Energeia Home
Vol. 7, No. 6, 1996
Understanding the Chaotic
Nature of Flames
M. Pinar Mengüç and J. McDonough
Department of Mechanical Engineering,
University of Kentucky
INTRODUCTION
Harnessing the power of combustion and
fire is one of the most important achievements of human kind. Since the dawn of
history, humans have tried to develop
various tools and techniques to avoid the
wrath of fire and to put it to use for their
comfort. Yet, they realized many times that
even a simple candle flame is as complicated
to understand as it is dangerous and beautiful. Probably their double nature is the
reason for the mythical symbolism of flames
and fires in all cultures.
Behind the flame’s intense beauty lies several
physical and chemical phenomena occurring
simultaneously, which are interwoven.
Among them, turbulent fluid flow, radiative
and convective heat transfer, chemical
kinetics, and phase change leading to soot
formation and oxidation, are the most prominent. Understanding the detailed, molecularlevel nature of each of these mechanisms is
still beyond our reach, although centurieslong research efforts and trial-and-error have
helped us to build today’s combustion
systems. Nevertheless, to develop safer,
cleaner, efficient, and smarter power production systems, we need a more thorough
understanding of the physics and chemistry
of flames.
Among all phenomena taking place in flames,
radiation transfer and turbulence deserve
particular attention: almost all flames are
turbulent in nature and most of the chemical
energy converted to thermal energy is
radiated out to the surroundings. There is a
strong interaction between radiation and
turbulence, as both influence temperature and species concentration profiles
within the flame significantly. Yet, the interaction of these two phenomena has
been studied by only a relatively small number of researchers. Among these,
particularly the works of Faeth and his students should be commended.
Recently, we began a research program to study
laboratory-scale turbulent flames. Our overall
goal has been to introduce a fundamental
numerical and experimental approach with
which the true time-dependent nature of sooting turbulent flames can be revealed. One of
the main outcomes of this effort was the
conclusion that these flames can be analyzed
with the tools of the “chaos” theory. It is probably natural for most of us (including those
who have nothing to do with combustion
systems) to call the behavior of most flames
chaotic. But, what exactly does “chaotic” mean
and how can the chaos theory help us to better
understand these combustion systems? In this
article, a brief introduction will be given to
answer these questions.
Radiation-Turbulence Interactions:
The main objective in the design of most
combustion chambers is to transfer the
thermal energy from hot combustion products to the refractories. A significant portion
of this energy (up to 90 % in large-scale
furnaces) is transferred radiatively. Radiant
energy emitted from a sooty flame is significantly larger than, for example, that from a
clean-burning natural gas flame.
Contribution of soot to overall radiative
transfer phenomena in combustion chambers
can be predicted if the soot shape, size, size
distribution, optical properties, and volume
fraction distribution are available. Among
these, soot-volume fraction plays a major
role in the flame’s radiative emission. In
general, soot formation and oxidation
processes are controlled by chemical kinetics,
which are a strong function of temperature
and species concentration distributions. The
profiles of these variables are affected by the
structure of the turbulent flow field and
radiative heating and/or cooling mechanisms. The fluctuations in the species
concentration affect the soot formation and
oxidation mechanisms, which in turn alter
the soot concentration distribution. Change
in soot concentration yields a decrease or
increase in radiative emission, which
translates into variations on temperature
(continued, page 2)
Flames, (continued)
profile everywhere within the flame. As
one might expect, with changing (and
fluctuating) local temperature, the rate of
chemistry and species concentration
distribution changes, and the cycle
continues. If the fluctuations in species
concentration and temperature are monitored, measured, and interpreted
correctly, a wealth of information can be
obtained about the characteristics of these
flames. Such an effort would require carefully conducted experiments and
accurate numerical simulations.
Numerical modeling of a turbulent
diffusion flame requires a thorough
simulation of small-scale fluctuations of
velocity, temperature, and concentration fields, in addition to the corresponding mean (or, say large-scale)
values. Most of the detailed timedependent information is lost if flow
field simulations are not carried out
rigorously. Even though some modern
techniques such as the direct numerical
simulation (DNS), or the additive
turbulent decomposition (ATD) are
mathematically rigorous and yield a
high level of accuracy, they are not
computationally feasible for application to complex practical systems.
Instead, it is preferable to “model” the
small-scale fluctuations and solve for
the large-scale parameters “rigorously.” This strategy allows us to save
significant amounts of CPU time, and
brings us to the realm of simulating
practical turbulent flames accurately.
The trick here is in the choice of
“models” to be developed for the
representation of small-scale fluctuations. If they are not accurate or do not
correspond to the real underlying
physics, then they are useless. On the
other hand, if these models are based
on experiments and a series of universal laws, the recommended strategy can
work for a variety of physical systems.
Chaotic Map Models:
Most flames are turbulent in nature,
meaning they are strongly time
dependent. Yet, long time exposures of
such flames within a combustion
chamber clearly show the boundaries
of the flame region. Repetitive exposures taken at different times of the
day, month, or year reveal almost
identical features. Also, if standard
techniques are used, time-integrated
temperature profiles, as well as, the
distribution of radiative emissions
along the flame can be measured with
confidence. Indeed, these long-time
“stable” features of such flames have
given scientists and engineers confidence to model and design the combustion chambers with reasonable success.
The problem is that these flames are not
intrinsically stable. They are dynamic
systems, and if there are small perturbations, either internal or external, radically different flame characteristics may
be observed. A number of researchers
have shown that the turbulence in a flow
field is not random, but deterministically
chaotic. However, time-integrated
measurements and modeling efforts
mask almost all of the rich timedependent physical phenomena taking
place in turbulent flames.
Figure 1 depicts four instantaneous
pictures of a laboratory-scale turbulent
ethylene diffusion flame over a onesecond time interval. The exposure for
each frame is 1/4000 second. It is
remarkable to note the significant
variations of the flame structure,
indicating time-dependent temperature
and species concentration gradients.
Realize that these gradients are directly
related to local velocity fluctuations,
which affect the chemical kinetics, and
consequently the radiant energy
emitted by the flame. It is not possible
to study these complex time-dependent
phenomena within the framework of
classical Newtonian dynamics.
Development of the chaos theory has
revolutionized our understanding of
dynamical systems. The theory has
been applied to explain the weather,
the fluctuations in population change
of a given species, dripping water from
a faucet, the swing of a pendulum, as
well as turbulent flows. The reader is
referred to books such as James
Gleick’s Chaos or Nina Hall’s Exploring
Chaos, for more detailed, but not
necessarily mathematically-involved
discussions of the subject.
All dynamical systems start functioning
at a steady stable level. If one of the
critical parameters is altered (e.g., if the
flow velocity is increased), eventually
Figure 1. The transient nature of ethylene-air diffusion flame, over one-second duration. The exposure for each frame is 1/4000 seconds.
2
Flames, (continued)
the system becomes unstable. With a
further increase in that parameter, a
chaotic behavior is observed. This
complex transition from stable to
unstable regime can be mimicked by an
amazingly simple expression, called a
logistic or chaotic map:
xn+1 = 4 r xn (1 - |xn|)
(1)
Here, x is the dependent parameter we
are interested in, such as local temperature, soot volume fraction, etc., which is
a strong function of time. Superscripts
n and n+1 are used to denote the value
of the parameter x at times t(n) and
t(n+1), respectively. The r, which is
known as the bifurcation parameter,
controls the transition from a stable to
an unstable state. For example, it can be
related to the flow velocity (or, say the
Reynolds number) if we are interested
in a turbulent fluid flow.
For low values of r, Equation (1) yields
steady solutions, meaning that the
values of x at times t(n) and t(n+1) are
the same. For example, if r is less than
0.25, only the trivial solution is valid
(i.e., x=0.0, no flow!). If r is between
0.25 and 0.75, this equation converges
to a single value of x: for r=0.5, x=0.5,
and for r=5/12, x is 0.4. These results
correspond to time independent
phenomena, such as those observed for
a steady laminar flow.
As a laminar pipe flow becomes unsteady
with increasing flow velocity, this logistic map becomes unsteady with
increasing r value beyond 0.75. For
example, at r=0.8, the solution begins to
fluctuate between x values of about 0.5
and 0.8. With further increase in r, say
above 0.9, the fluctuations become
unpredictable, or chaotic, similar to the
fluctuations in fully turbulent flows.
The relation between x and r are
depicted in Figure 2a-c, which are
called bifurcation diagrams. Note that
Figures 2b and 2c are enlarged versions
of Figure 2a, in order to show the
details. With increasing r, the solution
of Equation (1) goes through a period
doubling (note the “forks” in Figures
2), and then eventually yields more
unstable, chaotic solutions (as marked
with darker regimes). However, there
are some windows in r where chaotic
behavior is replaced with more uniform
periodic behavior.
After noting the surprising ability of
this simple equation to display the
features of a dynamical system such as
The Center for
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SOLUTION:
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PROPOSAL PRESENTATION:
The CAER is seeking a consortium of sponsors to participate in the advancement and application of this problem to
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the CAER.
If you are interested in attending, or if you would
like additional information, please contact:
Dr. B.K. Parekh, Associate Director
Center for Applied Energy Research
3572 Iron Works Pike, Lexington, KY 40511
PHONE: 606-257-0239 FAX: 606-257-0302
e-mail: [email protected]
(continued, page 4)
3
Flames, (continued)
fluid flow, one can hypothesize the use
of a series of these maps to explain
more complex systems, such as
radiating turbulent flames. Of course,
this hypothesis is useless unless
supported experimentally.
This work is supported by DOE-PETC's Advanced University Coal Research Program.
This is the first of a two-part series.
Pinar Mengüç is a Professor and Jim
McDonough is an Associate Professor in
UK’s Department of Mechanical
Engineering.
Figure 2. Logistic map based on Eq. (1). Here, r can be any parameter, such as the Reynolds number, or the axial location in the flame. The
parameter x is a dependent function, such as the local soot volume fraction; as the flame becomes turbulent (chaotic) the solution fluctuates
between multiple values of x. The second and the third frames show the same map in detail (note the range of r).
A Lesson from Dr. Teller
by Marybeth McAlister, Editor, Energeia
Kathie Sauer, graphic artist; Marybeth
McAlister, author; Dr. Edward Teller; and
Dr. Burt Davis, CAER Associate Director
W
hen I was in college (seemingly eons ago now), I proudly
wore a “No Nukes” T-shirt. I was
an English major with no background in science: fuel, nuclear or
otherwise. I wore that T-shirt and
espoused that philosophy with the
best of intentions. I was young,
liberal, and wanted to do what I
could to save the world, the whales,
the children, and a slew of miscellaneous causes. There was no
Vietnam to protest, so Three-Mile
Island was our chant.
I moved to New York after graduation and helped organize a Nuclear
Freeze march in Manhattan. There
were 200,000 people in
Central Park with me.
Again, mostly wellintentioned people
with good hearts,
but very few facts.
I had the opportunity
to spend three days
with Dr. Edward
Teller recently. He
was the CAER
Distinguished
Lecturer this year,
and spoke on the
history of atomic
weapons to a capacity
crowd at UK. Dr.
Teller’s views of
nuclear energy and a strong defense are
well known. In addition to the atomic
weapons lecture, he gave two technical
talks on underground nuclear reactors
for the next century. It was an exciting
week, as one of the great scientific
minds of this century discussed the
facts behind his strongly held belief
that nuclear energy would be the best
energy source for now and the future.
I was lucky enough to spend a good deal
of time with him that week. We talked
about my early foray into pseudo-radicalism, and my “No Nukes” philosophy.
He asked me what he could have done to
“reach me” then. I told him nothing,
because it was a period of growing up,
where good intentions were more
important to me than facts.
4
Frankly, I don’t know exactly what
my stand is on nuclear energy now.
The one thing I DO know, is that it’s
legitimate to believe fervently in
whatever you want, as long as you
have the knowledge, background,
and facts to support your argument.
With all of Dr. Teller’s amazing
stories of Hungary before World
War II, Los Alamos, Einstein, and
Trinity, the greatest impact he had
on me was the importance of
knowing what you believe as well
as why you believe.
. . . And News of A
Past Lecturer
Sir Harold Kroto, the first CAER
Distinguished Lecturer was recently
awarded the Nobel Prize for Chemistry for his work on the discovery of
Fullerenes, or Bucky Balls,
which was jointly
shared by
Richard Smalley
and Robert Curl.
Congratulations,
Dr. Kroto,
on receiving the
ultimate
accolade
from all of
us at the
CAER.
COMMENTARY
Forget-me-not (Myosotis sylvatica)
Frank Derbyshire, Director, CAER
What’s in a name?
Step one is to unobtrusively scan the
person of your protagonist to see if
you can spot a name badge or
similar adornment. The gaudy
monogram is uncommon these
days, and the name badge offers the
best of a bad bet. Sadly, these
insignia rarely fulfil their purpose
and promise. For a start, they are frequently obscured by
some article of clothing, or they are worn at waist level, or
they are sported at such a rakish angle that all one can see is
a reflection of the room lighting. But the worst impediment
is another consequence of having been on the scene for far
too long, when one’s “sell by” date has expired. That is,
myopia. Of course, it does not help that some namebadge
designers elect a type size so miniscule that it would be
incomprehensible to a literate peregrine falcon, while
others, in a frenzy of creativity, elect a font so ornate that its
proper place is in a mediaeval illuminated manuscript.
Nevertheless, the fact remains that you are (probably)
shortsighted. Short of removing one’s spectacles and
scrutinizing the name badge from an up-close and personal
vantage point - a prospect that is almost too horrific to
contemplate and could easily embroil you in a legal suit
over some form of harassment - the odds are that your
goose is well and truly cooked vis-à-vis name badge identification.
A man walked into the doctor’s office and said,
“Doctor, I’m worried.”
Doctor: “What is the problem?”
Man:
“I can’t seem to remember anything for more than
a few minutes.”
Doctor: “Really? And how long has this been going on?”
Man:
“How long has what been going on?”
This is one of many jokes that exploit the subject of a faulty
memory. I can’t remember most of them, but this particular joke is one that I don’t seem to be able to forget. The
subject of this article addresses the same topic. Specifically, my theme is concerned with the occasional and
temporary inability to recall faces and names and to be
able to place any matching pair in the correct combination.
This phenomenon is often attributed to the inexorable
advance of what I prefer to call maturity (other expressions
could also be used), although I believe that there are
alternative legitimate causes, as I shall discuss.
Stranger than fiction
Independent of their age, most people, at one time or another,
have had the experience of being accosted by person or
persons apparently unknown. Confusingly, the assailants
refuse to comport themselves like the complete strangers
that they obviously are. Without a trace of embarrassment, they will attempt to engage one in conversation and
may even have the effrontery to display an intimate
knowledge of one’s personal history, quoting names, dates,
or places with disturbing accuracy. These strange encounters tend to occur, more often than not, when one is
attending a meeting or is at some other function. Consequently, one does not have to be a Sherlock Holmes to
speculate that the intruder may be engaged in similar
business and that, risible as it seems, there exists the
remote prospect that there may actually be grounds
for this offensive familiarity.
Point and counterpoint
What next? The next resort, unpalatable as it may be, is to
engage in conversation. Clearly, with a few well-posed
questions, aided by your rapier-like wit, your assailant will
unwittingly offer some verbal aide memoire and the conundrum will be solved. Ha, ha. Be realistic. The following is
an example of a more likely outcome of the chat between
you and ?:
You:
“Where exactly did you start your travels to come
here?”
?:
“From home.”
Resistance is useless
and
When faced with this dilemma, a natural and perfectly
forgivable reaction, and one that I strongly endorse, is to
run away. On the other hand, one could always try to call
a policeman, even though it is well-known that a policeman is never around when one is needed. In any case, it is
probable that neither option is available and that you are
scuppered. Like any premeditated ambush, you, the
innocent ambushee, are caught unawares, because the
lowly and cunning ambusher has had ample time and
opportunity to develop a foolproof strategy. In simple
terms, by the time that the initial conversational salvo is
fired, there are few if any escape routes that would not
cause a major breach of polite behavior or even a diplomatic incident. The only recourse is to bluff. Stall to gain
time and hope to subtly elicit some revealing clue to the
identity and affiliation of one’s adversary.
You:
?:
“Have you seen anyone else here?”
“Just the usual crowd.”
It could be worse. For example, ? may not have a very good
command of your native tongue, in which case:
You:
“Where exactly did you start your travels to come
here?”
?:
“Thank you.”
and
You:
?:
“Have you seen anyone else here?”
“You are welcome.”
(continued, page 6)
5
Commentary, (continued)
At this juncture, there are few options
left: hope for the intervention of a third
party (warning - this could really put the
fat in the fire); become hopelessly inebriated (not recommended even if there is
enough sauce available - there isn’t
usually); feign a fainting fit; or hold your
ground. In the last eventuality, it is
essential to avoid giving direct answers
to questions. Just mutter words like “of
course,” “precisely,” “absolutely,” and
“ah yes” at appropriate moments, and
sooner or later your molester will think
you boring or completely mad or both
and give up and go.
Because of (a) and the repetition of (b),
many people have seen you whereas
your attention has been focused on the
presentation materials and the availability of free food and drink. Hence,
there is every excuse for the failure to
recognize someone who:
(i) you may never have met,
(ii) may have been but a face in the
crowd, or
(iii) asked a very awkward question.
1997 Hydrocarbon Resources
Gordon Research Conference
Fête takes a hand
Why has this happened to you? Well,
probably you deserve it. But there could
be other reasons as well. It is possible that
your memory is not really on the blink.
Try some simple tests. Write down your
name, address, and telephone number
and check the details against the information in your bag or wallet. If you score
close to 100 %, you might not be suffering
an age-related malfunction after all. At
least, not yet. In this case, I prefer the
following explanation:
(a)
(b)
You attend many such functions.
You usually give a presentation.
(Usually it is the same presentation as last time.)
I appreciate that for some this interpretation may appear to trivialize a
worrisome circumstance. As a fellow
sufferer, I fully sympathize with this
position, which is why I have left no
stone unturned to develop a cogent
argument that is based soundly on
logic and proven scientific facts and
that should satisfy the most concerned
and enquiring mind. Unfortunately, it
will have to wait as I cannot quite
remember it at the moment.
January 12-17, 1997
Holiday Inn, Ventura, CA
This conference will span a broad range of topics in hydrocarbon utilization from
mechanisms of conversion, to catalysis, to coke formation, to the preparation and use
of high-performance carbon materials. A panel discussion on the future directions
of hydrocarbon R & D will be included.
For more information, please contact:
Isao Mochida
Institute of Advanced Material Study
Kyushu University
Kasuga, Fukuoka 816, JAPAN
Phone: 81-92-583-7797
FAX: 81-92-583-7798
E-Mail: [email protected]
John H. Shinn
Chevron Research & Technology Co.
Richmond, CA USA
Phone: 510-242-2502
FAX: 510-242-4808, 510-242-1376
E-Mail: [email protected].
Energeia is published six times a year by the University of Kentucky's Center for Applied Energy Research (CAER). The publication features aspects of energy resource
development and environmentally related topics. Subscriptions are free and may be requested as follows: Marybeth McAlister, Editor of Energeia, CAER, 3572 Iron
Works Pike, University of Kentucky, Lexington, KY 40511-8433, (606) 257-0224, FAX: (606)-257-0220, e-mail: [email protected]. Current and recent
past issues of Energeia may be viewed on the CAER Web Page at www.caer.uky.edu. Copyright © 1996, University of Kentucky.
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