Induction zone exothermicity of acetylene ignition

C O M B U S T I O N A N D F L A M E 6 7 : 6 5 - 7 5 (1987)

65

Induction Zone Exothermicity of Acetylene Ignition S. M. H W A N G and W. C. G A R D I N E R , JR. Department of Chemistry, University of Texas, Austin, TX 78712

M. F R E N K L A C H Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802

and Y. H I D A K A Department of Chemistry, Faculty of Science, Ehime University, Bunkyo-cho, Matsuyama 790, Japan

Refractive index gradient profiles in the shock-initiated ignition of C2H2-O2-Ar mixtures were analyzed by means of computer modeling. It was found that product formation in the main route of C2H2ignition chemistry proceeds only as far as CO and H~O, effectively excluding CO2 as a possible product of the reaction of CH2 with O2 as had been assumed on the basis of earlier modeling results. The elementary reaction rate constant expressions k8 = 5.0 × 10 a4 e x p ( - 60 kJIRT) cm 3 mol a s t for C2H2 + OH ~ CH2CO + H, k9 = 2.7 × 10 j4 exp( - 63 kJIRT) cm 3 mol- n s- a for C2H2 + OH---' C2H + H20, and kt8 = 2.5 × 10 ~3cm 3 mol ~s a for CHCO + H ~ CHz + CO were derived in the context of a reaction mechanism consisting of 5 elementary reactions of C/H species, 10 elementary reactions in the H2-O2-CO system, and 28 reactions of C/H/O species, 4 of which involve electronically excited CH*. The same mechanism was found to match laboratory flame speeds and profiles about as well as previously reported mechanisms.

INTRODUCTION The chemistry of C 2 H 2 flames is presumed to be simple--compared to the combustion chemistry of larger hydrocarbon fuels--and to underlie the chemistry of all hydrocarbon combustion, a s C2H2 is formed by a variety of pyrolytic routes from alkenes and alkanes. Accordingly, there have been many efforts to derive reaction mechanisms and elementary reaction rate coefficient expressions for C2H2 combustion, particularly for the conditions pertaining to low-pressure laboratory flames [1-8] and shock tube experiments [9-28]. In this paper we report an analysis of the magnitude and Copyright © 1987 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

shape of refractive index gradient profiles in the shock-induced ignition of C2H2-Oz-Ar mixtures. These profiles are particularly sensitive to the heat release rates afforded by the induction zone reactions and show that significant fractional production of the final products CO2 and H20 in the induction zone reactions does not occur. This result is in apparent conflict with earlier modeling studies [24, 26] in which it was concluded that in order to model acetylene flames correctly the reaction of CH2 with 02, a major route of C - O bond formation in the induction zone, produces

0010-2180/87/$03.50

66

S. M. HWANG ET AL.

2H + CO2 directly. The same route had been suggested by Homer and Kistiakowsky [18] on the basis of exponential growth constant measurements for CO and CO2 concentrations in the shock-initiated reaction. In supplementary flame speed and profile modeling we found that the 43reaction mechanism adopted gives a quality of agreement with flame experiments similar to that obtained with much larger mechanisms previously investigated.

EXPERIMENTAL The refractive index gradient profiles were obtained for C 2 H 2 ; 0 2 : Ar = 0.5 : 1.25 : 98.25 and 0.5 : 5.0 : 94.5 mixtures as described previ-

ously [27]. Briefly, test gas mixtures with PI = 1.33 kPa (10 Torr) were heated in incident shock waves to temperatures in the range 1300-2200K; the refractive index gradient was measured by the laser schlieren method [29] with electronic signalto-noise ratios for the reactive heat release of 10 or more. Deflection signals were converted to refractive index gradients using the molar refractivities of the test gas components [30]. Interpretation of the profiles was carried out by means of numerical integration of the kinetic equations under the constraint of steady flow with laminar boundary layer formation [31]. The limiting flow length was computed from the formulas of Mirels [32]. The reaction mechanism and rate coefficient expressions used are shown in Table 1 [20, 28, 33--45].

TABLE 1 Reaction M e c h a n i s m and Rate Constant Expressions ~

m

Reaction

1 2 3 4 5

C2H2 + C2H2 + C2H3 + C2H + C2H 2 +

6

C2H 2 + 0 --~ CH2 + C O

4 . 2 + 16 2 . 0 + 12 1.2 + 39 8 . 0 + 12 3.5 + 13

M - - ' C2 H + H + M C2H2 ~ C4H3 + H M - - * C2H2 + H + M H 2 --~ H + C2H 2 C2H -* C4H2 + H

7 C2H2 + O --' C H C O + H 8

C2H 2 + O H ~ C H 2 C O + H

9 10 11 12 13 14 15 16 17 18

C2H2 + C2H3 + CH2CO CH2CO CH2CO CH2CO C2H + C2H + C2H + CHCO

O H --' C2H + H 2 0 0 2 --' C H 2 0 + C H O + M --' C O + CH2 + M + O --' C H O + C H O + O H --' C H C O + H 2 0 + H ~ C H C O + H2 0 2 --' C H C O + O 0 2 --~ C H O + C O 0 2 -'~ CO2 + C H * + H --* CH2 + C O

19 20

C H C O + O --' C H O + C O CH2 + 0 2 --" C O + O H + H

(A) (B)

(A) (B) (A) (B)

21 22 23

24 25

CH2 + 02 ~ C O + H 2 0 CH2 + H --' C H + H2 CH2 + O ~ C O + H + H CH20 + M ~ C H O + H + M C H 2 0 + H --" C H O + H2

(B)

4.1 + 0 8 4 . 3 + 14 1.0 + 14 5 . 0 + 14 2 . 7 + 14 4 . 0 + 12 3 . 6 + 15 1 . 0 + 13 1 . 0 + 13 3 . 0 + 13 6.0+11 2 . 4 + 12 4 . 5 + 15 1 . 5 + 13 2.5 + 13 1.2 + 12 1.3 + 13 9.1+12 3 . 9 + 12 4 . 0 + 13 5 . 0 + 13 5 . 0 + 16 2.5+13

-7.2

1.5

EA

Reference

447 192 213 11

W a r n a t z 1984 T a n z a w a 1980 Kiefer 1985 W a r n a t z 1984 W a r n a t z 1984

7 51 48 60 63 - 1 248 25 11 36

W a r n a t z 1984 W a r n a t z 1984 This w o r k This w o r k This w o r k Slagle 1984 W a r n a t z 1984 Estimated H w a n g 1984 Flwang 1984 L a u f e r 1984 L a u f e r 1984 Estimated This w o r k This w o r k W a r n a t z 1984 This w o r k This w o r k This w o r k W a r n a t z 1984 W a r n a t z 1984 W a r n a t z 1984 W a r n a t z 1984

105

6 6 6

320 17

ACETYLENE

INDUCTION

ZONE

67

EXOTHERMICITY TABLE 1 (continued)

Reaction

A

m

26 27 28 29 30 31 32 33

CHaO + O ~ CHO + OH CHzO + OH ---' CHO + H:O CH* + M ---' CH + M CH* + 02 ~ CH + 02 CH* ~ CH + h~, CH + 02 "" CO + OH CH + O --' CO + H CHO + M --' CO + H + M

3 . 5 + 13 3 . 0 + 13 4 . 0 + 10 2 . 4 + 12 1.9+06 2 . 0 + 13 4 . 0 + 13 2 . 5 + 14

34 35 36 37 38 39 40 41 42 43

H + 02 ---' OH + O O + H2 --* OH + H OH + H2 ---' HaO + H OH + OH ~ HzO + O H + 02 + M "--' HO~ + M HO2 + H --' OH + OH HO2 + H ---, H2 + 02 HO, + OH --' HaO + O: H2 + M --' H + H + M CO + OH ~ CO2 + H

7 . 8 + 15 1.5+07 1.0+08 1.5+09 7 . 0 + 17 1.5+ 14 2 . 5 + 13 2 . 0 + 13 2 . 2 + 14 4.4+06

Reference

Ea

15 5 0.5 0.5

70 -0.6 2.0 1.6 1.1 -0.8

70 32 14

4 3 402 -3

1.5

Warnatz 1984 Warnatz 1984 Hwang 1984 Hwang 1984 Becker 1980 Warnatz 1984 Warnatz 1984 Warnatz 1984 Warnatz Warnatz Warnatz Warnatz Warnatz Warnatz Warnatz Warnatz Warnatz Warnatz

1984 1984 1984 1984 1984 1984 1984 1984 1984 1984

Units are mol/cm 3, s, and kJ. Reverse reactions were automatically included in the computer program through equilibrium constants computed from polynomial fits to standard thermochemical data. The basic thermochemical data source was the I971 JANAF table (Ref. [39]) with the following emendations. For Call3, C4H2 and C4H3 the data of Duff and Bauer (Ref. [40]) were used. The JANAF enthalpy of formation of C:H was replaced by the value of Okabe and Dibeler (Ref. [41]). (This research was nearly completed when the revision proposed by Wodtke and Lee, Ref. [42], was published.) The thermochemical properties of CHACO were taken from Stull et al. (Ref. [43]). The properties of CHCO were derived from the properties of CHACO using the assumption that the C - H bond dissociation energy in CHACO is the same as that of C2H4. The difference between the bond dissociation energy used (Ref. [40]) and the value indicated by more recent determinations (Ref. [35]) is too small to affect any of the CHCO rate constants enough to change the profiles computed in this work. The thermochemical properties assigned to CH* were those of CH except for adding the term level of CH 2h (Ref. [44]) to the enthalpy of formation. The literature references for rate constant expressions are to Refs. [28] and [33-38]. The combined rate constant for reactions 20 and 21 is for both cases (A) and (B) the recommended overall rate constant for consumption of CH2, the division between 20 and 21 for case B being the relative channel efficiency recommended in Ref. [45]. Reactions of HO2 (CHO + 02 ~ CO + HO2 and CO + HOa ---' CO2 + OH) and the reaction of CHO with O (CHO + O --' COs + H) with the rate constants recommended by Warnatz (Ref. [33]) were included in a number of flame and ignition simulations, but were found to make no significant contributions.

RESULTS

together with indications of the error limits and m o d e l i n g r e s u l t s in F i g s . 2 a n d 3.

The form of the refractive index gradient profiles

As the refractive

index gradients

are the net

is s h o w n in F i g . 1. T h e e n d o f t h e i n d u c t i o n z o n e

results of a large number

is m a n i f e s t e d b y a v a l l e y in t h e r e c o r d t h a t s t a r t s

proceeding

e s s e n t i a l l y at z e r o r e f r a c t i v e i n d e x g r a d i e n t b u t n e v e r q u i t e r e t u r n s to z e r o , w i t h t h e l o n g t e r m

interpret them without computer simulations based upon assumed reaction mechanisms. Accounting

behavior characteristically showing evidence of s o m e i n s t a b i l i t i e s in t h e w a v e p r o p a g a t i o n . O u r

for the data was first attempted using the reaction mechanism and rate coefficient expressions of R e f . [ 2 7 ] . It w a s i m m e d i a t e l y a p p a r e n t t h a t t h e

i n t e r e s t h e r e is in t h e s h a p e o f t h e v a l l e y , w h i c h w e c h a r a c t e r i z e b y its d e p t h a n d its f u l l w i d t h at h a l f height.

The

depth

and

width

data

are

shown

computed always

of elementary

simultaneously,

refractive

too large,

index

there

reactions

is n o w a y

gradient

depth

with any combination

to

was

of rate

68

S . M . HWANG ET AL. 100

(a)

(b)

N I,

tm

,I

a

m

~s

Fig. 1. Typical experimental records of laser beam deflection. The positive signals correspond to incident shock front passage. The induction time tin, schlieren depth D, and schlieren width at half-maximum W are defined as indicated. (a) 0.5% C2H2, 1.25% 02, 98.25% Ar mixture, 7"2 = 1785K. (b) 0.5% C2H2, 5.0% 02, 94.5% Ar mixture, T2 = 1620 K. The original oscilloscope trace photographs for these runs are given in larger scale in Ref. [27].

lO

4

I 5

6

l 7

10 k K / T

Fig. 3. Full width at half-depth of the refractive index gradient valleys, in/~s laboratory time. Symbols and lines as in Fig. 2.

10 4

T

m13

,.-i o2

•

-

x

4t'~A

A

10 -7

"~A

/k

I

I

I

5

6

7

10 k K / T

Fig. 2. Maximum refractive index gradients: &, C2H2 : 02 Ar = 0 . 5 : 1.25:98.25; I I , C 2 H 2 : 0 2 : A r = 0 . 5 : 5 . 0 94.5. Open symbols show maximum refractive index gradients computed using the mechanism and rate constant expressions of Miller et al. (Ref. [26]). The bars indicate reading errors from the experimental deflection traces. The lines through the data are computed results using the mechanism and rate coefficient expressions given in Table 1. The computed values with and without inclusion of CH2 + 02 "" CO + H20 (cases A and B of Table 1) are so close to one another that a single line describes both simulations.

coefficients that could come close to reproducing the correct overall rate of the induction zone reactions, e.g., for computing correct ignition delays to the maximum valley depth. The reason was found by trial and error to be the high exothernficity and chain branching caused by the reaction of CHz with 02, which in the Ref. [27] mechanism was assumed to give the products CO2 and two H atoms. Only by changing the product channel to give CO was it possible to reduce the computed maximum depths so as to agree with the experimental values. When this was done, close agreement with experiment could be reached after minor adjustments of rate coefficients, as given in the entries of Table 1 for reactions 8, 9, 18, 20, and 21. The rate coefficients derived depend on whether CO + H20 is also included as an output channel for CH2 + 02, as suggested by the results of Shaub et al. [45]. The fits to the schlieren data with and without the CO + H20 channel are so close to one another that they are represented as single lines in Figs. 2 and 3. The fit to the tm data is likewise essentially identical for both choices and identical also to the fit shown in Fig. 2 of Ref. [27]. It was found that elimination of the reaction of CH2 with 02 entirely led--inevitably--to complete incompatibility of model predictions with

ACETYLENE INDUCTION ZONE EXOTHERMICITY both the literature and the present data; within the context of the assumed mechanism the only route found to reconcile computation with experiment was modifying the product distribution of the reaction of CH2 with 02. (In some earlier models of acetylene ignition--Refs. [18], [26], [27], [28], [33]--the CH2 + 02 --* C O 2 4- 2H reaction has been included; in others--Refs. [19], [20], [21], [25]--it has not. See discussion.) Sensitivity spectra were computed for the two mixtures in three ways: by setting individual rate coefficients to zero and by multiplications and divisions by 5 [46]. The results are shown in Figs. 4 and 5. Since the rate coefficient revisions required to fit the schlieren data have substantial effects upon the C2H profiles during the induction zone, we recomputed the integrated CH* profiles for comparison with the experimental data of Amrich [47]. Assuming that CH* is generated from C2H 4- O 2 at a rate whose temperature dependence is given by an Arrhenius expression with the activation energy derived by Matsuda et al. [20] and A-factor adjusted to match the observed integrated emission intensity, the radiative and quenching rate coefficients listed in Table 1 imply the comparison shown in Fig. 6.

69 2.4

30

7,9

+0.4 >'- +0.2 I.-H > I--4

o.0

O3 Z ~/~ -0.2 -0.4

2 5 6 7

8 g

i..-.!

i.-..i

-41.9

..41.9

18 20 22 31 34

REACTION NUMBER (b) k x t / 5

+0.4 )"

I--

+0.2

I.k-I O3 Z

0.o

Lm.! mL-mj-JI

-0.2

-o. 4 -0.6

2 5 6 7

8 9

18202234

REACTION NUMBER (c) k x 5 +0.4

FLAME MODELING +02

The conclusions drawn from these shock tube experiments suggest that models previously used for interpretation of laminar flames do not provide adequate description of the ignition process. The question then arises as to the ability of the Table 1 mechanism to account for flame speeds and profiles. To investigate this question a set of free and burner-stabilized acetylene flame computations was carried out using the approach and computer programs of Warnatz [24]. The computed laminar flame speeds are compared to the literature data in Fig. 7 [48-56]. It is seen that for lean and stoichiometric flames the computed speeds run through the center of the data spread, while for rich flames the computed speeds appear to be about 20 cm/s slower than measured. The leanest laboratory flame modeled was that of Eberius et al. [6], a 3% C2H2 in 02 flame

0.0

"

CO - 0 2

-0.4

2 5 6

7 8 9

REACTION

18202234-37 NUMBER

Fig. 4. Sensitivity spectra for C2H2 : 02 : Ar = 0 . 5 : 1 . 2 5 : 98.25, Pt = 1.33 kPa (10 Tort), 7"2 = 1700K. Ordinates are absolute sensitivities defined as (Y(0) - Y(std))/Y(std) in (a) or logarithmic response sensitivities (Ref. [46]) in (b) and (c). Reaction numbers are listed in Table 1. Open boxes = t m sensitivity. Filled boxes = schlieren width sensitivity. Dashed boxes = m a x i m u m refractive index gradient sensitivity. (a) Sensitivity computed setting rate coefficents to 0. (b) Sensitivity computed setting rate coefficients to 1/5 of Table 1 values. (c) Sensitivity computed setting rate coefficients to 5 x Table 1 values. All sensitivities greater than 0.04 are shown.

70

S. M. HWANG ET AL.

(a) k x 0

47 2,8

.

13

+0.4

10 -lo

>'- + 0 . 2 I---

ee

5'

m ~--

0.0

ii

Z ~_~ - 0 . 2

!

!

i

Li

%

• %

_J 0

i

r-1

%

-0.4

u --0.7 :....,~ -4).9

2

6

9 18 20 34 37

8

REACTION

I 4

10-11

NUMBER

J

I 5

IOkK/T Fig. 6. Computed and experimental integrated emission intensities of CH*; 0 , experimental data (Ref. [47]); © , computed with the Table 1 mechanism case A; O, computed with the Table 1 mechanism case B.

(b) k x 1/5 +0.4

>'- + 0 . 2 I.--

P--

~

0.0

i

i

I!

Z ~

-0.2

. . ' ~ .

-0.4

,Irx~rt~ -, •

150

•

52

6

~II s

•

9 18 20 34 37

8

i*"

•" REACTr0N

(c) k

NUMBER

•

>-

~'.

..

o 100

5

x

•

"'.

+0.4

-:

...... ! >-

+0.2

H ~--

0,0

z z rY

I i......

co

.....

Z ~0~ - 0 . 2

I

I

50 I 5

I 10

I 15

PERCENT ACETYLENE -0.4

2

5

6

7

REACTION

8

9

18 34 37

NUMBER

Fig. 5. Sensitivity spectra for C2H2 : 02 : Ar = 0.5 : 5.0 : 94.5, PI = 1.33 kPa (10 Torr), 7"2 = 170OK. Axes and notation as in Fig. 4.

Fig. 7. Computed and experimental laminar flame speeds. Solid line = computed with the Table l mechanism. Dotted line = computed by Warnatz (Ref. [24]). I , Smith, Ref. [48]; O, Bartholom6, Ref. [49]; &, Linnett et al., Ref. [50]; I , Friedman et al., Ref. [51]; 0, Gilbert, Ref. [52]; ~ , Gibbs et al., Ref. [53]; * , Scholte et al., Ref. [53], ~l[, Rallis et al., Ref. [55]; *, G0nther et al., Ref. [56].

ACETYLENE INDUCTION ZONE EXOTHERMICITY 0.06

(a)

1500

• •

71

•

1200

0.10

T O.OB

9OO

m H

1000 " tEl ~

0.04

%

z o

0.06 600

cw --5

0.02

500

uJ i---

~0.04 o

2 ,,=, i--

30O 0.02

J\*

i

I

5

10

1

15

2

3

DISTANCE/MM

DISTANCE/MM (b) 0.

004 I

(b)

0.004

L

=t +~'~

H20/I 0

z

,.':F o 002

"~ 0. 002 .._J o

LtJ "5

r.E .j:o 4.e¢ 0

~111 5

4'

I

I I

I

10

0

15

DISTANCE/MM Fig. 8. Computed and experimental species and temperature profiles for 3 % C2H2, 9 7 % 0 2 , flame at 76 Torr (Eberius et al.,

I

I

I

1

2

3

4

DISTANCE/MM Fig. 9. Computed and experimental species and temperature profiles for 4 . 6 4 % C2H2, 9 5 . 3 6 % 0 2 at 40 Torr (Vandooren and Van Tiggelen, Ref. [7]).

Ref. [6]).

burning at 76 Torr (Fig. 8). The agreement between computation and experiment is at the level generally found in flame modeling except for the CO and CO2 profiles, where it would appear that the model overpredicts CO and underpredicts CO2. Profiles for a second lean flame, studied by Vandooren and Van Tiggelen [7], are shown in Fig. 9. For this flame there is again an expected level of semiquantitative agreement, aside from the CO and CO2 profiles, except for the additional feature that the observed peak in the H2 profile is not reproduced in the computation. Profiles for the near-stoichiometric flame stud-

ied by Porter et al. [5] are shown in Fig. 10. For this flame the match between observed and computed CO and CO2 profiles is much improved over the lean cases; in fact all of the major species profiles show satisfactory agreement. The major disagreement seen is in the OH profile, which is computed to be about a factor of 4 lower than observed at the maximum and to be much more sharply peaked. The final flame modeled was the rich flame studied by Wenz [571 (Fig. 11). For this flame the CO and H2 profiles are computed to rise about 2 mm earlier in the flame zone than observed, the agreement being otherwise satisfactory.

72

S . M . H W A N G ET AL. 0.12

z

1800

(a)

009 /..

•

o

•

•

•

•

*

I.-I

,-

C3

,.=0.06 ,.,

~k/-

,I* h

',_.

7'

(a) 2000

- 1200

& & & 'a' & A

.,," ,'-

0.3

.<

Z

%

o0.2 H

%

,.,.< w

L~

-6oo

1000 ~

..~ 0.1

C02

,=~,~ii 20

40

DISTANCE/MM

60

A & & & & & &

I

5

10

DISTANCE/MM

o. 12. (b)

• 5

(b)

021

0.09~ z o a

oo6F

No ~ ~

L~j O. I 0

. . . .

• • •...2o

\ * 02 0

20

40

DISTANCE/MM

60

5

10

DISTANCE/MM

15

Fig. 10. Computedand experimental species and temperature profiles for 7.8% C2H2, 12.3% 02, 79.9% N2 at 18 Torr (Porter et al., Ref. [5]).

Fig. 11. Computed and experimental species and temperature profiles for 23.6% C2H2, 21.4% 02, 55 % Ar at 90 Torr (Wenz, Ref. 157]).

DISCUSSION

+ CO ---' CO2 + H. The success of the Table 1 mechanism in accounting for the profiles leads to the conclusion that whatever shortcomings the mechanism may have, it does describe the heat release profile adequately. We found by numerous modeling checks of other shock tube experiments (as presented in Ref. [27]) that the modifications which distinguish the Table 1 mechanism from its predecessors have essentially no effects at all upon the quality of match to the literature data as described previously. Within the scatter of the literature data there is thus no apparent possibility to improve upon the quality of match by adjustment of rate constants. In this respect the Table 1 mechanism should be regarded as superseding

Refractive index gradients are measures of the heat release rates, and so the traces analyzed here essentially measure the net overall exothermicity of the induction zone reactions. The failure of the first trial mechanism to account for the depth of the profiles can be attributed directly to the assumed mechanism being too exothermic. In chemical terms, the computed production of CO2 led to too much heat release; thus it must not be a part of the main chain reaction. Instead, CO2 production in the induction zone must proceed mainly by secondary routes, including the one traditionally assigned for hydrocarbon flames, OH

ACETYLENE INDUCTION ZONE EXOTHERMICITY previously proposed reaction mechanisms in which CO2 is produced from the reaction of CH2 with 02. Whether major extensions of it--reactions of C4H2 and of C3-species are not considered, for example--will permit improvements remains to be seen. The C2H profile generated by reaction 9 would be responsible for essentially all of the CO2 produced in the induction zone, by the further reaction (not included in Table 1) with 02 to produce ground state CH and CO2. The amount of CO2 actually produced in the induction zone is apparently enough to generate an exponential growth of ir emission at 4.2/~m [18], although the conclusion that the growth constants of CO and CO2 must be equal has been questioned [20]. From the limited information in the papers of Dove and Moulton, Glass et al., Homer and Kistiakowsky, and Jachimowski [15, 18, 19] it would appear that CO2 production is seen at the end of the induction period essentially synchronously with CO. In any event, the Table 1 mechanism generates equal growth constants for CO and CO2 during the exponential growth phase, the CO growth falling off at the end of the ignition delay as the OH + CO reaction comes into play. As discussed before [28], detailed analysis of the Homer and Kistiakowsky and Jachimowski records, or new CO and CO2 profiles by laser absorption spectroscopy, would give critical information to calibrate the induction zone reactions for providing a correct phase relationship between CO and CO2 at the end of the induction zone. The satisfactory agreement between computed and observed quantum yields for CH* emission supports the C2H profiles and related rate coefficients as being essentially correct. This then leaves the previously discussed conflict between computed and observed OH profiles as the second remaining unresolved difficulty in modeling the ignition of stoichiometric and fuel-lean mixtures [27, 28]. The modifications introduced into the mechanism here did not affect the relative time of appearance of OH. We note that the rate constants derived for reactions 8 and 9 are larger than previous suggestions; at our midrange temperature of 1700K, ks and k9 are factors of 2.8 and 1.2 larger than the recommendation of Warnatz [33]

73

for OH + C2H2 ~ products; see also Smith et al. [58], who suggest a rate constant expression for the high temperature reaction that gives 0.3 of the Warnatz recommendation at 1700K. The Table 1 mechanism considers C H 2 tO be unreactive to C2H2, which is unlikely to be the case. It would be useful to have more direct experimental data on CH2 profiles under conditions similar to the ones used in this work so that at least the rate constants for other CH2 reactions could be found. If the high temperature reaction of CH2 is inserted at a suitably high rate, the reactions of C3-species will have to be added to the reaction mechanism. Comparison of the conclusions drawn herein and in our previous studies of C2H2 ignition [27, 28] with the results of Miller et al. [26]--whose mechanism can be seen in Figs. 2 and 3 to be incompatible with our data--is difficult because of the large number of reactions included in their mechanism (77 C/H/O reactions in addition to H2O2-CO chemistry, compared to 28--of which 4 involve CH*--in our work) and the absence of a formal sensitivity analysis in their paper. The additional reactions asserted by them to be essential for flame modeling may be reasonable elementary reactions, but the matches shown in their paper are no better overall than the matches we obtain without such reactions. Aside from the discrepancies between their conclusions and those of the present study and its predecessors [27, 28], we agree with their conclusion that computing CO and CO2 profiles that match reliable flame and shock tube data presents a puzzling challenge to combustion modelers. Nonintrusive--i.e., laserbased--CO, CO2, and temperature measurements in premixed C2H2-02 flat flames and laser absorption profiles of OH, CO, and CO2 in the shockinitiated reaction should be capable of resolving whether the discrepancies noted above may be due to unappreciated inconsistencies in the data rather than shortcomings of computer models. CONCLUSIONS Refractive index gradient profiles in the shockinitiated ignition of C2H2-O2 mixtures provide information on the heat release profile generated

74

S.M.

by t h e i n d u c t i o n z o n e r e a c t i o n s . T h e e x p e r i m e n t a l profile data could be matched using a 43-reaction k i n e t i c m o d e l . T h e s a m e m o d e l is also c a p a b l e o f accounting for a wide range of shock tube and f l a m e d a t a - - n o t , h o w e v e r , f o r O H p r o f i l e s in the s h o c k - i n i t i a t e d r e a c t i o n o r f o r C O / C O 2 ratios in lean f l a m e s .

A c k n o w l e d g m e n t is m a d e to the donors o f the P e t r o l e u m Research Fund, administered by the A m e r i c a n C h e m i c a l Society, f o r partial s u p p o r t o f this research. This research was also s u p p o r t e d by the R o b e r t A . Welch F o u n d a t i o n a n d the U.S. A r m y Research Office. The f l a m e modeling was carried o u t while one o f us ( M . F . ) was on sabbatical leave at the Institut f i i r A n g e w a n d t e Physikalische C h e m i e der Universitiit Heidelberg; f i n a n c i a l s u p p o r t f r o m the A l e x a n d e r yon H u m b o l d t - S t i f t u n g a n d the hospitality o f J. W a r n a t z are gratefully a c k n o w l edged. REFERENCES 1.

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Received 19 November 1984," revised 29 August 1986