C O M B U S T I O N A N D F L A M E 62:121-133(1985) 121
Effect of Gravity on Laminar Premixed Gas Combustion II: Ignition and Extinction Phenomena
P A U L D. R O N N E Y *
Space Systems Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Minimum ignition energies and flame radii as a function of time were measured for near-limit, limit, and sublimit fuel-lean methane-air mixtures burning at one-g and zero-g. Minimum ignition energy values were the same at one-g and zero-g except for mixtures very near the zero-g flammability limit and leaner, where the zero-g values were much higher than the one-g values. For sublimit mixtures at zero-g a previously unreported mode of unstable flame propagation was observed; this mode was characterized by a flame radius increasing in proportion to the square root of the time lapse from ignition, an energy release often orders of magnitude greater than the spark energy input, and sudden extinction. This mode of flame propagation was observed at all gas pressures tested but was more pronounced at higher pressures. All zero-g propagation was spherically symmetric except for a few unusual flame extinguishments at high pressures. The principal conclusions are that flame extinguishment at zero-g is caused by a flame-front instability and that gravitational forces have a stabilizing effect on upward flame propagation. The cause of the instability could not be determined; further experiments which might aid in determining the cause are suggested.
I. B A C K G R O U N D
A study of near-limit flame propagation at one-g and zero-g which yielded new insight into the nature of one-g flammability limits and near- limit flame propagation is presented in the previous paper. ~ The experiments described in the present paper were designed to lead to a better understanding of the observed zero-g flammability limit and extinguishment phenom- ena for sublimit mixtures, and in particular, to attempt to determine to what extent the observed behavior was an ignition phenomenon as op- posed to a propagation phenomenon.
Ordinarily observed ignition phenomena are
* Present address: National Aeronautics and Space Admin- istration, Lewis Research Center, Cleveland, Ohio 44135. Referred to hereafter as Part I.
generally characterized as follows [1]: if a subcritical quantity of ignition energy is intro- duced into a combustible mixture, the resulting flame kernel (referred to as a nonignition flame kernel) rapidly decays and extinguishes after consuming a small quantity of fuel, whereas if the ignition energy is greater than a certain well- defined minimum threshold, a steadily propa- gating flame develops which consumes all of the available fuel. Investigations [2-5] have shown that in the early stages of flame kernel develop- ment from ignition sources of both subcritical and supercritical energy, the kernel radius in- creases logarithmically with time. For subcriti- cal ignition sources, the kernel radius increases in this fashion until it extinguishes, whereas for supercritical sources the kernel departs from this initial growth rate to assume the normal linear growth rate characteristic of steady laminar flame propagation.
0010-2180/85/$03.30
122 PAUL D. RONNEY
TABLE 1
Ratio of Energy Release to Ignition Energy Input in Subcritical Flame Kernels for Various Fuel-Air Mixtures at 760 Torr Initial Pressure
Ignition Extinction Calculated Energy Radius Enthalpy Release
The energy liberated by chemical reaction in flame kernels resulting from subcritical ignition sources appears to be about an order of magni- tude greater than the ignition energy input, E. The amount of energy liberated by subcritical flame kernels can be estimated from the en- thalpy, H, residing in the spherical flame kernel just before extinction, which is given by 2
H = pb(4xrb3/3)Cp(Tb -- Tu), (1)
where Cp is the gas specific heat at constant pressure.
Using the ideal gas relations, (1) becomes
4rT H = (1 - Tu/Tb)Porb 3, (2)
3 (Y- 1)
where T is the specific heat ratio of the gases. For lean methane-air mixtures, Tb varies from about 1500 to 2200K. Using an average Tb ~-- 1800K (The variance in Tb will cause only a small change in the 1 - TJTb term), Tu = 300K, and T = 1.4 (typical for air), the approximate result is
H ~ 12P0rb 3. (3)
Table 1 shows the ratio H / E computed from data taken from the literature. It is seen that for
2 Nomenclature is the same as in Part I.
nonigniting flame kernels 4 _< H / E <_ 12 for these experimental conditions.
Given this information, it is possible to determine to what extent the zero-g flame phenomena reported in Part I are ignition- related from measurements of minimum ignition energies and flame radii as a function of time at one-g and zero-g under the experimental condi- tions employed in Part I. A comparison of one-g and zero-g minimum ignition energies would also help to determine whether minimum igni- tion energies measured at one-g are "fundamen- tal" values or are affected by gravitational forces, as was found in Part I to be the case with flammability limits.
II. EXPERIMENTAL APPARATUS AND PROCEDURES
The experimental apparatus is described in Part I. However, for this study it also included a system for varying and measuring the energy used for ignition. Electric spark discharges were again used for the ignition source because a spark discharge system is relatively easy to construct and control and because most previous minimum ignition energy experiments have em- ployed spark ignition. The system consisted of two major components: a generator for produc- ing sparks of controllable duration and power and an analog computer for measuring the
EFFECT OF GRAVITY ON LAMINAR FLAMES II 123
energy dissipated in these sparks. This system is described in greater detail elsewhere [7].
The spark generator (Fig. 1) consisted of two separate spark-producing circuits: (1) a standard capacitive discharge system (shown in Fig. 1 on the left side of the spark gap) for producing a short duration, high voltage, low energy trigger spark to cause breakdown of the spark gap and (2) a lower voltage dc arc (shown on the right side of the spark gap) to sustain the spark once breakdown has occurred. To minimize the un- steady component of the overall spark, in each experiment the trigger spark voltage was set to the lowest value that would produce reliable breakdown of the spark gap. The dc arc current and duration were adjusted to provide the required total energy, which ranged from 0.1 mJ to 6 J at power levels of 30-450 W. The spark current and voltage waveforms had initial "spikes" due to the trigger spark followed by relatively steady dc values due to the dc arc. There was no detectable difference in the spark characteristics at one-g and zero-g.
The spark energy (E) was calculated from the relation
I ts
E= I(t) V(t) dt, (4) 0
where ts is the spark duration, I(t) is the spark current, and V(t) is the spark voltage. Prior investigators [2, 8] have employed oscilloscopes to measure I(t) and V(t), a scheme not practical in drop tests. Instead, an analog computer (cf. Fig. 1, Part I) was built to calculate spark energies. This device measured the voltage across the spark gap using a resistor-capacitor ladder network voltage divider and the spark
current using a current transformer. These signals were multiplied and integrated using solid-state electronics and the result was dis- played on a digital voltmeter. The performance of this device was tested at one-g by comparing results with those determined from oscilloscope traces and manual integration. The discrepancy between the two methods was always less than +10%.
In accordance with common practice, the spark gap was set to the quenching distance [1] for each combustible mixture. A few tests were performed at one-g with other spark gaps; minimum ignition energies were found to be only slightly affected by spark gap for gaps near the quenching distance. Similarly, the spark duration for each mixture was set to the value which was found to minimize the minimum ignition energy. A few tests were performed at one-g with other spark durations; minimum ignition energies were found to be only slightly affected by spark duration for durations near the optimal value.
The orientation of the spark electrodes at one- g, e.g., positive on top and negative on the bottom, vice versa, or horizontally opposed, had little effect on minimum ignition energies.
I l l . RESULTS
Figure 2 contains plots of one-g minimum ignition energies versus fuel concentration for several values of initial pressure. For a given pressure, the minimum value occurs for a mixture slightly leaner than stoichiometric. De- creasing pressure shifts the minimum ignition energy curves upward and to the left, i.e., toward higher energies and leaner mixtures. For
DC ARC j-TRIGGER SPARK POWER
ADJUST
+ SPARK
START ~ • SPARK ON ~ •
Fig. 1. Spark generator schematic.
124 PAUL D. RONNEY
D
,I.000
>.. 100
1 -
1
INITIAL PRESSURE,
Torr
O 1500 <> 760 A 250 ~7 100. D 5O
STOICHIOMETRIC ~ \ I
I ] I I I ] ' * l I 4 5 6 7 8 9 10
MOLE PERCENT METHANE IN AIR
TYPICAL ERROR LIMITS
Fig. 2. One-g minimum ignition energies as a function of fuel concentration for several initial pressures.
near-stoichiometric mixtures the minimum igni- tion energy is roughly inversely proportional to the square of the ambient pressure. These results are in agreement with those previously reported [11.
Figure 2 shows that as the one-g upward flammability limit is approached, the minimum ignition energy increases sharply. Because mini- mum ignition energy is inversely related to burning velocity [1, 9, 10], this increase is consistent with the conclusion in Part I that at the one-g upward flammability limit, Su ~ 0. The minimum ignition energy at this point does not appear to be infinite; hence it appears that Su :~ 0 but instead is very small. This observation is consistent with the conclusion in Part I that the one-g upward flammability limit measured in this work is a limit where the burning velocity is so low and the minimum ignition energy is so high as to render the mixture practically non- flammable but does not represent a fundamental barrier to flame propagation. The data also suggest that the observed one-g upward flamma- bility limits would have shifted to a slightly
leaner mixture had more spark energy been available.
The one-g downward flammability limits would not have changed had more spark energy been available because the minimum ignition energy for these limit mixtures (cf. Fig. 2) was much less than the energy used in the downward flammability limit tests.
Figures 3a-3d show the effect of gravity on minimum ignition energies and the zero-g extin- guishment radii for sublimit mixtures at initial pressures of 1500, 760,250, and 100 Torr. Data at 50 Torr (not shown) exhibited the same trends. The lower solid line in each plot is identical to the near-limit region of the corres- ponding curve in Fig. 2. The upper solid line is the minimum ignition energy for flame propaga- tion at zero-g throughout the vessel. The dashed curves are curves of constant extinguishment radius for the unstable mode of flame propaga- tion at zero-g; these flames will be referred to as Self-Extinguishing Flames, or SEFs. The dashed curves were obtained by mapping extin- guishment radii (measured from the film re- cords) for various combinations of spark energy and fuel concentration and drawing approximate best-fit interpolated curves through the data. The slight scatter of the data points (not shown) causes the actual locations of the dashed curves to be somewhat questionable, but the trends are clear. For reference, the enthalpy H [calculated from Eq. (3)] corresponding to the extinction radius for each dashed curve is also given.
It can be seen from the data in Figs. 3a-3d that the minimum ignition energies at one-g and zero-g are essentially the same except very near the zero-g flammability limit, where the mini- mum ignition energy at zero-g increases abruptly while the one-g value remains almost unchanged. For example, at 1500 Torr initial pressure, the minimum ignition energy at zero-g is about 6 mJ at 5.30% methane, 8 mJ at 5.29%, 115 mJ at 5.28% and greater than 3 J at 5.27%. The minimum ignition energy at one-g increases from about 4.5 mJ at 5.30% to 5.0 mJ at 5.25 %.
The steep rise of the zero-g minimum ignition energy curves near the zero-g flammability limits shows that the observed zero-g flamma-
EFFECT OF GRAVITY ON LAMINAR FLAMES II 125
'° FI ,col I F I (65J, I I
~ \ , ~ IO000~---|'2cm 11 4cm ' R-*o ~ooo E l ! loJ
2cm\ ~. ,- ZERO"9 MINIMUM F-- / I I (rsj) I I ~- (19J) k ~ ' IGNITION ENERGY ~ - i l 3Cm I ' II
IX ~ j ) , \ ~ ' l (33J' I II
'°i= \ ' , , , , , , I ~ TYPICAL ERROR LIMITS
~L I I I I I I I [7., I I I I 4.90 5.00 5.10 5.20 .5.30 5.40 5.50 5.60 4.60 4.70 4.80 4.90 5.00 .5.10 5.29
MOLE P ERCENT METHANE IN AIR MOLE PERCENT METHANE IN AIR Fig. 3. Near-limit propagation and extinction behavior. (a) Fig. 3. (b) 760 Torr. 1500 Torr.
I0 I I i I I I I 4.45 4.50 4.55 4.6o 4.65 4.7o 4.7~ 4.80
MOLE PERCENI METHANE IN AIR
Fig. 3. (c) 250 Torr.
I 4. 85
bility limits would have been essentially unaf- fected by increasing or decreasing the spark energy used in the flammability limit tests (see Part I).
Figures 3a-3d show that under many condi-
>.-
=._
10000 - - \ R • ,o
_-- \ 6era - _ ~ . _ _ ~ - " ~ . ~
=__~ (2oJ, " ¢
- - - -T - - - - -q ~m . " ,
_ (4.311 % ~
lO0-- "I' TYPICAL ERROR LIMffS
I [ I I [ I J 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55
MOLE PERCENT METHANE IN AIR Fig. 3. (d) 100 Torr.
tions the ratio of energy liberated by chemical reaction to the spark energy input (H/E) for SEFs is much higher than that found for nonig- nition flame kernels (see Section I). The largest H/E value found for SEFs occurred for 5.29% methane at 1500 Torr. For this mixture a 7 mJ
126 PAUL D. RONNEY
spark produced a SEF with a 5.9 cm extinguish- ment radius for which H / E ~ 70,000, about four orders of magnitude higher than in nonigni- tions. It is also noteworthy that for this mixture a 4 mJ spark produced no observable flame propagation [probably a nonignition occurred that was too small to observe; for these condi- tions with H / E = 10, Eq. (3) predicts an extinguishment radius of only 2.5 mm] and a 10 mJ spark produced normal flame propagation. It is surprising that the developing flame kernel can " r emember" after liberating 490 J of energy whether its initial spark was 7 mJ, in which case it extinguishes, or 10 mJ, in which case it propagates to the limit of the vessel. Figures 3a-3d show that other mixtures near the zero-g flammability limits also exhibit a marked effect of initial spark energy on the resulting extent and type of flame propagation.
Based on Figs. 3a-3d, it appears that the curves of constant zero-g extinguishment radius (dashed curves) become closer and closer to- gether near the zero-g minimum ignition energy curve (solid curve), asymptotically approaching an infinite extinguishment radius. This implies that combinations of fuel concentration and spark energy to the right of the zero-g minimum ignition energy curve represent normal self- propagating flames and not SEFs that might reach the self-extinguishment radius in a larger vessel.
At low pressures, the dashed curves of con- stant SEF extinguishment radius fold over to the left for lean mixtures and high spark energies as shown in Fig. 3d. It is significant that this " fo ld-over" portion of the dashed curves cor- responds to an energy ratio H / E of about 10, equivalent to that of nonignitions. Thus, under some conditions nonignition behavior probably results in more observable propagation than SEFs and becomes the dominant mode. The " fo ld-over" portions of the dashed curves are not seen on the plots for higher pressures, i.e., Figs. 3a-3c, because the " fo ld -over" point would be above the top of these plots except for very small extinguishment radii; the regions above the top of these plots could not be explored because they correspond to spark ener-
gies higher than those available in the apparatus used here.
It also appears that for spark energies below the " fo ld-over" points the dashed curves of constant SEF extinguishment radius asymptoti- cally approach the one-g minimum ignition energy curve for progressively smaller extin- guishment radii. This implies that the one-g minimum ignition energy limit is also the lower ignition energy limit for SEFs.
The three types of flame propagation ob- served in this work can now be visualized as regions on plots of spark energy versus fuel concentration as shown in Fig. 4. At one-g only the two well known regions exist but at zero-g there is an additional region corresponding to SEFs. This third region is further divided into two parts, one in which SEFs are actually observed and another above the " fo ld-over" point where nonignitions are observed instead. Perhaps the same regions would also occur on the rich side of stoichiometric although this was not tested in the current work.
In the region between the one-g and zero-g minimum ignition energy curves in Fig. 4 normal flame propagation is observed at one-g
" ~ ORMAL FLA
/ LONE-G MINIMUM IGNfflON ENERGY
COMMON NON-IGNITIONS
la) FUEL CONCENTRATION
t FOLD- J I FOLD-/ ~OVER A NODAL ~ OVER/ \ /I FLAMES I\ /
i \ / / / i" ~'/PRESUME[ X EF[ E,O-G
X l " MINIMUM / / \~ IGNmON /
COMMON NON-IGNITIONS 0% 100'/* (b) FUEL CONCENTRATION
Fig. 4. Schematic diagram showing regions of flame ignition and extinction behavior: (a) one-g, (b) zero-g.
EFFECT OF GRAVITY ON LAMINAR FLAMES II 127
but the less stable SEF propagation is observed at zero-g. Thus, it appears that some stabilizing factor which allows normal flame propagation to occur at one-g is missing at zero-g, suggesting that gravitational forces add stability to near- limit flame propagation, a hypothesis advanced in Part I.
Figure 4 shows that in general two ignition limits exist, one corresponding to the boundary between nonignitions and SEFs and another corresponding to the boundary between SEFs and normal flames. At one-g no SEFs are observed; hence at one-g the two boundaries coincide, at least within the available resolution. At zero-g the two limits are clearly separated; the boundary between nonignitions and SEFs is the same as at one-g but the boundary between SEFs and normal flames is different. Thus, it is likely that the boundary between nonignitions and SEFs is the same for all gravitational conditions and that for g > 1 the two boundaries will coincide. If this is the case, the limit observed at one-g would be a fundamental limit for normal flame propagation which is achieved at g _> go but not at g = 0. It is uncertain whether this limit would be achieved for go > g > 0 .
The inverse relationship between burning velocity and minimum ignition energy demon- strated for the one-g values does not hold for the zero-g values. As the zero-g flammability limit is approached, the zero-g minimum ignition energy increases sharply [see Figs. 3a-3d] but the burning velocity does not decrease corre- spondingly (see Part I, Fig. 5). Thus, the ignition limit at g = 0 shows anomalous behavior. This may indicate that flame phenom- ena at go > g > 0 would be more closely related to those at g = go than g = 0 because the case of g = go is of no special significance but g = 0 is a special case.
Figures 5a-5c show the relation between the zero-g flame radius and time lapse from ignition for several mixtures which exhibited SEFs in addition to normal flames and nonignitions. Similar behavior was found for other mixtures. It is seen that all SEFs for a given mixture follow nearly the same course in rb-t space and
extinguish suddenly at a radius which depends on the initial spark energy. The extinction radius is usually larger for higher spark energy. The observed flame radius appears to be propor- tional to t ~/2, in contrast to the logarithmic relationship between rb and t found in nonigni- tions. For spark energies higher than a critical value, for example, 72.1 mJ in Fig. 5a, the rb versus t course jumps to a different curve which (after an initial transient period) exhibits a steady propagation rate characteristic of normal flames. If the spark energy is increased still further, no significant change in the rb versus t course results. Thus, it can be seen that the difference between normal flames and SEFs appears at an early stage of development. The rb versus t courses of nonignitions do not show on Figs. 5a-5c because in the mixtures cited in these figures, nonignition flame kernels decayed and extinguished in too little time and distance to be observed with the apparatus used here.
None of the flames resulting from combina- tions of spark energy and fuel concentration corresponding to the region to the right of the zero-g minimum ignition energy curves in Figs. 3a-3d showed the rb versus t course characteris- tic of SEFs. Because the difference between normal flames and SEFs occurs at an early stage of development, this information helps confirm the assertion that flames in this region at zero-g are normal self-propagating flames and not SEFs that might reach the self-extinguishment radius in a larger vessel.
Figure 6 shows plots of rb versus t for SEFs observed at 760 Torr. Very similar results were found at other initial pressures. To avoid confu- sion, test conditions are specified for only a few sets of data points. It is seen that as the fuel concentration is decreased, the curvature of the resulting rb versus t plot increases and appears to approach the sharp logarithmic curvature characteristic of nonignitions as the "fold- over" point is reached.
An interesting feature of Fig. 6 is a "forbid- den" region in rb-t space in which no flame propagation of any kind can be observed. This is analogous to the " forb idden" region found for normal flames at zero-g (see Part I, Fig. 4b).
128 P A U L D. R O N N E Y
14-- .° 834mJ 78. z . ~ ' . . ' - " - n5
12 TYPICAL ERROR LIMITS
~- f ~NORMAL FLAMES 8
~s ~ , ~ 1 ~ ~ . c r . . x 7z. z mJ ___ / ~ A/-~xl~.42. 9 mJ S.E.F.
^ ~ . ~ " ~ - ~ ' ~ , . . . . ~ 19. 5 m j .......
~" 1 I I I I I I 0 .2 .4 .6 .8 1.0 1,2 1.4
TIME, sec
Fig. 5. Observed flame radius vorsus time for several values of init ial spark energy. (a) 5.07% methane at 760 Torr.
8 i~ J~r59.2mJ
2 ~ • TYPICAL ERROR LIMITS
• I I I I I I
12 E u~ ~. zo
4
m
2.32J ~
'301J
.z, TYPICAL ERROR LIMITS
2 - -
I I I I I I I I 0 .2 .4 .6 .8 1.0 1.2 1.4 .1 .2 .3 .4 .5 .6 .7
TIME, sec TIME, sec
Fig. 5. (b) 4.75% methane at 250 Torr. Fig. 5. (c) 4.42% methane at 100 Torr.
S ~ . , , ~ 62.8mJ
~ 3 ' ' "
~ 5.00%, ll.78mJ
, ~ 4.95%, 20mJ
2 5%, 20OmJ ~ 4. 85q,, 200ml
! ,[., TYPICALERROR LIMITS
T I I I I I I I I I I 0 .l .2 .3 .4 .5 .6 .7 .8 .9 l.O
TIME, sec
Fig. 6. Observed flame radius versus time for SEFs at 760 Torr initial pressure.
EFFECT OF GRAVITY ON LAMINAR FLAMES II 129
Perhaps stability considerations similar to those applicable to normal zero-g flames versus SEFs also apply to SEFs and nonignitions versus no propagation at all.
Figure 6 shows that for SEFs at a given pressure, r b -- t 1/2 o r r b / t 1/2 ~- constant, at least for mixtures very near the zero-g flammability limit. This relation is of the same form as the similarity parameter for transient thermal con- duction or molecular diffusion, r b / ( O t t ) 1/2 =
constant, where c~ is the diffusivity. This fact invites analysis to determine whether there is a corresponding similarity parameter for SEFs. The results of a simple analysis for thermal conduction are shown in Table 2. The values of ot are taken at the mean gas temperature, (Tu + Tb)/2, although the choice of temperature at which to evaluate c~ has little effect on the similarity of the results. The values of rb2/t are taken from Fig. 6 and corresponding figures (not shown) for other initial pressures. Table 2 shows that the thermal conduction similarity parameter is not constant for SEFs, but de- creases slowly with decreasing pressure. This analysis shows that the pressure effects on factors other than thermal conduction or molec- ular diffusion, probably chemical reaction, are necessary to account for the dissimilarities of SEFs at varying pressures.
Another unusual finding of this investigation is the appearance of nonspherically symmetric flames at zero-g, flames which fail in certain directions and not others. The asymmetry was found only for mixtures of 5.28 % methane in air at 1500 Torr initial pressure, which is the zero-g
TABLE 2
SEF Similarity Parameter for Thermal Conduction for Several Values of Initial Pressure
Pressure a rb2/t (Torr) (cm2/s) (cm2/s) rb/(ctt) llz
flammability limit at that pressure, and only for spark energies above those required to cause "n o rm a l " SEFs with an extinguishment radius of about 6 cm (about 15 mJ) and below those required to yield normal flame propagation (about 120 mJ). No normal flames or normal SEFs were observed under these conditions. Line drawings of the asymmetric flames are shown in Figs. 7a-7d. The spark electrodes are mounted vertically with respect to the figure. These drawings represent the only four asym- metric flames observed except for another flame with a shape very similar to that shown in Fig. 7d. Based on the film records it appears that the flames shown in Figs. 7a and 7d would have reignited into normal flames had more zero-g time been available, whereas the flames in Figs. 7b and 7c may have extinguished completely.
It should be understood that the film records provide only a two-dimensional projection of a three-dimensional image; therefore, it cannot be determined precisely what the total shapes of these flames were.
It appears from the film records that the asymmetric flames began as "no rma l " SEFs, then broke up in certain directions and in some cases reignited. Because there was no consistent failure location, it is unlikely that the observed behavior could be accounted for by the presence of the spark electrodes in the path of the flame front. It is unclear whether these asymmetric flame shapes represent distinct higher modes of SEFs or were merely caused by random pertur- bations. The fact that another flame similar to that shown in Fig. 7d was observed supports the higher modes hypothesis. On the other hand, the results have shown that disturbances initiated under certain conditions can propagate a consid- erable distance; hence random perturbations caused by factors such as spark discharge aerodynamics could account for the asymmetric zero-g flames. The fact that all these flames were mostly symmetric with respect to the spark electrodes supports this idea. In either case it is likely that other asymmetric flame shapes could be found.
It is also unclear why asymmetric flames were observed only with 5.28% methane at 1500
130 PAUL D. RONNEY
0. l l sec cm 0.63
1.08 Or---
O. I I sec 0.63
1.08
0.18 sec 0.63 1.09
0.17 sec 0.66 1.14
C-Z
1.53 2. O2
1.53 2.02
1.5l 2.(]6
1,63
2.11
Fig. 7. Sequential photographs of combustion of 5.28% methane at 1500 Torr initial pressure at zero-g. Spark energies: (a) 20.7 mJ, (b) 56.9 mJ, (c) 77.9 mJ, (d) 93.2 mJ.
Torr. This mixture is the most likely of those tested to exhibit extreme SEF behavior because SEFs are most pronounced for mixtures very near the zero-f flammability limit at high pres- sures, however, this does not explain why no asymmetric zero-g flames were found at 5.07% methane at 760 Torr, for example.
No prior experiments on the gravitational effects on ignition processes could be found for comparison with the results of this work. A theoretical study on the ignition characteristics of a CO + 202 mixture by Jones [11] predicted little effect of gravity on this fast-burning mixture and no phenomenon similar to SEF was reported. He did not attempt to extend the investigation to near-limit mixtures where such effects are more likely to be found.
Probably the reason SEF behavior has not been observed in detail before is that at least three experimental conditions are required: (1) zero-gravity, (2) a controllable, measurable source of ignition energy, and (3) mixture compositions very near the zero-g flammability limit. To the author's knowledge, no single previous investigation has met all three of these conditions.
IV. DISCUSSION
Before proposing an explanation for the unusual flame phenomena reported here, let us consider some factors which probably do not account for these phenomena.
Flammability limits are sometimes attributed
EFFECT OF GRAVITY ON LAMINAR FLAMES II 131
to "f lame stretch" [12], where the heat gener- ated by the flame is diluted, or "s t re tched," by conduction into an increasing cross-sectional area of cold gas, thus leading to a reduction in burning velocity and possibly extinction. Lewis and von Elbe [1] have shown that in an initially quiescent spherically symmetric system, the flame stretch limit is the usually observed minimum ignition energy limit. It has been shown here that this limit is separate from the zero-g minimum ignition energy limit and SEFs occur only for spark energies above the usually observed ignition limit (cf. Fig. 4); hence flame stretch does not seem to account for the phenom- ena observed at zero-g.
In Part I it was shown that heat losses probably could not account for the observed flammability limit and extinction behavior at zero-g and further evidence of this is the sensitivity of SEFs to the initial spark energy. For example, in the case of 5.28% methane at 1500 Torr, it is unlikely that the difference between a 7 mJ spark and a 10 mJ spark could result in the difference between an SEF with an energy release of 490 J before extinction and a normal flame if the SEF extinguished because of heat loss. The additional 3 mJ of spark energy would be small in comparison to any change in heat loss due to random factors such as slight variations in fuel concentration or ambient tem- perature, yet the additional 3 mJ was consist- ently needed to obtain normal flame propaga- tion. The effect of spark energy on SEF extinguishment radius also lends support to this notion.
It was demonstrated in Part I that the effects of rising unburned gas temperature and pressure during combustion due to flame kernel expan- sion probably could not have caused the ob- served zero-g flammability limit and extinguish- ment phenomena and further evidence of this can be seen in Figs. 5a-5c. In these figures the distinction between normal flames and SEFs appears at a kernel radius much smaller than that at which the temperature and pressure rise in the vessel become significant. Also, the zero-g near-limit phenomena are very sensitive to the initial spark energy; this would not be expected
if SEFs were caused by rising temperature and pressure during combustion because the spark adds very little to the total enthalpy and thus adds very little to the temperature and pressure rise during combustion.
Because of the very discontinuous nature of SEFs, as illustrated by the steep rise in the zero- g minimum ignition energy curves near the zero- g flammability limit (cf. Figs. 3a-3d) and the sudden change in rb versus t courses from SEFs to normal flames (cf. Figs. 5a-5c), it seems unlikely that any continuous phenomenon or set of phenomena could account for the observed behavior of these flames. The only phenomenon commonly thought to cause flammability limits and flame extinguishment that would appear capable of explaining the observed behavior is a flame front instability. Evidence presented in Part I and Part II shows that gravitational forces appear to add stability to laminar flame propaga- tion, which suggests that in the absence of gravity an instability could exist. The zero-g minimum ignition energy curves (cf. Figs. 3a- 3d) could be considered boundaries between stable and unstable regions in spark energy-fuel concentration space. Combinations of these two parameters outside the stable region could be considered perturbations near a stability limit and the amount of unstable propagation (i.e., the SEF extinguishment radius) is related to the distance from the boundary, with more unstable propagation occurring for perturbations near the boundary.
It is difficult to ascertain the nature of the apparent instability. Clearly it is at least parti- ally thermochemical in nature because it is very sensitive to spark energy and the state of the unburned gas. The instability is probably parti- ally mechanical in nature because it is very sensitive to the prevailing gravitational condi- tions even in the early stages of propagation, but on the other hand seems to be unaffected by other mechanical effects such as the geometry of the experimental apparatus or physical obstruc- tions (i.e., the spark electrodes). It is likely that at one-g natural convection deforms the devel- oping flame kernel into a more stable shape, but it is unclear whether the additional stability at
132 PAUL D. RONNEY
one-g results from a change in heat transfer, molecular species exchange, turbulence, or some unknown factor.
Rosen [13] developed a theory of stability limits for one-dimensional laminar flame propa- gation. He concluded that under certain condi- tions, a small disturbance in the heat production rate at a point in the flame front could grow without bounds in a way similar to the transition from laminar to turbulent flow in a nonreacting fluid. A flammability limit was defined as the limiting mixture for stable flame propagation. Rosen did not provide enough information on ignition and transient conditions to determine whether SEF or similar behavior could be predicted. Rosen's data appear to predict (using a typical overall activation energy of 30 kcal/ mole [14, 15]) that practically all methane-air flames with unburned gas at 300K are unstable, contrary to fact. Strehlow [16] suggested that if the temperature at the point of inflection were greater than (Tb -- Tu)/2, or similarly a short reaction zone were supporting a long preheat zone, the flame could be unstable. He did not provide any details to substantiate this idea. Contrary to Rosen, Layzer [17] and Richardson [18] concluded that all laminar premixed gas flames are inherently stable and small distur- bances die away without leading to extinction. Spalding [19] also deduced a result contrary to Rosen using qualitative arguments.
Further study is required to understand SEF phenomena better. The results have shown that the distinction between SEFs and normal flames appears at an early stage of development; hence there should be some difference in the state of the system for these two cases at this early time and thereafter. A practical way of obtaining information about the state of the system is through time-dependent temperature profile measurements. For flames with a Lewis number near unity, the temperature is a good indication of the degree of completion of reaction at that point [1, 9, 10] and temperature gradients indicate the direction and magnitude of conduc- tive heat transfer. Thus, a comparison of tem- perature profiles in normal flames and SEFs should help explain the difference in their
properties. It is likely that at least some portion of SEF temperature profiles is at a lower temperature than corresponding normal flames; otherwise, it is unlikely that SEFs could propa- gate slower than normal flames. Chemical spe- cies concentration and combustion vessel pres- sure measurements would also be useful.
To examine the effects of transport properties on SEFs, some tests should be performed with fuels chemically similar to methane but with different molecular diffusivities in oxygen, such as ethane and propane. To examine the effect of chemical kinetics on SEFs, some tests should be performed with fuels having reaction mecha- nisms very different from paraffins, such as hydrogen and carbon monoxide, or with small quantities of flame inhibitors or promoters added to the fuel. Tests performed at go > g > 0 could determine whether SEFs can occur in the presence of some degree of natural convec- tion.
A larger vessel and more zero-g time would allow improved study of asymmetric SEFs, enable a search for large symmetric and asym- metric SEFs, and extend the data to lower initial pressures, where the distances required for flame development are larger (cf. Figs. 5a-5c). This would require the use of another zero- gravity facility, such as an aircraft flying low- gravity trajectories or an orbiting spacecraft.
The authors are indebted to Prof. Glenn C. Williams at M.L T. for his invaluable advice and assistance. This work was supported largely by Grant No. NAG3-173 from the NASA-Lewis Research Center, Cleveland, Ohio. Special thanks is owed to Mr. James Tresler at NASA for his help with the drop tests.
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