t /oo3 - NASA · Twentv-Seve.th Symposium tlntemational on Combustion/l'he Combustion Institute, 1998/pp. 24,b5--2506 ... (ocitv at the flammability limit ISI.I,,,, ) is nonzero.

Twentv-Seve.th Symposium tlntemational on Combustion/l'he Combustion Institute, 1998/pp. 24,b5--2506

t

/ /oo3UNDERSTANDING COMBUSTION PROCESSES THROUGH

MICROGRAVITY RESEARCH

PAUL D. RONNEY

Department of Aero.rpace and Mechanical Engineering

University of Southern California

Los Angeles, CA 90089-1453, USA

A review of research on the effects of gravity on combustion processes is presented, with an emphasison a discussion of the ways in which reduced-gravity experiments and modeling has led to new under-

standing. Comparison of time scales shows that the removal of buoyancy-induced convection leads to

manifestations of other transport mechanisms, notably radiative heat transfer and diffusional processessuch as Lewis number effects. Examples from premixed-gas combustion, non-premixed gas-jet flames.

droplet combustion, flame spread over solid and liquid fuels, and other fields are presented. Promisingdirections for new research are outlined, the most important of which is suggested to be radiative reab-sorption effects in weakly burning flames.

1k__.._..

Introduction

. Gravity influences many combustion processes,particularly due to buoyant convection which affects

transport of thermal energy and reactants to and

from the chemical reaction zones. Recently, manyexperimental and theoretical studies of combustion

at microgravity _g) conditions have been con-

ducted. These studies are motivated by the need toassess fire hazards in spacecraft and to enable better

understanding of combustion processes at earth

_la_._vi].ty(lg)through the elimination of buoyancy

This paper discusses how new understanding of

combustion processes has been obtained throughgg

research, rather than providing a comprehensivereview of this rapidly changing field. First, com-

parisons of time scales for various chemical and

transport processes in flames, including buoyancy-induced transport, are given. Next, examples of un-

expected results and new understandings obtained

through gg research are discussed. These findingsare then summarized and future research directions

are suggested.

Comparison of Time Scales for Premixed-GasCombustion

To determine the conditions in which gravity canaffect flames, the estimated time scales for chemical

reaction (tchem), inviscid buoyant convection (t,nv),

viscous buoyant convection (t,_s), conductive heat

loss to walls (tc, ad), and radiant heat loss (trad) are

compared. Premixed laminar flames are considered

first because of their simplicity. Subsequent sectionsintroduce time scales for other flames.

The chemical time scale is (see Nomenclature)

td,em _ 6/SL where 6 = a/SL, thus ta ..... _, edS_. The

convective transport time scale is d/U, where d is acharacteristic flow length scale, U _, (gd( dp/p) )1i'- is

the buoyant convection velocity, and ztp the density

change across the flame. Because Ap/p - 1 for

flames, tin V _ d/(gd) 1/2 = (d/g) 1/2. For inviscid flov,,

d is determined by the apparatus dimensions, for

example the burner or tube diameter. For viscous

flow, d cannot be specified independently; instead d_" v/U, thus U _, (gv) 1/3 and t,_ _, d/U -, (vtU)/U ~

(v/g2) in the conduction time scale t_,n d is the flame

front temperature (Tf) divided by the rate of tem-

perature decrease due to conductive loss; thus t_,,, d

= Tf/(dT/dt) -, Tf/(pCph(Tf - T_)); thus tcond

aU/16,',. Similarly, for optically thin radiation, t_d

Tfl(AIpCp)- {y/(y- 1)}{P/4trap(_f - T4_)}.Two sets of time scales are shown in Table I, one

for near-stoichiometric hydrocarbon-air flames andone for near-limit flames, both at P = i atm. For

near-stoichiometric flames S L _ 0.40 m/s, Tf _* 2200

K, a - v 1.5 X 10 -4 m"/s and at, _" 0.56 m-L For

near-limit flames, SL _" 0.02 m/s, T r _ 1500 K, a _-v -_ 1.0 X 10 -4 m2/s and ap "- 0.83 m- L For both

cases g - 9.8 m/s "2,y -, 1.35, T, _- 300 K and d --

0.05 m (a typical apparatus dimension.)Several observations can be made on the basis of

these simple estimates:

1. Buoyant convection is unimportant for near-stoi-chiometric flames because t,_ ,> tchem and t,,, ">

tchem.

2. Buoyant convection strongly influences near-limitflames at lg because t,_s -< t_,h_mand t_,_ <- t_.h,m.

3. Radiation effects are unimportant at lg comparedto buoyant convection because t,_s <_ trad and tinv

'_ trad.

' 2485

https://ntrs.nasa.gov/search.jsp?R=20000000185 2019-03-20T07:31:21+00:00Z

J

¢

2486 INVITED PLENARY LECTURE

TABLE 1

Estimates of time scales for stoichiometnc and/mar-

limit hydrocarbon-air flames at [ arm pressure

Stoichionmtrie Near-LimitTime Sc_de Flame Flame

Chemistgrs' (t,l,,,,,,) 0.00094 s 0_5 s

Buo.vant, imsscid (t.,,) 0.1)71 s 0.071 s

Buoyant, _Sscous {t,,,) 0012 s 0.010 sConduction to tube wall

(t, ,,,,,0 095 s 1.4 s

Radiation Itr_.l) 0.13 S 0.41 S

4. Radiation effects dominate near-limit flames be-

cause t_ a _ t¢l,_.,., but these effects are only ob-servable at reduced gravi_ because of observa-tion 3.

5. The apparatus size (d) must be larger than about0.03 m to observe radiation-induced extinction;otherwise, conduction losses exceed radiative

losses (t_,,. a < G,,,O.

6. Many radiative loss effects can be studied in

drop-towers (test duration 2-10 s), because these

times are typically larger than t_ a.

7. Because tin, _ gt/2 and t,i _ _ gil3, aircraft-based

fig e_eriments at g _ 10 -2 go may not providesufficiently reduced buoyancy to observe radia-tive effects.

8. Because t,l_ _ v lm _ P-1_3 and t_ d _ p/A

pi/pl _ p_. t,_Jt,_a _ P- m. Thus, t_d is indepen-dent of P, but at higher P, buoyancy effects in-

terfere more strongly with radiative effects.

9. A Reynolds number Red _ Ud/v for buoyant flowis estimated as (gd)l/_d/v 2 = Grff2, where Gr a

gda/v e is a Grashof number. For Re a _ 103, thus

Gra >- 106, buoyant flow at lg is generally tur-bulent, thus, it difficult to obtain steady laminar

flames in large systems at lg.

The implications of these observations are dis-

cussed in the following sections. Essentially, anycombustion process where t_.h_,_ or tea d exceeds tin v

or t,i_ may be affected by gravity and is worthy of Bginvestigation.

PremixedGasFlames

since limits are different for upward, downward, and

horizontal propagation [5].Practically 'all flammability limit studies show that

burning ve(ocitv at the flammability limit ISI.I,,,, ) is

nonzero. Giov_gigli and Smooke [6] have shown

that there is no purely chemical flammability limit

criterion for planar unstretched flames: _vithout

losses, SL decreases asNnptotictflly to zero as dilution

increases. Consequently, loss mechanisms such as

those discussed below are needed to explain limit

mechanisms. The resulting predictions of SLj,, , in-

dicate that SL.I,,, usually depends only weakly onchemical reaction rate parameters. "Thus. "limit

mechanisms may be inferred bv comparing pre-dicted and measured S I Ji,. without detailed chemi-

cal knowledge. The mixture composition at the limit

affects SL.lim only weakly through Tf: thus, compar-ing predicted and measured limit compositions is not

especially enlightening; comparisons of SL.li,. values

is much more useful. Consequently. this discussion

emphasizes comparisons of predicted and measuredvalues of SL.li,r e

For upward propagation, Le W [7] showed that the

flame rise speed at the limit (,,, 0.33(gd)_,2)is iden-

tical to that of an inviscid hot gas bubble. This re-

lation was later verified for a wide range of tube di-ameters and mixtures [8]. Buckmaster and Mikolaitis

[9] showed how this minimum rise speed causes hv-

drod>aaamic strain at the flame tip, which causes e'x-

tinguishment for sufficiently low S L. The predicted

burning velocity of the limit mixture (SL.li,0 is, after

temperature-averaging transport properties:

_ T I](gct21t/4SL'lim = 2'8 exp[_ (1- _--)( 1 _ff/j\"'_]

(1)

The form of equation 1, SLjim _ (g_/d) TM, can beobtained by setting ti,,,, = tCh_.

For downward propagation in tubes, centrifuge

experiments [10] indicate that SLlim _ gt/3, inde-pendent of Le, which is reasonable since downward-

propagating near-limit flames are nearly flat andunstrained. Experiments [i1] and numerical simu-

lations [12] suggest extinction results from sinkingregions of cooling burned gas near the walls over-

taking the flame and blocking it from fresh reactants,

although the gt/3 scaling was not tested in Refs.

[11,12]. The gt,n scaling can be obtained by settingtchem = tvis, thus

Flammability Limits

The previous section showed that gravity effects

are significant only for mixtures with low SL, imply-ing mixtures highly diluted with excess fuel, oxidant,

or inert gas, but sufficient dilution causes flamma-

bility limits. Thus, gravity effects have significant in-

fluences on near-limit behavior, which is expected

SL.Iim _ (ga) t/3 (2)

Experiments [8] employing varying diluent gasesaria pressures confirm the a m sealing and lack of

dependence on tube size, which, together with the

gVa scaling mentioned above, supports the proposedmechanism.

Both upward- and downward-limit mechanisms

indicate that as g --+ 0, SLy, --+ O, implying arbitrarily

UNDERSTANDINGCOMBUSTIONPROCESSESTHROUGHMICROGRAVITYRESEARCH2487

_. t" 1.1=30 cm optical Ihickne._=2.35) \_.'_

......l" ............ Adiabatic _I000

0.4 o.5 0.6 o,7 0.8Equivalence ratio

FIC. 1. Predicted values of burning velocity, and peakflame temperature in CH 4 - (0.21 Oa + 0.49 N_ + 0.:30

CO,_;, mi-xtures under adiabatic conditions, _'ith opticallythin radiative losses and including reabsorption effectsI°6].

weak lnixtures could burn very slowly. However,

conductive or radiative losses prevent arbitrarily

weak mixtures froln burning even at g = 0. Theoriesthat relate flammability limit to heat losses [13-15]

predict a minimum Tf below which flame propaga-tion cannot occur because chemical reaction rates

are much stronger functions of temperature than

heat loss rates (exponential vs. 'algebraic). Conse-quently, because dilution decreases Tf, dilution in-

creases the impact of losses, leading to flammabilitylimits. For conductive losses, setting td,_m = tco,,dleads to

Pelim _ SL.li,,,d/o_ = constant (3)

with experiments [8,16] and computations [17] in-

dicating Pe_i_ ,= 40. For radiative losses, setting t,,h_m= L_d leads to [18,19]

SL.li, n -- 1 /1.2fl_A2f (4)

p-G qFor lean-limit CH4-air mixtures at 1 atm, equation4 yields SLJim _' 0.023 in/s, similar to detailed nu-

merical model predictions [20,21]. Such small SL.ti,,

are not observed at lg because of buoyant convec-

tion (tin,, < G_d and t,_ < G_d); equations 1 and 2

yield SL.li,,, '_ 0.033 and 0.078 m/s for upward and

downward propagation, respectively. Atpg, however,

predictions of equation 4 compare favorably to ex-

periments in large combustion vessels [19,22] using

varying pressures, fuels, and inert gases. Also, similarresults were obtained for CH4-air mixtures at 1 atm

in tubes with d = 0.05 m [23], suggesting these lim-its are apparatus-independent. Thus, radiative losses

may cause flammability limits when extrinsic losses

(conduction, buoyant convection, etc.) are elimi-

nated. In this instance, pg experiments enabled ob-

servation of phenomena not observable at lg.

These radiative effects apply only for optically thing_Lses (i.e., no reabsorption of emitted radiation),

which are inappropriate for large systems, high pres-

sures, or ,nLxtures with strongly absorbing luateri_d.With this motivation,/lg experiments [24] were con-

ducted using lean CH4-air mixtures seeded with SiCparticles. Because solids elnit/absorb as black- or

gray-bodies, whereas gases radiate in narrow spectralbands, particle-seeded gases etnit/absorb more ra-

diation than particle-free gases. Measurements of

propagation rates, pressures and postflame thermal

decays showed that, consistent with theoretical pre-

dictions [25], at low particle loadings the particles

increase radiative loss (optica/Iv thin conditions),

whereas at higher loadings reabsorption of emitted

radiation becomes significant, which decreases netradiative loss and augments conductive heat trans-

port.

Even for gases, computations [26] using detailedstatistical narrow-band radiation models show that

flammability limits are extended considerably ,a_th

reabsorption (Fig. 1). With gases, however, twomechanisms lead to flammability limits even with

reabsorption. One is the difference in compositionbetween reactants and products; if H;,O or other ra-

diatively active combustion products are absent from

the reactants, radiation from these species that is

emitted upstream cannot be reabsorbed by the re-actants. The second mechanism is that emission

spectra are broader at Tf than T_; thus, some radia-tion emitted near the flame front cannot be absorbed

by the reactants. Upstream loss occurs via both

mechanisms, leading to extinction of weak mixtures.

These results suggest that fundamental (domain-

and gravity-independent) flammability limits due to

radiative losses may exist at ,ug, but these limits are

strongly dependent on emission/absorption spectra

of reactant and l_roduct gases and their temperaturedependence ancl cannotbe predicted using gray-gas

or optically-thin model parameters.

Stretched Flames

Premixed gas flames generally are not fiat and

steady nor do they propagate into quiescent flows.

Consequently, flames are subject to "flame stretch,"

S _- (1/A)(dA/dt) [18], which affects SL and extinc-

tion conditions [18,27]. At lg, buoyancy imposesflame stretch comparable to ti/,,t, or tG I. At pg, weak

flame stretch effects that are insignificant at lg may

dominate. One example is expanding sphericalflames for which

1 dA 1 d (4nr_) - 2drfZ _ -_ -._ = 4n---_¢dS r dt (5)

For Le < 1, positive stretch increases Tr because the

increased chemical enthalpy diffusion to the flamefront in the form of scarce reactant exceeds the in-

creased thermal enthalpy loss. Because heat release

24,t38 INVITED PLENARY LECTURE

6Z,8mJ

._ TYPlCAtUIRI_ tIMES

i j i i i I i I I IIM[_ IK

FIC. 2. Characteristics of self-extinguishing flames in

CH4-air mixtures at i arm for various mole percent CH4and spark ignition energies [112]. The "x" symbols denoteextinction.

"I

_ 1°I

ao'

_i0 °i

i I

0

0 l_.zl_'kmmU in _rmal 8_vl_

6 Prweut mpplem_tn_expebouw Itnormtllrmvlty

0.4 L6 IJI

Equivalence_o

FIG. 3. Measured and predicted extinction strain rates

for strained premixed CHa-air flames at/zg [33] showingdual-limit behavior, that is, residence-time limited extinc-

tion at high strain rates (upper branch, "strong flames") andradiative loss extinction at low strain rates (lower branch,"weak flames").

reactions have high activation energies, small Tfchanges cause large changes in reaction rate and

thus S L. An evolution equation for nonadiabatic ex-

panding spherical flames is given by [28]:

dS 2S

_-_ + S 2InS 2 - R Q (6)

where S _ (drf/dt)/(SL(p,/pf)), R =* rf/(_tSI(Le, #,)),

l(Le, e) is a scaling function (I > 0 for Le < 1 and

I < 0 for Le > 1) and Q ** {flA(Tr)62}/{2(Tr - T,)}.

The terms in equation 6 represent unsteadiness,heat release, curvature-induced stretch, and heat

loss, respectively. For steady planar flames, equation6 becomes S '2 In S" = -Q, which exhibits a maxi-

mum Q -- 1/e = 0.3678 ... at S = e-l_, which

corresponds to SL._m from equation 4. For Le < 1,

the curvature effect (2S/R) opposes heat loss (Q),

'allowing mixtures that are nonflammable xs plane

flames (Q > l/e) to exhibit expanding spheric.a]flames until rt grows too large and thus the curvature

benefit too small. For mLxtures just outside the limit,

the extinction radius may be very large. Such behav-

ior, termed self-extingui'shin_ flames (SEFs). is ob-

served ex-perimentallv [19,22] (Fig. 2) at/_g in near-limit mixtures with" Le slightly less than unity.(Mixtures with lower Le exhibit diffusive-thermal in-

stabilities or flame balls discussed below.) Equation

6 also predicts, consistent with experimental obser-vations [29], that SEFs cannot occur for Le > 1

(thus, R < 0) because both curvature and heat lossweaken the flame.

Two experimental observations not predicted byequation 6 are that narrow mixture ranges exhibit

both SEFs and normal flames and that the energy

release before extinguishment can be orders of mag-

nitude greater than the ignition energy. Such behav-

ior is predicted bv computations [30] not subject to

scaling limitations of activation energy as_vnptoticsused to derive equation 6. These calculations also

show that for small initial rf, all mixtures exhibit ex-

tinguishment, corresponding to nonignition behav-ior [31]. Thus, in mixtures exhibiting SEFs, flames

extinguish at large curvature (small r t) due to largeS and at small curvature due to radiative losses. This

dual-limit behavior is also exhibited by many othertypes of flames described later.

Flames in hydrodynamic strain induced by coun-

terflowing round jets are frequently employed tomodel turbulence-induced flame stretch effects. At

steady state, the flame resides at the axial location

(y) where the axial velocity (Uv) equals St for the

given Z" = dU,/dy. As E increases, Uv increases, thus

the flame moves toward the stagnation plane(smaller y) and the burned gas volume (thus radia-tive loss) decreases. As with curvature-induced

stretch, for Le less than/greater than unity, moderate

hydrodynamic strain increases/decreases So, but for

all Le, large strain extinguishes the flame [32]. Con-sequently, btg experiments [33] in low-Le mixtures

(Fig. 3) reveal extinction behavior analogous tospherical flames. For large Z', the short residence

time (_Z'- _) causes extinguishment (Z'- t .. tehe,. )

along the "normal flame" branch, analogous to non-gnition behavior of spherical flames, In contrast, for

ow _', the residence time and burned gas volumeare large; thus, radiative loss is significant (t_a "

t¢.h_m), so radiative loss extinguishes the flame alongthe "weak flame" branch, analogous to SEFs. The

optimal _ ('-13 s-]) producing the minimum flam-

mable fuel concentration corresponds to Z'-t =0.08 s, which is less than t,_, or troy; thus, the C-

shaped response and the entire weak-flame branch

cannot be observed at lg. The optimal Z" is nearly

the same for model and experiment, indicating that

loss rates are modeled well, but the computed limit

IUNDERSTANDING COMBUSTION PROCESSES THROUGH MICRO(,RAVITY RESEARCH 2489

Temperature

C - 1-1/r

\

T - 1/r

Intodor filled

with combustion

products

/Fuel & oxygen Heat & productsdiffuse inward diffuse outward

FIG. 4. Schematic diagram of a flame ball, illustrated forthe case of fuel-limited combustion at the reaction zone.

The ox.-ygen profile is similar to the fuel profile except itsconcentration is nonzero in the interior of the ball. The

combustion product profile is identical to the temperatureprofile except for a scale factor.

'; • • • I .... I .... I ....

I1,_---_ Unstable to 3-d disturDances

I

. Equation of curve:

Unstable to 1-d

d_stur ba_,_

.... i .... i .... i ....

0.05 0.1 0.15 0.2

Dimensionless heat loss (Q)

A

----10

E

_ 5

_oe-0

.__0

Fzc. 5. Predicted effect of heat loss on flame-ball radius

and stability properties [42] showing radially unstable(small) flame-ball solution, radially stable (large) flame.b.all

solution, and three-dimensional instability for large flamebails.

composition is leaner than the experimental limit,

sut_,gesting that the chemical mechanism used is in-accurate for weak mixtures. Due to the radiant loss

decrease at moderate Z', the flammability limit ex-

tension also occurs for Le > 1, though, for suffi-ciently high Le, no C-shaped response or flamma-

bility limit extension occurs [34]. (For spherically

expanding flames, no flammability extension occursfor Le > 1 because in this case there is no mecha-

nism to reduce radiative loss by flame stretch.)

The combination of nonmonotonic response to Z"

plus the reduced radiative loss at larger Z" causes

several new extinction branches depending on

t_.h,..... t_,,t, X-t. and Le [34,35]. It is uncert_dn

whether these branches are physically observable

because thev have not been identified experimen-

tally and stabili_' analyses have uot been performed.

Flame Balls

Over .50 years ago, Zeldmich [36] showed that the

steady mass, energy,, and species conservation equa-

tions admit solutions corresponding to stationary

spherical flames, charactenzed bv a flame radius (rf).Fuel and o_'gen diffuse from t}ae ambient mixtureinward to the reaction zone while heat and combus-

tion products diffuse outward/Fig. 4). Mass conser-vation requires that the fluid velocity be zero every-

where. The temperature and species mass fractionprofiles have the form ct + ce/r, where cl and c_,are

constants. Corresponding solutions in planar and cy-

lindrical geometry cannot exist because the solution

forms cL + c2r and cl + c21n(r), respectively, are

unbounded as r -> _. Zeldo_ich [36] and others[37,38] also showed that flame-ball solutions are un-

stable and thus probably not l?hysically observable,although these solutions are related to flame ignition[37].

Forty years after Zeldovich [36], apparently stable

flame balls were accidentally discovered in drop-

tower experiments using He-air mlxt-ures [39] and

aircraft-based #g experiments using various low-Le

mLxtures [40]. The/ag en_4ronment facilitated spher-

ical symmetry and prevented buoyancy-induced ex-

tinction. For mixtures sufficiently far from flamma-

bility limits, expanding spherical fronts composed of

many individual ceils were observed, whereas for

more dilute mixtures, cells that formed initially did

not split and instead closed up on themselves to formflame balls. (For still more dilute mixtures all flames

eventually extinguished.) It was inferred that flameballs can occur in all near-limit low-Le mixtures;

however, the short duration of drop-tower experi-

ments and substantial g fluctuations in the aircraft-

based pg experiments precluded definite conclu-sions. Recent space shuttle experiments [41]confirmed that flame balls can exist for at least 500

seconds (the entire experiment duration.)

Zeldovich [36] noted that radiative losses might

stabilize flame balls; consequently, after their exper-imental observation, radiative loss effects on flame

balls were analyzed [42]. For moderate loss, two so-

lutions branches are predicted (Fig. 5), a strongly

nonadiabatic large-radius branch and a nearly-adia-

batic small-radius branch. For sufficiently strong

losses, no solutions exist, indicating extinction limits.

Stability analyses [42] predict that all small flames

are unstable to radial disturbances, and large flameswith weak loss (far from flammability limits) are un-stable to three-dimensional disturbances. Close to

extinction limits, the large-radius branch is stable to

both disturbances. These predictions are consistent

I

2490 INVITED PLENARY LECTURE

12

• e_ -- Peters & Rogg

t0 • • ..... GRI lI ..... Yeller

• O { • Exper+ments

_a ." !

_8

_ 4

0 t I I

3 3.5 4 4.5

Mole percent H in air2

Fro. 6. Comparison of computed flame-ball radii as a

function of H2 mole fraction in Hz-air mixtures for three

different H2-O _ chemical mechanisms, along with prelim-

inarv results from the STS-83 and STS-94 space experi-ments [4-5].

16

EE 12

._="O

8

_ 4E

U.

02

I I I I I I

Predictions

(without CO_

e_" (:3diCcio: Sradiat,0r

,4 6 8 10 12 14 16

Mole % H2

FIG. 7. Computed flame-ball radii as a function of the

H a mole fraction for steady flame bails in H2-Oz--COz

mixtures with H_:O_ = 1:2, for opticaUy thin CO_, radiation

and with CO_ radiation artificially suppressed (optically

thick limit for CO oradiation). Preliminary experimental re-sults from the STS-94 mission are also shown (filled circles)[45].

with the observed splitting cellular flames away fromlimits and stable balls close to limits. For Le close to

or larger than unity, all flame balls are unstable for

any loss magnitude [43], explaining why they are

never observed in (for example) CH4-air mixtures(Le _, 0.9) or C3H_-air mixtures (Le _ 1.7).

Numerical predictions of non-adiabatic flame balls

employing detailed chemistry, diffusion, and radia-

tion models [44,45] are qualitatively consistent withthese experimental and theoretical results. Still,

quantitative agreement has been elusive (Fig. 6) for

at least two reasons. First, flame-ball properties are

very sensitive to the three-body recombination step

H + 02 + H,O--* HO_ + H,O [45] whose ratevaries widely between dif(erent p-ublished H+-O, re-

action mecl_anisms. The second reason is reabsorp-tion of emitted radiation in mixtures diluted with

radiatively active CO O or SF_. An upper bound on

self-absorption of diluent radiation (ap _ o¢) is as-

sessed by neglecting diluent radiation entirelv be-cause as ap _ :o. radiative loss from the dilueni van-

ishes and no additional heat transport occurs due to

radiation. Agreement between predicted and mea-

sured flame radii is nmch better in this case (Fig. 7),

strongly suggesting radiation modeling mcluding

reabsorption is needed for accurate predictions inthese cases.

A key difference between propagating flames andflame balls is that propagating flames have convec-

tive-diffusive zones where temperature and concen-

tration approach their ambient values in proportion

to e -a'_, whereas flame balls have purely diffusive

zones where the approach is proportional to Ur.Plane flames respond on short time scales td,_.,, =&2/a, whereas the gradual 1/r flame-ball profiles pro-

duce properties dominated bv the far-field lengthscale tiff, and thus diffusion time scales (flrp+-/a [42J,

typically 100 s. These scales are relevant to stability

and extinction limits because they affect the times

for radiant combustion products to diffuse to the far-

field and indicate large volumes of gas (_/_r?)

where radiative loss affects flame balls. Such large

scales are confirmed by space experiments [41] and

numerical simulations [44.45]. Droplet and candle

flames (discussed later), which have quasi-spherical,

diffusion-dominated far-fields, exhibit analogous be-havior.

Gaseous Non-Premixed Flames

Stretched Flames

Non-premixed flames, where fuel and oxidant are

separated before combustion, are affected bv stretch

differently than are premixed flames. The most sig-

nificant difference is that the flame position is de-termined by the location of stoichiometric mixture

fraction, dictated by mixing considerations, rather

than being determined by balances between SL and

U as in premixed flames. Consequently, non-pre-mixed flames have considerably less freedom of

movement. Also, premixed flames have characteris-

tic thicknesses _ _ a/SL unrelated to the flow envi-

ronment, whereas non-premixed flames have onlv

the diffusion length scale 6 _ (a/Z') t/'2. With fixe_t

flame location and 6 increasing monotonically with

decreasing X, non-premixed flames with radiative

loss exhibit only simple C-shaped responses to strain(Fig. 8) [46], with a short residence time extinction

branch (t,.h_m > Z-l) and a radiative loss extinction

I

UNDERSTANDING (JOMBUSTION PROCESSES THROUGH MICRO(;RAVITY RESEARCH 2491

'i" I02

r-

o) 101

0

>

C

"i lOe

$ffl

• . 'nm7'

'0.qs.... o'2..... o._,s''Fuel corcer_al_on

FIG. _,Measured and predicted extinction strain rates

for strained non-premixed N.,-diluted C H_ versus air coun-

terflow flames at/_g [46] showing dual-limit response anal-

ogous to premi.xed flames (Fig. 3).

TABLE 2

Predicted scalings of flame heights (Lt) and residence

times (tr, t) for non-premixed round-jet and slot-jet flamesunder momentum-dominated and buoyancy-

dominated conditions

Flow

Geometry, Mechanism Lf tiet

Round-jet Momentum Uj_/D d_/DRound-jet Buoyant U,dffD (U_dffgD) t/o-

Slot-jet Momentum U_gt_/D d_/D

Slot-jet Buoyant (U_d_/D2g) V3 (l_d_g:D) 1/3

branch (tr_a < _r-I) rather than the compli-

cated responses found for premixed flames [34]. The

only significant difference in flame structures near

the two limits is _ [46], a situation quite unlike pre-mixed flames.

For the radiative extinction branch tel .... is still a

factor because traa _- 27- Z results in order unity de-

creases in flame temperature, thus causing exponen-

tially large decreases in td, e,,,. Even conditions far

from extinction at lg, therefore, may exhibit radia-

tive extinction at #g due to much larger residence

times. This mechanism also applies to radiative ex-tinction of other types of non-premixed flames dis-

cussed later. It is also somewhat analogous to the

lower branch of strained premixed flames (Fig. 3)and the large-radius branch of flame balls (Fig. 5).

The experiments shown in Fig. 8 suggests that noflames exist below some value of Z', whereas the

model predicts flames at arbitrarily low Z. Similar

behavior was seen for premixed flames (Fig. 3). This

suggests an additional loss mechanism not consid-

ered by the model, probably axial conductive heat

losses to the jets or radial couductive loss to inert

gases surrounding the reactant streams. This would

induce t_;,l,,j _ 2.9 s - i ifd is the jet spacing (_5 ram),

or 7.1 s- i if d is the jet diameter t 16 ,nm). Either of

these are roughly consistent _v-ith the minimum Z in

Fig. 8. Thus, apparatuses large enough to studv

flames at lg without substantial conductive loss,

where ma.ximum length scales are about (oct,_)I. __,are

insufficient for the weaker flames attainable at #g,where maximum len_h scales are about (ettr,,, 01'_,

Laminar Gas-Jet Flames

A fuel jet issuing into an o_dizing environment is

one of the simplest types of flames. Jost [47] and

Roper [48] estimated the flame height (LI-/and res-

idence time from jet exit to flame tip (ti_.t) by deter-

mining the height (y) where the transverse diffusion

time (d(y)2/D, where d(y) is the stream tube width)

equals the convection time (U(y)/y, where U(y) isthe axial velocity). When buoyancy and viscosity ef-

fects are negligible (momentum-controlled jets),

U(y) is constant and equals the jet exit velocity (U,,),whereas when buoyancy effects dominate, UIy)

(gy)l/._. In either case, mass conservation requiresthat d(y)eU(y) = d_Uo = constant for round jets or

d(y)U(y) = doUo = constant for slot jets. The re-

sulting estimated scalings for Lf and tie_ are given inTable 2. Transition from buoyancy-controlled to mo-mentum-controlled conditions occurs when the time

scale for the former exceeds the latter, which cor-

responds to U o > gd_D for either round jets or slot

jets. The scalings for momentum-dominated flames

presume constant U, which is reasonable for coflow-

ing Burke-Schumann flames, but for nonbuoyant jet

flames without coflow, the jet spreads and deceler-ates. For this situation [49]

D 2Sc l>_- n _ (7)

tjet= U(y) - D

Because Sc =* 1, the scalings ofLfand tjet are similarwith or without viscosity. Fig. 9 shows measurements

of Lf for CH4 flames [50]. Note that, as the scalings

predict, Lf/d o _ Re _ Uod,/v at both lg and/Jg, and

only small differences exist between lg and/ag flame

lengths.

All/Jg studies show larger flame widths (w) at #g

than lg due to lower U and longer tie t [50]. Also, w

is larger at #g because the temperatures are lower

(see below) and D _ T 1--_. Because w depends on

whether U is accelerating (buoyant jets), constant(nonbuoyant Burke-Schumann flames), or deceler-

ating (nonbuoyant jets), w is more difficult to predict

than is Lf [2]. The difference between lg and/lgwidths decreases as Re (thus, Uo) increases (Fig. 10).

The nonbuoyant widths increase slightly with Re,

2492 INVITEDPLENARYLECTURE

, , ,,,,,,! ..... ,,! , , ,,,,

1 O0 o 8ur_etranO et al {*q} a, ! •

• S ....... d .... {.g ' arm, f_o_• Sun_enand et al (pg 05 atmt

• Suntle,land et aJ (Vtg 025 arm)

• Cochtan and Mastca I_g) trio _

o • Bae,adon et a¢ (_g) _o # o"t_ t Bahadon & Stocker (_gl •"" 10 _%

- _o

eo_,oo_

1 _a_8

• i ,_..qll i , i ,.••ll A ......

lO lOO 1000Reynolds number (Re)

FIG. 9. Measured flame lengths, normalized by jet di-

ameter, as a function of the jet Reyno ds number for non-

premixed CH4-air jet flames at lg and,ug. Data is taken

from a variety of sources and compiled in Ref. [50l. The

data show a nearly linear relationship between flame length

and Reynolds number, with generally longer flame lengthsat/_g, due to the differences between residence times un-

der buoyancy-driven versus momentum-driven residencetimes.

._o

10

.... '1 • ....... I " " ' ' .... I

,to g *)_,o-o.o,o°O • °o_ 0

Oo _oo o o

0 o _0oO

oO o oo o

o ° _°° o L _?o

°O o° 0 . 0 Suncletland el &l. (tg)

oOO oO ° Oo : Sundertand et at. (.g. , aim)$unclertand et _. (pg, 05 Itm)

• S, mded=nd et _ (b_g, 025 aim}

• _(_ra_ and Mesk_

• O,a_lao_ et aL.==.1 s a = ==.,. | | i i,.,,I

1 0 1 O0 100(

Reynolds number (Re)

FIC. I0. Measured flame widths, normalized by jet di-

ameter, as a function of the jet Reynolds number for non-

premixed CH4-air jet flames at lg and pg. Data is takenfrom a variety of sources and compiled in Ref. [50]. The

data show larger flame widths atpg due to the differences

between accelerating flow at lg versus decelerating flow at

pg. The data also show that, consistent with theoretical pre-dictions, the width is nearly independent of Reynolds num-ber for nonbuoyant conditions, except at low Re whereboundary-layer approximations are invalid.

whereas 'all aforementioned models predict self-

similar flame shapes with no effect of Re. This maybe due to axial diffusion, not considered in these

models, which increases mixing over that with radial

diffusion alone. This suggestion is supported by theresults shown in Fig. 10 which show that w/d o islowest for lowest Re (=*20), where axial diffusion is

5O0

z3 400

300

200

• 100EE

rot" MicrogravdyiI •

• •.. W_O

• • ,dr.. 810 fl* i "¢ bruits

• * Earth grawty

==

I iooo ooo ooo,0o0 oo0 ooo,ooo ooo

Era. 11. Measured flame heights fi)r non-premLxed

C3Hs-air jet flames at lg and pg [5 l] showing transition to

turbulence Note lg flame lengths are shorter than ,agflame lengths, even at very high Re_lmlds numbers.

most significant, but as_lnptotes to fixed values athigh Re.

Compared to yellow lg flames, j_g gas-jet flames

are more red [49,50], indicating lower blackbodysoot temperatures and presumably lower m&xSmut_l

flame temperatures. This occurs because ti,.t is larger

at/2g and thus radiative loss effects (_ti,ffL_, l) are

greater. Drop-tower [51] and space [52] ex-perimentsindicate surprisingly large and consistent radiative

loss fractions (0.45--4).60) at big compared to 0.07-

0.09 at lg, for various fuels, pressures, O_ ,hole frac-

tions, and flow rates. Thus, differences in t),.t at lgand/_g result in widely varying characteristics even

for flames having nearly the same Lf.

Turbulent Flames

In turbulent non-premixed jet flames, D is not

fixed but rather is nearly proportional to u'Lt. Be-cause u' _ Uo and Lt _ do, Lr _ U,d_/u 'Lt _ d,, for

round jets; thus, Lf is independent of U,,. This pre-

diction is supported by classical lg e.weriments [.53]

as well as recent/_g experiments [54] (Fig. 11). Note

that L¢(ag)/Lf(lg) is practically constant even be-

yond the transition to turbulent conditions (high U,,and Re). Note also that the maximum Re at which

flame exists (the "blow-off" limit) is different at lgand/lg. This is surprising because blow-off condi-

tions are typically controlled by behavior near the

flame base [55], where buoyancy effects are often

considered insignificant. This suggests that blow-off

is partially affected by convection induced by the

buoyant plume far above the jet exit, even at very

high Uo. One would intuitively conclude that the lg

flames should blow-off at lower Uo because buoyantflow would induce higher "effective" U,,, which is

consistent with Fi_. 11. This shows that buovancyeffects are quite ubiquitous even under conditions

commonly thought to be unaffected by buoyancy.

UNDERSTANDINGCOMBUSTIONPROCESSESTHROUGHMICROCRAVITYRESEARCH2493

sootaccumulationisconvectedbv_t_alflowthroughtheflametip.Do_'nstream,forreasonsnotvetex-plained,thesootannulusfragments,creatingcrown-likestructures.Theseeffectsareonlyobser,ableat/tg where convection velocities arecomparable to

thermophoresis velocities, (_- 5 rends for the con-

ditions of Fig. 12 [60]).

FIG. 12. Direct photographs of sooting n-C4Hio non-

premixed gas-jet flames at lg (left) and,ug (right) at Re ",

42, jet diameter 1.0 mm. shox_ing e_Jdence of thermopho-

resis-induced agglomeration at ,ug. Photographs courtesy

of Professor O. Fujita.

Soot Formation Processes

Compared with ig flames #g gas-jet flames have

much greater tendencies to emit soot [49,56], indi-caring that increases in tie t (thus, greater time for

soot formation) plus broader regions in which com-

position and temperature are favorable for soot for-mation [56,57] outweigh lower temperatures at/lg,

which decreases soot formation [58]. Recent quan-titative measurements [56] show peak soot-volume

fractions about twice as high at #g than lg for 50%C2H_,/50% N2-air flames.

Surprisingly, _tg gas-jet flames exhibit "smoke

points," corresponding to critical U,, below whichsoot is consumed within the flame, and above which

soot is emitted from the flame [57]. Smoke points

are expected for buoyant round-jet flames becausetip

tiet _ Con; thus, increasing Uo increases the rime

available for soot formation. But for nonbuoyant

fames, jt.et _ lJo, suggesting no smoke point shouldexist. Fully elliptic numerical computations [59]

show that, for some circumstances, Let does increase

monotonically with U,,. which could explain smoke

points for nonbuoyant flames. This behavior was

suggested to result from axial diffusion effects [59],

but in this case t,et should asvmotote to constantI j /11.

values for large Lr, where axial diffusion is negligible.

Thus, simple explanations of#_ smoke points remainelusive. Residence-time considerations alone may be

misleading; soot precursor temperature-composi-

rion-rime histo_ effects are apparently also impor-tant.

With weak convection, thermophoretic forces,

which move particles toward lower temperatures,are an important effect. If convection and tempera-

ture gradients are in the same direction, the convec-

tive and thermophoretic forces may balance at somelocation. This leads to soot accumulation inside the

flame front at/Jg (Fig. 12) [60], where an annulus of

Condensed-Phase Combustion

Droplet Combustion

The first microgravity combustion experiments

were isolated fuel-droplet tests conducted by Ku-

magai and Isoda [61]. At lg. experimental measure-

ments of droplet burning rates are compromised by

buoyant convection, which destroys the spherical

symmetry and inducing additional heat and mass

transport, which alters burning rates and compli-cates modeling. Classical theory [62,6.3] predicts thatburning rates for spherically swnmetric buoyancy-

free droplet burning are given by

- =

K -- (8,,_,/poC p) ln(1 + B) (8)

In experimental studies, the droplet diameter dd

could be fixed by forcing fuel through a porous

sphere at rates that balances evaporation, leadin_toa steady mass burning rate (rh) -- (n/4)p_dK, but

most experiments employ fuel droplets where da de-

creases with rime. Somewhat surprisingly, many

fuel-droplet results follow equation 8 well despiteunsteadiness, heat losses, soot formation, and water

absorption effects discussed below.As with flame balls, steady solutions exist for

spherical droplet flames even in infinite domains,with the flame front located at

dr = d d In(1 + B)/ln(1 + f)

Whereas flame balls are convection-free, dropletflames exhibit Stefan flow due to fuel vaporization

at the droplet surface. Mass conservation dictates

that the Stefan velocity decays as 1# 3, causing tem-

perature and concentration profiles to vary, with ra-

dius in proportion to (1 + B) -d,t/_r rather than Ur

as in flame balls, although these profiles, when nor-

malized by flame radius, are indistinguishable at

large r. Unlike flame balls, heat losses are not re-

quired for stable droplet flames because the flamelocation cannot move away from the stoichiometriccontour.

The characteristic time scale for droplet combus-

tion is td.,p -- d_/a. This leads to two extinction lim-

its [64.65], one for small dr where tdm p < tcl .... andthus fuel and oxidant cannot react beibre interdif-

fusing and one for large df where td_o_ > L_d and

thus the temperature decrease from radiative loss

I2494 INVITED PLENARY LECTURE

E_1,2

_" 0.8. _ I__ Model: 25%_3S% O: / He

< 0.4 | _ 2s_o,l..s_s.=Q 30% 0 t / He STS-83

| • 35%Oz/HeSTS-83

| • STS-94: Air0.0 , •

0 I 2 3 4 5

IniUalOiameter [mmJ

FIC. 13. Effect of initial droplet diameter (d,_,,)on quasi-

steady burning rate (K) for heptane droplets burning in airand an Oz-He atmosphere at pg, showing that K decreases

with increasing d,l,,, apparently because of increased ac-

cumulation of soot and gas-phase radiant species for largerd,,, I7o].

q

qJ

Fro. 14. Direct photographs ofheptane droplets burningin air at ug showing spherically symmetric combustion

(left) and a soot "tail" formed by weak convection effects

(right) [68]. Photographs courtesy of Professor T. Avedi-sian.

reduces the reaction rate sufficiently to cause ex-

tinction. The former occurs when de < (_,hem) 1/2

and the latter when df > (¢rtrad) 1/2. Recent space ex-

periments have reported radiative extinction of large

droplets in air [66] and O,_-He [67] atmospheres.Even when radiation does not cause extinguishment,

it causes a decrease in K, especially when soot for-mation is significant [68,69].

In experiments, K is not constant as the quasi-steady model (equation 8) predicts, but rather de-

creases with increasing ddo (Fig. 13) [70]. This sug-

gests that nonsteady effects, specifically the diffusion

of thermal energy and radiant combustion productsinto the far field, may be significant; this would cause

changing radiative loss over time. Analogous behav-ior occurs in flame balls [41], where radiative loss

requires - 100 s to reach steady state even in flame

balls much smaller than _pical droplet flames. An-

other indication of unstea_ness in droplet flames isthat constant dr�d, values are not Eenerallv achieved

especially for l_trge droplets at fig _69,70],'in contrasi

to the predictions of the quasi-steady theorv. Un-steadiness effects in droplet fames were recently an-

alyzed by King [71]. The effect old, t,, on K has'also

been proposed [68] to result from soot accumula-

tion, which is more significant for larger d,l,, and actsto decrease net heat release and increase radiation.

As with non-premixed gas-jet flames, soot particlesin _tg droplet flames exhibit thermophoresis effects

[72,73], leading to soot ag,glomeration between the

droplet and flame front (Fig. 14). The ag,glomerates

may break apart suddenly, leading to muhiple burn-

ing fragments. Because velocit T and temperature

_radients are readily modeled in spherical dropletnames, such experimental observations enable as-

sessment of thermophoresis effects on soot particletransport.

Another complicating factor arises in fuels that are

miscible in water. The fuel may absorb water vaporfrom the combustion products, causing significant

departure from equation 8 and reducing flammabil-ity. Such behavior is found [74,75] in methanol

flames, where extinction diameters depend substan-

tially on d,lo due to water absorption during com-bustion.

Finally, in recent space experiments flame oscil-lations with amplitudes comparable to the mean

flame diameter have been observed [76]. The oscil-

lation amplitude ][_'ew with time with extinction typ-ically occurring alter eight cycles. The oscillation fre-

quency was approximately 1 Hz. Cheatham and

Matalon [65] predicted oscillations of roughly the

correct frequency in droplet flames of pure fuels un-der near-extinction conditions when the reactant

Lewis numbers are sufflcientlv high. To date, oscil-lations have been reported for methanoi/dodecanol

(80/20 mass fraction) bicomponent droplets burningin air; it is uncertain whether oscillations also occur

in pure fuels. Moreover, pg experiments in O_-Heatmospheres [67], with much higher Le, did not ex-

hibit oscillations. One possible explanation is thatdroplet support fibers were used in Ref. [76] but notRef. [67]. The fiber could increase conductive and

radiative losses, which encourage oscillations [65].Another explanation is that, because oscillations oc-

cur only near extinction conditions, depletion of ox-

ygen (leading to extinction) was much more signifi-cant in the smaller combustion chamber used in the

methanol/dodecanol experiments. Such oscillatory

instabilities are discussed further in the followingsection.

Candle Flames

An excellent example of the differences between

lg and pg flames is seen in perhaps the most com-

mon and familiar of all combustion processes---can-

dle flames. At lg, candle flames are supported by air

• ,m

Z

UNDERSTANDING COMBUSTION PROCESSES THROUGH MICROGRAVITY RESEARCH 2495

candle flames were noted [65]. Altenlativel.x; Buck-

master [79] showed that the flame "edge" separatin_

burning and nonburning re_ons of non-preufixed

flames exhibit oscillatory behavior at tfor quasi-sta-

tionary edges) Le > i -f 8/fl(1 - (T,/Tt )) _ 2 whenLe for the other reactant is unity. Le _ i for O2 in

N2, but Le for fuel vapors is probably closer to -9:

thus, edge-flame instabilities could explain the ob-served oscillations. While neither instability mecha-

nism has been definitively linked to the canclle-flame

experiments, both predict greater propensities for

oscillation with greater heat losses, which is consis-tent with the observation that oscillations occur near

extinction.

Fzc. 15. Direct photographs of candle flames at lg and

/_g, showing impact of buoyant flow on flame shape [77].

entrained _Sa buoyant flow, which generates a self-

sustaining flame and flow configuration. Obviously,

this mechanism cannot apply at/tg. The spherical

diffusion equation admits steady solutions for flame

balls and droplet fames without forced convection.

An interesting question is whether candle flames,which are not strictly spherical, can behave similarly.

Space experiments [77,78] indicate that candleflames can be steady for >45 rain, with flame shapes

typically hemispherical (Fig. 15). Eventually, the

flames always extinguished, whereas the spherical

flame model predicts that the flame would burn in-definitely. Protective screens used in the experi-

ments may have limited the O_, supply, eventually

allowing sufficient O2 depletion to cause extinguish-ment.

Before extinction, the candle-flame edge fre-

quently advanced and retreated periodically. The os-

cillation amplitude increased over time, and on one

retreating cycle, the entire flame ex'tinguished. With

larger wicks (thus, larger flame diameters), oscilla-

tions started spontaneously, whereas with smaller

wicks, oscillations occurred only when solid objects

were placed near the flame. Only a few cycles before

extinction were observed in the Spacelab experi-ments [77], whereas hundreds of cycles were ob-

served in the Mir experiments [78]. This is probably

because the protective screen was much more per-

meable in the Mir experiments, thereby decreasing

the O2 depletion rate and maintaining the flame at

near-extinction conditions much longer.At least two possible explanations for these oscil-

lations have been advanced Cheatham and Matalon

[65] showed that, near extinction, oscillatory insta-

bilities occur in spherically symmetric droplet flameswith radiative loss at sufficiently high Lewis num-

bers. Their predicted oscillation frequencies (0.7-

1.4 Hz) are comparable to experimental observa-

tions, however, the differences between spherically

symmetric droplet flames and roughly hemispherical

Flame Spread over Solid Fuel Beds

Flame spread over solid fuel beds is t3pically clas-

sifted as opposed-flow, where convection opposes

flame propagation, or concurrent-flow. Because up-

ward buoyant flow opposes flame spread, lg down-

ward flame spread is opposed-flow, whereas upward

flame spread is concurrent-flow. At /2g without

forced flow, flame spread is always opposed-flow be-

cause the flame spreads toward the fresh oxidant

with a self-inducedvelocity equal to the spread rate

(S/). At lg, self-induced convection is negligible be-

cause buoyancy-induced flows are typicaUv (got_) 1/3_, 0.10 rn/s _ Sf. Very, few concurrent-flow flame

spread have been conducted at /lg [80], conse-

quently, this section focuses on opposed-flow spread.

Sf is estimated by equating the conductive heat

flux to the fuel bed (= ;t(O'W)(Tf - T,)/6, where6 = a/U is the thermal transport zone thickness and

U is the opposed-flow velocity (forced, buoyant and/or self-induced), to rate of fuel bed enthalpy increase

( = p, CesL(T,, - T,)WSf). Assuming mixing-limited

reaction' (infinite-rate chemistry), for thermally thin

fuels, where heat conduction through the solid is

negligible, Sf is predicted to be [81,82]

n )._ Tr - T,= - _ (9)

Sf 4 p_Cp.sr_ Tv - T_

Note that Sf is independent of U and P. For ther-mally thick fuels, where heat conduction through the

solid fuel dominates, r_ is the thermal penetration

depth into the solid, estimated by equating the con-ductive heat flux to the fuel bed to the heat flux

through the fuel (=)_,(b'W)((T,. - T.)/r_), where

the subscript y refers to the direction normal to thefuel surface). This leads to the exact solution [81]

)._(Tv- T_) )._(T,.- T,)a

rs - ).(Tf- T,.)/J - ),(Tr- Tv) Sf

._.pCe (Tf- T,._ 2:=_ Sr = U _ \T,, - TJ (10)

Note that, unlike the thin-fuel case, for thick fuels

Sf _ Utp I.

• L_r- • _ _

_ ....... '" ,, "_i;: "'_ L, ,.. : IIIIIIII

2496 INVITED PLENARY LECTURE

' ,qlolw.lltllvEr, a,aa

/j × _c#it_irlmcrloi

u

i

_ L

10_ I _ I,llhl I , I,ILhl I , I_l,hl I J I_lJIkl

FIG. 16. Minimum mole percent O_ in N, supportingflame spread over a thin solid fuel bed, _ a function of the

opposed flow velocity IU) [8:3]. showing dual-limit behav-

ior, that is, residence-time limited extinction at high U andradiative loss extinction at low U.

Dual-limit e.'ctinction behavior is observed in #gflame-spread experiments (Fig. 16) [83]. The timefor thermal energy to diffuse across the convection-

diffusion zone (%if) is 8/U = ot/U_; thus, high-U

extinction occurs when t<_r < td,_, . or U >

(&t¢.h_,,,) _ and radiative extinction occurs when t_ifr

> t_d or U < (_t_a) _/2. (Surface radiative loss mayalso be important, particularly at moderate and

higher U [84].) Interestingly, the minimum O2 con-

centration supporting combustion (ZO2.iim), and thus

the _reatest hazard, corresponds to U _ 0.1 m/s,whicn is lower than buoyant convection at lg, andmight correspond to ventilation drafts in mannedspacecraft.

A radiative loss parameter can be defined as H

t,hH/C,a = odU_t,.,d.. Because H _ U -.' Sf is lower at

#_ where U is lower and thus H is hi_l_er. Exped-,uents [85] {Fig. 17) show that an imposed forced

flow at#g increases S{ because U/su,u of forced flow

and S[) increases and thus H decreases, whereas at

higher U (whether buoyant or forced), Sf decreasesas the high-U li,uit is app,'oached. For 21% O, or

lower, the infinite-rate chemisto' prediction of equa-

tion 9, St. _ U', is uever achieved. Only at :30% O,is T rhign enough that this condition is _lchieved. -

Because a _ P- _and t,,i _ P". H _ P- L thus for

thin fuels, S/should increase with P toward the ideal(adiabatic) value (equation 9). This is confirmed by

quiescent thin-fuel space e.'eperi,nents [86,871,which show Sr increasing from 3.2 to 5.9 mm/s as P

increases from 1.0 to 2.0 arm with fixed O, molefraction (0.50). For these conditions, H decreases

from 24 to 3.5, thus even at the highest P, radiativeeffects are probably still important. This is consistent

with computations [86] that predict S_ = 19 mm/s(almost independent of P) for adiabatic con-ditions

for this fuel/atmosphere combination.

Neither N._ nor O, emit thermal radiation: thus,

for flames in O.,-N._ atmospheres, onlv H,O and

CO_ combustion products radiate significantly. Forthese cases, t'¢pically a_ i _ 1.'2 m ::_ 6 and" thus,

radiative transfer is opticaUv thin (negligible reab-

sorption). When ard -> 1, reabsorption effects can-not be neglected. With reabsorption, some radiation

is not lost and may augment conduction to increase

Sf above that without radiation. This behavior is seen

experimentally [88] using strongly emitting/absorb-

ing CO_ and SF6 diluents (Fi_. 18), where St- ishigher and Zoo ira, is lower at#g than lg, whereas-theopposite (conventional) behavior is found in nonra-

diant diluents (not shown). These data indicate that,

for nonradiating diluents, ,ug is less hazardous be-

cause Z%._m is higher at#g than at lg (0.21 vs. 0.16

_" 2.0 v_ ......

_ _o_o2

ty 1.o

o4,1/': ' ;

0.01 .... , .... , ....o 50 1oo 50

CHARACTERISTIC RELATIVE VELOCITY, CM/S

FIG. 17. Flame-spread rate over athin solid fuel bed as a function of

the opposed-flow velocity (U). for

three values of the mole percent O_

[851, showing dual-limit response.Note that the infinite-rate ldnetics

prediction [81,82] that the spread

rate is independent of U is only sat-

isfied at O_, mole fractions higherthan that in air.

UNDERSTANDINGCOMBUSTION PROCESSES THROUGH MICBOGRAVITY RESEARCH 2497

2.5

• _g(CO z}

o ug (CO 2 }2

• lg (SFI)

_" : ug (SF=)

_3- I 0

go

05 _e_e

oo

0 I

20 25

J .ocoo

0 •[3

i I

I I I I

30 35 40 45

02 concenlratlon (mole %1

5O

FIG. 18. Flame-spread rate over a thin solid fuel bed at

lg (downward spread) and Fg as a function of O_ molefraction [88]. showing atT._0ica]beha,,aor in Oa-CO__ and

O2-SF _ atmospheres where the spread rates are higher and

the minimum Oe model fraction supporting combustion is

lower at itg.

F]c. 19. Fingering patterns observed in smoldering

flame spread over a thin paper fuel sample in pg [gl].Flaming combustion was inhibited by soaking the fuel sam-

ple in potassium acetate. An imposed convective velocity

of 0.05 m/s flows from right to left. Grid pattern scale is 10

mm by 10 mm. Photograph courtesy of Dr. S. Olson.

for He), whereas for radiant diluents,/zg is more

hazardous (0.21 vs. 0.24 for CO_). This is particularly

significant considering that COs-based fire suppres-sion systems will be used on the International Space

Station. To date, flame spread calculations have em-ployed optically thin radiation models with constant

ap [86,87] or variable depending on local tempera-

ture and composition [80] and thus cannot assess

reabsorption effects.

These discussions pertain to thin fuels, for which

steady pg spread is possible because theoretically St-

[,_L For thick fuels, S/_ U t, thus S/- is indeter-minate for quiescent/lg conditions (U = S/). When

unsteady solid-phase conduction is considered, r,

(aJ) Ir_, which resldts in Sf _ t -12 [8.91. C,mse-

quently, all fuel beds at quiescent/L_ conditions

eventually become tbermally thin tpenetration

depth greater than the bed thickness) unless the ra-diative effects, discussed later, are considered. Of

course, flames may extinguish clue to large d (thuslarge radiative loss) before reaching steady-state,thermally thin conditions.

A difficult?.' in comparing space experiments to

two-dimensional model predictions is that the fuel

bed width XV(30 mm for thin fuels [86,87] and 6.2

mm for thick fuels [89]) is smaller than the thermal

transport zone thickness (6). Consequently. these ex-

periments can hardly be considered two-dimen-

sional. Both lateral heat loss, which retards spread,

and lateral O2 influx, which enhances spread, are

probably important, thus their effects may partially

cancel. Some authors [86] suggest that radiativelosses decrease d to values much smaller than a/U

= a/S[, but the oxygen transport zone thickness

(_oz) is still Do.,./U, because no analog to radiative

loss exists for Oz transport. Because Le = a/Do,

1, d;o_" is nearly the same as _ in adiabatic flames.

Thus, the pg flames mentioned above have probably

benefited substantially from lateral Os influx, espe-

cially for lower pressures and O_ mole fractions,

where d/W _ a/S/W is largest. In fact, S[ might behigher at smaller W due to lateral Oz influx. Space

experiments using cylindrical fuel rods are planned

[90] to examine truly two-dimensional spread.

Recently, a surprising observation of fingering

fronts was found in space experiments using paper

samples treated to inhibit flaming combustion but

allow smoldering propagation (Fig. 19) [91]. Finger-

ing was observed at#g when U < 50 mm/s, whereas

smooth fronts were observed at lg for all U. This

was proposed [91] to result from limited Oz mass

transport at pg with low U, which caused the O2

consumption regions to become localized spots in-

stead of continuous fronts. This proposition does not

explain why heat conduction does not smooth out

potential fingers as it does (for example) in pre-

mixed-gas flames with Le > 1. The following alter-

native explanation is proposed here. Gas-phase heat

transport occurs on the length scale _ _ a/U, and

solid-phase transport occurs on the scale _ _ a,/u,where u_ is the smolder front velocity and a_ the

solid thermal diffusivitv. Oxygen transport occurs

only through the gas phase on the scale Do/U "a/U _ J. Radiative loss can suppress heat transport

through the gas, but no corresponding effect on 0-2

transport can occur. Thus, at low U, the effective Le

is aJDoz ,¢: 1. At higher U or at lg, d is smaller, gas-

phase heat transport dominates, and radiative effects

are weaker; thus, the effective Le is a/Do. , "= 1.These assertions are consistent with estimates [91]

24.t)8 INVITEDPLENARYLECTURE

30j I I]11 I_ I I I I I

20 " _/HGE

to

°lO

5

ol ; ,,-4 -2 0 2 4 6 8 10 12 14 16 18

Time (s)

Fzc. '20. Measured (thick lines) and computed (thin

lines) flame position versus time for fame spread over a 1-

butanol po_)l 20-ram _ade and 25-ram deep [971. The 10,

20, and 30 notations refer to the opposed-flow velocities

l U) in cm/s. Both computed results are for/zg conditions,

U = 30 chris, either with or without hot gas expansion

t HGE) The comparison of predicted and measured results

suggests a very strong influence of ex'pansion, which is

much less effective in the experiment because of the re-

laxation of expansion in the tvan_'erse dimension, a factor

not captured within the two-dimensional model.

of the relative importance of gas-phase and solid-

phase transport. Both premixed [27,39] and non-

remixed [92,93] flames with effective Le < 1 ex-ibit diffusive-thermal instabilities that cause

fingering patterns, whereas for Le - 1, the fronts

are stable. This explanation is also consistent with lg

experiments [94] on horizontal fuel beds burning in

oxidant channels of adjustable vertical height. At

small heights or low U, fingering similar to Fig. 19was observed. In this case, conductive loss to the

channel ceiling causes suppression of gas-phase heat

transfer. Apparently. in both cases, the key factor is

suppression of gas-phase heat transfer while allow-

ing solid-phase heat transfer, which reduces the ef-

fective Le (though this factor was not mentioned inRef. [9!.] or Ref. [94].)

Flanue Spread over Liquid Fuel Pools

Flame spread over liquid fuels encompasses prac-

tically all solid-fuel flame spread phenomena dis-

cussed above, plus liquid-phase flow effects. Typi-

caUy, Tv - T. is smaller for liquid than solid fuels,

thus Sf is higher. Also, if T,, - T. is small, some fuel

prevaporization occurs even at T = T., thus partially

premixed gas-phase combustion phenomena mayoccur. Because of the fuel surface temperature gra-

dient upstream of the flame, surface tension gradi-

ents are produced that cause the surface layer to

move upstream (awav from the flameL which in-creases Sf. At lg, this heated liquid laver must lie

near the surface, whereas at lzg. no limitation exists.

Experiments at IR, summarized#n [95], show that

at low fuel temperatures, the average Sj-is small (typ-ically 10 ram/s) and the spread tdternates between a

f:ast "jmnp" velocit), aud a slow "'crawl" s:elocitv. Athigher fuel temperatures, SFis faster and steads( For

the conditions exhibiting pulsating spread at ig ,g

flame spread cannot be maintained, whereas for theconditions exhibiting uniform spread at lg, steady

spread is 'also exhibited at fig [96]. Pulsating spreaclhas never been observed at #g. No definitive expla-nation for these observations has been advanced.

For the conditions exhibiting pulsating spread at lg

and no spread at fig, flame spread is still different at

lg and ug when forced flows comparable to buoy-

ancy-induced convection (U = 0.30 m/s) are im-

posed (Fig. 20/[97]. Specifically, Ig spread is _most

unaffected by the imposed flow, but/zg spread is

.steady with Sf being lower (_ 15 trim/s) than either

the lg jump Velocib' (_ 100 ram/s) or crawl velocity(_22 mm/s).

Detailed numerical modeling [98] predicts pulsat-

ing spread at gg for the conditions of Fig. 20 andvalues of Sf much closer to the measured lg Sf. Re-

markably, "if thermal expansion is artificially sup-

pressed, good agreement between the model and_g

experiments is found. It is proposed [97] that this

agreement results from three-dimensional effects;

specifically, in the experiment, flow induced by ther-

mal expansion is relaxed in the lateral dimension,

whereas the two-dimensional model does not permit

this. That three-dimensional effects might dominate

is surprising considering that, for this flame, gGVct/UW *- 0.02, thus, _ ,s_ W. Also, this hypothesis

does not explain why pulsating flame spread is ob-

served at ig but not ug. Consequently, in the case

of liquid-fuel flame spread, ,ug experiments haveidentified limitations in our current understanding

of combustion processes at lg.

Recommendations for Future Studies

Reabsorption Effects

The ,ug studies described here suggest new unre-

solved issues and opportunities for further improve-

ments in understanding. Perhaps the most important

are the effects of reabsorp8on of emitted radiation,

including both reabsorption by the emitting gas and,

in two-phase combustion, absorption by the con-

densed phase. All radiative effects discussed above

are critically dependent on the degree of reabsorp-tion. To study reabsorption effects requires radia-

tively active diluents (CO._, SFs), high pressures and/

or large systems. All of these conditions lead to

higher Gr a at lg and thus turbulent flow. Hence,,ug

II

UNDERSTANDING COMBUSTION PROCESSES THROUGH .MICROCRA'_;ITY RESEARCH

exl_eriments enable study of reabsorption effects

without the addition_d complications due to turbu-]euce.

Reabsorptioq effects are important not only to/_gstudies but _dso to combustion at high pressures and

in large combustors. For example, at 40 arm, _-pical

of premixed-charge internal combustion engines, ae18 m- i thus, a_ I = 0.045 m, for stoichiometric

combustion products. Because this length scale is

comparable to cylinder radii, reabsorption effects

within the gas cannot readily be neglected. Simpleestimates [99] indicate radiative loss may influence

flame quenching bv turbulence in lean mixtures.

Similarly, reabsorption cannot be neglected in at-

,nospheric-pressure furnaces larger than at; l _ 2.2

m. Moreover, many combustion devices employ ex-haust-gas or flue-gas recirculation; for such devices.

the unburned mixtures contain significant amountsof absorbing CO, and H20.

Mthough reabsorption of emitted radiation could

affect practically 'all types of flames reviewed here,

to date, reabsorption effects have been studied onlyfor propagating premixed-gas flames [24,26], flame

balls [45], and flame spread over thermally thin fuels

[88]. All have shown substantial differences from op-

tically thin behavior. Two examples of effects ex-pected for other flames are given below.

Reabsorption effects could be substantially moreimportant for droplet combustion than for flame

spread over solid fuels because for droplets, the Ste-

fan flow severely limits heat conduction to the drop-let surface. This is why heat release (B) affects burn-

ing rates (K) only weakly (logarithmically) (equation8). Radiative transfer is unaffected by the Stefan

flow. Equation 8 is readily extended to include sur-face radiative flux (q_):

12 =In 1 + 1 ; R _.,12 _ KPdCe82

(11)

Figure 21 shows the predictions of equation 11. (Al-

though equation 11 has apparentlv not been pre-sented previously, numerical studies [100,101] have

shown qualitatively similar predictions. Moreover,

these studies show that typical radiative absorption

lengths for liquid fuels at relevant wavelengths are

on the order of i mm, thus large droplets could ab-sorb most incident radiation.) For spherical shells of

radiant combustion _products having thickness di ,_dr, q_ _ A6/4. then tor typical values B = 8.5, A =

2 x 106 !,V/m 3, d_ = 10 mm d d = 5 mm C =

1400 J/kgK, :. = 0 07 W/mK,' and L,. = 4_) ky/kg,

equation 11 predicts R = 0.63 and 12//2R. 0 = 1.11;thus, moderate effects of radiative transfer are ex-

pected. For droplets in radiatively active di]uents

such as CO> the effect could be much stronger. Us-

ing the P1 approximation, for a sphere of unit

emissivity in an infinite gray gas, q, = [4/(2 + 3

2499

aed, i/2)]a(T 4 - T_) [102]. Using volume-averagedproperties T = 1000 K andae_:_. =- 20 ,i i R =

18 and thus 12/f2Uo,, = 8.0, i,l_licatiug radiation

dominates heat transport. As discussed later, at high

pressures radiative effects may prevail even in 02-N2 atmospheres.

Flame spread over thermally thick fuel beds m

quiescent atmospheres at/lg is _19ic_dlv consideredinherently unsteady [89], however radiative transfer

to the fuel bed could enable steady spread. If theflame is modeled by an isothermal ;,'olume with di-

mensions 6 × 6 x W, radiation iuduces a radiative

flux AO"W = A (ae/S_)W that augments the con-

ductive flux 2(cJW)(Tf - T,)/& Equating this total

heat transfer to p_Ce.:,(T,. - T=) WSf)Selds

Sf = :a_o_Ce,A,(T,.- T.I) - )..,(T r - T,)

(12)

which vanishes without gas radiation (A = 0). Thick-

fuel space experiments in O2-CO_ or O_-SF_ at-

mospheres could be employed to check (or steadyspread and test the accuracy of equation 12.

Whereas optically thin radiation modeling is rea-

sonably straightforward, modeling of spectraUv de-

pendent emission and absorption is challenging be-cause local fluxes depend on the entire radiation

field, not just local scalar properties and gradients.

Some relevant computations have employed gray-gas models [74], but recent studies [26,103] show

that these methods are probably inaccurate because

of the wide variation in spectral absorption coeffi-

cient with temperature, species, and wavelength.Comparisons of various radiative treatments for

small one-dimensional non-premixed flames have

been made [103]. Comparisons for larger, multidi-

mensional systems would be valuable. Moreover, re-

cent studies of/_g soot formation [52,56,57] may en-

able improved modeling of soot radiation at _g.

High-Pressure Combustion

All practical combustion engines operate at pres-

sures much higher than atmospheric. The impact ofbuoyancy for premixed flames scales as td,_,,,/t,_ _(ga/S_) _a _ P"-_, where n is the overall reaction

order (SL _ p,/.z- t). Because, typically, n < 4/3 for

weak mixtures [104], where buoyancy effects are

most important, the impact of buoyancy increaseswith pressure. Also, as discussed earlier, radiation

effects are more difficult to assess at higher pressure

due to increased interference from buoyant trans-

port. Nevertheless, few high-pressure/_g combus-

tion experiments have been performed. High-pres-sure droplet combustion experiments [1(_5] revealed

substantial but different increases in K with P at lgand/tg. Radiative effects were not discussed but

could have been important, because in equation 11,

7

I

25OO INVITED PLENARY LECTURE

5

2t_¢

aE

E

z

i ! 1 i

B=3

B=85

2 4 6 8

R= qflaC/2kL

FZG. 21. Predicted effect of radiative heat transport co-

efficient (R) on droplet burning rate constant referenced

to the ,,'due without radiative transport, showing impor-

tance of absorption of radiation at the droplet surface onthe resulting burning rate. B = 3 and B = 8.5 are char-

acteristic of methanol and heptane, respectively, burningin air,

the only pressure-dependent factor is qr - A - pl,

thus in Fig. 21, R _ P. (For most flames, lengthscales decrease with increasing P, which would de-

crease radiative effects; but for droplet flames, de

depends only on stoichiometry [75,76].) Conse'-quently, further assessment of radiative effects in

high-pressure droplet combustion and other types offlames appears warranted.

Three-Dimensional Effects

In earlier sections, effects of lateral heat and mass

transport on flame spread were discussed. To assessthree-dimensional ettects, pg experiments wifla vary-

ing fuel bed width (W) are needed. Complementarythree-dimensional modeling using codes such asthose developed by NIST [106], extended to include

gas-phase radiation, would be instructive. An ap-

proximate but much less expensiqe approach wouldoe to incorporate volumetric terms 62(T(x, y) - T,)/

"Wz and 6pDi(Yi(x , y) - yi _)/W 2, where x and y arethe coordinates parallel and perpendicular to thefuel bed, into the two-dimensionalmodel to account

for lateral heat losses and lateral diffusion of each

species i.Another three-dimensional effect is found in the

development of flame bails from ignition kernels.Currently, it is known that large flame balls are lin-early unstable to three-dimensional disturbances for

weak loss (Fig. 5), but the transition from splittingflame balls to stable flames is not well understood,

nor can the number of flame balls produced from an

ignition source be predicted. Modeling using three-dimensional premixed flame codes [107] is needed.

Gas-Jet Flames

Table 2 shows predicted scalings of flame lengths(Lf) and residence times (tier) for buo ant and non-

d( " Yb Want round-jet and slot-jet flames. Despite nu-

merous investigations of round-jet flames at/_g, no

,u_ slot-jet results are available to test those predic-

tions. Currently, it is unknown whether slot-jetflames at _tg would exhibit smoke points or whether

this information could be used to explain smoke

points in pg round-jet flames. Because L t- depends

on g for buoyant slot-jet but not round-jet flames, L/should be quite different at lg and/ag for slot-jetsbut not round-jets. Residual accelerations in aircraft

pg experiments will be more problematic for slot-jetthan round-jet flames because ti,. t - g-i;_, for buoy-

ant round-jet flames whereas ti,.t _ g- _,':_for slot-jetflames.

There has been little investigation of blow-off be-

havior of laminar gas-jet flames at fig. Dual-limit be-havior might occur for flames of fixed-mass flow rate

but varying d,,, with short residence time extinction

at small d,, (tier -- dO/U,,) and radiative extinction atlarge d,, (thus. large ti,t). Experiments should be con-

ducted by diluting the fuel rather than increasing U,,to obtain blow-off without transition to turbulence.

In this way, dual-limit behavior has been observed

at lg [92] with short residence time and conductiveloss (to the burner rim) extinction branches.

Quasi-Steady Spherical Diffusion Flames

As discussed previously, comparing predicted ra-diative extinction limits of droplet flames to experi-

ments is problematic because quasi-steady condi-tions may not be obtained, because extinction occurs

for sufficiently large droplet and flame diameters,

but the droplet diameter decreases throughout itslife. Numerical models can account for transient ef-

fects, but the multidimensional ignition process is

difficult to model quantitatively. Comparisons ofdroplet experiments and computations to corre-

sponding results obtained using fuel-wetted porousspheres would be most interesting. The fuel should

be forced through the porous sphere at slowly in-

creasing rates until extinction occurs when d/>(artrad) 1/2, thus obtaining truly quasi-steady extinc-

tion. Long/ag durations would be required to estab-

lish steady diffusion-dominated far-field tempera-

ture and composition profiles (thus, steady radiativeloss). Some preliminary results have been obtained

in aircraft experiments [108] but were severely com-promised by the residual g levels. Candle flames are

similar to wetted porous spheres, though withouttrue spherical symmetry or any means to control or

measure the instantaneous d d,

A siml_ler related experiment employs porousspheres through which gaseous fuel is forced at pre-

scribed m, resulting in a flame diameter d/_, rhCe/2nXln(1 + f). Some drop-tower experiments using

this configuration have been reported [109,110], al-though steady-state conditions were not obtained

due to short/,g durations. Steady-state behavior ap-

pears unlikely given the m (thus, air consumption

rates) and chamber sizes employed to date; near-wall

UNDERSTANDINGCOMBUSTIONPROCESSESTHROUGHMICROCRAVITYRESEARCH(_.xTgendepletionwouldbesignificantovertile times

required to reach steady-state (_ 10 s [1 i0]). Steady-

state behavior might be obtained in drop-towers by,,siug smaller m and diluted fuel x_ith enriched ox-

wen atmospheres to increase fand thus decrease dfand t,l_,,I, _ dj /a.

Catalytic Combustion

Catal_x'ic combustion holds promise for reduced

emissio]ls and improved fuel efficiencyin manycom-bustion systems [i11.112]. Because catalysis occursat surfaces, it is inherently multidinlensional and/or

unsteady, requiring reactant transport to the surface

and heat and p,'oducts transport from the surface.

Although boundary-laver approximations can be in-voked, probably the" only tn,lv one-dimensional

steady catalytic conflgurat{on is a spherical surface

immersed in nonbuoyant quiescent premixed gas--

a "catalytic flame ball." In this case, rf is fixed butthe surface temperature T, and fuel concentration

Y_ are unkmown. These are related through the en-

ergy conservation (including surface radiation) anddiffusion equations to obtain the surface reaction

rate in moles per second (O):

L = l- Le 1 + (13)

where e_ is the surface emissivity and properties with

the subscript s are evaluated at T -- T,- By varyingr,, Y_, pressure, and diluentgas, O(T, Y) can be in-ferred from equation 13 and the measured T s. Ofcourse, conditions must be unfavorable for initiationof propa atin_ flames flame balls that stand offg _ orfrom the surface.

Chemical Models

An important contribution of pg combustion ex-

periments has been improved understanding of ex-tinction processes, which are inherently related tofinite-rate chemistry. To obtain closure between ex-

periments and computations, accurate chemical

models are needed. For lean premixed hydrocarbon-

air flames, most models [21 26] predict higher SL

and caner flammability limits than experimental ob-

servations [22,33,113]. The discrepancv seems largerthan experimental uncertainty or unaccounted heat

losses could explain. In contrast, for H2-air flame

balls [45] and lg strained premixed H.2-air flames

[1141, these chemical models predict smaller balls,

lower SL, and richer flammability limits than exper-iments. These chemical models predict S L in

mLxtures away from extinction limits very faithfully.The discrepancies result largely from differences in

AS(}I

rates for H + O, + M reactions, particularly the

Chaperon efficiencies of _arious M species "[45].

These reactions are extremely important in near-limit flames due to competition between chain-

branching and chain-inhibiting steps near limits [21]but are much less important away from limits. Fur-

ther scrutiny of the rates for these reactions at in-

termediate temperatures (1100-1400 K) would bewelcomed.

Conclusions

Our understanding of combustion fundamentals

has been broadened by/_g ex'periments into regimes

not previously explored. In particular, these ex'peri-ments have helped integrate radiation into fl'ame

theo_: Although flame radiation has long been rec-ognized as an important heat-transfer nlechanism in

large fires [115], its treatment has largely been ad

hoc because of the difficulty of predicting soot for-|nation. Also, large-scale fires at 1_ are inevitably tur-

bulent, leading to complicated _ame-flow interac-

tions. Small-scale flames are laminar, oftensoot-free, and have_tggnificant influences of radia-

tion. As a result of radiation effects, both premLxedand non-premixed flames have exhibited dual-limit

extinction behavior, with residence time-limited ex-

tinction at high strain, or curvature and radiative

loss-induced extinction at low strain or curvature.

The high-strain limit is readily observed at Ig; whenforced flow is absent, buoyant flowcauses this strain.

For weak mixtures, these limits converge, but theconvergence and the entire low-strain extinction

branch can only be seen at/aft This dual-limit be-

havior is observed for stretched and curved pre-

mixed-_as flames, strained non-premixed flames,

isolatea fuel droplets, and flame spread over solidfuels. Besides radiative effects,/lg studies have en-abled observation and clarification of numerous

other phenomena, for example, thermophoresis ef-

eCt.S in soot formation, spherically symmetric drop-t burning diffusion-controlled premixed flames

(flame balls), and flame instabilities in droplets andcandle flames. Considering the rapid progress maderecently, further advances are certain to occur. It is

hoped that this report on the current state of un-

derstanding will help motivate and inspire such ad-vances.

ap

A

B

C s

Ce

Nomenclature

Planck mean absorption coefficientflame surface area

transfer number (chemical enthalpv gen-

eration/enthalpy needed for fuel evapo-ration)

stoichiometric molar ratio of fuel to air

constant-pressure heat capacity

I

_502

d

(Id

d,h,

d,

D

E

fg

Gra

H

K

LI

Lv

Le

tit

M

P

F

RgRe

sfSL

SL,lim

Sc

t d_m

tctiff

tdroptiny

tj_ttrad

t_isT

T_,IU _

U

%

Vot_

W

YY

fl

INVITED PLENARY LECTURE

characteristic flow-length scale or tubediameter

droplet flame diameter

droplet diameter

droplet initial diameter

jet exit diameter (round jets) or slot widthfslot jets)

mass diffusi_itv

overall activation ener_' of the heat-re-lease reactions

stoichiometric fuel to _tir mass ratio

acceleration of gravi ,tyearth gravity

Grashof number based on characteristic

length scale (d) = gd:_/v 2

heat transfer coefficient in a cylindricaltube = 162/d 2

radiative loss parameter for flame spread= t, lill,/t_,d = _,/['2t_a d

droplet burning rate constant lequation 8)flame len_h for gas-jet flameturbulence integral scale

latent heat of vaporization of liquid fuel

Lewis number (aCD = thermal diffusivity/reactant mass diffusivity)

mass burning rate

fuel molecular weightpressureradial coordinateflame radius

scaled flame radius (eq 6); radiation pa-rameter (eq 11)

gas constant

jet Reynolds number = Uod,/vflame spread rate over solid fuel bed

remixed laminar burning velocityurning velocity at the flammability limit

Schmidt number = v/D

chemical time scale

thermal diffusion time scale = odLr2

droplet flame time scale = d}/ainviscid buoyant transport time scale

residence time of non-premixed jet flameradiative loss time scale

viscous buoyant transport time scaletemperature

adiabatic flame temperatureturbulence intensityconvection velocity

local axial velocity'in counterflow configu-ration

jet exit veloci_gas-jet flame widthsolid fuel bed width

axial coordinate

fuel mass faction

thermal diffusivity

nondimensional activation energy =

E/R_T[

_,1 )2.1bu

6

72

A

12

P

O*

Z

minimmn o_'_en concentration support-ing combustion

flame thickness

gas specific heat ratio

thermal conductivity

radiative heat loss" per unit volume =

4(rae(T_ - T4,)

kinematic _Sseositydensity

fuel bed half-thickness (thin fuel) or ther-

mal penetration depth (thick fuel)Stefan-Boltzmann constantflame stretch rate

Subscripts

d droplet surface conditionf flame front condition

s solid-fuel or solid-surface condition

v solid- or liquid-fuel vaporization condition:¢ ambient conditions

Acknowledgments

The author expresses his deepest gratitude to the NASA-

Lewis Research Center for supporting his ,ug combustion

work for more than 10 years. Comments from Tom Aved-

isian, Yousef Bahadori, John Buckmaster, Mun Choi, Dan

Dietrich, Fred Dryer, Gerard Faeth, Guy Joulin, YiguangJu, Kaoru Maruta, Vedha Navagam, Takas'hi Niioka, SandraOlson, Howard Ross Kurt Sacksteder Dennis Stocker, Pe-

ter Sunderland, Gregory Sivashinskv, James Tien, KarenWeiland, Forman Williams, and anonvn_ous reviewers have

been invaluable in preparing this paper. The author also

thanks numerous others who offered useful suggestions

that could not be accommodated because of space limita-tions.

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COMMENTS

H. S. Mukunda, lndiml Institnte of Science. BanEah_re,

hulia. In vonr presentation, you credited the computa-tional denlonstration of the restllt on the absence ofa flam-

lnahilila' linlit in adiabatic flames to Giovan_gli and

Sinooke [1 ]. This result was first obtained m 1988 [2]. Youmight like to amend the citation snitabh:

REFERENCES

L. Oimangi_li. 'C and Svuooke. M.. Combnst. Set. Teehnol.

$7:241 i 1992).

:2. Lakshniisha, K. N,, et aL in Ttcenty-Secotld Syinposirlm

lutenmtional) on Combustion. The Combustion lnsti-

tnte. Pittsburgh. 19S8, pp. 1573-157S,

Author's Rtp)ly. In this earlier paper by the questioner

and his eollaborators [21. it was slio_Yn that the sohltions of

the nrlsteaa[)" planar one-dimensiomd adiabatic premLxed

flame equations do not predict anv flammahilitv limit fi)r

lean CH4-Oz.N _,mixtures--the bvrning velocil'vdecreases

asymptotically to zero as the mkxture strength is'decreased.

hi Sinooke and Giovan_gli (Ref. [1] of the comment), the

steady version of these equations was sol_ed for CH4-air

and Hz-air mixtures, and a sinli]ar conclnsion was reached.

Both tire impertant findings, because it is possible in prin-

ciple that unsteady effects could snppress limits of steadyflames or cause [irnits to occur for inixtures that tire flam-

inable ;is steady flames, Together they show that one inllSt

identify loss mechanisms of the appropriate magnitude to

explain flammability limits, which was one of the key pointsof my presentation.

j. P Gore. Purdue Unitersity, USA. _lkJll seem to have

drawn a conclusion based on your time-scale analysis that

"radiation is not important tit 1 g." For combustion nnder

high-pressure conditions, for fires llarge and sln;dl), and

for _dl flames as far as high activation ener_ reaction steps

are invoh'ed, radiation can be potentially inlportant. Could

you please re-examine and clarify your cnnchision regard-

ing radiation not being important at 1 _?

Author's Reply. Certainly radiation is an important

mechanism of heat transfer in flames even at I g--large

+,,

"l

4

[N",'ITEI) PI,EN.-t,I +,Y I,I-CTLTRE

r_uli_di_ *'h-:u_sti,r rh,, ,,;u,t, is h-u,, ()1 ,l:my+ I,u_t, ._..t,id_,ut_d

fir,._ ,'_ m t.Uldht_m. <_,'r liquid l'ut.l t+,.)In+ Th,' .,*+ns;_¢_'

I intt.tltlt'd t<J tilllkt 't, x,x_l'_th:tt tht' r;tdi_tti(m tt'_ulst+(+rt liI11t'

-.t.._tlt. +.. ]4)11_ '+I+ th;Lll tht. i+u()x;t+;t tr_tii+,l)_)d: ti=Hc '+.c_tlt+ .it

,.,trtl. ,zr;tx itx _tutl thus r+td/_tti()u (h)("_ ii()t l+l+ty,_tll inq+_>rt_tnt

r,,h. ,)t, h,.itl ILunt. _h-.t'tur<' ;lud (.\tili_.ti()it _._+llditi<)us ;it