United States
Environmental Protection
Agency
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S7-83-050 Jan. 1984
&EPA Project Summary
A Mathematical Model of
Electrostatic Precipitation for the
Texas Instruments
Programmable 59 Calculator
M.G. Faulkner and J.R. McDonald
A version of EPA's electrostatic
precipitator (ESP) model suitable for
use on a Texas Instruments Program-
mable 59 (TI-59) hand-held calculator
has been prepared. This version of the
model allows calculation of the ESP
collection efficiency, including correc-
tions for non-ideal effects and rapping
reentrainment in five size bands.
Program input data and the individual
and total collection efficiencies are
printed on a Tl Thermal Printer. This
model is described in detail including
program steps for its use. This version
and a full-scale model are compared.
This Project Summary was developed
by EPA's Industrial environmental
Research Laboratory, Research Triangle
Park, NC. to announce key findings of
the research project that is fully
documented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction and Summary
EPA's mathematical model of electro-
static precipitation was first published in
1975. Revision 1 of the model was
published in 1978. This model has been
widely used to study existing electrostatic
precipitators (ESPs) and to predict size
requirements and performance levels for
new ESPs. However, a computer of the
size required to employ the model may
not be available to some individuals who
desire to use the model. Therefore, EPA
sponsored the development of a reduced
version of the ESP model which may be
used on a programmable hand calculator.
A version of the ESP model was developed
by Southern Research Institute for use on
a Texas Instruments Programmable 59
(TI-59) calculator. The theory of ESP
operation on which the model is based
and the assumptions used, explained in a
previous report, are not repeated here.
The user is urged to obtain the earlier
report for use with this report in order to
understand the procedures.
The TI-59 calculator can write to and
read from magnetic cards, allowing a long
program to be entered into the unit in one
step. This is a necessary function: a
program of the complexity of the ESP
model requires the reading of many
magnetic cards. In addition, the use of the
accessory printer for the TI-59 allows the
creation of a permanent record for each
set of ESP operating conditions modeled.
Another advantage of the TI-59 is its
capability to vary the memory partition
between data storage and program steps
to suit a particular program. For the ESP
model, 70 data storage locations are
required, limiting the number of program
steps which can be entered to 400. To fit
into 400 spaces, the program is divided
into 8 sections, some of which must be
read into the calculator more than once to
complete the calculation.
The full scale ESP model allows the
user many options in the type of data
which may be used and in the types of
calculations which will be performed. The
limited size of the TI-59 severely limits
the options. The data must be in a
prescribed format. The calculation of the
ideal collection efficiency uses estimation
procedures rather than the exact calcula-
tions available on the full-scale model.
The program output is limited to efficiency
in each size band and overall collection
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efficiency. These are printed for the ideal
case, the ideal case corrected for several
non-ideal conditions not including rapping
losses, and the corrected case including
rapping losses. As an option, the fraction
of the effluent appearing in each size
band may be printed for the two corrected
conditions to serve as estimates of the
particle size distributions at the outlet of
the precipitator.
Each of the eight sections of the
program occupies a magnetic card. The
number of cards which are read into the
calculator varies with the desired program
output. A minimum of five cards are
required to run the model: cards 1-4 for
the ideal calculation and card Gforthe no-
rap corrections. To include rapping
reentrainment, cards 5 and 7 must be
added. Card 8 may be added if an estimate
of the particle size distribution at the ESP
outlet is desired. Once the ideal efficiency
has been calculated, it need not be
repeated to run additional sets of non-
ideal conditions. Only cards 5 through 8
need to be reread. The functions and
printed output of each card are described
below. The word NEXT, printed at the end
of each program segment, signifies that
the next card may be read in.
Card 1 is the equivalent of subroutine
LNDIST in the full scale program. This
card constructs a particle size distribution
histogram for a specified log-normal
distribution. The mass median diameter
(mmd) and geometric standard deviation
(<7P) which define the log-normal curve
and six particle size band endpoints are
supplied by the user. The calculator
computes and stores the average diam-
eters of five size bands and the fraction
of the inlet paniculate mass which occurs
in each band for later use. The fraction of
all of the paniculate mass in the 0.01 to
1000 //m size range which has diameters
outside the range of the five size bands is
added to the largest size band. The
program steps contained on card 1
occupy one card side. The input data are
printed.
Card 2 is used to enter data and
calculate constants which will be used
throughout the rest of the program. The
program on card 2 occupies two card
sides. The input data are printed.
Card 3 is used to enter data which is
unique to each electrical section of the
ESP, including the number of calculation
increments, the total collection plate
area, the applied voltage, the current, and
the wire-to-plate spacing. After the
calculations for all of the sections of the
ESP have been completed, card 3 is used
to calculate the ideal efficiency in each
size band and the ideal total efficiency.
This card is read in once for each
electrical section and once to complete
the ideal efficiency calculation. The
program material occupies one card side.
If LSECT, the first variable read by card
3, is not equal to zero, the input data are
printed. If LSECT equals zero, the printer
lists the particle diameter (//m) and ideal
efficiency (decimal) for each size band,
followed by the total ideal efficiency.
Card 4 calculates the particle charge
and the number of particles removed in
each size band for each increment of
length in the ESP section described by
card 3. This card is read in once for each
electrical section. This is a two-sided
card. However, since card Sonly occupies
one card side, it is only necessary to read
in side 2 of card 4 once. Side 1 must be
read in each time as card 3 writes over
this portion. There are no data entered in
this segment of the program and no
printed output.
Card 5 is the same as card 1. The
routine is used again at this point so that a
particle size distribution for rapping
reentrainment may be formed. If no
rapping information is desired, this card
is omitted. The full scale model has a built
in log-normal rapping size distribution
with a mmd of 6.0 //m and a ap of 2.5
which may be used with this routine in
the absence of other data.
Card 6 adjusts the ideal collection
efficiencies to compensate for several
non-ideal conditions. These conditions
include gas sneakage around the collec-
tion regions of the ESP and the velocity
distribution associated with the inlet gas
flow, but exclude rapping. In addition
there is an empirical correction to the
migration velocities of particles with
diameters less than 4.5/ym. This correction
was derived from comparisons with
migration velocities measured in full-
scale ESPs where the model predicted
values which were too low for small
particle sizes. Card 6 has two starting
points: the first is used if rapping
reentrainment is to be calculated later,
and the second is used if no rapping
information is desired or if a rapping
correction has previously been calculated
and the non-rapping conditions are being
changed for the same rapping conditions.
The program information on this card
occupies two card sides. The printer lists
the input data for this card, following
which, the particle diameter (yum) and
adjusted efficiency (decimal) for each size
band and the total adjusted efficiency are
printed.
Card 7 computes the rapping adjust-
ments to the efficiencies calculated by
card 6. Before card 7 can be run, card 5
must have been run toestablish a rapping
puff size distribution. The information on
this card occupies one side. No data is
entered in this portion of the program.
The printer lists the particle diameter (/urn]
and adjusted efficiency, including rapping
(decimal) for each size band, followed by
the total adjusted efficiency including
rapping.
Card 8 allows the user to estimate the
size distributions of the ESP effluent for
the no-rap and rapping conditions. This
routine prints the fraction of the particles
by mass which occurs in each size band,
in order of increasing size, for inlet gas
flow, adjusted no-rap outlet gas flow
(card 6), and adjusted outlet gas flow
including rapping (card 7). The fraction
printed for the largest size band in the
inlet distribution will appear to be larger
than it should since all of the mass which
lies outside the range of the five size
bands is included in the largest band. In
normal use, only a small portion of the
mass will come from particles smaller
than the five size bands. Most of the extra
mass will be in size bands larger than the
largest size band and will be collected in
the ESP. However, this effect may also
show up in the outlet fractions which are
based on the inlet fraction.
Conclusions
The procedure described in this report
provides a mechanism for modeling ESP
performance on a programmable calcula-
tor. The program is limited in that it
provides collection efficiency information
only. The full-scale model, designed for a
large computer, also prints migration
velocities, particle charges, outlet size
distribution, and other data. Of these,
only the migration velocities are available
in the hand calculator version. They are
not printed but may be retrieved from the
calculator memory. The other variables
are not available. Some, such as particle
charge, are calculated but are written
over by other variables. Others are not
calculated at all due to the limited
memory size.
Another limitation of the calculator
version of the ESP model is that it uses
only the estimation procedure available
in the full-scale model. For several
calculations, the full-scale model offers
the choice of a rigorous calculation for
maximum accuracy or an estimation to
save time. In the calculator version, the
limiting factor is memory size, which
necessitates the use of the shorter
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estimations. An additional limitation is
the use of only five size bands, again due
to the limited memory size.
The time required to model a three-
section ESP (5.5 m long) is about 37
minutes for the ideal calculation or 51
minutes for the ideal case plus three sets
of non-ideal conditions. It required 4
minutes to run the equivalent full-scale
model on a DEC PDP-15computer, which
is not a fast computer. However, the run
time for the PDP-15 does not include the
time required to enter the data, an
estimated 45 minutes. Data entry time is
included in the figures shown for the Tl-
59 version. Therefore the times required
to run the two versions are comparable.
The time required to run the rigorous
calculation (rather than estimates) with
16 size bands on the full-scale model is
1.25 hours plus 45 minutes for data
entry.
In spite of its limitations the calculator
verison achieves close agreement with
the full-scale version. For the purposes
for which it was intended, the calculation
of ESP efficiencies on a programmable
calculator, the calculator version of the
model performs very well. Therefore, it is
a useful tool for ESP model users
operating on a low budget, requiring
quick turn around time, or desiring only
efficiency information.
Recommendations
This version of the ESP model allows
the calculation of ESP efficiencies on a
relatively low-cost hand-held calculator.
This serves as a useful function in that it
provides the use of the ESP model to
people who may not have access to a
larger computer, whether due to high
operational costs, remote location, or
quick turnaround required on certain
projections. For the same reason, a study
to identify other important programs
which may be scaled down to fit on low
cost, easily portable, programmable
calculators may be beneficial.
M. G. Faulkner and J, R. McDonald are with Southern Research Institute, 2000
Ninth Avenue South, Birmingham, AL 35255.
Leslie E. Sparks is the EPA Project Officer (see below).
The complete report, entitled A Mathematical Model of Electrostatic Precipita-
tion for the Texas Instruments Programmable 59 Calculator," (Order No. PB
83-261 669; Cost: $14.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Industrial Environmental Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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