United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S7-87/027 Feb. 1988
&ER& Project Summary
Fundamental Combustion
Research Applied to Pollution
Formation: Volume IV.
Engineering Analysis
C. J. Kau, M. P. Heap, W. R. Seeker, and T. J. Tyson
This is the fourth and final volume
in a series documenting research activ-
ities conducted under the EPA's Fun-
damental Combustion Research (FCR)
program, applied to pollution forma-
tion. The FCR program had three major
objectives:
• To generate an understanding of
combustion behavior necessary to
aid in developing control strategies
to minimize NOX emissions from
stationary sources.
• To develop engineering models
which allow effective utilization of
a large body of fundamental infor-
mation in the development of new
NOx control techniques.
• To identify critical information
necessary for low-NO» combustor
development and to generate it in a
time frame which was consistent
with the needs of EPA's technology
development programs.
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
This report documents FCR program
efforts to develop engineering analysis
models, to allow the evolving body of
fundamental information to be utilized in
development of Iow-N0> combustion
control technologies.
Volume I in the series presents an
overview of the entire FCR program and
also describes FCR program efforts to
quantify the gas-phase chemistry con-
trolling NO, formation and destruction
during combustion. Volume II is a three-
part report describing studies related to
various aspects of the physics and
chemistry of two-phase systems: Volume
Ha addresses flame combustion pro-
cesses. Volume lib addresses devolatil-
ization and volatile reactions, and
Volume He describes studies of hetero-
geneous NO reduction processes.
Volume III documents the FCR program
efforts related to development and
evaluation of combustion measurement
techniques.
The prime contractor and EPA's project
officer were responsible for program
planning, management, and synthesis of
the overall combined inhouse and sub-
contract program. Approximately 70% of
the program effort involved subcontracts
to a variety of organizations throughout
the world, ensuring that the FCR program
had the benefit of the best scientific
talent available.
A substantial fraction of the experi-
mental studies reported in Volumes I, II,
and III were conducted through subcon-
tracts or were joint efforts involving both
EER and a subcontractor. Most of the
modeling, however, was performed by
EER directly. Volume IV discusses six
modeling studies conducted by EER in
support of FCR:
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1. A Computer Program for General
Flame Analysis
2. Mathematical Modeling of Micro-
scale Combustion of a Coal Particle
3. Data Analysis Through Inverse
Techniques
4. Microscale Mixing in Turbulent
Diffusion Flames
5. Numerical Model for Two-Phase
One-Dimensional Flow Reactor
6. Generation of Elliptic-Code Test
Cases
In Volume IV, each study is presented
as a separate report with individual
tables of contents, lists of figures,
conclusions, and references. The
remainder of this project summary
presents brief descriptions of the six
individual components comprising
Volume IV.
Part 1. A Computer Program
for General Flame Analysis
Most fundamental combustion
research studies investigating chemical
processes controlling pollutant formation
and destruction have been conducted in
relatively simple flow devices; e.g., well-
stirred reactors or flat flame burners.
Traditionally, evaluation of results from
such flame experiments has relied on
computational procedures designed to
analyze chemical processes in stirred or
plug flow reactors. The need for a
generalized computational procedure to
analyze chemical phenomena under flow
conditions where diffusional processes
exert an important influence (e.g., in the
active flame zone of a flat flame burner)
has long been recognized. Part 1 doc-
uments development of a computer code
capable of predicting or analyzing various
types of premixed or diffusion flames.
The specific FCR purpose behind devel-
oping this computer code was to analyze:
various flat flame data, opposed-jet
diffusion flame data, and co-flowing
diffusion flame data.
A generalized flame analysis proce-
dure (GFAP) was developed which allows
computational evaluation of a variety of
flow configurations including: one-
dimensional, time-dependent planar/
spherical flows; steady two-dimensional
planar flow; and steady axisymmetric
nonrecirculating flow. For each broad
flow category, the code has been opti-
mized for analysis of reacting chemical
kinetic processes. Specifically, GFAP can
treat up to 200 two- or three-body
simultaneous basis reactions involving
up to 52 species. In addition, the code
incorporates procedures to account for
laminar unequal species diffusion, radi-
ation heat transfer, flame holder recom-
bination chemical effects, and flame
holder heat loss. Flame holder heat loss
and recombination effects are important
phenomena influencing early chemical
kinetic processes in classical experimen-
tal devices such as flat flame burners.
The computation procedure used in
GFAP is an implicit finite difference
network. Except for cross-stream veloc-
ity, all dependent variables for all grid
points at the same coordinate line (or at
the same integration step) are solved
simultaneously in a coupled fashion.
Mathematically, this requires the inver-
sion of a block tridiagonal matrix at each
integration time step. For that purpose
a band-matrix factorization method has
been used. This method has been found
to require approximately 10 to 20% of
the computer run time of popular alter-
nate techniques such as implicit/explicit
methods or operator splitting methods.
This band-matrix factorization method is
described in detail in the report.
To illustrate use of the code, results
from four example test cases are des-
cribed. The first sample case is for a free
jet diffusion flame. The specific sample
presented considered a 0.635 cm diame-
ter (R0 = 0.3175 cm) jet of hydrogen
issuing into a still air environment at an
initial velocity of 1000 cm/sec. Figure
1 illustrates the calculated radial temper-
ature and major species concentration
profiles at axial location x/R0 = 5.0. As
shown, the flame front is predicted to
occur approximately 1 cm from the
centerline. The peak temperature of
about 2400°K occurs slightly on the fuel-
rich side of the flame front. Diffusional
effects are clearly shown by the spread
of the water concentration profile from
the flame front toward both the center-
line fuel core and into the quiescent
region outside the flame. A second
example calculation is presented for a co-
flowing diffusion flame. For this second
calculation the fuel jet was established
as a low Btu gas doped with model fuel-
bound nitrogen compounds. Combustion
air was provided as a co-flowing stream
(fuel and air jets are at different initial
velocities) in a confined annular arrange-
ment. The specific configuration modeled
represented a flame examined in a
previous EPA contract. This allowed a
comparison of model predictions with
experimental data. The final two exam-
ples presented in this part of Volume IV
were of a classical flat flame burner and
a constant strain-rate opposed-jet diffu-
sion flame. Use of this code for evaluation
of opposed-jet diffusion flames and co-
flowing diffusion flames formed a major
component of the effort described in Part
6 of this volume.
Part 2. Mathematical Modeling
of Microscale Combustion of a
Coal Particle
Several of the FCR program experi-
mental studies addressed various
aspects of the chemistry and physics of
burning pulverized coal particles. Volume
lla gave results from studies to visualize
the physical process of coal devolatiliza-
tion. Volume lib gave results from: a
study to quantify the volatility of fuel
nitrogen from coal (and oil), a study to
develop a chemical model of coal particle
devolatilization, and an effort to develop
a coal-fired well-stirred reactor. Volume
He gave results of an extensive evaluation
of reactions between nitrogenous gas-
phase species and solid surfaces such
as coal, char, or soot. In support of these
extensive coal experimental efforts the
FCR program also embarked on an effort
to develop a computer model describing
the microscale processes associated
with pulverized coal combustion. In
particular, the model was configured as
a module for incorporation into the GFAP
code described in Part 1.
Figure 2 is a schematic diagram of the
microscale environment for the combust-
ing pulverized coal particle assumed in
the model. The impermeable boundary
noted in the figure is a feature of the
model which allows the combustion
products from the flame zone to vitiate
the local oxidizer region and also allows
for variation of the overall reaction
stoichiometry. By adjusting the relative
size of this boundary it is possible to
evaluate fuel particle size effects. The
coal particle itself is assigned specific
physical properties (e.y., diameter, den-
sity, thermal conductivity). From a chemi-
cal and decomposition perspective,
however, it is assumed to consist of five
basic categories of constituents: (1) light
volatiles (H2, CO, CO2, moisture, and
aliphatics), (2) volatile nitrogen, (3) tar
(having chemical structure similar to
parent coal), (4) char (basically carbon
plus some residual nitrogen), and (5) ash
(including sulfur and other mineral
matter). As the coal particle is heated.
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Figure 1.
0.5 1-0
Radial Location (cm)
Distribution of stable species and temperature at x/R0 = 5.0.
2.0
Impermeable
Boundary
Figure 2. Microscale combustion of a coal particle in a confined space.
devolatilization begins with the evolution
of light volatiles, volatile nitrogen, and
tar. Evolution of these materials is
treated as three parallel processes
described as first-order chemical reac-
tions. The rates of these processes are
described through a rate constant cast
in an Arrhenius form. Different rate
constants are assumed for the different
components of these functional groups.
Char is basically the residual after the
light volatiles, volatile nitrogen, and tar
are evolved. The mass rate of char
oxidation is calculated as a function of
the particle's external surface area.
Expressions are incorporated into the
code to account for char oxidation as well
as gasification of char by CO2 and H2O.
The governing equations describing
the physical situation shown in Figure
2 and the chemical devolatilization
process were developed in their time-
dependent, one-dimensional (spherical)
boundary layer form. As the mass of the
coal particle evolves to the gas phase,
it is allowed to react with the surrounding
oxidizer. Those gas-phase reaction pro-
cesses are describable as a set of up to
200 simultaneous elementary reactions
involving up to 52 species. Burning of
the voilatiles releases heat which is
partially fed back to the coal particle (to
sustain devolatilization) and partially
transferred to the surroundings.
To illustrate use of the model, sample
cases were run in which 50 and 100 urn
initial diameter bituminous coal particles
were suddenly immersed in a puff of hot,
lean combustion products. The initial
background gas composition was
assumed to be the equilibrium combus-
tion from burning CH4 at an equivalence
ratio go = 0.6, and its temperature (Tgo)
was assumed to be 1662°K. By adjusting
the diameter of the impermeable boun-
dary consistent with an interparticle
spacing of 57 times the particle diameter,
the oxygen content at the end of the
combustion process was found to be
approximately 2%. Model output is
illustrated in Figure 3 as a plot of surface
mass flux versus reaction time. For the
50 /L/m particle (solid line), the first peak
occurs at about 2 ms and represents the
water content in the coal. The second
peak represents evolution of the COg
component in the light volatiles. The
predicted lifetime of the 50 fjm particle
is about 95 ms, while the lifetime of a
100 /um particle is about 350 ms. Dou-
bling the particle diameter approximately
quadruples the burnout time.
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10
Figure 3.
t (Sec)
Mass flux rate of SO and 100 fjm bituminous coal particles in high heat loss
environment.
In addition to prediction of coal particle
burnout times, the model can predict
chemical products from the burning
process. As described in other volumes
of this report, there are many uncertain-
ties in the appropriate description of the
physical and chemcal processes asso-
ciated with coal combustion. The current
model should be viewed as a numerical
framework for evaIuating various aspects
of the burning process and for evaluating
the relative importance of different
mechanisms. As an example of that
model's use, calculations were per-
formed to ascertain the characteristic
times for a variety of physical and
chemical processes associated with
pulverized coal combustion. Included
were evaluations of particle heat-up
times, devolatilization times, CO com-
bustion times, NO formation times, and
the time constant for NO reduction by
heterogeneous reaction. Using reaction
rate data for heterogeneous NO reduc-
tion reported in Volume lie of the report,
the characteristic time for this process
was calculated to be on the order of
minutes, a process far too slow to be of
practical importance in coal fired boilers.
Part 3. Data Analysis Through
Inverse Techniques
Much data have been generated (not
necessarily by the FCR program) from
experimental combustion systems,
including information on the in-flame
temperature and chemical species con-
centration profiles. Interpretation of
these practical flame data is generally
frustrated by a lack of information on the
interaction between chemical produc-
tion/destruction processes and turbu-
lent transport processes. For combustion
systems such as boilers with complex
furnace fluid mechanics, data on the
concentration profiles of pollutant spe-
cies are not sufficient to determine the
dominant location of pollutant formation
or the rate of the production process. To
extract that type of information from the
experimental data it is necessary to also
have information on the effective turbu-
lent species diffusivity. It is possible to
experimentally determine effective diffu-
sivity by measuring the concentration
profiles of non-reactive tracer gases as
part of an experimental testing program.
However, such data are generally not
part of the existing data base.
Part 3 of this volume reports on a short
FCR effort to develop a computational
procedure which could be used to extract
turbulent transport information from
experimental test data on velocity,
temperature, and species concentration
profile data. The methodology described
is called an "Inverse Analysis Tech-
nique." Specifically, the governing flow
equations are first set up in a finite
difference format, and the available
experimental data are used to extract
desired additional information on the
flow. For example, the turbulent eddy
diffusivity is the only unknown in the
momentum equation derived from mea-
sured velocity (and density) data. The
chemical production rate is the only
unknown in the species conservation
equation.
Numerical procedures were developed
which would use available experimental
data, cast that data in the form of the
governing flow equations, and extract
specifically desired additional informa-
tion. To evaluate the numerical proce-
dures employed, "data" were artificially
generated through use of the G FAP code
described in Part 1 of the volume.
Specifically, calculated velocity and
density profiles from co-flowing diffusion
flame calculations were input to the
Inverse Analysis and used to calculate
the viscosity profiles. Similarly, NO
concentration profiles were used to
calculate the distribution of the net NO
production rate. These analyses indi-
cated that the code was properly per-
forming the required mathematics but
that the input data had to be extremely
smooth in order for the code to produce
meaningful results. Brief attempts were
made to evaluate actual experimental
data from several sources. These
attempts were not successful because
the divergent terms in the governing
equations had to be evaluated from
sparsely measured data points ano
because of the procedure's extreme
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sensitivity to data smoothness. Based on
these observations, further efforts in this
area were not pursued.
Part 4. Microscopic Mixing in
Turbulent Diffusion Flames
One of the more significant areas of
recent fluid mechanics research related
to combustion is the notion that turbulent
flows are characterized by large-scale
coherent structures. The study of turbu-
lent fluid mechanics has led to re-
examination of classic as well as more
recent jet diffusion flame data. Part 4 of
this volume documents an effort to
develop a simple model describing the
chemical processes in a turbulent jet
flame. The focus of the effort is to
describe the NO formation process in
such a simple flow but to incorporate the
basic elements of modern turbulent flow
structure theory.
The rate of mixing and reaction in a
turbulent environment is much faster
than rates due to molecular diffusion
because of the ability of turbulence to
rapidly transport and mix properties. For
example, the combustion rate in an
industrial flare is many times higher than
the corresponding rates in a laminar
candle flame. Laminar transport is
controlled by diffusional processes.
The modern view of turbulent transport
and turbulent jet flame begins with
entrainment of air into the jet. Empiri-
cally, this entrainment rate is determined
by the jet momentum and is linear with
distance. The actual entrainment takes
the form of large-scale inviscid intertwin-
ing of fuel and air; i.e., air is carried into
the jets in large-scale eddies. The large
eddies cascade to smaller eddies due to
the dissipative nature of turbulence until
they are small enough for the reactants
to molecularly diffuse across the scale.
The final scale, or "Kolmongorov's micro-
scale," is the smallest turbulent scale at
which point viscosity smooths out veloc-
ity fluctuations. Within this framework,
reactions of fuel and air can occur in two
distinct regions: one is on the very thin
diffusive interface between fuel and air
on the large structures, and the other is
at the small scale where the entrained
air has been homogenized with the fuel.
The bulk of the reaction proceeds at the
microscale due to the relatively small
amount of interface surface area avail-
able for reaction on the large structures.
Because the reactants are finally hom-
ogenized by molecular diffusion, the
reactions are expected to occur at
stoichiometric conditions-similar to a
laminar diffusion flame.
A simple combustion model consisting
of coupled plug-flow and well-stirred
reactors has been developed which
incorporates the basic modern notions of
turbulence discussed above. The
approach is to follow a mass of fuel as
it leaves a nozzle and mixes with air at
the rate of entrainment of air. At any
given time, the mass of fuel and the air
entrained to that point are undergoing
the cascade to the smaller scales or have
already reached the smallest Kolmon-
gorov scale. To simplify the model,
reactions taking place on the interface
of the large structures are ignored
because the extent of reaction is small
relative to that taking place as the fuel
and air are homogenized at the small
scale. Fast reactions are completed when
the fuel and air are homogenized by
molecular diffusion in the small scale
flamelets. Slow reactions, however, take
place in two environments: the first
involves the homogenizing flamelet as
the fuel and air finally diffuse together
at stoichiometric conditions, and the
second is in the flame core as a homog-
enized packet of fuel and air entrains
more air and cascades to smaller scales.
The model is formulated as two inte-
racting reactors as shown in Figure 4.
The reactors A and B together contain
a unit mass of fuel to which air is added
at the entrainment rate. Reactor B
represents the flamelet wherein reac-
tions occur at stoichiometric conditions.
_d i m. 1
dt ' m0>
Flamelet
Well Stirred
Reactor
d trh,a)
dt ' rh0 >
Figure 4. Schematic of reactor model.
Reactor A represents the flame core
which has variable stoichiometry,
depending on the distance from the jet
entrance. These concepts are imple-
mented in the model by taking Reactor
B to be a well-stirred reactor and Reactor
A to be a plug-flow reactor. Residence
in the flamelet Reactor B is taken to be
the time to diffuse across the microscale
which is inversely related to the square
root of the initial jet Reynolds number.
The rate of mass interchange between
the two reactors is determined by the rate
of air entrainment into the flame and the
requirement that reactions in the flame-
let reactor occur at stoichiometric con-
ditions. Model predictions for a hydrogen
flame in air are presented to illustrate
the code (the same general case as that
discussed in Part 1). Results from these
initial calculations are compared with
experimental data, and the comparison
is used to set adjustabale model
parameters.
Part 5. Numerical Model for
Two-Phase One-Dimensional
Flow Reactor
A major goal of the FCR program's
modeling component was to provide
computational procedures to assist in
analysis o' data generated in the exper-
imental components of the program. As
described in Volume II, one of those
experimental efforts involved develop-
ment and testing of a coal-fired well-
stirred reactor. In support of that effort,
a computer Model was developed which
caii analyze various types of two-phase,
one-dimensional, nondiffusive reacting
flows (e.g., plug flows). The model is also
applicable to zero-dimensional, time-
dependent flow problems and zero-
dimensional steady problems with
asymptotic solutions (such as well-
stirred reactors). Thus, a more general
computational procedure was developed
to meet the anticipated data analysis
needs of the FCR program. This portion
of the report describes the code formu-
lation, the numerical method of solution,
and results from two sample test cases.
An appendix to this portion of the report
describes required code input parame-
ters and the various options built into the
code.
Part 6. Generation of Elliptic-
Code Test Cases
The focus of the FCR program was
development of fundamental information
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in support of EPA's efforts to control
emissions of NO, from stationary com-
bustion sources. The focus of the EPA
effort has been on combustion modifi-
cation which involves control of both the
thermal environment and the fuel/air
mixing history in flames. The various
computational tools described in earlier
portions of this report provide the EPA
with an ability to analyze coal combustion
processes under a variety of conditions.
Those tools do not, however, provide the
ability to analyze under the complex fluid
mechanic conditions characteristic of
practical steam-raising equipment. Spe-
cifically, those tools do not provide a
capability to analyze flame phenomena
or fluid mechanic phenomena in situa-
tions involving recirculating flow field.
When the flow field being analyzed
contains recirculation zones, the charac-
ter of the governing equations will be
elliptical (not parabolic). Numerical
procedures to solve multi-dimensional
elliptical equations are far more complex
than that required for the companion
parabolic problem.
A number of organizations, including
EPA, EER, and several of the FCR
program subcontractors, have been
involved with development of computa-
tional procedures to solve the flow field
equations in their elliptical form. Early
experience with these codes had
revealed a number of potential problems.
Some of those early difficulties may have
been associated with inaccurate models
of critical flow processes (e.g., insuffi-
cient models of the turbulent mixing
process or insufficient description of the
heat release process), but at least a
portion of those difficulties could be
traced to difficulties with the numerical
procedures used to solve the governing
equations. During the period of the
contract, many government and private
research organizations continued devel-
opment of advanced procedures for
solving the elliptic flow equations. Many
requests were received to have the FCR
contract support further development of
such models and/or application of such
a code to problems of particular interest
to EPA. There was strong technical
justification to providing such support, if
it could be shown that the code could
efficiently solve the governing equations.
However, there was equal justification
to withhold such support until it could
be demonstrated that a given code could
accurately perform the requisite mathe-
matics. Accordingly, an FCR program
effort was initiated to develop test cases
which could be used to evaluate the
numerical accuracy of any elliptic fk>w
code which might be supported as part
of FCR. Part 6 of this volume describes
results from the project to develop
appropriate test cases.
In developing a series of test cases,
it was important to focus on evaluating
a candidate code's ability to solve the
elliptic differential equations and not to
focus on the physics and chemistry
embedded within the equations. The
major effort in developing appropriate
test cases was to find flow situations with
known and verifiable descriptions of all
significant parameters and profiles.
Results from even the most carefully
conducted experiments would not be
suitable since failure of a code to
reproduce results could be due to inac-
curate modelsfor some phenomena such
as turbulence or it could be caused by
an inadequate numerical analysis tech-
nique. The solution found was to identify
a series of flow problems which, in their
base configuration, admitted to solution
through application of parabolic analysis
procedures which took on elliptic charac-
ter when subjected to a simple transfor-
mation. Two flow configurations meeting
these criteria identified: an opposed-jet
diffusion flame, and a co-flowing planar
jet flame. In their normal orientation,
both of these flames admit to analysis
using parabolic analysis procedures.
However, if the orientation of these flows
is rotated relative to the computational
grid structure, the governing equations
take on elliptic character.
To develop the elliptic code test cases,
an arbitrary opposed-jet diffusion flame
and an arbitrary co-flowing planar jet
flame were selected for analysis. These
flow cases were established in their
normal orientation and analyzed using
the computational tools described in Part
1. The results from these parabolic
analyses were then transformed to
generate the required elliptic flow cases.
Figure 5 illustrates the process used for
the opposed-jet cases. As shown (Figure
5a), the base analysis has the coordinate
origin located in the center of the
diffusion flame, with the oxidizer on one
side of the flame and the fuel on the
opposite side. The first transformation
step is to rotate the coordinates by an
angle and to carve out a new compu-
tational domain such that the active
flame extends diagonally across the
domain. Finally, the origin is translated
to one corner of the domain. Results from
the baseline can be used to specify all
necessary conditions on all boundaries.
An important aspect of the abov(
described procedure is that concern ove
a candidate model's description o
processes such as turbulent transport o
description of the chemical reactioi
process can be removed. For the tes
cases actually developed, a simpli
diffusive transport model was impose*
equivalent to a specification of molecula
diffusion with large "effective" coeffi
cients. Also, a simple, slow set of reactioi
chemistry was used. Both the turbuler
transport and the reaction chemistr
models were arbitrarily adjusted to mak
the initial problems as simple as possibl
while still maintaining critical feature
of the flow. An exact description of a
physical models used in developing th
test cases was provided as part of th
test case package along with instruction
indicating that these same submodel
were to be incorporated into the ellipti
flow codes. Full descriptions of th
resultant test cases as well as th
"correct answers" are included in thi
final part of the FCR report volume. Thes
test cases should have future use b
careful researchers who wish to subjei
their computational procedures to a
unbiased quality assurance evaluation.
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la) lb> (c) x"
Figure 5. Coordinate transformation of an opposed-jet diffusion flame.
C. Kau, M. Heap, W. Seeker, and T. Tyson are with Energy and Environmental
Research Corporation, Irvine, CA 92718.
W. Steven Lanier is the EPA Project Officer (see below).
The complete report, entitled "Fundamental Combustion Research Applied to
Pollution Formation: Volume IV. Engineering Analysis," (Order No. PB 88-
144 001/AS; Cost: $25.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 7O3-487-4650
The EPA Project Officer can be contacted at:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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Agency Cincinnati OH 45268
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