Burning velocities of chlorinated hydrocarbonmethaneair mixtures

COMBUSTION AND FLAME 55: 245-254 (1984)

245

Burning Velocities of Chlorinated Hydrocarbon-Methane-Air Mixtures A. K. GUPTA* and H. A. VALEIRAS Department of Chemical Engineering and The Energy Laboratory, Massachusetts Institute of Technology, Cambridge. MA 02139

Results are presented for the variation in burning velocities with equivalence ratio and reactant gases preheat temperature for a number of chlorinated hydrocarbon compounds in methane-air mixtures of different concentrations at atmospheric pressure. Flame velocity of the mixture is determined with a Bunsen burner by measuring the unignited mixture approach flow rates and the area of the flame front. The method provides acceptable results and compares favorably with widely published methane flame data. Activation energy for a particular chlorinated compound was calculated by relating the flame velocity to the overall combustion reaction rate. Results are compared with nonchlorinatedcompounds and the available data in the literature. The reasons for discrepancies are discussed. The results show that increasing chlorine content decreases flame velocity and shifts the maximum flame velocity from fuel rich toward fuel lean. The flame velocity increases with increasing gas preheat temperature.

1. INTRODUCTION Hazardous wastes are produced by many industries, and according to the EPA approximately 10-17% of all chemical wastes generated are hazardous. This relates to about 40-65 million metric tons of hazardous waste generated in 1982. Among the various types of wastes, chlorinated hydrocarbon compounds (CHC), such as CCla, CHC13, CzHsC1, CeHC13, C6H5C1, polychlorinated biphenyls (PCBs), etc., represent an important fraction of the wastes produced. A number of methods are available for the disposal of hazardous wastes and are basically designed to reduce the volume of the waste and detoxify it. Among the different methods available for CHC disposal, high temperature incineration and pyrolysis are attractive because volume reduction, heat and material recovery, and detoxification of wastes all can occur simultaneously [I-3]. The incineration of CHC produces pollutants such as HC1, Cle, COC12, NOx, CO, unburned hydrocarbons, soot, and polycyclic aromatic hydrocarbons, which * Present address: Department of Mechanical Engineering, University of Maryland, College Park, MD 20742. Copyright © 1984 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

must be controlled for a clean environment. Interest to date has been primarily confined to determining the effects of adding small quantities of halogens to large scale combustors [3]. The principal characteristics of these flames exhibited those of the nonchlorinated hydrocarbon flames [8, 10]. However, these incineration/combustion tests revealed no fundamental information such as flame speeds, flammability limits, rates of reactions, or soot formation. These parameters are important in establishing excess air levels, use of auxiliary fuel, combustor geometry, flow patterns, etc. Some data and a nominal mechanism for soot formation in CHC flames were provided by the authors in a previous paper [2]. The present paper provides data on the laminar flame velocity from a number of CHC-methane-air flames. The various CHCs investigated are chlorinated methanes, ethylenes, and chlorobenzene in methane-air mixtures as a function of overall flame equivalence ratio, fraction of CHC in the combustible mixture, and initial temperature. CHC flames have been studied relatively little in the past because of their unsuitability as fuel because of the corrosive and toxic nature of their combustion products. The limited data for CHCs

0010-2180/84/$03.00

246

A.K. GUPTA and H. A. VALEIRAS

reveal that their addition to methane-air flames reduces the laminar burning velocity with an order of effectiveness HCI
examined as follows. Designating a CHC compound by CxHyCI~, e.g., for trichloroethylene x = 2, y = 1, z = 3, then the overall reaction chemistry for the compound can be given according to (without any C12 formation)

and CH aCI
CxH~,Clz + ( x +Y- - - ~ ) 0 2

[4]. Kaesche-Krischer [6] studied the flame velocities of chlorinated methanes in varying oxygen atmospheres in nitrogen and found that they decreased in the order

(ii)

2

For compounds in which y < z, the formation of C12 must also be considered as follows:

CHzCI>CH2C12>CHC1 a. Combustion of CC14 did not occur even in a pure oxygen environment. Addition of the inhibitor did not significantly affect the flame temperature but did decrease the flame velocity. In this paper laminar burning velocities (Su) of a number of CHC in mixtures with methane are presented. A knowledge of S u is of interest both from the practical and the theoretical points of view (e.g., the square of Su is proportional to the overall rate of combustion). Large flame velocities normally indicate that combustion reactions are fast and that the reactants are rapidly consumed. Conversely, small burning velocities imply slow rates of combustion and can cause potential emissions problems due to flame quenching. Analysis of the flame propagation equations for first and second order combustion kinetics with Arrhenius temperature dependences can be shown to result in the following relationship between flame velocity and flame temperature [22] :

Su 2 ~ exp(--E/R T),

= x C O 2 + zHC1 + y - - z H 2 0 .

(i)

where E is the activation energy of the assumed rate expression. Various forms of the above equation have been used in the past to correlate the experimental data [ 17]. 2. C O M B U S T I O N O F C H L O R I N A T E D HYDROCARBONS

Although the complete chemistry of CHC flames is complex, the nominal CHC combustion can be

CxH~Clz + xO 2 = xCO 2 + yHCI + z - y C12 2

(iii)

Highly chlorinated CHC do not burn in air because of their small burning velocities. Therefore they require the use of either oxygen enrichment or an auxiliary fuel such as methane to sustain a stable flame. When methane is used as the auxiliary fuel, the mixture combustion stoichiometry, without any C1z formation, can then be given according to CxHyClz + R1 CH4 +

+x +

y4z)

09.

=(x+I)co2+zHCI+(2+Y2Z)H20, (iv) Where R is the molar ratio of chlorinated hydrocarbon to methane. According to the above equation, the stoichiometric oxygen requirement is defined as the amount of oxygen needed to convert all the carbon to CO2, with all the C1 converted to HC1, and with the remaining hydrogen converted into H20. This is acceptable since high temperature favors the formation of HC1 over C12 according to the Deacon reaction: H20 + Clz = 2HC1 + 1 02 .

(v)

The formation of HC1 is preferable to C1z be-

CHLORINATED HYDROCARBON BURNING VELOCITIES cause it is easier to remove from the gases by simple aqueous scrubbing. The mixture equivalence ratio ¢ can then be defined as the ratio of the actual fuel/oxygen to the stoichiometric fuel/oxygen. The stoichiometric fuel/oxygen is the amount needed to combust completely the fuel (CH 4 and CHC) with no excess oxygen remaining. This can be written for Eq. (iv) as (2/R) + x + [O' - z)/4] ¢ =

actual O z used

(vi)

That is, for ¢ = 1, the actual 02 used corresponds to the exact stoichiometric requirement based on Eq. (iv), and ¢ > 1 or ¢ < 1 corresponds to fuel rich or fuel lean mixtures, respectively. Chlorinated hydrocarbons also possess free radical scavenging characteristics which influence the rates and the mechanism of hydrocarbon combustion reactions. Scavenging is defined as a process that converts reactive radicals into stable molecules and/or unreactive radicals. During the combustion of conventional hydrocarbons many reactive radicals form and participate in the overall reaction network. Chlorinated compounds attach and deactivate these species, thus resulting in decreased flame speeds. Most of the previous work on the effect of CHC in flames has been concerned with flame inhibition [7-13]. Many of the inhibition studies have been motivated by the need to find effective fire suppressing chemicals [11]. Belles and O'Neal [11] found that iodine and bromine containing compounds were better inhibitors than chorine or fluorine compounds. Wilson et al. [8] showed that the major role of the inhibitor was to react with H atoms and thus prevent the chain branching reaction with O9.. The effect of halogens in flames is to increase the preheat zone thickness and increase the temperature at which combustion takes place over that of the uninhibited flame. These factors influence the flame velocity of the mixture. Hastie [9] analyzed 1 atm CH4-O z flames and found that the most significant radicals present were H atoms, OH, and CH a. The H atom concentration was high in the preflame region compared with OH and CH a. Studies of CFaBr in-

247

hibited methane flames [9] showed that CFaBr disappeared via the reaction H + CFaBr ~ Br + CF a and the HBr reacted rapidly with H atoms to form H z and Br. The kinetics and mechanisms observed in this flame are presented by Biordi et al. [10] Previous studies on the effect of halogens on flame velocity have dealt with the addition of less than 3% hologenated hydrocarbon. The flame velocity of CO/H 2 flames is reduced by the addition of both chlorine and bromine, and the effect of carbon tetrachloride is found to be the same as the equivalent amount of chlorine [12]. Other investigators have studied fluorocarbonoxygen mixtures and their combustion properties [13]. Trichloroeythlene-oxygen mixtures were studied and it was found that the flames exhibited two distinct flame fronts, indicating that combustion w a s taking place in two separate stages. Kaesche-Krischer [6] has also proposed a twostage mechanism in which chlorine monoxide was the intermediate compound formed. 3. EXPERIMENTAL

The detailed description of the experimental apparatus used in the present study is provided elsewhere [5]. The flames were produced and stabilized on a 1-cm-diameter Bunsen burner of quartz that was sufficiently long to ensure the presence of fully developed laminar flow at the exit. The gases used were of high purity, e.g., CH4 was 99.97% with the remainder being Ng_, 02, COz, H20, and C2+, air was pure gas with C1+ less than 2 ppm. Liquid methyl chloride and other CHC compounds were of better than 99.5% purity. The gas flow rates were regulated and metered using flow meters prior to their introduction into the burner. The experimental procedure consisted of electrically heating the gases to a desired temperature and injecting the liquid chlorinated hydrocarbons by a syringe pump into the heated gas stream (Fig. 1). The resulting gaseous mixture was then passed through a mixing chamber/surge tank. A fine temperature control of the gaseous mixture was required in order to prevent CHC condensation and to bring the gaseous mixtures

248

A.K. GUPTA and H. A. VALEIRAS

| Enclosure tGlass Camera/Lens

L ~ urner

FlowMeters

Mixing ~=~

~

CHCResevoir~_Hestl ElementnUgs

IC ~

I

Syringe Pump

Fig.1.Experimentalsetupforthedeterminationofflamevelocities. temperature to the desired initial value. The uniformity of the CHC delivery, evaporation, and mixing with the gases were satisfactory, as manifested through the observation of the distinct sooting limits (onset of yellow luminosity) in flames. Whenever the experimental conditions were changed, sufficient times were allowed to establish the steady state. Direct flame photography was used to determine the area of the visible Bunsen cone, and the total flame area was determined by numerical integration over the projected photographic image of the cone [15, 16]. In practice, however, the areas of the cones were determined through measuring the height of the visible luminous cones using a cathetometer and the cone angle method. This method was used primarily because of (a) the relatively simple experimental procedure, (b) the fast and inexpensive data acquisition method, and (c) data of quality comparable with other, more sophisticated, methods [14]. The accuracy of this method was checked by experiments with methane-air flames

and the results compared well with the available data in the literature to within 10-20% [15]. It must be recognized, however, that the flame front area determined by direct image flame photography corresponds to the outer region of the luminous Bunsen cone, and thus results in the overestimate of the actual flame front area and consequently an underestimation in the laminar burning velocity. Bare wire thermocouples were used to measure the maximum mean flame temperatures: Chromel/ Alumel for low temperatures and coated Pt/Pt13% Rh for high temperatures. Flame temperatures were measured by positioning the thermocouple at the center of the burner and by moving it vertically up and down until a maximum value was reached. The measured flame temperatures were corrected for radiation using the method developed by Kaskan [17]. A comparison of the measured and calculated flame temperatures shown in Table 1 reveals that the maximum error in the measured flame temperature is of the

CHLORINATED HYDROCARBON BURNING VELOCITIES TABLE 1 Calculated and Experimental Flame Temperatures for Chlorinated Hydrocarbon Compoundsa

Flame Temperature (K)

Experimental Maximum Flame Temperature (K)

CH4 CHaC1 CH2C12

2210" 2325* 2300*

2164" 2190" 2011"

CHCI3 CC14 C2HC13 C6Ha C6H5C1

2275* 2250" 2250* 2500 2450

1995 * 1840" 2032* 2290 2220

Compound

a Tp = 80°C (* at CHC to methane molar ratio of 1.0). order of 15-17%. As seen in Table 1, the introduction of various kinds of CHC compounds does not significantly alter the maximum mean flame temperature. 4. EXPERIMENTAL RESULTS AND DISCUSSIONS Prior to investigating CHC flames the accuracy and reliability of the technique was demonstrated on methane-air flames for which sufficient data exist in the literature. Laminar flame velocities of chlorinated methanes (CHaC1, CH2C12, CHCIa, and CC14), trichloroethylene, and chlorobenzene were investigated and Figs. 2-6 show the results for chlorinated compounds in methane-air mixtures as a function of equivalence ratio, initial temperature of the gases, and CHC to methane molar ratio (R). The results are also compared with methane and show that the flame velocities of all the chlorinated compounds are lower than those of methane in the decreasing order CH 4 > CHaC1 > CHaC12 > CHC1a > CC14. This behavior is the same as that reported by Garner et al. [4]. It is extremely gratifying that the results compare favorably with the available data on chlorinated methanes as shown by solid symbols in Fig. 2. The Schlieren method was used for the evaluation of flame velocity data shown in solid symbols, and therefore it is not surprising that those data points are somewhat higher than those obtained

249

in the present study [4, 21]. The burning velocity data showed the expected inverted U-shape behavior, with maxima in Su lying in the vicinity of unit equivalence ratio. The effect of increasing chlorine in the methane was to decrease the range over which the flame could be stabilized on the experimental burner. Flames of CHCla and CC14 mixtures were extremely unstable; consequently their burning velocities were rather difficult to measure unless a large amount of methane was used [5]. Some representative data are shown in Fig. 2. It must be recognized that the errors associated with the measurement of low burning velocities are likely to be high and can exceed 20%. The shift in maximum flame velocity from fuel rich to fuel lean with increasing chlorine content suggests that the additive chlorine reacts with the radical pool present in the reaction zone [18] so as to deactivate the species. Although the decrease in flame velocity with increase in overall chlorine content of the mixture is not an unexpected trend, the extent of S u depression is also a weak function of the chemical structure of the chlorinated hydrocarbon compound. The inhibition of the burning velocity by a halogen compound can be both physical and chemical in nature. The physical inhibition results in decreased flame temperature with increase in chlorine content of the mixture, while the chemical inhibition results in active involvement of chlorine compounds in the combustion chain reactions [4, 7]. The correlation of the flame velocities with the experimentally measured flame temperatures were also explored. Changes in flame temperatures at the same chemical composition and mass flow rates were affected by heating the precombustion gases, and a representative set of flame velocity data for the CHaC1 system is shown in Fig. 3. From such data the Arrhenius plots for the squares of the buming velocities were made in accordance with Eq. (i), and the activation energies determined from the slopes of these plots are presented in Table 2. Clearly the slopes of these Arrhenius plots are not activation energies in general, as combustion reactions seldom have simple kinetics, but they merely show the temperature sensitivity of the measured laminar burning velocity. It is

250

A.K. GUPTA and H. A. VALEIRAS 50

m

i

i

i

A

CH4

O CH3C1

40

~,~A

L~

O CH2C12 -~ CHC13

U~

~&

(> CCI4

.,,j. r,J

>..-

I"-¢--3

R=

30

I

k

A

1.0

TO - 80" C

.--,I

,,,

20

i,..J

~o-... X \

t0 .-..0

0

O.B

I

I

I

I

1.0 1.2 1.4 l.B EOUIVALENCE F:IATID

Fig. 2. Flame velocities of chlorinated m e t h a n e - m e t h a n e - a i r mixtures (shaded data points from literature CH 4 [ 21 ] ; others, [ 4 ] ); R = CHC/CH4 molar ratio.

50

I

I

=

=

0 TO - 140" C

40

[] TO A TO .

U'J

80* C 20* C

C3 >I,,-.I--4

30 /,,O "~-O.

C.~ C) .--I LLJ m,i

\

20

..-J IJ -

10

0

0.8

I

I

I

I

'I.0 'I.2 1.4 I .6 EOUIVALENCE RATIO

Fig. 3. Effects of precombustion temperature on the flame velocities of CH3C1-CH 4air mixtures.

CHLORINATED HYDROCARBON BURNING VELOCITIES 50

I

251

"1

1

A

R - 0.48

o

R-I.0

0

R-1.5

f.~

0

R-2.0

f.,,

T O - BO* C

40

>: I.---

30

Q ._.1

,,/

\

LLJ

UJ

20

--J I.L

JO

0

O.B

I

I

I

I

i.O i.2 ~.4 1.6 EQUIVALENCE RATIO

Fig. 4. Effects of R on the flame velocities of CH3CI-CH4-air mixtures; R = CHC/ CH 4 molar ratio.

50

I

1

I

40

I

,", R - 0.5. D

R-

1.0

T o - 80 ° C

>:

3O

I---

L~

>

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-~

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-_1

u_

a\ \A

"\

tO

I~

O.B

I

I

I

I

t.0 t.2 1.4 1.6 EQUIVALENCERATIO

Fig. 5. Flame velocities of C2HC13-CH4-air mixtures; R = CHC/CH 4 molar ratio.

252

A. K. GUPTA and H. A. VALEIRAS TABLE

50

2

I

I

I

l

Activation Energy as a Function of Equivalence Ratio for CHCs Studied in This Project i1

Compound Methane

R

¢

E (kJ/mol)

-

0.95 1.00 1.10 0.95 1.00 1.10 1.25 0.95 1.00 1.10 1.25 0.95 1.00 1.10 1.25 0.95 1.00 1.10 1.25 0.95 1.00 1.10 1.25 1.10 1.25 1.10 1.25 0.95 1.00 1.10 1.10 1.25 0.95 1.00 1.10 0.95

279 300 340 250 291 273 250 272 258 260 231 229 251 294 301 233 253 249 217 168 126 108 102 176 183 120 160 147 152 140 165 163 124 149 151 88

-

Methyl chloride

0.48

0.82

1.50

2.00

Methylene chloride

0.5

1.00 1.50 Chloroform

0.5

1.00 Carbon tetrachloride

0.5 1.00

estimated that the activation energies given in Table 2 are at best accurate to within a factor o f 2 in view o f the presence o f m a n y errors associated with the experimental measurements, particularly that o f t e m p e r a t u r e . Since the activation energies for the Su are relatively large, an accurate knowledge of the flame temperature would be needed. However, our flame temperature measurements (presented for completeness) were probably correct to within

II I1 " l r - . ~ l l

40 co -~. "5>-" v-¢-~ --J LU > t~ .~ ...J u-

30

\ D~

z~

20 Benzene To = 80 C

JO

0 O.B

[3

Chlorobenzene To = 80 C

I~

To = 115 C

•

TO = 135 C

I

I

I

I

J.O

1.2

t .4

1.6

EflUIVALENCE RATIO Fig. 61 Flame velocities of C6H 6- and C6HbCl-air mixtures.

about 100°C under best circumstances; thus the temperature data presented in Table 2 should only be used to draw qualitative conclusions and to establish trends in data. An examination o f Table 2 shows that the activation energies for the S u decrease consistently with increasing chlorine substitution in a given CHC compound. This correlates reasonably well with the relative carbon-chlorine bond strength o f the weakest chlorine bond o f a CHC molecule. That is, as the chlorine substitution in a CHC is increased, the individual C-C1 bond strength decreases, suggesting increased propensity for CHC decomposition with increased chlorine content. The effects o f chlorinated hydrocarbon molecular structure on flame velocity can be seen, for example, by comparing chloromethane and dichloromethane under the conditions o f equal chlorine content in the combustible mixture. The flame velocity for CH4-CHaC1 at R = 2.0, @ = 1.0, and Tp = 80°C should be equivalent to the flame velocity o f CH4-CH2C12 at R = 1.0,

CHLORINATED HYDROCARBON BURNING VELOCITIES = 1.0, and Tp = 80"C. The corresponding flame velocities for the two compounds at the above conditions were found to be 19 and 15 cm/s, respectively. This observation was consistent throughout and suggests that the combustion mechanism of CHaC1 is somewhat different than that of CHzC12. The lower burning velocity of the CH2C12 mixture may be due to its earlier decomposition in the flame-a result of its weaker C-C1 bond compared with the C-C1 bond in CHaC1. The above reasonings are also supported by the C-C1 bond energies (Table 3) and the activation energies for the inhibition reactions (Table 2). The experimental activation energy results shown in Table 2 reveal that the activation energy for the overall combustion reaction decreases with increasing chlorine content. This suggests that the higher the chlorine content in the additive, the earlier the molecule pyrolyzes and the higher the extent of inhibition of the flame. It is known that the CHC molecules pyrolyze early in the preheat zone at a temperature that is much lower than that required for combustion reactions to occur [19]. The CI radicals scavenge the H atoms present in the preheat zone to form HC1. This, in turn, decreases the free radical pool concentration in the preheat zone, reducing the energy produced and thus increasing the zone TABLE 3 Bond Dissociation Energies of Compounds Relevant to CHC Combustiona

Parent Complex HC1CH 3-

C2H5Cell bCC1aOHCH2CICHCI2C2HC14CH2=CH-

Bond Strengthb H CI 104 103 104 98 110 96 119 101 96 94 108

a Reference [ 19]. b All units in keal/mol at 298K.

103 58 84 81 95 73 60 91

253

thickness [20]. The higher temperatures in the reaction zone overcome the inhibiting effect, and therefore the net effect of the chlorine is to inhibit the flame in the preheat zone only. The extent of this effect depends on the location in the preheat zone at which the CHC molecule is pyrolyzed. This is consistent with results for other halogen inhibited flames [ 10]. The only aromatic chlorinated compound investigated in the present study was chlorobenzene (Fig. 6). The flames produced with C6H5C1 were very stable, and therefore it was not necessary to use any auxiliary fuel. The flame velocity, when compared with the nonchlorinated counterpart, benzene, was found to be significantly lower (max Su "~ 40 cm/s for C6He and 27 cm/s for C6H5C1). The effect of equivalence ratio on flame velocity for CsHsC1 was not as pronounced as that found for chlorinated methanes. CsHsC1 flames were highly sensitive to the preheat temperature of the gases as shown in Fig. 6. Flame velocity increased by about 60% with increase in preheat temperature from 80 to 135°C. The activation energy associated with the change was calculated to be about 180 kcal/mole, which was far in excess of the C-C1 bond dissociation energy of 90 kcal/mole (Table 3) for CsHsC1. In view of this discrepancy and the associated experimental difficulties described earlier, the chlorobenzene data should be used with reservation. 5. CONCLUSIONS The experimental results presented here have demonstrated that the effect of adding chlorinated hydrocarbons to a methane-air flame depends upon the composition of the CHC molecule. In general the flame velocity and the maximum flame temperature decrease with increase in chlorine content of the molecule and decrease in preheat temperature of the gases. For a particular compound, increasing the chlorine content shifts the maximum flame velocity from fuel rich toward fuel lean. It is postulated that the CHCs decrease the flame velocity of methane=air flames by scavenging the available radical pool in the preheat zone. Further experimental data

254 covering a wide variety of c o m p o u n d s , including a mixture o f CHCs, should be investigated for better u n d e r s t a n d i n g and reliable operation of industrial incineration systems for hazardous wastes.

This research was supported by the U.S. Environmental Protection Agency through Grant No. R. 808314310. The authors would like to thank S. Senkan f o r m a n y discussions and Jeanine Matouk, Jeffrey Sakaguchi, and Jeffrey Oehler f o r their assistance in taking the experimental data.

REFERENCES 1. Kiang, Y-H.,Hazardous Waste Processing Technology, Ann Arbor Science, Ann Arbor, 1982. 2. Senkan, S., Robinson, J. and Gupta, A. K., Combust. Flame 49:305 (1983). 3. TRW Report to EPA 68-01-2966, November 1977. 4. Garner, F. H., Long, R., Graham, A. J., and Badaksian, A., 6th Symposium (lnt'l) on Combustion, Reinhold, New York, 1957, p. 802. 5. Valeiras, H., S.M. Thesis, M.I.T., June, 1982. 6. Kaesche-Kirscher, B., Chem. lng. Tech. 35:856 (1963). 7. Fristrom, R. M., and Van Tiggelen, P., 17th Symposium {lnt'l) on Combustion, The Combustion Institute, Pittsburgh, 1979, p. 773. 8. Wilson, W. E., Jr., O'Donovan, J. T., and Fristrom, R. W., 12th Symposium (lnt'l) on Combustion, The Combustion Institute, Pittsburgh, 1968, p. 929.

A . K . G U P T A and H. A. V A L E I R A S 9. Hastie, J. W., Combust. Flame 21:187 (1973). 10. Biordi, J. C., Lazzara, C. P., and Papp, J. F., 15th Symposium ([nt'l) on Combustion, The Combustion Institute, Pittsburgh, 1974, p. 917. 11. Belles, F. E., and O'Neal, C., 6th Symposium (lnt'l) on Combustion, The Combustion Institute, Pittsburgh, 1956, p. 806. 12. Palmer, H. B., and Seery, D. J., Combust. Flame 4:213 (1960). 13. Matula, R. A., and Agnew, J. T., Combust. Flame 13:101 (1969). 14. RaUis, C. J., and Garforth, A. M., Progress Energy & Combustion Science 6:303 (1980). 15. Andrews, G. E., and Bradley, D., Combust. Flame 18:133 (1972). 16. Gaydon, A. G., and Wolfhard, H. G., Flames, Their Structure, Radiation and Temperature, Chapman and Hall, London, 1979. 17. Kaskan, W. E., 6th Symposium (Int'l) on Combustion, Reinhold, New York, 1957, p. 134. 18. Burgoyne, H. J., CuUis, C. F., and Lieberman, M. J., 12th Symposium (lnt'l) on Combustion, The Combustion Institute, Pittsburgh, 1968, p. 943. 19. Rosser, W. A., Wise, H., and Miller, J., 7th Symposium (Int'l) on Combustion, The Combustion Institute, Pittsburgh, 1959, p. 175. 20. Senkan, S. M., Private Communications, M.I.T., 1982. 21. Fells, I., and Rutherford, A. G., Combust. Flame 13: 130 (1969). 22. Glassman, I., Combustion, Academic Press, New York, 1977.

Received 14 October 1982; revised 30 August 1983