Effect O2 Soot Formation In Methane Propane

Effects of Oxygen on Soot Formation in Methane, Propane, and n-Butane Diffusion Flames 6MER L. GtiLDER National Research Council of Canada, Combustion Technology, IERT, Building M-9, Ottawa, Ontario KlA OR6, Canada

Gverventilated coflow axisymmetric laminar diffusion flames of methane, propane, and n-butane were used to study the influence of oxygen addition to the fuel side on soot formation. The line-of-sight soot volume fractions and the visible flame profiles were measured as a function of axial location along the centerlines of pure fuel flames, and the flames in which the fuel was diluted either with oxygen or nitrogen at selected temperatures of the reactants, to maintain a constant adiabatic flame temperature. The relative influences of dilution and direct chemical interaction effects of oxygen in the fuel gas mixture were quantified. It was found that, when allowance was made for the influence of dilution and thermal effects, the addition of oxygen to the methane diffusion flame chemically suppressed soot formation. This suppression was argued to be due to the reduction in acetylene concentration in the pyrolysis products as the oxygen mole fraction in methane was increased. The chemical influence of oxygen addition to methane decreased when the adiabatic flame temperature was decreased by decreasing the temperature of the reactants. In propane and n-butane flames, on the other hand, oxygen addition chemically enhanced soot formation. The degree of enhancement was small for low mole fractions of oxygen, but increased with increasing oxygen. When oxygen is added to the fuel side of a diffusion flame, two counteracting chemical effects are expected: Oxygen promotes fuel pyrolysis and hence production of hydrocarbon radicals and H atoms which enhance soot formation. On the other hand, aromatic radicals and critical aliphatic hydrocarbon radicals are removed by reactions with molecular oxygen and oxygen atom. The net chemical influence is the difference of these two counteracting effects.

INTRODUCTION There is a growing interest in oxygen enrichment applied to natural gas fired industrial furnaces for the purpose of increasing the heat flux from the flame. Adding oxygen to the air stream or to the fuel stream, while keeping the air-to-fuel ratio constant, elevates the combustion temperature, and consequently, increases the heat flux. Oxygen enrichment of the intake air of internal combustion engines has also been considered for a long time as a measure to control exhaust pollutants (especially particulate emissions from diesel engines) and to improve thermal efficiency [l, 21. A basic understanding of the role of oxygen addition to diffusion flames has, therefore, some practical implications. Since the first observation of the presence of small percentages of oxygen inside the flame cone of a pure methane diffusion flame [3], there have been several studies devoted to deciphering the role of oxygen in soot production and oxidation in diffusion flames of various hydrocarbons. The addition of oxygen to acetylene [4] and ethylene [5-121 enhances soot

formation. Wright [8] and Hura and Glassman [lo] observed an increase in soot upon oxygen addition to propylene diffusion flames, although Jones and Rosenfield [7] reported a decreased rate of soot formation. Hura and Glassman [lo] found that the presence of small amounts of oxygen in ethylene causes a substantial increase in the radical pool (primarily H atom) and, subsequently, increases the pyrolysis rate over a wide range of temperatures. This effect was found to be very weak in the temperature range of interest in propane flames which suggests that oxygen addition does not have any significant catalytic effect on the pyrolysis of alkanes [lo]. The observed suppressive effect, when oxygen is added to propane and isobutane, was entirely attributed to dilution [ll]. Wey et al. [131 observed a significant increase in soot concentrations upon oxygen addition to propane in an underventilated Wolfhard-Parker diffusion burner flame. The measured increase was much larger than that would be expected due to an increase in flame temperature resulting from oxygen addition [13]. The findings of Du et al. [12] contrast conclusions of Refs. 10 and 13. In a counterCOMBUSTIONAND

OOlO-2180/95/$0.00 SSDI OOlO-2180(94)00217-G

FLAME

101: 302-310 (1995)

Copyright 0 1995 by The Government of Canada Published by Elsevier Science Inc.

EFFECTS

OF OXYGEN

ON SOOT FORMATION

flow diffusion flame, when allowance was made for the dilution effect, oxygen addition (up to 30%) to propane resulted in a significant chemical suppressive effect on soot formation [121. Oxygen addition caused the promotion of soot formation as the oxygen mole fraction approached 40% in the fuel gas mixture [121. The other investigators reported very small changes in soot formation with oxygen addition to propane [6-8, 101. In a near-sooting ethylene inverse diffusion flame, Sidebotham and Glassman [14] observed a shift towards species associated with oxidation rather than an increase in the pyrolysis intermediates, when oxygen was added to the fuel side. They concluded that oxygen addition does not enhance the ethylene pyrolysis rate [14], and the enhancement of soot formation is not due to an earlier transition to soot inception. There is no study on the influence of oxygen addition to methane in diffusion flames, except the work reported by Saito et al. [15, 161 in which the maximum oxygen mole fraction in the fuel gas mixture was 0.045. Their results indicated that the small percentages of oxygen present in the pure methane diffusion flame do not affect either the pyrolysis of the methane or subsequent reactions leading to formation of soot [151. The objective of the present work was to investigate the effects (thermal, dilution and chemical) of oxygen addition on soot formation in overventilated coflow laminar diffusion flames of methane, propane, and butane. The emphasis was on methane, since no data exists in the literature for oxygen mole fractions higher than 0.045 in the fuel gas mixture. One of the aims was to resolve the controversy about the effect of oxygen addition to propane on soot formation. Using the techniques employed previously [12, 17-191, the relative influences of dilution, thermal, and direct chemical interaction effects, as a result of oxygen addition, on soot formation were quantified. METHODOLOGY When a gaseous diluent or additive is added to the fuel side of a diffusion flame, one can expect the influence of three potential effects

303

on soot formation [12, 191: (i) a dilution effect resulting from the change in the amount of carbon per unit mass of the fuel gas mixture, (ii> a thermal effect due to a change in the flame temperature field upon diluent addition, and (iii) a direct chemical interaction (excluding the changes in chemical reaction rates as a result of a change in temperature) due to changes in species concentrations. To assess the relative influences of the thermal, concentration, and chemical effects of gaseous additives on soot formation, the following parameters in the diluted and the undiluted flames should be taken into consideration: the characteristic flame temperatures, residence times, the flame diameters, and fuel and oxidant mole fractions. In diffusion flames of methane, propane, and butane, flame temperatures are expected to change substantially upon oxygen addition to fuel side. The adiabatic flame temperature was taken as the indicator of the temperature field of the lower regions of the flame where soot inception and nucleation occur. The use of the adiabatic flame temperature as the characteristic flame temperature is justifiable, as discussed by Gomez and Glassman [20] and Axelbaum and Law 1211. The evidence for the correlation between adiabatic flame temperatures and the measured temperatures in oxygen-added flames are illustrated in Figs. 1 and 2. In these figures, the symbols are experimental measurements and the dashed lines represent the best fits obtained by least squares. Figure 1 shows the relationship between uncorrected thermocouple measurements in a Wolfhard-Parker diffusion burner and the adiabatic flame temperatures with various oxygen mole fractions Xo, in ethylene [51. In ethylene and propane flames, there is an almost perfect correlation between measured maximum flame temperatures in a counterflow diffusion flame and the adiabatic flame temperatures at various oxygen concentrations Yo, in oxygen-enriched air [22] (Fig. 2). Also, the peak temperature increase in the counterflow diffusion flames of ethylene, propane, and n-butane upon 10% oxygen addition to fuel side were 29, 17, and 11 K, respectively 1101; Corresponding increases in calculated adiabatic flame temperatures are 28, 17, and

304

b. L. GtiLDER

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Wolfhard-Parker burner Fuel: Ethylene/Oxygen

?? xo*=o

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5mm Above the Burner Exit

2400

2450

1 2550

2500

Adiabatic Flame Temperature,

K

Fig. 1. Correlation between thermocouple measurements in a Wolfhard-Parker diffusion burner and the calculated adiabatic flame temperatures with various oxygen mole fractions in ethylene. X0* is the oxygen mole fraction in the fuel stream. Dimensions in the legend box denote the measurement locations with respect to the flame sheet. Experimental data, shown by symbols, are from Chakraborty and Long [5].

12 K, respectively. Further, in the experiments of Wey et al. [13], the increases in the maximum flame temperature were about 25 and 50 K for 10 and 20% oxygen mole fraction, respectively, in propane diffusion flames; corresponding increases in calculated adiabatic 2300

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2000

1800

1900

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1900

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2400

2500

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TABLE 1

f

Summary of Experimental Conditions and Results of Oxygen and Nitrogen Addition to Methane’

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flame temperatures were quoted as 18 and 40 K, respectively [13]. In order to compensate for the thermal effect of oxygen addition to the fuel, the adiabatic flame temperatures were kept constant by changing the temperatures of the reactants. Thus, the observed changes upon oxygen addition would be only due to dilution and the direct chemical interaction of oxygen. A summary of experimental conditions is tabulated in Tables l-4. To determine the influence of dilution alone, fuels were diluted with nitrogen while keeping the adiabatic flame temperature fixed by changing the temperatures of the reactants (Tables 1-4). The difference between the oxygen diluted and nitrogen diluted flames, at the same adiabatic flame temperature, would give the chemical influence of the oxygen on soot. The dilution effects of nitrogen and oxygen were considered equal for identical adiabatic flame temperatures and additive fractions, because both gases have similar transport properties. The line-of-sight average light extinction and the flame diameter were measured, as a function of the axial position, along the centerlines of methane, propane, and n-butane flames. The fuel flow rates were 365, 119, and 81 ml/min, respectively, under all conditions studied in this work.

2600

2

b

: i I I

700

K

Fig. 2. The relationship between measured maximum flame temperatures in a counterflow diffusion flame and the calculated adiabatic flame temperatures with various oxygen concentrations in the oxidizer stream. Yo, is the oxygen mole fraction in the oxidizer stream (oxygen index of air). Experimental data, shown by symbols, are from Vandsburger et al. [22].

Nitrogen Addition (Tad = 2400 K)

Oxygen Addition (Tad = 2400 K)

; ._

T, (K)

Xo,

F,

i”, (K)

XN,

F,

670 650 633 612 590 565 528

0. 0.025 0.05 0.075 0.1 0.125 0.16

1. 0.9 0.81 0.75 0.76 0.66b 0.62’

670 688 700 712

0. 0.1 0.15 0.2

1. 0.89 0.85 0.8

“X0, and XN2 are the mole fractions of oxygen and nitrogen in the fuel gas mixture, respectively, E is the normalized maximum soot volume fraction, Tad is the calculated adiabatic flame temperature, and T, is the temperature of the reactants. b Corrected for residence time change.

EFFECTS

OF OXYGEN

TABLE 2 Summary of Experimental Conditions and Results of Oxygen and Nitrogen Addition to Methane” Oxygen Addition CT,, = 2300 K)

Nitrogen Addition (Tad = 2300 K)

r,(K)

X0,

F,

T, (K)

XNZ

F,

450 430 410 388 363 336 295

0. 0.025 0.05 0.075 0.1 0.125 0.16

1. 0.935 0.87 0.82 0.78’ 0.756 0.72’

450 461 472 487 499 531

0. 0.05 0.1 0.16 0.2 0.3

1. 0.94 0.9 0.85 0.81 0.71

a See footnote of Table 1. ’ Corrected for residence time change.

TABLE 3 Summary of Experimental Conditions and Results of Oxygen and Nitrogen Addition to Propane” Oxygen Addition (Tad = 2400 K) T, (K)

X0,

592 576 558 516 457 371 300

0. 0.05 0.1 0.2 0.3 0.4 0.46

Nitrogen Addition (Tad = 2400 K) F,

1. 0.98 0.956 0.92’ 0.96 0.89b 0.9b

305

ON SOOT FORMATION

T, (K)

XNz

E

592 600 610 623 641 664

0. 0.1 0.2 0.3 0.4 0.5

1. 0.89 0.8 0.71 0.61 0.48

A schematic of the burner assembly is shown in Fig. 3. The fuel nozzle of the burner is a stainless-steel pipe of 12.7 mm inner diameter. Air is supplied from a concentric converging nozzle of 100 mm inner diameter. Both the air and fuel streams are heated by regulated electric heaters. Temperatures of the reactants were monitored by thermocouples near the exit of the fuel and air nozzles, and kept within +2 K of the desired reactant temperature. The fuel and the oxygen flow rates were monitored by calibrated rotameters. The air, before exiting from the converging nozzle, passed through a bed of glass beads and a set of wire-mesh screens to prevent flame instabilities. A flame enclosure made of flexible steel mesh with appropriate holes protects the flame from air movements in the room while providing optical access. The burner assembly sits on a positioning platform with accurate vertical and horizontal movement capability. The line-of-sight average soot volume fractions along the centerline of the flames were measured by the transmission of an Ar-ion (5 14.5 nm) laser beam. The visible flame diameter was measured by a reading telescope with an eyepiece. Typical flame diameters over the lower half of the flames were around 5-10 mm. Each division of the scale on the eyepiece corresponds to 0.125 mm. The repeatability and the reproducability of the flame diameter

‘See footnote of Table 1. ’ Corrected for residence time change. Laminar i diffusion flame ----A_+

TABLE 4 Summary of Experimental Conditions and Results of Oxygen and Nitrogen Addition to n-Butane’ Oxygen Addition (Tad = 2400 K)

:Flexible steel :mesh screen p

Air nozzle

Nitrogen Addition (T,, = 2400 K)

r,(K)

Xo,

F,

T, (K)

XN,

c

586 574 561 528 484 422 300

0. 0.05 0.1 0.2 0.3 0.4 0.515

1. 0.97 0.946 0.91b 0.886 0.96 0.946

586 592 600 611 625 643

0. 0.1 0.2 0.3 0.4 0.5

1. 0.9 0.81 0.7 0.59 0.5

’ See footnote of Table 1. b Corrected for residence time change.

Heated Fuel (t N 2 or 02) line

Fig. 3. Schematic diagram of the diffusion flame burner assembly.

306

6. L. GULDER

measurements were within f 1 scale division. The soot volume fraction F then can be calculated assuming Rayleigh extinction. The complex refractive index of the soot particles was taken as m = 1.89-0.48i, from Lee and Tien [23], to be consistent with our previous soot work. A schematic of the experimental rig was reported previously [24]. RESULTS AND DISCUSSION Methane In order to assess the effect of the flame temperature on soot formation in methane flames, soot profiles were measured in pure methane flames in which the adiabatic flame temperature was changed from 2400 to 2228 K by changing the temperature of the reactants (Fig. 4). Axelbaum et al. [17] and Axelbaum and Law [21] and our previous work [18, 191 showed that soot formation rate in diffusion flames is first order in fuel mole fraction in the fuel gas mixture, when the remainder of the fuel gas is an inert diluent like nitrogen. It was further demonstrated [18, 191 that maximum soot volume fraction in coflow diffusion flames scales as follows: . 7.

Frn -xF,O

1.4 -

E

exp(

METHANE

:

365mVmin

0

10

1.2 -

(1)

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20 30 40 50 Height Above the Burner, mm

60

70

Fig. 4. The line-of-sight average soot volume fraction profiles, as a function of axial position, of methane flames with different temperatures of the reactants. Corresponding adiabatic flame temperatures are noted near the best fit curves to the soot data points. For clarity, data for Tad = 623 K are not shown.

where X,,. is the mole fraction of fuel in the fuel gas mixture, r is the characteristic residence time, E, is the activation energy, and Tad is the adiabatic flame temperature. The activation energy inferred from the experimental data was 200 kJ/mol [18, 193 for C, and higher carbon number hydrocarbons. The maximum soot volume fractions from the soot profiles in Fig. 4 are plotted in Fig. 5 against the inverse of the Tad. The characteristic residence time was taken as the square root of the distance from the axial point of the first appearance of soot to the axial location where the maximum soot volume fraction is measured. In accordance with Eq. 1, the slope of the best fit line in Fig. 5 yields an overall activation energy of about 200 kJ/mol. The variation of the soot volume fraction profile with oxygen and nitrogen in methane flames with Tad = 2400 K are shown in Figs. 6 and 7, respectively. Since the adiabatic flame temperature is kept constant by changing the temperature of the reactants, the observed effect in Fig. 7 is due to dilution only, whereas in Fig. 6 it is due to combined effects of dilution and direct chemical interaction of oxygen. The normalized soot volume fractions for these two sets of experiments, as summarized in Table 1, are plotted together in Fig. 8. The maximum soot volume fractions of methane flames with lo%, 12.5%, and 16% oxygen were corrected for the changes in residence times in these flames. Uncorrected values are also shown in Fig. 8 with empty circle symbols. Nitrogen-diluted flames did not show any change in flame heights or diameters with nitrogen fraction. The reduction in maximum soot volume fraction due to oxygen addition is more than that can be attributed to the dilution effect, Fig. 8. Oxygen addition to methane seems to chemically suppress the soot formation. The suppression effect is significant even with the small fractions of oxygen in methane. This observation does not agree with the results of Saito et al. [15, 161 who reported no effects of small oxygen mole fractions (up to 0.045) in the methane stream. When oxygen is added to the fuel side of a diffusion flame two counteracting chemical effects can be expected as far as the soot formation is concerned. Due to an accelerated chain

EFFECTS

OF OXYGEN

ON SOOT FORMATION

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METHANE

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T,,=2400K

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4.2

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(1 I Tad) 104, K-’

Height Above the Burner, mm

Fig. 5. The Arrhenius plot of the normalized maximum soot volume fractions versus the inverse of the adiabatic flame temperature.

branching, the oxygen added to the fuel side promotes the pyrolysis of the fuel [25, 261 and hence production of hydrocarbon radicals and H atoms which enhance soot formation. On the other hand, aromatic radicals and critical aliphatic hydrocarbon radicals, like C,H, and C,H,, are removed by reactions with molecular oxygen 1271 and oxygen atoms. The net

Fig. 7. The line-of-sight average soot volume fraction profiles, as a function of axial position, of methane flames at selected temperatures of the reactants and nitrogen mole fractions correspondmg to Tad = 2400 K.

chemical influence is, then, the difference of these two counteracting effects. The present results indicate that the net chemical influence of oxygen is suppressive in methane which has a unique sooting behaviour quite different from other alkanes [lo]. In the pyrolysis of pure methane, acetylene is one of the major intermediates 1251. When oxygen is added to methane (i.e., a rich premixed flame), the computed profile of H atoms is higher than that calculated for pyrolysis, but l.lr,,

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,-

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-._

F

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0

10

20

30

40

50

Height Above the Burner, mm

Fig. 6. The line-of-sight average soot volume fraction profiles, as a function of axial position, of methane flames at selected temperatures of the reactants and oxygen mole fractrons correspondmg to r,,, = 2400 K.

0.00

0.05 0.10 0.15 0.20 Mole Fraction of Additive, XNz and X0

0.25

Fig. 8. The variation of the isolated dilution add chemical effects of oxygen addition to methane, Tad = 2400 K.

6. L. GULDER

308 acetylene is no longer one of the important intermediate species [2.5]. Acetylene is formed from vinyl and its consumption in methane oxidation is by OH, H, and predominantly by 0 atoms [28, 291. A higher concentration of H atoms (as compared with those of pure methane pyrolysis), and the presence of OH and 0 in oxygen-added methane diffusion flames, result in a lower acetylene concentration. If it is assumed that the soot formation mechanism is mainly controlled by a radicalbased acetylenic addition route leading to the chemical growth of PAHs, then the reduction in the acetylene concentration, as a result of oxygen addition to methane, could be one of the possible causes of the chemical suppression of soot formation. The influence of oxygen at a lower adiabatic flame temperature, Tad= 2300 K, is shown in Fig. 9 (conditions are summarized in Table 2). At a lower flame temperature, the chemical suppressive effect of oxygen is clearly weaker.

Propane and Butane Using the same technique employed for methane flames, relative influences of dilution and direct chemical interaction effects of oxygen addition to propane and butane were quantified as shown in Figs. 10 and 11 (Tables 3 and 4, respectively). When allowance is made for the dilution effect, oxygen addition to propane

1.1 c

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0.7

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T& = 2400 K

119 ml I min

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V.”

0.0

0.1

0.2

0.3

0.4

0.5

J

0.6

0.7

Mole Fraction oi Additive, XNz and X0

Fig. 10. The variation of the isolated dilution kd chemical effects of oxygen addition to propane, Tad = 2400 K.

and butane enhances the soot formation chemically, although the degree of enhancement is small at low oxygen mole fractions in the fuel gas mixture. This observation for propane does not agree with the results of [12] which showed a significant chemical suppressive effect of oxygen addition (up to 30% oxygen mole fraction) on soot, when allowance is made for thermal and dilution effects. In Ref. 12 the maximum measured temperature increased 50 K (from 1990 to 2040 K) when 10% oxygen was added to propane in a counterflow diffusion flame (measured increase was 130 K for 20% oxygen). In

1.1 1

METHANE,

T.,, = 2300 K

365 ml I min

Dilut/on Effect

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1

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a

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0.3 0.1

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Fig. 9. The variation of the isolated dilution an> chemical effects of oxygen addition to methane, Tad = 2300 K.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Mole Fraction of Additive, XNz and X0

0.7 1

Fig. 11. The variation of the isolated dilution and chemical effects of oxygen addition to butane, Tad = 2400 K.

EFFECTS

OF OXYGEN

309

ON SOOT FORMATION

a similar flame [lo], on the other hand, the corresponding increase was measured as 17 K (from 1859 to 1876 K). The calculated adiabatic flame temperature increase for 10% oxygen addition to propane is 17 K (39 K for 20% oxygen), which agrees with the measurements reported in Ref. 10 but far smaller than those in Ref. 12. Further, measurements of Wey et al. [131 in propane diffusion flames showed about 25 and 50 K increase for 10% and 20% oxygen mole fractions, respectively, which agree closely with the calculated adiabatic flame temperature changes. The discrepancy in the temperature increase upon oxygen addition to propane seems to be the reason for conflicting results of the present work and those of Ref. 12. It seems that the net balance of the two counteracting chemical effects of oxygen addition is to enhance the soot formation in propane and butane flames. Although it was argued that the oxygen addition does not have any significant catalytic effect on the pyrolysis of propane [lo], the present results and the results of Wey et al. 1131claim otherwise. It should be noted that flames which contain high percentages of oxygen in the fuel stream may not be strictly characterized as diffusion flames. A final observation is that the data in Figs. 8-11, showing the behaviour of soot as a result of nitrogen dilution, agree with the first order dependence of soot formation on initial fuel concentration in the fuel gas mixture, as per Eq. 1.

pyrolysis intermediates, as the oxygen fraction in methane is increased. The chemical influence of oxygen addition to methane decreases when the adiabatic flame temperature is decreased by decreasing the temperature of the reactants. For higher alkanes, propane and n-butane, oxygen addition enhances the soot formation by direct chemical interaction. This enhancement is small for low mole fractions of oxygen, but increases as the oxygen fraction is increased. The observed chemical enhancement of soot formation is the net balance of the two counteracting chemical effects of oxygen addition to propane and n-butane. I thank M. F, Baksh for his capable assistance with the experimental work. The work described herein has been supported by National Research Council’s internal funds (Sub-project CSF 02) and by the PERD Program (Project no. 15113).

REFERENCES Quader, A. A., Cornbust. Sci. Technol. 19:81-86 (1978). 2. Iiada, N., SAE Paper No. 930603, Society of Automotive Engineers, Warrendale, 1993. 3. Smith, S. R, and Gordon, A. S., J. Phys. Chem. 1.

60:759-763

(1956).

4.

Kent, J. H., and Bastin, S. J., Cornbust. Flame 56:

5.

Chakraborty, B. B., and Long, R., Combust. Flame

6.

Deardon, P., and Long, R., J. Appl. Chem. 18:243-251

29-42 (1984). 12:469-476

(1968).

(1968).

7. Jones, J. M., and Rosenfield, J. L. J., Combust. Flame 191427-434 (1972).

CONCLUDING REMARKS The influence of oxygen addition to the fuel side on soot formation in overventilated axisymmetric laminar diffusion flames of methane, propane, and n-butane was investigated. The relative influences of dilution and direct chemical interaction effects of oxygen mole fraction in the fuel gas mixture on soot formation were quantified. When allowance is made for the influence of dilution and temperature, addition of oxygen to methane chemically suppresses soot formation. This suppression was argued to be due to the reduction in acetylene concentration in the

8. Wright, F. J., Fuel 53:232-235 (1974). 9. Schug, K. P., Manheimer-Timnat, Y., Yaccarino, P., and Glassman, I., Cornbust. Sci. Technol. 22:235-250 (1980).

10. Hura, H. S., and Glassman, I., Combust. Sci. Technol. 53:1-21

(1987).

11. Hura, H. S., and Glassman, I., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1989, pp. 371-378. 12. Du, D. X., Axelbaum, R. L., and Law, C. K., TwentyThird Symposium (International) on Combustion, The

Combustion Institute, Pittsburgh, 1991, pp. 15011507. 13. Wey, C., Powell, E. A., and Jagoda, J. I., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, pp. 1017-1024. 14. Sidebotham, G. W., and Glassman, I., Combust. Sci. Technol. 81:207-219

(1992).

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15. Saito, K., Williams, F. A., and Gordon, S. A., Combust. Sci. Technol. 47:117-138 (1986). 16. Saito, K., Williams, F. A., and Gordon, S. A., Combust. Sci. Technol. 51:285-305 (1987). 17. Axelbaum, R. L., Flower, W. L., and Law, C. K., Combust. Sci. Technol. 61:51-73 (1988). 18. Giilder, 6. L., and Snelling, D. R., Combust. Flame 92:115-124 (1993). 19. Giilder, G. L., Cornbust. Flame 92:410-418 (1993). 20. Gomez, A., and Glassman, I., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1987, pp. 1087-1095. 21. Axelbaum, R. L., and Law, C. K., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1991, pp. 1517-1523. 22. Vandsburger, U., Kennedy, I., and Glassman, I., 23.

Cornbust. Sci. Technol. 39263-285 (1984). Lee, S. C., and Tien, C. L., Eighteenth Symposium (International) on Combustion, The Combustion In-

stitute, Pittsburgh, 1981, pp. 1159-1166.

24.

Giilder, 6. L., and Snelling, D. R., Twenty-Third Symposium (International) on Combustion, The Combus-

tion Institute, Pittsburgh, 1991, pp. 1509-1515. 25. Tabayashi, K., and Bauer, S. H., Combust. Flame 34:63-83 26.

(19791.

Frenklach, M., Clary, D. W., Yuan, T., Gardiner, W. C. Jr., and Stein, S. E., Cornbust. Sci. Technol. 51:265-283

(1986).

27.

Frenklach, M., and Wang, H., in Advanced Combustion Science (T. Someya, Ed.), Springer Verlag, Tokyo, 1993, p. 170. 28. Hennessy, R. J., Robinson, C., and Smith, D. B., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1987, pp.

761-772. 29. Wamatz, J., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1993, pp. 533-579. Received 21 April 1994; revised 16 August 1994