEAKAGE FRACTION • 0.10 /SECTION GAS VELOCITY SIG^AG • 0.10
RAPPING MMD • 6.000E+00 UM RAPPING SIGMAP • 2.500E*00
*»•»•*»*•*•»••*•***«•*••*••»*«*»*«**•»•»•»•<
STOP 011111
-------
APPENDIX J
OUTPUT DATA FOR EXAMPLE 2 (REVISION 1)
225
-------
*************************************
E.P'.A'. ESP MODEL
I.e,«,L..R'.T'.P, AND SO.R'.l'.
REVISION I.JAN, i. UTS
A************************************
Or INPUT DATA FOR DATA SET NUMBER J
DATA ON CARD NUMBER 1
NENOPT • u NOATA • i
DATA ON CARD NUMBER 2
LAI E8P| SCAcSZrTt/lOOOACFMiCALCULATED V.I FOR EACH ELECTRICAL SECTION
lo
a\
DATA ON CARD NUMBER S
NCIT • t NDIST • 1 NVI • 2 NX • 15 NV • IS NITER • 1 NCALC • 0 NRAPO • t NIFF • t NTENF • 1 NONID • I
DATA ON CARD NUMBER 4
NN • 10 NUMINC • 20
DATA ON CARD NUMBER 5
iriNAL • 20 JI1 • 2 JI2 • 21 VI8KIP • 1 VIIAME • 2
DATA ON CARD NUMBER *
DL • 0.0*500 6»N//kCF PU • 10.0000 FT FTAO • 99.00000 K 00 • 1089,00 K6/M**3 EPS • S'.!OOE«00
VRATIO • l.OJOO US • 0.000165 M.*J/V-8fC PPATH * 1.0000 EBD • 1500000. V/M RHOCG8 • J.OOE*0«
DATA ON CARD NUMBER T
AIMUCKf 1) • 0.00 4?I66Vf 1) • 0.00 AZNUMJf 1) • 4.0
-------
»8NUCK< 2) m 0.10 AZIC6YC 2) • 0.10 AZNUM|( 2) • 4.0
DATA ON CARD NUMBER
CNOPTC |) •
ENOPT( 6) «
O.JOO UM ENDPTC 2) •
0.800 UM ENDPT< 7) •
0.300 UM ENOPTt 3) • O'.«00 UM
I.000 UM END»T( 8) • T.200 UM
4) • O.fOO UM ENO'Tt » • 0.600 UM
9) • 1.400 UM ENO'TdO) • l.BOO UM
DATA ON CARD NUMBER 9
ENOPT(ll) * 2.200 UH ENOPTM2) • 3.000 UM ENDPT(lS) • 4.000 UM ENOPTO4) • 4.000 UM ENDRT(U) • 10.000 UM
ENDRTO6) • 20.000 UM
DATA ON CARD NUMBER 10
MCU( 1) • 0.0000 * PRCU( 2) • 0.0076 S PRCUC 3) • O'.OSAS * »RCU( 4) • 0.2682 * MCU( S) • 0.8*82 «
PRCU( 6) • 2>849 ( PRCUC 7) • 5.»6»5 X RRCU( 8) • 9.5315 * MCU( 9) • 12.8110 I MCUtlO) • 19,7004 *
to
to
OATA ON CARD NUMBER tt
MCU(H) • 2*.8*41 I PRCU(12) • 38.B042 X MCU(IS) • M.2S1* X MCU(14) • 48.1769 I PRCU(ll) • 79.1014 X
MCUC16) • 100.0000 X
OAT* ON CARD NUMBER 12
NUM8EC • 3 LSCCTC 1) • * L8ECT( 2) • 6 LSECT( 3) • 12
DATA ON CARD NUMBER 13
ABC 1) v 6.2500E»00 FT**2 VOSt 1) • a.OBOOE+04 V TC8( 1) • 6.2500E»OS A HLB( 1) • 6.2500E+00 tl
ACB( 1) • *.687SE«02 IN BBC 1) • S.OOOOE+AO IN NH8( 1) • 9.0000E«00
OATA ON CARD NUMBER 1*
BVB( 1) • 2.SOOOE»00 I" V6B( 1) • 3.0533E«02 FT.*J/M1N VCABBt 1) • 4.88I3CtOO FT/BEC TEMPBC 1) • 7'.*000t*0l P
M( 1) • 1,OOOOE*00 ATM V!8B( 1) • l'.8000E«05 KQ/M.BEC LXNCB( 1) • «.1667E>01 FT
-------
DATA ON CARD NUMBER is
•Me n • «.OOOOE«OI STARTK n « *.ooooe*os A/H**2 ITARTZC n • a'.ooooe-os A/N**I
8TART3( 1) • l'.OOOOC"05 A/M**2 VSTAR( 1) • J.8008E»0« V
DATA ON CARD NUMBER t*
Al( 2) • 6.2900E«00 FT**2 V08( 2) • a.oBOOEtOA v TC8( 2) • *'.2SCOE-OS A H18C I) • *.2300EtOO FT
ACI( 2) • «.687SE«02 IN $8( 2) • 5'.OOOOE+00 IN NN8C 2) • S.OOOOE*00
DATA ON CARD NUMBER IT
IVK 2) • 2.3000E+00 IN VG8( 2) • 3.0SJ5E40Z FT«*3/MIN VfiA88( 2) • *.88S»400 rT/iBC TE"M{ 2) • 7*.tOOOI*01 9
H{ 2) • l.OOOOE+OO ATM VI88( 2) • I'.BOOOE-OS K6/M.8EC CINcK 2) • «.U4Tt-01 FT
DATA ON CARD NUMBER IS
to
RFB( 2) • «.OeOOE.01 STARTtt 2) • 6.8000E-05 A/M**2 ITART2( 2) • l'.OOOOE«05
•TARTS( 2) • 2.0000E-05 A/M**2 V8TAR( 2) • 3'.8000E*0« V
DATA ON CARD NUMBER 1*
Al( » • 1.2500E»01 FTi>*2 V0t( S) • J,»*OOE*04 V TC8( J) • 1.2500E-0* A WL8( S) • 1.2500E»01 FT
AC»f S) • «.6B7SE»02 IK B8( S) • 5.0000E»00 IN NH8( S) • 1.0flOOC*01
DATA ON CARD NUMBER 20
8V8C S) • 2.SBOOE400 IN V68( 3) • 1.0933C+02 FT**S/MIN VSAB8( 3) • «.885JE*00 FT/8EC TEMF§( S) • T.fcOOOE*0» F
F8( 3) • !.0000e+00 ATM VI8IC 3) • 1.8000E-05 KC/M.8EC UNc8( 3) • «,U*Tf-01 FT
DATA ON CARD NUMBER 21
RF8( 3) • 9.0000E-01 ITARTU 3) • 6.0000E-05 A/M**2 |TART2( 3) • 2.0000E-05 A/M**2
8TART3C 3) • 2.0000C-05 A/M*«2 V8tAR( 3) • J.8000E»0« V
-------
CUEAN GAS VOLTAGE-CURRKNT OeNSITY.flELO AT THE PLATE RELATION|MJP COR SECTION NO. 1
VM • .J.8000E+04 ACDNTY • *'.OI7»E-05 »FPLT • -1.79026*05
VH • .3.S206E+04 ACDNTV • T.933TE-OS AEPLT • -l.SSVEtOS
VH • -3'.889*E+0« ACDNTV • 9.9193E-OS AEPLT • .I.943SE+OS
VH • -j'.951SE+04 ACONTV • 1.1904E-0« AEPLT • .Z.0232E+05
VH • .4'.0098E+04 ACONTV • J.S890C.04 ABPLT • •2,0993E»OS
VH • •4*.0*S*E*04 ACDNTV • 1.58T4E-04 AEPLT • .Z,17*2E«05
VH • .4*. 1193E*04 ACONTV • 1.78S9E-04 AEPLT • •2.2424E+05
VH • .4.07ME*04 ACONTV • 1.A291E-04 AEPLT • -2.1842E40S
to
ro
INCMMCNTAU ANALVIII Of PRECIPITATOR PERPORMANCC
LAi EIPl |CA«82FTZ/IOOOACPH,CALCULATED V-! FOR EACH ELECTRICAL SECTION
CALCULATION it IN SECTION NO'. • i AMD THE SECTION LENGTH is • o.7*n M
COLLECTION AREA • 5'.8l»E-01 MS
MIRE TO PLATE • I'.ZTOE-OI N
CURRENT/M • 4.9Sse.es AMP/M
t/» HIRE TO HIRC • 6.ssoE»ot N
TEMPERATURE • 297,112 «
ION MOBILITV • 1.T95E-04 M2/VOLT.
DUST HEI6HT • 2.ISOE.05 KO/SEC
sec
APPLIED VOLTAGE • «.080E*0« VOLTS
CORONA HUE RADIUS • l.|9|E-0] N
CURRENT OENSITV • l.*|Se»04 AMR/M2
GAS FLOH RATE • J.444E-01 MS/SEC
PRESSURE • 1.008 ATM
MEAN THERMAL SPEED, • 4.aJ*E+8f X/8IC
LENGTH INCR. "O.tf70843* N
RIOVR
0,82*7
o.rjje
0.711*
0.70*0
0.7027
0.70*7
ERAV6
,0»SE*OS
.08SE»OS
.0858*85
EPLT
,1842E*85
,1S42E*OS
|l8«2E*09
APIB CMCO
13,4
til*
11,4
.lS83C*tl u!$
.1S82E413
,1S>2E*iS
MMO
7.30E-06
*,3*E-Ot
1.90E-C6
l.*2E-06
TOTAL CURRENT • 9.44*E*OI AMPS
CORONA HIRE LENGTH • J.90»E»00 M
DEPOSIT E PIELO • r.M*t«os VOLT/M
OAS VELOCITY • i.«»01*00 M/SEC
VISCOSITY • r.se«E-oi KOSM.SEC
PART. PATH^ARAM.JB S'.700E«08 M
INPUT EPS/INCH, • IT.4*
HEIGHT DUST LAYER J(PART)
.228C-0* 5.570E-04
,*04F»0* B.859E-0*
.02*E«A5 9,J»OE-84
'.832E-0* 8.794E-0*
,138C'06 8.174E-0*
,3*1E*0* 7.479E-0*
9.22r.08
i,t'*e-o7
i.zee.07
1.S3E.07
1.341.07
J(ION) INCR. NO,
,*2E«04
.411-04
.*2E-OC
.42E-04
.62E.O*
t
2
3
4
5
*
-------
U>
O
CLEAN GAS VOLTAGE-CURRENT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO. I
VH • -3.SOOOE+04 ACONTY • 6.0276E-09 AEPLT • -1,7902E*09
VM • -3.8206E+04 ACDNTY • T.9337E-05 AEPLT • -1.85m«09
VM • -3.68«*E*04 ACDNTV • 9.919JE-09 AEPLT • -1,9439E*09
VM • -S.9913E404 ACDNTV • l'.l«0«E-0« AEPLT • -2,0232E»09
VH • .4.0098E+04 ACDNTV • 1.I890E-04 AEPLT • -2.0993E+09
VH • .4.0*5*E*04 ACDNTV • l'.S»7«E-04 AEPLT • -2.1722EtOl
VM • -4.1193E+04 ACDNTV • 1.78S9E-04 AEPLT * -2.2424E+09
VH • -«.0711E+04 ACDNTV m 1.*2S1E-04 AEPLT • -2.1842E*OS
CALCULATION IS IN SECTION NO'. • 2 AND THE SECTION LENGTH IS • 0.7*25 M
COLLECTION AREA • 9'.812E-01 M2
WIRE TO PLATE • I'.ZTOE-OI N
CUHRENT/M • 4.9SSE-OS AMP/H
1/t NIKE TO MIRE • 6.350E-02 M
TEMPERATURE • 297.222 K
ION MOBILITY • 1.795E-04 MJ/VO
DUST HEIGHT • 2.150E-05 KG/SEC
APPLIED VOLTAGE • 4.080E«04 VOLTS
CORONA HIRE RADIUS • 1.191E-03 M
CURRENT DENSITY • 1.629E-04 AMP/M*
GAS PLOW RATE • 1.444E-01 MS/SEC
PRESSURE • 1.000 ATM
•SEC MEAN THERMAL SPEED • 4.43AE+02 M/SEC
LENGTH INCH. BO*. 127084)9 M
TOTAL CURRENT • «.««tt>OI AMPS
CORONA HIRE LEN8TH • 1,90»E»00 M
DEPOSIT E FIELD • l'.b2tl40S VOLT/M
6AS VELOCITY • l.«f01*06 M/SEC
VISCOSITY • I'.SOOE-OS KB/M.SEC
PART. PATH PARAM*. • ,S'.?OOE»OS M
INPUT EFF./INCR, • 17.4*
RIOVR
0.7089
0.7134
0.71*0
0.7290
0.711J
0.7377
ERAVO
2.085E+05
2.0S9E+09
l'.0«5E+05
2.om»09
2»OB5E+09
2.085E+09
EPLT
2.1842E+05
2.1S42E+05
2.1S42E+09
2.1842E+05
2.1S42E+05
2.t842EtOS
AFID
2.15«3E«13
2. 1583E»13
2.1S83E413
2.1583E+13
2.1S83E*13
2.1S83E+13
CHCD
H.9
n't
11,8
1 1.*
12.0
HMD
1,44E-06
1.32E-0*
1.18E-0*
1.07E-06
9.89E-OT
9.29E-07
HEIGHT
7.585E-0*
*,849E-0*
*.i7or-o*
5.55M-0*
5.004E-04
4.517E-0*
DUST LAYER
*,784E-04
*.12*E-04
s.9i*e-o4
4.970E-04
4.478E-04
4.040F-04
J(PAR7)
.32E-OT
.29E-07
.29E-07
.21E-OT
.16E-07
.12E-07
J(ION-)
1,*2I-0«
1,*2E-04
1.62E-04
l.»2E«0«
lr*IE-04
ll*2E-Oi)
INCR.
7
S
f
10
It
12
CLEAN GAS VOLTAGE-CURRENT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO. 9
VH • .3.0000E+04 ACDNTV • A.0277E-OS AEPLT • •1.7908E+OS
VH • •J.8205E+01 ACDNTV • 7'.«IS>E*OS AEPLT • •l.lf«*Et09
-------
VH • -J.9Sm*04 ACOMTY • 1.U04E-0* «PLT • *2.0232E*05
VH • -4.0098E*0* ACDNTY • 1.3B89E-04 AEPLT • -2,0993E*05
VH • .)*.9S14E*04 ACDNTV • 1.3081E-04 AEPLT • «2,0279E*05
CALCULATION 18 IN SECTION NO'. • 3 AND THE SECTION LENGTH IS • 1.92*0 M
COLLECTION AREA • l'.l*2E*00 M?
HIRE ro PLATE • t'.270E-oi M
CURRENT/H • }.t84E-OS AMP/M
1/2 MIRE TO HIHC • 4.JSOE-02 H
TEMPERATURE • 297.222 K
ION MOBILITY • i.T95E-oa MZ/VOLT-SEC
DUST WEIGHT • 2.1508-05 KS/SEC
APPLIED VOLTAGE • J.960C*Oa VOLTS
CORONA WIRE RADIUS • f.l91E-OI M
CURRENT DENSITY • 1.208E-04 AMP/M2
6*8 PLOW RATE • 1.444E-01 H3/8EC
PRESSURE • t.OOO ATM
MEAN THERMAL SPEED • 4.43*E»02 M/IEC
LENGTH INCR. •0.12708435 M
TOTAL CURRENT • l.flOflE-flfl AMPS
CORONA MIRE LEM6TH • J,81«*08 M
DEPOSIT E FIELD • r.20BE*03 VOLT/N
c*s VELOCITY • i.«9oE*oo M/SEC
VISCOSITY • r.spoE-os KB/M.SEC
PART. PATH PARAM. • S'.TOOE-OB M
INPUT erp./iNCR, • tr,fl6
Co
H
RIOVR
0,*«47
0,7020
0,70*4
0.71*7
0.7140
0.7S12
0.7382
0.7451
0,7520
0.79S7
0,7*52
0.771*
ERAVO
2.001E+05
2.001E+OS
2.001E*05
2.001Ef05
2.001E*09
I.001E»05
2.001E+OS
2.001E*05
2.
-------
CHARGING RATES FOR PARTICLE SIZES FROM SUBROUTINE CHARGN OR CHCSUM
s»i THEORY USED FOR PARTICLE CHARGING
INCREMENT NO.
0/OSATF FOR INDICATED PARTICLE SIZES
to
Co
NJ
0.2SOOE-06
1 '.8603
2 .1302
S .4762
« .5763
S ,6522
6 ,7130
T ,7645
S .6083
9 .8467
10 .880*
it ,9116
12 ,9395
13 ,9579
14 ,9752
15 ,9916
Ik ,0072
IT ,0219
IS 2,0360
19 2.0*95
20 2,0624
21 2,0747
22 2.0666
23 2,0980
24 2.1089
o.uooe-os
i 0.7479
2 0.9532
3 1,0611
« 1,1232
5 1.1653
6 1.1967
7 1.2217
6 1.2423
9 1.2598
10 .2750
11 .2085
12 ,3004
13 .3070
14 .3132
15 ,3132
16 ,3132
17 .3132
10 .3132
1* 1,3132
20 1,3132
H J.3I32
0.3500E-06
1.0325
1,2853
1.4174
1.5066
1,5738
1,6276
1,6723
lj7107
1,7441
1,7738
1,8005
1,8248
1,8403
1.8550
1,8689
1,8821
1,8946
1,9066
1,9160
1,9289
1.9394
1,9495
1,9592
1.9592
0.2000F.-05
0,7141
0,9108
1,01«2
1,0811
1.1241
1.1553
1,1795
1.1992
1,2158
1,2300
1.2425
1.2536
1,2594
1,2594
1,2594
1.2594
1.2594
1,2594
1,2594
1,2594
1.2594
0.4500E-06
0.9918
1,2346
1,3567
1.0380
T.4987
1.5470
1.5871
1,6214
1,6512
1,6776
1,7013
1,7228
1,7364
1,7492
1,7612
1,7727
1,7836
1,7940
1.8040
1,8135
1,8226
1,8314
1,8314
1.8314
0.2600E-05
0,6800 .
0.8690
0,9651
1,0352
1,0814
1,1133
1,1373
1,1564
1,1721
1.18SS
1.1971
1.2073
1.2123
1,2123
1.2123
1,2123
1.2123
1.2123
1,2123
1,2123
1.2123
0.5SOOE-06
0.9523
1.1900
1,3049
1.3803
1.4362
1,4805
1.5172
1,5484
1,5755
1,5995
1,6210
1,6405
1.6526
1,6639
1,6747
1,6849
1.6946
1.7039
1,7128
1.7213
1,7213
1,T213
1,7213
1.7213
O.S500E-OS
0,6459
0,8260
0.9159
0,9818
1,0335
1,0694
1,0949
1.1143
1.1298
1.1427
1,1537
1.1632
1.1676
1,1676
1.1676
1,1676
.1676
.1676
.1676
.1676
.167*
0.7000E«06
0,9013
1.1363
1.2438
1.3130
1*3638
1.4038
1.4366
1.4647
1.4889
1.5103
1.5294
1,5467
1,5571
1.5670
1,5763
1.5652
1.5937
1.6017
1.6094
1.6094
1,6094
1.6094
1.6094
1.6094
O.SOOOE-05
0.6124
0.7808
0.6656
0.9242
0,9730
1.0141
1.0461
1,0666
1.0855
1.0968
1.1098
1.1191
1.1230
1.1?30
1.1230
1.1230
1.1230
1.1230
1,1230
1.1230
1.1210
0.9000E-06
0,6506
1,0790
1,1615
1,2472
1,2940
1,3301
1*3602
1,3653
1,4070
1,4261
1,4431
1,4384
1,4675
1,4760
1,4641
1,4916
1,4990
1,4990
1,4990
1,4990
1,4990
1,4990
1,4990
1.4990
0.8000E-OS
0,5762
0,7332
0.8132
0,6676
0,9086
0,9440
0,9766
1,0046
1,1260
1.0461
1,0596
1,8702
1.0740
1.0740
1,0740
1,0740
1,0740
1.0740
1,0740
1,0740
1.0740
e.nooe-05 o.i
0.6118 0
1.0324 fl
1.1364 1
1.1991 1
1.2436 1
1.2779 1
1,3057 1
1.3190
1.3491
1,3*66
1.3622
1.3963
1.4043
1.4120
1*4192
1.4260
.4260
.4260
,4260
.4260
.4X60
.4260
.4260
1.4260 I
0.1SOO|»04
0.5399
0.6»25
0.7556
0,6062
0.6449
0,8749
0.8999
0.9224
0,9434
0.9633
0,9622
0.9963
1,0064
1.0130
1.0185
1.0233
1.0233
1.0233
1.0233
1.0233
1.02SS
300E-05
.7611
.9919
,1015
.1633
.2064
.2392
.2656
.2676
.3064
.3229
.3374
.3505
,3576
.3647
,3713
.3713
,3713
.3713
.3713
,3713
.3713
.3713
.3713
1,3713
-------
21 1.3132 !,««• 1,2123 1,U74 1.1130 1.07«0 1.8135
21 1.3132 '..?$«• 1.Z12S 1.U7* 1.1110 l,8T«0 1.0231
2* 1.3132 !,2?M 1.2123 1.1*7* 1.1230 1.07«0 1.0233
N)
-------
CHARGE ACCUMULATED ON PARTICLE SIZES IN EACH INCREMENT
INCREMENT CHARGE FOR INDICATED PARTICLE SIZES
to
Co
i
1
s
4
9
4
7
8
»
to
tl
1C
IS
14
IS
1*
17
IS
19
10
21
21
13
24
1
2
3
t
S
*
T
8
9
to
11
12
13
10
15
1*
IT
1*
1«
20
21
22
23
21
0'.2500E*06
0,t»ll3E«l7
0.22722E-17
0.2S21BE-17
0,Z6927E-1T
0.28224E-17
0.2926BE-17
0.30141E-17
0.30891E-17
0.315476-17
0.321306*17
0.326556*17
0.33132E-17
O.S3446E-IT
0.337426-17
0,340226*17
0. 342886-17
0.345406-17
0.347816*17
0.350106*17
0.352306-17
0.354416-17
O.S5644E-17
0.358386*17
0.3*02*6*17
0*.1600E*05
0.39980E-16
0.50958E-16
0.5*7276-16
0.*0047E*16
0.62294E.16
0.63975E«16
0.65310E*16
0,660131-16
0.67350E-16
0.68163E-16
0,6B8HOE-16
0.69521E.16
0.69871E.1*
0.7Q201E>16
C.70201E-16
0.70201E-16
0.70201E-16
0.70201E-16
0.70201C-16
0.7020IE-J6
0.70201E-1*
0.70201E-J*
0.70291E-1*
0.7fl281f«l»
0.3500E-06
0.31194E.17
0.38632E-17
0.a2S24E«17
0,«551«E.17
0.47548E-17
0,«9l73e.l7
0.50525E-17
0.91683E-17
0.52695E-17
0.53593E-17
0.54399E-17
0. 551316-17
0.55601E-17
0.560U5E-17
0.56«65E-17
0.96863E-17
0,57242E-17
0.57603E-17
0.57948E-17
0.58278E.17
0.58994E-17
0.58899E-17
0,5919tE.17
0.59191E.17
0'.2000E-OS
0.5922BE-16
0.75536E-16
O.B4119E-16
0.89667E-16
0.93232E-16
8.95816E.16
0.97826E-16
0.99461E-1*
0.1008«E-15
0.10202E-1S
0.1030SE-19
0.10397E-15
0.10443E-15
0.1044SE-15
O.lOaOSE-if
0.1044SE-15
0.1000SE-15
0.10fl«5E-15
0,1044Se-lS
0.10445E-1*
0.10445E-1!
0.10««5E.15
e,10045E-19
0.10445C-15
0.4SOOE-06
0.0696JE-17
0.58463E-17
0.60245E-17
D.6809ZE-17
0.70966E-17
0.73295E-17
0.7515aE-17
0.76776E-17
0,78189F-17
0.79000E-17
Q.80S63E-17
0.81S81E-17
0.8?222E-17
O.B2B27E-17
0.83399E-17
0.83903E-17
0.8a«60E-17
0.8fl9S2E-17
O.BS423E*17
0,65874E-17
0.86306E-17
O.B6722E-17
0.86722E-17
0.86722E-17
0.2600E-03
0.9471ZE-16
0.12104E-1S
O.I3443E-15
0.1««I8E-H
0.15063E-1S
0.1S507E-15
O.HB41E-15
0.16107E-15
O.U326E-19
0.16S12E-15
0.16673E-1S
0.16815E-H
0.16886E>1§
0.16886E-15
O.U886E-H
0.1<>886E.15
0.16A86E-15
O.I686*e-l?
0,16»86E»U
0.16AB6E-15
O.U886r-15
8.16886E-H
O.U886E-H
O.U886E-J?
0.5500E-06
0.65249E-17
0.81534E-17
O.B9407E-17
0.9a575E-17
0.98407E-17
0,10iaOE-16
0.10395E-16
0.10609E-16
0.1079SE-16
0.10960E-16
0.11107E-16
0.11248E-16
0.11323E-1*
0.11401E-16
0.1147SE-U
0.11545E-16
O.I16UE-16
0.11675E-U
0.1173AE-16
0, U79flE.lt
0.11790E-16
0.11794E-16
O.I1794E-U
0.11794E-16
0.3500E-05
0,1621«E-15
0.20741E-15
O.I2998E-15
0,2«65aE-15
0.25950E-15
0.2685flE-15
8,2709?!'. 15
0.27979E-15
0.28369E-15
8.28693E-15
O.Z8968E-15
0.29208E-1S
0.29319E-15
fl.29319E.J5
0.29319E-15
8.29S19E-15
0.29319E-15
0.29319E-15
0.29319E-15
0.29319E-15
0.29319E-15
0(2«II«E*1S
0.29119E-15
0,2«3t«E-lS
8.7000E-06
0;97t89E-l7
0,1?252E"16
o;i3«HE.16
0.141S8E-16
0,1070kE-16
0.15137E-16
0.15492E*16
o'l5791E-16
0,160SSE-16
0,1628«-1*
0,1649JE-16
0.16678E-16
0.16790E-16
0.16B9TE-16
0,169976.16
0.17093E-16
o'l7184E-16
0.17271E-16
0.17354E-16
0,17354E»16
0.17354C-16
0.17354E.16
0,17354E>16
0.17354E-16
0.5000E-OS
0.3124SE-19
0.39842E-1S
0.aOt6flE.l5
0.07158E-15
0.096«6E-1?
0,517«6E-15
0'53S79E-H
O.S4S24E-15
0,55SB5E-l!
0.96067E-15
0.96629E-15
0.97103E*1S
0.5730SE-15
0.57303E-15
0.57303E-15
0.57303E-15
0.57303E-1S
0.5730JE-U
0.57303E-15
0.57303E.15
0,57303E«J5
0,57J03I«JS
0.57S03E«15
O.f7303fll
0'.9080E-06
fl.ia633E-l*
fl,188l5E«16
0.20620E"!*
0.21749E-16
0.22560E-16
8.23199E-16
0.2371Se*U
0.20156E-16
0.24S35E-16
0.20867E-16
0.25164E-16
«.25431E*16
0.25589E.t6
R.2573BE-14
0.25879E-16
8.26812E»16
0.26148E-16
8,261«OE«16
0.26140E-1*
0,26laOE-i*
0.26U8E-16
0.26140E-16
n,26l«OE-16
O.J41«OE«16
o'.eoooE-os
0.74992E-1S
B.95430E-1S
0.109B4E-14
0,112»5C-14
9.11828E-1*
O.J2286E-10
0.12710E-10
0.13078E-14
9.13379E-10
A.1361SE*I4
8.13790E-14
0.13929E-14
0.1397BE-14
0.1397BE-14
0.13978E-14
0.>397BE«14
0.13978E«1«
0.13978E-IO
0,1J»78E-1«
0.1397BE-14
0.13978E-H
0,13978C«1«
O.I)t7flC*l«
0.1397«f.|4
0.1100E-05
0.20870E«U «
0.26541E-U
0.292UE-16
0.30828E-16
0.31972E-16
0.32BS3E-16
0.33548E-16
0.30167E-16
Q.S4»I3C-U
0.35134E-16
0.35535E-16
8.39B96E-16
0.36103E-16
0.362991*16
0.364B4E-16
0.36660E-16
0.36668E-16
8.3666nE»16
0.36660E-16
0.36660E-16
8.36668E-16
0.366606*1*
0.36660E-16
0.36669E.J6
0'. 1SOOE.04
0.246366*14
0.31143E-14
0.344891*14
0.367B9E-I4
0.38553E-14
0.399206*14
0.41060E-10
0,420916-14
0.4S048E*i
-------
(•ARTICLE SIZE MANGE STATISTICS
CORRECTIONS ro» MOMIDEALITIES USINO SET NO*, i or CORRECTION PARAMETERS
SIZE I
.500E-07
.500E-07
.500E-07
,500E-07
.OOOE-07
, OOOE-07
,100E-06
, SOOE-06
,600E-06
, OOOE-06
.600E-06
,500E-06
.OOOE-06
.OOOE-06
.IOOE-05
:CF INLFT X
,589 0,008
,4|4
.320
.261
.205
.159
.130
.110
.090
.072
.055
.041
.029
.018
.010
0,049
0,212
0,597
2.119
2,985
3,582
3.283
6,865
7,164
11,940
10,447
14,925
14,925
20.899
OUTLET « COR. OUTLET X
O',0210 0,0244
(
c
1
J
7
7
6
1 j
12
16
12
1 1
0
,1359
,5826
,5937
.4026
10896
.9404
'.7915
,9352
,0059
.9421
'.0625
19052
,0698
.5220
0,1308
0,5215
1,3«28
4.7063
6,1893
6,9556
6,0162
11,5594
10,8313
15.7103
11,8169
12.6892
6,6496
4.8066
NO-RAP EFF.
59,6767
59,4811
60.0682
61.2279
62,9750
65,5043
67,8036
69.9588
72.6349
75,6592
79,3911
83,2307
88,4146
96,0395
99.6172
NO-PAP M
5,67)
5,612
5,702
5>85
4,172
6.6U
7,040
7,470
8,050
8,777
9,811
11,092
13,389
20,056
34.904
NO-RAP P
40,1233
40,5189
39,9318
38.7721
37,0250
34,4957
32,1964
30,0412
27,3651
24.3408
20,6069
16,7693
11,5854
3,9605
0.3628
COR. EFF.
45.0424
54.0537
57.8917
60,0837
62.0046
64.5J33
66.7758
68.6506
71.1920
74.1)11
77.4871
80.6474
85,4531
92.3770
96,0648
COR, H
3,718
4.831
5.373
5.705
6.011
6.437
6,845
7.205
7,731
8.399
9.142
10.201
11.975
15.989
20.096
COR. P
54,9576
45.9463
41,1083
39,9163
17,9954
35.6767
33,2241
31,3494
28.8080
25,8689
22.5129
19,)526
14,5469
7.6230
3.9312
EFFICIENCY • STATED • 99'.00
COMPUTED • 79,9829
CONVEROCNCC OBTAINED
to
OJ
U1
ADJUSTED NO.RAP EFF, • 85'.4759
HMD OF INLET SIZE DISTRIBUTION • J.9«7E+00
SIBMAP OF INLET SIZE DISTRIBUTION • 2'.145E+00
L06-MORHAL GOODNESS OF FIT • 0.985
MHO OF EFFLUENT UNDER NO-RAP CONDITIONS • 2.063E»00
IISNAR OF EFFLUENT UNDER NO-RAP CONDITIONS • 1.804E+00
LOO.NORMAL OOOONESS OF FIT • 0.995
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS • n.9s5
SISMAO* O'.OOO MJTH 0,000 SNEAK46E OVER
NTEMP • 1
RMND • 6.00
RSIOMA • 2.50
CORR. EFF. • 82.8902
CORRECTED NMD OF EFFLUENT • 2.«S1E»00
CORRECTED 8I6MAP OF EFFLUENT • 1.969E«00
LOO-NORMAL aOODNESS OF FtT • 0.990
CORRECTED PRECIPITATION RATE PARAMETER • 10.97
4.000 STAGES
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS LOADINGS
to
U)
IDEAL UNADJUSTED
2.««OC*00
Z.58*E+00
2>95E+Ofl
S.J36E+08
J.800E*00
4.7«6E+00
7,8366+00
*,««8E«00
i,ss«*oi
2.006E+01
IDEAL UNADJUSTED
EFFICIENCY**)
J.2«8E*01
I,610E>01
J.826E»01
4.576E+01
5.3U2E*OJ
7. 1666*01
'.604E+01
DH/DLOGD(MG/D8CM)
2,5<>aE-01
l.ttlBE+00
1.0?nE+01
l,785E*ei
2.365E401
J.2(i
-------
SUMMARY TABLE OP ESP OPERATING
PARAMETER! AND
E8P PERFORMANCE I
DATA SET NUMBER 1
EFFICIENCY • sz.8902 « ac* •
M**Z/(M**S/SEC)
ELECTRICAL CONDITIONS!
SIZE DISTRIBUTIONSI
NONIOEAL PARAMETER8I
AV6. APPLIED VOLTAGE • «.011EtOa V
AVS. CURRENT DENSITY • 10,34 NA/CM**2
RESISTIVITY • l.OOOE+09 OHM.CM
INLET HMD • J.987t*00 UM INLET SI6MAP • 2'.1*5E»00
OUTLET MHO • I.aSlEfOO UM OUTLET 8IOMAP • l>k«E+00
GAS SNCAKAGE FRACTION • 0.00 /SECTION GAS VELOCITY SIGMAO • 0.00
RAPPING HMD • k.OOOEtOO UM RAPPING SISMAP • J.500E»00
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NONIDEALIT1ES USING SET NO, 2 OF CORRECTION
SIZE
2.500E-OT
3'.500E-07
«, soot. or
5,500E-07
7.000E-07
9,OOOE«07
1.100E-06
l,300E-06
J,600E-06
2,OOOE-06
l,»OOE«06
3.500E-06
S.OOOE-06
8,OOOE-06
1.500E-05
:CF
.589
.4J4
.320
.261
.20;
,150
.130
.110
.090
.072
,055
.041
.029
.018
.010
INLET x
olooe
0,049
0,212
0,597
2,119
2,985
3.582
3,283
6.865
7,16«
il,9ao
10,447
18,925
18,925
20.899
OUTLET X C(
0^0186
0.1202
0,5166
1,4190
«.6S21
6*. a 184
7.2618
6,2760
12.1309
ll.«797
16,6809
12,3687
13,1920
5.7287
l'.546t
)R. OUTLET X
0,0218
0,1179
0,0732
1,2708
«,3230
5,7flOfl
6.5130
5,6«
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS
to
CO
ID
IDEAL UNADJUSTED
HIS. VEL.(CM/SEC)
2',,«aOE + 00
I,782E*80
2.995E+00
3.336E+00
3.800E+00
«,272E+00
8,7fl6E+00
s.a6i!*co
*.«07E+00
T*w5W*TvO
9.9fl8E»08
i uor*ni
2.806E+01
3.«90E*01
IDEAL UNADJUSTED
EFPICIENCYCX)
NQ.RAP
J.610E*01
«,576Ef01
6.155E+01
T.l«>8E»Ql
7.9886*01
3.111E-02
2.«3bE>01
t,57lE*80
5.277E*01
J.88JE+C1
S,65tE*01
2.209Et01
7.613E+80
!.9t«EtOO
PUPF
OH/OLOGOCMO/DSCM)
r,07«E«62
3,S«9E-OI
7,r- -
PUFf
DH/DLOODCM8/D8CM)
fl.185E.82
2.7ME«01
5,069E-01
7.801E-81
1.876E*88
1.523E*00
2.107E+00
2.831E*00
3.624E+80
«.211C+00
0.11flE»80
1.6S1C+00
5.fl28t»00
1.1TOE*81
2.08JE»01
2.87IE+6I
3.a2«E*91
S.«3flE+ei
3,28lE*8l
2.630£*01
D!IT*!IUT!ON(«)
«.lbOE-OZ
1, 02|l«01
i,78aE»ei
2,6ait.ei
7,«93E«81
i.ujE+eo
S,831E*60
8,7911+00
i.eioE+ot
U709E+81
5.675E*80
OIAM.JN)
1,1001*07
>.i«OI*OT
«,|00t»07
1.9001*07
7(OOOC*07
9.080E-07
i.tOOE*0*
1.1881.8*1
1.608E.O*
2.888E-0*
2,»00l«0e
1,1001*06
5.000E.66
8,0001.0*
|,fOOC*05
-------
to
£t
O
SUMMARY TABLE OF ESP OPERATING
PARAMETERS AND PERFORMANCE
DATA 8ET NUMBER Z
ESP PERFORMANCEl EFFICIENCY • 79.1710 * 8C» • 1,610E»01 M*«Z/tM«»l/8EC)
ELECTRICAL CONPITIONSI »VG, APPLIED VOLTAGE • A.OUEfOa V
AV5, CURRENT DENSITY « 10,J« NA/CM«*I
RESISTIVITY • 1.000E*0« OHM.CM
SIZE DISTRIBUTIONSI
NONIOEAL PARAMfTERSl
INLET HMD • 3.987E+00 UM INLET II6MAP • 2'.|t5C*00
OUTLET HMD • 2,573E»00 UM OUTLET 8IGMAP • l,«76E+eO
GAI SNEAKAGE FRACTION • 0.10 /SECTION OAS VELOCITY II8MAO • 0,10
RAPPING MHO • 6.000E + 00 UM RAPPING SI6MAP • t.SOOEOO
STOP Otilll
-------
APPENDIX K
OUTPUT DATA FOR EXAMPLE 3 (REVISION 2)
241
-------
************ *»•#***«•***#•***#*#*****
E.P.A1. ESP MODFL
T.F.».L.-R.T.P. ANO SO.B.I.
RrvlSION II, AUG., 1«T9
*****•**»**»•*»•******•***»****•»*•*
PRINTOUT OF INPUT OAT* FOB DATA SFT NUMBER 1
DATA ON CAHO NUMBER 1
NENDPT • 16 NOATA • 1
DATA ON CARD NUMBER 2
LAB ESPi SCA«82FTJ/1000ACFH|CALCULATED V.I FOR EACH ELECTRICAL SECTION
^ DATA ON CARD NUMBER 3
to
NE8T • 2 NDIST • 1 NVI • « NX • IS NY « 15 NITER * 1 NCALC • A NRAPD • 1 MEFF « | NTEMP • t NONID • I
DATA ON CARD NUMBER «
NN • 5 NUMJNC • S
DATA ON CARD NUMBER s
IPINAL • 20 JIl • 2 JI2 » 21 VISKIP • 1 VISAME « 2
DATA ON CARD NUMBER 6
Dt « O'.OHOO BRN/ACF »L * 10.0000 FT FTAO • ««. 00000 X DO > 10(10.00 KS/M«*J EPS • 5.100F + 00
VRATIO • 1.8100 U8 « 0.000165 H«*J/v»JFC FP4TH • l.eo«0 F80 * 1500000, V/M BHOC63 • 1,««F»09 OWM.C^
DATA ON CARD NUMBER f
ASNUC»
-------
ASNUCM ?) • 0.10 AZTOGY( ?) i 0,1° »ZNUt-S( 2) • a.O
DAT* ON CARD *'UHBER 8
ENDPT( I) •
ENDPTt 6) •
0.160 U*
o.eoo UH
2) i
ENDPTC T) «
o.^oo 'in F.NDPTC jj •
1.000 U* ENPPTC 8) •
o.aeo U* ENDPT( «) •
1.200 UM ENDPTt 9) i
O.SOO UH ENDPTt 5) « 0,600 U«
l.UOO UH ENOPTflfl) • 1,«06 UH
to
ilk.
u>
DATA ON c*»o NUMBER 9
ENOPTtllJ • 2.200 UM ENOPTtiaj • 3,000 "* fwOPTflS) • fl.OOO UM
ENOPTJ16) • 20,00« UM
D*TA ON CARD NUMBER 10
6,000 UH fNOPTflS) • 10,900
0.0561 X PMCUC «)
9.5515 X P»CUt <»
P*CU( 1) • 0.0000 I PRCUC 2) • 0.0076 X PRCU( 1) •
MCUC 6) • 2.«8«5 * PRCUC 7) « ?.9695 * PRCU( 8) •
DATA ON CARD NUMBER 11
PRCU(ll) • 2».«6«J X PRCUC12) » 11.8042 X PRCU(IJ) • «9'.2516 X PRCU(1«) • 6«.1T65 » PRCU(IS)
PRCU(I6) • 100.0000 X
0.2682 X PRCUC 5) • 0,8652 X
12.8S50 X PRCU(IO) • 19,700(1 X
70.JOJU X
ON CARD NUMHe* 12
NUHSEC • 3 LSECT( 1) « 6 L8FCT( 2) * 6 LSECTC I) • 12
DAT* ON CARD NUMBER 13
A8( 1) • 6.2500E»00 FT««2 VOSf 1) • «.OflftOP*8« V TCS( 1) • 6.2500E-05 A
ACS( 1) • 4.68TSF.02 IN BS( 1) * 5.0000E«00 IN MMS( 1) * S.0000f»00
DATA ON CARD NUHBFR i«
SYSf 1) • 2.5000E»00 I" ^CSt 1) • T.05Jjr»02 FT..J/MIN V5AS8( 1) •
U « A.?SOOr«00
FT/gfC TFMP8( 1) • 7.6000E»0!
P8( I) « 1.0000f»flO ATM VtSSC 1) » l.*tnflE-05 KG/M-SEC
I) s «,1667E-01 FT
-------
DATA ON CARD NUMBER IS
RFSC 1) • '.OOOOE-01 STARTH 1) = 6.0000F.05 A/M*»2 ST*RT2{ 1) • 2.0000E-05 A/M**2
8TART3C l) • Z'.OOOOC-OS A/M**2 VSTARC 1) • S'.8000E*0« V
DATA ON CARD NUMBER 16
A$( 2) • »'.2500E+00 FT**2 V08( 2) • a.0800E*Oa V TC8( 2) • fc.2500t«05 A ML8( 2) • 6.2500E»00 FT
AC»t 2) • «.*8T5E.02 IN BS( 2) a 5.0000E»00 IN NWSC 2) • 5.0000E+00
DATA ON CARD NUMBER 17
8VSC 2) • 2.5000E*00 IN V68( 2) • 3.0S33E»02 FT**S/HIN VQASSC 2) • O.B89SE+00 FT/SEC TEMP9C 2) • T.fcOOOEOl F
R«( «) • t.OOOCE»08 ATM VI33C 2) » I'.BftOOE-OS KS/M.SEC LINC8( 2) • S.U67E-01 FT
DATA ON CARD NUMBER 18
M
RF8( 2) • «.OOOOE.81 8T4RTK 2) • 6.0000E-05 A/M**; 8TART2( 2) « 2.0000E-05 A/M**2
ITARTJ{ I) • 2'.oeOBf-05 A/M**2 VSTAR( 2) • 3.8000E*OB V
DATA ON CARD NUMBER 1*
A8( J) • 1.2300E+01 FT**2 V08( 3) • S.96DOE+04 V TC9( 55 * 1.2500f-0« A NLS( 3) • 1.2500E+01 FT
ACBt S) • «.fr675E.02 IN BBC 31 • 5.0000E»00 IN M"SC 3) • I'.OOOOE^Oi
DATA ON CARD NUMBER 20
8YBC S) • 2.SOOOE+00 IN V6S( 3) • 3.09S3E*02 FT..3/MJN VCASS( 3) > a.88S3E+OS FT/SEC TfM»S( J) . T.6000E+01 F
FBC 1) • l.flOOOE+00 ATM VI88C 3) • 1.8000E-05 K6/M.8EC LINC8( 3) • U.UbTE-01 FT
DATA ON CARD NUMBER 21
RF8( 3) s 4.0000E.O! 8TARTK 3) s t.OOOOF-OS */M.»? START2r 3) • 2.0000E-OS A/M..?
8TART3C 3J « 2'.OOOOE-05 A/M«*2 vsTAHf 3) s 3.8000E*0« V
-------
CLEAN SAS VOLTAGE-CURRFNT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO. i
VH • -S'.T698E»006
8.928E-06
8.655E-0*
8.152E-0*
T.566E-06
7.702E-0*
7.292E«Oa
6.768E>na
3.27E-06
6.77E-08
8.17E-08
9.*60F.08
9.77E-08
t.65f-fl«
1.65f«0a
1,65F»0«
1.65E«04
1.65E.6U
1.65E-OU
-------
CLEAN GAS VOLTAGE»CURRENT DENSITY-FIELD AT THE PLATE RELATIONSHIP FOR SECTION NO. 2
VH • .3.769BE*0« ACDNTY • 6.0C08E-05 AEPLT • -1.777JE+05
VH • .3'.8S4TE*0« ACDNTY • I.OOOOE-1S AEPLT • -1.8fci7E+05
VH • .j'.8965E*0« ACDNTV • f.OOOOE'04 AEPLT • .1.9«k9E»OS
VH • -3'.9«7E*0* ACDNTV • l'.2«0»E-0« AEPLT • -2.0248E+05
VH • .«'.0125E+04 ACDNTY • 1.4000E-04 AEPLT • .2.0988E«OS
VH • .«'.0»TSE»0« ACONTY • l'.»OOOE-0« AEPLT • -2.1»97E»OS
VH • .4.120«E»04 ACDNTV • l.SOOOE'04 AEPLT • •2.2I76E*OS
VH • .«'.OS02E*04 ACDNTV • 1.6478E-04 AEPLT • .2.1861E+8S
CALCULATION is IN SECTION NO'. • 2 AND THE SECTION LENGTH is « o.Ttts M
COLLECTION AREA • 5.812E-01 M2 APPLIED VOLTAGE • 4.080E*04 VOLTS TOTAL CURRENT • 9.578E-05 AMPS
HIRE TO PLATE • i'.270E-oi M CORONA HIRE RADIUS • i.i«iE-o3 M CORONA WIRE LENGTH • I.»O&E«OO M
CURRENT/M • i'.02*E.»5 AMP/M CURRENT DENSITY • 1.648E-04 AMP/M2 DEPOSIT E FIELD • l.»48E»03 VOLT/M
1/2 HIRE TO HIRE « t.ssoE-oz M GAS FLO* RATE • t.«4«E>oi MS/SEC GAS VELOCITY • I.«*OE»OO M/SEC
TEMPERATURE • 297.122 K PRESSURE • 1.000 ATM VISCOSITY • l'.800E«OS KG/M.SEC
ION MOBILITY • 1.793e>*« M2/VOLT.SEC MEAN THERMAL SPEED • «.aJ»E»02 M/SEC PART, PATH PARAM. • S.700F-08 M
DUIT HEIGHT • 2.1SOE-05 KG/SEC LENGTH INCR. •o'.i2708«si M INPUT EFF./INCR, • n.a»
RIOVR ERAVG EPLT AFID CMCD HMD HEIGHT OUST LAYER J(PART) J(ION) INCR. NO,
.*5E-oa 7
,*SE-0« 8
.45E.88 4
,«5F«Oa 10
,*5E.B« It
.65F-«a 12
.7094 2.05*E*«S 2'.l861E»OS 1.1826E + 13 11,» 1,«7E-06 6.967E-0* 4.2S2E-04 «,79E-08
.7082 ?', OStEfOS 2,l8*lEtOS l,182fcE+13 11,7 l,JaE-0» 6,J88F-06 5.714E«Oa 9.71E-06
.7117 2.0«6E»()S 2,l8*lEf05 1.1826E411 11,7 1.22E-0* ?.8«6E-0» 5.229E-0*
.TIS9 2,056Et05 2.l8»1t>05 1.182fcE*lS 11,8 1,1IE-** 5.347E-06 4.78JE-Oa 9.J7E-08
.720* 2.05»E+85 2.18*1E4>OS 1.1824E+I3 11,9 1.02E-0* 4.894F«0* 4.377E-04 V.1SE-08
.7252 2.056E+C5 J.l8tlE»B5 1.1826E+U 12.0 9.SSC-OT 4.48«E»06 a.Ollf.Ofl 8.91E-08
CLEAN GA8 VOLTACE.CURRFNT OENSITY.FIELO AT THE PLATE RELATIONSHIP FOR SECTION NO. 3
VH * .3.T701E+04 ACDNTY * i.OOOOE-OS AEPLT • .l.T777F»05
VH • .J.83?OE+04 ACDNTY • H.OOOOE-05 AEPLT • .1,86SIE«OS
VH • .].8968E+0« ACONTY • 1.0300E-0« AEPLT * .1.9471^*05
-------
VW • .}'.9560E»Oa ACDNTY • 1.2000E-OU AEPLT • -2,025?E*05
VW • .a'.0128E*0« ACDNTY • l.«OOOE-Ofl AEPLT • «2,09«3E+OS
VW • .3'.9601E»00 ACDNTY • 1.2la2E«Oa AEPLT • «
to
•b
vj
CALCULATION IS IN SECTION NO'. • 1 AND THE SECTION LENGTH IS • 1.5230 M
COLLECTION AREA • l'. 1*2E + 00 H2
WIRE TO PLATE • i'.?7oE-oi M
CURRENT/M • 3,7026-05 AMP/M
1/2 HIRE TO MIRE • 6.350E-02 H
TEMPERATURE • 297'.222 K
XON»MO«ILITY • 1iT95E-0« "2/VOLT-SEC
OUST WEIGHT • Z.ISOE-OS KG/SEC
APPLIED VOLTAGE « S.960E*Ofl VOLTS
CORONA WIRE RADIUS • 1.1»1E-03 *
CURRENT DENSITY • 1.214E-04 AMP/M2
GAS PLOW RATE » l.aa«E«Ot Hj/SEC
PRESSURE • 1.009 ATM
MEA-M THERMAL SPEED • U.UlfcE + 02 M/SEC
LENGTH INCR. •0.12TOn«35 M
TOTAL CURRENT • i,ui2E«oa AMPS
CORONA WIRE LENGTH • S.«12E»00 H
DEPOSIT E FIfLO « r,Zl«E»03 VOLT/M
GAS VELOCITY • l.fl90E+00 M/SEC
VISCOSITY • i.sooE-05 KG/M.SEC
PART, PATH PARAM. • 5'.70DP«06 M
INPUT Err,/INCR. • 1T,«6
RIOVR
0,4785
0.6844
9.6««3
0.4962
0.7021
0.7081
0.714)
O.WO*
0.726*
0.7331
0.759)
0.7454
ERAVG
CPLT
CMCD
HMO
WEIGHT
DUST LAYER JfPART)
JtlONJ INCR. NO.
1.963E*05 2,0306E*05
1.963E+05 2.0J06E+05
2,0306E*03
2.0386E+05
1.963Et05 2,0306E*05
1.963Ef05 2.0306E*05
1,963E+05 2,OJ06Et03
1.963E+05 2.0306E+05
.2742E+12
.2742E*12
. Z-f "2C + L?
,2743E*12
.274JE*12
,274E«06 ,918E»00
3.023E-06 ,704E>0«
2.804E>06 .508E-0"
2.603E-06 ,32»E-0«
2.42ftE-06 ,)65E.O«
2.254E>06 2.016E-OU
2.104E-06 1.882E-04
1.967F>06 1.760E-0"
1.643E-06 1.649F.Q4
1.730E-0* 1.547E-04
8.02E-08
7.76E-08
7.50E-08
7.25E-08
7.01E-08
6.76E-08
6.5JE-08
6.2iF-08
6.01E-08
5.77F-08
5.55F-08
5.14E.08
1.21E.64
1,21E-0«
1.21F..04
1.2U-OU
1.21E.04
1.21E-04
I.21E-04
1.2ir«04
1.21F-04
t .21 E*04
I.21E-OU
1.21F-94
1)
to
15
14
17
18
19
20
21
22
23
DESIGN EFFICIENCY • 99.00
UNCORRECTEO COMPUTED ErFICIENCY * 75.83
-------
00
CHARGING RATES FOR PARTICLE SIZES FROM SUBROUTINE CHARGN OR CHQSUM
SUM OF CLASSICAL FjfLD AND DIFFUSIONAL CHARGES USED FOR PARTICLE CHARGING
INCREMENT NO. O/OSATF FOR INDICATED PARTICIE SIZES
0'.2500E-06
1
2
to
.1602
.4*06
.5699
.6701
.7538
,8182
.8720
,9180
.9582
,991T
11 2.0256
12 2,0545
11 2.0730
14 2.0903
15 2,1067
1* 2,1222
IT 2.1168
IS 2.150T
t» 2,1640
20 2,1767
21 2,1188
22 2,2001
2! 2,2114
24 2.2221
0'.1600E-05
1 0.6882
2 0.8329
I 0,9131
« 0.9681
5
6
1
g
9
10
11
12
13
10
15
16
17
18
19
20
21
1.0096
.0126
.0699
,0929
.1128
.1302
.1456
,1*94
,1671
.I7a3
.1*11
.1875
,1935
.1992
.1992
.1992
.1992
0.3500E-06
f,0713
1.3024
1J4J36
1,5251
1.5949
1,6S11
1,6980
1,7160
1,7729
1,8037
1,8313
1,8562
1,8719
1.8866
1,9005
1,9135
1.9260
1,9J77
1,9489
1,9596
1,9698
1,9796
1,9796
1.9796
0.2000E-05
0.6528
0.7915
0'.B682
0,9208
0,9603
0,9918
.0177
,0396
.0584
10749
,0895
!02S
,1097
.116«
,1227
^1286
,1302
.1102
. 1 342
. I 302
.1342
0'.4500E-06 0.5500E-06 0.7000E-06 0.9flOOr-86
0'.9970 0.9376 0.8703 0.8062
,2075
,3265
,4092
.4721
'.5227
1,5649
1,6008
1,6121
.6596
,6843
,7065
,7203
,7332
,7453
,7568
,7676
,7779
,7878
,7971
,8060
,8060
,6060
.6060
.1335
.2438
,3203
.3764
.4250
,4636
.4966
.5255
.5507
,5733
.5936
.6060
.6176
,6265
,6369
.6486
.6579
,6667
,6751
.6631
.6831
,6631
,0506 0,9731
.1517 1.0662
.2216
.2747
.1172
.1524
.3624
,4064
,4313
,4516
.4700
,4809
.4912
,5009
.5100
.5166
.5266
,5146
.5420
.5420
,5420
,5420
.J30S
,1792
,2161
,2503
,2776
.1013
,3221
,3406
,3572
,3669
.3760
,3646
,3927
,4001
.4075
,4144
,4144
.4140
,4144
,414a
.6831 1.5420 1.4144
0'.2600E«05 0.3500E-05 O.SOOOE^OS 0.8000E-05
0,6175 0.5850 0.5545 0.5253
0.7507 0.7133 0,6785 0,6456
0,6241 A. 7639 0,7466 0.7115
0,8743 9.8321 0,7910 0,7563
0.9121 0,8682 0,6276 0,7fl99
0,9421 8,8969 0,8554 0.8165
0,9667 0.9205 0,8780 0,8363
0.9875 0.9«04 0,8971 0.8566
l'.0054 0.9574 0.9134 0,8723
1,0210 0,9723 0.9276 0,8660
1,0349 0.9655 0,9402 0.8980
1.0472 0,9972 0.9514 0.9087
1,0539 .0014 0,9572 0,9142
1.0601 .0092 0.9627 0,9J9«
1,0660 ,0147 6.9678 0.9242
1.0715 .0196 0.9726 0.9J87
1.0766 .0247 0,9726 0,9287
1.0766 .0247 0.9726 0,9217
1,0766 .0247 0,9726 0.9287
1.0766 .0247 0,9726 0,9287
1.0766 .0247 0,97?6 0.9287
O.llflOE-05
0,7605
0,9164
1.0062
1.0666
1,1125
1,1490
1,1792
1,2048
1.2269
1.2461
1,2616
1,2790
1.2679
1.2963
1.3041
1.3115
1,3165
1.3251
1,3251
1.1251
1,1251
1.1251
1,3251
1.1251
0',1500E>04
0,5002
0.6176
0.6*17
0.7251
0,7560
0.7838
0,6009
0,6226
0,6378
0,8510
0,6627
0.8731
ft. 8783
0.6832
0.8877
n.8920
0.6920
0.8920
0.8920
0.6920
0,8920
0.1300E-05
0,7262
0,8777
0,9618
,0196
.0633
,09*1
.1269
.1512
1,1722
1.1907
1,2070
1.2217
1.2300
1.2378
.2451
,2520
.2565
.2647
.1647
.2647
.2647
.2647
.2647
.2647
-------
22
25
1.1992
1.1992
1.1992
1.1342
1.1342
1,0766
1.0766
1.0766
1.0247
1.0247
1.0247
0.9726
0.9726
0.9726
0.9287
0.9287
0.9287
0.8920
0.8920
0.6920
-------
CHARGF ACCUMULATED ON PARTICLE SIZES IN EACH INCREMENT
CHARGE FOR INOICATER PARTICLE SIZES
tn
o
1
2
3
a
5
b
7
8
9
10
11
12
13
1«
15
16
17
18
19
20
21
22
23
2U
1
2
3
(1
5
b
7
8
9
to
11
12
13
14
15
Ib
P
18
19
20
21
22
23
2tt
fl'.25pOE-Ob
0.1S957E-J7
0.23215E-J7
8.25b50E-l7
0.27353E-17
0.28b5bE-17
0.29707E-17
0,3658bE-j7
8.313J8E-17
8.31995E-17
0.3257bE-l7
0.33097E.J7
0,335b8E-lT
0.33870E-17
0,3ai5«E-l7
0.3a«21E-J7
0,32«E-lb
0.53Sl3E-lb
0.5«70bE«Jb
0.5588aE-lb
0.5fe9flOE-U
0.5778'E-lb
0.58578E-lb
fl.5928flE.lb
e.59b76E-jb
0.bOOa7E.lb
0.b0393E.Jb
0,b87)9E.Jb
0.blO?7F-lb
fl.bl3j9E.Jb
0.bl3l9E-J6
8.bl3j9E-16
0,bl3l9E.Jb
fl.bl3l9E.Jb
fl.M3l9E.Jb
e.bjSj'E.jb
fl'.3508E-0*
9,30959E»17
0.37b35E-17
8,aia29E-17
0.auo71E.l7
0,ab889E-17
0.«7713E-17
8,a90b7E-l7
8.5022SE-17
8.51232E-17
0.52123E-17
0.52920E-17
0,5S*aflE-l7
0.5«093E-17
0.54518E-17
0,5a919E-17
0.55297E-1T
8,55b5bE-17
0,5599bE-17
0, 5b320E.lt
0.56b2^E«lT
8.5b924E-17
8.5T20bE-17
0.5720bE-17
0.57206E-17
0'.2000E>05
0.51782E-lfc
8.b279JE-lb
8.b8B73E>lb
9.730«lE-lb
0,7bl80E-lb
0,78b7«E-lb
0.80730E>lb
8' 82abbE-lb
0.839blE-lb
fl.852b8E.lb
0.8b17
8.70«7bE«17
Q.72504E«17
0.739J9E-J7
0.751bRE-17
0.7b?B17
O.B0971E.17
0.8l39ttC.i7
0.81798E-17
0.81798E-17
0.8J798E-17
0.81798E-17
0.2bOfle.05
0'.8227lE-lb
0.10081F.15
0.10979E.J5
0.11618E-15
0.1Z151E-15
8.12550E-15
0,12879E.JS
Ojl-SlSbE-l1!
0.1339SE.1?
0.13b03E-15
0.137B7E-15
0.13952E.15
O.lttOiiOF.l?
0.lai23E.lS
0.14201E.15
8.1a27aE-!3
O.US«%F.15
0.la3a3F-1ti
0,la3a3F«15
0,la3«3F.15
0.la3»3E«l'»
o.iasaSE-is
0.ia3a3E-15
8. la3a3F«l^
0.5588E-flb
O.biablE-17
0.7U2BBE-17
0.81SiaE.l7
0.8b52«E.l7
8.9033U-17
ft.93390E-l7
8.9593BE-17
0.9809
0.103IJE-16
8.10a4aE>l6
8.10525E-16
O.lObOlE'lb
0.10b73E-l*
O.lOTaoE-1*
0.10BOUE»lfc
O.lOHblE.J*
0.10923E-16
0.109T8E-16
0.11030F.lb
fl.1163flE.Jb
0.11030E»lb
O.llOJOE-li
0.3588E-05
0,ia050E-15
0.17132E.JS
0.18826E-J!
0.19984E-15
0.20853E-15
0.215a2E«l5
O.Z2108E.15
0.22585E-15
0.2299SE-15
0.23352E-15
0.23668E-1S
8.23958E-15
c.zaiooE.j?
0,2«239E.l5
8.2a378E"l5
8.2att9iE-lS
C,2«b09E-l5
t>.?4b09E«l5
0.2a609E«l5
0.2ab09F-l5
0.2Ub09E'l5
8.2ab09E.l5
0.2*689E-15
8.2«b09E-l5
P.7008F-86
fl,89755E-17
O.lOBS'iE-lb
0' ll«T»e-16
0,12599E-t6
0.13iabE-lb
O.ISSBSE-U
P,139aBF«16
8.U25«E-lb
0'.ia5?bE-lb
0,ia7blF-lb
0.1«972E-lb
0 15161E-16
0.15274E-16
0 15380E«lb
0,15«79E"lb
0.15S73E-lb
0.15bb2F-lb
0.157a7E-lb
0;i5B27F-lb
0.15903F-1*
O.I5903f.lb
0.15903E"1(>
0.15903F-16
«.!5903E.lb
a'.5008E-05
0,270611-15
0.331UE-1?
0'.3b437E-15
0,38703E-15
8 aottfllE-15
0,aj7abF-t5
8.«285!E-15
8'.a3780E"lS
0,aa?77E-l?
0.a527lE-15
8,a5885E-15
0.ab«32E-l'5
0.«b71bE-19
8.ab982F«15
0.a7232E-15
8.a7abbF-l5
0.47flbbE-S5
ft.fl7abbE-lS
0,a7abbF«l5
0,a7abbF-i5
0.a78bbE-l'5
fl.a7abbE.l5
8.a7a6bF-l?
0.a7abbF-15
0.9008E"Ob
6.13aa7E-lb
0,lb229E-16
0,17783E-lb
8.1B855F-1*
8,19b67E-16
O.JOJlbF-lb
0,20853E«16
8.2l309E-lb
0.217fl3E-lb
0.22050E-lb
0,22359E-lfe
0,22b3bE-16
0.22T98E-16
0.22950E-lb
0.23093E-lb
0.23227E-lb
0.23355E-lb
0,?3a7bE-lb
0.23590E-16
0.23590E-1*)
8.23598E-16
8,23598E-lb
8,23590E"tb
8,23590E-lb
0.8000F-05
0,*5395E-1^
fl,8037lF-l"5
0.88568F-15
8.9aj53f-15
0,963SaE-15
B.lfllbaE-lfl
o.ioa35E»ia
0,10bb3E-14
fl,10859F-lE-ia
0.1l50«F-|fl
8,1 15blE"l«
6,ll5bir-ia
8,1 l5fclE-ia
8,1 l5blE-l"
8.1 !5blE-l«
9,1 156!E-1«
8.11561F-1"
8.1 l5blF-l«
8.1 ISblF-lU
O.I100E.05
8. l«706fc-1«>
0,22S82E-lft
0.2a7a3E-lii
0.2b23lE»lb
0.2735fcE.lb
0,2825«E'lb
0.2899bE-lb
0.29625E.lb
«,3fllb9E«lb
fl.30bttbE.lb
0.31078E.16
8,3ia5ie.l<>
0.3lb70E-lb
8,3lB75E-lb
0.320b7E»lb
0.322«9E«lb
0.3i>42lE>lb
fl.32583E.lb
0.32583E-lb
9.325ftJE«lb
9.32SB3E'ib
0.32583E-lb
0.3?S8SE.lb
O.S2583e«l*
0.1500E«Oa
0.218J2E.H
0,2b95aE-la
0.297b2E-ia
8.3lbS7E-lU
0.330»lE-la
C.3a207E-la
fl.35129E«U
9.3590aE-U
0.3b'sb7E«l1«
8.37S51E-U
n.3BloaE.ia
0.383S2E-lil
8.185«»E«m
0.387aaE.ia
0.39932E-KJ
9.38932E-1U
8,38932E-la
0.3'«932E-ia
8.38932E-1U
n.3«032E-m
8.3«93?f -la
0.38932E-U
0.3«93?E«1«
0.1380f:.05
fl.2472«F..lb
0.29««1E.16
0.3?7abF.16
8.3«7HE-lb
fl.3b2fl?E-16
0.37387E-lb
8.383b6E.l«i
0.3919?E"lb
8.J99J JE-lb
O.U053flt-lb
0.aj09^E>16
8,lb
0.a2392E>lb
0.a2b27E-lb
9,a28a9E-l6
8.a3059E.lb
8.U3059E«lb
0.«S059E-lb
9.a3059F«1b
8.a3es9E.Jb
8.a3059F-lb
6,(i3059E-lfc
-------
PARTICLE SIZE RANGE STATISTICS
NJ
ui
CORRECTIONS FOR NQNIDEALITIES USING SET NQ. 1 OF CORRECTION PARAMETERS
SIZE CCF
2.500E-07 1.589
3^500E-07
4,500F-07
5.500E-07
7.000E-07
9.000E-07
1^100E-06
1.300E-06
.414
.320
.261
.205
.159
.130
,110
1,600E-06 1.090
2,OOOE-06 1.072
2,600E-06 1,055
3,500E-06 1.041
5,OOOE-06 1.029
8.000F-06 1.018
1.500E-05 1.010
INLET x
o.ooe
0,019
0,212
0,597
2.119
21985
3,582
3,283
6,865
7,164
11,940
10,447
14,925
14,925
20.899
OUTLET % COR. OUTIET X
0.0162
Oll085
O.U771
lj
4.
6*.
7.
t>f
»2l
"J
irJ
12'
13J
5j
0".
3291
6137
21 19
1198
2122
1510
6408
1454
8117
6244
5649
9735
0.0196
0,1077
0,4395
1.195?
1.1335
5^5731
6,4035
5,6399
11,1047
10,7093
16,0948
12,5131
14,0606
7,5235
4.4820
NO-RAP EFF,
60'.4177
58.U853
58.0627
58.5306
59.4501
61.2373
62,9766
64.7594
67.0329
69,7332
73,2526
77.1581
82,9965
93.0549
99.1324
NO-RAP W
5.757
5.161
5,398
5 468
5.607
5,887
6,172
6 479
6.89J
7 424
8.192
9,172
11,005
16.567
29.488
NO-RAP P
39.5823
41.5147
41,9373
41.4694
10.5199
38,7627
37.0234
35,2406
32.9671
30,2666
26.7474
22.84J9
17.0035
6.9451
0.8676
COR. EFF.
45.0462
52.8613
55.8074
57.3150
58.aaa6
60.2208
61.9115
63.4039
65.5377
68.1497
71.2798
74.4fli2
79.9277
89.2598
95.4306
COR. W
3.719
4.672
5.073
5.292
5.455
5.726
5.996
6.244
6.617
7.107
7.749
8.484
9.975
13.859
19.168
COR. P
54.9538
47.1387
44.1926
42.6550
11.5554
39.7792
38.0885
36.5961
34.4623
31.8503
28.7?02
?5.5188
20.0723
10.7402
4.5694
EFFICIENCY - STATED « 99'.00
COMPUTED « 75.8299
CONVERGENCE OBTAINED
ADJUSTED NO-RAP EFF. • 81.3734
HMD OF INLET SIZE DISTRIBUTION • 3.9g7E*00
SIGMAP OF INLET SIZE DISTRIBUTION * 2-.165E + 00
LOG-NORMAL GOODNESS OF FIT * 0.985
HMO OF EFFLUENT UNDER NO-RAP CONDITIONS * 2.218E+00
SIOMAP OF EFFLUENT UNDER NO-RAP CONDITIONS « 1.825E+00
LOC.NORMAL GOODNESS OF FIT « 0.99S
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS « 10.139
o.ooo WITH o.ooo SNEAKAGE OVER
NTEMP • i
RMMO • 6.00
RSIGMA • 2'.50
CORR. EFF. a 78'.6939
CORRECTED Mwp OF EFFLUENT • 2.565F+OQ
CORRECTED 8IGMAP OF EFFLUENT • 1.<»5SF + 00
LOG-NORMAL GOODNESS OF FIT • 0.992
«.000 STAGES
CORRECTED PRECIPITATION RATE PARAMETER •
9.60
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES' AND DISCRETE OUTLET MASS LOADINGS
NJ
Ul
NJ
IDEAL UNADJUSTED
MI6. VEL'.(CM/8EC>
2,«76E*00
J,5lTE+00
2,633E*00
2.782E+00
3.031E+00
S,383C«09
J,7«5E»00
a.M*I*90
4.6T6t+00
3.«m*flO
6.50JE+00
8.226E*00
J.101E*01
1,65TE*01
IDEAL UNADJUSTED
EFFICIENCY(I)
'
J.311E+01
S.611E«Ot
3,861E+01
I. +
4,528E«01
4.805E+01
5.290E+61
5.820E+01
,*
7.J90E+01
NO.RAP
DM/DLOGDCKG/OSCMI
RAPPING PUFF
5jo77E»00
1.H7E + 91
1.939E+01
2.719E+81
3.850E+01
3,101E*81
Z,3fl8E+91
7,S86E*00
9.780E-81
1.877E-92
3,S59E-82
8,09TE-92
1.<|51E«81
2.769E-91
5.08aE-81
7.823E-01
1.080C+00
1.527E»99
2.H3E + 90
A.223E+09
a|l73E+C9
NO»RAP«RAP PUFF
DH/DL06D(HG/DSCM)
3.851E.02
2.483E»01
1.56'»E»80
S.222E«99
t • 1"4E»51
1,989E»81
2 • 7?6C *0 1
2 v 9 i 4E + 0 i
3.520E+01
4.251E401
4. l33E*91
3,«65E»Ot
2.762E*91
1.173E+81
5.151E»00
RAPPING PUFF
DISTRIBUTION^)
U.560E-02
1.022E-01
1 .T84E-01
2.442E-01
7.95SE-01
1 ,1 JZE«00
1 • 424E*80
1 ,6ME»00
J.831E+00
4 i234E*00
8 ,791E»00
1,044E*9!
1.709C«01
2.114E401
2,887E*91
PARTICLE
OIAH.(M)
2.509E-07
3.509E-07
4.500E-07
5.509E.8T
T.009E-07
9.099E-07
1.109E-86
1.309E-06
1.609E-06
2.000E-06
2.609E-06
3.569E »96
S.099E-96
fl.fl09£«0fc
1.S09E.09
-------
SUMMARY TABLF OP ESP
PARAMETERS AND PERFORMANCE
KJ
(J\
U>
DATA SFT NUMBER 1
ESP PERFORMANCE!
EFFICIENCY « 76.6*39 *
8CA • l'.610E*01 M**2/fM**3/8EC)
ELECTRICAL CONDITIONS!
SIZE DISTRIBUTIONSi
NONIOFAL PARAMETERS!
AVG, APPLIED VOLTAGE a «.020E+Oa V
AV6. CURRENT DENSITY « 10.26 NA/CM**2
RESISTIVITY « f.OOOE+09 OHM.CM
INLET MHO • 3.»87E*00 UM
OUTLET HMD • 2.565F*00 UM
INLET SICMAP • 2.165F+00
OUTLET 8T6MAP m 1.955E*00
GAS SNEAKAGE FRACTION i 0.00 /SECTION GAS VELOCITY SIGMAG • 0.00
RAPPING MHO « 6.000E*00 UM RAPPING 8IGMAP • 2.5006+00
I*****************************************************************************************
-------
PARTICLE SIZE RANGE STATISTICS
to
CORRECTIONS FOR
USING SET
2 of CORRECTION
SIZF CCF INLET X
2,500E-07 1.589
S,500E-07
4.500E-07
5,500E-07
7,OOOE-07
9,OOOE-07
1,100E-06
1.300E-06
l' 600E-06
2,OOOE-06
2,600E-06
3,500E-06
5,OOOE»06
.414
.320
.261
,205
.159
.130
.110
,090
. 072
.055
.041
.029
8,OOOF-06 1.018
1.500E-05 1.010
0,008
0,049
0,212
0,597
2 965
3,582
3,283
6,665
7,164
11,900
10.407
14,925
14.925
20.899
OUTLET t COR. OUTLET X
0^0146
0.0968
0'.4338
1,2108
4,2174
5.7151
6'.5904
5'. 7957
ll',4532
11,1226
16.7251
12' 6663
14,4817
7.0835
2*. 1666
0,0179
0,0991
0.0064
l', 1090
3,849U
5.2223
6.0384
5.3511
10',6336
10.3620
15.8719
12.6051
14,7625
6,5951
5.0562
NO-RAP EFF.
56.1311
54.2253
53.7920
3U,2255
55,0865
56,7860
56.4090
60,1622
62,3479
64. 9«577
68,3849
72.2046
76,1006
69.2881
97'.6386
NO-RAP N
5,118
4.8S4
4.796
4' 854
4,972
5.212
5,455
5.717
6,067
6,514
7,153
7^953
9.030
13,876
23.268
NO-RAP p
43,6689
05.7747
06.2060
05,7745
40.9135
43.2120
41.5506
39.6376
37,6521
35.0423
31.6151
27,7950
21 .8990
10.7119
2'. 36 14
COR. P.FF.
00.5296
08.5172
51.5029
53.0221
50.0660
55.7562
57.3680
58.7863
60 8303
63.3506
66.3625
69.0877
70.9859
85.0362
93.8815
COR. w
3
0
0
u
0
5
5
5
5
6
6
7
8
11
17
.228
.124
.095
.693
.832
.065
.296
.506
.822
.235
.771
.373
.606
.968
.350
COR. P
«59'.4T04
51.4826
48.0971
06.9779
45.9300
44.2438
42.6316
41.2137
39,1697
36.6494
33.6175
30.5123
25.0141
14.5636
6.1165
EFFICIENCY - STATED • 99.00
COMPUTED = 75,8299
OBTAINED
ADJUSTED NO-RAP EFF. = 77'.0303
HMD OF INLET SIZE DISTRIBUTION e 3.987E*00
SICHAP OF INLET SIZE DISTRIBUTION « 2'.i65E*oo
LOG-NORMAL GOODNESS OF FIT = 0.985
HMD OF EFFLUENT UNDER NO-R»P CONDITIONS s 2.423E*00
SIGMAP OF EFFLUENT UNDER NO-RAP CONDITIONS » 1.889E+00
LOG-NORHAL GOODNESS OF FIT s 0.994
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS • 9,206
SIGMAG* O'.IOO WITH 0.100 SNEAKAGE OVER 4.000 STAGES
NTEMP * 1
RMMD • 6.00
RSIGMA « 2.50
CORR. EFF. a 74*.7107
CORPECTFD HMD OF FFFLUENT « 2.663E*00
CORRECTED SIGMAP OF EFFLUENT e 1.968F.+00
LOG-NORMAL GOODNESS OF FIT = 0.992
CORRECTED PRECIPITATION RATE PARAMETER « 8.54
-------
UNADJUSTED MIGRATION VEtOCITIfS *ND EFFICIFNCIES, AND DISCRETE OUTLET M*3S LOADINGS
Ul
Ul
IDEAL UNADJUSTED
"IS. VEL'. (CM/SECJ
2,517E*00
3,031E*00
3.38SEtOO
1.65TE+01
2.949E«81
IDEAL UNADJUSTED
J.28SE+01
31331E+01
3,a55E*fll
3,611E+fll
3.861E+01
4.280E+01
U.528E+01
«,8fl5P+01
5.290C*01
5,820E+01
6.512E»ni
7,3aoE+8i
8.300C+81
9.913E+01
NO»RAP
1,6U8E»00
5.60«E*00
1,237E*01
S,052E*C1
3.172E+01
«.677E+01
J,77«E+01
3,OiaEt01
2.662E*00
BARRING PUFF
1.093E-82
3.613E-0?
fl.l?7E-02
2,8HF-81
1.S50E488
2,1«5E*88
2.882F+00
U.208E+80
fl.235E480
PUFF
OM/DLOCO(MC/OSCM)
a,167E-02
3.258E-81
1.722EtOO
5.75JE+OB
1.265E*81
2.213E»81
3.131E+61
S.2«2E»81
a.oooE+ei
«.»38E*01
«.1«3E*01
1.5«lf*OJ
6.897F*80
RAPPJNG PUFF
-------
Ul
SUMMARY TABLE OF E9P OPERATING
PARAMETERS AND PERFORMANCE
DATA SET NUMBER
ESP
EFFICIENCY • Ta.7107 *
8CA • l'.610E*Oi M**2/(M**S/SCC)
ELECTRICAL CONOlTIONSl
SIZE OISTRIBUTIONSI
NONIDEAL PARAMETERSI
AVC. APPLIED VOLTAGE • 0,020E»0« V
AVG. CURRENT DENSITY • 10,26 NA/CM**2
RESISTlVITr • l.090r*09 OHM.CM
INLET MMD • 3.987F*09 UM
OUTLET MMO • 2.66JE+00 UM
INLET SISMAP • 2.ifc5E*80
OUTLET SI6MAP • 1.968E+00
GAS SNEAKAGE FRACTION • 0.10 /SECTION GAS VELOCITY 8IGHAG • 0,10
RAPPING MMO • b.oooE+oo UM RAPPINO SIGMAP • 2,SOOE*Ofi
STOP 011111
-------
APPENDIX L
OUTPUT DATA FOR EXAMPLE 3 (REVISION 1)
257
-------
E.P.A. ESP MODEL
T.E.P.L.-R.T.P. AND SO.R'.I.
REVISION I,JAN. 1, 1978
•««*•»•«»««••«*•••*•****»***•••«•***
PRINTOUT OF INPUT DAT* FOR OAT* SET
to
(SI
CO
DATA ON CARD NUMBER 1
NCNDPT « u NDAT* * i
DATA o* CA»O NUMBER 2
LAB E8Pi 3CA»«2FT?/1000ACP"|CALCUL*TEO V.J FOR FACM ELECTRICAL SECTION
DATA ON CARD NUMBER i
NEST • 2 NOIST • i NVI * 2 NX • 15 NY « is NITER = j NCALC » o NRAPD • ) NEFF • i NTEHP • i NONJD •
DATA ON CARD NUMBER «
NN • 10 NU»INC * 20
DATA ON CARD NUMBER 5
IFIN»L • zo JIl « 2 JI2 « ?1 VISKIP « i VISAME • ?
DATA ON CARD NUMRfR »
DL • o.ofcsoo GPN/ACF PL « ic.nono FT ET»O * 99.00000 x DD • lono.oo KG/H«*S EPS « S.IOOE+OO
VBATIO • 1.0100 MS s 0.000165 «**2/v.srC FP1TM • l.nflOO f80 • 1500000. V/M RnOCGS x 1.00F*09 OHM.C"
PAT* ON CARD MJMBFR 7
i) s O.n0 *?r&Grt 1) r 0.00 A7NU»«S( 1) s U.O
-------
ASNUCKf 2) * 0.10 AZIGGYC ?} • C.lO AZNUMS( 21 * tt'.O
OATi ON CARD NUMBER 8
ENOPTC 11 c
6) »
O.?00 UM £NOPT( 25 e
7) •
C,*00 UM ENDPTC 1) •
1.000 UM CNO'TC 8) •
O.«00 UM fNRPfC ll) •
1.200 UM fNOPT( <)) *
0,500 UM ENOPTC 5) • 0,600 U*
1,400 DM ENOPT(10) • 1,800 UM
3,000
fl.OOO
f"DPT(lU)
6.000
DATA ON CAPO
JNDPTM1) * 2.SOO UM
ENDPTU6) *. 20.000 UM
DATA ON CARD NUMBER 10
PRCU( 1) « 0.0000 X PRCUC 25 s 0.0076 X PRCUC 3J • O'.056l X PRCU( «) • 0.2682 X PRCU( 5) « 0.86S2 X
P»CU( 6) • 2'.98«5 S PRCU( 7) « 5,9695 X PRCUC 8) • 9.5515 X PRCUC 9) • 12,8350 X PRCUCIO) • 19,700* X
10,000
DATA ON CARD
It
P«CU(11) • 26,8645 X P"CU(1?J « S8.R042 X PP-CUC13) • fl9'.25l6 X PRCU(t«i • 6«,1765 X PRCUC15) « T9,101« X
PRCUU6) • 100.0000 X
DATA ON CARD NUMBER 12
NUMSFC « 1 LSfCTf I) « 6 LSfCT< 25 • 6 LSECTf 3) • 12
DAT* ON CARD NUMgCB 13
Alt 1) • 6.2500E + 00 rT«*2 VPS( 1) •
-------
DATA ON CARD NUMBER is
RF8( 1) « 9.0000E-01 STARTJt 1) > 6.0000F-05 A/H«*2 ST»RTZ( 1) • Z.OOOOE«05 A/M*«2
»TART1( l) • 2.0000E-OS »/M*«2 VSTAR( 1) « 3'.eOOOE»Ofl V
DATA ON CARD NUMBER 16
AS( 2) * 6.2500E*00 FT*«2 VOSl 2) » a.O«OOE*0 0.»8TSF.02 IN B8( 2) « 5.0000E+00 IN NHSC 2) • 5,0800E*00
DATA ON CARO NUMBER IT
tin 2) « 2.5000E+00 IN VCS( 25 « 3.05J3E«02 FT*«3/MIN V6AS8C 2) •
-------
CLEAN 0*8 VOLTAGF-CURRINT DENSlTV-FIfLO AT THE PLATE RELATIONSHIP FOR SECTION NO. 1
VM » .3.6008E+Oa ACONTY • 6.0?7fce-OS AEPLT • -l,7902Ft05
VW « -Y..B206E*Oa ACDNTY • T.«1S7E>OS AFRIT • .1.8597E+05
V* * -3'.S896E + 0« ACONTY « 9.9J9V-05 »FPLT « .1,9<|J5E»05
V* * .l'.<)513E + 0« ACONTY • 1.l9oaf-0« AFPLT • >2,02S2Et05
V* • -
-------
CLEAN GAS VOLTAGE.CURHCNT DENSITV.FIELD IT TWF PLATE RELATIONSHIP FOR SECTION NO. 2
VW • -S.«OOOE»0« ACONTY • 6.02TfcE-05 AFPLT « •
V* « -S'.820tE*0« ACONTY • T.9JJTF.-05 AFPLT s • l,
vw t •s'.es^fcE+oo ACONTY • »,9i93F-o5 AEPLT • .i.9a«E*os
vw * -j'.95m»o
VH • .a'.OTllE+0« ACDNTY « 1.6251E-Oa AEPUT • .2.1802E»05
^ CALCULATION IS IN SECTION NO. • 2 AND THE SECTION LENGTH IS * 0.7fc25
(0 COLLECTION AREA * S.812E-01 M? APPL1F.O VOLTAGE « 9.08»E*0« VOLTS TOTAL CURRENT • 9.a«»t»05 AMPS
WIRE TO PLATE • i'.27oe-oi M CPRONA WIRE RADIUS • i.i«lC*os M CORONA WIRE LENGTH • i,906E»on M
CURRENT/M • 0.955F-05 AMP/M CURRENT DENSITY • 1.625E-04 AMP/M2 DEPOSIT E FIELD * 1.625E*03 VOLT/M
1/2 MIRE TO WJRE • b'.!30E-02 M CAS FLOW RATE « 1.0»aE«81 MJ/SEC GAS VELOCITY • l,tt»OE*00 M/8EC
TEMPERATURE • 297.222 * PRESSURE • 1.000 ATM VISCOSITY • 1.800E-05 K5/M.8EC
ION MOBILITY • J.7*5E-0« «2/VOLT«8EC MEAN THERMAL SPEED » «.43*E+02 M/SEC PART. PATH PARAM. • 5'.700E»08 M
DUST HEIGHT • ?.isos-os KG/SEC LENGTH INCR. •o'.i2708as4 M INPUT EFF./INC*. • IT.a*
0,7270 2.08SE+05 2,l8a3E+05 2.1581E+1J 11,6 l.«*E-06 7.lOSr-0*
2,l8«2E*65 2.I58|F»1J 11,» l,JSF-Ot 6,a87F-06 "5.80SE-Oa
0.7J56 2.0«5E + 05 2.l8«2E*85 2.1582EfI3 11.9 1,20E-0(> S.9HE-06 5.290E-8«
*.737t J,0«5£t05 2;i8«2E«n5 2.158?E»1J f2.0 t;0«E-0* 5,t»OE-06 «.82lE-Oa
0.7826 Z.085E+05 ?.!8«2Ef05 2.1582E*!) 12.1 l.Olt-0* a.916E-06 i
0.7«T5 J.085E»05 J.l8a2E+05 J.1582E+I3 12.2 9.4UE-07 a.a9if.ofc i
FRAVG EPLT AFIO CMCO MMp WEIGHT OUST LAYER JtPART) J(ION) INCR. NO,
.OSF-07 l,fc2E«fl« 7
,01E«07 1.62F»Oa 8
,03E>07 1.62E«8a 9
.OOE-07 1.62F.na to
|SOE>08 l|62E-o« 12
CLEAN 8AS VOLTAGF-CUBRFNT OENSITY.FIELO AT THF PLATE RELATIONSHIP FOR SECTION NO. 3
V* « -*.8000E*0« ACONTY a 6.0277F-05 AEPLT * .1.7982E+05
VW c -3.8205E*0« ACONTY * 7.9SJ2E-05 AFPLT • -I.8596E+05
VW ^ .3.8896E«0« ACDNTY ( 9.81Q?£-05 AFPLT • .
-------
V« « «3'.9512E»Oa ACONTY i j,l«p«F.o« AMLT i -2, 02326*05
yw s -a'.0098F + 0« ACDNTY s 1.3RB9F-00 AEPLT • -2.0993E*05
VW * «3'.P51flF*OII
i -2.0?79F*Q5
CALCULATION IS IN SFCTION NO*, c 1 AND THF SECTION LENGTH 13 » 1.5258
COLLECTION AREA • J.162E+00 MJ
*I«E TO PLATE « r.2W-oi M
CURRENT/* • J.68aF-05 AHP/M
1/2 WIRE TO *IRf 3 6.5SOF-02 M
TEMPERATURE • 297.222 K
ION MOBILITY • I.TQ^T-O* ><2/voLT«3FC
OUST KFIGHT • 2.i5or.os KC/SEC
APPLIFD VOLTAGE «
COPONA WIRE RAPTUS
CURRENT OFNSITY •
G»S FLO*- RATE s 1 ,
s 1,000
THERMAL SPEED
;TW INCR, «0'. I270ftajs M
3.960E+OU VOLTS
= l.t91E«nj M
1.208F-OB AMP/M2
TOTAL CURRENT » l.ttO«E-0«
CORONA WTHF LENGTH « ?.«12EfOO **
DEPOSIT F FIFLI5 = l.?fl8F»03 VOLT/M
RAS VELOCITY « t.a<>oF»no M/SF.C
VISCOSITY * I.BOOF-OS KC/H.SFC
PART, PATH PARAM, c 5,7QOE»Oa M
INPUT FFF./INCR, = 17,a»
ERAVC
tPLT
AFIO
to
cr>
U)
0,70«2
0.7102
0.7162
0,7222
0.7281
0.7301
O.T«OS
0,7«66
0.7528
0,7391
0,7*92
0,7711
2,00l£f05
2.001E+05
2,001E*05
2.001F+05
2.001E+05
2,001E*05
2.001E*85
2.001E«05
2.001E»05
2.001E+05
2.001E*05
?.001E»05
?.0279Ef05
2.0279E+05
2.0279E+05
2.0279E+05
2.0279F+05
2,0279E*05
2.0279E+05
2,0279E+fl5
2.0279E+05
2.0279E+05
2.0279E+05
2.0279E+OS
1.7773E+11
1.7773E+1J
1.7773E+13
1.77T3E+13
1.7773E*1S
1.7773F*t3
1.7773E+15
1.777UE+13
1.777UE+13
1.777aE*13
1.777aE»13
1.77T8E+13
DESIGN
P.5
8,6
8.7
8.7
8.8
8.9
6,9
9,0
9.1
9.2
9.2
9.3
8.66E-07
«,17E-Q7
7.77F-07
7,«0£«07
7.17E-07
6.92E-07
6,69E-07
6.50E-07
6.33E-07
6,1»E«07
6.06E-07
5'.95E-07
3.821E-06
3.515E-06
3.2aSE-0«>
2.779E-06
2.391F-06
2.221E-06
2.072F-06
1.935E-06
1.810F-06
2.901E-na
Dl.'ST LAYER J(PART)
8.25F-08
T.96E-OB
7.69E.08
7.fl2E-08
7.15F-08
6,87r-08
6.59F.-08
6.33E-08
6.07E-08
5.82E-08
5.59E-08
JCION) INCR. NO,
?,139E-0«
1.853E-0«
1.731K-0«
1.S18E-00
1.2lE«Oa
1,?1E>0(I
1.21E-Oa
,21E.O«
,?ie-oa
13
14
15
16
17
18
19
20
21
22
23
2a
• 99.00
UNCORRECTEO COMPUTED FFFICIEMCY « 76,96
-------
NJ
(Tl
CHARGING RATES *OP PARTICLE SIZFS FROM SUBROUTINE CMAUGN OK CHGSUM
SUM nr CLASSICAL FIELD AND DIFFUSION CHARGES USED FOR PARTICLE C"ARRIMG
tNCI»E"F*T NO. (3/OSATF FOR INOICATfO »i»TTCLF 5I7F.S
0
1
2
3
0
5
6
7
8
9
10
11
12
11
10
IS
16
17
18
19
20
21
22
21
20
.2500F-06 0.1500F-06 0'.0500E-06
1.1096 1.060'' 0,9$72
1.0000 l.?.S69
1.5510
1.6506
1.7336
1.7972
1,8503
1.8957
1.9352
l'.97tlO
2.0013
2.0?95
2.0077
2.0607
2.0808
2.0959
2.1103
2.1239
2.1369
2,1093
2.1610
2.1723
2.1831
?.1831
.0171
,5082
.5776
.6135
.6799
.7195
.7539
.7803
.8110
.8358
,8511
.8658
.8795
,8923
.9005
.9161
,9271
.9375
.9«75
.9571
.9571
.9571
.1930
.3119
.3906
.0575
.5080
.5099
.5856
.6165
.6057
,6680
.6899
.7035
.7163
.7281
.7196
.7503
.7600
.7701
.7791
.7880
.7880
.7889
.7880
0,55006"
8.9287
1.1208
1.2109
1.3076
1.3659
1.0125
1.0511
t.OKUl
1.5126
1.5576
1.5599
1 .5800
1.5921
1 .6038
1.6106
1,6208
1.6305
1 .6116
1.6521
1.6606
1.6606
1.6606
1 .6606
1.6606
0.1600F-05 0.2000F-05
1 0.6835 0.6088
2 0.8267 0.7863
3 0.9080 0.8603
0 0.9602 0,9i»l
5
6
7
8
9
10
11
12
11
10
15
16
17
18
19
20
21
.0065 0.9586
.0002 0.9908
.0679 1.0172
,09J2
.1111
.1?88
.1002
.1581
.1658
.1731
.1799
. i860
.19?0
.1981
.1981
.0390
.05*5
.0751
.0896
.1029
.1101
.1169
.1PJ3
.12'3
.1309
.1109
.1309
.19B1 1.1309
.19*1 T.1309
0'.2600E«05 C.3500F.-
0.6100 0.5827
0.7066 0.7102
0.8215 0.7821
0.8730 O.S320
0.91)8 0.8692
0.9025 0.8987
0.9677 0.9229
0,9889 0.9«32
1.0071 0.9606
1.0229 0.9756
1.0368 0.9889
1.0093 1,0008
1.0560 1,0071
1.0620 .0131
1.06*3 .0186
1.0719 .0238
1.0791 .0287
1.0791 .0287
1.0791 .0387
1,0791 .0287
1.0791 .0287
0.7000F-06 0.9000E-06
0,8622 0.7992
1.0390 0.9616
1.1008
1.2112
1.2607
1.3070
1.3027
1,3727
1.3986
1.0211
1.0016
1.0597
1.0706
1.0009
1.0905
1,0995
1.5081
1.5162
1.5238
1.5)11
1.5111
1.5111
1.531 1
1.5311
.0570
.1220
.1716
.2108
.2033
.2707
,2900
.1151
.1136
.1501
.1596
.3689
.1775
.1855
.1911
,0003
,0071
.0071
.0071
.0071
.0071
.0071
0.5000F.-05 0.8000E-05
0.551.0 0.5206
0.6760 0.6000
0.7061 0.7121
0.79ai 0,7585
0,8100 0.7911
O.P5KO o.«208
0,8*17 0.8012
0.90)2 0,8620
0.9179 0.8781
0.9320 0.8920
0.9051 0.9003
0.9560 0.9151
0.96?0 0.9208
0,9680 0.9261
0.973? 0.9110
0.9781 0.9356
0.98?7 0.9156
0,9827 0.0356
0.9827 0.9156
0,98?7 0.9156
0,9827 0.9156
0.1100E-05 0.1300E-"*
0,7503 6,72«7
0,9101 0,8700
0.9988 0.9555
1.060? 1,0103
1.1066 1.0588
1.10J6 1.B901
1.171)1 .1233
1.1999 ,1078
1.2221 .1690
1.201S ,1875
1.2587 ,2038
1.270? ,2185
1.2811 .2269
.2915 .2307
.2093 ,?.0?0
,5067 ,2090
.3117 .2555
,3?0? .2616
.1202 ,?616
.1202 ,?616
1.3202 .2616
1.1*0? ,?616
1.320? ,?616
1.1?02 .2616
O.lSOOF-00
0.5002
0.617?
0.6832
0.7285
0.7623
0.7891
0,8109
fl,8?9?
0,6048
O.ft5«?
0.8701
0.8806
0.8860
0.8911
0.8958
0,9902
0.9002
0.90C2
0.9002
0.900?
0.900?
-------
22
23
20
1.1081
1.1981
1.1981
1.1349
1.13U9
1.13U9
1.0791
1,0791
1.0791
1,0287
1.0287
1.0P87
0.9827
0.9B27
0.9827
0.9356
0.9356
0.9356
0.9002
0.9002
0.9002
to
(T>
cn
-------
CH»«GE »CC'iMMl ATErt PN PARTICLE SIZFS tM EACH INC»EMF".T
kJT tuAPCt FOB INDICATED PARTTTLE SIZES
NJ
C.J'iOOE-Ob
1 0.19H9E-17
2 0.23'8aF.-l7
3 0.26501E-17
a 0,?8?b5E«l7
0.3SOOE-06
6
7
8
10
11
12
13
IS
16
17
18
19
20
21
22
21
20
,3n701E-l7
.M608E-1 7
.32383E.17
.330S7E-17
,3a979E-17
.35271E-17
0.3ai86F.-17
.3bOa9E.lT
.J6282E-17
.3b7l5F-17
,3b9lbE-17
.37109E.17
.37293E-17
.37293E.17
o.aaei5E-i7
O.aSSbSE-17
0.50755F-17
0.5195U-17
0.53908F..17
ol5Sab5E-17
O.Sb371E-l7
n.56781E.17
0.5717SE-17
57'5aiE-lT
57890E-17
58222E-17
5B538E-17
5S«aOE.17
0.59I2BE-17
0.5912BE-17
0.59128E-17
o.a<,7abE«i7
0,5b51U-17
0.62123E-17
0.6901*E-17
0.73302E-17
0.75081E-17
P.7b5a*E-17
0.77836E.17
O.BOO??F-17
0.80b67E«17
0.81271E-17
0.81839F-17
0.82375E«17
0.828B2EM7
0.63362E-17
0.eS«18F.17
0.8a25?E-17
0.8ubbbE"17
0.6abb6E*!7
6,bi635E-17
0.7b79iE«17
0.8ala?E-l7
0,8959af.l7
9.9J587E.17
0.9678SE-17
0.10910E-16
0.11Qb3E-16
0.11133E-1*
0.11199F-16
0.11!b2E>lb
0.11321E-1*
0.11378E-16
0.11378E-lb
0.11378E«lb
n,7000F-06
C^11208F.1«)
0.12301F.-1*
O.llOblf-lb
0,ia097E-lfc
0.18802F-16
0.1bP7lE-lb
o[lb2blE-lb
0.11378E-K.
0.1bS)OF-16
0,lb51HE-16
0.16510F-16
0.1b510F-lb
0.1b510E-16
fl.9000E«06
0.1b«02F.«lb
p'.19571E-16
0.211 l«E»lb
0.?lb8PE*16
0.22'i71l'.l6
O.?1254t-lb
0.?S870E-lh
0,?albOF.«16
P.?a53bE-lh
0,?a53»>E-lb
0,?aS3bE-lb
0.?a536F-lb
0.?tt53bE-lb
n.2a53bF-lft
«.1tOPF-OS
p'.23397F.-lfc
o|?72'S7t-l*
0.29a01F-lb
0.10lS5E-l(>
0.31918E-lb
0.3236BE-lh
0.3?757E-lb
A.33201E-lb
O.H803F.-1*
P.35772E-lb
O.U9aiE-lb
0.339aiE-lft
P.1300F-OS
fl'.3C9Rlf.lb
0.
0. a 1 * n £ -1 b
Q.a?2b9E>16
o.«a2i?f-lb
o,aa69oF>i6
0.aa909E-lb
0,aa909E-16
0.1600E-OS
1 0.3b539E»16
2 I
3 i
a <
5 0.53B09E-16
7 o!57088E-lb
» 0.5833bE-lb
9 I
10 I
11 I
12 0.bl9o9F-lb
13 i
ia I
15 P.b3079E-l(.
16 I
1*
20
21
22 0.*a050F-16
23 O.baOSOE'lb
2a
0.2000E-05
0.5J913F-16
0,b5218E.tb
0.71b8*E-lh
0.7bia7E-lb
0.7950bE.lb
P.82l71E.lb
P.SbZObE-lb
n 87787E-lb
p.8916SF-lb
0.9ia70E.ldi
0.9316?r-lh
0.9U126F-1A
0.9ai2*E-lb
0.260PE«OS
0.8558UE-1*
0.10S99F-15
0. I
0.1377aE.15
O.U027E-15
o*. laaau-i-s
0.ia797F.lS
".:
0.15030F-15
".1503PE-1S
0.1S03PE-11;
0.1505PE.1S
0.15P^PF-15
0.35POE-05
0,Ub32E-l?
0.17833E-15
0.19baaE-l5
0.8POOF-05
0.21826E-15
0,225b7F-lS
0.23l7aE-15
0,23fe8aE.lS
0.2ai20E-lS
0.2aa99E-l5
0.2557BE-15
B.257Q9E.15
0.25832F.-1S
0.25832F-15
0.2S83PE-15
O.ISOJT-IS
8.25832E-15
o!25»3?E-15
0,fl3R01F-l5
0.a7?73F-l5
0.2529PP-15 O.S9K
ft,B9907E-l5
0.50ia2F.-i5
0.«J873E-15
0.9?fc75F-l9
P.98717E-1S
P.10325F..ia
0.10b82C*ia
0,1097SF-ia
6,ua28r-ia
n.U609F.ia
O.T1769F-J«
0.1l9]PE-ia
P. I 198«F-ia
P.l?117F-]a
0.12177E-10
0.)?'77F-ia
n.i?i77F-ia
P.12177F-1U
P.1?I77E'ia
e.i?i77E-ia
0.1?177F-ia
P.HOOE-Oa
«.??825E-la
n.2xib«E.ia
P.3tOPbE-ltt
0.37002E-la
0.3783bE«ia
fl.39703E.la
0,«018SE«la
P,aOb59F«ia
o!aio7?E-ia
p.aift7SE-ia
i.atoTSf-la
o.aio7SE-ia
0. aio75F.«iu
»,a!075t»ta
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NO^IDEALITIES USING SFT NO. \ Of CORRECTION PARAMETERS
to
a\
SIZE
2'.500E-07
3f500F-07
1,500E«»07
5.500E-07
7.000E-07
9.000E-07
T.100E-06
1,300E-06
1,600E»06
2,OOOE"06
2.600E-06
3.500E-06
5.000F-06
8,OOOE»06
1.500E-05
CCF INLET x
.589 0.008
.111 0'.019
.320 0.212
.261 0,597
.205 2.119
.159 2.985
.130 3'.582
.110 3.283
.090 6,865
.072 7,164
.055 11,910
.011 10.117
.029 la. 925
.018 14,925
.010 20.899
OUTLET X
0'.0167
0.1123
0.1931
1.3729
1.7520
6'.3771
7 '. 2 8 6 1
6.3371
1 2 ', 3 4 1 6
11.7596
17.1893
12.7207
13.21)07
5'. 1734
0'.8075
, OUTLET *
0.020?
0.1109
O.U516
1,2?65
1.2297
S.6A19
6,5123
5.7199
11.2182
10,766?
16,0808
12,4193
13,7666
7.280R
4.5! 19
NO-RAP EFF,
61.5779
59.6828
59.3001
59.7818
60.7853
62.6362
61.4?55
66.2164
68.5608
71.291U
71,8217
7S.7053
84.1609
93.9378
99.3212
NO, RAP M
5', 942
5.613
5^5*1
5.65"
5.815
6.115
6,420
6.716
7.188
7,752
8,567
9.608
11.565
17.112
31.010
NO-RAP P
38.1221
40.3172
10.6996
10.2182
39.2147
37.3638
35.5745
33.7536
31.1394
28.7086
25,1783
21.2947
15.5391
6.0622
0.6758
COR. EFF,
16,3205
54.1006
57,0617
58,6050
59.7872
61.6272
63.3683
64.9009
67.0765
69.7197
72.8635
76.0483
81.4J50
90.1708
95.6500
COR. *
3.865
4.837
5.251
5.479
5.659
S.950
6.238
6.501
6.901
7,421
8.102
8.877
10.493
11.410
19.473
COR. P
53.6795
45.8994
12.9383
11.3950
10.2128
38.3728
36.6317
35.0991
32.9235
30,2803
27.1365
23,9517
18,5850
9.6292
4.3509
EFFICIENCY . STATED « 99.00
COMPUTFO m 76.9621
CONVFRCPNCF OBTAINED
ADJUSTED NO-RAP FFF, « 82.5108
HMD OF INLET SIZF. DISTRIBUTION • 3.987C*00
8ICH4P OF INLET SIZE DISTRIBUTION * a
LOG-NORMAL GOODNFSS OF FIT * 0.985
HMD OF EFFLUENT UNDER NO«RAP CONDITIONS * 2.
SIGHAP OP EFFLUENT UNDER N(VR*P CONDITIONS •
LOG-NORMAL GOOPNfSS OF FIT • 0.995
PRECIPITATION RATE PARAMETFR UNDER NO. RAP CONDITIONS s 10.831
182E*00
1.818E+00
SIGMAG*
NTfMP • 1
BMMO « 6.00
o.ooo WITH o.ooo SNEAKASF OVER i.ooo STAGES
COBR. EFF. m 7q'.«513
CORBECTF.O MMO OF EFFLUENT
CORRF.CTFO 8IGMAP OF E
LOG-MO»MAL GPODNESS OF FIT
2.516F. + 00
r 1.956F + 00
0.992
CORRECTED PRf CTPITATTON BATF PAPAMFTFR s
9.95
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES! AND DISCRETE OUTLET MASS LOADINGS
ro
o>
00
ID8AL UNADJUSTED
MIC, WEI'. (CM/SEC)
2,356E+00
2,600F+00
2,72«E»00
2.879E+00
J,5iaE«00
3.«96E+08
a,876f*00
5,65SE*00
B.blTE^OO
1.156E+01
l.TfllE+01
UNADJUSTED
FFFICIFNCV(X)
3.373E+OJ
5.420F+01
3I769E+01
U.659E+01
6.677E+01
8j«06E+81
9'.932E + 01
2,5S2E«91
l.UUSE+00
o,9?3E+00
1,OB8E+01
J.fc88E*01
3.211E+01
7.617E-01
RAPPING PUFF
1.069F-02
3.533E-82
7.9URE-0?
2.7U9E-OJ
7.765E-OJ
1.071E+00
1.916F+00
2.S18E+80
3.607E+00
U.115E+00
«,1«2E+00
MO-HAP+RAP PUFF
3.7«>2F-82
2,905E-01
HOflE + 01
2.691E+91
2.795E+01
3.362Ff01
3.906F»01
3.252F+81
2.558E+01
RAPPING PUFF
DISTRIBUTION(X)
U.360E-02
1.822E-01
1.78UE-8J
7,9S3E«01
1 ,I32E*88
l.fcfclE+00
3,fl31E+00
«,?3flf+88
8.791E+00
1.709E+01
2,1iaF+01
2.B87C+01
01AM. C»O
Z.500E-07
3.500E-07
a,588E-07
S.500E-07
7.800E»07
9,888E«07
1.108E-86
l.JOOE.Ob
1.600E-06
2.400E»06
2.600E-06
3.900E-06
5.000E-06
S.OOOf.O*
-------
SUMMARY TABLE OF E8P OPERATING
PARAMETERS AND PERFORMANCE
OAT* SET NUMBER
ESP
EFFICIENCY • 79.851J X
SCA » 1.610E+01
cr>
vo
ELECTRICAL CONOlTIONSl
AVG, APPLIED VOLTAGE * O.OME + OU V
AVG, CURRENT DENSITY • 10,49 NA/CH**3
RESISTIVITY • 1.000E*09 OHM-CM
SIZE OISTRIBUTIONSI
NONIOEAL PARAMETERS!
INLET MHO « 3,«87E*00 UM INLFT SIQMAP • 2.165C+00
OUTLET MM|) • 2.506E*00 U" OUTLET II6MAP • 1.956P + 00
RAS 5NCAKAGE FRACTION • 0.00 /SECTION CAS VELOCITY SI6«A6 « 0.00
RAPPING MHO • 6.100E+00 UM RAPPING SICMAP • 2,500E*00
-------
PARTICLE SUE RANGE STATISTICS
to
~j
o
CORRECTIONS FOR N
USING SET MO. g OF CORRECTION PABAMF.TF.RS
SIZF CCF INLET X OUTLET X C0«. OUTLET X
2.500E-07 1.589
3.500E-07 1.414
4.SOOE-07 1.320
5,500E-07
7.000E-07
9.000E-07
1,100E-06
1.300E-06
1J600E-06
2.000E-06
2.600F-06
3.500E-06
S.OOOE-06
8,OOOE-06
1.500E.05
.261
.205
.159
.130
'.110
.090
.072
.055
.041
.029
.018
.010
0.008
0.049
0,212
0.597
2.119
2,985
3,582
3.283
6.865
7.164
11,940
10.407
1 4.925
ltf.925
20.899
0.0152
0.1017
0 '. 4 0 6 6
1,2457
4.3284
5,8493
6,7315
5.9005
11,6190
1 1,2346
16.7918
1218226
14.2193
6.7369
T.9570
0.0160
0,101*
0.41 60
1,1351
3.9300
5, SI 79
6.1335
5.0229
10.7016
10.4058
13.8900
12,5539
14.5430
8,3?95
4.9899
NO-RAP FFF,
57.2627
55.3868
5«,9903
55.4376
56.3817
58.1498
59,8652
61.621'!
63.8560
66,5080
69.9648
73.7878
79.6530
90.3599
98.0001
NO-RAP »
5'.281
5,014
4,959
5.021
5.150
5. an
5.671
5.949
6,321
6,795
7.471
8,317
9,890
14,531
24.301
NO-RAP P
42.7373
40.6132
45.0097
Oa.5624
a 3 . 6 1 8 3
41.850?
40.1348
3«.37B«5
36.1440
33.4920
30.0352
26.212?
20,3470
9,6401
1.9999
COR. EFF.
41.7072
49.6955
52,7080
54.2378
55.3642
57.1211
58,7874
60.2097
6?, 3fl?8
64,9056
67.9^84
71.07B9
76.5076
86,5193
94.2501
COR, V
3.352
4.268
4.651
4.856
5.011
5.260
5,506
5.731
6.067
6.504
7,072
7.706
9.008
1J.44R
17.745
COR, P
58.2928
50,3045
O7.?9?0
45.7622
44.6358
02,8789
41,2126
39,7503
37,6572
35,0944
32.0316
28.9211
23,4524
15.4*07
5.7459
EFFICIENCY - STATED a 99.00
COMPUTED a 76.9624
OBTAINED
ADJUSTED NO-R4P F.FF, s 78.6433
*MD OF INLET SIZE DISTRIBUTION a 3,987E*00
SICMAP OF INIET SIZE DISTRIBUTION • 2'.165E*00
LOG-NORMAL GOODNESS OF FIT s 0.985
MMD OF EFFLUENT UNDER NO-RAP CONDITIONS « 2.386E+00
SI6M4P OF EFFLUFNT UNDER NO-RAP CONDITIONS » 1,881E*00
LOG-NORMAL CPODNESS OF FIT * 0.995
PRECIPITATION R*TE PARAMFTFR UNDER NO.RAP CONDITIONS = 9.590
o.mo WITH 0,100 SNEAKAGF
SIGHAG"
NTEMP « 1
RMHD » 6.00
RSIGMA * 2.50
CORR. EFF, a 75'.9318
CORRECTED MMO OF EFFLUENT
CORRECTED SIGMAP OF
LOG-NORMAL GOOONTSS OF FIT
2.641E+00
0.992
CORRECTED PRECIPITATTON RATT PARASETFR a
4.000 STAGES
ft.
-------
MIGRATION VEIOCITIFS AND EFFICIENCIES, AND oiscwfiE OUTLET MASS LOADINGS
TDEAL UNADJUSTED
NIG. VEL.CC'VSEC)
21556E+00
2.72«E+00
2,87<»E»00
S
3.510E+00
3.8«6e*00
a.286E*00
4,«76E+00
8.617EfOO
1,156E*01
UNADJUSTED
CIENC
3,373E+01
3.97U + 81
4.32JE+01
fl.65?E+01
6.677E*01
7,502E*81
2,995E-02
2.8?3E-01
2,<»«8Et01
S,OS6E*01
3.691C+OI
2.800E»01
1,0556+01
CAPPING PUFF
J.090E-02
3.602E-0?
8.103E-0?
2.K9JE-81
5.i«se-oi
1.092E+00
2,673E+fln
J.67«E+00
PUFF
«.085E-02
3.t»ae«8i
1.679F+80
5.602E+00
1.229E+01
3.027E+OJ
3.16SE401
J.«a6E*01
a.68«E+01
l.«73E*9i
RAPPING PUFF
OISTRIBUTION(I)
a,3681-02
1.822C-01
1.78aE-01
l,l3?EtOft
J.831E*00
8)791E»80
l|709E»81
PARTICLE
OIAM.(M)
2.SOOC-87
3.588E-07
«.?OOE»07
5.500E«07
7.800E-07
9,008t-07
l,100f-06
1.300E.O*
1.400E-06
2.000E«0*
2.fcOOE«Ot
3.500E-06
S.808E«06
1.500E-05
-------
to
•vl
NJ
»*****l»***«»««t»»**»«»*******»***«t**»******»*«t*****t»*********«***»**«**«***»*»**»********»*****»**t*****»*******»
SUMMARY TABLE OF ESP r|PFR»TING
PARAMETERS ANft PERFORMANCE
PATA 3FT NUMBER 2
ESP PERFORMANCr.1 FFFICIENCV • 75.9318 * 8C» • 1.610E*Ol M**2/(M**S/SEC)
ELECTRICAL
SIZE DISTRIBUTIONS!
AVG. APPLIED VOLTAGE • «,OUE + 0« V
AVG. CURRENT DENSITY * 10.49 NA/CM**2
RESISTIVITY > 1.000E*09 OHM.CM
INLET MMR * J.987»*00 UM
OUTLET MMO « 2.6«lE*00 UM
INLFT StGMAP = 2.145F+00
OUTLET SI6MAP s 1.9feTE+80
CAS SNEAKAGE FRACTION « o.io /SECTION GAS VFLOCITY SIGMAR * o.io
RAPPING MHO * fc.rOOE+00 UM RAPPING SIGMiP a 2.500E+00
•***«*****•*«**<*»**•**»**«»****»»»****»**»»********•****»**•*«**»***»**«************»****»****«****»***»**•***»****
•TOP 011111
-------
APPENDIX M
OUTPUT DATA FOR EXAMPLE 4 (REVISION 2)
273
-------
E.P.A. FSP
T.E.*.L..R.T.P. AMD Sn.P.T.
PFVISTON II, AUG.. 1<>7«
PRINTOUT OF INPUT DATA FOR DATA SET NUMBF.P
NJ
DATA ON CAPO MJMRFR 1
NENOPT • I« «JDAT» . |
OAT* ON CARD NU«BFR 2
FULL-SCALE, COLO-SIOE FSPl PLAMT At SCA«a«JPT?/l flOOACFM) J»15.«U»/FT?
DATA nn CAPO NUMBER J
3 MX • 10 NY • in NITER « j NCAIC • o NRAPO • i NEFF « i MTE-P • i HOMO • ?
NEST • i NDIST • i NVI
DAT* ON CARD NU**BPR a
NN • 5 NU"INC • 3
DATA ON CARD NUMBER 5
OL « f.06600 GPN/ACF PL « 27.0000 FT FTAO * 99.60000 X 0" • 2?70.00 KS/"**3 EPS * l.(100E»02
VPATIO « 1.2000 US « O.OOK220 M*»?/v.SFC FPATH : 1.0000 FRO • 1500000. V/M RnOCGS « S.OOE+10
DAT* ON CARD ^UKBFR 6
ASNUCKf 1) » 0.0ft AZISGVf |J s O.flO A7NIJMS( 1> * J'.O
2) « 0.10 A^TCRVf 2) = 0.3^ AZMiMSf 2) » .1.1
DATA ON CAPO NU*BER
-------
1) *
£NOPT( «) E
0.100 I'M fMD^Tf 2) *
1.9flfl UH ENDPT( 7) E
p. 3(10 IJM ENOPTf
1,100 UM ENDPTC
I). SCO UM E^OPTf UJ =
3.900 M" ENOPK 9) >
0,900 l>» fJnPTt 5) « 1,300 UM
5,100 UH FNt>PT(10} • 6,900 U*
DATA ON CARB *U«BFP a
ENDRT(ll) » 10.100 UK ENCpT'l2)
DATA ON'CIRD NUMBER 9
EMDPTtl?) a ?5.100 U* EMOPT(1«) « 2«,900 MM
P"CU( 1) • 0.0000 X PRCUt 21 • O.PJ30 t PBCUC 1) = O.?«60 » PRCMf • t.1890 X PRCUC 5) «
P»CU( 6) • 1.5i«0 X PP-CUC 7) • 7.0<|«0 X P«CUt *) « §.TOOP x P»CU( 9) * IO.J520 X PBCUC10) •
O*T* ON CARD NUMBFR 10
PRCUC11J • J5.»380 X PP.CUC12) • ?0.«8«0 X PRCUCII) « 32.5990 X PRCU(U) c IOO.OAOO X
om ON CARD NUMBER 11
NUMIEC • 1 HfCTf 1) • 10 L3ECT( ?) • 10 LSFCTf I) » 10
OAT* ON CARD NUHHFP. 12
2.00<10 X
l?,3jaO X
T«»2 V08f
IN BSC 1)
«.0600E+0« V TC8(
0 IN NHS( 1)
?.7300F-01
FT
AC8( 1) •
D*T* OM C*»0 NUMBER 1]
8ri( 1) • 3.»250f»00 IN \/K5( 1) • 3.?7?«F*04 FT««J/MtN
P»( 1) • l.0000f*00 AT" VTSSf 1) » ?.2«OOF-05 «C/«-8EC
11 s u.inflOE*')') FT/SFC TF«PS( 11 • }.|SOOE«02 F
1) « 9.00nOf-oi rr
*8( 2)
2)
FT»»2 V05(
IM BS( 2)
TN
2)
n*Ti nw c*Rf>
-------
3Y$( 2) • 3.42506*00 IN VG3{ 2) • 3.2T?«E*05 FT*«3/MIN VGA$8( 2) * «,1000E*00 PT/SEC TfMP3( 2) • S.lSOOf+02 r
P3( 2) • 1.0000E*00 ATM VI33( 2) * 2'.2»06C-05 KG/M.SfC IINCSC 2) • 9.0000E-01 PT
DATA ON CARD NUMBER 16
to
-j
^ A3( 3) • 2.6«60E*OA FT**2 VOS( 3) • U.2«SOE*8fl V TCS( 3) • S'.SBOOE-Ol A WL8C 3) • 1.57fOE»Ofl PT
ACS( 3) • 8.2500t«OZ IN 83( 3) • 5.SOOOe*00 IN NMS( 3) * l.2000E*01
DATA OH CARD NUMBER 17
$Y3( 3) • 1.62506*00 IN VC3f 3) c 3.272aE+05 PT**3/MIN VCASSC 3) • 4.1000E+00 FT/SEC TEHP8( 3) • 3.1300E+02 P
S) • l.OOOOe+00 ATM VI83( 3) • 2.2900C-OS KC/M^SCC LINCt( 31 • 4.0000E-01 PT
-------
INCREMENTAL ANALYSIS OF PRECIPITATOR PERFORMANCE
FULL-SCALE,COLO.IIDE Itfl PLANT A| SCA«24SFT2/1000ACFM|J»H.9UA/FT2
CALCULATION 18 IN SECTION NO'. • 1 AND THf SECTION LENGTH IS • 2,7050 M
COLLECTION AREA • 2.4*1E+03 M2
HIRE TO PLATE • I'.IQTE-OI M
CUR*ENT/M • 5,t94E«05 AMP/M
1/2 MIRE TO WIRE • 9.208E-02 H
TEMPERATURE • 430.000 K
ION MOBILITY • 3.4*3E"0« M2/VOLT-
OUST KflOHT • t.9*9E>01 KG/SEC
SEC
APPLIED VOLTAGE • 4.0*OE*0« VOLTS
CORONA HIRE RADIUS » 2.096E-OS M
CURRENT DENSITY • 1.109F»04 AMP/K2
GAS FLOW RATE • 1.5«8E*OZ *S/SEC
PRESSURE • 1,000 ATM
MfAN THERMAL SPEED • S.339E*02 M/8EC
LENGTH INCR. »0.27450000 M
TOTAL CURRENT • 2.730E-01
CORONA MIRE LENGTH • 4.795E*03 M
DEPOSIT i FIELD • j.5«7E*e« VOLT/M
GAS VELOCITY • j,25o£+oo M/SEC
VISCOSITY • 2.290E-os KG/M.SEC
PART. PATH PARAM. • S.246F'08 M
INPUT EFF./INC*. • t*.Sl
to
ROVRI
3,15**
2.5220
2.0*57
1.7*8*
1.5705
1.32*4
I.2512
1,1*54
1.1512
ERAVG
2,90*Ef03
?>!?*!>!?.
EPLT
2,0373E*05
APID
2.«0tt*05
2'.*0*E*05
?>!!*!'??
l'7B3SEt05
1.7435E*05
1,7149E«05
2.*0*Et05
1,*774E*85
1,**50E«05
l.*595E»05
,731*E*12
.8944E«12
.38**E*12
.8138E+12
.1S23E*12
.4972E412
.7*29E+12
,«843E«12
CMCD
u.
1' r
!!'
u'
u.
HMD
2129E-05
2,27E-05
2.22E-05
2.14E-09
1,98E-05
e'osE-o»
4^19E-0*
MEIOHT
1.49*E«03
1.185E-01
DUST LAYER J(PART)
J(ION) INCR. NO.
3.727E-04
2.035E*04
1.1S2E-04
7.498E-05
5.212E-09
3.913E-09
3.HOE-05
CALCULATION 18 IN SECTION NO*. •
COLLECTION AREA • ,2'.«*1E»OI N2
MIME TO PLATE • i.3*TE-oi M
CURRENT/* • *'.om-05 AMP/M
1/1 MIRE TO HIKE • *.2osE«o2 M
TEMPERATURE • '10,000 K
ION MOBILITY • S.4*3E»04 M2/VOLT-8EC
DL'BT HEIGHT • *.9*9E>01 K0/8EC
S.38E-0*
2 AMD THE SECTION LENGTH IS • 2.7450
S.646E«02
4.471E-02
2.*0*E>02
1.407E-02
T.teiE-03
4.4*2E«03
2.830E-03
1.9*7E-03
1.477E>03
1.174E-03
*.12E-07
5.13E-07
4.09E-07
J.32E-07
2.S7E-07
2.97E-07
2.37E-07
2.20F-07
l.lOE-04
1.10E-04
I.10E-04
l.tlE-04
l.UE.OH
l.tiE-Oa
l.lir.9«
1.11E.04
l.liE-fl0«
APPLIED VOLTA8E • fl.H8?*0« VOLTS
CORONA MIRE RADIUS • 2.A«6E-03 M
CURRENT DENSITY • l.T40f-0« AHP/M]
GAS FLOM RATE • I.S«SE«02 M]/SEC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • 9.!)5f»02 M/SEC
LPNGTH INCR, »0.2T«50000 M
1
2
3
4
6
7
8
9
10
TOTAL CURRENT • 4.330E»oi AMPS
CORONA MIRE LENGTH • 4,795E»01 M
DEPOSIT E FIELD • s.798r*04 VOLT/M
GAS VELOCITY • i,290E+oo M/SEC
VISCOSITY • 2.290E»OS K8/M.SEC
PART. PATH PARAM'. • e'.24*E>oe M
INPUT EFF./INCR, • it.ei
ROVRI
ERAVO
EPLT
AFIO
MHO
MEIGMT OUST LAYER J(PART)
CALCULATION IS IN SECTION MO'. • 3 AND THE SECTION LENGTH IS • 2.7450 *
J(ION) INCR. NO.
1.07**
1.05*0
.•495
.0150
.0270
.020*
.01*1
.0124
.00**
.0974
.OI4F+05
,OI4E+05
,0!4E*05
,014E»05
,01«E»05
,014E»05
.oi«e»o5
,014t»05
,01«E»05
,01«E»05
r.«it*e«o5
|.80*lf»05
.80I9E«OS
,798»E«05
,7««*f»05
.798feE«OS
,798*E405
,7»8*e»05
,7«8*E*Of
,7«8*E*05
*.7875E*12 »7'.
».«?0«E»I2 17.
1.0079E»13 17,
I,018!E*13 17,
.02*OE«13 17.
.0122E*13 17.
.0370E»13 17,
.0«08Etl3 17.
.0437E+13 17,
.04*OE*13 17.
3r«JC"0* 2.805 *.644F-04
2,lSt«0» 1.535F-05 5.795E-B4
2.05t«06 t.347E'OS 5.084E-04
1,98E-0* 1.187E-05 «,«8ir-0«
1.91E-0* J.051F-05 S.965E-04
1.85E>0* «.329F>0* 3.421E-04
1.79E»0* 8.308E*0* 3.l3*f*04
2,18E<>07
2.07E-07
1.9*E>07
1.85r-OT
.74F-07
,*3E«07
,5flE-07
.aaf.07
,35E«fl7
.27E-87
,7*F>04 U
,7*E«04 12
,7*E-04 13
,7*E«ft4 14
,7*C»0
-------
COLLECTION AREA • 2.461E+OS «?
HIRE TO PLATE « t'.s«7E-oi H
CURRENT/M • l.|64E>04 AMP/M
1/2 HIRE TO HIKE • V.20BE-02 M
TEMPERATURE • 430.000 K
ION MOBILITY • 3.46SE-04 M2/YOLT.8EC
DUST HEIGHT • 6.969E-01 KG/SEC
APPLIED VOLTAGE • 4.24SF»04 VOLTS
CORONA HIRE RADIUS • 2.0«6E«OS M
CURRENT DENSITY • 2,268£«04 ANP/MJ
GAS FLOH RATE • l.S4SE«0( M3/SEC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • S.JS5E*02 N/SEC
LENGTH INCR. «0'.27450000 M
TOTAL CURRENT • S.580E-01 AMPS
CORONA HIRE LENGTH • 4.79SE«01 M
DEPOSIT E FHLO • 1.134E«OS VOLT/M
CAS VELOCITY • i.25«E»oo M/SEC
VISCOSITY • 2.(*oE»os KB/N.SBC
PART. PATH PARAM. • e.2atE-oe M
INPUT EFF./INCR. • it.Si
ROVRI
.0045
.0015
.00(7
.0021
.401*
.0012
.0010
.0007
1,000*
1.0004
E8T.
ERAVB
3,Ol9EfOS
JoS9E»05
,039E»05
.039E+05
,om«o5
EPLT
1.88701*05
1.88701*05
l,e870E*05
1,8870E*OS
1,6870E*05
1,8870E»05
1.8870E*05
1,88TOE*OS
1,6S70E*05
1.8B70E»05
AMD
.34071*13
.ln2lE*ll
.I412E+13
,1440E»11
,3a«*E*lJ
,I460E*13
.34*2E*13
CMCO
M'.7
22,7
22,7
22,7
22,T
«'T
22>
22,7
M,7
HMD
i;7SE-06
1.67E-06
1,»1E-0*
1,S6E-06
lj42E-0»
l'j4E.fl»
l.JOE-0*
HEIGHT
T.77«f-0»
6.934E«0*
6.19IE-0*
5.538E>0*
DUST LAYER J(PART)
4.«4*C»06
• *9.60
(2'. 7
UNCORRECTED COMPUTED EFFICIENCY • 94.12
3.231E-06
2.914E-0*
2.93*E-Oa
Z,»l7t«0»
2.337E-0*
2.0901-04
1.S71E-04
l.*7*E-04
1.507E-04
1.J55E-04
1.220E-0*
1.100E-04
1.25E-07
1.17E-07
I.10E-07
1.03E-07
9.68C-08
9.01E-08
8.42E-08
7,B7E«OB
7.S4E.OB
6.B6E«OB
2.27E'04
2.27E.04
2.27E.OO
2.27E.04
2.27E.04
2,(7E»04
2.27E*04
Z.27E.04
2.27E.04
2.27E.04
INCR. NO.
21
22
23
24
25
2*
27
28
2*
10
INCREMENTAL ANALYSIS OF PRECIPITATOR PERFORMANCE
NJ
-J
GO
FULL>SCALE.COLD-SIDE E'Pi PLANT Af SCA«24IFT2/IOOOACFM|J»15.9UA/FT2
CALCULATION IS IN SECTION NO'. • 1 AND THE SECTION LENGTH IS • 2.74JO M
COLLECTION AREA • . 2.4HE«OJ N(
HIRE TO PLATE • t.i*7E>oi M
CURRENT/H • 5.694E-05 AMP/M
1/2 HIRE TO Mine • 9.208E-02 M
TEMPERATURE • 430.000 K
ION NOBILITY • >.4*3E>04 M2/VQLT<
OUST HEIOHT • t.94«E»01 KC/SEC
>SEC
APPLIED VOLTAGE • K.OkOEtOa VOLTS
CORONA HIRE RADIUS • 2.0*tE>03 M
CURRENT DENSITY • f. 109E-Ofl AMP/M2
GAS FLQH RATE • l.S4BE««2 M3/8EC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • 5,j3SE»o2 M/SEC
LENGTH INCH, "0.27050000 M
TOTAL CURRENT • 2.7SOE-01 A"PS
CORONt HIRE LENGTH • «.7*5E«03 M
DEPOSIT E FIELD • S.347E*04 VOLT/M
OAS VELOCITY • i.2soE*oo M/BEC
VISCOSITY • 2.290E-OS KS/M»8EC
PART. PATH PARAM. • e.2«»E-08 M
INPUT EFF./INCR, • 15.14
ROVRI
ERAVC
EPLT
AFIO
CMCO
MHO
HEIGHT
DUST LAYER J(PART)
J(ION) INCR. NO,
2.9685
2.4100
2.0041
.7174
.55*9
.4(81
.112*
.(60S
.2046
.1610
2.90*E+Of 2.0050E»05
2,90*E»05
2 906E*05
2^90*E*05
2.90*E»05
2*«06E*0!
2.«06E*05
2,906E*05
2.906E»05
,9055E«05
.8291E*05
,7771E*05
.7407E»05
,7iaSE»05
.6944E*05
,67B9E*05
.66TOE+05
,6577E*OS
CALCULATION IS IN SECTION NO'. •
2.1207E»12 11,
2.8586E»12 11,
3.4375E*12 11,
3.9652E»12 11.
4.4250E*12 11,
4,t23«E«12 11,
5.1*84E*!2 11,
5.4655E+12 11.
2,2«E»OS
2.27E-05
2,2«-05
. Z.1«E»05
l.»7E-05
1.28E-05
7,96E»06
5.49E-06
5,7l92E*l2 11,1 4.KE-0*
5.93I6E*12 11.1 3.16E-06
2 ANO THE SECTION LENGTH IS •
1.517E-01
1.182E-OJ
6.638E-04
I.679E-04
2.008E»04
1,1*SE-0»
7.421E-05
5,im-03
1,B8*C«05
I.092E'OS
2.7450 M
S.727E>02
4.460E-02
I.581E.02
1.384E-02
7.580E-03
A.OOTE-03
2.801E-03
1.950E»OI
l,o»7|«03
1.167E-01
4.98E-07
6.24E.07
5.17E-07
4.06E'07
J. 351-07
2.8TE-OT
2.58E-07
2.S7E-07
J. 201-07
2,06E>07
1,IOE«04
1.10F-04
1,1 OF. Oil
l.UE>04
i.UE-oa
l.UF-04
1.11E>0«
1.I1E-M
I.IIE'04
1.1 If -10
1
2
3
4
5
6
7
8
9
10
COLLECTION AREA • 2'.461Et03 M2
HIRE TO PLATE • f.mr-oi M
APPLIED VOLTAGE • 4.2lOE*04 VOLTS
CORONA WIRE RADIUS • 2.096E-03 M
TOTAL CURRENT • u.noE-oi AM»S
CORONA WIRE LENGTH • S,T9»E*03
-------
CURRfNT/M • 9.0J1E-05 AMP/M
1/2 WIRE TO WIRE • 9.20««02 «
TEMPERATURE • 430.000 K
ION MOBILITY • 3.463E»04 M2/VOLT-8EC
OUST HEI6HT • 6.969E-01 KG/SEC
CURRENT DENSITY a 1.760E-04 AMP/M?
GAS FLOW RATE « 1.5«8E+02 H3/SEC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED « 5.335E+03 M/SEC
LENGTH INCR. «0'.27450000 M
OEPOlIT g FIELD • 8.798E+04 VOLT/M
GAS VELOCITY • 1.250^*00 M/SEC
VISCOSITY • 2.290F-05 KG/M.SEC
PART. PATH PARA*. « 6.246E-OB M
INPUT EFF./INCR, « 15.34
tO
ROVRI
ERAVG
EPLT
AFID
HMD
WEIGHT
OUST LAYER J(PART)
CALCULATION 18 IN SECTION NO'. • 3 AND THE SECTION LENGTH 18 « 2.7450 M
JCION)
COLLECTION AREA • 2'.461E + 03 M2
WIRE TO PLATE • i'.S97E-oi H
CURRENT/* • iii*ae-o« AMP/M
1/2 WIRE TO MIRE • 9.j08E-o2 M
TEMPERATURE • 430.000 K
ION MOBILITY • S.4fc3E-04 M2/VOLT-SEC
OUST HEIGHT • 6.969E-01 KG/SEC
APPLIED VOLTAGE •
CORONA HIRE RADIUS
CURRENT DENSITY •
GAS FLOW RATE • 1
4.245E*04 VOLTS
• 2.096E-03 M
2.268E-04 AMP/M2
,5«8E*02 M3/8EC
. NO.
.0830
.0651
.0510
.0400
.0314
.0247
.0194
.0152
.0120
.00*4
3lol4E+OS
3.014E+05
3.014E+05
S.014E+05
3.0l4EioS
3.014E»05
3,014Et05
3.014E+05
3,01«E+05
3.0UE+05
1.8135E+05
1.8080E+05
1,8036E+05
l,6002Et05
1,8002E+05
1.8082E+05
1.8002E+05
1.8002E+05
1,8002E+05
1.8002E+OS
9.7295E+12
9.8937E+12
1.0026E+11
1.01S2E+13
1.021TE+13
1 .0284E+13
1.0S37E*13
1.03T9E+13
1 .0413E+13
1.043«E»13
17,6
IT!*
17,6
JT;*
17.6
17,6
ITJ*
17,6
17,6
17.6
2182E-06
2.45C-06
2.32E-06
2,22E-06
2,13E-06
2,05E-06
1,9TE«06
1,9!E-06
1.65E-06
1.79E-06
2.825E-05
2.375E-05
2.028E-05
1.752E-05
1.528E-05
1,341E'OS
1.182E-05
1 . Q46E>05
9.2P8E-06
8.273E-06
1.066E-03
S.963E-04
7.655E-04
6.612E-04
5.768E-04
5.061E>04
a.atlE-OU
3.948E-04
3.505E-01
3.122E-04
2.18E-07
2.07E-07
1.95E-07
l.SttE-07
1.7SE-07
1.63E-07
1.53E.07
1.4(lE«07
1.35E-07
1.26E-07
.76E-04
.76E-04
.76F..OO
.76E.OU
,76f-0a
,76E-Ofl
.76E-04
.76E-04
,76E*04
,76E«04
11
12
13
14
IS
16
17
18
19
20
PRESSURE •
MEAN THERMAL
LENGTH INCR. •0'.27450000 H
1.000 ATM
SPEED • 5.335E+02 M/SEC
TOTAL CURRENT • 5.580B-01 AMPS
CORONA WIRE LENGTH • 4.795E+03 M
DEPOSIT C FIELD • 1.13«E+05 VOLT/M
GAS VELOCITY • 1.250E+00 M/SEC
VISCOSITY • 2.290E-09 KG/M.SEC
PART. PATH PARAM. • e'.246E-08 M
INPUT EFF./INCR. « 15,34
ROVRI
ERAV6
ERLT
AFID
C"*CD
"HO
WEIGHT
OUST LAYER JtPART)
jdONj INCR. NO.
.0058
,0046
,0036
,0028
.0022
.0017
.0014
,0011
.0008
.0007
,039Ef05
.OS9E+05
,039E«05
,0»9E+05
,OS*Ef05
,039E»05
,0 J'E»05
.03*6+05
.039C+05
,039E«05
.8875E»fl5
.8875E»05
.8875E+05
.8875E+05
,8875E»05
.8875E+05
.8875E+05
.8875E+05
.8875e+OS
.8875E+05
.3390E+1S
.3406E+13
,3ai9E*13
.3430E+I3
.343BE+13
,3444E»1S
, 3449E+ 1 3
.3053E+13
.3456E*13
.3459E+13
22,7
22.7
22,7
22,7
22,7
22.7
22,7
22,7
22 7
22.7
1, 73C»06
1.67E-06
1.61E-06
1.56E-06
1,51E-06
1.46E-06
1,42E-06
1.37E«06
1.33E-06
1.30E-06
7,7«2E-06
6.902E-06
6.165E-06
5.513F-06
4.94QE-06
4.429E-06
3.975E-06
3.574E-06
3.21BE-06
2.902E-06
2.922E-04
2.605E-04
2.327E-04
2.081E-04
1.864E>04
1.672E*0«
i.sooe-04
1.34*E-04
1.21«E.O«
1.09SE-04
1.25E«07
1.17E-07
1.10E«07
1.03F.07
9.61E-08
8.99E-08
8.39E-OB
T,8«C«08
7.32E-08
fc.8uf.08
2.27E-04
2.27E.04
2.27E.04
2.27E«'»a
2.27F.04
2.27F«Oa
2.27E.04
2.27E-04
2.27E-04
?,?7E«04
21
22
23
24
25
26
27
26
29
30
-------
CHARGING RATES FOP PARTICLE SlZfS FROM SUBROUTINE CHARON OR CMG8U"
8RI THEORY USED FOR PARTICLE CHARRING
INCREMENT NO.
IS/OSATF FOR
PAPTTCLE sizes
to
00
o
0
i
2
3
4
5
6
T
8
4
10
11
12
13
1«
15
1*
IT
18
19
20
21
22
21
24
25
It,
27
28
29
10
0
1
2
3
«
5
6
7
ft
9
10
11
12
1J
1«
15
.2000E-06
0.5314
0.7618
0.9210
.0579
.1668
.2550
.J295
,1936
.4494
.4988
.5703
.6298
.6806
.7209
,7642
.7994
.8312
.8602
1,8869
1.9116
1.9411
1.9481
1,9930
2.0161
2.0376
2,0578
2,0767
2,0945
2. ilia
2. 1274
.6000E-05
0.4145
0.6189
0.7200
0.7812
0.0211
0.8486
0.8685
0.8814
0.8951
0.9044
0.9?71
0.9418
0.9523
o,96oo
0.9670
0.4000F-06
0.5228
0.7543
0,9215
1,0642
1.1669
1,2460
1,3100
1.3634
1,4091
1,4488
1,5080
1,5562
1.5968
1.6117
1.6620
1,6896
1,7141
1,7364
1,7567
1.7755
1,7981
1.8187
1,8376
1,8551
1.8714
1,8865
1,9008
1.9141
1,9268
1.9387
O.B500E-05
0,4323
0,6163
0,7172
0,7783
0.8179
0,8450
0,8644
0.8788
0.8898
0.89*4
0,9211
fl,9J53
0.9450
0.9521
0.9575
0'.WO£-06 0.1100E-05 0.1600E-05 0.2500E»A5
0,4934 0.4720 0.4586 0.4470
0,712« 0.6797 0.6579 0.6388
0,8587 0.8079 0.7749 0.7468
0.9817 0.9027 0.8505 0.8156
1.07J1 0.98)2 0.9164 0.86M
1.1384
1.1890
1.2301
1,2646
1,2941
1.3399
1,3763
1.4065
1.4322
f.4546
1.4743
T.4920
1.5080
1,5225
1,5359
1.5522
1.5670
1.5806
1.5930
1.6046
1.6154
1,625«
1.6349
1.6A38
1.6522
.0406 0.9688 0.9017
.0828 1.0068 0.9335
.1161 1.0157 0.9611
.1434 1.0589 0.9819
.1665
.2039
.2329
.2566
.2765
.2937
.3088
.3222
.3142
,3452
.3552
.3676
.3789
.3891
.3985
,«071
.4152
.4227
.4298
.0781 0,9986
.1110
.1357
.1554
.1719
.1859
.1981
.2090
.2186
.227«
.2151
.2455
.2545
.2627
.2702
.2771
.2835
.2835
.2835
.4298 1.2835
.4298 1.2835
.0285
.0498
.0664
,079<>
.091?
.1009
.109U
,1170
.1238
.1299
.1379
.1450
.1513
.1571
.1625
.1625
,16?5
.1625
.1625
.1625
0*.1250E-oa 0.2000F-04 0.2750E-ft«
0.4310 0.4305 0.4304
0.6152 0.6149 0.6149
0'.7164 0.7162 0.7KS?
0.7776 0.7775 0.777*
0.8172 0.8171 0.8171
O'.844l 4.8442 0.8442
0.8636 0.8635 0.8635
0.8779 0.8779 0.8779
0.8888 0.8888 0.8M8
0.8974 0.8973 0.8973
0.9202 0.0201 0.9201
0.9343 0.9312 0.9142
0'.9439 0.9438 0.9438
0.9508 0,9507 0,9507
0.9560 0.9559 0.9559
0.3500E»05
0.4409
0.6286
0.7324
0.7965
0.8197
0.8709
0.8951
0.91JO
0.9324
0.9484
0.9749
0.9970
1.0133
1.0859
1.036?
.0448
.0522
.0588
.0646
.0698
.0766
.0827
.0881
.0881
.0881
,OM!
.0881
.0881
.0881
.0881
0.4500E»o5
0,0174
0.6211
0,7251
0.7871
0.8282
0.8570
0,87*4
0.8950
0.9085
0.9199
0.9431
0.9599
0.9736
0.9B5B
0.9969
.0059
.0114
.0199
.0254
.010«
.0369
,0426
.0476
1.0U76
1,0476
1.0476
1.0476
1.0476
1.0U76
1.0476
-------
16 0.9727 0,9617 0.9601 0.9600 0.9600
17 0.9777 0.961? 0,9601 0.9600 0.9600
18 0,9823 0.9617 0.9601 0.9600 0.9600
19 0.9833 0,96t7 0,9601 0.9600 0.9600
20 0,9823 0.9617 0.9601 0,9600 0.9600
21 0,9883 0,9691 0,9663 0,9662 0,9662
22 0,9883 0,9681 0,9663 0.9662 0.9662
23 0.9883 0,9681 0.9663 0,9662 0.9662
2U 0,9883 0.9681 0.9663 0.9662 0.9662
25 0.9883 0,9681 0.9663 0.9662 0.9662
26 0.9883 0.9681 0.9663 0.9662 0.9662
27 0,9683 0.9681 0.9663 0.9662 0.9662
28 0,9883 0.9661 0.9663 0,9662 0.9662
29 0,9883 0.9681 0,9663 0.9662 0,9662
30 0.9863 0.9681 0.9663 0.9662 0.9662
to
CO
-------
4CCUMUUTEO ON P»RTK.UE SIZFS IN EiC" TNCRF."FNT
INCREMENT CM*PSE FOP lupicmn P»RTICIF SIZES
oo
to
1
2
3
a
5
6
7
8
«
10
11
12
13
ia
15
16
17
18
19
20
21
22
21
ft
25
26
27
28
29
10
0.2000E-06
.98670E.18
.13578E-17
,16ae8E-l7
,tB6tt6E-l7
.20778E-17
.22357E-17
.236B5E-17
.2«826e«l7
.2S82IE-17
.26700E-17
.27978E-17
.29833E-17
,?9939E-17
.30729E-17
.31B28E-17
.32055E-17
.S2622E-17
.SJ139E-17
.33614E-17
.S005aE-17
.3a588E-17
.350616-17
.J5505E-17
,359t6E-17
.S6299E-17
.36658E>17
.36995E-17
.ST313E-17
.176HE-17
.S7900E-17
0.4800E-06
0.28569E-17
fl.alP2flE.17
0.50362E-17
0.58155E-17
0.63772E-17
8.»809aE-17
0.71589E-17
0,7a50«E.J7
0.77005E-17
0.79178E-17
0.82ai2E-17
0.85016E.17
0.87262E-17
0,B9J72E-17
0,90846E>17
0.92336E.17
0.9S676E-17
0.94892E-17
0.9600aE-17
0.97029F-17
0.98265E-17
0.99391E-17
0.100U3E-U
fl.lfllS8E.16
0.10227E-16
0,10310E-16
0.10530E.16
0.10595E-16
0.109fcJE-l».
0.17518E-1*
0.1R297E-1*
0.19915E-1*.
0.20619E>l14i
0.23635E-16
0.23886E»U
0.2aS23E-l*
0.2fl5l5E-U
0.2a692E.i6
0.2S013E.16
0.25159E-1*
0.25296E>16
0.25a26F.16
8.25IOOE-1«>
0.2983SE.16
0.3610RE-1*
0.ai216E.16
0.«2225F«16
8,aj070f.16
0,a7IUOE-16
0.a777SE-16
8,aP677E-t6
0.500a7E-lfc
0.5050fcE.lfc
0.50920E-16
8.51297E-16
0,5t6aaE-16
O.S2262E'16
8,52539f-16
0,52800E>16
0.52808E.16
0,5906 JF.-lfc
0.77779E-16
0.80013F-16
0.83297E-16
6.85825E-16
0.87732F-16
0.909Jpf.i6
0,91fclaF-16
0.92S59E.16
Op«4820F-lfc
0.96?iaF>16
8,96«12E-16
(I 9«l2aF-16
0.986S8E.16
0.99152E-16
0.99152F-16
8.99152E-16
0.99J52E-16
0.2500F-OS
O.M762E-1*.
0.1197nE-!5
0. J50PF..05
0.16192F-1S
0.16«'>7E-15
0.17a92E-15
O.J9272F-15
0.199S3F-15
0.20235F-15
«.20aa7F-15
0.20620E-15
fl,20789E-15
0.2093U-15
0.21858F-15
0.21173E-1S
0.2132JE-15
6.21855E-15
0.21S7«E-15
0.21683F-15
8.21783E-15
n,21783E-l5
8.21783E-15
0.217S3E-15
0.21783F-15
0.21783E-15
0.30765F.-15
0.-<19lflE-l?
0.32796E-1S
0.5a7a9E-lS
0.3S7J9E-15
0.36531E.J5
0.37965E-1S
0.3A261('tt
0.39006E-15
0.39J97S.15
0.39S67E-15
0.39867E-15
0,39867E-iS
0.39867E.15
9.39867E-15
O.J7703E-15
O.a3fl72t.l5
n.50it3E-lS
O.S31U5E-15
0,5al50F-15
•IS
0.58071F.-1S
0.5H90UF.15
0.hl3l«E.15
0.61704E-15
0.fc2739E-lS
0.63043E.1S
4.63385E'!5
0.633B5E-15
1 0.46706E-15
2 0.6«S2«E>!5
3 0.77385E-15
a 8.85967E-15
9 0.88251E.J5
6 0.91206E.15
7 0.933a«E.15
8 0.9fl953E.l5
10
II
12
13
ia
16 I
17 0.105(>8E-ia
is o.iossSE-ja
19 0.1P558E-ia
0.97209E-15
0.102!6F-|fl
0.6500E-05
0.93203E-15
0.13267E.14
B,l5a63E.ld
n.!6760E-ia
0.16217F-14
8.l9183E.ltt
fl.l9369f.la
0.19860E-H
P.20l65F-la
0.20527E-H
0.20735F.U
0.2073SE-14
fl.20735E.la
fl.20735F.ja
0.1250E-OU
0.20091E.14
0.28676E>1«
0.33392E-ta
0.36?a3E»ia
0.38069E>ia
fl.3«35IE«M
0,ao921F«ia
o.ajasnE'ia
0.«l827E«ia
0.a«7«9E-ia
0.2000E-OU
0.5l358E-ia
0,73361E>ta
O.SSattSE'ia
0.92750E-ia
0.97a79E«l«
0.10fl7tr-l3
O.loa73£-13
0.10603E>13
0.10705E-13
0.10977E-1S
0.1114SF-13
0.1
0.11U53E-13
0.11«51E-13
0.11U53E-13
0.2750E-04
0,97fl67F-l«
0.13868E-1J
0.16153F-13
0.18a2«E»13
0.19039F-1J
0.20237E.13
0,2fl75?F-i3
0.21070F.H
fl.21286F.13
0,2l550E.iJ
0.2165JE«13
0.21»51F"13
0.2I651F-13
-------
20
21
22
23
2a
25
26
27
28
29
30
0.10558E-14
0.10623E-1«
0.10623E-1U
0.10623E-1U
0.2073SE-10
0.10623E-1U
0.10623E-JU
0.10623E-i
-------
00
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NONJOEALITIES USING SET NO'. 1 Of CORRECTION
SIZE CCF
2.000E-07 2.123
4.000E-07 1.530
7.000E-07 1.297
1P100E-06 1,188
1,600E-06 1.130
2.500E-06
3,300E«06
4.500E-06
6,OOOE.06
8,500E«06
1,250E-05
2,OOOE«05
2.750E-05
.083
.059
.046
.035
.024
.017
.010
.008
INLPT X
o'.033
0,253
0,903
0,815
1,520
3.524
1,652
1,652
1,982
3,304
4,846
12,115
67.401
OUTLET X
0'.7203
7'.4214
23.1836
15,2173
19.2314
23'.2«589
6'.0486
3' 7049
1,0448
0,1301
0.0022
0^0055
0.0309
COR. OUTLET X
0,4536
4.5547
14.5134
10,24t>6
13,8084
19,1755
6,9775
6.6554
5,8876
6,2833
5.0000
4.0677
2.3772
NO-RAP EFF,
95,2710
93.6452
94.4380
95.9550
97.2590
98.5701
99.2068
99.5141
99.8858
99.9915
99.9999
99,9999
99.9999
NO-RAP h
6'. 398
5.778
6,058
6,726
7,541
8.906
10.101
11.169
14'.205
19,645
32.033
30,924
69.820
NO-RAP p
4.7290
6.3548
5.5620
4.0450
2.7U10
1.4299
0.7932
0.4859
0.11 "2
0,0085
0.0001
0.0001
0.0001
COR. EFF.
95.0353
93.4839
94.1826
95.4494
96.7119
98,0305
98.4713
98.5418
98.9248
99.3117
99.6265
99.8785
99.9872
COR, *
6.296
5.726
.964
.479
.160
.234
.766
.865
.504
10.439
11.721
14.075
18.799
COR. P
U.9647
6.5161
5.8174
4.5506
3.2*81
1.9695
1.5287
1.4582
1.0752
0.6883
0.3735
0.1215
0.0128
EFFICIENCY . STATED « 99'.32
COMPUTED " 99.3273
CONVERGENCE OBTAINED
ADJUSTED NO*RAP EFF. » 99.T834
MHO OF INLET SIZE DISTRIBUTION • 4.465E*oi
IICMAP OF INLET SIZE DISTRIBUTION • 3.122E+00
LOG-NORMAL GOODNESS OF FIT • 0,984
HMD OF EFFLUENT UNDER NO-RAP CONDITIONS s 1.314E*00
SIGMAP OF EFFLUENT UNDER NO-RAP CONDITIONS s 1.B91E+00
LOG-NORMAL GOODNESS OF FIT « 0.997
PRECIPITATION RATE PARAMETER UNDER NO-RAP CONDITIONS 8 12.862
SISNAG* O'.OOO WITH 0.000 SNEAKAGE OVER
NTEMP a 1
RMMO a 6.00
RSIGMA • 2.50
CORR'. EFF. • 99'.638l
CORRECTED HMD OF EFFLUENT a 2.667E+00
CORRECTED SIGMAP OF EFFLUENT t 2.796E+00
LOG-NORMAL GOODNESS OF FIT » o.98«
CORRECTED PRECIPITATION RATE PARAMETER s 11.79
3.000 STAGES
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS LOADINGS
to
00
(Jl
IDEAL UNADJUSTED
"16. VEL.(CM/SCO
2,7S9E*00
3,274E*00
o,osi£*oo
S,ll6f*00
7,013E*00
I,lt7F*81
l.«20E*01
1,965E*81
3,203E»01
6.982C*01
IOEAL UNADJUSTED
EFFICIENCV(«)
7.151E»01
7.201E+81
7.902E+01
,647E+Oi
1.000E»82
1.000E*82
i.oeee»o2
NO-RAP
DM/oj.OGD(MG/OSCM)
2,3?«E«01
5.1fl9E*80
1,598E*81
,338Et80
.895E+80
,Z?5E*80
.2JOE-01
,0?2E-83
.250E-02
SAPPING PUFF
1.158E-02
.386E-01
.«18F-Oi
l.n3lE+Ol
NO.RAP+RAP PUFF
DH/DLOGO(MG/03CM)
2.1"OE»01
5. ?8oE»00
1 . "*2Ft01
1.650F»Ot
2.155E+01
2.SJ9E+81
1 , SOOEf 01
1.U69E+81
l.|53E«01
9.765F*88
7.hl6E+00
1.622E+00
8.j87f*88
RAPPING PUFF
DISTRIBUTION(X)
5.350E-02
2.806E-61
l.S86E*00
2.83aE«00
S.728E+00
1.308E+01
8,358E*06
1.105E+01
1 ,310E + ni
1 ,5«5£ + 01
1,2«5E»01
1.013E*01
5,9186*08
PARTICLE
OIAM.(M)
2.008E»87
U.OOOE-07
7, OOOE»07
1.100E-06
1.600E.06
2.500E-06
3.508E.86
O.SOOE-06
».OOOE»06
R(^08E»06
1.750C-OS
2.480E-OS
2.750E-05
-------
SUMMARY TABlF OF ESP OPERATING
PARAMETERS AND PERFORMANCE
DAT* SET NUMBER 1
00
ESP PERFORMANCEl
EFFICIENCY « 99.6381 X
ELECTRICAL CONDITIONS!
SIZE OISTRIBUTIONSl
NONIDEAL PARAMETERS!
AVC. APPLIED VOLTAGE « fl.l72E*0« V
AVS. CURRENT DENSITY • 17.12 NA/CM**2
RESISTIVITY • S.OOOE*IO OHM.CM
INLET MMD : 4.465E*01 UM INLF.T SI6MAP • 5.1?ZE*00
OUTLET MMO • 2.667E*00 U* OUTLET SIGMAP « ?.796E+00
GAS SNEAKAGE FRACTION • 0.00 /SECTION CAS VELOCITY SIGMAG • 0.00
RAPPING MMD • fe.OOOE + 00 ()» RAPPING SIGMAP > 2.500E + 00
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NONIDEALITIES USING SET NO. 2 OF CORRECTION PARAMETERS
SIZE
2.000E-07
4,OOOE-07
7,OOOE-07
1.100E-06
1.600E-06
2.500E-06
3.500C-06
fl,500E-06
6,OOOE-06
6.SOOE-06
1.250E.05
2,OOOE-05
2.750F.05
CCF
2.123
.530
.297
.186
.130
.083
.059
.006
.035
.020
.017
,010
1.006
INLET X
0.033
0.253
0,903
0,615
1.520
3,580
1.652
1,652
1.962
3.304
4,8«6
12,115
67.401
OUTLET %
0.0012
4'3398
10.3436
10.5249
15.4375
20'.9331
910291
7,6160
5.2527
OJ6493
2,8772
0.2936
0.0620
COR, OUTLET
0.3266
3.1396
10,5717
B,2518
12.5663
21.0337
8.6301
8,7766
7.5790
7,«fl95
5,712«i
3,2058
1.7527
X NO-RAP
91'.8099
89'.5041
90.3176
92,1262
93.8092
95.6873
96,6685
97,1160
96.3646
99.1422
99.6381
99.9852
099.9994
NO-RAP t
5.257
0.734
4.895
5,330
5.833
6.591
7,132
7,035
8.650
9.977
11.767
18,093
69.620
NQ-PAP P
8.1501
10.«559
9.6824
7,8718
6.1906
tt.3127
3.3315
2.6640
1.6150
0.6578
0.3619
0.0106
0,0006
CO".
91.0343
89.2596
89.6674
91.2369
92,8007
94.7359
95,3717
95.0019
96.6904
97.9U38
98.9796
99.7710
99,9775
COR, >
5.152
a.678
0.800
5.105
5,530
6.173
6,003
6,«57
7.106
8.144
9.610
12.706
17,610
COR. P
8.5657
10.7402
10.1326
8.7631
7.1553
5.2641
4.6*83
0.5981
3,3096
2.0562
1.0202
0.229C
0,0225
to
00
EFFICIENCY - STATED • 99.32
COMPUTER = 99,3273
CONVERGENCE 08TAINED
ADJUSTED NO.R»P EFF, • «9'.3904
MHO OF INLET SIZE OlSTftlSUTXON • 0.465E*01
IICMAP OF INLET SIZE DISTRIBUTION • 5.122E«00
LOG-NORMAL GOODNESS OF FIT • 0.960
MHO OF EFFLUENT UNDER NO-RAP CONDITIONS • 2.066E«00
8IGHAP OF EFFLUENT UNDER NO-RAP CONDITIONS « 2.253E*00
LOO-NORMAL GOODNESS OF FIT • 0.997
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS * 10.690
o.25o
NTEMP • 1
RMMO • 6.00
R8IGMA • 2.50
COM. EFF. • 99.1345
CORRECTED HMO OF EFFLUENT • 2.927E400
CORRECTED SIGMAP OF EFFLUENT « 2.596F«00
L06«NORMAL GOODNESS OF FTT « 0.996
CORRECTED PRECIPITATION RATE PARAMETFP >
0,100 SNEAKAGE OVER 3.000 STAGES
9.96
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET HASS LOADINGS
to
oo
00
IDEAL UNADJUSTED
MIG. VEL*. (CM/SEC)
2,633000
2.739C+00
3.271E+00
8,081E+00
5.116E+00
7,013E»00
9,093E*00
l.«20E*01
l,965Etfll
S.203E+01
5.092Et01
fc.962Et01
IDEAL UNADJUSTED
EFF1CIENCYC*)
7.151C+81
7,2916*01
9.B69Et01
9.999E*01
1,OOOE*92
1.000E*fl2
r.OOOE + 02
NO-RAP
LOCD(M
^oosE-o
8.«T2E*00
5.079E+01
5.922E*01
2,905E»01
1,733E*01
5'.615E-01
3.533E-61
RAPPING
2.303E-01
1.I32E»00
3.?32E+00
6.320E+00
,l?OE*Ot
•527EtOJ
.727Ef01
.«17E»01
,700E*01
6.112E+00
NO«RAP+RAP PUFF
0M/PLOGD(MG/DSCM>
a.209E-01
8.702F*00
2.5«7E*01
3.l77EtOJ
a.689E*01
6.199E+01
5.aasE+oi
0.<>32E + 01
3.55or+01
2.917E*01
2.080E+01
6>70aEtOO
l.«5«€+01
RAPPING PUFF
DISTRIBUT10N(X5
S.350E-02
2,AOfcE-01
1.S86E+00
2,83ttE+00
5.72nE+00
1.308E401
B.35SE+00
1,105E»01
1.319F+01
J ,515E + 01
1.205E+01
i.OlSE+01
5.918E+00
PARTICLE
D1AM.(«)
2.000E-07
a.OOOE*07
7.800E.07
1.100E«06
1.600E.06
2.500E.06
3.SOOE-06
tt.SOOE-Ob
6.000E-06
8.300E-06
1.250E-05
2.000E.05
2.750E.05
-------
10
00
V£>
A*******************************************************************************************************************
SUMMARY TABLE OF ESP OPERATING
AND PERFORMANCE
DATA SET NUMBER 2
ESP PERFORMANCEl EFFICIENCY •
8C» •
M**2/(M««J/«c)
ELECTRICAL CONDITIONS!
SIZE OISTRIBUTION8I
NONIOEAL
AVC. APPLIED VOLTAGE •
-------
APPENDIX N
OUTPUT DATA FOR EXAMPLE 4 (REVISION 1)
290
-------
A************************************
E.P.A. ESP MO&ei
T.E.R.l.-R.T.P. AND SO.R.l'.
REVISION I,JAN. j, 1978
*************************************
PRINTOUT Or INPUT DATA FOP DATA SET
DATA OH CARD NUMBER i
NtNOPT • 10 NDATA • 1
DATA ON CARD NUMBER 2
rUU«SC*l.e. COLO-SIDE E8P| PL AWT A| SCA«2«SFT2/1000ACFM| J»15.9UA/FT2
DATA ON CARD NUMBER 3
NEST • i MOIST • i NVI • i NX • to NV • 10 NITER • 3 NCALC • o NRAPO * i NEFP • i NTCHP • i NONID • 2
DATA ON CARD
NN • 10 Nl/HINC • ?0
DATA ON CARD NUMBFR 5
OL • 1.46600 CRN/ACF PL • 27.0000 FT ETtO • 9«.6000n * OP • 2270.00 KG/M**3 EPS • )'. OOOE + 02
VRATIO • 1.2000 US * 0.000220 M«»2/V-SFC FPATH • 1.0000 C»n • 1500000. V/H RHOCR8 • S.flOEtlO
DATA ON CARD NUMBER 6
A«NUC«C i) • ".on Ajiccvr tj • o.oo AZwumf n » J.n
A|NUCK( 2) • 0.10 AjTGGYf 2) » 0.25 A7MiM«( it • 1.0
DATA r»
-------
ENDPTc
t) • 0.100 UN ENDPTf 2) • 0.300 UH ENDPTC 1) • o.SoO UH ENOPTC a) • 0.400 UM ENDF-T( 5) • I.SOB UK
6) • 1,^00 »l" ENDPTC 7) f 5,100 UM ENDPTC 8) • 3.900 I'M ENDPTf 9) • 5,100 UM EMpPTUO) • 6,900 UM
OAT* ON CARD NUMBER s
ENDPTC11) • 10.100 UM ENDPTC12) • 10.000 UH ENDPTU3) • 25.100 UM ENDPTC14J • 29.900 UM
DATA ON CARD NUMBER *
PRCUC 1) • 0.0000 X PRCUC 2) • 0.0330 X PRCUC 3) • 0.2860 X PRCUC 4) • 1.1890 X PRCUt 5) • 2.0000 X
PRCUC 6) • 3.5240 X P"CU( 7) • 7.0080 X PRCUC S) • 6.7000 X PRCUC 9) • 10.3520 t PRCUCtO) • 12.3300 I
DATA ON CARD NUMBER 10
PRCUC11) • 15.63*0 X PRCUM2) • ?0.4e«0 X PRCIU13) • 32.5990 X PRCU(ia) • 100,0000 X
DATA ON CARD NUMBER U
^ NUMIEC • 3 LSECTC 1) • 10 L8ECT( 2) • 10 LSECTC 3) • 10
to
DATA ON CARD NUMAER 12
A8C 1) • 2.6«60E*0« FT**2 V08C 1] • «.0600E»Ofl V TC3C 1) • 2.7300E-01 A HLSC 1) • 1.5720E*04 fl
AC8C 1) • B.2500EiQ2 IN BBC t) • 5.500CE*00 IN NMSf 1) • t.200or+01
DATA ON CARD NUMBER 13
SV8C 1) • 3.6250E+00 IN VGS( 1) • 3.?724F«05 FT**3/HIN VCASSC 1) • ".1000E+00 FT/SEC UMPSC 1) • J.l5n8E*02 F
P8C 1) • l.OOOOE*00 ATM VI88C 1) « 2.2900E-05 KG/M-SEC LJNCSC 1) • 9.000flE»01 FT
DATA ON CARD NUMBER 14
ASC 2) • ?.61feOE+Oa FT**2 VOS( 2) • a.?innF+0« V TCSC 2) • 4.33nOE«01 A WLS( 2) • l.ST20E+Oa FT
AC8C ?) • fl.25nOF.02 IN 83( 21 • 5.500CE+00 IN NHSC 2) « 1.2flOOF>01
DATA ON CARD
-------
ro
vo
OJ
SVS( 2) • ).f>2 « i.ennor+oo *TH vrssr ?) « ?.?90ftr-05 «G/M«SEC LINCSC 2> • 9.ooooe-ot ft
0»T» ON C»Rf> NUMBER 16
*8t J) • 2.6«bO£»00 rT**2 VOS( J) a fl.?«SOE*04 V TCS( 3) • S.SSOOr-01 A MLS( I) • 1.5720E+04 FT
ACIt S) • fl.?500E.02 IN BSf S) • S.5000C«00 IN NkSf 3) • l.?OOOE*01
DATA ON C»»0 NUHRfR 17
3»3f 5) • S.*250F*00 IN VC3( I) • 5.27?aFf05 FT**3/MTN Vc*83( 3) • «.inoot+00 FT/SEC TE^^8( 3) • 3.1500E+02 F
1) • J.OftOOE*00 ATM VI88( 3) • 2.2900F-OS KG/M>SEC UINC8C 31 « 9.0000E-01 FT
-------
INCREMENT*!. ANALYSTS OF PHECIPtTATOR PERFORMANCE
FULL-SCALE.COLO-SinE ESPl PLANT *» SCA»243FT?/1000ACFMfJ«l5.9UA/FT2
CALCULATION IS IN SECTION NQ°. • 1 AND THE SECTION LENGTH IS • 2.7450 M
COLLECTION ARE* » 2.461E+03 M?
WIRE TO PLATE • 1.39TE-01 M
CURRENT/M • 5.694E-OS AMP/M
1/2 WIRE TO WIRE « 9.20«E«0? M
TEMPERATURE • 430.000 K
ION MOBILITY • 3.463E-04 Mg/VOLT-SEC
DUST WEIGHT • 6.9fe9E-01 KG/SEC
APPLIED VOLTAGE • 4.060F. + 04 VOLTS
CORONA WIRE RADIUS • 2.096E-03 M
CURRENT DENSITY • 1.109E-04 AMP/MZ
GAS PLOW RATE • 1.548E*n2 M3/8EC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • 5.335E+0? M/SEC
LFN6TH INCR. "0.27450000 M
TOTAL CURRENT • 2.730E-01 AMPS
CORONA WIRE LENGTH • 4.795E+03 M
DEPOSIT 6 FIELD • 5.54TE+04 VOLT/M
GAS VELOCITY • i.250E*oo M/SF.C
VISCOSITY • 2.290E«os KG/M.SEC
PART. PATH PARAM. • 8.246E-OB H
INPUT EFF./INCR. « 16.61
\O
ROVRI
3.1566
2.5167
2.0587
1.7622
1.5647
,4261
.3250
.2494
.1921
.1484
ERAVG
2.906E+OS
2.906E+05
2'.906E + 05
2,906E+0«
2.906E+05
2.906E+05
2.906E+05
2.906E*05
2,906Ef05
2.906E+05
EPLT
2.0924E*05
1,969JE+05
1 ,8644E*05
l,S269Et05
t.7873E*85
1.7588E+05
1 .7376E+05
1.7218Ef05
l,7096Et05
1.7002E+05
AFID
2.1B25E+12
2.7374E+12
3.3464E«12
3.9093E+12
4.4030E+12
4.8306E+12
5.1994C412
5.5139E+12
5.7786E+12
5. 99906+12
CMCO
11,1
11,
11.1
11,1
11.
1 1.
J J
1 1
11.
HMD
2,29E-05
L 2.27E-05
2.22E-05
2,13E-05
1,91E-05
1.20E-05
7.46E-06
5.13E-06
3,90E-06
3.19E-06
WEIGHT
1.523E-03
1 .195E-03
6.B78F-04
3.6S3E-04
1.966E-04
1.134E-04
7.195E-05
5.023E-05
S.792E-05
3.025E-05
OUST LAYER
5.750E-02 <
4.511E-02
2.596E-02
1.379E-01
7.426E-03
4.J82E-03
2.715E-03
1.896E-03 i
1.431E-03 i
1.142E-03 i
J(PART)
I.82E-07
.23E-07
.22E-07
.11E-07
.3BE-07
.93E-07
.64F-07
>.42E-07
5.25E-07
•.10E-07
J(ION)
,10E«Ofl
,10E>04
.lOE.oa
.1 !E*n4
,11E»04
, 1 1E«04
.11E-04
,I1E»04
.tlE-04
1.11E-04
NO,
CALCULATION IS IN SECTION NO. • 2 AND THE SECTION LENGTH IS • 2.7050 M
COLLECTION AREA • 2.461E»03 MJ
MIRE TO PLATE • 1.397E-01 M
CURRENT/M • 9.031E-05 AMP/M
1/2 HIRE TO WIRE • «.20§E-oa *
TEMPERATURE • «30.000 K
ION MOBILITY • 3.463E-04 M2/VOLT-SEC
DUST WEIGHT • 6.969E»01 KG/SEC
APPLIED VOLTAGE • 4.210E+04 VOLTS
CORONA MIRE RADIUS • 2.096E-OS M
CURRENT DENSITY • I.T60F-04 AMP/M2
GAS FLOW RATE » 1.548E+02 M3/SEC
PRESSURE • 1.000 ATM
*EAN THERMAL SPEED • 5.335E«02 M/SEC
LENGTH INCR. BO.27450000 M
10
TOTAL CURRENT • U.330E-01
CORONA WIRE LENGTH • 4.795E+03 M
DEPOSIT E FIELD • e'.798E+oa VOLT/M
GAS VELOCITY • i.25oE»oo M/SEC
VISCOSITY • 2.290E-05 KG/M.SEC
PART. PATH PARAM. • e.2a6E-o« M
INPUT EF^F./INCR. « 16,81
ROVRI
1.0750
1.0577
1.0443
.0341
.0263
.0202
.0156
.0120
.0093 3
,0072 3
ERAVG
.014E+05
.014E+05
.014E+05
.0 14F+05
,014E*05
.01UF+05
.OlflE+05
,01«E+05
,M4E*(!5
.OlaE+05
EPLT
.8591E+05
.8536E+05 <
,8495Et05
.8Ufc3E+OS
,B463E«05
,R4is3E4n5
.8463F.+Q5
,8463E*05
8463Et05
.«463E*05
AFIR CMCD
5.8ni8E+12 17.
».9fe?oE+ia 17.
,0090E*t3 17.
.Ol9of*13 17,
,0268E*13 17,
.0328F+J3 17,
,0375Efl3 17.
.0412F.4J3 17^
,Oa«oE+ti 17,
,046?E+IJ 17.
MMD WEIGHT DUST LAYER JCPARTJ
t> 2,68E-06 2.766F-05 1.044E-03 2.22F-07
(i 2,41E-06 2.324F.-05 B.770E-04 ?.10f«07
2.28E-06 1.981E-05 7.476E-04 1.98E-07
2'.17E-06 1.707E»n5 6.441E-04 1.R6E-07
2,08f.06 1.4B5F-05 5.604E-04 1.74E-07
2.00E-06 t.30flE-05 4.905E»04 1.64E-07
1.93E-06 1.144E-05 4,317E«0« 1.53E«07
1.B7F-06 l.OMF-05 3.B14E-04 1.44E-07
1,80E-06 8.9«?E»06 3.382E-04 1.35F-07
1.74E-06 7.47QF-06 3.006C-04 1.26E-07
J(TON)
I .76E-04
.76E-04
.76E-04
.76E-04
.76E-04
.76E-04
,76E>04
,76f-0«
, 76E"1«
.T6F-04
,00'f i.0l«t+n5 .n«ejt»
CALCULATTON Is IN SECTION NO
• 3 AND THE SECTION LENGTH is • 2.7450 M
INCR. NO.
11
12
13
14
15
16
17
16
19
?0
-------
COLLECTION A»EA * 2.461E+03 MJ
HIRE TO PLATE • i'.397E-oi M
CURRENT/M • l.lfcflF.OU AMP/M
1/2 MIRE TO MIRE • 9.?o«E«o2 M
TEMPERATURE • 430.000 *
ION MOBILITY « S.fl63E-0« M2/VOLT-9EC
DUST WEIGHT « 6.969E-oi KG/SEC
APPLIFD VOLTAGE a 4,245E*0« VOLTS
CORONA WIRE RADIUS • 2.096E-03 M
CURRENT DENSITY • 2.268F-04 AMP/M2
GAS FLOW RATE » 1.5U8E+02 MS/SEC
PRESSURE • 1,000 ATM
MEAN THERMAL SPEED » 5.335E+02 M/SEC
LENGTH INCR. 10.27490000 M
TOTAL CURRENT • 5.580E-01 AMPS
CORONA WIRE LENGTH • fl,795E*03 M
DEPOSIT E FIELD • 1.134E+05 VOLT/M
GAS VELOCITY • i,Z5oE*oo M/SEC
VISCOSITY • %2.290E-os KG/M.SEC
PART. PATH PARAM'. • 8'.246E-oe M
INPUT EFF./INCR, • 16,61
ROVRI ERAVG EPLT AFIO
I.ft043 3.039E*05
,0033 3.039F+05
,0026
,0020
,0015
.0012 '
,0009
.0007
1,0005
1,0004
,039E*05
.039E+05
.039F+05
.039E+05
,039F*05
,039E*05
.039E+05
.039E+05
.9360E+OS 1.3409C+13
.93SOF«05
.9360E+05
,93*OE*05
.9360E+05
.9360E+05
.9360E+05
.0360E+05
.3423F. + 1 3
.3433E+13
,3«aiE*13
.3447E+13
.34526+13
.3455F+13
,3458E*13
,9360E*05 1.3460E+13
.9360E+05 1.3462E+13
CMCD
22'. 7
22,7
22^7
22>
22,7
22; 7
22j7
22.7
MMO WEIGHT OUST LAYER
1,69E-06 7.U51E-06 2.813E-Q4
1.63E-06 6.633F-06 2.503E-04
1,57E-06 5.916E-06 ?,?3JE-0«
1.5JE-06
1,47E«06
1,43E-0*
1.38E-06
1,34E-06
1,30E-06
1.26E-06
.287E-06
.727E-06
.235E-06
.798F-06
.412E-06
.068E-06
.995E-04
,784E»04
.598E-04
.433E-04
.288E-04
,158E>04
.763E-06 1.041E-04
J(PART)
1.24E-07
1.16E-07
1.09C.07
1.02E-07
9.49E-08
8.H6E-08
8.27E-08
7.72E«08
7.19E-08
6.71E-08
J(ION)
2.27E-04
J.27E-OU
2,27E»OU
*,27E-oa
2.27E-04
2.27E-04
2.27E-04
2.27E-04
2.27E-04
2.27E.O*
INCR. NO,
21
22
23
24
25
26
27
28
29
30
,60
UNCORRECTFO COMPUTED EFFICIENCY • 99,37
NJ
(O
cn
INCREMENTAL ANALYSIS OF PRECIPITATOR PERFORMANCE
rULL-8CALEiCOLO-SIDE C8P| PLANT A| 8CA«24jrT2/1000ACFM|J«15.9UA/FT2
CALCULATION IS IN SECTION NO'. • 1 AND THE SECTION LENGTH IS • 2.7450 M
COLLECTION AREA • 2'.461E + 03 H;
MIKC TO PLATE • i'.397E-oi M
CURRFNT/M • 5.694E-05 AMP/M
1/2 HIRE TO WIRE • 4.208E-0? M
TEMPERATURE • 430.000 K
ION MOBILITY • 3.46JE-04 M2/VOLT-8EC
OUST HEIGHT • 6.969E-oi KG/SEC
APPIIRD VOLTAGE • 4.060Et04 VOLTS
CORONA HIRE RADIUS • 2.096E-03 M
CURRENT DENSITY • 1.109F-04 AMP/M2
GAS FLOW RATE • l.S48E*02 H3/8EC
PRESSURE • 1,000 ATM
MEAN THERMAL SPEED • 5.335F+02 M/SEC
LENGTH INCR. •0.2745000A M
TOTAL CURRENT • 2.730E-01
CORONA WIRE LENGTH • 4.79SE+03 M
DEPOSIT E FIELD • S.547E+04 VOLT/M
GAS VELOCITY • i.25or*oo M/SEC
VISCOSITY • 2.2?oe-os KG/M.SEC
PART. PATH PARAM. • 8'.2fl*F.o« M
INPUT EFF./INC*. • 15,55
ROVRI
2.9945
2.«206
2.0061
.7356
,5533
.423*
.3282
.1557
.2000
1.1568
ERAVG EPLT
2.906E*05 2.0637E+05
2.906F«0S
2 . 906E^ 05
2 . 906E 4 05
2.9n6F*05
2.906E«05
?.906E»05
2.966F+05
.9518E+05
,8744E»05
,8216E*05
.T«49E*05
,758«E*05
,73*4E»05
.72328*05
2,90fcE»n5 l.7llSE*n5
?.90bF»OS 1.7021E»05
AFIO
?.J006F*12
2!«ufcOE»ia
3.«340F*12
3.9690E**1 2
4.4353E»12
4.8384E*12
9, 1 «69f »12
5.4A63E»12
5.7fll?E» 1 2
5.9556E*!?
C»«CD
11,1
11,1
11,1
11.1
11.1
11,1
* 1 f *
11.1
11.1
11.1
MMO
2.29E-05
2,26E-05
2,22E-05
2.13E-05
1,89£-05
1.18E-05
7 38E-06
5,08E-06
3,8ME>06
3.18E-06
WEIGHT
1.542F-03
1.193F-03
6.816E»04
3.610F-04
1 .944E-04
1.122E-04
7.128F-05
4.985F.05
3.768F-05
3.0096-05
DUST LAYER
5.B21E-02
4.502E-02
2.572E-02
1.362E-02
7.335E-03
4.234E-03
2.690E-03
1.B81E-03
1.422E-03
1.136E-03
JfPART) JCION)
5.D3E-07 l,10E-Ofl
6.34F-07
5.25E-07
4.13E«07
3.39E«07
2.93E-07
2.64E-07
2.42E-07
2.25F.07
2.IOE-07
.10E-A4
.10E-04
.11E-04
, 1 1E-01
.iie-04
.tlE-04
.HE-na
.1 1E-04
.11E-04
CALCULATION Is IN SFCTION NO. • ? AND THE SETTION LENGTH 18 • 2.7450 M
COLLECTION »RF» • 2.«fclE»03
HIRE TO PLATE • r.397e-oi M
D VOLTAGE • 4.210E»04 VQLT8
CORONA WIRE RADIUS • 2.096F>03 M
INCR. NO,
1
2
3
4
5
6
7
B
9
10
TOTAL CURRENT • 4.330E>01
CORONA WIRE LENGTH • «.795C»03 M
-------
CURRENT/* 8 9.031F«ftS AMP/M
1/2 WIRE TO WIRE s 9.20BE-02 M
TEMPERATURE » aSO.OOO K
ION MOBILITY > J.abSE-Ofl Mg/VOLT-SEC
OUST WEIGHT « 6.969F-01 KC/SEC
CURRENT DENSITY * 1.760E-04 AHP/M?
GA$ flOW RATE • 1,54SE*02 «3/8EC
PRESSURE • 1.000 ATM
MEAN THERMAL SPFEO • 5.335F*02 M/SEC
LENGTH INCR. «0.27850000 M
DEPOSIT E FIELD » B.79BE*04 VOLT/H
GAS VELOCITY • 1,2506*00 M/SEC
VISCOSITY • 2.290E-05 KG/M.SEC
PART. PATH PAR**. • 8.286E-08 M
INPUT EFF./INCR. « is.55
ROVRX
ERAVG
EPLT
AFIO
HMO
WEIGHT
OUST LAYER JtPART)
1.0805 3.0iaE+05 J.8607E+05
1.0628 3.018E+05 1.8553E+OS
.0890 3.0iaE»05 1.8510E+05
.0383 3.018E+05 1.S876E+05
.02*9
.0230
.0183
.0103
.0112
.0088
,010Ef05
.OlaEfOS
.018E4-05
.018E+05
,018E»05
.018E»05
.8876E+05
.J876E+05
.B876E+05
,88766+05
.8876E+05
.8876E+ftS
9.
9.
1.
1.
1.
1.
1.
1.
1.
1.
7525E+1?
9ia9E+l2
Ona5E+!3
oia<>f+n
0231E+15
0296E+13
01««E+1J
OJ8SE+13
OU20E+13
OU45F+1J
17.6 2'.67E-Ob
17.6 2.40E-06
17,6 2',27E-06
17.
17.
17.
Mr
IT,
nr
17.
2,17E-06
2,08E-06
2.00E-06
1.93E-06
l',8fcE-06
1.80E-06
1.7UE-06
2.752E-05
2.313E-05
1.97JF-0?
1.699E-05
l.a79E-05
1.2«aE-05
1.139E-05
1.007E-05
8.92SE-06
7.9S9E-06
1
a
7
6
5
a
a
S
3
2
.039E-03
,729E-Ofl
,au?E-oa
,«13E-oa
.580E-08
.8B5E-oa
,300E-0«
,799E«oa
.369E-04
.996E-OU
2.21E-07 1.76E«0«
2.10E-07 1,76E-C«
1.97E-07 1.76E-04
1.85E-07
1.7aE-07
1.63E-07
1.53E-07
l.OJE-07
1.3flE-07
,76F«fla
,7*e-oa
,76E-0«
.76E-04
,7<>E«ea
.76E«fltt
1.26E-07 1.76E«Oa
CALCULATION IS IN SECTION NO. « 3 AUD THE SECTION LENGTH IS • Z.7850 M
COLLECTION AREA • 2'.861E + OJ M?
WIRE TO PLATE • i.397E-oi M
CURRENT/M * 1.168F.OU AMP/M
1/2 WIRE TO WIRE « 9.208E-02 M
TEMPERATURE • 4JO.OOO K
ION MOBILITY * S.a63E-04 M2/VOLT-SEC
DUST WEIGHT • 6.969f-oi KG/SEC
APPLIED VOLTAGE • 8.245E+08 VOLTS
CORONA WIRE RADIUS • 2.096E-03 M
CURRENT DENSITY • 2.268E-08 AMP/M2
GAS FLOW RATE • 1.588E*02 HJ/JEC
PRESSURE • 1.000 ATM
MEAN THERMAL SPEED • S.335Ct02 M/SEC
LENGTH INCR. •0'.27850000 M
JCION) INCH. NO,
11
12
13
14
15
16
17
IB
19
20
TOTAL CURRENT • 5.5BOE-01
CORONA WIRE LENGTH • 4.79SE+03 *
DEPOSIT E FIELD • I.13«r>05 VOLT/M
GAS VELOCITY • i,25oE»oo M/SEC
VISCOSITY • 2.290E-05 KG/M.SEC
PART. PATH PARAH'. • B.246E-08 M
INPUT EFF./INCR, • 15.55
VO
ROVR1
ERAVG
EPLT
AFID
CMCD
MHO
WEIGHT
DUST LAYER JtPART)
.oos4 :
.0042
,0033
.0026
.0020
.0016
.0012
.0010
1.0000
1.0006
i.039EfOS 1.9363E405 1
. 059E + 05 1.9363E + 05 1
,039E*05 1.9363E*05
,039Et05 1,9363E»05
,039E*05 1.9363E*05
.039E*05 1.9363E+05
.039F+05 1.9363F4Q5
.039E+05 1.936JE*05
,039E*.05 1.9363E*05
.039E*05 1.9363E+05
,3395E*13 22',7
.3atlE*IS 22.7
.3U23E+13 22.7
,3a33Etl3 22,7
.3«40F»13 22,7
,3aa6E*13 22,7
.3851E+13 22,7
.3454Etl3 22,7
,3a57E+15 22.7
.3U59E+1J 22.7
'.68E-06 7.422E-06 !
.62E-06 6.606E»06 i
,57E-06 5.692E-06 i
,5?E-06 5.266E-06 1
.47E-06 8,709F«06
,82E-06 4.219E-06
,38E-06 3.783E-06
,3aE>06 3.399E>06
1,30E-06 3.057E-06
1.26E-06 2.753E-06
•.B01C-04 1.28E-07 2.27E-04
>.193E-08 1.16E-07 2.27E-04
>.228E»08 1.08E-07 2.27C-04
.987E-08 1.01E-07 2.27C«0«
.777E-08 9.46E-08 2.27E«04
1.592E-OU 8.8flE-08 2.27E-04
1.82BE-08 8.25E-OB 2,27E>08
1.2B3E-08 7.69E-08 2.27E>04
1.15UE-08 7.17E-OB ?.27E.6a
1.039F-04 6.69E-OB 2.27E-00
JCION) INCR. NO,
21
22
23
24
25
26
27
26
29
30
-------
(•O
vo
CHARGING RATES FOR PARTICLE 3IZFS FROM SUBROUTINE CHARGN OR CHr.SUM
SRI THEORY USEO FOR PARTICLE CHARGING
NO. O/OSATF FOR TNDICATED PA»TTCLE SIZES
0.2000E-06
1 0.5293
2 0.7611
0.9222
1,0587
1.1669
1,2554
1,3299
1.J939
1,4498
10 1,4992
11 1,5706
12 1,6301
13 1.6809
l» 1.7252
IS 1.7644
16 1,7996
17 1,8114
18 1,8604
19 1,8871
20 1,9117
21 1,94J2
22 1.9683
23 1.9«32
24 2.0163
25 2,0378
2* 2,0979
27 2.0768
28 2.0947
29 2.1116
30 2.1276
0.6000E-05
1 0.4311
2 0,6208
3 0.7265
4 0,7919
5 0.8355
6 0,8664
7 0.8M5
8 0,907«
9 0,9217
10 0.9314
11 0.95M
12 0.9754
13 0,9870
14 0,992«
1? 0.9998
0.4000E-06
0.5206
0.7536
0.9229
1.0651
1.1677
1.2469
1.3110
1.3647
1.4106
1.4505
1.5100
1.5584
1.5991
1.6342
1.6650
1,692«
1.7170
1.7394
1.7598
1.7786
1,8014
1.8221
1.8411
1.8587
1.8750
1.8903
1.9045
J.9J80
1.9307
1.9427
0.8500E-OS
0.4289
0.6184
8.7241
0.7893
fl.8326
0.8632
0.8859
0.9033
0.9171
0.9283
o.«532
0.9699
fl.9814
fl.9889
0.9919
0'.7000F.-06
0.4911
0,7130
0.8609
0.9861
1.0774
1,1432
1.19«2
1.2357
1,2706
1,3005
1,3468
1.3836
1,4141
1.4401
1,4627
1.4827
1.5005
1,5166
1,5313
1,5448
1.5613
1.5762
1,5899
1,6025
1,6141
1,6250
1,6351
1.6447
1.6537
1.6622
0'. 1250E-04
0'.«277
0.6174
0.7232
0,7884
0,8318
0,8624
0.8850
0.9024
0.9161
0,9272
0.9521
0,9687
0.9803
0,9«79
0.9918
0.1100E-05
0.4693
0.6794
0.8104
0.9085
0.9919
1,0502
1.0931
t.1268
t.1544
1.1777
1.2156
1.2449
1.2687
1.2888
1,3060
1.3212
1,3346
1.3467
1.3577
1,3678
1.3802
1,3914
1.4017
1,4111
1.4197
1,4278
1.4353
1.4424
1,4424
1.4424
0.2000E-04
0.4272
0.6170
0.7230
0.7883
0.8317
0,8623
0.8849
0.90?3
0.9160
0,9271
0.9520
0.9686
0.9802
0.9878
0.9917
0.1600E-05 0.2500C-05 0.3500E-05 0.4500C-05
0.4555 0.4436 0.4373 0,4339
0.6576 0.6388 0.6293 0.6244
0.7773 0.7500 0.7370 0.7308
0.6596 0,8215 0.8046 0,7969
0.9244 0,8725 0.8508 0.8413
0.9793 0.9122 0.8847 0,8733
1.0184 0,9455 0.9)13 0,8975
1.0478 0.9721 0,9330 0,9167
1.0712 0.9920 0.9512 0,9324
1.0906
1.1234
1.1480
1.1677
1.1840
1,1978
1.2099
1.2206
1.2301
1.2388
1,2466
1.2565
1.2654
1.2735
1.2809
1.2877
1.2940
1.2940
1.2940
1.2940
1.2940
.0079 0.9644 0,9453
,0368 0.9921 0,9710
,0573
.0732
.0861
.0969
.1062
.1143
,1216
.1281
,1340
.1416
,1484
.1545
,1601
.1601
.1601
.1601
.1601
.1601
.1601
.0088 0,9886
.0216 0,9982
.0319
.0405
.0479
.0543
.0600
.0652
.0652
.0719
.0719
.0719
.0719
.0719
.0719
.0719
.0719
.0719
.0719
.0055
,01)7
.0172
.0220
,0220
,0220
,0220
,0285
.0285
,0285
,0285
.0285
.0285
.0285
,0285
.0285
.0285
0.2750E-04
0.4270
0.6170
0.7229
0.7883
0.8317
0.8622
0.8849
0.9023
0.9160
0.9271
0.9520
0.9686
0.9802
0,9878
0.99|7
-------
to
\£>
CO
16 0.9958
17 0.9958
18 0.9958
19 0.995*
20 0.9956
21 .0021
22
23
24
25
26
2T
28
.0021
.0021
.0021
.0021
.0021
.0021
.0021
29 1.0021
SO 1.0021
0.9919
0.9919
0,9919
0.9919
0.9919
0.9996
0.9996
0.9996
0.9996
0.9996
0.9996
0.9996
0.9996
P. 9996
0.9996
0.9918
0,9918
0.9918
0,9918
0,9918
0.9992
0,9992
0,9992
0,9992
0.9992
0.9992
0,9992
0.9992
0.9992
0.'9992
0.9917
0,9917
0,9917
0.9917
0.9917
fl.9991
0,9991
0,9991
0.9991
0.9991
0.9991
0,9991
0.9991
0.9991
0.9991
0.9917
0.9917
0.9917
0.9917
0.9917
0.9991
0,9991
0.9991
0.9991
0.9991
0.9991
0.9991
0.9991
0.9991
0.9991
-------
CHARGF ACCUMULATED ON PASTICLE SIZES IN EACH INCREMENT
INCREMENT CHARGE FOH INDICATED PARTICLE 8I7E8
ro
VD
VO
1
2
3
a
5
6
7
9
9
10
11
12
15
14
IS
Ifc
17
IB
19
20
21
22
23
2A
25
2*
27
28
29
30
0'.2000E-06
0 ,9a287£"18
0.1 3139E.J 7
0.16«28E-17
0. IflftbOE-lT
0.207S7E-17
0.223ME-17
0.23692E-17
0.2a8S2E-17
0.25828E-I7
0.26707E-17
0.27980E-17
0.29039F.-17
0.299«a£.i7
0.307ja£-l7
0.3ia33E-17
0.32059E-17
0.32626E-17
0.33ia3E«17
0.3S618E-17
0.3afl57E-l7
0.3«S83E-17
0.3506a£.l7
0.35507E-17
0.33919E.J7
0.36302E-17
0 36661 E.I 7
0.36998E.J7
0.37316E-17
O.S76J7E-17
0.379Q2E.17
O.aoOOE-06
0 ,26aa9£»l 7
0.ail86E-l7
0.50a37£.17
0.58206E-17
0.*3813E.17
0.68H2E-17
0.7i6a7E-!7
0.7a579£«17
0.770S7E-17
0.79269E-17
0.82517E-17
n.B516SE-!7
0.87389E.17
O.B9308E-17
0.90990E-17
0.9£U87£«1 7
0,93833E«l 7
0.9505aE.17
0.96172E-17
0,97201E-J7
0.96aa3E-17
0,99575E-17
0.10061E-16
0.10158E-16
0,102a7E-16
0.10330E-16
0. 10a08E.lt,
0,10a82E'16
0.10551E-16
0.10617E-16
0.7000E-06
0.75571F-17
0.10957E.16
0.132aSE«16
0.1517at.l6
0. 16580E.16
0.17592E-16
0.1 B377£»l fc
0 , 1 9016E*16
C.19552F-1&
0.20012E-16
0,20785E«16
0.21J92E-1*
0.21761E-1*
9, 221 61£«1 1>
0.22509E-16
0.22816E'1<>
0.23091E.16
0.23339F.16
0.23S65E.I6
0.23773E-U
0.2a026F>16
0.2/I256E-16
0, 2a466£.16
0,2a660F»l 6
0.2a839£-J6
8. 2SOOf>F'16
0.25162E-16
0.25309F.16
o.25aa8E"i k
0.25578E-16
0.1100E.05
0,17331E«16
8.25090E-I6
0.29927E-J6
0.33551E-16
0.36630E-16
0.38783E-16
0,ao36SE>16
Of a 1610E-16
0. a2631C-16
0.a!a93£.16
o,aae90E'i6
0.a5972E-lb
O.U6852E-16
8 .a759?£*16
O.«8230£-16
0,a6789E-16
0, a928b£-l 6
0.a9733E-l(>
8.50139E-16
0.50510E-16
0.50970E-16
0.51385E-U
0.51762E-16
0.52109E-16
0,52a30£-lfc
0.52727E-16
0.53C05E-16
0.53266E>16
0,;3266E*16
O.S3266E'16
0» lfr^OE*05
0 jSl99E*16
0,50BOflE-16
0.600'!?E-lfe
0.66aOfcE-16
0.71015E-16
0.75655F-16
0.78676E-16
0.«09UflE.16
0.82752E-16
0 8U2"8F-16
0,867B5E-16
0.88b88F'16
0,90205E-lfe
0.9146SE.16
0,925J6E«16
0.9JU69F-16
0,9a293E-l*
0,95031F-16
0 9S698E'! h
0,9ft306E-16
0,9707J£-16
0,97758E-16
0,9«J81E-16
0.98951E-16
C,99a76F-16
0.99962E-1*
0,99962F-16
0,99962E-14
0.99962E-J6
0.99962E-16
0.2508E.05
0.83125E-16
0.11970E-15
0.ia053E-15
0. 1539a£«15
0 , 1 63a9£«{5
0.17893E-15
P.17717F-15
8.18215E-15
8.18589E-15
8,18887E«15
8.1 9a29£'15
fl,19813E-15
0.20HOE-1S
O^OSSlE-l?
0.2055ae«15
0.20728E-15
0.20881E-15
0.21016E-15
0.21138E«l?
8.2i2«9E«15
0.21392E-1!
0.21519E.J5
0,?1630E-15
0.2173BE«15
0.21738E-15
0.21738E-15
0.21738E«15
0.2173BE-15
0.2J738E-15
8.217S8E-15
O.J500E.05
0.1602aE.15
0.25057E-15
0.2T80aE-15
0.29«79C«15
0.31172E-15
0.32ai6E«15
0.3336BE.13
0.3at65E*lS
C.3«85tiE-15
0.35337E-15
0.36352E-15
0.16963E-15
0.37a30£.15
0.37807E-1S
0.38123E-15
0.3»3»3E«1?
0.3S630E-1S
0.38839E-1S
0.3902BE-19
0.39028E-15
0.39275E-15
0.39275E-15
O.S9275E-15
0.3927'5E.15
0.39275E«15
0 , 39279£. 19
0.39J73E-15
0.39275E-13
8.39275E-15
0.39275E-15
0.a500F-09
0.26252E-15
fl.37780E.15
0,aa2l7E-13
0,a82l9E»15
0.50903E-13
0.52837E-15
0,5a303E-15
0.55«69E«15
0.56«12e-15
0.5719ta
17 O.I0703E-1*
IB 0.|n7fl3E«l«
19 8.107o3E-ia
0.8500E.03
0.92a77E«l5
o l3333E-la
fl.l70!6E-la
o|lB610E.l«
o.l9a79£.la
fl.l9773E-la
O.l250£-0a
0,l9937E«lfl
0.28776E'ia
0.3370A£.]a
0.36750E-la
0.38770E»la
o.aoi95F.ia
O.ai250£.ia
0.21321E-U 0.860U7E-ia
0.213B6C.10
fll2t3B6E.la
0.«*22(-F-1«
0.2000E>Oa
o,5096?E-ia
0.7361lE>ia
0.2750F-0«
0.992l7E«ia
0.10287E-13
O.l0557£«l3
8,l092BE'l3
0.1l06nE-l3
0.11357E-I3
O.H596E.13
O.H69ae-l3
0.11831E-13
C.11B31E-I3
0.11831E-13
0.1630ar>13
0.17778E-13
0.18756F-J3
0.20ja«£.l3
0.20699E-13
0,2090«£.lS
0.2ia70F.13
0.218a6F-l3
O.J2107E-13
0.118311-13
0.22367E-13
0,?2J6TE-13
0.22367F-13
0.22167F-13
0.22367?-13
-------
CO
o
o
20
2i
22
23
24
25
26
27
28
29
30
0.10703E-ta
0.10771E-14
0.10771E-14
0.10771E-14
0.10771E-14
o.tn77lE«i
-------
PARTICLE SIZE RANGE STATISTICS
CORRECTIONS FOR NONIDEALITIES USING SFT NO'. I OF CORRECTION PARAMETERS
SIZE CCF TNLET x
2,OOOE-07 2.123 0.033
4.000E-07
7.000E-07
1,100E-06
1,600E-06
2,500E-06
3.500E-06
4.500E-06
6,OOOE-06
0,500E-06
1,250F-05
2,000E-05
2.750E.05
.530 0.2S3
.297 0,903
.180 0,815
.130 1,520
.003 3.524
.059 t'.6S2
.046 1,652
.035 1.902
.024 3,304
.017 4,046
.010 12,115
.000 67.401
OUTLET X COR. OUTLET X
0'.7460
7.7149
23;7497
15,2607
19.0143
22.9679
5 '.985 7
j' 571 i
0,0603
0,0061
0,0025
0,0062
0.0346
0,0596
4,6397
14,5019
10,1210
13,5163
18,8*10
6,9609
6,6668
5,9268
6,444ft
5,1520
4,1915
2.4497
NO-RAP EFF.
95,6337
94.1103
94,9201
96.3834
97.5B39
90.7412
99,3002
99.5025
99,9J62
99,9950
99,9999
99,9999
99.9999
NO-RAP M
6,565
5.930
6,240
6,960
7.006
9 173
10,404
11.407
14.053
20,751
33.981
54.024
74.070
NO-RAP P
4,3663
5.8097
5,0799
3.6166
2,4161
1,2500
0.6990
0.4175
O.OB30
0,0050
0,0001
0.0001
0.0001
COR. EPF.
95.4127
93.9591
94.6006
95.9093
97.0700
90.2351
90.6104
90.6706
99.0150
99.3575
99.6490
99.0060
99.9800
COR. "
6.462
5.005
6.151
6.702
7.402
0.464
8.966
9.059
9.667
10,503
11.055
14.209
10.934
COR, P
4,5073
6,0409
5,3194
4.0907
2.9292
1,7649
1.3096
1.3294
0,9050
0,6425
0,3502
0.1140
0.0120
EFFICIENCY - STATED • 99.37
COMPUTED • 99,3736
CONVERGENCE OBTAINED
U)
O
ADJUSTED NO-RAP FFF, • 99'.8069
«MD OF INLET SIZE DISTRIBUTION • 4.465E+01
3IOMAP OF INLET SIZE DISTRIBUTION • 5.122E+00
LOG-NORMAL 6000NE8S OF FIT • 0.904
MMO OF EFPLUCNT UNDER NO-RAP CONDITIONS • 1.336f»00
SI8MAP OF EFFLUENT UNDER MO-RAP CONDITIONS • 1.919£»00
LOO-NORMAL GOODNESS OF FIT • 0.997
PRECIPITATION RATE PARAMETM UNDER NO.RAP CONDITIONS • 13.103
SUMAC* o.otfo WITH o.ooo SNEAKACE OVER s.ooo STAGES
NTEMP • 1
RMMO • 6.00
RSIGMA • 2.50
COHII. EM. • 99.6706
CORRECTED MN» OF EFFLUENT • 2.fcS7E*00
CORRECTED SICMAP OF EFFLUENT • 2.016f*00
LO«-NORt»AL COOONESS OF FIT • 0.980
COMCCTCD PRECIPITATION RATE PARAMETER • 11.90
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, »NO DISCRETE OUTLET MASS LOADINGS
U)
o
to
IDEAL UNADJUSTED
HIS. VEL.CCM/SFC)
2.782E+00
2.S14E+00
3.377E+00
4.223E+08
5.296E+80
7.223E+00
9.331E+00
1,149E+01
l.a85E+01
2.875E»01
3.398E+01
5,402E+<>1
7.«OTE*01
IDEAL UNADJUSTED
EFFICIENCV(t)
7.243E+01
7.387E+81
8.003E+OJ
8.666E+81
9,2flOE*01
9.6B1E+01
9.883E+01
9,'I58E + 01
9.992P* 01
9.999EtOJ
l.OOOE+82
l,088E+fl2
1.000E*02
NO.RAP
RAPPING PUFF
a,772E+00
1.2T7E+01
8.238EfOO
8.9Q2E-01
7,t«lE-02
1.086E-82
1.225E-01
6.019E-81
3.362E+80
5.960Etno
8.120E+00
9.186E+00
9.0«4EtOO
7,i«et+eo
4.S31E400
7.544E+00
NO»RAP+RAP PUFF
DM/DLOGD(NG/OSCMT
2.254E-01
,895E*00
.337E+01
.083E+81
,919E*Ot
.878E+01
.057E+8I
9.11SEtOO
7,102E+88
«.335E*80
7.686E*80
RAPPING PUFF
DISTRIBUTION*)
5.350E-02
2.806E-01
2.834E*08
5,728E+ee
1,308E»01
8.358E+8ft
1.185E+01
1.318E+01
1.245E»OJ
5,91BE*80
PARTICLE
.OOOE-07
.OOOE.07
,eeoE«07
,688E«06
.508E-0*
.500E-06
.SOOE-Ob
.800E-06
.SOOE-06
.250E.05
.OOOE-OS
.750E-05
-------
*****»**•***•*******«*****••«
SUMMARY TABLE OF E9P
PARAMETERS ANR PERFORMANCE
DATA SET NUMBER 1
ESP PERFORMANCE!
ELECTRICAL
U)
O
Ul
EFFICIENCY • 99.6706 *
SC*
a'.769E*01 H**2/(H**3/SEC)
SIZE DISTRIBUTIONS!
NONIOEAL PARAMETERSl
AVG. APPLIED VOLTASE • 4.172E+04 V
AVG. CURRENT OEN8TTY • 17.12 NA/CM**2
RESISTIVITY • 5.008E*10 OMM-CM
INLET MMD • 4.46SE+01 UM INLET SIG*AP • 5.122E*00
OUTLET MMD • 2.48TE+88 UM OUTLET SIGMA? • 2.816E+00
GAS 8NEAKAOE FRACTION • 0.00 /SECTION 6A8 VELOCITY 8IOMAO • 0.00
HAPPING MMO • 6.000E+00 UM RAPPING 8IOMAP • 2.500E+00
-------
PARTICLE SIZE RANGF STATISTICS
CORRECTIONS FOR NONIDEAUITIES USING SET NO'. 2 OF CORRECTION PARAMETERS
SIZE CCF IKILFT X
Z.OOOE-07 2.123 0.033
4.000E-07
7.000E-07
1.100E-06
1,600E-06
2.500E-06
3.500E-06
4,500E-06
6,OOOE-06
B.500E-06
1.250E-05
2.000E-05
.530 0.253
.297 0.903
.188 0.815
.130 l'520
.083 3.524
.059 1.652
.046 1.652
.035 11982
.024 3.304
.017 4,846
.010 12,115
2.750E-05 .008 67.401
OUTLET t
0'.4509
4' 4488
14,5658
10.5527
15.3888
25.0413
9'. 1685
7',92S9
5.1532
416876
2,3997
0,1864
0.0325
COR. OUTLET
0'.3301
3,162?
10,621"
8.2078
12,4518
21,4094
8.9240
8.8757
7,571?
7,9611
5,4557
3.2093
1.7999
t NO-RAP EFF.
"2,3311
"0,1301
90,9462
92.7324
94.3174
96.0115
96.8849
97.307B
98,5406
99,2037
99.7220
99,9910
99.9997
NO-RAP H
5,384
4.855
5,036
5.497
6,013
6.755
7.273
7.579
8.863
10.133
12.340
19.619
74.070
NO-RAP P
7,6689
9.8699
9.0538
7.2676
5. 6826
3.9885
3.1151
2.6922
1.4594
0.7963
0,2780
0.0086
0.0005
COR. EFF.
91.9336
89,8582
90.5155
91.8797
93.3947
95.1014
95.6443
95.6679
96.9J99
98.0571
99.0922
99.7864
99.9785
COR. « COR. P
5. 278 S.0664
4.798 10. IMS
4.939
5.264
5.6*7
6.324
6.570
6.582
7.297
8.263
,4845
,1203
.6053
,8986
.3557
.3321
,0801
.9429
9.859 0.9078
12.892 0.2136
17.703 0.0215
EFFICIENCY . STATED • 99'.37
COMPUTED * 99.3736
CONVERSANCE OBTAINED
U>
O
ADJUSTED NO-RAP FFF. • 99'.4387
HMD OF INLET SIZE DISTRIBUTION • 4.465E*01
SI6NAP OP INLET SIZE DISTRIBUTION • s'.l?2E + 00
LOG.NORMAL GOODNESS OF FIT • 0.984
MUD OF EFFLUENT UNDER NO-RAP CONDITIONS • 2.044E+00
SIGMAP OF EFFLUENT UNDER NO-RAP CONDITIONS • 2.230C400
LOG-NORMAL GOODNESS OF FIT • 0.997
PRECIPITATION RATE PARAMETER UNDER NO.RAP CONDITIONS • 10.866
o'.25o MITH o.ioo SNEAKACE OVER 3.000 STAGES
NTEMP • i
RMMD • 6.00
RSIGMA • 2.50
CORR'. EFF. • 99.1937
CORRECTED MMD OF EFFLUENT • 2.924E+00
CORRECTED SIGMAP OF EFFLUENT * 2.600F»00
LOG-NORMAL GOODNESS OF FIT » 0.996
CORRECTED PRECIPITATION RATE PARAMETER » 10.11
-------
UNADJUSTED MIGRATION VELOCITIES AND EFFICIENCIES, AND DISCRETE OUTLET MASS
U)
o
IDEAL UNADJUSTFO
MIB. VEL.fCM/SEC)
2,702E*00
2,81«E+00
3,J77E+00
«.22JEtOO
5.296E+00
9.3J1E+00
l,a85E+01
2.075E+01
7.«07E+01
IDEAL UNADJUSTED
7.203E*01
7.387E+01
8.003E+01
8.666E+01
.200E+01
,883E*01
OOOE*02
1.0DOE»02
NO-RAP
2.275E+01
2.7J2E*01
1,565E»01
U1SOE+01
J.2A2E-01
RAPPING PUFF
DM/DLOGOCMG/pSCM)
NO«R*P»B»P PUFF
1.082E+00
3.092E*00
6.0«6C+DO
1.072E+01
l,fl60E+fll
7.789OOO
S,96«E-01
8.21TE+00
2.388E+01
4.328E401
5,769E*01
S.128E*01
3^30«Et01
1.85lE*01
8,118E*00
PUFF
DISTRIBUTION!*)
S.150E-02
2,80*E»01
t.satE+oo
.
9.720C+00
l.SO«*01
B.JME+OI)
1.105E+01
1.310E*01
.2451*01
.OUE+OJ
PARTICLE
OIAM.(M)
8.000E-OT
fl.OOOE.8T
7.000E.OT
l.JOOE-0*
1.600E.O*
z.sooe-o*
3.500C.06
fl.SOOE-Ofc
8.900E-0*
1.250E.OS
2.750C-04
-------
ft*************************
U)
o
en
SUMMARY TABLE OF ESP OPERATING
PARAMETERS AND PERFORMANCE
DATA SET NUMBER 2
ESP PERFORMANCEl EFFICIENCY • «9.1«37 X SCA
ELECTRICAL CONDITIONS!
M**2/fM**3/SEC)
AVG. APPLIED VOLTAGE • 4.178E+00 V
AVS. CURRENT DENSITY • IT. 12 NA/C*««?
RESISTIVITY • 5.ADOE+10 OHM. CM
SIZE DISTRIBUTIONS!
NONIDEAL PARAMETERS!
INLET StGMAP • s'.
OUTLET SlC^AP • 2.600E+00
INLET HMD • «.«65E*«1 HM
OUTLET HMD • 2.«20E*00 U*
OAS 8NEAKAOE FRACTION • 0.10 /SECTION GAS VELOCITY SIGMAG • 0.25
RAPPING HMD • 6.000E+00 UM RAPPING 8IGMAP • 2.508E*00
STOP 011111
-------
APPENDIX 0
DEFINITION OP VARIABLES USED IN THE PROGRAM
307
-------
LIST OF VARIABLES, DEFINITIONS, AND UNITS
FOR THE MAIN PROGRAM OF THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NWIRE - Number of wires per electrical section per gas
passage in a particular electrical section
LTHICK - Thickness of the collected participate layer in a
particular increment of length (mm/min)
JPART - Current density due to particles in a particular
increment of length (A/m2)
JION - Current density due to ions in a particular incre-
ment of length (A/m2)
LINC - Length of the increments taken in a particular
linear electrical section (m)
NWS(I) - Number of wires per electrical section per gas
passage for the different linear electrical sections
LINCS(I) - Lengths of the increments taken in the different
linear electrical sections (ft)
VISKIP - Indicator which determines whether or not a dirty-
gas voltage-current curve is calculated in each
increment of length
VISAME - Indicator which determines whether or not a clean-
gas voltage-current curve is calculated for each
of the electrical sections or just the first elec-
trical section
CHKSUM(K) - Fractional increase in charge from one increment to
the next for the different particle sizes
DIAM(K) - Diameters of the different particle sizes (ym and m)
ONO(K) - Initial number of particles per cubic meter of gas
in each particle size band (#/m3)
DXS(K) - Total number of particles removed per cubic meter of
gas in each particle size band under ideal conditions
and with no empirical corrections (#/m3)
308
-------
XMV(K) - Effective migration velocities for the different
particle sizes under ideal conditions and with no
empirical corrections (m/sec)
PCNT(K) - Percentage or fraction by mass in the inlet particle
size distribution of the different size bands (% and
decimal)
RAD(K) - Radii of the different particle sizes (m)
CCF(K) - Cunningham correction factor for the different
particle sizes
PRCU(L) - Cumulative percent by. mass up to each particle size
in the inlet particle size distribution (%)
LSECT(I) - Number of length increments in the different linear
electrical sections
PS(I) - Gas pressure in the different electrical sections
(atm)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
ATOTAL - Total collection plate area of the precipitator
(m2)
DD - Mass density of the particles (kg/m3)
ETAO - Estimated or design overall mass collection
efficiency (%)
DL - Inlet mass loading (grains/ft3 and kg/m3)
PL - Total electrical length of the precipitator (ft
and m)
RHO - Resistivity of the collected particulate layer
(ohm-cm and ohm-m)
NS - Number of different particle size bands in the inlet
particle size distribution
ZMMDI - Specified or fitted mass median diameter of the
inlet particle size distribution based on a log-
normal distribution (ym)
SIGMI - Specified or fitted geometric standard deviation of
the inlet particle size distribution based on a log-
normal distribution
309
-------
NONID - Number of nonideal conditions of gas velocity non-
uniformity and gas sneakage and/or particle reen-
trainment without rapping to be considered
NRAPD - Number of rapping puff particle size distributions
to be considered
TDK - Temperature of the gas in a given electrical sec-
tion (°K)
NUMSEC - Number of linear electrical sections in the precip-
itator
NEFP - Indicator which determines whether the unadjusted,
ideal or adjusted, no-rap efficiency is used to
determine the mass reentrained due to rapping
NTEMP - Indicator which specifies whether the precipitator
is cold or hot side
GFIT - Linear-correlation coefficient obtained in the log-
normal fit of the inlet particle size distribution
VOL(K) - Total volume of particles per cubic meter of gas
in the different size bands (m3/m3(gas))
XNO(K) - Number of particles per cubic meter of gas in each
size band at the start of each increment (#/m3)
Q(K) - Charge on each particle size at the end of a partic-
ular increment (coul)
WS(K) - Total weight of material per cubic meter of gas
removed in each size band in a particular incre-
ment (kg/m3)
ITL(M) - Identifying label for the calculations
DW(J) - Amount of material removed per increment on a total
weight basis (kg)
AS(I) - Collection plate areas for the different linear
electrical sections (m2)
VOS(I) - Applied voltages for the different linear electrical
sections (V)
TCS(I) - Total current for the different linear electrical
sections (A)
WLS(I) - Total wire length for the different linear electri-
cal sections (ft2)
310
-------
ACS(I) - Corona wire radii for the different linear electri-
cal sections (in.)
BS(I) - Wire-to-plate spacing for the different linear
electrical sections (in.)
SYS(I) - One-half the wire-to-wire spacing for the different
linear electrical sections (in.)
VGS(I) - Gas volume flow rate for the different linear
electrical sections (ft3/min)
VGASS(I) - Gas velocity for the different linear electrical
sections (ft/sec)
TEMPS(I) - Gas temperature for the different linear electrical
sections (°F)
VISS(I) - Gas viscosity for the different linear electrical
sections (kg/m-sec)
QSAT(K) - Saturation charge for the different particle sizes
(coul)
U - Ion mobility adjusted for temperature and pressure
(m2/V-sec)
E - Elementary charge unit (coul)
EPSO - Permittivity of free space (cou!2/nt-m2)
PI - Value of the constant ir
ERAVG - Average electric field used for particle charging
(V/m)
BC - Boltzmann's constant (J/°K)
TEMP - Gas temperature in a particular linear electrical
section (°R)
EPS - Relative dielectric constant of the particles
VAVC - Root mean square velocity of the ions (m/sec)
OLDQ(K) - Charge on the different particle sizes in the incre-
ment prior to the one under consideration (coul)
OLDXNO(K) - Number of particles per cubic meter of gas in each
size band at the start of the increment prior to
the one under consideration (#/m3)
311
-------
RFS(I) - Roughness factor for the corona wires in the dif-
ferent linear electrical sections
STARTl(I) - Specified initial current density at which the
calculation of a voltage-current curve starts in
a given electrical section and the initial current
density increment size (A/m2)
START2(I) - Specified increment in current density which is
used in place of STARTl(I) when the Jll-th point
on the voltage-current curve is reached (A/m2)
STARTS(I) - Specified increment in current density which is
used in place of START2(I) when the Jl2-th point
on the voltage-current curve is reached (A/m2)
VSTAR(I) - Estimate of the applied voltage corresponding to
the first point on the voltage-current curve as
defined by STARTl(I) (V)
XDC(J,K) - Charge on each particle size at the end of each
increment (coul)
EAVG(N) - Average electric fields for particle charging in
subincremental lengths (V/m)
CHFID(N) - Average free ion densities for particle charging
in subincremental lengths (#/m3)
ECOLL(N) - Average electric fields at the plate in subincre-
mental lengths (V/m)
ECLEAN(N) - Average electric fields at the plate for clean gas
in subincremental lengths (V/m)
ENDPT(L) - Particle diameters in the inlet cumulative percent
by mass distribution (ym and m)
NENDPT - Number of particle diameters in the inlet cumulative
percent by mass distribution
ARD50(II) - Rapping puff mass median diameters (urn)
ARSIGM(II) - Rapping puff geometric standard deviations
ASNUCK(JJ) - Fractions of gas sneakage and/or particle reentrain-
ment without rapping
AZNUMS(JJ) - Number of stages over which gas sneakage and/or
particle reentrainment without rapping occur
312
-------
AZIGGY(JJ) - Normalized standard deviations of the gas velocity
distribution
VCOOP(KK,LL) - Values at different grid points of the electric
potential in a wire-plate geometry under conditions
of no space charge (V)
TMPP - Ionic mean free path multiplied by a factor (m)
NVI - Indicator which specifies whether to base the elec-
trical calculation on known voltages and currents
or on calculated voltage-current characteristics
NPRINT - Indicator which designates when to print certain
sectionalized data
NSECT - Indicator which keeps track of which electrical
section the calculation is in
SLNGTH - Length of a particular electrical section (m)
A - Collection plate area of a particular linear elec-
trical section (m2)
VO - Applied voltage in a particular linear electrical
section (V)
TC - Total current in a particular linear electrical
section (A)
B - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AC - Corona wire radius in a particular linear electrical
section (m)
WL - Total wire length in a particular linear electrical
section (m)
CL - Total current per length of corona wire in a partic-
ular linear electrical section (A/m)
CD - Average current density at the plate in a particular
linear electrical section (A/m2)
ET - Average electric field in the deposited particulate
layer in a particular linear electrical section (V/m)
SY - One-half the wire-to-wire spacing in a particular
linear electrical section (m)
VGAS - Gas velocity in a particular linear electrical sec-
tion (m/sec)
313
-------
P - Gas pressure in a particular linear electrical
section (atm)
VIS - Gas viscosity in a particular linear electrical
section (kg/m-sec)
W - Total weight of particles per second passing into
a particular linear electrical section (kg/sec)
XPI - Overall mass collection efficiency per increment
based on the estimated or design efficiency (%)
RIOVR - Ratio of the ionic space charge density to the total
space charge density
EPLT - Absolute value of the average electric field at the
plate in a. particular length increment (V/m)
AFID - Average reduced free ion density for particle
charging in a particular length increment (#/m3)
XCD - Average current density at the plate in a particular
length increment (nA/cm2)
ZMD - Interpolated mass median diameter of the collected
particulate layer (m)
WT - Total weight of material per cubic meter of gas
removed in all particle size bands in a given length
increment (kg/nr)
I - Index which runs over the different incremental
lengths in its major usage
ROVRI - Ratio of the total space charge density to the ionic
space charge density
NCALC - Indicator which determines whether to use equation
(12)* for particle charging or the sum of the clas-
sical field and diffusion charges
NI - Number of subincremental lengths into which the
incremental length is divided
VRATIO - Ratio of the peak applied voltage to the average for
use in particle charging
NF - Number of increments taken along the length of the
precipitator
NREAD - Indicator which specifies the unit number of the
input device for reading data into the program
Equation numbers which are superscripted by this symbol refer to
equations contained in reference 2.
314
-------
NPRNT - Indicator which specifies the unit number of the out-
put device for printing data from the program
SCOREF - Overall mass collection efficiency under no-rap +
rap conditions (%)
CZMDL - Fitted log-normal mass median diameter of the outlet
particle size distribution under no-rap + rap
conditions (ym)
CSIGMO - Fitted log-normal geometric standard deviation of
the outlet particle size distribution under no-rap
+ rap conditions
NRUN - Indicator that specifies which set of nonideal
conditions is under consideration
SNUCK - Particular value of ASNUCK(JJ)
ZIGGY - Particular value of AZIGGY(JJ)
RMMD - Particular value of ARD50(II)[ym]
RSIGMA - Particular value of ARSIGM(II)
LK - Indicator which determines whether or not the input
data are printed at a certain location in the program
DV - Total volume per cubic meter of gas occupied by
particles [m3(particles)/m3(gas)]
NN - Number of increments in the Runge-Kutta integration
of equation (12)*
NUMINC - Number of increments in the Simpson's Rule integra-
tion over 0 in equation (12)*
NX - Number of grid points in the x-direction for the
numerical calculations of electrical conditions
NY - Number of grid points in the y-direction for the
numerical calculations of electrical conditions
NDATA - Indicator which determines the type of data set that
is to be read into the program
NEST - Indicator which specifies whether to use extensive
calculations or estimation procedures in determin-
ing precipitator performance
NDIST - Indicator which specifies whether the user is to sup-
ply the inlet particle size distribution or the pro-
gram is to calculate a log-normal distribution
315
-------
NITER - Indicator which determines the maximum number of
iterations over a loop that converges on overall
mass efficiency or the number of iterations that
will be performed over each incremental length of
the precipitator in order to obtain self-consistent
solutions for the electrical conditions
IFINAL - Indicator which causes the calculation of successive
points on the voltage-current curve to cease after
IFINAL points
JIl - Indicator which allows the initial increment size
on current density in the calculation of the voltage-
current curve to be changed after JI1-1 points are
determined on the curve
JI2 - Indicator which allows the second increment size on
current density in the calculation of the voltage-
current curve to be changed after JI2-1 points are
determined on the curve
US - Ion mobility at standard temperature and pressure
(reduced ion mobility)
FPATH - Factor which scales the ion mean free path
EBD - Electrical breakdown strength of the gas near the
collection electrode or the collected particulate
layer (V/m)
NDSET - Counter which keeps track of the number of the
particular set of nonideal conditions which is under
consideration
D50 - Same as ZMMDI (ym)
SIGMAP - Same as SIGMI
SCHARG - Saturation charge number from the field charging
equation
CHRFID - Average free ion density for particle charginq
(#/m3)
TIMEI - Initial value of time for particle charging (sec)
TIMEF - Final value of time for particle charging (sec)
V - Value of the quantity [e2/4ire0akT] found in equa-
tion (12)*
FACTRE - Value of the quantity [-rrva2/2] found in equation
(12)* [m'/sec]
316
-------
RSIZE - Radius of a particular particle (m)
CNUMBR - Charge number of a particular particle at time TIMEF
J - Index which runs over different particle size bands
II - Index which runs over subincremental lengths
ITER - Counter which keeps track of the number of itera-
tions which is limited by NITER
OLDQF(K) - Value of field charge on the different particle sizes
at the end of a given increment or subincrement
(coul)
OLDQT(K) - Value of diffusion charge on the different particle
sizes at the end of a given increment or subincre-
ment (coul)
SOLDQF(K) - Value of field charge on the different particle
sizes at the start of an increment which must be
saved for the iteration procedure over subincrements
in a given increment (coul)
SOLDQT(K) - Value of diffusion charge on the different particle
sizes at the start of an increment which must be
saved for the iteration procedure over subincrements
in a given increment (coul)
CMKS - Value of the quantity [4Tre0] found in equation (12)*
[cou!2/nt-m2]
KA - Index which runs over the different linear electrical
sections
ZWT - Total weight of material per cubic meter of gas
removed up to a given increment (kg/in3)
RATIO - Value of the quantity [(K-l)/(K+2)] found in the
particle charging equations
G - Value of the quantity [K+2] found in the particle
charging equations
INDEX - Indicator which keeps track of how many increments
the calculation is into a particular linear electri-
cal section
NCOOP - Indicator which allows certain calculations to be
made only at the start of a new linear electrical
section
317
-------
SX - Wire-to-plate spacing in a particular linear electri-
cal section (m)
RF - Roughness factor for the discharge wires in a partic-
ular linear electrical section
START - Particular value of STARTl(l) [A/m2]
DSTART - Particular value of START2(I) [A/m2]
CSTART - Particular value of START3(I) [A/m2]
VSTART - Particular value of VSTAR(I) [V]
ZMFP - Ionic mean free path (m)
VAVG - Root mean square velocity of the ions (cm/sec)
VC - Value of the quantity [e2/kT] found in the charging
equations (coul/V)
FACTRC - Value of the quantity [Trv/2] found in the charging
equations (m/sec)
COEFFC - Value of the quantity [eirb] found in the charging
equations (coul-m2/V-sec)
TINC - Time interval for the gas to travel one increment
(sec)
DTINC - Time interval for the gas to travel one subincrement
(sec)
L - Index which runs over the different particle size
bands
R -
Value of the quantity [eEo/kT(K+2)] found in equa-
tion (12)* [m"r]
RR - Value of the quantity [eE0/kT] found in equation
(12)* [m-1]
RG - Same as RR
VW - Operating applied voltage corresponding to a spec-
ified current density (V)
UEQ - Effective charge carrier mobility (m2/V-sec)
NEC - Indicator which determines whether or not the average
current density, average electric field, and average
electric field at the plate are to be calculated in
the subincremental lengths
318
-------
AEPLT - Average electric field at the plate in a particular
increment (V/m)
ACDNTY - Average current density at the plate in a particular
increment (A/m2)
NZ - Index which runs over subincremental lengths
CDCLN - Average current density at the plate when the gas
is clean (A/m2)
USUM - Sum of effective charge carrier mobilities over the
subincremental lengths in a particular incremental
length (m2/V-sec)
WSSUM - Total weight of material per cubic meter of gas
removed in a particular size band in a particular
subincrement (kg/m3)
RHOSUM - Sum of the ratio of the ionic space charge to the
total space charge over the subincremental lengths
in a particular incremental length
SW - Cumulative sum of estimated amount of material
removed per second in successive length increments
(kg/sec)
OROVRI - Ratio of total charge density to ionic charge dens-
ity in increment prior to the one the calculation
is in
XS - Computed value of the exponential argument in the
Deutsch equation for the estimated or design overall
mass collection efficiency
ETAPF - Overall mass collection fraction per increment based
on the estimated or design efficiency
FID - Average free ion density (#/ms)
AVGFID - Average reduced free ion density for particle charg-
ing (#/cm3)
PROT - Total charge density due to particles that remain
after passing through a given increment (coul/m3)
SERAVG - Average electric field in a particular increment
(V/m).
XIPC - Initial value of charge number on a given particle
size at the start of a new increment
319
-------
H - Increment size for the Runge-Kutta integration of
equation (12)* [sec]
DCONST - Value of the quantity [ (K-l)a3/(K+2)] found in
equation (12)* [m3]
CONST - Value of the quantity [2(K-l)a3E0/(K+2)] found in
equation (12)* [V-m2 ]
S - Value of the quantity [3a] found in equation (12)* [m]
ECONST - Value of the quantity [3eE0a/kT(K+2)] found in
equation (12)*
FCONST - Value of the quantity [ (K-l)eE0a3/kT(K+2)] found in
equation (12)* [m2 ]
COEFF - Value of the quantity [bqs/4e0] found in equation (12)*
[m3/sec]
CTIME - Time at the end of a given increment (sec)
EMV(K) - Unadjusted, ideal migration velocities for the dif-
ferent particle sizes in a given increment (m/sec)
X - Exponent used in the Deutsch equation to determine
the unadjusted, ideal collection fractions for the
different particle sizes in a given increment
EFF - Unadjusted, ideal collection fraction for a given
particle size band in a given increment
DXNO - Number of particles per cubic meter of gas removed
from a given particle size band in a given incre-
ment (#/m3)
DNSIOM - Ion density in the absence of particles (#/m3)
DELTNP - Number density of charges transferred from ions to
particles in a given subincremental length (#/m3)
SUMMOB - Weighted summation of particle mobilities (mz/V-sec/
m3)
PNUM - Total number of particles per unit volume of gas
entering a given subincremental length (#/m3)
PHOP - Total average particulate charge density in a given
subincremental length (coul/m3)
TCHRG - Average particle charge density for a given particle
size in a given subincremental length (coul/m3)
320
-------
PMOB - Weighted particulate mobility in a given subincre-
mental length (m2/V-sec)
TDNSP - Total average particulate charge number density in a
given subincremental length (t/m3)
RDNSI - Average reduced ion density in a given subincreraental
length (#/m3)
SUMCD - Sum of the average current densities at the plate from
the different increments in a particular linear elec-
trical section (A/m2)
SUMVO - Sum of the applied voltages from the different incre-
ments in a particular linear electrical section (V)
SKIP - Electric field at the plate in the increment prior
to the one the calculation is in (V/m)
SIGMA - Difference between the ratio of the total space
charge density to the ionic space charge density in
the (I+l)-th and I-th increments
VERGE - Initial estimate of the space charge density at the
corona wire to start the calculation of the electric
field at the plate (coul/m3)
CVERGE - Converged value of the space charge density at the
wire in calculating the electric field at the
plate (coul/m3)
ZTM - Cumulative sum of the weight of material per cubic
meter of gas collected up to a given particle size
in a given increment (kg/m3)
CZA - Ratio of the partial sum of the weight of dust re-
moved per cubic meter of gas up the K-th particle
size in a given increment to the total weight of
dust removed per cubic meter of gas in a given
increment
CZB - Ratio of the partial sum of the weight of dust re-
moved per cubic meter of gas up to the (K-l)-th
particle size in a given increment to the total
weight of dust removed per cubic meter of gas in
a given increment
TL1 - Difference between CZA and CZB for use in interpolat-
ing to find the mass median diameter of the collected
dust
321
-------
TL2 - Difference between 0.50 and CZB for use in interpolat-
ing to find the mass median diameter of the collected
dust
KJ - Index which runs simultaneously with the index which
runs over the different particle sizes and keeps
track of the (K-l)-th particle size
ETC - Ideal, unadjusted overall mass collection efficiency
for the entire precipitator (%)
DIFF - Difference between the calculated ideal, unadjusted
overall mass collection efficiency and the estimated
value
322
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE PRTINP USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
LK - Indicator which determines whether or not the input
data are printed at a certain location in the program
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
NDSET - Counter which keeps track of the number of the
particular set of nonideal conditions which is
under consideration
DL - Inlet mass loading (kg/m3)
DLB - Inlet mass loading (grains/ft3)
PL - Total electrical length of the precipitator (m)
PLB - Total electrical length of the precipitator (ft)
RHO - Resistivity of the collected particulate layer
(ohm-m)
RHOCGS - Resistivity of the collected particulate layer
(ohm-cm)
NCARD - Counter which keeps track of the number of each
successive imput data card
NENDPT - Number of particle diameters in the inlet cumulative
percent by mass distribution
NDATA - Indicator which determines the type of data set that
is to be read into the program
ITL(M) - Identifying label for the calculations
NEST - Indicator which specifies whether to use extensive
calculations or estimation procedures in determin-
ing precipitator performance
NDIST - Indicator which specifies whether the user is to
supply the inlet particle size distribution or the
program is to calculate a log-normal distribution
323
-------
NVI - Indicator which specifies whether to base the elec-
trical calculation on known voltages and currents
or on calculated voltage-current characteristics
NX - Number of grid points in the x-direction for the
numerical calculations of electrical conditions
NY - Number of grid points in the y-direction for the
numerical calculations of electrical conditions
NITER - Indicator which determines the maximum number of
iterations over a loop that converges on overall
mass efficiency or the number of iterations that
will be performed over each incremental length of
the precipitator in order to obtain self-consistent
solutions for the electrical conditions
NCALC - Indicator which determines whether to use equation
(12)* for particle charging or the sum of the clas-
sical field and diffusion charges
NRAPD - Number of rapping puff particle size distributions
to be considered
NEFF -
NTEMP -
NONID -
Indicator which determines whether the unadjusted,
ideal or adjusted, no-rap efficiency is used to
determine the mass reentrained due to rapping
Indicator which specifies whether the precipitator
is cold or hot side
Number of nonideal conditions of gas velocity non-
uniformity and gas sneakage and/or particle reen-
trainment without rapping to be considered
NUMINC -
NN - Number of increments in the Runge-Kutta integration
of equation (12)*
Number of increments in the Simpson's Rule integra-
tion over 0 in equation (12)*
IFINAL - Indicator which causes the calculation of successive
points on the voltage-current curve to cease after
IFINAL points
JIl - Indicator which allows the initial increment size
on current density in the calculation of the voltage-
current curve to be changed after JIl-1 points are
determined on the curve
324
-------
JI2 - Indicator which allows the second increment size on
current density in the calculation of the voltage-
current curve to be changed after JI2-1 points are
determined on the curve
VISKIP - Indicator which determines whether or not a dirty-
gas voltage-current curve is calculated in each
increment of length
VISAME - Indicator which determines whether or not a clean-
gas voltage-current curve is calculated for each
of the electrical sections or just the first elec-
trical section
ETAO - Estimated or design overall mass collection
efficiency (%)
DD - Mass density of the particles (kg/m3)
EPS - Relative dielectric constant of the particles
VRATIO - Ratio of the peak applied voltage to the average for
use in particle charging
US - Ion mobility at standard temperature and pressure
(reduced ion mobility)
FPATH - Factor which scales the ion mean free path
EBD - Electrical breakdown strength of the gas near the
collection electrode or the collected particulate
layer (V/m)
ARD50(II) - Rapping puff mass median diameters (um)
ARSIGM(II) - Rapping puff geometric standard deviations
ASNUCK(JJ) - Fractions of gas sneakage and/or particle reentrain-
ment without rapping
AZIGGY(JJ) - Normalized standard deviations of the gas velocity
distribution
AZNUMS(JJ) - Number of stages over which gas sneakage and/or
particle reentrainment without rapping occur
NDCARD - Indicator which determines how the arrays ENDPT(L)
and PRCU(L) should be printed
ENDPT(L) - Particle diameters in the inlet cumulative percent
by mass distribution (ym and m)
325
-------
D50 - Specified or fitted mass median diameter of the
inlet particle size distribution based on a log-
normal distribution (ym)
SIGMAP - Specified or fitted geometric standard deviation of
the inlet particle size distribution based on a log-
normal distribution
PRCU(L) - Cumulative percent by mass up to each particle size
in the inlet particle size distribution (%)
NUMSEC - Number of linear electrical sections in the precip-
itator
LSECT(I) - Number of length increments in the different linear
electrical sections
AS(I) - Collection plate areas for the different linear
electrical sections (m2)
VOS(I) - Applied voltages for the different linear electrical
sections (V)
TCS(I) - Total current for the different linear electrical
sections (A)
WLS(I) - Total wire length for the different linear electri-
cal sections (ft2)
ACS(I) - Corona wire radii for the different linear electri-
cal sections (in.)
BS(I) - Wire-to-plate spacing for the different linear
electrical sections (in.)
NWS(I) - Number of wires per electrical section per gas
passage for the different linear electrical sections
SYS(I) - One-half the wire-to-wire spacing for the different
linear electrical sections (in.)
VGS(I) - Gas volume flow rate for the different linear
electrical sections (ft3/min)
VGASS(I) - Gas velocity for the different linear electrical
sections (ft/sec)
TEMPS(I) - Gas temperature for the different linear electrical
sections (°F)
PS(I) - Gas pressure in the different electrical sections
(atm)
326
-------
VISS(I) - Gas viscosity for the different linear electrical
sections (kg/m-sec)
LINCS(I) - Lengths of the increments taken in the different
linear electrical sections (ft)
RFS(I) - Roughness factor for the corona wires in the dif-
ferent linear electrical sections
STARTl(I) - Specified initial current density at which the
calculation of a voltage-current curve starts in
a given electrical section and the initial current
density increment size (A/m2)
START2(I) - Specified increment in current density which is
used in place of STARTl(I) when the Jll-th point
on the voltage-current curve is reached (A/m2)
STARTS(I) - Specified increment in current density which is
used in place of START2(I) when the Jl2-th point
on the voltage-current curve is reached (A/m2)
VSTAR(I) - Estimate of the applied voltage corresponding to
the first point on the voltage-current curve as
defined by STARTl(I) (V)
327
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE SPCHG1 USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
I - Index which runs over the incremental lengths
SW - Cumulative sum of estimated amount of material
removed per second in successive length increments
(kg/sec)
ROVRI - Ratio of the total space charge density to the ionic
space charge density
OROVRI - Ratio of total charge density to ionic charge dens-
ity in increment prior to the one the calculation
is in
ETAO - Estimated overall mass collection efficiency (%)
XS - Computed value of the exponential argument in the
Deutsch equation for the estimated overall mass
collection efficiency
LINC - Length of the increments taken in a particular
linear electrical section (m)
PL - Total electrical length of the precipitator (m)
ETAPF - Overall mass collection fraction per increment based
on the estimated efficiency
W - Total weight of particles per second passing into
a particular linear electrical section (kg/sec)
DW(J) - Amount of material removed per increment on a total
weight basis (kg)
CD - Average current density at the plate in a particular
linear electrical section (A/m2)
E - Elementary charge unit (coul)
Ion mobili
(m2/V-sec)
U - Ion mobility adjusted for temperature and pressure
328
-------
ERAVG - Average electric field used for particle charging
(V/ra)
FID - Average free ion density (#/m3)
SUM - Total particulate charge density in a given incre-
ment based on saturation charges (coul/m3)
NS - Number of different particle size bands in the inlet
particle size distribution
L - Index which runs over the different particle size
bands
QSAT(L) - Saturation charge for the different particle sizes
(coul)
XNO(L) - Number of particles per cubic meter of gas in each
size band at the start of each increment (t/m3)
LSECT(I) - Number of length increments in the different linear
electrical sections
NSECT - Indicator which keeps track of which electrical
section the calculation is in
TC - Total current in a particular linear electrical
section (A)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
ZC - Ratio of the particulate charge density to the ionic
charge density (ratio of 200 times the particulate
current to the total current)
AFID - Average reduced free ion density for particle
charging in a particular length increment (l/m3)
AVGFID - Average reduced free ion density for particle
charging (#/cm3)
XCD - Average current density at the plate in a particu-
lar length increment (nA/cm2)
UEQ - Effective charge carrier mobility (m2/V-sec)
XPI - Overall mass collection efficiency per increment
based on the estimated efficiency (%)
329
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE SPCHG2 USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
I - Index which runs over the incremental lengths
ETAO - Design overall mass collection efficiency (%)
XS - Computed value of the exponential argument in the
Deutsch equation for the design overall mass col-
lection efficiency
LINC - Length of the increments taken in a particular
linear electrical section (m)
PL - Total electrical length of the precipitator (m)
ETAPF - Overall mass collection fraction per increment
based on the design efficiency
DELTNP - Number density of charges transferred from ions to
particles in a given subincremental length (#/m3)
SUMMOB - Weighted summation of particle mobilities (m2/V-sec/
m3)
PNUM - Total number of particles per unit volume of gas
entering a given subincremental length (#/m3)
RHOP - Total average particulate charge density in a given
subincremental length (coul/m3)
J - Index which runs over the different particle size
bands
XNO(J) - Number of particles per cubic meter of gas in each
size band at the start of each increment (#/m3)
XDC(I,J) - Charge on each particle size at the end of each
increment (coul)
TCHRG - Average particle charge density for a given part-
icle size in a given subincremental length (coul/m3)
330
-------
CCF(J) - Cunningham correction factor for the different
particle sizes
VIS - Gas viscosity in a particular linear electrical
section (kg/m-sec)
RAD(J) - Radii of the different particle sizes (m)
DIFF - Difference between the charge on a given particle
size in the (I+l)-th and I-th increments (coul)
II - Index which runs over the subincremental lengths
Q(J) - Charge on each particle size at the end of a partic-
ular increment (coul)
OLDQ(J) - Charge on the different particle sizes in the incre-
ment prior to the one under consideration (coul)
PMOB - Weighted particulate mobility in a given subincre-
mental length (m2/V-sec)
TDNSP - Total average particulate charge number density in
a given subincremental length (#/m3)
CHFID(II) - Average free ion densities for particle charging
in subincremental lengths (#/m3)
DNSION - Ion density in the absence of particles (#/m3)
RDNSI - Average reduced ion density in a given subincremental
length (#/m3)
PIR - Ratio of the total charge density which can be
accepted by particles in a given subincrement to
the available free ion density
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
AFID - Average reduced free ion density for particle
charging in a particular length increment (f/m3)
AVGFID - Average reduced free ion density for particle charg-
ing (#/cm3)
U - Ion mobility adjusted for temperature and pressure
(m2/V-sec)
E - Elementary charge unit (coul)
UEQ - Effective charge carrier mobility (m2/V-sec)
331
-------
RIOVR - Ratio of the ionic space charge density to the total
space charge density
XPI - Overall mass collection efficiency per increment
based on the design efficiency (%)
332
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE EFLD1 USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
VO - Applied voltage (negative value used in calculations)
IV]
PI - Value of the constant TT
EPSO - Permittivity of free space (cou!2/nt-m2)
AC - Radius of the corona wires (m)
RO - Radius of the corona wires (m)
ROC - Radius of the corona wires (cm)
RF - Roughness factor for the corona wires
TDK - Temperature of the gas stream (°K)
P - Pressure in the gas stream (atm)
RELD - Relative air density [6 = (T0/T)(P/P0)1
EORO - Product of the corona starting electric field and
the wire radius
CD - Average current density at the plate (A/m2)
UEQ - Effective charge carrier mobility (m2/V-sec)
VERGE - Initial estimate of the space charge density at the
corona wire to start the calculation of the electric
field at the plate (coul/m3)
QZERO - Space charge density at the corona wire (coul/m3)
I - Index which runs over grid points in the x-direction
NX - Number of grid points in the x-direction for the
numerical calculations of electrical conditions
J - Index which runs over grid points in the y-direction
333
-------
NY - Number of grid points in the y-direction for the
numerical calculations of electrical conditions
MOBILT(I,J) - Array containing the values of effective charge
carrier mobility at the different grid points (m2/
V-sec)
MAXJ - Upper limit that the calculated average current
density at the plate cannot exceed (A/m2)
MINJ - Lower limit that the calculated average current
density at the plate cannot fall below (A/m2)
NX1 - Number of grid intervals in the x-direction for the
numerical calculations of electrical conditions
NY1 - Number of grid intervals in the y-direction for the
numerical calculations of electrical conditions
SX - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AX - Interval size in the x-direction (m)
SY - One-half the wire-to-wire spacing in a particular
linear electrical section (m)
AY - Interval size in the y-direction (m)
AXS - Value of the quantity fax2] (m2)
AYS - Value of the quantity [a 2] (m2)
ASP - Value of the quantity [(a 2+a 2)/e0] (m^-nt/coul2)
x y
ASS - Value of the quantity [1/2(a 2+a2)] (m~2)
x y
Z - Counter which keeps track of the number of times
the calculation iterates due to lack of convergence
in the average current density at the plate
VCOOP(I,J) - Array containing the values of electric potential
given equation (26)* at the different grid points
(V)
V(l,j) - Array containing the value of the electric potential
at each point in the grid during an iteration (V)
IZ - Same as Z
NPRNT - Indicator which specifies the unit number of the out-
put device for printing data from the program
334
-------
LL - Counter which keeps track of the number of times
the calculation iterates due to lack of convergence
in the electric potential at each point in the grid
RHO(I,J) - Array containing the value of the space charge
density at each point in the grid during an itera-
tion (coul/m3)
EX{I/J) - Array containing the value of the component of the
electric field intensity perpendicular to the plates
at each point in the grid during an iteration (V/m)
EY(I,J) - Array containing the value of the component of the
electric field intensity parallel to the plates at
each point in the grid during an iteration (V/m)
Ql - Value of the quantity [2b. ] along the line AD
11 i
where b. .is the effective charge carrier mobility
1' J
which is a function of position (m /V-sec)
Q2 - Value of the quantity [2b. a ] along the line AD
(m3/V-sec) lfl x
Q3 - Value of the quantity [2b. a ] along the line AD
(m3/V-sec) *'» V
Q4 - Value of the quantity [2b. a a ] along
(mVv-sec) 1,1 * Y
the line AD
Q5 - Value of the quantity [-eoE (2b, a -a b. )]
x 11i y y i~~111
along the line AD (cou!2/nt-sec)
Q6 - Value of the quantity te02Exz(2b. a -a b._ )2]
along the line AD {coul'*/nt2-sec2)
Q7 - Value of the quantity [4b2 a a 2e0E p. ] along
i, \ x y x i— i f i
the line AD where p. .is the space charge density
x f j
at the different grid points (coul2-m2/V2-sec2)
Q8 - Value of the quantity [-/Q6+Q7] along the line AD
(coul-m/V-sec)
PI - Value of the quantity [2b. .] along the line AB
(m2/V-sec) 1'3
P2 - Value of the quantity [2b. .a ] along the line AB
(m3/V-sec) irD *
335
-------
P3 - Value of the quantity [2b .a ] along the line
AB (m3/V-sec) lrD y
P4 - Value of the quantity [2b .a a ] along the line
AB (mVv-sec) ifJ x y
P5 - Value of the quantity [-e0E (2b .a -a b . )]
y i»3 x x 113 i
along the line AB (coul /nt-sec)
P6 - Value of the quantity [e02E 2(2b .a^a^ ._ )2]
along the line AB (coul'*/nt2-sec2)
P7 - Value of the quantity [4b2 .a 2a e0E p ] along
i »J x y y i / j — i
the line AB (cou!2-m2/V2-sec2)
P8 - Value of the quantity [-/P6+P7] along the line AB
(coul-m/V-sec)
Rl - Value of the quantity [2b. ] along the line BC
(m2/V-sec) 1/NY
R2
- Value of the quantity [2b. KTVa ] along the line BC
1'NY X
R3 - Value of the quantity [2b. MVa ] along the line BC
(mVv-sec) a'NY Y
R4 - Value of the quantity [2b. a a ] along the line
LL t \ -^- i " » *^ J
BC (m4/V-sec)
R5 - Value of the quantity [~e °EX ^b^^a -a ^ Ny) ]
along the line BC (cou!2/nt-sec)
R6 - Value of the quantity [e0 2Ex2 (2bi^Nyay-aybi_ j ^y) ]
along the line BC (coul Vnt2-sec2 )
R7 - Value of the quantity [4b? Nyaxa2EoExPi_ Ny] along
the line BC (coul2-m2/V2-sec2 )
R8 - Value of the quantity [-/R6+R7] along the line BC
(coul-m/V-sec)
Dl - Value of the quantity [2b. .] for interior points in
the grid (m2/V-sec) '-1
D2 - Value of the quantity [2axb± ] for interior points
in the grid (m3/V-sec)
336
-------
D3 - Value of the quantity [2a b. ] for interior points
in the grid (m3/V-sec) Y 1'-1
D4 - Value of the quantity [2a a b. .] for interior points
in the grid (mVv-sec) x Y ^
D5 - Value of the quantity [-EO (E (2a..b. --a b. .) +
x Y -1-1 j y j-"" i»j
E (2a b. .-a b. . ))] for interior points in the
y x i/j x 1,3-1
grid (coul /nt-sec)
D6 - Value of the quantity [D5«D5] (coul4/nt2-sec2)
D7 - Value of the quantity [4bJ .a a eo(a E o. . +
J-»jxy y x i— i , j
a E p. . )] for interior points in the grid (coul2-
x y i/j~i
m2/V2-sec2)
D8 - Value of the quantity [-/D6+D7"] for interior points
in the grid (coul-m/V-sec)
OLDV(I,J) - Array containing the value of the electric potential
at each point in the grid during the previous itera-
tion (V)
OLDRO(I,J) - Array containing the value of the space charge dens-
ity at each point in the grid during the previous
iteration (coul/m3)
CDNSTY(I,J) - Array containing the value of current density at
each point in the grid (A/m2)
ACDNTY - Average current density at the plate (A/m2)
EPLT - Sum of the values of the electric field intensity
at the plate (V/m)
AEPLT - Average electric field at the plate (V/m)
CVERGE - Converged value of the space charge density at the
wire in calculating the electric field at the
plate (coul/m3)
337
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE EFLD2 USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
IVCK - Indicator which terminates the calculation of points
on the voltage-current whenever the specified applied
voltage is reached and interpolated upon
VO - Specified operating applied voltage (V)
VSTART - Particular value of VSTAR(I) [V]
VW - Operating applied voltage corresponding to a spec-
ified current density (V)
AC - Radius of the corona wires (m)
RO - Radius of the corona wires (m)
TDK - Temperature of the gas stream (°K)
P - Pressure of the gas stream (atm)
RELD - Relative air density [<5 = (T0/T)(P/P0)]
ROC - Radius of the corona wires (cm)
RF - Roughness factor for the corona wires
EORO - Product of the corona starting electric field and
the wire radius (V)
I - Index which runs over grid points in the x-direction
NX - Number of grid points in the x-direction for the
numerical calculations of electrical conditions
J - Index which runs over grid points in the y-direction
NY - Number of grid points in the y-direction for the
numerical calculations of electrical conditions
UEQ - Effective charge carrier mobility (m2/V-sec)
338
-------
MOBILT(I,J) - Array containing the values of effective charge
carrier mobility at the different grid points (m2/
V-sec)
PI - Value of the constant IT
EPSO - Permittivity of free space (cou!2/nt-m2)
START - Particular value of STARTl(I) [A/m2]
SSTART - Initial value of START which is saved (A/m2)
MINJ - Lower limit that the calculated average current
density at the plate cannot fall below (A/m2)
MAXS - Particular value of current density on the voltage-
current curve (A/m2)
NX1 - Number of grid intervals in the x-direction for the
numerical calculations of electrical conditions
NY1 - Number of grid intervals in the y-direction for the
numerical calculations of electrical conditions
SX - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AX - Interval size in the x-direction (m)
SY - One-half the wire-to-wire spacing in a particular
linear electrical section
AY - Interval size in the y-direction (m)
AXS - Value of the quantity [a 2] (m2)
J\
AYS - Value of the quantity [a2! (m2)
ASP - Value of the quantity [(a 2+a 2)/e0] (m"-nt/coul2)
x y
ASS - Value of the quantity [l/2(a 2+a 2)](m~2)
x y
IFINAL - Indicator which causes the calculation of successive
points on the voltage-current curve to cease after
IFINAL points
II - Index which runs over the different current densi-
ties to be used on the voltage-current curve
JI1 - Indicator which allows the initial increment size
on current density in the calculation of the voltage-
current curve to be changed after JIl-1 points are
determined on the curve
339
-------
DSTART - Particular value of START2(I) [A/m2]
JI2 - Indicator which allows the second increment size on
current density in the calculation of the voltage-
current curve to be changed after JI2-1 points are
determined on the curve
CSTART - Particular value of START3(I) [A/m2]
MAXJ - Upper limit that the calculated average current
density at the plate cannot exceed (A/m2)
QZERO - Space charge density at the corona wire (coul/m3)
NWIRE - Number of wires per electrical section per gas
passage in a particular electrical section
Z - Counter which keeps track of the number of times
the calculation iterates due to lack of convergence
in the average current density at the plate
VCOOP(I,J) - Array containing the values of electric potential
given equation (26)*at the different grid points
(V)
V(I,J) - Array containing the value of the electric potential
at each point in the grid during an iteration (v)
IZ - Same as Z
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
LL - Counter which keeps track of the number of times
the calculation iterates due to lack of convergence
in the electric potential at each point in the grid
RHO(I,J) - Array containing the value of the space charge
density at each point in the grid during an itera-
tion (coul/m3)
EX(I,J) - Array containing the value of the component of the
electric field intensity perpendicular to the plates
at each point in the grid during an iteration (V/m)
EY(I,J) - Array containing the value of the component of the
electric field intensity parallel to the plates at
each -point in the grid during an iteration (V/m)
340
-------
Ql - Value of the quantity [2b. ] along the line AD
1 • \
where b. . is the effective charge carrier mobility
which is a function of position (m2/V-sec)
Q2 - Value of the quantity [2b. a ] along the line AD
(m2/V-sec) ifl x
Q3 - Value of the quantity [2b. a ] along the line AD
(m3/V-sec) 1.1 y
Q4 - Value of the quantity [2b. a a ] along the line AD
(mVv-sec) 1,1 x y
Q5 - Value of the quantity 1-eoE,(2b. a -a b. )]
x !* i y y 1-1 i i
along the line AD (coul /nt-sec)
Q6 - Value of the quantity Uo2E 2(2b. a -a b. )2J
x i,i y y i—i,\
along the line AD (coul /nt2-sec2)
Q7 - Value of the quantity [4b.2 a a 2eoE p. ] along
1ii x y x i—1,1
the line AD where p. . is the space charge density
11 J
at the different grid points (coul2-m2/V2-sec2)
Q8 - Value of the quantity 1-/Q6+Q7] along the line AD
(coul-m/V-sec)
PI - Value of the quantity [2b .] along the line AB
(m2/V-sec) 1'3
P2 - Value of the quantity [2b .a ] along the line AB
(it\3/V-sec) i.D x
P3 - Value of the quantity [2b .a ] along the line
AB (m3/V-sec) »»D y
P4 - Value of the quantity [2b .a a ] along the line
AB (mVv-sec) I'D x y
P5 - Value of the quantity l-e0E {2b .a -a b . )]
y i»3 x x i, 3 — i
along the line AB (coul /nt-sec)
P6 - Value of the quantity [e02E 2(2b .a -a b . )2]
y i»3 x x i, j—i
along, the line AB (coull'/nt2-sec2)
P7 - Value of the quantity [4b2 .a 2a e0E p . ] along
i»3 x y y 1,3—1
the line AB (cou!2-m2/V2-sec2)
341
-------
P8 - Value of the quantity [-VP6+P7] along the line AB
(coul-m/V-sec)
Rl - Value of the quantity [2b. . ] along the line BC
(m2/V-sec) 1/NY
R2 - Value of the quantity [2b. a ] along the line BC
(m3/V-sec) I,NY x
R3 - Value of the quantity [2b. a 1 along the line BC
(m3/V-sec) lfNY y
R4 - Value of the quantity [2b. a a ] along the line
BC (mVv-sec) i,NY x y
R5 - Value of the quantity [-e0Ex(2bi^Nya -a b..__^ Ny]
along the line BC (cou!2/nt-sec)
R6 - Value of the quantity [eo2E2(2b. a -a b ]
A j., IN i y y i — i , JN Y
along the line BC {coulVnt2-sec2)
R7 - Value of the quantity (4bi/NYaxay °Expi-!^Ny] along
the line BC (cou!2-m2/V2-sec2)
R8 - Value of the quantity [-/R6+R7] along the line BC
(coul-m/V-sec)
Dl - Value of the quantity [2b. .] for interior points in
the grid (m2/V-sec) /D
D2 - Value of the quantity [2a b. .] for interior points
x 11 j
in the grid (m3/V-sec)
D3 - Value of the quantity [2a b. .] for interior points
in the grid (m3/V-sec)
D4 - Value of the quantity [2a a b. .] for interior points
in the grid (mVv-sec) Y '-1
D5 - Value of the quantity [-e0(E (2a b. .-a b. .) +
x y 1/D Y i~i / j
E (2a b. .-a b. . ))] for interior points in the
y x -'2 -"-'J"1
grid (coul /nt-sec)
D6 - Value of the quantity [D5-D5] (coulVnt2-sec2)
D7 - Value of the quantity [4b? .a a e0(a E p. . +
11 j x y y x i— i, j
avE,,P-i + )] for interior points in the grid (coul2-
x y *• i j ~ i
m2/v2-sec2)
342
-------
D8 - Value of the quantity [-VD6+D7] for interior points
in the grid (coul-m/V-sec)
OLDV(I,J) - Array containing the value of the electric potential
at each point in the grid during the previous itera-
tion (V)
OLDRO(I,J) - Array containing the value of the space charge den-
sity at each point in the grid during the previous
iteration (coul/m3)
CDNSTY(I/J) - Array containing the value of current density at
each point in the grid (A/m2)
ACDNTY - Average current density at the plate (A/m2)
TEST - Absolute value of the difference between the calcu-
lated average current density at the plate and the
specified value (A/m2)
TEST1 - One percent of the calculated average current den-
sity at the plate (A/m2)
EPLT - Sum of the values of the electric field intensity
at the plate (V/m)
AEPLT - Average electric field at the plate (V/m)
EBD - Electrical breakdown strength of the gas near the
collection electrode or the collected particulate
layer (V/m)
OLDVW - The value of applied voltage at the point prior to
the one under consideration (V)
OLDCD - The value of average current density at the plate
at the point prior to the one under consideration
(A/m2)
NEC - Indicator which determines whether or not the aver-
age current density, average electric field, and
average electric field at the plate are to be calcu-
lated in the subincremental lengths
K - Index which sequences the grid strips in the basic
area for which the calculations are performed
RSUM - Average charge number density in a particular grid
strip (#/m3)
ESUM - Average electric field intensity in a particular
grid strip (V/m)
343
-------
EAVGS (K) - Array containing the average electric field inten-
sities in the different grid strips in the basic area
for which the calculations are performed (V/m)
CHFIDS(K) - Array containing the average charge number densities
in the different grid strips in the basic area for
which the calculations are performed
NYY - Index which renumbers the grid strips so that by
symmetry the area covered by the half-wire spacing
which was not considered in the calculations can be
taken into account
EAVG (L) - Array containing the average electric field inten-
sities in the different grid strips which cover an
area between successive wires (V/m)
CHFID(L) - Array containing the average charge number densities
in the different grid strips which cover an area
between successive wires (#/m3)
L - Index which runs over and numbers the first (NY-1)
grid strips in a given wire-to-wire spacing
KK - Index which runs over the different grid strips in
the basic area for which the calculations are per-
formed
Ml - Number of the first grid strip in the last (NY-1)
grid strips in a given wire-to-wire spacing
M2 - Number of the last grid strip in a given wire-to-
wire spacing
M - Index which runs over and numbers the last (NY-1)
grid strips in a given wire-to-wire spacing
LL - Index which sequences the grid strips in the basic
area for which the calculations are performed
NN - Index which runs over points in the y-direction
ECOLLS (LL) - Array containing the average electric field inten-
sity at the plate in the different grid strips in
the basic area for which the calculations are per-
formed (V/m)
LI - Index which renumbers the grid strips so that by
symmetry the area covered by the half -wire spacing
which was not considered in the calculations can be
taken into account
344
-------
ECOLL(L) - Array containing the average electric field inten-
sity at the plate in the different grid strips which
cover an area between successive wires (V/m)
L2 - Index which runs over the different grid strips in
the basic area for which the calculations are per-
formed
II - Number of the first grid strip in the last (NY-1)
grid strips in a given wire-to-wire spacing
12 - Number of the last grid strip in a given wire-to-
wire spacing
I - Index which runs over and numbers the last (NY-1)
grid strips in a given wire-to-wire spacing
345
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE CHARGN USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
H - Increment size used in the Runge-Kutta scheme (sec)
H2 - One-half the increment size chosen for the Runge-
Kutta scheme (sec)
YI - Time at the start of a given increment or subincre-
ment of the precipitator (sec)
Y - Time at the end of a given increment or subincre-
ment of the precipitator (sec)
XI - Number of charges on a given particle size at the
start of a given increment or subincrement of the
precipitator
X - Number of charges on a given particle size at the
end of a given increment or subincrement of the
precipitator
I - Index which runs over the different points spec-
ified for use in the Runge-Kutta scheme
NN - Number of points specified for use in the Runge-
Kutta scheme
ECHARG - Elementary charge unit (coul)
SCHARG - Saturation charge number from the field charging
equation
NUMINC - Number of increments in the Simpson's Rule integra-
tion over 0 in equation (12)*
CONST - Value of the quantity [2(K-l)a3E0/(K+2)] found in
equation (12)* [V-m2]
EZERO - Average electric field used for particle charging
(V/m)
346
-------
V - Value of the quantity [ez/4neoakT] found in equa-
tion (12)*
RSIZE - Radius of a particular particle (m)
ECONST - Value of the quantity [3eE0a/kT(K+2) ] found in
equation (12)*
CMKS - Value of the quantity IATTEO] found in equation (12f
Icoul2/nt-m2]
RR - Value of the quantity leE0/kT] found in equation
(12)* [m-1]
FCONST - Value of the quantity [ (K-l)eE0a3AT (K+2) ] found
in equation (12)* [m2!
FACTOR - Value of the quantity [irva2/2] found in equation
(12)* [m3/sec]
COEFF - Value of the quantity [bqs/4E0] found in equation
(12)* [mVsec]
AFID - Average reduced free ion density for particle
charging in a particular length increment (#/m3)
Tl - Value of the charge -number rate to the particle
surface at the point (XI, YI) multiplied by the
stepsize H for use in the Runge-Kutta scheme
T2 - Value of the charge-number rate to the particle
surface at the point (XI+H2, YI+T1/2) multiplied
by the stepsize H for use in the Runge-Kutta scheme
T3 - Value of the charge-number rate to the particle
surface at the point (XI+H2, YI+T2/2) multiplied
by the stepsize H for use in the Runge-Kutta scheme
T4 - Value of the charge-number rate to the particle
surface at the point (XI+H, YI+T3) multiplied by
the stepsize H for use in the Runge-Kutta scheme
347
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR FUNCTION SUBPROGRAM RATE USED IN THE
ELECTROSTATIC PRECIPITATOR PERFORMANCE MODEL
ECHARG - Elementary charge unit (coul)
SCHARG - Saturation charge number from the field charging
equation
NUMINC - Number of increments in the Simpson's Rule integra-
tion over 9 (not used)
CONST - Value of quantity [2(K-l)a3E0/(K+2)] found in
equation (45) [V-m2]
EZERO - Average electric field used for particle charging
(V/m)
V - Value of the quantity [e2/47re0akT] found in equa-
tion (45)
RSIZE - Radius of a particular particle (m)
ECONST - Value of the quantity [3eE0a/kT(K+2)] found in
equation (45) [V-m2]
CMKS - Value of the quantity [4ire0] found in equation (45)
[cou!2/nt-m2]
RR - Value of the quantity [eE0/kT] found in equation
(45) [m-1]
FCONST - Value of the quantity [(K-l)eE0a3/kT(K+2)] found
in equation (45) [m2]
FACTOR - Value of the quantity [irva2/2] found in equation
(45) [m3/sec]
COEFF - Value of the quantity [bqs/4e<>] found in equation
(45) [mVsec]
AFID - Average reduced free ion density for particle
charging in a particular length increment (#/m3)
NTIME - Instantaneous charging time (sec)
348
-------
NUMBER - Instantaneous number of charges on a given particle
size
INTGRL - Value of the integral appearing in equation (45)
NE - Negative of the instantaneous charge on a given
particle size (coul)
T(I) - Roots of the Legendre polynomials of third order
A(I) - Gaussian weighting functions
THZERO - Maximum angle (60) for field charging in radians
YFUC - The quadrature being computed
THETA - Values of the angle 6 taken for the integration
over 9 in equation (45)
CTHETA - Value of the quantity fcos 6]
TCONST - Value of the quantity [2(K-l)a3E0cose/(K+2)] (m2-V)
EGOS - Value of the quantity [E0 cos 6] (V/m)
Cl - Value of the quantity tq/4TTe0E0cose]
CO - Value of the quantity [(K-l)a3/(K+2)]
RZERO - Radial distance from the center of a given particle
at which the total radial component of the electric
field is zero (m)
ARGl - Argument of the exponential function inside the
integral in equation (45)
YVAL - Integrand of the integral in equation (45)
RATEl - Contribtuion to the particle charging rate due to
the second term in equation (45) [t/sec]
ARG3 - Argument of the exponential function in the third
term in equation (45)
RATE2 - Contribution to the particle charging rate due to
the third term in equation (45)
RATE3 - Contribution to the particle charging rate due to
the first term in equation (45) [f/sec]
RATE - Total instantaneous charging rate to the entire
surface of a given particle (#/sec)
349
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE ARCCOS USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
A - Numerator of the ratio A/B whose inverse cosine
is to be determined
B - Denominator of the ratio A/B whose inverse cosine
is to be determined
ACOS - Value of the quantity [cos-1(A/B)] (radians)
RATIO - Value of the ratio A/B
T - Variable used to generate the different numerical
coefficients in the series representation of the
inverse cosine function
SUM - Sum of successive terms in the series representation
of the inverse cosine function
TERM - A particular term in the series representation of
the inverse cosine function
U - Variable used in the generation of the numerical
coefficients in the series representation of the
inverse cosine function
V - Variable used in the generation of the numerical
coefficients in the series representation of the
inverse cosine function
W - Variable used in the generation of the numerical
coefficients in the series representation of the
inverse cosine function
350
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE ZERO USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
Cl - Value of the quantity [q/4ireoEocos6] found in
equation (52)*
CO - Value of the quantity [(K-l)a3/(K+2)] found in
equation (52)* [m3]
RZERO - Radial distance from the center of a given particle
at which the total radial component of the electric
field is zero (m)
B - Value of the argument of the inverse cosine function
found in equation (55)*
C - Value of the inverse cosine function found in equa-
tion (55)*
D - Factor multiplying the cosine function found in
equation (12)*
351
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE CHGSUM USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NVI - Indicator which specifies whether to base the elec-
trical calculation on known voltages and currents
or on calculated voltage-current characteristics
I - Index which runs over incremental lengths
II - Index which runs over subincrernental lengths
OLDQF(J) - Value of field charge on the different particle
sizes at the end of a given increment or subincre-
ment (coul)
OLDQT(J) - Value of diffusion charge on the different particle
sizes at the end of a given increment or subincre-
ment (coul)
ITER - Counter which keeps track of the number of itera-
tions which is limited by NITER
SOLDQF(J) - Value of field charge on the different particle
sizes at the start of an increment which must be
saved for the iteration procedure over subincrements
in a given increment (coul)
SOLDQT(J) - Value of diffusion charge on the different particle
sizes at the start of an increment which must be
saved for the iteration procedure over subincrements
in a given increment (coul)
E - Elementary charge unit (coul)
SCHARG - Saturation charge number from the field charging
equation
SATCHG - Saturation charge for a given particle size from
field charging theory (coul)
CHRFID - Average free ion density for particle charging
352
-------
U - Ion mobility adjusted for temperature and pressure
(m2/V-sec)
EPSO - Permittivity of free space (cou!2/nt-m2)
TIMEF - Final value of time for particle charging (sec)
TIMEI - Initial value of time for particle charging (sec)
CF1 - Value of the quantity [(N0be/4e0)(tf-ti)] found in
equation (15)*
CF2 - Value of the quantity. [l/(l-q./q )1 found in
equation (15)*
QF - Charge on a given particle size in a given increment
or subincrement due to field charging (coul)
V - Value of the quantity [e2/4ire oakT] found in equation
(15)*
ARC - Value of the quantity lqie/4ire0akT] found in
equation (15)*
RSIZE - Radius of a particular particle (m)
VAVC - Root mean square velocity of the ions (m/sec)
BC - Boltzmann's constant (J/°K)
TDK - Temperature of the gas in a given electrical sec-
tion (°K)
QT - Charge on a given particle size in a given incre-
ment or subincrement due to diffusion charging
(coul)
CNUMBR - Total charge number on a given particle size in a
given increment or subincrement
353
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LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE PRTINC USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NPRINT - Indicator which designates when to print certain
sectionalized data
NSECT - Indicator which keeps track of which electrical
section the calculation is in
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
ITL - Identifying label for the calculations
SLNGTH - Length of a particular electrical section (m)
A - Collection plate area of a particular linear elec-
trical section (m2)
VO - Applied voltage in a particular linear electrical
section (V)
TC - Total current in a particular linear electrical
section (A)
B - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AC - Corona wire radius in a particular linear electrical
section (m)
WL - Total wire length in a particular linear electrical
section (m)
CL - Total current per length of corona wire in a partic-
ular linear electrical section (A/m)
CD - Average current density at the plate in a particular
linear electrical section (A/m2)
ET - Average electric field in the deposited particulate
layer in a particular linear electrical section (V/m)
354
-------
SY - One-half the wire-to-wire spacing in a particular
linear electrical section (m)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
VGAS - Gas velocity in a particular linear electrical sec-
tion (m/sec)
TDK - Temperature of the gas in a given electrical sec-
tion (°K)
P - Gas pressure in a particular linear electrical
section (atm)
VIS - Gas viscosity in a particular linear electrical
section (kg/m-sec)
U - Ion mobility adjusted for temperature and pressure
(m2/V-sec)
VAVC - Root mean square velocity of the ions (m/sec)
TMFP - Ionic mean free path multiplied by a factor (m)
W - Total weight of particles per second passing into
a particular linear electrical section (kg/sec)
LING - Length of the increments taken in a particular
linear electrical section (m)
XPI - Overall mass collection efficiency per increment
based on the estimated or design efficiency (%)
NVI - Indicator which specifies whether to base the elec-
trical calculation on known voltages and currents
or on calculated voltage-current characteristics
RIOVR - Ratio of the ionic space charge density to the total
space charge density
ERAVG - Average electric field used for particle charging
(V/m)
EPLT - Absolute value of the average electric field at
the plate in a particular length increment (V/m)
AFID - Average reduced free ion density for particle
charging in a particular length increment (l/mj)
XCD - Average current density at the plate in a particular
length increment (nA/cm2)
355
-------
ZMD - Interpolated mass median diameter of the collected
particulate layer (m)
WT - Total weight of material per cubic meter of gas
removed in all particle size bands in a given length
increment (kg/m )
LTHICK - Thickness of the collected particulate layer in a
particular increment of length (mm/min)
JPART - Current density due to particles in a particular
increment of length (A/m2)
JION - Current density due to ions in a particular incre-
ment of length (A/m2)
I - Index which runs over incremental lengths
ROVRI - Ratio of the total space charge density to the ionic
space charge density
356
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LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE PRTCHG USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
NCALC - Indicator which determines whether to use equation
(12)* for particle charging or the sum of the class-
ical field and diffusion charges
NEST - Indicator which specifies whether to use extensive
calculations or estimation procedures in determin-
ing precipitator performance
JS - Index which is utilized in dividing the output data
for particle charging into sets of eight columns
each with a column for each particle size band
KS - Index which is utilized in dividing the output data
for particle charging into sets of eight columns
each with a column for each particle size band
NS - Number of different particle size bands in the inlet
particle size distribution
DIAM(J) - Diameters of the different particle sizes (um and m)
J - Index which runs over the different particle size
bands
I - Index which runs over incremental lengths
NF - Number of increments taken along the length of the
precipitator
NVI - Indicator which specifies whether to base the elec-
trical calculation on known voltages and currents
or on calculated voltage-current characteristics
NI - Number of subincremental lengths into which the
incremental length is divided
N - Number of the subincremental strip having the max-
imum values of average electric field and current
density
357
-------
PI - Value of the constant TT
EPSO - Permittivity of free space (cou!2/nt-m2)
RAD(J) - Radii of the different particle sizes (m)
TMFP - Ionic mean free path multiplied by a factor (m)
EAVG(N) - Average electric fields for particle charging in
subincremental lengths (V/m)
EPS - Relative dielectric constant of the particles
VRATIO - Ratio of the peak applied voltage to the average for
use in particle charging
XDC(I,J) - Charge on each particle size at the end of each
increment (coul)
QSATM - Saturation charge for a given particle size based
on the last electrical section and the subincre-
mental strip containing the largest values of
average electric field and current density (coul)
YY(J) - Array containing the ratio of the charge on a given
particle size to the saturation charge in the last
electrical section for a given increment
QSAT(J) - Saturation charge for a given particle size based
on the last electrical section and the average
electric field for the entire section (coul)
358
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE ADJUST USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NRUN - Indicator that specifies which set of nonideal
conditions is under consideration
NS - Number of different particle size bands in the inlet
particle size distribution
NSl - Number of particle size bands plus one
NUMSEC - Number of linear electrical sections in the precip-
itator
NUMSl - Number of electrical sections less one
TDK - Temperature of the gas stream in the last electrical
section (°K)
PS(NUMSEC) - Pressure of the gas stream in the last electrical
section (atm)
CONVF - Conversion factor which converts kg/ACM to mg/DSCM
NRAPDC - Counter which keeps track of the number of rapping
puff particle size distributions that have been
considered
X - Ideal, unadjusted overall mass collection fraction
(or efficiency) [no units or %]
I - Index which runs over the different particle size
bands
DXS(I) - Total number of particles removed per cubic meter of
gas in each particle size band under ideal conditions
and with no empirical corrections (#/m3)
ONO(I) - Initial number of particles per cubic meter of gas
in each particle size band (#/m3)
EFESR - Ideal, unadjusted mass collection fraction for a
given particle size
359
-------
PCNT(I) - Percentage or fraction by mass in the inlet particle
size distribution of the different size bands (% and
decimal)
ARD50(J) - Rapping puff mass median diameters (ym)
ARSIGM(J) - Rapping puff geometric standard deviations
RMMD - Particular value of ARD50(J)[pm]
RSIGMA - Particular value of ARSIGM(J)
RPRCU(I) - Cumulative fraction by mass as a function of particle
size for the rapping puff
RPCNT(I) - Percentages by mass in the different particle size
bands for the rapping puff (%)
NONCK - Counter which keeps track of the number of sets of
nonideal conditions of nonuniform velocity distribu-
tion and gas sneakage and/or particle reentrainment
without rapping that have been considered
ASNUCK(K) - Fractions of gas sneakage and/or particle reentrain-
ment without rapping
SNUCK - Particular value of ASNUCK(K)
AZIGGY(K) - Normalized standard deviations of the gas velocity
distribution
ZIGGY - Particular value of AZIGGY(K)
AZNUMS(K) - Number of stages over which gas sneakage and/or
particle reentrainment without rapping occur
ZNUMS - Number of stages over which gas sneakage and/or
particle reentrainment without rapping occur for
a particular case
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
Y - Adjusted overall mass collection fraction (or
efficiency) under no-rap conditions (no units
or %)
XEP - Adjusted mass collection fraction for a given
particle size band under no-rap conditions
360
-------
XMV(I) - Effective migration velocities for the different
particle sizes under ideal conditions and with no
empirical corrections (m/sec)
WY - Adjusted migration velocity for a given particle
size under no-rap conditions (cm/sec)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
ATOTAL - Total collection plate area of the precipitator
(m2)
Fl - Correction factor for the migration velocity of a
given particle size in order to account for non-
uniform velocity distribution
F2 - Correction factor for the migration velocity of a
given particle size in order to account for gas
sneakage and/or particle reentrainment without
rapping
WYS - Migration velocity of a given particle size cor-
rected only for gas sneakage and/or particle re-
entrainment without rapping (cm/sec)
WYV - Migration velocity of a given particle size cor-
rected only for nonuniform velocity distribution
(cm/sec)
ZNLFF - Combined correction factor for nonuniform velocity
distribution and gas sneakage and/or particle
reentrainment without rapping
WYSV - Migration velocity of a given particle size cor-
rected only for nonuniform gas velocity distribu-
tion and gas sneakage and/or particle reentrainment
without rapping (cm/sec)
WUNCOR(I) - Unadjusted, ideal migration velocities for the
different particle sizes (cm/sec)
EUNCOR(I) - Unadjusted, ideal mass collection efficiencies for
the different particle sizes (%)
DIAM(I) - Diameters of the different particle sizes (urn and m)
PXS(I) - Number of particles per cubic meter of gas for a
given particle size that are removed by the precip-
itator under adjusted, no-rap conditions (l/m3)
361
-------
IDC - Indicator which controls when the summation of
outlet emissions over the different particle size
bands will be performed
SPO - Total outlet emissions under adjusted, no-rap
conditions (#/m3)
SCPO - Total outlet emissions under rap + no-rap condi-
tions (#/m3)
IX - Indicator which determines when the total electri-
cal length up to the last electrical section will
be calculated
SCOREF - Overall mass collection efficiency under no-rap +
rap conditions (%)
XY - Percentage by mass in a given particle size in the
inlet particle size distribution (%)
PENTR - Percentage by mass of a given particle size that
penetrates through the precipitator under adjusted,
no-rap conditions (%)
PCTOT(I) - Percentage by mass in a given particle size band
in the no-rap outlet emissions (%)
CLPTLS - Total electrical length of the precipitator exclud-
ing the last electrical section (m)
IS - Index which runs over the different linear electrical
sections
LSECT(IS) - Number of length increments in the different linear
electrical sections
LINGS(IS) - Lengths of the increments taken in the different
linear electrical sections (ft)
NYX - Index which starts and terminates a loop in which
the mass loss due to rapping and the mass leaving
the precipitator under no-rap conditions are deter-
mined
XEFF - Overall mass collection fraction for either unad-
justed, ideal or adjusted, no-rap conditions
NEFF - Indicator which determines whether the unadjusted,
ideal or adjusted, no-rap efficiency is used to
determine the mass reentrained due to rapping
362
-------
EXPONT - Argument of the exponential function in equation
(2) for either the unadjusted, ideal efficiency
or the adjusted, no-rap efficiency
DL - Inlet mass loading (kg/m3)
PL - Total electrical length of the precipitator (m)
XMELS - Mass entering the last section of the precipitator
from either unadjusted, ideal or adjusted, no-rap
calculations (kg/m3)
XMCLS - Mass collected in the last section of the precip-
itator from either unadjusted, ideal or adjusted,
no-rap calculations (kg/m3 or mg/DSCM)
XMLLS - Mass leaving the last section of the precipitator
from either unadjusted, ideal, or adjusted, no-
rap calculations (kg/m3)
NTEMP - Indicator which specifies whether the precipitator
is cold or hot side
RAPLOS - Mass contained in the outlet emissions due to
rapping (mg/DSCM)
YMELS - Mass entering the last section of the precipitator
from adjusted, no-rap calculations (kg/m3)
YMCLS - Mass collected in the last section of the precip-
itator from adjusted, no-rap calculations (kg/nr or
mg/DSCM)
YMLLS - Mass leaving the last section of the precipitator
from adjusted, no-rap calculations (kg/m3)
DD - Mass density of the particles (kg/m3)
RNS - Number of particles per cubic meter of gas in a
given size band that are contained in the emissions
due to rapping (#/m3)
EFFWR - Mass collection fraction for a given particle size
containing all corrections and adjustments
CRNP - Number of particles per cubic meter of gas in a
given size band that are collected after rappinq
(#/m3)
COREFF - Mass collection efficiency for a given particle
size containing all corrections and adjustments (%)
363
-------
WYP - Migration velocity for a given particle size con-
taining all corrections and adjustments (cm/sec)
CPENTR - Percent penetration of a given particle size con-
taining all corrections and adjustments (%)
CPCTOT(I) - Percentage by mass in a given size band contained
in the no-rap + rap emissions (%)
SL - Number of particles per cubic meter of gas of a
given particle size band exiting the precipitator
under no-rap conditions (#/m3)
RAD(I) - Radii of the different particle sizes (m)
WSL(I) - Weight per cubic meter of gas of particles in a
given size band exiting the precipitator under no-
rap conditions (kg/m3)
ENDPT(I) - Particle diameters in the inlet cumulative percent
by mass distribution (ym and m)
OLD - Value of the quantity [AlogioD] for a given particle
size band in the size distribution histogram
DMDLD(I) - Value of the quantity [AM/AlogioD] for the different
particle size bands in the outlet emissions under
no-rap conditions (mg/DSCM)
RDMDLD(I) - Value of the quantity [AM/Alog10D] for the different
particle size bands in the outlet emissions due to
rapping only (mg/DSCM)
CDMDLD(I) - Value of the quantity [AM/AlogioD] for the different
particle size bands in the outlet emissions under
no-rap + rap conditions (mg/DSCM)
CCF(I) - Cunningham correction factor for the different
particle sizes
ETAO - Estimated or design overall mass collection effic-
iency (%)
ZMMDI - Specified or fitted mass median diameter of the
inlet particle size distribution based on a log-
normal distribution (ym)
SIGMI - Specified or fitted geometric standard deviation of
the inlet particle size distribution based on a log-
normal distribution
NDIST - Indicator which specifies whether the user is to
364
-------
supply the inlet particle size distribution or the
program is to calculate a log-normal distribution
GFIT - Linear-correlation coefficient obtained in the log-
normal fit of the inlet particle size distribution
PRCUNR(I) - Cumulative percentage by mass as a function of
particle size for the outlet emissions under no-
rap conditions (%)
SUMNR - Summation over the different particle size bands of
the percentage by mass contained in each size band
for the outlet emissions under no-rap conditions (%)
ZMDL - Fitted mass median diameter of the outlet no-rap
emissions based on a log-normal distribution (um)
SIGMO - Fitted geometric standard deviation of the outlet
no-rap emissions based on a log-normal distribution
ZGFIT - Linear-correlation coefficient obtained in the log-
normal fit of the outlet no-rap emissions
COREFW - Precipitation rate parameter under no-rap + rap
conditions (cm/sec)
WZ - Precipitation rate parameter under no-rap condi-
tions (cm/sec)
PRCUC(I) - Cumulative percentage by mass as a function of
particle size for the outlet emissions under no-
rap + rap conditions (%)
SUMC. - Summation over the different particle size bands
of the percentage by mass contained in each size
band for the outlet emissions under no-rap + rap
conditions (%)
CZMDL - Fitted mass median diameter of the outlet no-rap
+ rap emissions based on a log-normal distribution
(ym)
CSIGMO - Fitted geometric standard deviation of the outlet
no-rap + rap emissions based on a log-normal distri-
bution
CGFIT - Linear-correlation coefficient obtained in the log-
normal fit of the outlet no-rap + rap emissions
M - Index which runs over the different particle size
bands
365
-------
NONID - Number of nonideal conditions of gas velocity non-
uniformity and gas sneakage and/or particle reen-
trainment without rapping to be considered
NRAPD - Number of rapping puff particle size distributions
to be considered
366
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE WADJST USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
DIAM(I) - Diameters of the different particle sizes (ym and m)
I - Index which runs over the different particle size
bands
WY - Enters the subroutine as the unadjusted, no-rap
migration velocity for a given particle size and
leaves as the adjusted, no-rap migration velocity
(cm/sec)
ONO(I) - Initial number of particles per cubic meter of gas
in each particle size band (t/m3)
PXS(I) - Number of particles per cubic meter of gas for a
given particle size that are removed by the precip-
itator under adjusted, no-rap conditions (f/m3)
ATOTAL - Total collection plate area of the precipitator (m2)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
EFESR - Mass collection fraction for a given particle size
under adjusted, no-rap conditions
CFACT(L) - Correction factors for the no-rap migration velo-
cities of the different particle sizes
DCHECK(L) - Particle diameters corresponding to the different
correction factors given by CFACT(L) [ml
L - Index which runs over the different values of
CFACT(L) and DCHECK(L)
WFACT - Interpolated correction factor for the unadjusted,
no-rap migration velocity of a given particle size
367
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE LNDIST USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
D50 - Specified or fitted mass median diameter of the
inlet particle size distribution based on a log-
normal distribution (ym)
SIGMAP - Specified or fitted geometric standard deviation of
the inlet particle size distribution based on a log-
normal distribution
PRCU(I) - Cumulative fractions by mass up to specified particle
sizes
PCNT(J) - Fractions by mass contained in specified particle
size bands
Y(K) - Values of the log-normal distribution function at
different values of the independent variable for use
in integrating the function over the specified size
bands
Z(K) - Cumulative integrals resulting from the integration
of the log-normal distribution function over a spec-
ified particle size band
AREA(J) - Amount of the distribution accumulated in a given
particle size band
NS - Number of particle size bands
ENDPT(I) - Particle diameters specified for use in constructing
the log-normal distribution histogram (ym)
NENDPT - Number of particle diameters specified for use in
constructing the log-normal distribution histogram
PI - Value of the constant TT
SIGMAZ - Value of the quantity [In a ]
N - Total number of particle size bands used in construct-
ing the log normal distribution histogram
368
-------
UINC - Number of points used in the Trapezoidal Rule
integrations over the different particle size bands
ASUM - Value of the integration of the log-normal distri-
bution function over the entire distribution
K - Index which runs over the NS different particle size
bands specified by the user
j - Index which runs over the N different particle size
bands used in the construction of the log-normal
distribution histogram
X2 - Upper limit of integration for a given particle size
band
XI - Lower limit of integration for a given particle size
band
DX - Stepsize taken for the Trapezoidal Rule integration
of the log-normal distribution function over the
different particle size bands
D - Value of the integration variable at different points
in a given particle size band
SGT1 - Value of the quantity [l/oz/2~7]
SGT2 - Value of the quantity [2oz2]
I - Index which runs over the different points in a
given particle size band in performing the Trape-
zodial Rule integration of the log-normal distribu-
tion function
SUM - Total fraction by mass contained in the histogram
specified by the user
CHECKl - Difference between 1 and the calculated total mass
fraction contained in the histogram specified by
the user
CHECK2 - Difference between 1 and the calculated cumulative
fraction by mass up to the largest particle size
specified by the user
369
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE QTFE USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
DX - Stepsize used in the Trapezoidal Rule integration
scheme
Y(I) - Function values used in the integration scheme
Z(I) - Cumulative integrals resulting from the integration
scheme
NINC - Number of points used in the integration scheme
SUM2 - Cumulative integral up to a given point in the
integration scheme
DDX - One-half of the specified stepsize
I - Index which runs over the different points in the
integration scheme
SUM1 - Cumulative integral up to the point prior to the
point under consideration
370
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE LNFIT USED IN THE ELECTRISTATIC
PRECIPITATOR PERFORMANCE MODEL
PRCU(I) - Known or calculated cumulative percentages supplied
by the user (%)
D50 - Fitted mass median diameter based on a log-normal
distribution (urn)
SIGMAP - Fitted geometric standard deviation based on a log-
normal distribution
GFIT - Linear-correlation coefficient obtained in the log-
normal fit
Z(I) - Natural logarithm of the actual particle diameters
corresponding to the known or calculated cumulative
percentages
Y(I) - Calculated natural logarithm of the particle diam-
eters corresponding to the known or calculated
cumulative percentages based on a true log-normal
distribution
ENDPT(I) - Actual particle diameters corresponding to the
known or calculated cumulative percentages (urn)
NENDPT - Number of particle diameters corresponding to the
known or calculated cumulative percentages
NSTAG - Number of points used in the log-normal fit pro-
cedure
I - Index which runs over the different particle diam-
eters corresponding to the known or calculated
cumulative percentages
J - Index which sequences the points which are actually
used in the log-normal fit
XY - Cumulative mass fraction less than a given particle
size
371
-------
XYY - Square root of the natural logarithm of the square
of the reciprocal of XY
A - Y-intercept of the fitted straight line
B - Slope of the fitted straight line
372
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE CFIT USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
A - Y-intercept of the fitted straight line
B - Slope of the fitted straight line
R - Linear-correlation coefficient for the straight
line fit
NSTAG - Number of data points that are fitted to the straight
line
Z(I) - Values of the independent variable
Y(I) - Values of the dependent variable
XN - Running sum over the number of data points
SUMX - Summation over all data points of the values of
the independent variable
SUMY - Summation over all data points of the values of
the dependent variable
SUMXY - Summation over all data points of the values of the
product of the independent and dependent variables
SUMXX - Summation over all data points of the values of the
square of the independent variable
SUMYY - Summation over all data points of the values of the
square of the dependent variables
I - Index which runs over the different data points
373
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE PRTSUM USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
ATOTAL - Total collection plate area of the precipitator
(m2)
VG - Gas volume flow rate in a particular electrical
section (m3/sec)
SCA - Specific collection area of the precipitator
(m2/m3/sec)
VOSUM - Sum of the applied voltages in the different linear
electrical sections (V)
CDSUM - Sum of the current densities in the different lin-
ear electrical sections (nA/cm2)
NUMSEC - Number of linear electrical sections in the precip-
itator
LSECT(I) - Number of length increments in the different linear
electrical sections
LINGS(I) - Lengths of the increments taken in the different
linear electrical sections (ft)
I - Index which runs over the different linear electri-
cal sections
VOS(I) - Applied voltages for the different linear electrical
sections (V)
TCS(I) - Total current for the different linear electrical
sections (A)
AS(I) - Collection plate areas for the different linear
electrical sections (m2)
AVO - Average applied voltage over the entire precip-
itator (V)
PL - Total electrical length of the precipitator (ft
and m)
374
-------
ACD - Average current density over the entire precipitator
(nA/cm2)
RHO - Resistivity of the collected particulate layer
(ohm-m)
RHOCGS - Resistivity of the collected particulate layer (ohm-
cm)
NPRNT - Indicator which specifies the unit number of the out-
put device for printing data from the program
NRUN - Indicator that specifies which set of nonideal
conditions is under consideration
SCOREF - Overall mass collection efficiency under no-rap +
rap conditions (%)
ZMMDI - Specified or fitted mass median diameter of the
inlet particle size distribution based on a log-
normal distribution (ym)
SIGMI - Specified or fitted geometric standard deviation of
the inlet particle size distribution based on a log-
normal distribution
CZMDL - Fitted log-normal mass median diameter of the out-
let particle size distribution under no-rap + rap
conditions (ym)
CSIGMO - Fitted log-normal geometric standard deviation of
the outlet particle size distribution under no-rap
+ rap conditions
SNUCK - Particular value of ASNUCK(JJ)
ZIGGY - Particular value of AZIGGY(JJ)
RMMD - Particular value of ARD50(II) [ym]
RSIGMA - Particular value of ARSIGM(II)
375
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE CMAN USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
NX - Number of grid points in the x-direction for the
numerical calculations of electrical conditions
NX1 - Number of grid intervals in the x-direction for the
numerical calculations of electrical conditions
NY - Number of grid points in the y-direction for the
numerical calculations of electrical conditions
NY1 - Number of grid intervals in the y-direction for the
numerical calculations of electrical conditions
SX - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AX - Interval size in the x-direction (m)
SY - One-half the wire-to-wire spacing in a particular
linear electrical section (m)
AY - Interval size in the y-direction (m)
I - Index which runs over grid points in the x-direction
J - Index which runs over grid points in the y-direction
X - Value of x representing grid points (m)
Y - Value of y representing grid points (m)
VW - Electrical potential at the wire (V)
VCOOP(I,J) - Array containing the values of static potential
at the different grid points (V)
NWIRE - Number of wires per electrical section per gas
passage in a particular electrical section
M - Series sum in equation (1) is taken from -M to M
376
-------
SUMX - Term in the sum for x-component of static electric
field
SUMY - Term in the sum for y-component of static electric
field
SI - Parameter used in computing x-component of field
at wire
S2 - Parameter used in computing y-component of field
at wire
EXSUM - Parameter used in computing x-component of static
field
EYSUM - Parameter used in computing y-component of static
field
H3 - Sine function in equation (2)
F3 - Sine function in equation (1)
MUM - Sum in equation (1)
DENOM - Sum in the denominator of equation (2)
PI - Value of the constant IT
El - Arguments for the hyperbolic cosine functions in
equation (1)
Fl - Arguments for the cosine functions in equation (1)
Gl - Arguments for the hyperbolic cosine functions in
the denominator of equation (2)
Hi - Arguments for the cosine functions in the denom-
inator of equation (2)
E2 - Hyperbolic cosine functions in the denominator of
equation (2)
F2 - Cosine functions in the denominator of equation (2)
G2 - Hyperbolic cosine functions in the denominator of
equation (2)
H2 - Cosine functions in the denominator of equation (2)
TT - Argument for the logarithmic function in equation (1)
TB - Argument for the logarithmic function in the denom-
inator of equation (2)
377
-------
F - Logarithmic function in equation (1)
G - Logarithmic function in the denominator of equation
(2)
E3 - Hyperbolic sine function in equation (1)
G3 - Hyperbolic sine function in equation (2)
ECX(I,J) - Array containing values of the x-component of the
static field
ECY(I,J) - Array containing values of the y-component of the
static field
XI(I) - Array containing x-components of grid points
Y1(J) - Array containing y-components of grid points
LTEST - Logical variable which determines when to use X1&Y1
NVII - Integer which determines when the approximations
are used
EXO - Parameter used to compute x-component of field at wire
EYO - Parameter used to compute y-component of field at wire
378
-------
LIST OF NECESSARY VARIABLES, DEFINITIONS, AND UNITS
FOR SUBROUTINE EFLD3 USED IN THE ELECTROSTATIC
PRECIPITATOR PERFORMANCE MODEL
IVCK - Indicator which terminates the calculation of points
on the voltage-current whenever the specified applied
voltage is reached and interpolated upon
VO - Specified operating applied voltage
-------
NWIRE - Number of wires per electrical section per gas
passage in a particular electrical section
VCOOP(I,J) - Array containing the values of static potential
at the grid points (V)
V(I,J) - Array containing the value of the electric potential
at each point in the grid during an iteration (V)
NPRNT - Indicator which specifies the unit number of the
output device for printing data from the program
RHO(I,J) - Array containing the value of the space charge
density at each point in the grid during an itera-
tion (coul/m3)
EX(I,J) - Array containing the value of the component of the
electric field intensity perpendicular to the plates
at each point in the grid during an iteration (V/m)
EY(I,J) - Array containing the value of the component of the
electric field intensity parallel to the plates at
each point in the grid during an iteration (V/m)
LTEST - Logical variable which determines whether a uniform
grid spacing is used
NVII - An integer which determines whether measured operating
conditions are used or a theoretical I-V curve is
generated
ECX(I,J) - x-component of the static electric field
ECY(I,J) - y-component of the static electric field
Xl(I) - Position of grid points in the x-direction
Yl(J) - Position of grid points in the y-direction
AX(I) - Grid point separation in the x-direction
AY(J) - Grid point separation in the y-direction
Z - Dummy arguments in statement functions COSH(Z) and
SINH(Z)
R - Ratio Rl/Sx
Al - Constant = ir/2Sx
Bl - Constant = 2J/be0
380
-------
MOBILT(I,J) - Array containing the values of effective charge
carrier mobility at the different grid points (m2/
V-sec)
PI - Value of the constant TT
EPSO - Permittivity of free space (cou!2/nt-m2)
START - Particular value of STARTl(I) [A/m2]
SSTART - Initial value of START which is saved (A/m2)
MAXS - Particular value of current density on the voltage-
current curve (A/m2)
NXl - Number of grid intervals in the x-direction for the
numerical calculations of electrical conditions
NY1 - Number of grid intervals in the y-direction for the
numerical calculations of electrical conditions
SX - Wire-to-plate spacing in a particular linear elec-
trical section (m)
AX - Interval size in the x-direction (m)
SY - One-half the wire-to-wire spacing in a particular
linear electrical section
AY - Interval size in the y-direction (m)
IFINAL - Indicator which causes the calculation of successive
points on the voltage-current curve to cease after
IFINAL points
II - Index which runs over the different current densi-
ties to be used on the voltage-current curve
JI1 - Indicator which allows the initial increment size
on current density in the calculation of the voltage-
current curve to be changed after JI1-1 points are
determined on the curve
ubTART - Particular value of START2(I) [A/m2]
JI2 - Indicator which allows the second increment size on
current density in the calculation of the voltage-
current curve to be changed after JI2-1 points are
determined on the curve
CSTART - Particular value of START3U) [A/m2]
381
-------
BIR - Constant = (Bl)*5
Cl - Constant = BlSy/ir
VWIR - Space charge contribution to the potential from
points outside Sy
EXWIR - Space charge contribution to the x-component of the
field from points outside Sy
EYWIR - Space charge contribution to the y-component of the
field from points outside Sy
El - Independent variable associated with Fl in the method
of false position
E2 - Independent variable associated with F2 in the method
of false position
E3 - The latest estimate of the root of F in the method
of false position
Fl - Negative value of the function in the method of
false position
F2 - Positive value of the function in the method of
false position
F - Function in the method of false position whose root
determines when the specified operating voltage has
been obtained
NW - Number of wires per electrical section per gas passage
in a particular electrical section
Rl - Distance from the wire at which the analytic solutions
are matched
SUMl - A sum over the wires which contributes to the static
potential at the wire
SIG1 - A sum over the wires which contributes to the static
potential at the wire
RM - Floating point whole number used to avoid problems
with mixed mode arithmetic
CH - Hyperbolic cosine function in the static potential
expression evaluated at y = Sy
POTl - A constant used in evaluating the static potential
at the wire
382
-------
SUMV - A sum over the space charge cylinders which contri-
butes to the static potential at the wire
SUMW - Quantity = 2SUM1
SQON - A parameter to help simplify the coding of the
mathematical expressions in the electrical solutions
SQOP - A parameter to help simplify the coding of the
mathematical expressions in the electrical solutions
RNN - A parameter to help simplify the coding of the
mathematical expressions in the electrical solutions
RNP - A parameter to help simplify the coding of the
mathematical expressions in the electrical solutions
ARGR - A constant = TrRl/2Sx
FAC1 - The expression represented by F in equation (22)
ACOS - The value of ARCCOS (Sy/Rl) in equation (22)
DUM - The quantity shown in brackets in equation (22)
RLAM - The predicted value of static potential at the wire
RAD - A parameter used to simplify the coding of the
mathematical expressions in the electrical solutions
RASX - A parameter used to simplify the coding of the
mathematical expressions in the electrical solutions
RARl - A parameter used to simplify the coding of the
mathematical expressions in the electrical solutions
RONSP - A parameter used to match the charge density pro-
files at x = Rl
CLAM - A parameter used to match the x-components of the
electric field at x = Rl
WLAM - A parameter used to specify the effective value of
space charge density outside the region of Sy
VNAUT - A parameter used to match the potentials at x = Rl
VT - The total potential at the wire
ICOUNT - An integer which counts the number of tries to match
the specified operating voltage in the method of
false position
383
-------
Ill - Do loop parameter which increments x over the
grid points
112 - Do loop parameter which increments y over the
grid points
SQRN - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
SQRP - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
SQXN - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
SQXP - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
ARGX - Quantity = irx/2Sx
ARGY - Quantity = iry/2Sy
RAXY - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
RASXY - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
RAR1Y - Parameter which simplifies coding the mathematical
expressions in the electrical solutions
COSHY - Hyperbolic cosine evaluated at iry/2Sx
SINHY - Hyperbolic sine evaluated at uy/2Sx
CX - Cosine function evaluated at Trx/2Sx
VXYJ - Space charge contribution to the potential
EXJ - Space charge contribution to the x-component of the
electric field
EYJ - Space charge contribution to the y-component of the
electric field
RHOJ - Space charge density
SUMEX - A sum over space charge cylinders which contributes
to the x-component of the electric field
SUMEY - A sum over space charge cylinders which contributes
to the y-component of the electric field
384
-------
COSX - Cosine function evaluated at trx/2Sx
SINX - Sine function evaluated at fry/2Sy
COSHN - The hyperbolic cosine function containing the negative
sign in equations (8) - (13)
COSHP - The hyperbolic cosine function containing the positive
sign in equations (8) - (13)
SINHN - The hyperbolic sine function containing the negative
sign in equations (10) - (13)
SINHP - The hyperbolic sine function containing the positive
sign in equation (10)
DENON - Quantity = COSHN2 - COSX2
DENOP - Quantity = COSHP2 - COSX2
TERMV - Logarithmic contributions to the potential from space
charge at a point outside Sy
TEREX - Quantity used in summing the contributions to the
x-component of the field from space charge outside
Sy
SUMEX - The sum contributing to the x-component of the field
due to space charge outside Sy
TEREY - Quantity used in summing the contributions to the
y-component of the field from space charge outside
Sy
SUMEY - The sum contributing to the y-component of the field
due to space charge outside Sy
OLDV(I,J) - Array containing the value of the electric potential
at each point in the grid during the previous itera-
tion (V)
OLDRO(I,J) - Array containing the value of the space charge den-
sity at each point 4- 4-w- —-J J ' - ••
iteration (coul/m3)
sity at each point in the grid during the previous
CDNSTY(I,J) - Array containing the value of current density at
each point in the grid (A/m2)
ACDNTY - Average current density at the plate (A/m2)
EPLT - Sum of the values of the electric field intensitv
at the plate (V/m) *
385
-------
AEPLT - Average electric field at the plate (V/m)
EBD - Electrical breakdown strength of the gas near the
collection electrode or the collected particulate
layer (V/m)
OLDVW - The value of applied voltage at the point prior to
the one under consideration (V)
OLDCD - The value of average current density at the plate
at the point prior to the one under consideration
(A/m2)
NEC - Indicator which determines whether or not the aver-
age current density, average electric field, and
average electric field at the plate are to be calcu-
lated in the subincremental lengths
K -
RSUM -
ESUM -
EAVGS(K) -
Index which sequences the grid strips in the basic
area for which the calculations are performed
Average charge number density in a particular grid
strip (#/m3)
Average electric field intensity in a particular
grid strip (V/m)
Array containing the average electric field inten-
sities in the different grid strips in the basic area
for which the calculations are performed (V/m)
CHFIDS(K) - Array containing the average charge number densities
in the different grid strips in the basic area for
which the calculations are performed (#/m3)
NYY - Index which renumbers the grid strips so that by
symmetry the area covered by the half-wire spacing
which was not considered in the calculations can be
taken into account
EAVG(L) - Array containing the average electric field inten-
sities in the different grid strips which cover an
area between successive wires (V/m)
CHFID(L) - Array containing the average charge number densities
in the different grid strips which cover an area
between successive wires (#/m3)
L - Index which runs over and numbers the first (NY-1)
grid strips in a given wire-to-wire spacing
386
-------
KK - Index which runs over the different grid strips in
the basic area for which the calculations are per-
formed
Ml - Number of the first grid strip in the last (NY-1)
grid strips in a given wire-to-wire spacing
M2 - Number of the last grid strip in a given wire-to-
wire spacing
M - Index which runs over and numbers the last (NY-1)
grid strips in a given wire-to-wire spacing
LL - Index which sequences the grid strips in the basic
area for which the calculations are performed
NN - Index which runs over points in the y-direction
ECOLLS(LL) - Array containing the average electric field inten-
sity at the plate in the different grid strips in
the basic area for which the calculations are per-
formed (V/m)
LI - Index which renumbers the grid strips so that by
symmetry the area covered by the half-wire spacing
which was not considered in the calculations can be
taken into account
ECOLL(L) - Array containing the average electric field inten-
sity at the plate in the different grid strips which
cover an area between successive wires (V/m)
L2 - Index which runs over the different grid strips in
the basic area for which the calculations are per-
formed
II - Number of the first grid strip in the last (NY-1)
grid strips in a given wire-to-wire spacing
12 - Number of the last grid strip in a given wire-to-
wire spacing
I - Index which runs over and numbers the last (NY-1)
grid strips in a given wire-to-wire spacing
387
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-80-034
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
A Mathematical Model of Electrostatic
Precipitation (Revision 2)
5. REPORT DATE
February 1980
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S) R. B.Mosley, M.H.Anderson, and
J.R. McDonald
8. PERFORMING ORGANIZATION REPORT NO.
SORI-EAS-80-065
3777-1
9. PERFORMING OROANIZATION NAME AND ADDRESS
Southern Research Institute
2000 Ninth Avenue, South
Birmingham, Alabama 35205
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
68-02-2193
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Update; 1/76 - 12/78
14. SPONSORING AGENCY CODE
EPA/600/13
15.SUPPLEMENTARY NOTES IERL-RTP project officer is Leslie E. Sparks, Mail Drop 61,
919/541-2925. This document augments, but does not replace, EPA-600/7-78-llla.
is. ABSTRACT The report Describes modifications to the EPA/Southern Research Institute
computer model of electrostatic precipitation (ESP). The modifications include a new
semi-empirical approximation procedure for predicting electrical conditions in an
ESP. Comparisons between the results from the approximation procedure and more
exact procedures are presented. A new integration procedure for calculating par-
ticle charge is also presented. Complete FORTRAN listings of the revised ESP
model and the new subprograms are provided. Example problems are included.
The modified model requires significantly less computer time than does the earlier
model. Comparisons of results obtained using the earlier and the modified models
over a wide range of possible ESP geometries and electrical operating points
indicate that for practical purposes the modified model can be used in place of the
more rigorous earlier model.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Pollution
Electrostatic Precipitation
Mathematical Models
FORTRAN
b. IDENTIFIERS/OPEN ENDED TERMS
Pollution Control
Stationary Sources
c. COSATI Field/Group
13 B
13H
12A
09B
8. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
401
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
388
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