Modeling plays a vital role in providing physical insights into behavior revealed by experiment. The program at the University of Illinois is designed to improve our understanding of basic combustion phenomena through the analytical and numerical modeling of a variety of configurations undergoing experimental study in NASA's microgravity combustion program. Significant progress has been made in two areas: (1) flame-balls, studied experimentally by Ronney and his co-workers; (2) particle-cloud flames studied by Berlad and his collaborators. Additional work is mentioned below. NASA funding for the U. of Illinois program commenced in February 1991 but work was initiated prior to that date and the program can only be understood with this foundation exposed. Accordingly, we start with a brief description of some key results obtained in the pre - 2/91 work

Buckmaster, John

English

NASA Technical Reports Server

MODELING OF MICROGRAVITY COMBUSTION EXPERIMENTS
John Buckmaster
University of Illinois N 9 3 "= 2 0 1 9 7
Urbana, Illinois 61801
Introduction
Modeling plays a vital role in providing physical insights into behavior revealed by experiment.
The program at the University of Illinois is designed to improve our understanding of basic
combustion phenomena through the analytical and numerical modeling of a variety of
configurations undergoing experimental study in NASA's microgravity combustion program.
Significant progress has been made in two areas: (i) flame-balls, studied experimentally by
Ronney and his co-workers [1]; (ii) particle-cloud flames studied by Berlad and his collaborators
[2]. Additional work is mentioned below. NASA funding for the U. of Illinois program
commenced in February 1991 but work was initiated prior to that date and the program can only be
understood with this foundation exposed. Accordingly, we start with a brief description of some
key results obtained in the pre - 2/91 work.
Flame Balls - Results Prior t0 2/91
Flame-balls are stationary, premixed spherical flames observed in certain near-limit mixtures [1].
They have zero flame-speed. Their study is likely to lead to an improved understanding of
flammability limits. The configuration is sketched in Fig. i.
Reference [3], The structure and stability of non adiabaticflame-balls, provides the first description
of mathematically stable flame-balls. The stabilizing mechanism is heat loss by thermal radiation.
The analysis assumes that the Lewis number (Le) is significantly less than 1. Only for such
mixtures are flame-balls observed.
Reference [4], The structure and stabifity of non adiabatic flame-balls: II. Effects of far-field
losses, is an extension of Ref. [3]. For physical flames there will be losses in the near-field (in
and near the burnt gas) and the far-field. Dealing simultaneously with both leads to technical
(mathematical) difficulties and these are dealt with here. Differences in the effects of the two losses
are revealed by Fig. 2. Near-field losses can generate a three-dimensional instability (the upper
thick portion of curve A), far-field losses do not. The lower thick portions of both curves def'me
regions of one-dimensional instability. Note that for curve B this includes a portion of the top
solution branch.
Flame-balls are only observed ifLe is sufficiently small (< 0.5?) In Ref. [5], The structure and
stability offlame-balls: A near-equidiffusionalflame analysis, it is shown that radiation is not
stabilizing when Le = 1 and there is a critical Lewis number Lec (< 1) such that stability requires
Le < Lec. The closer Le is to Lec the smaller is the range of parameter values for which stable
solutions exist.
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Flame-ballscanbestabilizedby heatlossotherthanby radiation.Convectiveheatlossesgenerated
byweakshearor strainingflowsarediscussedin Ref. [6], Flame balls stabilized by suspension in
fluid with a steady linear ambient velocity distribution. These are far-field losses. As noted
earlier, a key difference between near-field and far-field losses is that the former can give rise to
three-dimensional instabilities, the latter do not (see Ref. [9], discussed below).
Flame-Balls - Post 2/91 Results
In flame-ball experiments carried out in the KC-135 (see Ronney, this proceedings), unsteady
flame-strings have been observed. A straight fame-string is a cylindrical counterpart to the
spherical flame'bai1. Flame-strings display a sausage or peristaltic instability. These instabilities
are analyzed in Ref. [7]. For perturbations ~ e °a+i_ where x is distance measured along the
cylinder axis, Fig. 3 shows the manner in which_ varies with the wave-number k. The flame
structures must have a minimum length if they are to support unstable waves, i.e. short cylinders
are stable.
Reference [8], Influence of boundary-induced losses on the structure and dynamics of.flame-balls,
shows that conductive heat losses to a cold wall can stabilize flame-balls. Configurations of this
kind might well be important ibr space experiments designed to examine the structure of a
stationary flame-ball.
The results of Ref. [3], [4] imply the response sketched in Fig. 4. This shows the maximum
temperature in a flame-ball as a function of mixture strength. The stable region ties between points
A and B. The implication is that insufficiently reactive mixtures can not support flame balls (static
quenching at A' or dynamic quenching at A); and that overly reactive mixtures will lead to non-
spherical flame-balls. These conclusions are consistent with expenment.
The point B is a neutral stability point for three-dimensional instabilities and a transcritical
bifurcation analysis can be carried out, valid in the neighborhood of B, which describes unsteady
three-dimensional, weakly-nonlinear deformations of the flame-ball. In Ref. [9], The three-
dimensional dynamics offIame-balls, an equation for the flame-ball shape is derived:
x 2 (y2 + z 2)
42 5K + 21 5K = 1
14 1 ---.-_
4 (t c-t) 4 (t c-t)
3 iL .... _
(1)
where 5K is a positive parameter that vanishes at B, and tc is a critical time at which 'blow-up'
occurs. Equation (1) describes the first observable manifestation of the instability, and
corresponds to an elongating prolate spheroid. Prolate spheroids have been observed by Ronney.
The experimental spheroids, once they become long enough, neck and split. We believe that this is
due to the flame-string instability discussed in Ref. [7].
The analytical worl_ of Ref' [31-[91has been remarkab-iy-successful in providing a description of
flame-balls that agrees, qualitatively, with the experimental observations. Quantitat_e ....... ""
comparisons are only meaningful with detailed numerical simulations, and a program Of this kind
has recently been embarked upon in collaboration with M. Smooke. Figure 5 shows the
variations of maximum temperature with mixture strength described in Ref. [10], Analytical and
numerical modeling of flame-balls in H2/air mixtures. This work predicts a static flammability
limit of 3.5% H2 by volume. This is close to the experimental value. Predicted flame-ball sizes
=
166
areconsistentwith observationsbutprecisecomparisonis not possibleat this timesincethenature
of theexperimentalimageis uncertain.
It isclearthatat thistime anunusuallystrongsynthesisof experiment,theoryandnumericalwork
haselucidatedthephysicsof flame-balls.
Flame-Balls - Future Plans
In all the work completed to date radiation losses are only accounted for within the framework of
an optically thin field. There is reason to believe that this is not always correct, and a more general
approach is under development.
Additional numerical work is planned. It would be appropriate to construct steady solutions for the
various mixtures that have been used experimentally. Moreover, because of the importance of the
stability boundaries in defining the existence of flame-balls it is important to identify them
numerically. This would not be excessively difficult for the one-dimensional stability boundary,
but the three-dimensional boundary is a different matter. Reduced chemistry schemes might be
useful in this connection.
Particle Cloud Flames
Reference [2] describes experiments on flames propagating in particle-air mixtures. A mixture of
lycopodium and air in a tube that is open at one end, closed at the other, is ignited at the open end.
For some mixture strengths and flame locations unsteady propagation is observed which, we
believe, is driven by an acoustic instability. Reference [11], An acoustic instability theory for
particle-cloudflames, contains a mathematical description of a plausible mechanism. Because of
slip (thermal and kinematic) between the two phases, an acoustic wave generates fluctuations in the
mixture flux fraction entering the flame; there are time dependent fluctuations in the difference
between the particle velocity and the gas velocity relative to the flame. These fluctuations generate
variations in the heat generated by combustion, and these can drive the acoustic wave via the well-
known Rayleigh criterion. Apart from the inclusion of slip the flame model is similar to that of
Seshadri et al (this proceedings).
Additional theoretical aspects are briefly discussed in Ref. [12], The structure and stability of
laminar flames. It is well known that a classical (gaseous) unbounded deflagration can support a
pulsating instability if Le is large enough, but this constraint demands exotic mixtures. However,
modifications to the flame configuration can move the domain of instability and make it accessible
to certain everyday mixtures. Heat loss to a burner is such a modification. Supplying the fuel in
particle form is another. It is possible, therefore, that the instability observed by Berlad et al is
intrinsic in nature, albeit modified by the acrustic Constraints, rather than the acoustic creature
discussed in Ref. [11]. These and related aspects are presently being explored. However, the
termination of the experimental program limits the progress that can be expected in our
understanding of these flames. In view of the importance of particle cloud burning, and
recognizing that the microgravity environment is exceptionally congenial for its study, this author
believes that a new initiative in the area would be most valuable, preferably one tied closely to
modeling efforts.
Self-Exting_ji_hing Flames
Self-extinguishing flames (SEFs) are generated by the point ignition of certain near-limit mixtures
[ 13]. An essential characteristic of a SEF is that it extinguishes at a radius of several centimeters
after the release of chemical energy several orders of magnitude greater than the spark initiation
energy. Because of this disparity one might expect that the final behavior of these flames is
independent of the spark energy, but that is not the case. A SEF which extinguishes after releasing
167
energyequalto 103timesthesparkenergycanbeconvertedtoa non-extinguishingflameby
doublingthesparkenergy.We havebeenengagedin attemptsto understandthissensitivitybythe
useof simpleasymptotictreatments.In Ref. [14], The effects of confinement andheat loss on
outwardly propagating sphericalflames, asymptotic methods are used to derive a model equation
for the evolution of the spherical flame:
dV_2VdRR L+V213kR3-1nV], dR=v'dt (2)
Here R is the flame radius, t is time, L is a heat-loss parameter that accounts for radiative losses,
and k is a confinement parameter that accounts for the pressure risein_e fixed volume chamber.
Solutions to equation (2) can display extreme sensitivity to the initial data, as exemplified by Fig.
6. However, we are not prepared to claim that confinement effects are significant in Ronney's
experiments, but merely present these results as a simple example of sensitivity.
Acknowle_ment
The work described here was supported by the NASA-Lewis Research Center, and by AFOSR. It
owes its genesis to the unusual intellectual generosity of Paul Ronney. After discovering fl_e-
balls in the laboratory, he came to the opinion that radiation plays a key role in their existence and
invited me to Princeton and asked me if I thought that it would be possible to do some modeling.
That question, his videotapes, and his physical insights, have fueled this endeavor.
References
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[4]
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[12]
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[141
Ronney,P. Combust. Flame, 82, 1990, 1-14.
Berlad,A., Ross,H., Facca,L., and Tangirala,V. Combust. Flame, 82, 1990,448-450.
Buckmaster,J., Joulin,G., and Ronney,P. Combust. Flame, 79, 1990, 381-392.
Buckmaster,J., Joulin,G., and Ronney,P. Combust. Flame, 84, 1991, 411-422.
Lee,C, and Buckmaster,J. SlAM J. Appl. Math.. 51, 1991,1315-1326.
Buckmaster,J., and Joulin,G. J. Fluid Mech., 227, 1991, 407-427.
Buckmaster,J. Combust. Sci. and Technol., 84, 1992, 163.
Buckmaster,J., and Joulin,G. Combust. Sci. and Technol., in press.
Buckmaster,J., Gessman,R., and Ronney,P. 24th Symposium, in press.
Buckmaster, J., and Smooke,M. Submitted. Some results from this paper were presented
in-a posier sessionat the _24_ g-y_mp0sium, and a{e recorded in the book of abstracts.
Buckmaster,J., and Clavin,P. 24th Symposium, in press.
Buckmaster,J. Article in Annual Review of Fluid Mechanics, Vol. 25, to appear, 1993.
Ronney,P. Combust. Flame, 62, 1985, 121.
Buckmaster,J., and Lee,C. 24th Symposium, in press.
168
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Fig.5. Numerical
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together, but their
final fate depends on
the initial data.
170


Modeling of microgravity combustion experiments

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