United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S7-91/001 Apr. 1991
v^EPA Project Summary
A Self-Consistent
Deutschian ESP Model
M. G. Faulkner and J.L. DuBard
The electrostatic precipitator (ESP)
model developed by Southern Research
Institute (SRI) for EPA provides an ac-
ceptable simulation of the performance
of cold-side utility fly ash ESPs with
typical values of inlet mass loading. To
increase the accuracy of model predic-
tions in unusual situations, such as
high inlet mass loading or abnormally
low current, a revised version of the
model has been developed. The revised
model is unique in that it rigorously
calculates the effects of particulate
space charge on the interelectrode
electric field and on subsequent par-
ticle charging.
This Project Summary was devel-
oped by EPA's Air and Energy Engi-
neering 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
A more general and more powerful
mathematical model of electrostatic pre-
cipitation (ESP) has been developed
by Southern Research Institute (SRI). The
standard version of the ESP model devel-
oped by SRI'for EPA, now in its third
revision, provides an acceptable simulation
of the performance of cold-side utility fly
ash ESPs with typical values of inlet mass
loading. To increase the responsiveness
of the ESP model to situations having
high inlet mass loading and/or abnormally
low corona current, a revised version of
the model has been prepared.
Both versions of the model apply the
Deutsch equation to narrow particle size
bands over short ESP length increments
to determine particle collection efficiency.
In the standard version, the effects of
particulate space charge are estimated
by a formula that predicts an effective
mobility for combined ions and particles
and a reduced ion density for particle
charging. These estimated values are then
used to separately calculate the electric
field at the plate and the particle charge
which are required for the Deutsch equa-
tion.
The revised version differs from the
standard version in that the former treats
the particulate space charge explicitly, al-
lowing the interrelation of the particle
charge and electric field calculations. The
charge and field calculations are alternated
until they become self-consistent within
each length increment throughout the en-
tire ESP. Self-consistency occurs when
the charge used for the space charge in
the field calculation is the same as that
calculated using the results of the field
calculation. The explicit treatment of the
space charge directly relates the particle
charge and electric field calculations, and
therefore the collection efficiency calcula-
tion, to the dust load present in the gas
stream.
The revised ESP model report includes:
• operating instructions for the
revised model,
• descriptions of the input data,
the video display during
operation, and the output data,
• a discussion of the underlying
theory of the revised model, and
yy Printed on Recycled Paper
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• comparisons of the revised and
standard (Revision 3) models in
terms of logic and calculated
results.
Operating Instructions
Although the revised ESP model de-
scribed in this report was developed on a
main-frame computer, it can be run on an
IBM PC-compatible microcomputer. Be-
cause the model performs a large number
of mathematical calculations, equipping the
microcomputer with a math coprocessor
minimizes the time required for running
the model. The revised ESP model,
ESPREV.FOR, is written in Microsoft-
compatible FORTRAN and occupies
67,574 bytes of memory. The executable
file, ESPREV.EXE, occupies 264,298
bytes of memory.
To run the model, type ESPREV and
press enter. The program will prompt the
user for the names of a file containing
input data and a file into which to write the
output data. The revised ESP model reads
the same input data format as the standard
version of the model. The instructions for
creating a data set, excerpted from the
standard model instruction manual, are
given in an appendix. Descriptions of the
video display generated by the model and
the output data are given in the report.
Due to the large amount of data gener-
ated by this model, the output data are
written to a file. To obtain a hard copy of
the data, it is necessary to print this file
using a PRINT command. An option for
shortening the amount of output data
generated is provided.
Theory
The underlying assumptions for the re-
vised version of the model are listed be-
low.
1. The space charge due to charged
particles is constant in a given length in-
crement and is uniformly distributed in the
gas stream. This allows the development
of a rigorously Deutschian model, as these
were the conditions for which the Deutsch
equation was derived. The assumption of
uniformity is particularly good for fine par-
ticles in a turbulent gas flow. The fine
particles are especially important in ESP
modeling as these are the most difficult
particles for an ESP to collect.
2. The space charge due to ions is
neither uniformly distributed nor constant
because the ions follow the electric field
lines, which are non-uniform in the
interelectrode space.
3. The total space charge density is
the sum of the particulate and ionic space
charge densities. In the revised model,
the particulate and ionic densities are
treated separately and explicitly, in con-
trast to the estimated treatment of a com-
bined ionic and particulate space charge
found in the standard version of the model.
4. The current is ionic except in the
laminar boundary layer at the collection
plate. This is due to the assumption that
the particles are stationary in a given length
increment. This is a good approximation
since the particulate mobility is several
orders of magnitude less than the mobility
of the ions. Since the particles are sta-
tionary, only the ionic current density ap-
pears in the current continuity equation.
5. The ionic mobility is used only in
the calculation of the ionic current density
on the plate. The mobility drops out of the
equations in the remainder of the
interelectrode space.
6. The particulate current density is
included when determining the total cur-
rent density on the plate and is computed
from the calculated charges and Deutsch
migration velocities of the different size
particles.
7. Overall electric field convergence
is tested using the measured average plate
current density.
8. The calculations of the electric field
and the particle charge are alternated un-
til self-consistency is obtained in each in-
cremental length before proceeding to
the next incremental length in the ESP.
The self-consistency is determined by
comparing the changes in the average
electric field between successive field-
charge iterations. When the change in the
field is sufficiently small, the calculation is
assumed to have converged.
9. The algorithm in the revised ESP
model includes corrections for the non-
ideal effects of gas sneakage, non-uniform
gas flow, and rapping reentrainment. The
gas sneakage calculation is made at the
end of each section of the ESP. The non-
uniform gas flow, and rapping
reentrainment calculations are made at
the end of the efficiency calculation.
Evaluation
The primary reason for the develop-
ment of the revised ESP model was to
provide an ESP performance model that
is responsive to changes in dust loading.
This goal has been met. Data compari-
sons show that the revised model clearly
demonstrates the effects of its explicit
space charge calculation. Examination of
the calculated particle charging rate with
changes in inlet dust load show charge
retardation and then suppression as the
dust load is increased. Similar suppres-
sion of charging due to high mass loading
has been measured on a pilot ESP at
SRI. The standard ESP model gives the
same charging rate for all dust loads.
The second reason for revising the ESP
model was to eliminate the three deficien-
cies that have been identified in the stan-
dard model:
1. The space charge effects are not
explicitly calculated but are estimated
based on an effective mobility which ac-
counts for fast moving ions and slow mov-
ing particles. The effective mobility is not
a composite of mobilities but is given by
an equation that applies only to small par-
ticles near the collection plate.
2. The electric field and particle charge
calculations are not mathematically con-
nected.
3. An empirical correction factor must
be applied to the average migration ve-
locities of small particles to make their
calculated efficiencies match measured
data.
The first two deficiencies were elimi-
nated by the structure of the revised model.
It was hoped that making the revised
model rigorously Deutschian would remove
the need for an empirical correction factor
for small-particle migration velocities (the
third deficiency). A comparison of mea-
sured migration velocities to migration ve-
locities calculated by the revised model
for 10 cold-side utility ESPs chosen from
the SRI ESP data base shows that this
was not the case. By including an empiri-
cal correction factor similar to the one in
the standard model, the performance pro-
jections can be corrected.
Conclusions and
Recommendations
The revised ESP model represents an
improvement over the standard model in
that the calculations of particle charge and
collecting electric field required for the
Deutsch equation are not separate but
are interrelated such that the charging and
field calculations are made self-consistent
in each length increment of the ESP. The
algorithms used in the revised model are
conceptually rigorous, except for the con-
tinued use of an average interelectrode
electric field in the charging calculation.
These features result in a model that is
responsive to changes in dust load as
well as electrical conditions.
Following the theoretical efficiency cal-
culation, two non-rigorous corrections are
applied to model predictions: the calcula-
tion of rapping reentrainment and the cor-
rection of small-particle migration veloci-
ties. The rapping correction must be em-
pirical in nature because no applicable
theory exists. That a correction factor is
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necessary for a rigorously Deutschian
model to match the small particle migra-
tion velocities in full-size ESPs indicates a
shortcoming in the Deutsch theory, possi-
bly due to an oversimplification in the un-
derlying assumptions of the theory. At this
time, however, no competing theories of
ESP particle collection do not also require
empirically derived constants. The revised
model has been tested against the SRI
data base of conventional utility fly ash
ESPs to verify that the same answers are
obtained as from Revision 3. However, a
careful measurement program on several
high-dust-load ESPs is required before the
revised model can be validated.
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M. Faulkner and J. DuBard are with Southern Research Institute, Birmingham, AL
35255
Louis $. How's is the EPA Project Officer (see below).
The complete report, entitled "A Self-consistent Deutschian ESP Model. "(Order No.
PB91- 149518/AS; Cost: $17.00, 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:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental
Research Information
Cincinnati, OH 45268
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Penalty for Private Use $300
EPA/600/S7-91/001
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