FLAME PROPAGATION A c t i v e Particle Diffusion Theory DOROTHY MARTIN SIMON National Advisory Committee for Aeronautics, Lewis Night Propulsion Laboratory, Cleveland, Ohio
T h i s work was begun for the purpose of correlating the measured burning velocities of hydrocarbon-air mixtures with fundamental properties of the combustible mixtures. The burning velocity correlates with the equilibrium flame temperature and the relative diffusion concentration of atoms and free radicals ahead of the flame. Specific rate constants calculated by the Tanford and Pease equation using the calculated atom and free radical concentrations were nearly the same for all hydrocarbons studied. The results indicate that the maximum flame velocities of hydrocarbon-air mixtures are consistent with an active particle mechanism of flame propagation. The Tanford and Pease equation with an average specific rate constant of 2.33 X ml. molecules-' second-' may be used to predict the burning velocities of hydrocarbon-airmixtures at atmospheric pressure and an initial temperature of 25" C. The correlation of equilibrium flame temperature and burning velocity could also be used for the estimation of burning velocities.
.
Dd k,
= coefficient of diffusion into unburned gas = rate constant for interaction of a radical with one combus-
L
= molecules per cubic centimeter of gas a t mean tempera-
Q' Q
= initial mole fraction of combustible =
B,
=
tible ture mole fraction of potential combustion products, carbon dioxide and water a term, near unity, arising from radical recombination
By using an average k , calculated from the experimental data, it was shown that the fundamental flame velocities for the system carbon monoxide-oxygen-nitrogen over a range of concentrations could be calculated from the equilibrium concentration of hydrogen atoms by the square root law. In the same way this equation was also used for the prediction of the flame velocities of the systems methane-oxygen-nitrogen ( I 1 ), 1,3-butadiene-oxygen-nitrogen, butadiene-oxygrn-helium, and butadiene-oxygen-argon ( I ).
1
8
ECENTLY two comprehensive investigations of fundamental flame velocities have been reported. One is the series of flame velocities for hydrocarbon-air mixtures, including alkanes, alkenes, alkadienes, alkynes, cycloalkanes, and benzene, which were determined by the tube method in the laboratories of the National Advisory Committee for Aeronautics (NA4CA)(4, 5 ) . The other is a list of flame velocities for hydrocarbons and some nonhydrocarbons in air determined by the Bunsen burner method a t Experiment Inc. (J). In the former investigation the effects of certain molecular structure factors on flame velocity were observed:
R
5
60
;d
,
C2H4-02-N2
LINNETT AND H O A R E ~ '
, /
0
n-ALKANES
0 ~ ~ A N C H EALKANES D A n-ALKENES
4 RANCHED
ALKENES
0 ?-ALKADIENES
9 BRANCHED
I
ALKADIENE: 4 E-ALKYNES 0 BRANCHED ALKYNES V CYCLOALKANES b BENZENE
I0-3
1. Flame velocity increased with the degree of unsaturation in the order alkane < alkene < alkadiene (isolated bond system) &Z alkadiene (conjugated bond system) < alkadiene (cumulated bond system) Ei alkyne. 2. Within any homologous series, except the alkane series, flame velocity decreased with increasing chain length. 3. Flame velocity decreased with alkyl substitution.
These two series of experimental data are used as the basis of this discussion of the active particle diffusion theory of flame propagation. In the past it has been suggested that the rate-determining step in the flame propagation process might be the diffusion of active particles, These active particles like hydrogen and oxygen atoms or hydroxyl radicals then act as chain carriers for the flame reaction. On the basis of such a diffusion model for propagation, Tanford and Pease ( I d ) formulated the square root law of flame propagation as 1 /2
I/'! =
g]
[ z B ~ i ~ iQBi lii~
where
vf
z
Pi
= fundamental flame velocity = refers to the ith radical = partial pressure in the burned gas
[6.5 PH+Po+PoH] ATMOSPHERES
Figure 1. Variation of Flame Velocities Determined by the Tube M e t h o d (7,2) Relative atom and radical concentrations for 56 hydrocarbons
Linnett and Hoare ( 8 ) reported that the fundamental flame velocities for the ethylene-oxygen-nitrogen system over a range of compositions giving flame velocities from 35 to 73 centimeters per second could be correlated with the relative atom and free radical eoncentrations. This correlation is plotted in Figure 1 as the dashed curve. The relative active particle concentrations were considered t o be the sum of the equilibrium concentrations of hydrogen atoms, oxygen atoms, and hydroxyl radicals tinies thcpir relative diffusion coefficients, which were 6 5 , 1, and 1 for hgdiogen, oxygen, and hydroxyl, respectively. In each of the previous investigations one combustion system over a range of compositions was studied; now, since maximum flame velocities are available for many hydrocarbons in air, many combustion systems a t one composition may be considered In a previous paper (10) the flame velocities of a number of hydrocarbons in air including alkane, alkene, and alkyne hydrocarbons, benzene, and cyclohexane were Etudied. Unfortunately, 18 of the
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INDUSTRIAL AND ENGINEERING CHEMISTRY
34 compounds had nearly the same flame velocity and there was little duplication of flame velocities for various hydrocarbon series. Subsequently maximum flame velocities for 22 new hydrocarbon-air mixtures were determined by the tube method (6). These hydrocarbons in general belonged to the alkadiene or cycloalkane hydrocarbon series, and the flame velocities overlapped the three series previously studied. These new flame velocity data are considered in this investigation together with those previously reported. Since there is some uncertainty in the measurement of flame velocity, a consideration of the Bunsen burner flame velocities for some of the same hydrocarbon-air mixtures on the basis of the Tanford and Pease equation should show whether the theoretical consideration of the flame velocity data is sufficiently dependent on the method of flame velocity determination to invalidate the conclusions.
Table
I.
A t o m and Free Radical Concentrations and Flame Temperature For Hydrocarbon-Air Mixtures Hydrocarbon Volumd
Te
PH x 103 Atmospheres 0.79 0.80 0 80 1.78 1.54 1.32 1.29 1.59 1.56 1.35 1.30 1.29
PO x 104, Atmoepheres 0.73 0.82 0.55 4.33 2.47 1.53 2.09 2.58 2.49 2.97 1.66 1.86
POH
x 108, Atmospheres 1.25 1.33 1.07 3.07 2.25 1.75 2.07 2.36 2.31 2.50 1.85 1.94
Compounds % ' K.L 2,2-Dimethylpentane 2.12 2245 3 3-Dimethylpentane 2.12 2253 2:2,4-Trimethylpentane 1.92 2236 1 2-Butadiene 4.27 2420 113-Butadiene 4.34 2377 3.47 cis-1,3-Pentadiene 2337 trans-1 ,a-Pentadiene 2350 3.37 1,2-Pentadiene 2381 3.45 2,3-Pentadiene 3.43 2377 3.33 2372 1,4-Pentadiene 1 5-Hexadiene 2338 2.83 2:Methyl-l,3-butadiene 2344' 3.41 2,3-Dimethyl-l,3-butadi2.85 2316 1.16 1.30 eneb 1.61 2-Butyne 4.36 1.73 2401 3.11 2.57 3-Hexyne b 3.05 2304 1.38 0.71 1.17 3,3-Dimethyl-l-butyneb 2.88 1.39 2339 1.59 1.76 4-Methyl-1-pentyne b, 2.87 2346 1.40 1.67 1.87 4-Methyl-2-pentyne b 3.00 2311 1.36 0.85 1.29 Cyclopropanec 0.076 1.08 2329 2.19 . 2.23 0.90 Cyclopentane 3.16 2265 0.78 1.26 Methylcyclopentane 2.75 2228 0.85 0.38 0.85 Methyloyclohexane 2.43 2186 0.74 0.18 0.56 a Calculated e uilibrium flame temperature. b Heats of com%ustion calculated by a n increment method from Bureau of Standards values. C H e a t of combustion 578.6 kg.-cal. per mole used.
Table
Hydrocarbon Data
PH 10s Volume Te Atmog % O Id. pheres Name 0.86 Propane 4.6 2240 0.65 Butane 3.4 2260 2.8 0.57 Pentane 2295 0.63 2.0 2280 Heptane Ethylene 7.4 2385 1.15 10.7 2595 4.21 Acetylene 1.62 5.4 2475 Propyne 2.2 2375 0.92 1-Heptyne 1.05 4.8 2370 Cyclopropane 0.61 2.5 2300 Cyclohexane 2.8 2375 0.68 Benzene a Flame speed d a t a of Experiment Ino.
PO 108, Atmospheres 0.09 0.14 0.39 0.22 0.59 1.37 1.32 0.66 0.51 0.36 0.80
x
x
POH
x
103, Atmospheres 1.72 2.12 3.47 2.63 4.36 6.05 6.14 4.31 4.03 3.17 3.89
Maximum Flame Velocity, Cm. per Seconda 45.6 45.9 44.4 42.4 74.5 157 71.3 53.0 55.3 43.6 47.8
The Bunsen burner data are plotted in the same way in Figure 2. The calculated atom and free radical concentrations and the equilibrium temperature are given in Table 11. Again the alkanes, alkynes, cycloalkanes, and benzene give one correlation while ethylene and acetylene appear t o deviate. This fact indicat,es that the method of flame velocity measurement does not affect the correlation. (Acetylene was not included in the NACA list of hydrocarbons.) The acetylene-air mixture has a higher flame temperature and a higher total concentration of *activeparticles than any other mixture studied, so that linear extrapolation of the flame velocity correlation curve may not be valid. HC-CH
p 0
0
9
Y
00-
H2C=CH,
,,' g-ALKANES o g-ALKENES A n-ALKYNES v CYCLOALKANES 0 BENZENE d ALKADIENES o
60-
d Equilibrium flame temperatures and product concentrations were calculated for the NACA data by the method previously reported ( I O ) . A less precise method, which has been found to be sufficiently accurate for correlation of the flame velocity data, was used for the Experiment Inc. data. Equilibrium flame temperatures were estimated by the Hottel, Williams, and Satterfield method (6) and equilibrium product concentrations were calculated by the method of Huff and Calvert ( 7 ) . Relative atom and free radical concentrations for the 56 hydrocarbon-air mixtures a t the concentration for maximum flame velocity as determined by the tube method are plotted against the fundamental flame velocities in Figure 1. The active particle concentration and flame temperatures for the 22 new hydrocarbon-air mixtures are given in Table I. The same data were given for the other hydrocarbons in a previous paper ( I O ) . In Figure 1a curve parallel t o the ethylene curve was drawn through the hydrocarbon data in order t o demonstrate the similarity of the two correlations. Although the rate of reaction of the active particles with hydrocarbons has not been considered, all the hydrocarbon points appear to lie on one curve except for the ethylene point which lies on the original Linnett and Hoare curve. The curve shows that regardless of the chain length, the degree of unsaturation, or alkyl substitutions, the fundamental flame velocities correlate. The position of the ethylene point suggests that there may be a fundamental difference between the behavior of ethylene and the other hydrocarbons studied.
II.
2119
402 4
Ib
io
io
40
5c
c6.5 PH+ Po+POH] ATMOSPHERES
Figure 0 . Variation of Flame Velocities Determined b y the Bunsen Burner M e t h o d Relative atom and radical concentrations for hydrocarbons (3)
Sachsse and Bartholome ( d , 9 ) considered the flame speed data for oxygen-enriched air-hydrocarbon mixtures. The hydrogen atom concentrations calculated by these authors are plotted against the fundamental flame velocities in Figure 3. The calculated flame temperatures in degrees Kelvin are written below the experimental points. These data cover a much higher flame speed range since the combustible mixtures are enriched with oxygen. The part of the Sachsse and Bartholome curve covered by all the hydrocarbon-air mixtures of the NACA investigation lies between the two arrows in Figure 3. In this case the flame temperatures of the acetylene flames and the active particle concentrations are in the range of other experimental points and again acetylene behaves in a different manner from the other hydrocarbons. The equation, which was used to evaluate the data, is (IO)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
where 72 is the number of moles of potential combustion products per mole of combustible. Equation 2 includes the factor n, because the rate of formation of combustion products (carbon dioxide and water) is not equal t o the rate of consumption of the hydrocarbon, and n has a different value for each hydrocarbon. Equation 1 was derived for carbon monoxide combustion, in which case n is equal to one. The measured fundamental flame velocities, the calculated equilibrium free radicial xnti atom concentrations, the _______ diffusion coefficient., 600 and the reconibiHC-CH nation factors mere
t h a t values foi the 56 hydrocarbonair mixtures could be calculated. From the fact that the fundanient,al f l a m e velocity correlates with the relative atom concentration (Figu r e I ) , it may be predicted that
--
‘“r
.
--
9 2
’
aoL
HC=CH
/b:
