United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S7-90/003 May 1990
&EPA Project Summary
A Model of Turbulent Diffusion
Flames and Nitric Oxide
Generation
J.E. Broadwell, T.J. Tyson, and C.J. Kau
A new view is described of mixing
and chemical reactions in turbulent
fuel jets discharging into air. Review
of available fundamental data from jet
flames leads to the idea that mixing
begins with a large scale, inviscid,
intertwining of entrained air and fuel
throughout the jet. Significant
molecular mixing is delayed until the
end of a cascade to the Kolmogorov
scale. A simple mathematical model
incorporating these ideas is presen-
ted. This model predicts a Reynolds
number dependence for the nitric
oxide (NO) formation rate that is in
good agreement with measurements
in both methane (CH4) and hydrogen
(H2) jets burning in air. These
mathematical model concepts have
been incorporated into a simplified
computer program capable of treat-
ing the detailed chemical kinetics of
a gas flame. The model has been
used to predict NO formation in H2/air
and CH4/air flames. Results compare
favorably with experimental data.
This Project Summary was
developed by EPA's Air and Energy
Engineering 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 central focus of EPA's combustion
research program has been development
of combustion control technologies to
limit formation of nitrogen oxides (NOX)
from fossil fuel fired flames. The
Fundamental Combustion Research
(FCR) program has helped advance
understanding of critical combustion
processes controlling NOX formation. As
part of the FCR program a series of
studies have been pursued to develop an
improved understanding of the coupling
between fundamental fluid mechanics
and chemical processes in turbulent
diffusion flames. The impetus for these
efforts is twofold: (1) control of mixing
between fuel and combustion air is a
central feature in low NOX burner
systems (by delaying the mixing, more of
the fuel nitrogen in coal reacts under fuel
rich conditions which is conducive to
converting the bound nitrogen to
molecular nitrogen); and (2) the more
fundamental impetus is that since the
middle 1970s a new understanding of
basic turbulent mixing processes has
been evolving. The current FCR study
provided for development of a
mathematical model of a simple turbulent
diffusion jet flame incorporating the basic
elements from the new understanding of
turbulent mixing. The flow configuration
modeled in this study is a circular jet of
gaseous fuel issuing into still air.
The Basic Concept
The new understanding of turbulence
is based on the concept that mixing
between fuel and air is initially driven by
large coherent structures (often referred
to as eddies) which macroscopically
entrain air and engulf it into the fuel jet.
Both theoretical considerations and
experimental data show that the
macroscopic entrainment of a turbulent
jet (at high Reynolds number) becomes
independent of Reynolds number and is
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linearly proportional to the axial distance.
The large structures transport engulfed
material deep within the jet with mixing
between fuel and air occuring at the
interface between the fluids. At any axial
location macroscopically entrained fluid is
molecularly mixed at a uniform rate with
the jet fluid. This leads to the concept,
supported by experimental data, that
there is no radial variation' of the
reservoir-jet mixture ratio in the mixed
fluid. In this view, the usual bell-shaped
mean concentration profiles arise only
from a radial variation in the ratio of
mixed fluid to pure reservoir fluid.
Additional features of the model are
that mixing takes place at the interface
surfaces (or flame sheet) separating fuel
and oxidizer and that the combustion is at
stoichiometric conditions. The interface
surface associated with the large scale
structures break down to small scale
through inviscid instable motion. This
cascade of length scales causes the
quantity of interface surface area to
increase: most of the surface being
generated just before the structures
reach the Kolmogorov scale. The
interface surfaces are homogenized by
molecular diffusion at this scale.
Process is Modelled
This rather complex process has been
modelled as a combination of two major
combustion zones: a flame sheet zone
and a flame core zone. The flame sheet
zone represents the interface between
fuel and air where combustion is
occurring at stoichiometric conditions.
The characteristic scale for this zone is
the Kolmogorov scale since that is the
scale where most of the interface surface
is generated. The flame core zone
consists of the mixture of the combustion
products and the as-yet unreacted fuel
which are molecularly mixed. After its
formation, the flame sheet zone
subsequently conglomerates into the
flame core structure via molecular
diffusion. Numerically, the flame sheet
zone can be simulated by a well stirred
reactor with proper characteristic
residence time. The flame core zone can
be represented by a plug flow reactor,
which originally contains 100% raw fuel,
and is continuously fed by the
combustion products from the flame
sheet reactor. In the meantime, the flame
core zone also has to provide the flame
sheet reactor with the rich mixture which
contains a sufficient amount of raw fuel
for stoichiometric combustion (corres-
ponding to the rate of microscopic mixing
of fresh air). The above ideas are best
described with the help of Figure 1 which
presents a schematic of the reactor
arrangement. The term
dt \m /micro
o
represents air engulfed into the jet by
large scale structure which subsequently
cascades to the Kolmogorov scale. This
air addition rate is matched stoichio-
metrically by fuel addition from the flame
core
dt m
These two streams react in the well
stirred reactor representing the flame
sheet zone. Combustion products from
Qrad
the flame sheet zone flow to the flam6
core zone, diluting the fuel in the plug
flow reactor.
The numerical model embodying the
above concepts provided a simple
treatment for heat loss by radiation and
used an existing one-dimensional chem-
ical reactor code. The governing species
and energy equations for both reactors
are solved using a fully implicit, backward
finite difference formulation. Reaction
chemistry was described using a set of
181 simultaneous elementary reactions
and 36 species for CH4/air flames. .This
reaction set was developed previously as
part of the FCR program and includes
treatment of thermal NO and fuel nitrogen
mechanisms. For H2/air flames the kinetic
set can be reduced to 17 species and J30
elementary reactions.
After developing the model and
empirically establishing values for
necessary constants the computer code
was exercised to predict flame
characteristics which could be compared
to experimental data. Figure 2 illustrates
one of those comparisons in a plot of the
NO mass fraction at the jet center line
versus the axial distance 'down the flame.
Model predictions are compared to the
experimental data of Bilger and Beck
[presented at 15th Symposium
(International) on Combustion]. The
flames simulated in this figure used
hydrogen as the fuel and the general
agreement of prediction and theory is
encouraging.
Additional work is required to fully test
the model under critical conditions and to
better establish the empirically set
constants. Analysis of model predictions
may provide valuable insights into basic
Figure 1. Schematic of reactor model.
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processes controlling NO emissions.
Limited analysis shows that NOX
formation occurs in the flame sheet zone,
while the flame core zone provides strong
NO destruction. This NOX result is as
expected, but the ability to evaluate the
separate roles of different regions of the
flame could be of significant value in
future NOX control studies.
200
I
a
§
'
w
I
O
750
TOO
50
—— Model Prediction
/ /
N \
A l -
ilt
Iff
\\
X
4
O
*
N.
Experimental Data -
Bilger & Beck
Case/
Symbol
1 n
2 A
3 O
DO
(mm)
1.59
3.18
6.35
(cm/sec)
9,669
13,674
19,323
I
Ren
1,537
4,348
12,270
I
I
I
20
60 100
Axial Distance (X/D0)
140
Figure 2. Comparison of model calculated NO versus measurements (Fr = 6 x 70-5; for HJair
flames.
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J.E. Broadwell is with TRW Space and Technology Group, Redondo Beach, CA
90278; and T. Tyson and C. Kau are with Energy and Environmental
Research Corp., Irvine, CA 92718.
W. Steven Lan/er is the EPA Project Officer (see below).
The complete report, entitled "A Model of Turbulent Diffusion Flames and Nitric
Oxide Generation," (Order No. PB 90-155 557/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
Official Business
Penalty for Private Use $300
EPA/6QO/S7-90/003
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