On the mechanisms of flame propagation limits and extinguishment-processes at microgravity

On the mechanisms of flame propagation limits and extinguishment-processes at microgravity

Twenty-Second Symposium(International)on Combustion/The Combustion Institute, 1988/pp. 1615-1623 ON THE MECHANISMS OF FLAME PROPAGATION LIMITS EXTING...

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Twenty-Second Symposium(International)on Combustion/The Combustion Institute, 1988/pp. 1615-1623



PAUL D. RONNEY Department o f Mechanical and Aerospace Engineering Princeton University, Princeton NJ 08544 U.S.A.

Microgravity (Ixg) experiments are employed to study the behavior of freely propagating spherically expanding premixed gas flames near the flammability limit in the absence of flow induced by natural convection. Temporally and spatially resolved temperature measurements in near-limit normal flames and Self-Extinguishing Flames at Ixg are obtained. From comparison of these data to a simple numerical model, it is determined that the primary mechanism of heat loss from these flames is by nonluminous radiation from the burned gases. Based on comparison with existing theories of flammability limits it is found that some of the experimentally observed limits are probably caused by these heat losses. A simple theory of nonadiabatic propagation of curved flame fronts with general Lewis number is found to describe many of the features of the /zg (convection-free) flammability limits and extinguishm e n t processes.

Introduction In prior studies, 1'2 it has been found that freely propagating spherically expanding premixed gas flames at microgravity (tzg) conditions exhibit a flammability limit with a very low burning velocity at the limit and an unstable mode of flame propagation at sub-limit conditions, termed Self-Extinguishing Flames or SEFs, which do not occur at earth gravity. SEFs are characterized by an energy release before extinguishment which is often orders of magnitude greater than the ignition source energy, a flame kernel radius which increases in proportion to the square root of the time lapse from ignition, and sudden extinguishment at a finite propagation rate. Further work3'4 has shown that these la,g phenomena are related to the unequal rates of diffusion of thermal energy and mass (the so-called Lewis number effect) and are mostly independent of the chemical reaction mechanism. Of particular importance is the observation4 that SEFs occur almost exclusively in mixtures with Lewis number* (Le) less than a critical value near unity. Despite this information, the causes of the Ixg flammability limit and SEFs have not yet been

*In this work the Lewis number is defined as the ratio of the thermal diffusivity of the entire mixture to the mass diffusivity of the scarce reactant, whose concentration is assumed far from stoichiometric. As discussed previously, 4 this definition must be modified when the reactant composition is near stoichiometrie.

identified. In particular, the role of heat losses, which are known5 s to cause extinguishment under certain conditions, has not been established. While some data 1-3 suggest that heat losses do not play a role, recent resultsa'9 show that the thermal decay in the burned gases is significant in mixtures which exhibit flammability limits and SEFs. Furthermore, since these flame fronts are spherical and emanate from a point source of ignition (an electric spark of small dimensions), it may be supposed that flame front curvature plays a role. The effects of curvature and Lewis number are well known and have been reviewed extensively, s'l°'u Hence, the goal of this work is to determine the mechanism of heat loss from near-limit flames at I,tg and from this information to determine the mechanisms of flammability limits and SEFs at lzg, taking into account heat losses, Lewis number effects, flame front curvature, and possibly chemical effects, To this end a series of I~g experiments are performed in which temporally and spatially varying temperature measurements in the flame fronts and burned gases are made. This enables estimation of the direction and magnitude of heat transfer and heat losses in the system, Tests are performed with several fuels in oxygen/nitrogen mixtures at varying stoichiometries to examine the effects of Lewis number and fuel chemistry. From these results a mechanism of heat loss is postulated and compared to a simple numerical model. From this information, mechanisms for the Ixg flammability limits and SEFs are hypothesized. Predictions of a model based on these mechanism are compared with experimental observations.




Experimental Apparatus The experimental apparatus has been described in previous work, Lz.9 hence only a brief description will be given here. The system consists of a constant-volume cylindrical combustion vessel 25 cm in diameter and 25 cm in length, a spark generator, a motion picture camera, an array of fine-wire thermocouples for recording gas temperatures, and a data acquisition system for measuring and recording thermocouple voltages. The response time of the thermocouples is estimated to be 50 ms in air at 760 torr pressure, which may be insufficient to resolve the temperature rise as the flame front passes but is adequate to resolve the temperature decay in the burned gases (cf. Fig. la and lb). Corrections for radiant heat loss from the thermocouple bead were made. Initial gas compositions were determined by the partial pressure method. Microgravity was obtained during 2.2 seconds of free-fall in a drop tower at the NASA Lewis Research Center in Cleveland, Ohio.

18001 I I [ Profiles

510% CH4 in air, 760 t o r r . micro-g at 2.2.3,5, a . 5 , 5 . 5 , 6 , 5 , 7 . 5 , cm from spark

! )


1400 l

,ooo i









1 l

200 L 0

I Time.

2 seconds

1800 5,09~ CH4 in air. 760 tort, micro-g Profiles at 2.2l).5,45,5.5 cm from spark ADIABATIC

Experimental Results The thermal characteristics of flames in lean CH4air mixtures at 1500, 760, and 250 torr initial pressure and lean NH3-air, rich C3Hs-air and H2-OzN2 mixtures of varying stoichiometries at 760 torr were examined. In the first three of these fuels, SEFs have been observed. ~-'4 The thermal characteristics of a normal flame in a lean-limit (5.10% CH4 in air) mixture at 760 torr and an SEF in a mixture just below the I~g flammability limit (5.09% CH4) are shown in Figs. la and lb, respectively. Each curve corresponds to the temperature history at a point a fixed distance from the ignition source, i.e. at a particular thermocoupie junction, The following features of Figs. la and lb should be noted: The gas temperature at the thermocouple junction remains at ambient until the flame front passes. At this point the temperature rises rapidly to a peak which is followed by a slower decay in the burned gases. In normal flames the temperature decreases to a minimum value then increases again due to the pressure rise caused by expansion of the flame kernel in the constantvolume vessel. As explained in previous work, L2'4 this pressure rise has little effect on the measured burning velocities and extinguishment processes. In SEFs, the temperature decreases monotonically after the passage of the flame front. The peak temperature of the limit flame is about 90% of the adiabatic value. For thermocouples at small radii (measured from the spark source), the temperature histories are similar in normal flames and SEFs up to a time after the temperature peak where a discon-


g ~ 1000













_ ,Y_.J_ / 200

- -


, !







FIG. 1. Measured thermal characteristics of methane-air flames at microgravity, a) Lean-limit normal

flame, b) self-Extinguishing Flame with visible extinguishment radius 4.7 era, extinguishment time 0.62 see. tinuity occurs in the SEF temperature history but not in that of the normal flame. Beyond the discontinuity, the rate of temperature decay in the SEF increases. For thermocouples at radii close to but less than the extinguishment radius,** the discontinuity may be quite sharp; for thermocouples at smaller radii the discontinuity is more gradual. For thermocouples at radii larger than the extinguishment radius, peak temperatures are low and no discontinuity is observed. **Here extinguishment is defined by the disappearanoe of luminosity on the film records.

MECHANISMS OF FLAME PROPAGATION The trends discussed above apply to flames initiated by relatively low energy sparks. For higher energies (several Joules), the temperature at the first thermocouple sometimes exceeds the adiabatic value but for thermocouples at larger radii, superadiabatic temperatures are not observed. Thus, in agreement with previous estimates, z most of the sensible energy content of the gas in SEFs is due


to the heat release from combustion and not from the ignition source. As discussed previously, 2 this distinguishes SEFs from non-ignitions. 12 The time at which the discontinuities in the temperature histories of SEFs appear seems to be closely related to the extinguishment event. In practically all cases the time of extinguishment was 0.1 to 0.2 see before the appearance of the discontinuities. The

TABLE I Characteristics of limit flames at rnicrogravity. Composition refers to equivalence ratio (qb) of fuel in air where one number is given and equivalence ratio of fi~el to oxygen in percent nitrogen of total mixture where two numbers are given. Hydrogen flames contain 0.23% CF3Br for visibility except for ~ = 1.25 which contains no CF~Br. Lewis numbers for H2-O2-N~ mixtures are taken from the estimates given in reference 31.


Pressure, Torr

Estimated E~ kcal/mole



calculated, cm/sec

measured cm/sec

0.532 0.513 0.474 0.441 0.418

47.4 43.6 31.6 27.8 26.2

1.30 1.73 2.46 3.48 4.68

1.04 1.47 2.02 2.80 3.67

0.96 0.96 0.96 0.96 0.96

Composition (see legend)

Estimated Lewis number


1500 760 250 100 50


760 760 760 760 760 760 760

0.25,54.7% 0.75,81.5% 0.88,83.2% 1.00,83.6% 1.20,79.6% 1.50,73.4% 2.00,62.5%

43.6 43.6 43.6 43.6 55.7 55.7 55.7

1.71 1.73 1.75 1.82 2.33 2.48 2.72

1.44 1.61 1.47 1.94 2.61 2.15 2.70

0.96 0.98 0.99 1.00 1.01 1.03 1.05



4 I. 4




1500 760 450 250 100

0.525 0.508 0.501 0.491 0.486

38.7 38.7 38.7 38.7 38.7

1.17 1.61 2.08 2.76 4.35

3.81 4.85 5.41 5.76 8.48

1.78 1.78 1.78 1.78 1.78





N Hz (lean)

1500 760 250 100 50

0.695 0.700 0.711 0.711 0.773

53.6 53.6 53.6 53.6 53.6

1.30 1.84 3.26 4.61 7.56

1.07 1.44 2.09 1.81 2.82

0.86 0.86 0.86 0.86 0.86

N H3 (rich)

760 250 100 50

1.649 1.604 1.530 1.472

69.8 69.8 69.8 69.8

1.55 2.78 4.63 6.80

2.65 3.66 5.03 4.84

1.05 1.05 1.05 1.05


760 760 760 760 760

0.50, 87.5% 0.60,86.2% 0.70, 85.2 % 0.90,82.9% 1.25,83.9%

33.9 40.1 54.2 66.2 69.8

0.597 0.730 0.993 1.38 1.22

~ 0.6 1.11 1.43 4.27 2.61

0.38 0.40 0.42 0.53 0.91

CzH6 (lean) C,H8 (lean)

C3Hs (rich)





discontinuities occur at nearly the same time at different thermocouples. Results corresponding to Figs. la and lb for other initial pressures (not shown) are qualitatively similar but with different time scales which reflect the effect of pressure on limit burning velocity (cf. Table I.) Furthermore, limit flames and SEFs in lean NH3-air and rich C3Hs-air mixtures also exhibited these same trends. The thermal decay immediately behind the flame front for all these limit flames is nearly the same, in the range of 500-1000K/sec. For limit Hz-O2-N2 flames the thermal decay is much lower, about 100K/sec or less.

mal characteristics this code has been modified so that the flame position is a prescribed input which is obtained from experimental data and thus is not a predicted quantity. The thin flame sheet is considered to be only a source of heat and combustion products in chemical equilibrium. In the case of SEFs, this source is terminated at the time of extinguishment observed on the film records. Figure 2a and 2b show the predicted thermal charateristics of the flames corresponding to those of Figs. la and lb, respectively. Simulated thermocouples are placed in the same locations as in the experiments. Comparison of these figures shows that the model correctly predicts many of the ob-

Modelling of Thermal Characteristics 1800

In order to ascertain the importance of heat losses in limit behavior at I~g, it is necessary to determine the mechanism of heat loss in near-limit flames and SEFs as evidenced by the thermal decay seen in Figs. la and lb. Attempts to ascribe this decay to conductive heat loss to the spark electrodes or thermocouples (the only available heat sinks) were unsuccessful. In particular, the slow decay in nearlimit Hz-O2-N2 mixtures cannot be explained in this way; if conductive losses were important, the decay rate should vary linearly with temperature. Other evidence which suggests that conductive loss is not an important factor has been presented previously, t Furthermore, convective losses due to buoyancy are absent in the Ixg experiments. Hence, volumetric losses due to nonluminous radiation from the product gases seem to be the most likely cause of the observed thermal decay. This could also explain the slow decay in near-limit Hz-O2-N2 mixtures; these flames have much lower limit flame temperatures and lower concentrations of radiant products than the other flames studied. In order to test this hypothesis, the predictions of a simple numerical model were compared to the experimental observations. The features of this model are as follows: Solution of mass and energy conservation equations for ideal gases One-dimensional spherical geometry Thermal conduction within the gas; adiabatic boundaries Constant volume chamber Convection due to gas expansion Heat loss by non-luminous gas radiation; t3'14 no reabsorption of emitted radiation (optically thin approximation) Frozen composition in the burned gases This model is based on a computer code used previously in studies of flame ignition and propagation, ts hence, the details of the model will not be given here. For the purpose of modelling ther-

5,10& CH4 i~ a i r , 760 t o r r , micro-g at 2 . 2 , 3 5 , 4 5 , 5 . 5 , 6 . 5 , 7 . 5 , cm from spark


] i


~ 1400 7, ~ 1000

~ 600


d_ L ; 200 I



2 seconds



5.09% CH4 in a i r , 760 t o r r , mtcro-g P~of~les at 2.2. 3 5 . 4 . 5 . 5 . 5 cm from spark

[ i





600 ~













[ Time,

2 seconds

FIG. 2. P r e d i c t e d t h e r m a l c h a r a c t e r i s t i c s o f m e t h ane-air flames at mierogravity for same conditions

as in Figure 1. a) Lean-limit normal flame, b) SelfExtinguishing Flame.

MECHANISMS OF FLAME PROPAGATION served thermal characteristics of these flames, in particular the thermal decay rates, the presence of discontinuities in SEF temperature histories, and the relative sharpness of these discontinuities. In Fig. 2b, agreement beteween the model and experiment for the SEF is excellent for the thermocouple nearest the spark source but poorer agreement is seen for thermocouples at larger radii, i.e. nearer the extinguishment radius. This is probably due to the assumption in the model that chemical reaction ceases completely and instantly at the time of observed SEF extinguishment, whereas in the experiment presumably a more gradual but still rapid decrease in reaction rate occurs. Similar agreement between the model and experiments was found at other pressures and for other fuels. Hence, it appears that the thermal characteristics of these flames can be interpreted in terms of the hypothesis outlined above.

Modelling of Flammability Limits Since the thermal characteristics of near-limit flames at Ixg seem to be dominated by heat losses from nonluminous gas radiation, an assessment of the effects of these losses on flame extinguishment is warranted. Several models which relate flammability limits to volumetrically distributed 5 s heat losses such as gas radiation are available. - These models predict that the effect of heat loss on burning velocity for a steady planar flame is given by*** S21n(S2) = - Q


where the symbols are defined in the Nomenclature. Note that this is not a general expression for burning velocity, but rather an expression for the effect of heat loss (Q) on the dimensionless burning velocity (S) of a flame with known adiabatic burning velocity (Su,aa.) Probably the most important prediction of these models which is easily tested experimentally is the burning velocity at the flammability limit (S,,lim); this limit occurs at the largest value ( = l / e ) of Q which admits a real-valued solution to Eq. (1). Some algebra shows that S~,lim can be expressed within reference to S~.a,/, such that Su,li m =

(l / puCpTb)(CLbkbEa/Rg) 1/2


where C is a constant of order unity which reflects the effects of temperature on heat loss. Note that this expression is independent of Lewis number and ***The original work of Spalding~ predates the method of activation energy asymptotics 1~ upon which the others are based, hence the form is slightly different but yields very similar results.


gas expansion and depends only weakly on the chemical reaction mechanism through E a. Williamss (p. 281) shows that C ~ 1.2 is appropriate for limits caused by radiant heat loss, hence this value is employed here. The above models apply only to steady planar flame fronts; the effects of curvature and unsteadiness are discussed in the following section. Another important assumption of the models is that the gases are optically thin. Gas radiation data 13'14 studied here with the exception of the rich-limit C3Hs-air mixtures. A comparison of calculated (using Eq. 2) and observed limit burning velocities is presented in Table I. In the calculations, the experimentally observed limit composition is used to determine Tb at the limit assuming chemical equilibrium. For this Tb and composition, the radiant loss (Lb) and transport properties (kb) are then computed from procedures given in Refs. 14 and 17, respectively. The activation energies (Ea) are determined from the slope of so-called Arrhenius plots (not shown) of the logarithm of burning velocity versus the reciprocal of adiabatic flame temperature, is The burning velocity data needed for these plots are taken from this work and previous txg experiments. 1'3"4"19"z° Table I shows that many of the observed limit burning velocities correlate well with values calculated assuming that extinguishment is caused by radiant heat losses. In particular, lean CH4-air and NH3-air mixtures at 250 torr and above, CH4-O2N2 mixtures of all stoichiometries at 760 torr, rich NH3-air mixtures at all pressures, and H,~-Oo-Nz mixtures at equivalence ratios (~b) of 0.7 and lower**** show good agreement. Lean C2H6-air and C3Hs-air mixtures and H2-O2-N2 mixtures with -> 0.9 exhibit considerably higher values of Su.lim than is predicted by the models. This is expected since for these mixtures the observed limits are due to insufficient ignition energy, 4 hence, the radiant flammability limits are not reached and Su,lim should be higher than the radiation model predicts. Lean NH3-air mixtures at 100 torr and below and rich C3Hs-air mixtures exhibit anomalously low observed values of Su,lim. Closer agreement between calculated and observed values of SuAim can be obtained (for eases where the limit is not due to insufficient ignition energy) if a correction factor23 is applied to the observed burning velocities which accounts for col****Agreement may be fortuitous in lean H2-O2N2 mixtures because these mixtures exhibit discontinuous cellular flame fronts. This is due to their low Lewis numbers, which in turn modifies the extinguishment conditions. 2~'zzThe importance of these effects in Ixg flames are discussed in more detail elsewhere. 2°



lapse of the burned gas kernel due to thermal decay. This correction is the ratio of the average gas density in the burned gas kernel to the density of adiabatic burned gases. The data in Fig. la show that this factor is about 1.11 when the flame radius is 6,5 era, thus the corrected observed S,,li~ is 1.63 em/see, which is closer to the calculated value (el. Table 1). Since temperature data were not obtained for many of the limit flames shown in Table I, this correction has not been included in the values of Su3im reported in this table. In any ease the correction is not sufficient to account for the anomalously low observed values of S,,lim for lean NH3air mixtures at low pressures and rich Calls-air mixtures. A possible reason for these anomalously low values of Su.lim is the slower approach to chemical equilibrium in the burned gases at low pressures and (possibly) for rich mixtures; this would cause the product composition to favor nonradiant or weakly radiant species such as O, OH, H, H2, and CO over the strongly radiant species H~O and COg. This would in turn lead to an overestimate of Lb and thus S~,li~o. In the ease of the rich-limit Callsair flames, the discrepancy may also he due to the violation of the optically thin approximation previously mentioned, Another important prediction of the models is that the peak temperature of the limit flame (Tin=*) is given by Tin=* = Tb (1 - 1/13).


A comparison of some predicted and measured values of T~=* for limits which are thought (based on Table I) to be due to radiant losses is given in Ta-

ble IL It can be seen that the measured peak temperatures are close to but generally slightly lower than the predictions. Hence, the peak temperatures again indicate that extinguishment due to heat losses is likely. Again rich C~Hs-air mixtures are an exception. Anomalously high peak temperatures in C3Hs-air mixtures have been reported previously.4 Furthermore, in agreement with experimental observations, the models predict that the rate of thermal decay in the burned gases in limit mixtures is essentially independent of pressure. A limit caused by volumetric heat losses such as gas radiation should be independent of the experimental apparatus. 8 To our knowledge only one of the p,g limits reported here have been measured in a different apparatus. Strehlow and Reuss 24 found a lean flammability, limit and a limit burning velocity for lean CH4-air mixtures in a Standard Flammabilit3' Limit Tube ~ which are practically the same as those reported here. This is further evidence that this limit is in fact caused by radiant losses.

Proposed Mechanism of SEFs: Since many of the /~g flammability limits seem to be caused by radiant heat losses, the mechanism of SEFs may be related to radiant losses as well. A model of SEF behavior should explain, at a minimum, the observations 1-4 that 1) flame kernels of small radii can propagate in mixtures which are outside the planar flammability limit but extinguish at larger radii, 2) the kernel radius at extinguishment may be very large for mixtures just outside the limit, and 3) only for Le < 1 can 1) and 2) be observed. Such a model is proposed here.

TABLE II Measured arid predicted peak flame temperatures (T,,~*) at the radiant extinguishment limit. Pressure, Tort

T,,~*, K measured

T,~*, K calculated

Tb, K calculated

1500 760 250

1410 1375 1350

1438 1392 1297

1537 1494 1425

CHa-O~-N: (~ = 0.25)





Calls-air (rich)





NH3-air (lean)





Hz-Oz-N~ (dp = 0.50) (~b = 0.60) (~b = 0.70)

760 760 760

660 820 850

772 870 962

811 911 999

Mixture CH4-air (lean)



Equation (1) can be extended to take into account unsteadiness and spherical curvature, yielding the following relationship:26

dSIdR + S21n(Sz) = 2S/R - Q

where R is the scaled dimensionless flame radius (which may be positive or negative although the physical flame radius (r) is of course strictly positive), dS/dR is an unsteady term, and 2S/R is a curvature term. The quasi-steady flame (dS/dR = 0) is extinguished if no real value of S satisfies Eq. (4) for the given R and Q. Inspection of Eq. (4) and the definition of R show that only when Le < 1, so that R > 0, can a quasisteady solution exist for small r but not large r. As Le ~ 1, R ~ ~, hence at Le = 1 curvature no longer leads to increased flammability, and when Le > 1, R < 0, hence curvature renders the mixture less flammable (i.e., the flame can exist at large r but not small r). This explains why only for Le < 1 can an outward propagating spherical flame kernel exist at small r but extinguish due to heat losses at large r, Furthermore, when Q is only slightly larger than the value required to extinguish the plane flame, R must be very large before the contribution of the curvature term is small enough that no quasi-steady solution to Eq, (4) will exist. This explains why SEFs with very large extinguishment radii may occur in mixtures just outside the planar flammability limit. Numerical analysisz~ shows that the unsteady term has little effect on these predictions. Hence, the essential characteristics of SEFs discussed in the previous paragraph are described by this model. Equation (4) also enables a quantitative comparison of this model with experimental observations. This is done by computing S(R) = SJSu,aa = (e/ S,.aa)(dr/dt) for fixed Q, i.e, for a particular mixture (since Q depends only on the properties of the mixture), from which r may be determined as a function of time (t). Figure 3 shows the results of such computations for a family of simulated lean Chaair mixtures. Each curve corresponds to a developing quasi-steady flame kernel in a different mixture, In this simulation S~,aa(cb)is taken from experimental data 1 obtained at pog and the other physical parameters are computed in the manner discussed in previous sections. Quantitative agreement between Fig. 3 and experimental results> l'z in terms of the extinguishment radii and the shape of the r-t trajectories, is very good tor mixtures just outside the planar flammability limit but less satisfactory for mixtures further removed ti'om the limit. In the latter case the curvature of the predicted r-t trajectories is not as sharp as is seen in the experiments and the predicted extinguishment radii are too high. The model also does not predict the following experimental observations: 1) the value of dr/dt of SEFs at extin-









f'"'7 t /




! 2






........ --


I if










flnme Fli~mes


Time, seconds

FIC. 3. Predicted flame front dynamics of near-limit normal flames and Serf-Extinguishing Flames in lean methane-air mixtures at mierogravity. Compositiol~s range from 5.60% CH~ to 4.60% CH~ (~b = 0.565 to + = 0.459) in 0.10% steps. guishment is less than that of the planar flame at extinguishment, 2) the SEF extinguishment radius is sensitive to the ignition source strength for some mixtures, and 3} some mixtures may exhibit both normal flames and SEFs depending on ignition source strength. Consideration of the unsteady term (dS/dR) improves agreement between prediction and observation somewhat for 1) and 2) but not for 3). It is suspected that in the low burning velocity regime of interest here, the chemical reaction rate cannot be adequately represented by a one-step overall reaction with Arrhenius kinetics, hence Eq, (4) is not strictly valid; chemical quenching effects ~'zg may need to be considered to obtain better agreement. Discussion and Conclusions The thermal characteristics of near-limit spherical premixed flames at I~g may be attributed to combined effects of radiant heat loss, gas conduction and convection, and rapid cessation of chemical reaction in extinguishing flames. For mixtures with Lewis numbers near unity, the txg flammability limits are probably caused by radiant heat losses from the product gases, To our knowledge this is the first demonstration of this type of limit, These limits cannot be seen at earth gravity (one-g) because of the low limit burning velocities; at one-g buoyancy completely distorts these flames. Lzz For some mixtures, particularly those with high Lewis numbers, these radiant limits are not



seen because an ignition limit is reached before the flammability limit. For mixtures with low Lewis numbers, the formation of cellular flames renders simple one-dimensional models of flammability limits inappropriate. It cannot be stated that these radiant limits constitute a fundamental limit to flame propagation. In systems of sufficiently large size, reabsorption of emitted radiation would negate the heat losses. In such cases radiation could become an aid. to propagation similar to thermal conduction to the unburned gases. This has been demonstrated ~ for premixed flames seeded With inert, radiant particles. A simple model of nonadiabatic curved flame propagation describes many of the features of the dynamics and extinguishment properties of near-limit flames and SEFs at p~g but a more accurate chemical model is probably needed for a better description of these phenomena.


c Co Ea

Constant in Eq. (2) Specific heat at constant pressure Dimensional activation energy

I(Le, •) (1 - eJ

dT T k

L Le Q R

r S s.

Su.lim T Tmax* t

Thermal conductivity Heat loss per unit volume per unit time Lewis number Dimensionless heat loss = CLbSad213/kbTb Dimensionless flame radius = (r/Sad)/ 13I(Le, e) Gas constant Flame front radius Dimensionless burning rate = S~,/S,,ad Burning velocity Burning velocity at the flammability limit Temperature Peak temperature of limit flame Time

Greek Symbols


Dimensionless activation energy = Ea/ RgTb Thermal thickness of flame = kb/puCoS u


~b p

Fuel-air equivalence ratio Gas density


Subscripts ad Value b u

for adiabatic plane flame Value at adiabatic flame temperature Value at initial temperature

Acknowledgments This work was supported by the NASA Lewis Research Center, the National Research Council, the National Science Foundation Presidential Young Investigator program and the Gas Research Institute. Special thanks is owed to Mr. James Tresler at NASA for his help with the microgravity experiments. REFERENCES 1. RONNEY,P. D., WACHMAN, H. Y.: comb. Flame 62, 107 (1985). 2. RONNEY, P. D.: Comb. Flame 62, 120 (1985). 3. RONNEY,P. O.: Aeta Astronautica 12, 915 (1985). 4. RONNEY,P. D.: Comb. Sci. Tech. 59, 123 (1988). 5. SPALDING,D. B. : Proc. Roy. Soc. (London) A240, 83 (1957). 6. JOULIN, G., CLAV1N, P.: Acta Astronautiea 3, 223 (1976). 7. BUCKMASTER, J.: Comb. Flame 26, 151 (1976). 8. WILLIAMS, F. A.: Colnbnstion Theory, 2nd ed., Benjamin-Cummins, 1985. 9. RODRIGUEZ, T. A., S. M, Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 1984. 10. SIVASHINSKY,G. I.: Ann. Rev. Fluid Mech. 15, 179 (1983). 11. CLAVIN, P.: Prog. Energy Comb. Sci. 11, 1 (1985). 12. LEWIS, B., VON ELBE, G.: Combustion, Flames, and Explosions of Gases, 3rd ed., Academic Press, 1987. 13. HOTTEL, H. C., SAROFIM, A. F.: Radiative Transfer, McGraw-Hill, 1967. 14. LECKNER, B.: Comb. Flame 19, 33 (1972). 15. KAILASANATH,K., ORAN, E., BORIS, J.: Comb. Flame 47, 173 (1982). 16. BUSH, W. B., FENDELL, F. E.: Comb. Sei. Tech. 1, 421 (1970). 17. HIRSCHFELDER,J. O., CURTISS, C. F. AND BIRD, R. B.: Molecular Theory of Gases and Liquids, Wiley, 1954. 18. GLASSMAN,I.: Combustion, 2nd ed., Academic Press, 1987. 19. OKAJIMA, S., IINUMA, K., YAMAGUCHI, S., KUMAGAI, S,: Twentieth Symposium (International) on Combustion, p. 1951, The Combustion Institute, 1985. 20. RONNEY, P. D.: "A Study of the Propagation, Dynamics, and Extinguishment of Cellular Flames Using Mierogravity Techniques," 27th Aerospace Sciences Meeting, Beno, Nevada, Jan. 9-12, 1989. 21. JOULIN, G., SIVASHINSKY,G. I.: Comb. Sei. Tech. 31, 75 (1983). 22. JOUL1N, G.: Comb. Sci. Teeh. 47, 69 (1986). 23. ANDREWS, G. E., BRADLEY, D.: Comb. Flame 18, 133 (1972).



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27. ANDREWS, G. E., BRADLEY, 1).: F o u r t e e n t h S y m p o s i u m (International) on Coml~ustion, p. 1119, T h e C o m b u s t i o n Institute, 1973. 28. PETERS, N., SMOOKE, M. !).: C o m b . F l a m e 60, 171 (1985). 29. TAM, R. Y., LUDFORD, G. S. S.: Coral). F l a m e 72, 27 (1988). 30. JOULIN, G., EUDIER, M.: "'Badiation-l)ominated Propagation and Extinction of Slow, ParticleL a d e n G a s e o n s F l a m e s , - this S y m p o s i u m . 31. JOULIN, G., MITANI, T.: C o m b . F l a m e 40, 235 (1981).

COMMENTS E. K. Dabora, Univ. of Connecticut, USA. Can you speculate on the behavior of hydrogen-air flames at I~g conditions? Author's Reply. W e have p e r f o r m e d m a n y exp e r i m e n t s in h y d r o g e n - a i r flames at I~g. S o m e of this work is d i s c u s s e d in t h e written paper. A m o r e t h o r o u g h discussion a p p e a r s in R e f e r e n c e 20 of t h e written paper. T h e m o s t i n t e r e s t i n g result is that for lean mixtures, propagating cellular structures are o b s e r v e d (as e x p e c t e d ) b u t in sufficiently dilute mixtures, t h e s e cells cease propagation after about 1 second a n d form (apparently) stable, stationary, spherical flamelets w h i c h are about 1 cm in diameter.

R. S. Sheinson, Navy Research Laboratory, USA. O n your experimental t e m p e r a t u r e traces of t h e lean m e t h a n e flame (5,1%, 760 torr) two of t h e traces have m a x i m a b e t w e e n t h e flame front a n d c o m p r e s sion h e a t i n g peaks. W h a t is this d u e to? You m e n t i o n e d as a possible cause for t h e poorer a g r e e m e n t of t h e C3H3 flame data that t h e C O was optically thick. C O is a weak 1R absorber. W h a t c o n c e n t r a t i o n s did you have? C o u l d t e m p e r a t u r e s / e n e r g y level population inaccuracies b e a contribu t i n g factor?

Author's Reply. T h e thermocouple wires are strung diametrically across t h e c o m b u s t i o n vessel. Initially t h e y are taut, b u t as t h e flame front p a s s e s t h e t h e r m o c o u p l e wire, t h e r m a l expansion causes t h e m to b e c o m e slack. In the case to w h i c h you refer, two adjacent t h e r m o c o u p l e s b e c a m e tangled, as indicated by their similar r e s p o n s e s after this time. At this point, w h i c h is at t i m e s later t h a n t h o s e of m o s t interest, t h e data from t h e s e two t h e r m o c o u ples m u s t b e disregarded. C O is a relatively poor broadband IR e m i t t e r and absorber, however, data in r e f e r e n c e 13 of t h e writt e n p a p e r s h o w that C O is an excellent a b s o r b e r of its o w n emission, which is what I imply by t h e s t a t e m e n t "optically thick.'" For example, a s s u m i n g an adiabatic e q u i l i b r i u m c o m p o s i t i o n for t h e richlimit CzH3--air mixture at one a t m o s p h e r e for which t h e partial p r e s s u r e of C O is 0.191 atm, t h e net h e a t loss p e r unit v o l u m e from t h e b u r n e d gas kernel drops from 4.68 × 10SW/m 3 to 3.18 × 105W/ m 3 to 1.92 × 105W/m 3 as t h e k e r n e l radius increases from 2.5 cm to 5 e m to 10 cm. F o r t h e optically thin HzO a n d CO,, t h e v o l u m e t r i c h e a t loss is a h n o s t constant over this range of k e r n e l radii. Your s u g g e s t i o n of t h e r m a l (or chemical) none q u i l i b r i u m effects is a n o t h e r possibility, h o w e v e r , we have no data on t h e c h e m i c a l c o m p o s i t i o n or population distributions in t h e b u r n e d gases of these flames.