United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S7-88/018 Dec. 1988
&EPA Project Summary
Mathematical Modeling of
Single Droplet Trajectories in
Combustor Flow Fields
W. S. Lanier and S. B. Robinson
In liquid hazardous waste incin-
eration, the ballistics of some large
single droplets can limit destruction
efficiency. Mathematical modeling
and experimental work were per-
formed in this study to examine the
behavior of individual fuel droplets
sprayed into a combustor, to
determine which parameters could
influence incinerator effectiveness. A
computer model has been developed
to predict the motion, heating, and
evaporation of such a droplet in a
heated environment. The model is
based on droplet behavior governed
by fluid mechanics and contains
formulations to predict the effect of
droplet spacing on drag and
evaporation as well as the effect of
evaporation on drag. The gas flow
field can be specified with mean
velocities or a randomly fluctuating
turbulent field, based on experi-
mental values for the standard
deviation of the velocity. Numerical
predictions of the Initial heating and
evaporation of an isolated burning
droplet are compared to experi-
mental results. The predictions,
which utilized measured temperature
and velocity gas fields, compared
well to experimental observations.
The correlation of droplet penetration
with droplet incineration suggests
that incinerator failure modes may be
predicted on the basis of droplet
atomization parameters and gas field
conditions.
This Project Summary was devel-
oped 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
The first of several tasks in the EPA's
Fundamental Combustion Research
program (FCR III) was to examine more
closely the characteristics of a single
droplet in a combustion environment.
This report summarized the modeling
work performed to predict the trajectory
and the evaporation of a single droplet. It
included a description of the theory,
development, and operation of the
computer code and is accompanied by a
user's manual. This computer code is to
be used in conjunction with experiments
which are performed by EPA in an
inhouse research program. This model is
applicable to liquid injection hazardous
waste incineration.
Computer Model
The model developed for this program
is expected to increase the under-
standing of droplet combustion in liquid
injection incineration. It is quite important
to know the behavior of individual
droplets in a hazardous waste incinerator.
In these incinerators, waste must be
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destroyed to a degree greater than
99.99%. The incinerator is said to fail if
this destruction efficiency is not
achieved. If there are droplets which are
larger than the mean droplet size, they
tend to concentrate on the outer edge of
the spray core, with sometimes
unpredictable behavior. This model can
be used to help predict the behavior of
these rogue droplets, and to determine
additional information that might be
required to fully characterize the
incinerator.
The computer model for predicting a
droplet's trajectory was adapted from a
model developed at University of
Sheffield for the U.S. Air Force Office of
Scientific Research. The work presented
by the University of Sheffield included an
algorithm for predicting droplet tra-
jectories in three dimensions, including
droplet evaporation and initial heat up
effects. The model was used to predict
the environment inside a gas turbine
combustor, primarily as a tool to assist in
combustor design. Starting with the
University of Sheffield equations, the
computer model was written in
FORTRAN IV. Two models were
developed one to characterize a droplet's
path in two-dimensional space and the
other in three-dimensional space.
Initially the two-dimensional version was
written for an IBM PC, but the three-
dimensional version, requiring much
more storage space, was maintained and
executed on an IBM 3070 mainframe
computer. Subsequently, the three-
dimensional version has been modified
to be manageable by an IBM PC/AT.
Use of Program
The initial effort for the FCR III
program was to examine the effects of
droplet spacing on droplet drag.
Experiments were performed at the EPA
to determine this effect, and empirical
relations were developed from the
experimental results. The next effort
examined the effect of evaporation on
drag. It was postulated that as a droplet
evaporates, the environment immediately
surrounding the droplet will change,
changing the drag force on the droplet. A
theory was incorporated into the model
to account for the effect of evaporation
on drag. The effect of burning has also
been included into the evaporation
equation, based on the theory that the
burning rate of many droplets can be
expressed as a function of the burning
rate of an isolated droplet. The original
model accounted only for evaporation,
not burning. Finally, the effect of
turbulence in the background gas was
included in order to provide a more
realistic model of actual conditions in an
incinerator.
Experiments were performed over a
wide range of droplet and flow field
conditions. Corresponding numerical
predictions are compared to experi-
mental results in Table 1 and Figure 1.
Experimental results were recorded for
location of droplet ignition and final
burnout, whereas the model predicts only
burnout location. Model predictions show
penetration into the combustor to
approximately the same location as the
experimental ignition point for most test
cases. However, the time predicted for
droplet heating to the ignition
temperature is about 30-50% of the
time predicted for droplet burning, which
is approximately the order of magnitude
seen in experimental testing. It is not
currently understood why the model
predicts burnout too early. This could
indicate oversimplifications in the model
or perhaps some physical phenomena
which are unaccounted for. Another
possible reason for the inconsistency is
the fact that a multi-component fuel was
used in the experiments which was
difficult to characterize and model
correctly. The model assumes that the
fuel has a single boiling point, with no
evaporation until it heats up to the boiling
temperature. In addition, it assumes a
homogenous droplet with constant
droplet properties. These assumptions
are not totally valid for a multi-
component fuel with a variable boiling
point (depending on the percentage of
various constituents) and hence the
predicted droplet penetration may be
skewed.
Code Limitations
The model allows the user to predict
droplet trajectories within an incinerator
at a variety of initial droplet and
background gas conditions. Never-
theless, there are some limitations to the
code. The geometry of the incinerator is
limited, in the 3-D case, to a circular
cylinder. Dimensions are specified as
program inputs Eventually this code
may be expanded to handle droplet
sprays and group combustion, but
presently it is assumed that only one
droplet is injected at a time. Another
limitation is the characterization of the
fuel. It is assumed that the droplet
properties are constant with temperature,
and that there is a single boiling point for
the fuel. This is not realistic for all fuels,
but is an assumption necessary to
simplify calculations.
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Figure 1. Droplet trajectories—experimental results and model predictions. (Sheet 1 of 2).
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Figure 1. Sheet 2 of 2.
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W. S. Lanier and S. B. Robinson are with Energy and Environmental Research
Corporation, Durham, NC 27707.
James A. Mulholland is the EPA Project Officer (see below).
The complete report, entitled "Mathematical Modeling of Single Droplet Trajec-
tories in Combustor Flow Fields," (Order No. PB 88-252 010/AS; Cost: $21.95,
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/600/S7-88/018
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