Chemical kinetics in the combustion processes: A detailed kinetics mechanism and its implementation

FrOg. I~ncrgl Comhu~t Sct 1987. ~,o1 13. pp 199 248 Printed in Great Britain All rights reserved

(136U 12~5/X7 $,100+ 5(I Cop}right I[~ 1987 Pcrgarnon JournaN Lid

CHEMICAL KINETICS IN THE COMBUSTION PROCESSES: A DETAILED KINETICS MECHANISM AND ITS IMPLEMENTATION V. YA. BASEVICH Institute oJ Chemical Physics, U.S.S.R. Academy of Sciences, 4 ul. Kosighin'a, 117334 Moscow, U.S.S.R.

Abstract--This paper is concerned with the kinetics mechanism of oxidation of small molecules in the H - C - N - O system. As fuels, hydrogen, methane, methyl alcohol, acetylene, ethylene, ethane, and methylamine were considered. Oxygen, hydrogen peroxide and nitric acid were considered as oxidants. A comparision is made of calculated and experimental data on ignition delays, flame velocities, stabilization limits and product compositions obtained under static conditions, in flow, in flame propagation and in shock tubes. Combustion in turbulent media and promotion of combustion are treated in some detail. The ecological aspects of combustion processes, namely production of NO. CO and hydrocarbons in the flame and the effect of turbulence on their yields, is also discussed. Editors Note--This is a specially invited paper which summarizes extensive work in the Soviel Union on development and validation of kinetic models for combustion. The original manuscript was extensively revised by Professor C. T. Bowman, Stanford University, to conform with English language and usage. N. Chigier, Editor, Progress in Energy and Combustion Science.

CONTENTS Introduction 1. Detailed Kinetics Mechanisms 1.1. H - O system 1.2. H - C - O system 1.2.1. Methane 1.2.2. Methyl alcohol 1.2.3. Acetylene 1.2.4. Ethylene 1.2.5. Ethane 1.3. H - C - O - N system 1.3.1. Methylamine 1.4. Oxidanl--H,O2 1.5, O x i d a n t - - H N O 3 2. Application of Detailed Kinetics Mechanisms to Combustion Processes: Determination of Physico-Chemical and Technical Characteristics 2.1. Spontaneous ignition 2.2. Stabilization limits 2.3. Laminar flame propagation 2.4. Turbulent combustion 2.4.1. Physical characteristics 2.4.2. Kinetic characteristics 2.5. Promotion of combustion 2.6. Chemi-ionization 2.7, Technology: methane-based production of acetylene and synthesis gas 2.8. Ecological aspects of combustion processes Conclusions References

INTRODUCTION

O n e of the most i m p o r t a n t aspects of the theory a n d practice of c o m b u s t i o n is the knowledge of kinetics m e c h a n i s m s , i.e. of the set of e l e m e n t a r y chemical processes which occur in the course of a chemical reaction a n d d e t e r m i n e its rate a n d p r o d u c t yield. A detailed kinetics m e c h a n i s m will describe n o t only a p a r t i c u l a r e x p e r i m e n t carried out u n d e r specific c o n d i t i o n s but also the entire a r r a y of available e x p e r i m e n t a l data. This m e c h a n i s m should

199 200 200 210 210 213 215 216 217 220 220 222 222 223 223 224 225 226 227 231 234 238 239 240 244 244

be sufficiently c o m p r e h e n s i v e to identify b o t h the m a i n route a n d the significant details of a reaction. T h e generality of the m e c h a n i s m will m a k e it valuable for prediction, since it describes a chemical process u n d e r c o n d i t i o n s differing from those used to o p t i m i z e a given scheme. T h e evolution of detailed kinetics m e c h a n i s m s is related to the a d v e n t of electronic c o m p u t e r s which p e r m i t the solution of large systems of kinetics equations. E m p l o y i n g various m a t h e m a t i c a l procedures and 199

200

V. YA. BASEVlCH

using a detailed kinetics mechanism, we can establish the principal stages of a combustion process for any particular conditions and obtain a characteristic reaction mechanism which is generally smaller than the starting mechanism. An objective of the current world-wide intensive investigation into elementary reactions and rate constants is to provide an experimental basis for the devdopment of detailed kinetics mechanisms for various chemical systems. Detailed kinetics mechanisms help to establish the quantitative characteristics of combustion processes, including the rate of energy release and product yields. They are also needed for optimizing and modeling combustion processes. In addition, they are useful in kinetics investigations. For example, the study of the rate constants of elementary reactions requires consideration of all possible secondary processes which may affect experimental results. Here, detailed kinetics mechanisms provide the basis for identifying the main reaction route and separating all secondary reactions. Development of detailed kinetics mechanisms, with subsequent numerical verification over a wide range of conditions, answers the question whether all Ihe aspects of the studied reaction are self-consistent and reliable. Detailed kinetics mechanisms also provide explanations of phenomena which are not evident in the consideration of simple schemes. Specific examples of this are the explanations of ignition limits and the nature of cool flames, The problems involved in the construction of detailed kinetics mechanisms today are due to the scarcity or lack of kinetics data on many reactions which occur in combustion. The rate constant is a most important characteristic of an elementary reaction, which determines the reaction rate. However, quantum chemistry, despite its remarkable advances cannot ensure accurate calculation of rate constants. Theoretical issues pertinent to this area of kinetics are outlined in several review papers and monographs.t -5 For this reason, we have, more often than would be desirable, used estimates of the rates of elementary reactions which cast doubt on the validity of the resulting mechanisms. However, this is not an intrinsic drawback of the detailed kinetics mechanism. As we gain more comprehensive and specific information about the kinetics of elementary reactions, the validity and reliability of detailed kinetics mechanisms will be improved further. The validity can be ascertained by comparing kinetics data for various experimental conditions to calculations based on the detailed kinetics mechanism. Evaluation of the consistency of the findings is one of the tasks of the present study. In these comparisons it is essential to preserve, as far as possible, not only the reaction mechanism itself but also the rate constants used (in other words, we should not optimize the mechanism for any par-

titular experiment). Below we present data obtained by the author with coworkers which generally satisfy the above requirement. Numerous similar investigations were underway at the same time, as is seen from the list of references. Calculations of this kind are rather time-consuming, and during this period of time some new significant reactions may be revealed and some rate constants may be determined more accurately. Thus, when introducing new reactions and rate constants, we have to redo the earlier calculations. Indeed, our calculations have been checked, selectively, for particular experiments which represent a diversity of experimental data, so as to eliminate the effect of systematic errors and to encompass a sufficiently wide range of conditions. The aspects treated below, important as they are, constitute just a small portion of general kinetics theory whose basis is outlined in several fundamental monographs and treatises; see, for example Refs 1, 2, 4-10.

I. DETAILED KINETICS MECHANISMS

The number of fuels and oxidants used in practice and important for the theory of combustion is very large. The commonly used fuels often have complex multicomponent compositions. At present, however, detailed kinetics mechanisms have been developed only for a limited number of simple fuel-oxidant combinations. Some of these are treated in the following discussion. Complex fuels can be represented by simple ones, and the latter often find practical'applications, 1.1. H-O System The main features of chemical processes described by kinetics mechanisms can be demonstrated using, as an example, hydrogen oxidation. The hydrogen-oxygen system is the simplest one among combustible gases. The overall reaction is written 2H2 + O 2 = 2 H 2 0 , which does not correspond to the actual process and indicates merely that two hydrogen molecules and one oxygen molecule ultimately produce two molecules of water. This act of a termolecular collision resulting in the production of water, as a chemical process, is not realizable in practice because of its extremely slow rate. Quantum chemistry is able to account for the slow rate of this process but cannot as yet provide a complete theoretical calculation of hydrogen oxidation. Here, experiment must be used to assist in developing a model for the oxidation process. It is evident from experiments that there are several elementary steps resulting in hydrogen oxidation and production of water. Experiments have shown that this conversion gives rise to unstable species, namely highly reactive atoms and radicals,

Chemical kinetics and to relatively more stable molecular products. The unstable species react with each other, with the initial components and the reaction products, thereby affecting the entire process of chemical conversion. In the hydrogen-oxygen system, these species are the H and O atoms, hydroxyl OH, hydroperoxyl HO2 and hydrogen peroxide H202. Their rate of formation and concentrations can be recorded using modern experimental methods, which enable us to establish the reaction mechanism (for a more comprehensive discussion of the approach see monographs and review papers). 2~ The hydrogen oxidation mechanism has become one of the first detailed kinetics mechanisms whose study has elaborated and verified many basic concepts of chemical kinetics, among them the theory of branching-chain processes. 1.2.6- ~.~1- i3 Now let us outline briefly the main kinds of elementary chemical reactions occurring in the gasphase, including hydrogen oxidation, and point out their contributions to the overall reaction process. A unimolecular reaction is written as a process with a single initial component (say, molecular hydrogen) resulting in its decomposition or isomerization; for example, H2=H+H. In accordance with the law of mass action, the rate of reaction is W=

d[H2] dt

-

k~[H2],

where [H2] is the hydrogen concentration, t is the time, k~ is the rate constant of a unimolecular reaction for high pressures (for low pressures, there is a different reaction rate law: see below). The ordinary empirical expression for the rate constant of a unimolecular process (and of any other elementary reaction) has the form k~ = A ~ T"exp( -

E~/RT),

where A~ is the preexponential factor, E~ is the activation energy, T is the temperature, n is the exponent of the temperature (it is often taken that n=01 and R is the gas constant. As a rule, the reaction rate constant k increases with a rising temperature (E is positive). A unimolecular reaction proceeds in this way only at sufficiently high pressures, where the ratedetermining step of the process is the decomposition of a molecule. At low pressures, the slowest process determining the reaction rate is bimolecular activation of a decomposing molecule on collision with a particle (M), atom, radical, or molecular product, which remains chemically unchanged. This process is written as follows (the numbers correspond to Table 1, the negative sign designates the reverse process): H2+M=H+H+M.

(-11)

201

The rate of this bimolecular reaction is given by d[H2] W -

dt

-

k - l , .o[H23" [M],

where k_ ~~,0 is the rate constant for low pressures. For moderate pressures, both the activation and decomposition of a molecule are significant. In the two cases of our example, there is an initiation reaction giving rise to active centers, since two unstable species are produced which are ready to react chemically. Bimolecular reactions involve two partners participating in the chemical process: H2+O2=H+HO2, H+O2=OH+O. H 2 + O H = H z O + H, H2+O=OH+H.

(-17a} t-41 {11 1-61

The first of these reactions { - 17a} is an initiation reaction; reaction (11 is a propagation step, where the interaction of a molecule with a radical will again produce a molecule (here the final product, watert and an active species (atom H). Processes t - 4 ) and ( - 6 ) are the so-called branching reactions, where the reaction of a single active center will produce two active centers capable of chain propagation, and the reaction may be highly accelerated. The maximum number of participants is found in a termotecular reaction, for instance: H+H+M=H2+M,

(11)

H+OH+M=H20+M.

(13)

Here the particle M removes energy otherwise the hydrogen or the water molecule could decompose again to the initial components. This kind of recombination reaction will cause chain terminatmn: a stable molecule forms instead of the two active specials capable of accelerating the reaction. The rate of a termolecular process (111 is dH W. . . . dt

k~,o[H].[H].[M ],

where k~l.0 is the corresponding rate constant. Uni-, bi-, and termolecular reactions are the only possible elementary chemical processes in the gas phase. Referring again to the overall hydrogen oxidation reaction, we note that hydrogen may oxidize by the route involving processes ( - 1 7 a , - 4 , 1, -61 and others. Hydrogen oxidation proceeds only under specified favorable conditions, i.e. temperature, pressure, mixture composition, and some other parameters (heat removal, particle recombination at the wall of a reaction vesselt. Let us take as an example the ignition peninsula for hydrogen-oxygen mixtures.

17 26 27 17d 8 I'4 28 30 14a 29a 32 21 24 43 44 45 47 66 48 70 86 46a 68 69 70a 31 33 35 39 40

H+HOz=OH+OH O + HO_,=O, + O H OH + H O 2 = O , + H_,O H+HO.,= H,O+O OH + H_,O, = H O , + H_,O H + HzO_,= H , O + O H OH + O H + M = H.,O_, + M O + H,O_, = O , + H_,O H + H_,O_, = H~ + HO_, H O , + HOz = H20., + O_, O + HzO_, = H O , + OH CO + OH = CO2 + H C O + HO_,= CO, + OH H_,CO+OH = H C O + H 2 0 H_,CO + H = HCO + H_, H.,CO + O = H C O + O H HCO+ HO,= H2CO+O2 H+CO+M=HCO+M HzCO + HO_, = H , O z + H C O H C O + O 2 = HO2 + C O HCO + O = CO2 + H HCO+H+ M=H2CO+M H C O + O H = CO + H_,O H C O + H = C O + H., H C O + O = C O + OH CHa+OH=CH3 + H20 C H 4 + H = C H 3 + H _, CH,, + O = CH3 + OH CH4 + O=CH_, + H : O CH3 + H O z = C t t 4 + O 2

H+O2+M=HO,_+M

OH+H2=H+H20 OH+O=H+O_, OH+H=O+H., OH + O H = O + H _ , O H+H+M=H.,+M O+O+M=O2+M OH + H + M = H _ , O + M O+H+M=OH+M OH + O H = H_, + O 2 H + HO2= H.,+O,

1 4 6 9 11 12 13 19 83 17a

7

Reaction

No. 15 17 2 17 103 i18 118 101 19 56 47 37 54 71 54 31 66 50 42,5 16 40 14 26 62 45 30 28 26 30 14 17 96 73 88 73 71 17 2 0 34 54

Heat of reaction (kcal/mol) 2,4.10 l° 4,16.109 6,9.109 1,44.10 TM 3,6.109 1,8.109 3,6.10 I° 1,44.10 l° 6.107 6.109 4,14.109 2.10 "~ 6.10 j° 6.109 &10 s 7,8.109 7,05.109 1,61.108 2,8.10 ~° 7.109 2,4.10 l° 2,8.10 ~° 2,9.109 1,33.10 lj 3,6.10 II 6.10 ~° 8,4.10 ~ 5,35.10 ~' 1.108 6-108 6.10 ~° 1,2.109 6,3.108 6.10 TM 6.10 TM 6.108 6.10 ~° 2.10 Ij 2,05.10 ~° 2.10 I° 4,3.10 s

A (mol'l'sec)

0 5 0 8,5 11,6 7,8 7,8 -0,4

-3,2

5,2 -0,78 7,04 0 0 0 0 0 20,4 0 0 0 0 0 0 1,6 4,2 --9,6 6,4 4,2 !,5 6,4 5,7 23 1,5 1,5 5,5 5,6 -- 17 8 7,25 0

Elkcal/mol)

Forward

TABLE I. Combustion mechanism

37 37 41 72 43 77 77

1 37 40

32 32 32 32 34 35 36 37 38

27 28 29 28 30 29 31 32

23(A) 24 25 24 17

20

1,14.1011 7,8.10 '0 1,5.10 t° 1,51.10 II 1,74.1013 7,4.1013 8,3.1014 3,1.1013 2,5.109 1,1.10 l° 5,7.1012 i,62.109 9A3.10 ~° 9,9.10 l° 5,28.108 8,45.109 6,4.108 4,07.1013 4,77.10 ~° 1,6.109 3,67.10 II 2,89.109 1,12.1013 4,26.10 j2 1.1011 3,7.10 '~ 2,3.10 l° 3.108 1,6.10 ~ 1,6.'108 5,5.10 ~" 6,8.10 ~~ 5.10 I~ 8,9.10 It 1,9.10 jt 8,5.108 6,9.109 4,8.109 2,2.108 8,3.10 s 6,10 j°

Reference A Imol.l.sec) 20A 15,9 8,9 17 105 120 120 104 39 56 48,8 37.6 54 71,2 54,4 32,6 72,6 42 91,4 20 41,8 20,4 30,4 85 46,4 31 33,4 32 14,7 22 24,4 96 72 88 78 71,6 24.8 12,5 7,0 41,4 55

Elkcal/mol)

Reverse

I

39

39

33

26

21 22

Reference

..<

CHs+H+M=CH.~+M

55 38

('H~ + tt~O~ = CtI,t ~HO_, 42 C H ~ + C H 3 = C H 4 + C H ~ 50 CH3~- H~CO=CH~+ HCO 72 CH3 + H C O = C H , , + C O 53 CH~ + HzCO=CH,, + CO 54 CH3 + O H = C H 2 + H ~ O 59 C H 2 + O = H C O + H 65 CH~+ H 2 0 = H2CO+Hz 57 CH3 + O z = H~CO+OH 56 C H 3 + O = H z C O + H 74 C H O + H , C O = CH3 +CO~ 3d C H , + O 2 = C O + O H + H 4d C H 2 + O z = C O 2 + H + H 87 CHs +O2 + M = C H s O z + M 88 CHsO 2= H2CO+OH 89 CHsOz + C H 4 = CHsOzH + CHs 90 C H s O + O H =CHsOzH 91 CHs + H O 2 = H2CO+ HzO 95 C H + H 2 0 = C H 2 + O H 96 C H + H 2 = C H 2 + H 97 C H + O H = C H 2 + O 98 C H + O H = C O + H 2 99 C H + O = C O + H la CHsOH + O=CH2OH + OH 2a CH3OH=CH2OH + H20 3a CHsOH + H =CH2OH + H2 4a C H s O + HO2=CH3OH + Oz 5a CHs +OH + M=CH3OH + M 6a C H s O = H2CO+OH 7a C H s O + O H = H , C O + H20 8a C H s O + H = H2CO+H2 9a C H s O + O , = H 2 C O + H O 2 1.16 H z C O + H + M = C H s O + M Id C2H2 + O = C O + C H z 2d C 2 H , + O H = C O + C H 3 6e C , H + H + M = C z H z + M 7e C 2 H + H , = C , H , + H 8e C2H + O z = C O + HCO 5d C z H ~ + O , = C H ~ + C O z lb C ~ H 4 + O = C H s + H C O

Reaction

No. I01 14 17 28 71 82 34 79 36 51 68 28 32 57 22 29 13 43 122 8 23 25 177 175 0 17 2 54 92 79 96 81 25 22 73 56 128 25 217 81 43

Ileal of reaction (kcal/mol)

15.8 4,3 9.24 4,5 0 0 2.76 0 2,5 10 0 4,5 3.5 0 2 25 10 0 0 8,9 5,1 4.6 0 0 2 7.27 8.5 52 0 0 0 0 5,3 6A 32 4,64

0 40 0.7

6.109 6.10 ~° 6.109

57

56

54 55

51 51 51 51

50 50 51 51 52 51

30 37 37 37 30 30 30 47 48 30 49 49

3.4.1011 5.107

6.109 6.109 1.109 1,2.109 6.109 6.109 6.109 6,2. l01 i 2.8.10 II 3.2. ! 0 n 4,7.109 2,05.10 s 6.109 2.101'* 7.9.10 s 8,3.109 1,8.10 I° 2,8. l0 s 2.1012 5.2.109 3,3.101° 6.109 6.109

2,73.101~/T

3,3.10 l° 3,8.101 i 1,7.101 i 3,3105 4.10 ~

2,2.101° 9.5.10 9 7,4.10 a'~

2.10 ~4 6,06.10 s 1,9.109 1,5.101~ 7,8.1012 6.10 I~

122 46

9,3 52 69 79 96 81 30,5 30 78 62 96 20

23,2

78,6 38,2 61,6 68,2 32,2 33,8 54,8 30.6 56 23 43 122 18,3 29,5 31 179 177 1

88 19 27.4 33,2 72.2 82,6 37.2

E (kcal/moll

E (kcal/mol) Reference A (mol'l'secl

1.109 6.5.107 6.107 6.10 t° 6.10 t° 6.10 TM 6.109 6.109 6.109 3.10 I° 1,86.101° 6.109 6.109 1.8.10 s 3,6.108 1.10 tz 6.109 6.107 1,2.109 3,1.109 6,6.10 s 3.10 s 6.109 6.109 4,3.109 6.109 1,3.109 2,64.10 s 3,6.109 6.109 6.109 6.10 I° 6.109 1,2.10sT 2.10 j° 7,8.109

Reverse

Forward

(~ontint.'d)

A (mol'l'sec)

TAI.II I. I.

56 56

51

53

50 50 50

45 46

Reference

bo

C2H5 + O2 = C H 3 C H O + OH CH3CHO+ OH =CH3CO+ H20 CH3CHO+ H= CH3CO+ H 2 CH3CHO+ O= CHjCO+ O|t CH3 + C O 2 + O H = C H 3 C H O + O 2 CH3CO+HOz=CH3CHO+Oz C H 3 C O + H202 = C H ~ C H O + H O 2 CH 3 + H C O + M = C H 3 C H O + M CH3 + C O = C H 3 C O CH3CO+ H=CH 3+CHO CH3CO+ O= CH30+CO C2H5 + O H = C 2 H 4 + H 2 0 C2Hs+H=C2H4+H 2

13c 14c 15c 16c 17c 18c 19c 20c 21c 22c 23c 24c 25c

5C 6c 7c 8C 9c 10c IIc 12c

4c

C_,H4 + O H = CH3 + H , C O C_,H4 + OH = CH.~ + H C O C_, H.L + OH = C,H~ + H.,O CzH3 + H_, = C_,H4 + H C.,H3 + HO2 = C2H4 + O., C z H , + H_,= C2H 4 C2H3+O=CH3 +CO C,H3 + O H = C H 3 + H C O C2H3 + H=C2H_, + H 2 C2H3+O2=C,H2+ HO 2 C.,H3 + O H = C2H2 + H 2 0 C_, H3 + O = C_,H_, + OH CH3+CH3=C2Ha+H2 C_,H4+ H + H = CH3 + C H 3 CH3 + C H 3 = CzH,, C2H.+OH =C2H5 + H20 C2Hf,+H=C2H5 +H 2 C2Hc,+O=C2H5 +OH C2H5 + HO2 = C2H~, + O 2 C2H5 + H202 = C / H a + HO_, C2H 5 + O H = C H 3 0 + C H 3 C_,H5 + H = CH3 + C H 3 C2H5 + H = C H , ~ + C H 2 C2Hs + O = C H 3 + H2CO C2Hs + O _ , = C H 3 0 + H , C O

Reaction

2b 2b' 2b" 3b 4b 5b 6b 7b 8b 9b 30c 31c 2e 3e 2C 3c

No.

61 23 8 6 II 48 8 68 3 27 87 85 7O

15 46 17 I 57 41 117 46 63 7 78 61 55 48 83 2O 5 3 51 11 4 15 32 83 55

Heat of reaction (kcal/mol)

6.109 6.109 6.109 6.109

1,5.102T

4 9,6 4 - 1,2 8 0 0 6 0 10 IO l0 10 4 3A 2,3 26,8 17,2 --0,8 --20 6,8 4.80 0 0 0

0

8,4.109

1,8.10 I1 7,4.10 TM 4,6.109 3,2.10 s 4,9.108 3.10 TM 4.10 TM 6.109 6.109 2,4.10 s Case a 6.109 Case b 6.108 C a s e c 6.109 3,4.10 TM 6.109 I,!.10 TM 7AT 1,6.107 4,9.108 7,9.10aT

0,9 0,9 0,9 12,8 -0,2 0 0 0 0 10 0 0 38

E(kcal/mol)

4,5.109 6.109 6.109 5,8.108 1,4.108 2,9.104 6.109 6.109 6.109 6.109 6.109 6.109 2.1013

A (mol'l-secl

Forward

TABLE !. (continued)

64 64 64 64

64

64 66 66 67 64

64

64 65

61 62 63 64

57 57 57 57 64 64 60

58

41,6

6.10 TM

3,2.108 3.10 TM 1,1.109 9,1.108 6.108 3.10 s 6.108 2.1014 2.10 TM 6,6.107 !,6.101° 7,2.109 1,6.109

1,6.10 il 1,4.10 TM 3,8.10 s 6,9.109 &10 s 8.109 6,7.107 3,3.108 2,1.10 s 1,7.10 s

72 28 12,2 9,4 20 30 6 52 16 28 84 80 66

24 14,2 7,0 50 19 IA 12,6 36 80 62

83

12 54 42 !16 46 62 15 76 60

6.109 6.109 1,7.1012/T 2,1.109 1,5.109 6,3.109 1,8.109 23.10 TM 2,8.109

1013

17A

E(kcal/mol)

1,4.109

Reference A [mol.l.sec)

Reverse

64 68

64

64 64

60

57 57 59

Reference

,1-

<

0~

,.<

C2Hs +H2 = C H 3 + C | t 4 C2H~ + H=C2H~, CH~NH2 + O = CH~NH + OH CH3NH2 + O H = C H ~ N H + H 2 0 CH~NH~ + H = C H ~ N H + H2 CH3 + N H 2 = C H 3 N H z CH3NH + H O z = C H 3 N H 2 + O 2 CH~NH + O = C H j O + N H CH~NH + OH = C H , , + H N O CH3NH + H = C H ~ + N H 2 CH~NH + O ~ = C H 3 0 + H N O NH2+H+M=NH3+M NHz+HO2=NH3+O 2 NH2+OH=NHj+O NH2+O=HNO+H NH2+NO=N2+H20 NHz+NHz=NH3+NH NH2+NH=NH~+N NH3+OH=NH2+H20 NH3+H=NH2+H 2 HNO+OH=NO+HzO NH+NO=Nz+OH HNO+O=NO+OH NH+O2=NO+OH NH+OH=NO+H 2 NH+H=N+H2 NH+O=N+OH HNO+H=NO+H 2 NH+NH=NHz+N CH2+NH=HCN+H 2 CH3+N=HCN+H 2 CH+NH2=HCN + H2 CN+H+M=HCN +M CN + H 2 0 = HCN + O H CN+H2=HCN+H CN+OH=HCN+O CN + O 2 = C O + N O CN+OH=CO+NH

z

C2Hs + O = C z H , , + O H C2H4+H+ M=C2Hs+M

26c 27c 28c le 4e 2.1 2.2 2.3 2.4 2.5 2.6 2,7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36

CzHs+Oz=C2H4+HO

Reaction

No. 68 33 14 12 98 15 32 17 81 39 14 40 15 12 104 565 2,5 25 120 15 21 14,5 0 69 93 52 50 69 20 18 55 6,3 117 118 153 122 4 19 21 106 57 . 0 0

6.10 j°

5

6.10

6.109 6.109

0 , 1 3 2 T ~'2~''

6.10 I° 6.10 I° 6.10 ~° 6.10 ~" 6.109 1,83.10"T 5,1.109 6.10 TM

0 0 -9.4 4,1 5,3 - 18,2 0 0

0

0 8

1.84 17.4 0 0 0 0 1.5 4,2

3,2.109 2,7.10 TM 6.10 s I. 109 6.109 5,1.10 ~' 1,6.10ST °'s~ 6.10 z° TM

4

6.10 j°

4 - 15 - 1,4 1,6 0 0 10

69 69 69 69

0

6.10 '~ 3,2.10s T 2,5.10 s 5,7. I 07 6.10 ~ 1,1.10 '~ 6.10 ~°

69 70 71

2,57 0,45 5,3 9,4 -0,35

1,45.10 ~o 6,1.109 6,3.10 I° 5,8.105T 5,5.108 6.10 ~° 6. I 09

69 69

69 82

69 75 69 69 76 73 69 77 78 79 55 69 69 69 69 69 80 69

64

64

0 2 8 9

6.109 3.102T 6,9.109 8,7.10 j°

6.8.109 1,6.10 ~"

1.79T 2,2"''

1,3.109 3,1.10 ~' 2,5.109T ".~,, 2,5.10 t 1.1.10 j 2.8.10 ~ 3,9.10 I 1.5.10 I 2.9.10 ~ 5.7.10 I 5.8.10 I 6.109 3,6.10 I

6.6.109

6,9. I 0 s 6.109 4.5.10 s 6.9.109 1013 2,4.109 9,5.109 2,1.10 l° 10~, 6.109 1,5.109 3.2.10 9 5,3.107 3,1.10 ~ 1.2.10 j3 6.9.109 109 3,8.109 1,4.10 TM 4.3.10 II 2.8.1012 2.109 3,6. 109 1.3.109

E Ikcal/mol) Reference A (mol'l'sec)

(kcal/mol)

A (mol'l'sec)

Forward

Heat of reaction

TABI.E I. (continued)

60

110

15,2 7O 94 53 50 70 25 24 55 15 116 115 154 117 10.5 27 5.2

15.6

64 40 18 21 98 17.5 32 22 84.4 39 14 40 14 15 91 56 4.8 25 122 25 26

83

81

73 69 74

72 69

56

64

E ¢kcal/mol) Reference

Reverse

CN+O=CO+N CN +NO= CO+N2 CN+NH~= HCN+NH 2 HCN+OH=NH2+CO H C N + N H = CH2 + N2 N+HCN=CH+N2 NO+HO,=NO~+OH NO2+ H=NO+OH NO+O+M=NO2+M NO2 + O = N O + O 2 NO+NO+O2=NO2+NO2 NO+NO3 =NO2 +NO2 NOz+O+M=NO3+M NO+ 0 2+ M = NO 3 + M CHa+NO2=CH~O+NO N+NO=N2+O N+O2=NO+O NO+NO=N2+O 2 N+OH=NO+H NO2+OH+M= HNO3+ M OH + HNO3=NOa+ H,O

Reaction 74 149 18,5 24 30 2 8 29 72 46 26 23 49 3 18 75 32 43 49 48 18

0 0 6,9 6 0 9,3 0 0 -8,6 0,6 -0,6 1,3 -7,8 - 1,7 0 0,5 7,5 85 0 0

5,4.107

Elkcal/mol)

6.109 7,2.107 6.109 6.10 a 6,8.10 a 7,2.109 8,7.10 a 2,9.10 t° 5,8.104T 10 l° 4,9T 1,5.107 2,8.107T 7,65T 1,3.10 TM 2,75.10 ~° 1.10 l° 1,41.1012 4.10 TM

A (mol-l.sec)

Forward

93

55 91 92

90

89

88

87

69 84 85 69

3.10 l° 1,3.109 4,8.109 4,2.109 2,8.109 8.10 s 6.109 3,5.10 s 1,1.1013 2,2.109 4.109 7,8.10 s l0 t4 1,2.108 2,46.10 I° 5.10 l° 2.109 2,85.1013 1,5.10 II 6.10 ~

Reference A ( m o l ' l ' s e c )

*The Arrhenius parameters for these five reactions are combined so as to fit the methane cool flame. °a

2.37 2.38 2.39 2.40 2.41 2.42 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.1 1.2

No.

Healt of reaction (kcal/mol)

TABLE I. (continued)

78 154 27 31 30 11 8 29,4 65 46 27 24 43 3,2 18 75 39,4 128 48,6 30,1

E(kcal/mol)

Reverse

88

91

89 89 89 89

89

88

86

Reference

.< ..r,

rrl

.< ..< .>

Chemical kinetics

!10--

"I"

Ix

440

460

480

500

5~0

540

Tt*C)

FIG. I. Ignition peninsula for a stoichiometric hydrogenoxygen mixture.J4

207

and the reaction is accelerated, resulting in ignition, Fig. 2. The subsequent decrease of the reaction rate is attributed to consumption of the initial components. Away from the limit, the reaction leads to a fast and practically complete conversion of hydrogen into water. This is the so-called chain explosion which may occur under conditions of high heat removal without temperature rise. This explosion is impossible without branching processes ( - 4 , - 6). A further increase in the pressure results in the second ignition limit (2), where the termination occurs by the reaction H+O2+M=HO2+M

Fig. 1. It separates the region where the chemical reaction is very slow or does not proceed at all (to the left of the boundary, toward low temperatures) from the region where the reaction is fast. When several elementary processes take place simultaneously their collective properties will be evident. These are described in terms of the theory of branching-chain reactions. Below the first limit (11, the reaction is described primarily by r e a c t i o n s ( - 1 7 a , - 4 ) a n d by chain termination at the reactor wall

which produces the low-activity radical HO2. The reaction rate for the second limit is approximately W = d[H] = 2k _ 4[H]" [O2-1 - k~[H-1 • [O2] • [M] = 0. dt Above the second limit, where 2k_4
H + wall = termination,

H202+M=OH+OH

with an effective rate given by

(7}

(29a)

+M(-28)

and the higher the heat release, making the temperature rise. A general solution for the problem can be approximately obtained using the following system of equations: 2:'16

W = d[H-] = - k ~ [ H ] ,

dt where k,,. is the rate constant of termination at the reactor wall. As the pressure is" raised, the first ignition limit occurs. With allowance for the above reactions alone, the limit is defined by the relation

dnj/dt = ~.W,;

(I)

J

dT

~S

pc ~ = ~ hijWH+-~ ( T -

(II}

U

dH W = - - = 2k_ , [ H ] ' [O2] - k~[H-1 =0. dt When W < 0 , no reaction occurs, whereas with W > 0 , i.e. with 2k-a[O2] > k , , the H-atoms build up

: /

osc

.r /

,2'

4

I l

E

-o.

/ f

02:

•:

g:

/ , , ~ ,,,,,.o.------

.

2 •

_/----

6/" ¢

7 I

/

2.?; ;/ I0

20

30

aO

.... .._o

r

SO 60 'c t s e c ) / 3 7 0

."*

,," "/'0

~0

,. ~I0

I00

FIG. 2. Kinetic curves for the combustion reaction of stoichiometric hydrogen-oxygen mixtures in a static reactor/s To = 758 K. P0, atm.: 14).0111, 24).0106, 3-0.0101.4-0.00965, 54).00925.6-0.0087, 7-0.0083.84).0079 (AP stands for the variations in the pressure, mmHg}.

where n~ is the concentration of the j-th-component, t is the time, T is the temperature, p is the density, c is the heat capacity, WH and ho are the reaction rate and heat of the i-th reaction involving the j-th component, respectively, ¢ is the coefficient of heat transfer to the reaction vessel wall, S and V are the reaction vessel surface and volume, respectively, Tw is the reactor wall temperature. The initial conditions are: t = 0 , n;=n;o, T= T o. Reaction (29a) reduces the role of termination reaction (7), since reaction ( - 2 8 ) is the so-called degenerate branching step, where the branching product is formed and builds up in the course of the reaction. A chain reaction, even if it is unbranched (i.e. if the branching rate is equal to or less than the termination rate), may also result in a thermal explosion, provided it is accompanied by heat generation. The nature of the third limit of hydrogen ignition is related to a chain-thermal explosion. The authors of Ref. 8 and of other studies 1: compiled and generalized experimental data on hydrogen oxidation mainly near the ignition penin-

208

V. YA. BASEV1CH

sula. They listed all the important known elementary steps of this process, Table 1, reactions (1, - 4 , - 6 , 7, - 8 , - 14a, - 11, - 8 3 ) as well as initiation reactions involving ozone, wall termination reactions and the corresponding rate constants obtained experimentally. The cited work outlines the general behavior of simple branching-chain reactions of hydrogen (as well as of hydrocarbons and some other fuels) including those accompanied by heat generation. They contain numerous experimental and theoretical findings and the comparisons substantiate the theory on a quantitative basis. Since the time of the studies cited above, the kinetics mechanism of hydrogen combustion has been refined. Thus, the author of study 17 suggests a mechanism of hydrogen oxidation for conditions away from the ignition peninsula, namely for detonation characterized by high temperatures and pressures. Hence, the mechanism was supplemented by some reactions of bi- and termolecular recombination of active species which are significant in this case due to the high concentrations of atoms and radicals, Table l, processes (11-13, 19, 83). As was elucidated in Refs 18, 19, the mechanism responsible for ignition of hydrogen-oxygen mixtures, which was suggested in Ref. 8 and supplemented by these recombination processes, is applicable to the description of laminar flame propagation, Fig. 3. This follows from the comparison of the calculated and observed rates of heat release in the flame zone at low pressures p. The theoretical basis for the calculations is provided by a system of equations for the stationary one-dimensional propagation of a flame 2'~'16

d dnj/p dn/p d~c DjP ~ - - p°u" dx

d - dx

k

dT dcT - --poUn dx ~-

+ ~,, Wu=O j

at- E

u

huWij=O

(Ill)

(IV)

where x is the coordinate along which the flame propagates, T is the temperature, 2 is the heat conductivity, u, is the laminar flame propagation

,7" -,

0~1.

4-

E "6

oz

0.4

//"2 o8

I.z

ts

Ccm)

FIG. 3. Rate of heat generation in the reaction zone in a low pressure hydrogen-oxygen flame. I-H2]o= 7.2 9;~, [O:]o= 92.8Q,',, To=295K, Po=0.068atm., flame velocity u,= 19.6 cm/sec. 1--experiment, 2 --calculation.

velocity, P0 and p are the initial and the local values of the density, n~ and Dj are the concentration and the diffusion coefficient of the j-th component, c is the heat capacity, Wq and ho are the rate and heat of the reaction of the i-th elementary reaction involving the j-th component, respectively. The boundary conditions for x = 0 and x = 1 (the end of the reaction zone} are T-

PoUnC

nj

•

= To; x=O

u.po dx/I~= o = hi°

dT =0: dxx=l

--dn) x=t = 0 . dx

The heat release rate profile is calculated on the basis of equations of material balance in which the terms related to the formation and consumption of each substance were derived using the kinetics scheme listed in Table 1, namely processes (I, - 4 , - 6 , 7, 11, 12, 17, 28). The temperature T(X) was obtained from a fast-response resistance thermometer mounted in a central-ignition spherical bomb. The rate constants listed in Table 1 were employed in the calculations which were made chronologically far later than the experiments. The parameters used in this calculation can be taken from the relevant references, However, once some new parameters were introduced, their applicability to the earlier calculations was checked in specific experiments. In Table 1, forward reactions are represented as exothermic processes, whereas the reverse reactions are given as endothermic processes. Strictly speaking, allowance should be made for all forward and reverse reactions. In a particular calculation, however, one need take account of only those reactions which contribute to the development of the process. The hydrogen-oxygen mechanism, particularly near the second ignition limit and for higher pressures, involves reactions of hydrogen peroxide. 95 The species forms as an intermediate of hydrogen oxidation, and with due account of its reactions the calculated and the observed second limits of ignition are in excellent agreement, Table 2. This calculation allows for about ten reactions. A detailed kinetics mechanism for hydrogen oxidation over a wide range of temperatures, pressures and mixture compositions will include a greater number of elementary reactions than are involved in the above calculations, and should comprise at least three parts: --descriptions of the initiation reaction, chain propagation, branching and linear termination (the first power of the active species concentration): - - t h e second-order chain termination (the second

209

Chemical kinetics TARL~2. Second ignition limit for a hydrogen-oxygen mixture in a 55 mm dia 200 mm long vessel coated with boric acid 9" To = 773 K. 9~' Mole fraction of O, P. mm Hg

0.72 0.56

0,42

0.28

0,14

Calc.

8 0 . 7 81.4 82.8 85,7 92.6

Exp.

82

83

0.10

0,07

97

102,3 115,6 123,7 133,8

84,5 86.5 93,5 97.5 104

0.035 0.025 0,0175 0,0125

116

123

132

145.1 140.5

power of the active species concentration), namely 1.7 msec. The calculations provide a good qualitative the recombination reactions which are important description of the reactions of H 2 0 2 over a temperwith high concentrations of active species at high ature range 453-1060 K (180 C-787 Ct and for prestemperatures: sures from 0.01 to 6.2 atm. - - r e a c t i o n s involving hydrogen peroxide, which are It has been shown 2~ that neglecting the hydrogen significant at high pressures. peroxide reactions at 803-1038 K, near the ignition peninsula, in the combustion of hydrogen-oxygen A detailed mechanism including over 20 reactions and which considers all of the above processes is given in studies 2"96-99 and presented in Table 1 (the 4~ dl / first 22 forward and reverse reactions). The validity. / 6/ of this mechanism has been checked in a number of calculations modeling spontaneous ignition and flame propagation. ,~ / Figure 4, points 1--4, shows, as an example, the -~ v / II-I measured values of hydrogen ignition delays and ~ 0 A-2 / / v- 3 those calculated using the detailed mechanism. The 11,-4 / D-5 delays were calculated by a standard program, by ~" / o x°6 solving a system of equations of material balance (I). t)-8 The criterion for ignition was an abrupt increase A. 9 / 0-1o in the rate of a chemical reaction. The experimental ., o-II ~v / 0 I -[2 data are for a temperature range 979-2130 K and ~,-13 for pressures from 0.23 to 5 atm. The discrepancy ,/ I I ] I r 2 4 -4 "2 0 between the measured and calculated delays is less t¢'r (sec exp. 1 than an order of magnitude. Consider the reaction of a mixture containing FIG. 4. Comparison of the calculated 3°'L6'97'98 and experimental ignition delays. hydrogen peroxide as an initial compound. Since hydrogen peroxide appears in the mechanism of Table 1, it may be used without any variation. The Composition, o , Reference to investigations of the reaction mechanism for H 2 0 2 N [H:]~ [CH4]o [02]o To, K Po, atm. experiment have been reported elsewhere. F o r example, the author of Ref. 113 studied the thermal decomposition 1 5 -6 979 2 100 of H 2 0 2 and established a rate constant of ( - 2 8 ) . 2 8 -2 1038 5 101 6.7 -13.3 1038 1 102 Reference 32 deals with flow conditions at low 3 1 -1 1453 0.233 103 pressures. The authors of this paper determined the 4 2130 0.365 rate constants of the reactions between H 2 0 2 and H -33 67 979 2 104 5 and O atoms. Using these rate constants, the authors 1453 2 of Ref. 27 performed calculations for the experi6 -2 8 1228 1 102 1453 1 mental conditions in the works. 32']]3 Table 3 lists 10 19 1453 3 105 the values of concentrations of H2, H, O, O2, H 2 0 , 7 -2130 3 and H 2 0 2 in the reaction between H 2 0 2 and O. The 8 -10 19 1453 3 106 experimental data are taken from Ref. 32: the calcu2130 3 -2 3 2130 0.167 107 lated values are taken from Ref. 27. Table 4 gives the 9 9.5 19 979 1 108 concentrations of HzO,, and H O 2 / H 2 0 2 in the H 2 0 2 10 - -9.5 19 1048 1 109 11 decomposition reaction as a function of time. The 1223 1 experimental data are from Ref. 113: the calculated 1336 1 1523 1 values are taken from Ref. 27. Figure 5 plots the yield 17 33 923 0.272 I10 of H 2 0 2 vs initial concentration in its reaction with 12 - -33 67 696 0.347 111.112 the products of a discharge in a h y d r o g e n - o x y g e n 13 748 0.347 mixture containing hydrogen atoms (H =0.04 o~,) and 786 0.347 hydroxyl (OH=0.0114°,,l. at a reaction time of JPECS 13-3-D

210

V. YA. BASEVICH TABLE 3. Product yields for the reaction O + H202 (mol/cm 3 x 10-to) T =453 K. P = 0,0125 atm. (calc., 27 exp.32). 1-!, Time. msec

Calc.

0 5 10 15

. 0,123 0,300 0,439

.

H

Exp.

Calc.

. 0,048 0,152 0,304

. 1,32 1,94 2.21

O

02

H,O

H:O2

Exp.

Calc.

Exp.

Calc.

Exp.

Calc.

Exp.

Calc.

Exp.

1,12 1,88 2,40

19.5 15,3 13,0 11,5

19,5 17,3 14,9 13,9

. . . 3,36 2,52 5,30 4,20 6,46 5.25

. 0,952 1,55 1.91

0,65 0.91 1,10

4,60 2.83 1,77 1.13

4,60 3,30 2.47 1,55

TABLE 4. Thermal decomposition of H 2 0 2. [ H 2 0 2 ] o = 0,13 %. T = 1060 K, P=6,2 atm./calc., 27 exp.SZ). [H202]" 104 mol/l

[HO2] : [HzO2] o

Time, m sec

Calc.

Ex p.

Calc.

Exp.

0 0,05 0.1 02 0,3 0A

0.935 0,802 0300 0,538 0.417 0,328

0,935 0,814 0.698 0.520 0,386 0.297

--0,030 0,027 0.023 0.020 0,017

-0,058 0,071 0.061 0,053 0,046

,z.*

7.n! s, z.~

O. (,/.)

2S

OS

0.5 2O

0

,< O.Z

lit

0

°%.

0

or,..

O

S

-e~ e .

O ' O O I L+ ~ + 0,003

o

I

IS

I

17.~

1

20

I 22.5

o

25

[ H2Oz] o x I0 3 (% }

OH + . I s [ HZ| 0 |'1.1

+

4I IO

FIG. 5. H202 yield vs initial concentration. 27 [H]o=0.04%, [ O H ] o = 0 . 0 1 1 ° / To=803 K, Po=0.01 atm.. t = l . 7 m s e c . Symbols--experiment: curves~alculation.

FIG. 6. Reaction products of the atomic oxygen flame hydrogen, za I-O]o=0.5 °/.., 1O21o =0.82 %, T = 1160 K, P = 0.01 atm., t=2.5 msec.

mixtures m a y result in a p p r e c i a b l e errors, a l t h o u g h at t e m p e r a t u r e s exceeding 1200 K these reactions m a y be neglected. As the kinetics a n d the rate c o n s t a n t s are defined m o r e closely, h y d r o g e n c o m b u s t i o n can be described m o r e accurately a n d reliably. T h i s is confirmed by the c o m p a r i s o n of the calculated a n d o b s e r v e d yields of p r o d u c t s o b t a i n e d in Ref. 28 for an oxygen a t o m - h y d r o g e n flame, Fig. 6. T h e calculated characteristics of c o m b u s t i o n are presented below. T h e kinetics m e c h a n i s m of h y d r o g e n c o m b u s t i o n is also given. 1,4- t 17

1.2. H-C-O System 1.2.1. Methane T h e experience in the a p p l i c a t i o n of the h y d r o g e n c o m b u s t i o n m e c h a n i s m has revealed that a chemical reaction can be described to satisfactory accuracy for various physical conditions. Hence, the next step is to c o n s t r u c t a detailed kinetics m e c h a n i s m for m e t h a n e o x i d a t i o n , including a kinetics scheme of c o m b u s t i o n of c a r b o n m o n o x i d e a n d f o r m a l d e h y d e formed as intermediates.

Chemical kinetics Methane is the simplest hydrocarbon fuel and also is a fuel used in practice. A lot of facts on the kinetics of its oxidation, mainly for a low-temperature range ( <900 K), are summarized in monographs and papers, see Refs l, 6, 12, 13, l l l , 112, 118-120. Using the results on low-temperature oxidation and high-temperature kinetics in flames, the authors of Refs 43, 48, 121-123, have shown that the reactions involving the active species of a hydrogenoxygen flame (OH, H, O) and hydrogen proper also are important in methane oxidation. They suggested a mechanism which has been generally used in later work. Thus, according to Ref. 121 methane oxidation in flames proceeds as follows CH4 + OH = CH 3 -k H 2 0

(31 )

C H 4 + O = C H 3+ O H

(35)

CH 3 -4-0 2 = H2CO "4-OH

(57)

H2CO + OH = HCO + H 2 0

(43)

HCO + OH = CO + H 2 0

(68)

CO + OH = CO 2 + H

(21 )

H+H20=OH+H

2

O+H2=OH+H 2OH=H20+O

(-l) (-6) (9)

H+O2=OH+O

(-4)

O+O+M=O2+M.

(12)

Basic to this mechanism are the reactions of O and OH with the initial reactant methane, and the degenerate branching reactions of hydrogen. The main conversion route corresponds to the sequence

211

spin-forbidden reactions (in accordance with the Wigner rule). An analysis has revealed that the CH radical does not play a major role in the methane oxidation process. Hence, neither this species nor its reactions have been included in the mechanism. The kinetics mechanism considered is tabulated in Table 1, reactions (1)-(74). Here, certain well-known reactions are absent, for example, the recombination of methyl radical to produce ethane by 2CH:---~C2H 6. Similar reactions result in the formation of other hydrocarbons. These reactions are followed by reaction of these hydrocarbons with active species. Including these reactions would render the mechanism very complicated. Within this mechanism, chain termination due to methyl radical recombination by the above-mentioned route is simulated by reaction (42). Rate constants were taken from the literature; when data were not available, the activation energy was calculated using semiempirical formulas: ~ E = 11.5-0.25h for h~<46 and E = 0 for h > 4 6 with exothermic reactions; E = 11.5+0.75h for endothermic reactions; (h being the heat reaction, kcal/molk the preexponential factor for a bimolecular reaction was taken to be about A = I 0 - ~ cm3/molec.sec (6.109 l/mol, sec). The values of A and E of the reverse reactions were calculated from the equilibrium constants taken from Ref. 127. If the activation energy is less than the heat absorbed, then the activation energy of the reverse process is negative. In this case, extremely high values of the rate constants are obtained at low temperatures, In general, the deviation of a rate constant from the Arrhenius relationship at

_-

CH4--*CH 3--*H2CO--* H CO---*CO--*CO 2 during which molecular hydrogen and water also form. Quantitative calculations, restricted approximately to the framework of the above mechanism, have been carried out also in Refs 124-126 where the authors compare calculations with experimental results. In calculations conducted practically simultaneously (published in Refs 97, 98 and then in Refs 30, 99) an attempt was made to elucidate the extent to which the reaction scheme based on this mechanism, but including many possible elementary reactions, provides a general description of methane oxidation. The basis of the scheme to be checked was provided by the detailed kinetics mechanism of hydrogen oxidation to which many probable but unstudied reactions of radicals formed in methane combustion (CH 3, CH2, H2CO, HCO) were added. Reactions were selected from a great number of possible elementary reactions with due consideration of their probable rates and observing the following rules: (i) to eliminate all reactions (except for several initiation reactions) which proceed with a high activation energy and (ii) to eliminate almost all

Iol

)

(b)

o E

~oo

400 (~sec)

FIG. 7. Reaction products of methane oxidation in a shock tube. [CH,,]o=2~o, fO2]0=3%~, [Kr]=95~/o, T=2130K. P=0.167atm. a. Experimentfl °: b. Calculation.9~'9a I-CH4, 2--H20. 3--CO2, 4--CO.

212

V. YA. BASEVICH

"E

The detailed kinetics mechanism was verified first by calculation of ignition delays for a wide range of initial conditions. The temperature range considered was 973-2130 K and the pressure range was 0.1673 atm., Fig. 4, points 5-11. Simultaneously. the product yields in a shock tube, Fig. 7, and in an atomic o x y g e n - m e t h a n e flame were modelled. The latter products were analyzed more closely in Ref. 37 at a pressure of 0.01 atm, Fig. 8. The calculations yielded more or less satisfactory agreement with experiment. An acceptable consistency also was observed in the description of methane flame propagation, Table 5.12s In the latter case the calculation was performed using Eqs (III), with an assumption of a step-like temperature rise in the flame zone

4.2", 4

4-

+

il 0.~

0

o.'r i)~

CO

0.~[-

(DI~) O.IZ'~ o

E

0

t

0

~

0

COl

0~..

O.S

•

0

• '

41~°

~

x

0"1' 4~I 0.5 O.Z'J o

x

x

x

x

0.2S

OH

! 0

x

I

*t

N

* 3

~CH4] 0 I%1

FIG. 8. Reaction products of the atomic oxygen-methane flame. 37 1:O]o = 3 o/, [Oz]o = 3.8 %, the rest is He, T = 803 K P=0.01 atm., t = 1.3 msec. Symbols---experiment; curves-calculation. low temperatures must be taken into consideration. The rate constants obtained in this way are a tentative and rough approximations. The values A and E adopted in the calculations have been corrected, when appropriate. When there are many crude estimates of parameters, the correction also may prove to be very approximate. The total number of elementary reactions included in the original detailed kinetics mechanism was 86.

x <0

T= TO

x >~O

T = T,

(IW)

from the initial value To to the final value 7",.. The values of the temperature and of the flame velocity were taken from experiment. The accuracy obtained is discussed below in the section dealing with the calculation of combustion characteristics. Allowance was made only for reactions that make the largest contributions to the kinetics under particular calculation conditions. The extension of the detailed kinetics mechanism to low temperatures has not required any major changes. 46 Successful calculations of the half-time of conversion up to hundreds of minutes are shown in Fig. 4, points 12-13. The calculations made with the specified rate constants permitted the selection of reactions important for the detailed kinetics mechanism and related to the fractions of the product yield as high as 10-100 % over the entire range of calculation conditions (about 30-40 elementary reactions, including forward and reverse reactions). Another 30 processes account for 1 - I 0 o; of the yield. If we write both forward and reverse directions for all the needed reactions, the result will be 2 x 55 processes (including (3d and 4d) introduced later, see the section on acetylene combustion}. N o t e that the selection was based on the comparison of the reaction rate integrals throughout the calculation time.

(V)

l=SWisdt.

The selection has revealed that methane is consumed primarily in the processes CH4 + OH---~CH3 + H 2 0 and C H 4 + H----,CH 3 + H 2. The main source of H atoms is the reaction H2 + OH----~HzO + H. Water

TABLE 5. Maximum values of concentrations in the reaction zone of a flat CH4-Oz flame. °,,. / _ o [ C H ~ o -- -9 , 5 o:,,, 1:O21o-90,5 Y,,, 7",.= 1900 K, P=0,049 atm. Species

HzO

COz CO

Experiment lz9 Calculation 1 2 8

17,2 6,75 17,9 7,60

4,5 3,2

OH

O

2,1 2,4 1,25 1,2

H

Hz

0 , 4 3 0,56 0 , 3 8 0,32

HO 2 CH 3 HzCO 0,02 0,08

0.16 0 , 1 5 0 , 0 8 0,04

CH_,

HCO

<5.10 -~" 0.02

<4.10 -3 0.012

Chemical kinetics is produced in the reactions CH4 + OH---*CH3 + H20, H2CO+OH---~HCO+H20, and H2+OH---*H20 +H. Carbon monoxide forms in the reactions HCO + M ---.H + CO + M, and HCO + O2--*CO-,HO2. Carbon dioxide is produced in the reactions C O + O H - - , C O 2 + H and C O + H O 2 - - * C O 2 + O H . A maximum yield of hydrogen is related to CHa + H--*CH3 + H2. Degenerate branching occurs with the H 2 0 2, H 2, and H2CO molecules. The selection of the primary reactions has show that at T=700-1000 K the main branching reaction ~s H202+M=OH+OH+M, while at T > 1200 K the main branching reaction is H+O2=OH+O. Supplementing the methane kinetics scheme 46 with reactions (87-89, 90, 91, 2c), Table 1, we can model, using Eqs (I-III, a cool flame and cool-flame ignition 94 observed in Ref. 130. This calls, however, for certain variations in the Arrhenius parameters for reaction (571 which is still uncertain (preexponential factor A = 1.56.10 9 l/mol, sec, activation energy E = 25 kcal/molt. An analysis of the solution has revealed that the cool flame mechanism is related to an initial acceleration of the oxidation reactions followed by their slowing down due to the thermal decomposition of peroxide radicals, with production of formaldehyde which then reacts with the major active species. The variations introduced into the kinetics in order to describe the cool flame do not affect the calculated characteristics of the reaction beyond this region. Criteria were put forward in Ref. 131 for estimating the accuracy of the calculations using a detailed kinetics mechanism for methane oxidation reported by various authors. The authors calculated the parameters characterizing the discrepancy between the experimental values X,~v and the calculated values Xe~

pM = log(Xc,ffX,xv) for eight detailed kinetics mechanisms suggested in the literature. The experimental parameters were taken from particular experiments and included induction periods and the exponent of the CO2 concentration rise in the induction period, and others, see Table 6. The values of pM for the methane oxidation mechanism suggested in Ref. 46, obtained in Ref. 132 (chronologically up to Ref. 94) are tabulated in the next to last column: the logarithmic mean deviation of the calculated values is 0.03, the logarithmic standard deviation is 0.33 (the deviation corresponds to a coefficient=21. The deviations are generally not worse than those calculated in Ref. 131, because the experimental parameters chosen by the authors of Ref. 131 have not been optimized. The kinetics mechanism of methane combustion also can be found in Refs 117. 133-137.

213

1.2.2. Methyl alcohol The investigation of CH3OH combustion is important not only because it is an important fuel but also because CH3OH often forms as a by-product of the combustion of methane and other hydrocarbons. Reference 51 examines a possible mechanism of the methyl alcohol reaction using, as an example, its flame with atomic oxygen. The primary reaction of oxygen atoms with mythyl alcohol appears to produce the alcohol radical CH2OH and hydroxyl radical. 138'139 Formaldehyde, identified in Ref. 140 as a primary product, is more likely to form in the submquent elementary reaction of CH2OH with the O,H atoms, hydroxyl OH and molecular oxygen 02. The qualitative pattern is the same also in this case if methoxyl radical forms. There is no reason to claim that the subsequent route of conversion of formaldehyde and of the product molecular hydrogen includes any steps typical solely of methyl alcohol oxidation. Most probably these reactions are the same as in methane oxidation. This is evident in the study of the reaction O + C H 3 O H from the formation of carbon monoxide and the appearance of hydroxyl and atomic hydrogen. It follows from the above considerations that to describe the methyl alcohol reaction with oxygen atoms quantitatively, the processes of Table 1 should be supplemented by the reactions of methyl alcohol and its radical (la-9a). Values of rate constants were available only for two reactions (la and 3al. For the rest of the nine reactions rate constants were estimated. Also in the scheme are reactions for the conversion of formaldehyde, formyl radical, carbon monoxide and hydrogen. At sufficiently high temperatures, the above mechanism suggests a chain reaction, with formaldehyde and hydrogen functioning as intermediates to provide degenerate branching. This mechanism and the rate constants for a constant temperature and pressure were used to calculate the yields of all the reaction products analyzed in the relevant experiments. The calculated results are represented by solid lines in Fig. 9. As is seen. in all the cases the calculations and the observations generally agree qualitatively. The discrepancies are within a factor of 2-5. The calculations make it possible to assess the role of particular reactions in the overall oxidation mechanism. Let us take, as an example, the reactions of methyl alcohol and its radical. The reaction of CH3OH with O atoms (lal initiates the oxidation process, and its rate determines largely the rate and extent of reaction. However, the yield of all the reaction products is also affected, although to a lesser degree, by the reactions of CH3OH with OH (2al and H (3al formed in the course of the reaction. For instance, as the rate constant k2a increases by an order of magnitude, the yields of H2CO. CO, and H

Induction period, sec Exponent of growth of C O z concentration in the induction period, c i

Exponent of growth CH" and C2" {twice of OH'), I/sec. The same

la b

2a

Maximum [CO].[O],molZ/cm 6 Time to m a x i m u m [ C O ] . [ O ] , sec

Exponent growth of flame emission of CO([CO].[O]),l/sec The same

4a b

5a

Variations in the exponent of absorption of CH4 for time 2.10 5 2.10 a, sec The same

7a

*According to Ref. 131.

b

Growth r a t e o f [ C H 3 ] , m o l / c m 3 - s e c The same

6a b

b

Induction period, sec The same

3a b

b

Parameter X

No.

P,

1,14 1,13

i,43 1,43

0,28 0,33

2200 2500

0,25 025

1600 10 1820 10

1600 1600

2195 2195

1750 2000

1,5 1,9

0,15

2000

1800 2400

0,15

arm.

2000

T,K

9 9

1 1

0,21 0,02

I 1

1,67 1,67

1 !

0,05

0,05

CH 4

1,06 1,03

2 2

--

4,32

4,32

CO

I 1

2 2

19,5 19,4

2 2

3,33 3,33

1 1

2,13

2,13

Oz

Composition, % (the rest is Ar)

0,017 0,01

1,79.10 5 3,9.10 -4

3,02.10'* 1,2.104

3,8.10 t5 2,1.10-5

1,38.10 J 3,23.10 '*

2,61.10 s 7,15.106

4,6.103

3,3.10-'*

Experiment*

0,0081 0,014

3,2.10 5 3,5.10 4

6,14.10'* 2,24.104

1,8.10-15 5.10 5

0,34.10-3 0,7.10-'*

2,62.105 7,36.106

9,6.103

2,5.10-'*

Calculation ~32

Value X

TABLE 6. Deviation of calculated parameters from experimental data

-0,32 0,15

0,25 -0,05

0,31 0,27

-0,31 0,38

-0,61 -0,66

0 -0,02

0,32

-0,12

Accord ~32

pM Range of

- 0 , 8 0,02

0,08-2,13

-0,04-0,8

-0,3-0,3

-0,72-0,58

-0,3-1,0

-0,8-0,8

values ~3~

¢3 .v,

<

.-< .>

Chemical kinetics

i

215

The kinetics mechanism of methyl alcohol combustion is treated in Refs 137, 142, 143 as well.

o.II

o /

O.i~

/

0,4

CH~OH

o o

o.z , . ~

0.4

OZ • 0

O.Z~

A A 0 (*le) 0.~F / ~ ~ " " ~ o

HZ t3 CO

~

°'z~..~ 0 o

0¢

¢¢

¢ Coz

.

0.04

•

•

•

&....... HzCO

O'°°qsF ~ " ~ +

o. 1

•~

~

I

"

O.Z~. 0.5 0.~/'~ [ CH30H]0 I%1

I HzO~'

I

FIG. 9. Reaction products of the atomic oxygen-methyl alcohol.5~ [0].=0.65 °., T=453 K, P=0.01 arm.. t= msec. Symbols--experiment: curves--calculation. are changed by 5-9 o,,. A higher rate constant k3. taccording to Ref. 141) will change the yields of H2CO, CO, and H2 by 5-20 o/o.The yields of all these reaction products are particularly sensitive to the variation in the rate constants of the reactions between CH2OH and O, H, OH: when the rate constants are varied by an order of magnitude, the corresponding yields are changed by several percent to hundreds of percent. The reaction between CH2OH and 02 is less significant, since the same extent of variation in its rate constant will introduce no more than a 10 o,, change in the product yields. The high value of the activation energy indicates that reactions ( - 4 a ) and ( - 5 a ) may be important only in the absence of initiation and at high temperatures. Calculations have revealed that for these conditions the reactions of hydrogen peroxide have only a slight effect on the yields of all the reaction products.

1.2.3. Acetylene A number of studies, for example Refs 144-147, suggest kinetics mechanisms for acetylene oxidation and establish the rate constants of some elementary reactions. Different as they are, these mechanisms have very much in common. In the opinion of most authors, in the combustion of lean mixtures, acetylene is mainly consumed in the reactions O + C2H2--*CO+CH2 (ld) and OH + C2H2---->CO+ C H 3 (2d). Clearly, there are other reactions involving acetylene consumption, specifically the reactions between the H atoms and C2H2. It can be supposed that the conversion of carbon monoxide CO, methyl CH3, and methylene CH2, which form in reactions (ld) and (2d), is close to that of methane combustion. Hence, we can elaborate a theoretical scheme of the reactions related to oxidation of acetylene-oxygen mixtures based on the general concepts of methane combustion. Below, we verify this scheme for a propagating flame and compare it with experiment. However, a more detailed and comprehensive reaction mechanism is needed for the description of combustion of rich acetylene mixtures or of acetylene cracking. The mechanism of the acetylene combustion reactions studied in Ref. 49 begins with two reactions of acetylene consumption, (1 d) and (2d), followed by two branching reactions which were found to be necessary, i.e. C H 2 + O z - - - ~ C O + O H + H (3d) and C H 2 + O 2 - - , C O 2 + 2 H (4d), Table 1. The latter reaction was discussed elsewhere. ~'LT,14s The calculated results presented below show that the required flame velocity is achieved with the introduction of one of them. The rest of the mechanism corresponds to the methane mechanism (reactions 1-14, 14a, 14d, 17, 17a, 17d, 19, 19a, 21, 24, 26, 27, 28, 28a, 29a, 30, 30a, 31, 33, 35, 42--45, 46, 46a, 48, 54, 57, 59, 66, 68, 69, 70, 70a, 83, 86a). To make the mechanism applicable at moderate temperatures, the reactions of hydrogen peroxide which become important over a range < 1200 K are included. Table 1 also contains the rate constants of reactions (ld) and (2d) taken from the literature. The rate constants of reactions (3d) and (4d) have been selected on the basis of calculations. The calculation method relied on the flame with a step-like temperature rise. Calculations were performed for the conditions of experiments ~4; in which the final and intermediate products were measured in a flat acetylene-oxygen flame. The initial acetylene and oxygen concentrations in the experiments were [C2H2]o = 7.2 % and [02]0=89.2 %, with the rest being He and At. The pressure was P = 0.0144 atm., the temperature was T = 960 K. A comparison of the observed and calculated

216

V. YA. BASEVlCH TABLE 7, Maximal values of concentrations in the reaction zone of a flat flame. o/ the balance is Ar, T= 960 K. P--0,0144 arm. [C2H.,]o--7.2 ~,,.1~O2]o - 89,2/o, o

Species

__

CO2

CO

H.,O

[C2H:]~=o

H

O

H~

OH

Experiment ~4v

7.4

6,5

6.0

5.0

2.27

2.0

0.67

0.24

Calculation't9* 0,93 K3d. l0 -s 3.24 I/tool" sec 4,9

5,1 5,5 8,5

12,1 12,1 7.8

6,1 6,1 5.6

2,8

1,54 1,95 2.88

1,83 2,06 2,55

0,64 0.59 0.67

0.24 0.24 0,25

2.5 2,4

*K,~---0; K21 ---1,6.10a l/tool .see.

profiles revealed that if no account is taken of reactions (3d) and (4d) the value of the rate constant of the reaction C O + O H - - - * C O 2 + H (21) should be somewhat higher. With a "mean" rate of this process and with Arrhenius parameters A = 2.9.109 l/tool, sec and E = 5.7 kcal/mol ~4, reactions (3d) and (4d), with a rather high rate constant ,-, 1.8. l0 s l/mol, sec. must be introduced. It is remarkable that introduction of this reaction into the methane oxidation kinetics will hardly affect its combustion rate, since in that case CH 2 forms as a by-product. The calculated and the experimental concentrations of the products in the reaction zone are in good agreement. Their maximum values for the three calculation cases are compared in Table 7. The calculations are in satisfactory accord with the observations. A conclusion can be drawn that the proposed mechanism is plausible and that the rate constants have been chosen correctly. It is also established that the oxidation mechanisms of acetylene and methane have very much in common, which permits a unified approach. The kinetics mechanism of acetylene combustion is also considered in Refs 117, 137, 149, 150. 1.2.4. Ethylene Experiments have shown that in the reaction of ethylene with atomic oxygen, ~St-t53 the C = C bond breaks and the products formed are typical of methane combustion. This observation enables us to develop an oxidation mechanism for an ethyleneoxygen flame in a lean mixture. This mechanism might be sufficiently complete to describe the yield of all of the main reaction products without involving a more detailed and comprehensive reaction mechanism needed to describe rich mixtures. 57 It seems probable that the primary reactions are CzH4 with O atoms and hydroxyl OH. Evidently, the main route is the reaction between CzH 4 and O atoms, since the concentration of atomic oxygen is normally the highest in lean mixtures. In accordance with studies 151-153, the reaction between C2H 2 and O atoms occurs by C 2 H , t + O - - * C H j + H C O (lb, Table l ). The less important reactions of C2H4 are, at the same time, less studied. An example is the reaction between C2H 4 and OH, which may occur by three possible routes:

C2H4 + OH---FCH3 + H2CC C2H, + OH-~CH,~ + HCO C2H,L + OH-*C2 Hs + H20. It follows from analysis 151 that co~ ethylene produces acetylene CzHz and CzHa. Since the main route of CzH4 cc lean mixtures, as previously noted, appe C = C bond breakage, formation of C2H is a subsidiary route of ethylene conver fore, an attempt was undertaken to descr studied kinetics of their formation and c, without distorting the general patterr oxidation. For a quantitative verificatie some possible reactions suggested earlier authors. In addition to reaction (2b"), fo CzH 3 is assumed to occur by CZH~.+ H --+CIH3 + H 2 C~I-I 4 -,/--O2-.-.~C2 H 3 + H O 2 .

The consumption of C2H 3 occurs by the r C2H3 + O --*CH3 + CO C2H3 + OH----,CH3 + HCO C2H 3 + H -"*C2H 2 + H 2 CzH 3 + 02 "-*C2H 2 + HO 2. The latter two reactions for acetylene p should be supplemented by a possible direc of ethylene decomposition with production C2H,~ ( + M)---*C2H2 + H2 ( + M). The Arrhenius parameters, namely the energy E and the preexponential factor known for only three of the above listed fib, 2b", 5b). For the rest of the reactioJ empirical estimates were made. The values E were taken from Ref. 58 for reactions (21~ from Ref. 59 for reaction ( - 5 b l , Table I. TI reactions produce C2H2, CH,, CH3, H2C( CO, H 2, HOz, and H20. Reactions involvi species were treated in the foregoing di, Hence, the subsequent portion of the me, comprises the detailed kinetics mechanisms ylene and methane (in Ref. 57: l b-9b, l d, 2 1-14, 14a, 14d. 17, 17a, 17d, 19, 19a, 21,22,24 28, 28a, 29a, 30, 30a, 31-35, 37, 39, 42-46, 46a 52-57, 59, 62, 65, 66-69, 70, 70a, 71, 74, 81, 83,861.

Chemical kinetics

217

TABLE8. Maximum concentrations in the reaction zone of a flat flame, o,.. [C2H4] ° =6.55 '~,,, [02]0=93.45 o~, T= 1900 K, P=0.0535 Species

CO

O

OH

H

H2

Experiment ~~~ Calculation 5-

7.5 5.0

3,67 3,3

2,1 1.9

0.62 1.7

0,62 0,58

H 2 C O C2H2 0.22 0.02

0.16 0.027

CH 3

C2H 3

CH e

0.13 0.061

0.0035 0,0018 0 . 0 0 2 5 0.0032

The kinetics calculations were carried out for gen as intermediate product of the oxidation process. The kinetics mechanism of ethylene combustion is experimental condition15~ for which detailed data on final and intermediate products in a flat ethylene also found in Refs 117, 137, 154, 155. flame were available. The initial ethylene and oxygen 1.2.5. Ethane concentrations in the experiments were [C2H4]o= There is ~ need to search for reaction schemes for 6.55°,0 and [02]0=93.45°,. The pressure was 0.0535 atm. and the maximum temperature was 1900 K. combustion of more complex hydrocarbons such as The calculated and the observed concentrations C2H6156'15"~ and C3H 8. The suggested mechanisms agree in the order of magnitude. Their maximum at present seem to be somewhat incomplete. The accuracy of these mechanisms must be determined by values are compared in Table 8 (the reaction C2H4 + comparing the calculations with experimental obserOH in accordance with (2blt. vations. Transition from methane to ethane is a These results indicate that the proposed reaction step of fundamental importance, since the molecule mechanism is plausible. Let us examine the important reaction steps in this mechanism. The conclus- acquires a C-C bond which introduces certain new features to the kinetics. The ethane combustion ions drawn on the basis of this analysis are mechanism includes, naturally, the scheme of oxidependent upon the selected reactions and rate constants. However, even in this case they are of dation of the new stable product--acetaldehyde, definite interest. The contributions of particular which is an intermediate of the reaction. At an early stage of detailed kinetics mechanism elementary reactions are most convenient to estimate in terms of the value of integral 1 with respect to (VI. development, two mechanisms of ethane combustion were put forward and examined. One of them ~56 The principle reaction of ethylene consumption is, as expected, (lbt; reaction (2bl takes place at a slower assumes that the initiation reaction is the breakage rate. If (2b) is replaced by (2b'}, then the calculated of the carbon bond and formation of methyl radicals C2H6----*2CH3. The formation of CH 3 is also typical concentration of methane turns out to be about two orders of magnitude higher. The route (2b") results in of methane oxidation. Hence, it is claimed in Ref. 156 a 20-fold excess of the calculated concentration of that the subsequent reactions coincide completely with the oxidation mechanism of CH4. The convenC2H4 over the experimental value. tionality of this step is obvious, since generally C2H 6 Allowing only for the reaction of C2H,~ with O and OH (Ib, 2b~ and omitting all the reactions of CzH 3 may decompose at a slower rate than it would react and C2H 2 (3b-9b, ld, 2dl we arrive at product con- with the main active species, like hydroxyl OH, H centrations consistent with the experimental values and O atoms. The second mechanism ~s~ considers (in this calculation we take that [C2H3-I = the initial reaction of ethane to be with OH, H, O. and 02' which results in abstraction of an H atom [C2H2] =OI. The primary reaction responsible for the appearand formation of hydrocarbon molecules and radance of acetylene is C2H,, ( + Mt---*C2H2 + H2 (+ M) icals which react, in turn, in the same way. The ( - 5 b l and that for the radical C2H 3 is C2H,,+ carbon chain is believed to break only when C2H 2 H---*C2H3 + H 2 (3bt. These species are largely con- and C2 H react with O and O2, respectively, to sumed in C2H2+O----~CH2+CO (ldl and C2Ha+ produce CH2, CO and CHO. Thus, no allowance is made for the highly probable reactions of ethyl O2---'C2H2 + HO2 (9bl, respectively. It is worthwhile noting that under these conradical involving C-C-bond breakage and production ditions, just as in the majority of cases of highof h ydrogen-con taining species. The ethane combustion mechanism °4 outlined temperature oxidation of hydrocarbons, the fastest branching reaction is H + O2---*OH + O ( - 4 ) , while below is based on the CH4 combustion mechanism. the main source of H atoms is HCO+M----~H+ Furthermore, an account is taken of numerous reCO + M{ - 66). actions suggested earlier by various authors, inIt would be important if this mechanism could be cluding those reactions involving acetaldehyde. Table extended to the combustion of rich-mixtures. 1, reactions (2c-28cl. Considering the findings as a whole, and comparing The first reactions (2c-7ci involve ethane decomthem with the kinetics calculations carried out for position as well as production of ethyl radicals. Next. methane and acetylene flames, a conclusion may be unlike Ref. 157, several possible reactions of C2H~ drawn regarding a common characteristic of the with OH, H and O are introduced to C-C bond mechanism underlying the combustion of various breakage and production of hydrogen-containing hydrocarbons as well as the important role of hydrospecies.

218

V. YA. BASEVICH

The ethane combustion mechanism 6+ outlined below is based on the CH+ combustion mechanism. Furthermore, an account is taken of numerous reactions suggested earlier by various authors, including those reactions involving acetaldehyde, Table 1, reactions (2c-28c). The first reactions (2c-7c) involve ethane decomposition as well as production of ethyl radicals. Next, unlike Ref. 157 several possible reactions of C2H~ with OH, H and O are introduced, leading to C - C bond breakage and production of aikyl radicals and oxygen-containing species (8c-11c). The reaction between C2H 5 and 02 may produce CH3CHO and OH, provided it is analogous to the reaction between CH3 and 02 or it may give H2CO and C H 3 0 upon C - C bond breakage (12c). Here the authors assume reactions of CH~CHO both with C - C bond breakage ( - 1 7 c , - 2 0 c ) and with H atom abstraction, formation of CH3CO and subsequent decomposition by unimolecular ( - 2 1 c ) reaction or by reaction with H and O (22c-23c). The next group of reactions (24c-28c) leads to formation of C2H+.~sT All the above-mentioned reactions yield products (Hz, HzOz, H2CO, HCO, CH+, CH3, CH2, CH30, C2H,+, CO) which appear in the mechanism of combustion of CH+, CH3OH, C2H2, and CzH+. Hence, the list of elementary reactions involved in C2H 6 oxidation should be supplemented by the reactions of these species. Table 1 contains the Arrhenius parameters used. The values of A and E have been taken from the literature, or selected in calculations, or estimated approximately in accordance with semiempirical formulas. At sufficiently high temperatures, the mechanism concerned involves a branching reaction, with hydrogen functioning as an intermediate which ensures degenerate branching. Two different sets of calculations were performed. In one, all the reactions of the mechanism were considered in order to determine if ethane dehydrogenation is the main route of the combustion reaction and if it is possible to calculate the observed reaction products without this reaction. In the second set of calculations, all the reactions of ethyl leading to ethylene production were deleted. The calculated kinetics curves for the conditions of atomic flame experiments are represented by solid lines in Fig. 10. The points correspond to the observations. In the experiment, the concentration of H2Oz is 0.005 %; in calculations it is always under 0.003 %. The calculated and the observed results agree qualitatively. Data reported elsewhere permit an additional verification of the proposed mechanism: (1) The atomic oxygen-ethane flame, t58 Table 9 compares the calculation with an experiment carried out at a temperature of 310 K, a pressure of 0.0077 atm., initial concentration [C2H6]o = 1.19- 10 -~ mol/cm 3, ratio [C2H6]o : [ O ] o = I :0.77, and a reaction time of

/ o.| --

o,

-~:, co o

o.4-

Q

o

~ O

0.~

( ~'lo)

0.203

~

A

0.1 -0.09

0.04 -o.o,1 --

• •

H ~..v

0.004-O.OOZ -- ~

*

~

OH

[C~H6 10 I * / * )

FIG. 10. Reaction products of the atomic oxygen-ethane flame."+ [0]o=0.8°,. T=453 K. P=0.001 atm., t=3 msec. Symbols--experiment: curves- calculation. 30 msec. (2) Oxidation of CH3CHO. Some authors consider acetaldehyde to be an important intermediate product of ethane oxidation. Hence, it is essential to determine how well the mechanism can fit the oxidation reaction of CH3CHO itself. The conditions should be selected so that the experimental data fall in the so called "high-temperature" oxidation region ~59 where the mechanism is close to that of combustion. We can suppose that the conditions of CH3CHO in flow reactions ~6° are in this region: the temperature is 623 K, the pressure is 1 arm. and [ C H 3 C H O ] o = 1.5 ",,. Table I0 compares the experimental and the calculated concentrations for a reaction time equal to the half-time of conversion -~lsec. In the calculations, the reaction ( - 17c) has been introduced to account for the high

Chemical kinetics

219

TABLE 9. Comparison of normalized experimental and calculated concentrations [ y ] / A [ C : H ( , ] in the atomic oxygen-ethane flame, [C2H(,]o = 1,19.10- 9 mol/cm 3 T = 310 K, P = 0.0077 atm., t = 30 msec

[C2 H(,]/[C2H(,]o %

CO,

CO

H20

H2

H2CO

CH,~

8,3 11,8

0,94 1,13

1,0 0,74

0.88 0,35

1,95 1,59

0,03 0,025

0,07 0,025

Experiment ~58 Calculation ~,a Set 2 Case a

TABLE 10. Comparison of experimental and calculated concentrations, %, of [CH3CHO]o. Jet conditions: [CH3CHO]o = 1,5 %.: T = 6 2 3 K, P = 1 atm., t = 1 sec

Experiment j6° Calculation 64 Set 2 Case a

CH3CHO

CO

50

14

54,5

51

CO2

H2CO

H202

8,5

2,5

10 9.4

3,0

24

TABLE t 1. Ignition delay times ZK

743 TM

13201~2 14901('2

P, a t m o [C2H,]o " [O2],~ Experiment Calculation(,,) msec Set 2, Case a

7,5 6 19,8 7.104

7.5 2 7 0,23

2.104

0.28

reactivity of C H 3 C H O . T h e actual process is likely to be m o r e c o m p l i c a t e d a n d ( - 1 7 c ) is just an overall process. As is k n o w n , acetyl p e r o x i d e d e c o m p o s e s C H 3 C O O O H - - - ) C H 3 + CO2 + O H , while it seems to form in the reaction between C H a C H O a n d 0 2 . (3) I g n i t i o n delays. N o e x p e r i m e n t a l d a t a on the intermediates c o n c e n t r a t i o n s t h r o u g h o u t the reaction are available for h i g h e r t e m p e r a t u r e s in the spont a n e o u s i g n i t i o n region. T h e only p a r a m e t e r w h o s e value can be used to c o m p a r e c a l c u l a t i o n s with experiment, is therefore i g n i t i o n delay. A b o v e is a selective c o m p a r i s o n with the findings of some workers, T a b l e 11. E x p e r i m e n t s T M were carried out in a smalld i a m e t e r (3.8 cm) steel cylindrical b o m b . T o allow for r e c o m b i n a t i o n of active centers on the wall, the reaction m e c h a n i s m was s u p p l e m e n t e d by two termi n a t i o n r e a c t i o n s ( H 2 0 2 a n d OH), with rate constants c o r r e s p o n d i n g to diffusion transfer rates. T h e e x p e r i m e n t selected for the p u r p o s e of c o m p a r i s o n is a " h i g h - t e m p e r a t u r e " region of C2H 6 oxidation. Experiments157.162 were carried out in shock tubes.

1760 Is~

0.06

3,6 6.4 0,053

0,306 2,2 7.8 0.032

1,25 8.75 0,028

0,04

0,074

0,054

0,048

It can be seen t h a t in general the calculations qualitatively agree with the e x p e r i m e n t a l data. (4) Reaction products in flame propagation. Experim e n t s 16a p r o v i d e m e a s u r e m e n t s of the c o m b u s t i o n p r o d u c t s in a fiat flame for a n ethane--oxygen mixture. In this case, the c a l c u l a t i o n s were b a s e d on a system of s t a t i o n a r y e q u a t i o n s describing oned i m e n s i o n a l flame p r o p a g a t i o n with c o n s i d e r a t i o n of diffusion at a step-like t e m p e r a t u r e rise. In the experiments, the initial c o n c e n t r a t i o n of e t h a n e was [ C 2 H 6 ] o = 6 . 3 °//o a n d t h a t of oxygen was [ 0 2 ] 0 = 93.7 ~o- T h e pressure was 0.041 atm. a n d the comb u s t i o n t e m p e r a t u r e was 2000 K. T a b l e 12 c o m p a r e s the m a x i m u m e x p e r i m e n t a l a n d calculated concent r a t i o n s of species in the reaction zone. In ten cases, the discrepancy does n o t exceed an o r d e r of m a g n i tude; in two cases it is over an o r d e r of magnitude. It is evident from T a b l e s 9-12 t h a t the calculations are in r e a s o n a b l e accord with the o b s e r v a t i o n s over wide ranges of temperatures, pressures, a n d m i x t u r e compositions. T h e a b o v e calculations were c o n d u c t e d with the

TABL~ 12. Maximum concentrations in the reaction zone of a flat flame, o,. [C.,H,], =6.3 0,,, [ 0 2 ] . =93.7 °,,. T = 2000 K. P = 0,041 arm. Species

CO

H_,

C2H,

H2CO

CH 3

HO 2

C.,H2

CH4

C2H5

CH30

CHO

CH_,

Experiment 1~3 7 Calculation Sel 1. Case b ~'4 5.5

0.8

0.58

0,19

0.14

0.08

0.025

0.02

0,01-0,05"

0.001

0.001

0,001

0.4

0.10

0,05

0,07

0.43

0.02

0.01

0.24

0.02

0.02

0,002

*Privale communication.

220

V. YA. BASEVICH

values of A and E of the reaction (12c) according to the cases (a), (b) and (c). The observed differences are small and unimportant. This implies that the route of oxidation involving the reactions of C2Hs with C - C bond breakage, production of alkyl radicals and oxygen-containing species, is quite possible as is the dehydrogenation route. The reaction may follow the two channels simultaneously; however, the details cannot be determined from the observation of the overall kinetics. The contribution of a particular elementary reaction of various stages in the reaction can be. estimated quantitatively from the value of the reaction rate integral I with respect to (V). The major participants of the reaction (those with concentrations which are comparable by an order of magnitude with those of the initial species), according to the second set of calculations are CzH6, OH, H, O, HO2, HCO, CH 3, H2, H20, H202, CO, COz, H2CO, C2H5, 02 and CH4. It can be concluded from the values of ! that ethane is consumed primarily by C2H 6 + OH, H, O, M. In the ignition process at low temperatures, the maximum branching rate is determined by H 2 0 2 + M - - * 2 O H + M : at high temperatures ( > 1200 K) it is determined by H + O2---,OH + O. The C - C bond breaks in the atomic flame in the reaction C2H 5 + O---*CH 3 + HzCO. In the remaining cases the bond breaking occurs in the reaction between C:H5 and 02 as well as OH or by the decomposition of CH3CHO. Atomic hydrogen forms in the reaction O+OH---*O 2 + H or in the decomposition of formyl H C O + M---,H + CO + M, whereas molecular hydrogen forms in the reaction between H and C2H6, CH4 and H2CO. Water is produced in the reaction between C2H6, H2, H2CO and OH, carbon monoxide in the reaction between HCO and O2, M, carbon dioxide in the reaction between CO and OH, HO2. Clearly, the reaction mechanism resembles in many respects that of CH4 combustion. Due to a lack of experimental data we cannot presently determine rigorously either the main reaction route or the elementary reactions. Many familiar reactions are omitted in the mechanism of Table 1. The mechanism being discussed should be treated as a hypothetical one, requiring further verification and refinement on the basis of various experimental observations. The kinetics mechanism of ethane combustion is also examined, etc. ~37.164.165 1.3. H-C-N-O System 1.3.1. Methylamine Methylamine is one of the simplest representatives of amine-substituted hydrocarbons used either in its own right or as an additive to fuels. A knowledge of the combustion mechanism is essential for describing the energy release process and for getting insight into the kinetics of formation of final products, some of which are ecologically undesirable.

The H - C - N - O system is very complex, but even the available data on the kinetics of combustion of H 2 with 02, of hydrocarbons C1 and C2 with 02 justify an attempt to determine a combustion mechanism for this system, We endeavored to construct a mechanism of methylamine combustion using an atomic oxygen flame. 69 The original intention to use just a few reactions was not successful. Further efforts were focused therefore on the development of a detailed mechanism. Analogous to many familiar reactions of O atoms, the initiation is likely to abstract an H atom from a molecule. Since C - H bond (93.7 kcal/mol) is stronger than the N - H bond (87.2kcal/mol), 166 we will assume that the reaction takes place according to O + C H 3 N H 2 - , C H 3 N H + OH.

(2.1)

The atomic hydrogen formed by (2.1) followed by O + OH---,Oz + H

(4)

may react with the reactant molecules in OH + CH3NH2---,CH3NH + H 2 0 H + CH3NHE---,CH3NH + H2 .

(2.2) (2.3)

At high temperatures and in the presence of 02 the following initiation reactions may be of importance for ignition CH3NH2---,CH3 + NH 2 (-2.4) CH3NH2 + O2----,CH3NH + HO 2. ( - 2 . 5 ) Subsequent reactions can be represented only tentatively. The reaction of CH3NH with O as well as H, OH and 02, may ultimately yield species like CH3, C H 3 0 , CH4, HNO, NH and NH z. Since there are no data on the reactions producing these species, the reactions written below should be interpreted only as overall processes: CH3NH + O---*CH30 + NH CH3NH + OH---,CH,~ + H N O CH3NH + H---~CH3 + NHz CH3NH + O:--*CH30 + HNO.

(2.6) (2.7) (2.8) (2.9)

Table 1 lists possible subsequent reactions involving species formed in the above reactions. The reactions of CH4 and CH 3 with O atoms were considered earlier in the methane oxidation mechanism. It is appropriate therefore, to include all the reactions of the methane oxidation mechanism with the corresponding kinetics parameters as a component of the H - C - N - O mechanism. In addition, the previously described reactions of the C H 3 0 radical should be included. The reactions of NH, NH2, and HNO formed in the reactions cited above have been also examined by various workers, for example Ref. 78. There are known rate constants for some of these reactions. These reactions, numbered (2.101-(2.27} in Table 1, include reactions that are likely to produce NH 3. This portion of the scheme also describes the oxi-

Chemical kinetics dation of NH 3. and in conjunction with the H - O reactions it constitutes a significant part of the detailed kinetics mechanism for the H - N - O system. The combustion of rich mixtures of hydrocarbons, particularly those containing bound nitrogen, is accompanied by formation of HCN and NH3 .1~'7 Significant quantities of HCN are produced on addition of NH 3 to hydrocarbons. Consequently, we expect that reactions of NH 2, N and NH, which are typical of ammonia combustion, with intermediate species of hydrocarbon combustion will produce HCN. Hence, a portion of the kinetics scheme reflecting production and oxidation of HCN, reactions (2.28)-(2.40). is included. Also included are reactions (2.41) and (2.42) suggested in Ref. 167 which account for the formation (reverse reaction) of HCN and of the so called prompt NO in hydrocarbon flames. These reactions involve molecular nitrogen and CH2 and CH. The CH 2 radical appears in the methane oxidation mechanism. Production and consumption of CH is described by reactions (95)-(99) which extend the methane portion of the mechanism in the first half of Table 1. Arrhenius parameters for these reactions are specified on the basis of the estimates made in Ref. 50. Nitric oxide formation in the high-temperature oxidation of methane-air mixtures occurs by the so-called extended Zel'dovich mechanism, reactions (1.12)-(1.15). Reactions (1.3)-(1.10) occur over a wide temperature range and result in formation and decomposition of NO2 (see Ref. 89). Here reaction (1.11) seems to be indispensable. Wherever possible, we used the values of rate constants of forward and reverse reactions available elsewhere, making references to the relevant literature. In other cases, the Arrhenius parameters were estimated empirically. Having been selected, the parameters were not changed in subsequent calculations, see Table 1. The suggested mechanism has been applied to calculate the kinetics for CH3NH 2 combustion in an atomic oxygen flame. Figure 11 shows the calculations (solid lines) and the observations (points). The calculated value of OH is <0.001% (experiment <0.006 %): the value of [NO2] is <0.005 ° 0 (experiment--0.003 %) over the entire range of [CH3NH2-10. The experiment and the calculations are in reasonably satisfactory agreement. The calculations make it possible to establish the main (in addition to CH3NH2, O and 02) reaction products, i.e. those with final values greater than 10 % of the consumed CH3NH2. These are H2, CO, H, CH a, NO, H,O, H2CO, N 2. NH 3 (the last four have not been measured). Next, we estimated the contribution of each elementary reaction in the course of conversion of CH3NH 2 and of certain reaction components. In the reaction (2.1). about 12-20°,, of the O atoms are

221 I

o

O

o OG

03

@

F

•

~"

CI'I3NH' " " • •

o,~[-- AfU---~ ,, o.,o~-/~" ~ e, '~

o~,a~

co

O

~

O'O?S!X~XN OD'bxx H X 0.0~

oL* \ oo~[- c , O.Ol o~,~go~ 0.02 •

~0

, g e

~ o° 0 ~ o°

•

o o.F',

.

o~l

•

i'l---q~o---m-

o[..ff ~

DD

0"01$rAO0 0 0 ~ ~ o.oo~ o

0

0 COz a 0 O.Z 0.4 0.1 [. CH3NHZ]0 ('/.)

o~l

FIG. 1l. Reaction products of the atom oxygen-methylamine flame.69 [0]o=0.22 o,, T= 1160 K, P=0.01 atm., t=2.5 msec. Symbols--experiment: curves--calculation. consumed. The relative contribution of the CH3NH2 consumption reactions involving OH (2.2) and H (2.3) varies between 22-45 %. Nitric oxide forms primarily by N + OH----,NO + H (1.15), N + O 2 - - - . N O + O (1.13), (2.21) and (2.23) involving the radicals NO and NH. The relative contributions of these reactions differ but are of the same order of magnitude. Reactions (2.29) and (2.28) involving the N atom, the NH radical, and the CH 3 and CH 2 radicals, make nearly equal contributions to the formation of HCN. The atomic N in the above-mentioned processes is formed in reactions (2.24), (2.25), (2.16) and (2.27). NH3 forms in the reaction between NH 3 and H2 ( - 2 . 1 8 ) o r 0 2 (2.11). The fast reaction (2.12) is not efficient because the reverse reaction proceeds even faster. In principle, the proposed mechanism is applicable

222

V. YA. BASEVICH

not only to the reaction of CH3NH2 in an atomic flame but also to the combustion of CH3NH 2 at atmospheric and higher pressures and to other cases of combustion of species involved in the kinetics scheme. Therefore, it was of interest to elucidate the degree of generality of the mechanism. We performed additional calculations for experiments under substantially different conditions reported in the literature. Although these calculations were based on Eq. (1), with no reference to diffusion, in some instances the agreement was satisfactory. For example, an atmospheric combustion of a rich mixture, ct=0.525 (=l/ta), 0.63 H2+0.1 CH4+0.27 02 with an admixture of 0.0078 NHa in a flame of 1816K t67 yielded in 3 msec 0.04 % NO, 0.05 % HCN, and 0.12 NH 3 in the reaction products. The calculated values for these conditions are 0.0425 %, 0.216 % and 0.088 % respectively. In the case of a rich hydr0carbon-air mixture containing no nitrogen with ~t=0.67 burned in a flame of 1930 K at atmospheric pressure, the authors of Ref. 169 obtained 0.0015 % NO, 0.018 % HCN and 0.0006% NH3. The calculations for a methane-air mixture under the specified conditions predict for a 3 msec reaction time 0.0042 %, 0.0028 ~o and 0.00005 % respectively, i.e. the accuracy is within an order of magnitude. It should be borne in mind, however, that modeling flame propagation by a kinetics program for a constant temperature and with no allowance for the diffusion may involve uncertainties. It is evident from the N O formation reactions that their activation energies are low and that the formation of N O from a nitrogen-containing molecule requires an oxidizing atmosphere and relatively high concentrations of O and OH (region [CH3NH2]o < 0.1%, Fig. 11). A temperature rise at a constant pressure will facilitate the production of NO. This is not in conflict with the observed reduction in the N O yield with an increasing temperature over a lowtemperature range in the presence of NH3 .t7° The latter effect is attributed to reactions (2.14) and (2.20). If the temperature and pressure are raised simultaneously, this may prevent N O production because of lower concentrations of N, OH and O and result in the formation of N2 and other products. Presently, we cannot identify all of the elementary reactions because the experimental data are insufficient and the system concerned is complex. Many familiar reactions are excluded from the mechanism of Table 1. The mechanism under discussion should be regarded as a first approximation to be verified and clarified on the basis of various experimental results. The kinetics mechanism underlying the combustion of nitrogen-containing compounds is examined in Refs 171,172. 1.4. Oxidant--H202 The substitution of H202 for 02 as an oxidant depends on the comparative readiness of the former

H2

0I

o.~~

Oz

0.15

0

(*Io)

O 0 O.IS~-•

H202

0.0'3

o

• O.S

• I

I*

1.5

CHzJoC*/,)

,*

E

FIG. 12. Reaction products in the H2-H202-Ar system. 28 i'H202]o=0.319/,~, T= 1233 K. P=0.0134 atm.. t=4.25 msec. Symbols----experiment: curves--calculation.

to decompose thermally with production of two hydroxyl radicals. The reaction starts at a temperature corresponding to that at which the hydrogen peroxide decomposition becomes appreciable. As indicated above, hydrogen peroxide is an essential component of the detailed kinetics mechanism for oxidation of hydrogen and hydrocarbons. As a result, the kinetics mechanism for H 2 0 2 as an oxidant coincides with that for an oxygen system. Calculations were compared with experiment under flow condition using a CH4-H202 system 33 and an H 2 - H 2 0 2 system, 2a Fig. 12. In the experiments, there was some initial concentration [O210 due to its presence in liquid H202 which was used to produce the gas-phase H 2 0 2. In the two cases, the experimental and the calculated results are in satisfactory agreement. 1.5. Oxidant--HN 03 Nitric acid decomposes as easily as H 2 0 2 producing nitrogen dioxide and hydroxyl, t73"174 which is why it is utilized as an oxidant. 175't76 The resulting hydroxyl radical reacts with the nitric acid, forming a highly reactive radical NO3 and water, reactions (1.1) and (1.2) in Table I. The above reactions, in conjunction with the detailed kinetics mechanism for the H - N - O system enable us to establish the kinetics of the hydrogen reaction with nitric acid. 28 The reaction is rather fast, and the concentrations of OH, H and O could not be recorded because of their rapid recombination in the gas sampler of an EPR-spectrometer. Experimental data on the reaction between CH4 and HNOa are shown in Fig. 13. 88 The start of the reaction corresponds" to the onset of HNOa decomposition. The calculated kinetics curves agree well with the experiment at a reaction time of 5 msec.

Chemical kinetics

223

2.1. Spontaneou.s Ignition !

CH4

P

~

Ip

b

N02

O~ (B/o) I.~

D

0,

0

O

~

"

5

I=" 0

A

0

~

I C1.~10 I"/.1 FIG. 13. Reaction products in the CH4-HNO3-Ar system.ss FHNO3].= 7 o. T= 1067 K. P=0.01 arm. Symbols experiment: curves calculation.

2. APPLICATION OF DETAILED KINETICS MECHANISMS TO COMBUSTION PROCESSES: D E T E R M I N A T I O N OF P H Y S l C O - C H E M I C A L AND TECHNICAL CHARACTERISTICS

Having knowledge of the kinetics one can establish many physico-chemical and technical characteristics of combustion processes. These characteristics include ignition delays, stabilization limits, laminar and turbulent flame velocities, heat generation rates, and reaction product composition. These characteristics depend on the chemical properties of the reacting substances and the initial composition of a mixture as well as on particular physical conditions, namely temperature, pressure, hydrodynamics and combustion chamber geometry. A theoretical description of the characteristics and kinetic behavior of the combustion process can be obtained, in principle by solving a system of equations, the form of which is governed by a specific problem. Mathematical theory underlying the solution of various problems related to combustion is outlined in Ref. 16. In addition to ignition and laminar flame propagation, we will consider the theoretical description of the turbulent combustion process, for which there is as yet no generally accepted approach. We will also consider the issue of combustion promotion (improvement, acceleration) by unstable products, atoms, and radicals.

The time-dependent characteristics of the ignition process as well as the induction period [ignition delay) and the time for conversion to a specified degree of reaction can be established by solving jointly the equations of material balance Ill and temperature (2 }. Examples of ignition delay time calculations for the isothermic ignition of hydrogen and methane mixtures are given in Fig. 4. Having a detailed kinetics mechanism we can calculate the combustion characteristics for conditions where it would be difficult to set up an experiment and where it is advisable that experimentation should be preceded by calculations. Here we assume that the reaction mechanism remains the same over the range of conditions of interest. Initially, experimental studies of the kinetics of hydrogen oxidation were concerned with the ignition peninsula. ~s~3 More recently, the)' cover temperatures ranging from about 600-2000 K and pressures ranging from hundredths of atmospheres to 10 a t m Practical applications of hydrogen combustion are possible at even higher pressures and temperatures. Once the temperature and pressure are raised, the reaction generally is accelerated and the combustion time is reduced. At very short times, the effects of excitation and relaxation processes may show up. If the characteristic time for hydrogen combustion is greater than 10-6-10 ~ sec ordinary kinetic equations assuming an equilibrium energy distribution can be employed. Using these assumptions, we performed kinetics calculations of ignition near stoichiometric hydrogen-air mixtures for temper-

_ ,o7#y ~- ,o• [-//// t~'///

/ 'I,

t~O0

//.

ZOO0 T(K)

3000

FIG. 14. Variations in the hydrogen oxidation mechanism. 1"" Principal reactions: I: 1. _+4, -6. 11. -83: at T~>900K steps -1.9 are supplemented: at T~> 1200 K new steps are supplemented: II: 1. 4-4, - 6 , 7 . 11. 17, 17a, 17b, -83: at T>~1200K new steps are supplemented: ili:

- 1. - 6 .

- 13, - 1 4 .

-83:

IV: 1. -4, -6.7.8. -28.29a. -83: V: 1, 7.8.14. -14a. -28a. 29a. -83: V1:1,7.8 -28,29a, 83: A: -+1, +_4, +6, -+11. +_13. _+83: C: the mechanism contains man 3' steps: B: the conversion half-time ~<10-6 sec.

224

V. YA. BASEVICH

atures ranging from 600 to 4000 K and pressures from 0,01 to 350atm. 17r The calculations have revealed that for maximum temperatures and pressures the calculated half-times of conversion are reduced to 10-8. The same calculations have established the principle steps in the detailed kinetics mechanism for various temperatures and pressures, Fig. 14. 2.2.

Stabilization Limits

An important practical characteristic of combustion processes is the limits of flame stabilization in a flow, which are defined both by chemical and physical factors (including hydrodynamics and turbulence). Reference 95 reports kinetics calculations of the limits of stabilization of the hydrogen-air flame by a so-called active stabilizer (the jet contains active species). The combustion process occurs as shown in Fig. 15. A high-temperature gas-containing active species flows in the central channel and mixes with a fresh fuel mixture supplied through an external channel. Reaction is started in the mixing zone and subsequently it either spreads across the entire crosssection (with flame stabilization) or ceases (with no flame stabilization). An empirical criterion for stabilization is used. According to this criterion, the combustion efficiency near the stabilizer is ~/-- I

-

EH~] - -

t>0.95,

rH2]o where [H2] and [H2]o are the local and the initial concentrations of hydrogen, respectively. Calcu-

lations were made for the region corresponding to short times behind the stabilizer, where the turbulent diffusion coefficient, D , which depends on time and determines the mixing of the main flow and the active jet, is small compared to the molecular diffusion coefficient, D r. In accordance with the criterion, the combustion coefficient for mixed coaxial flows (fresh mixture and active jet) was calculated using a system of differential nonstationary equations of material balance and heat in the axisymmetric co-ordinates, together with the appropriate initial and boundary conditions:

Po ?njP?t = ~'J Wij + lr Dip ?njl pp?r+ ~r ~ Dip ~nj/p?r c'T

I

~T

?

?T

poC ~tt = X hijWiJ +r2 ~r + ~r )" ~-"

(VI)

I)

The initial and the boundary conditions are t = 0 , for O<<,r<~rl; T= T o n~=n~o for

T= T I n)---nil r~ < r < < . r o

T ?n/p where rl and r0 are the radii of the internal and external channels respectively; the other nomenclature is similar to that used earlier. The experimental data on stabilization limits for various pressures and mixture compositions, points in Fig. 16, compare approximately with the calculated results. (The positive sign corresponds to the calculated region of stable combustion where r/I>0.95,

X2

BI

:z?,,r, U FIG. 15. Flow diagram and designation of coordinates. Region 1= mixing or combustion zone.

Chemical kinetics

225

I m crn i

-- 12OO

71211

/,

OI

t- 9(2r3 Io 1301

0.05

I

5

0

?o -900

H2 0

+ ~ ~

~

02" E

I

7.5

I0

30O

I

12.5

r

[ H2] 0 (%1

FIG. 16. Comparison of the observed and calculated stabilization limits for hydrogen-air flames.9~ Velocities: U mean, u--root-mean-square fluctuation. 7.5 mm dia stabilizer. Symbols---G. experiment: calculation "'+"--stabile flame. "-"--flame blow-off.

while the negative sign refers to the region where there is no stabilization and the flame is blown off.) It is evident from the comparison that the inequality D,
~

H2

_

°61 - '~ -

o4-

~

,~

0.2--

O6 t

---2

"~ ~'~ \

o4

0.2

~% O

0 2/

I " ~.

,,.,..

OH

2.3. Laminar Flame Propagation The earliest kinetics-based calculations of flame propagation were conducted. 1~8'~79 These calculations yielded the profiles of products and the heat generation rate over the width of the combustion zone. The calculation is straight-forward, once the flame velocity and the reaction zone temperature profile are known from experiment (Fig. 3). 18'19 Substantial savings in computer time (at the expense of accuracy) may be made by the assumption of a step-like temperature rise in the combustion zone, according to Eq. (IV ~), and solution of the material balance Eq. (III). The results obtained in the latter case agree within an order of magnitude with those yielded in the joint solution of Eq. (III) and energy Eq. (IV). By solving jointly the systems of Eqs (III) and (IV) we obtain, along with the product profiles, the temperature profile and the flame velocity. Figure 17 shows, as an example of the calculated results for a hydrogen-air flame. ~s°'as~ The flame velocity was calculated to be u,=48cm/sec, while the experimental value is 60 cm/sec. The same figure depicts (broken line) the calculated step-like temperature rise for a specified flame velocity determined by the complete set of equations. 5; This comparison justifies the application of kinetics calculations to the flame using the assumption of a step-like temperature rise. 49'5v'64'12s Once the kinetics are known, the characteristics of JPSCS 13-3-E

O'~OF~

O.I

0

02

0.3

Icml

FIG. ]7. Comparison of concentration profiles in a hydrogen-air flame [ H : ] . = 17.3 ~, T<,= 293 K. P= ] atm. The calculated flame velocity u.=48 cm;sec. The solid line-calculation s°'sl on the basis of HI-IV: the broken line-calculation 57 on the basis of II|-|VJ

I&--

,o

,g

40

I~0

n [ HaOz]o (°/.I

FIG. 18. Laminar velocity u, and flame zone thickness ,~, of a hydrogen peroxide decomposition flame? s: T~,=373 K, P=0.34 atm.

226

V. YA. BASEVICH

flame propagation can be calculated for conditions where no experiments have been carried out. Thus, the authors of Ref. 182 predicted parameters of a laminar hydrogen peroxide decomposition flame (the initial concentration of the latter is 30-50 Vo) which has not yet been observed experimentally, Fig. 18. Reference 183 deals with the calculation of the characteristics of a stoichiometric laminar hydrogenair flame over initial temperatures ranging from 293 to 600 K and pressures from 1 to 100 atm. including the yield of nitric oxide. The studies referred to in the previous Section i deal with numerous instances of the application of detailed kinetics mechanisms to the calculations of laminar flame velocity and the product profiles.

2.4. Turbulent Combustion Along with physical conditions, the kinetics also determine the characteristics of turbulent flame propagation. The theoretical approach to calculation and modeling of turbulent combustion will be treated in a more detailed fashion in this section. The calculation of the characteristics of a reacting system governed by the chemical properties have been considered so far in terms of the known methods of kinetic modeling and theory of combustion. However, there are no generally accepted methods to describe mathematically the rates of chemical reactions in turbulent media. Hence, we will first introduce a mathematical procedure permitting this description, then verify it by calculation of characteristics of a laminar flame and finally we will employ it to calculate chemical characteristics in turbulent media. T~ae rate of a chemical reaction is determined by the concentration n~ and by the temperature T. The fluctuations of the temperature and concentration in a turbulent medium result in complicated nj and T distributions. This has been observed in a number of works.~ sa- ~s6 Figure 19 reproduces the temperature records made i n ' t h e combustion zone of a lean

turbulent hydrogen-air flame [the time is marked in 0.01 sec). The amplitude of temperature fluctuations corresponds to the difference between the initial and final temperatures of combustion, Tc - T 0. The length of the zones in which the instantaneous temperature undergoes sudden changes is only a small portion of the space in which the mean temperature goes from its initial to the final value. The instantaneous values of nj and T may differ from the mean values by a factor of ten or more. This is attributed to the fact that the characteristic combustion time r is shorter than the time of turbulent fluctuations, defined by the reciprocal of their frequency v(rv <~1). There are two ways of including turbulent fluctuations in the solution of a particular kinetic problem. The origin of one way is traced to Reynolds who suggested it for the Navier-Stokes equations. In this approach, the variables appearing in the balance differential equations are represented as a sum of the mean and fluctuating components and then a time-averaging is carried out. In this approach the equations contain functions which must be modelled independently. A second way is to employ the well-known Monte Carlo method, where calculations are made using random values and the resulting solutions are timeaveraged. Taking this approach, we have to model the random turbulent velocity field. The approach has an important advantage. Using averaged parameters we cannot determine actual instantaneous values of these parameters in turbulent media (this is the reason why there are various models of turbulent combustion~aa-19°). However, transition from instantaneous to averaged parameters is unambiguous. Thus using the Monte Carlo method, it is possible to establish the instantaneous pattern of the phenomenon. Furthermore, the solutions are of an ab initio nature, so that the form and character of the correlation functions used in the solution of averaged differential equations can be controlled. The Monte Carlo method, described above, will be applied to several problems involving mixing and combustion.

I0

rnsee

FIG. 19. Example of temperature fluctuations in the combustion zone of a turbulent hydrogen-air flame,t87 [Hz]o=8.5 °~i,T=293 K, P=0.5 atm.

Chemical kinetics

227

corresponding to the assumption of isotropic, homogeneous and quasi-stationary turbulence as well as 2.4.1.1. Mixing process. Mixing is a simple case to the lack of an effect of mixing upon velocity which can be used as an example of the calculation of fluctuations, is not obligatory and can be generally the instantaneous characteristics of a flow, say the varied in any way. instantaneous concentration.~ 91 The velocity, v(y,t), was modeled as follows. With Consider the stationary process of isothermal mix- t = 0 for m random points distributed uniformly over ing of two substances flowing at the same velocity the interval (0,Y3), values of fluctuating velocities from coaxial channels, Fig. 15. Neglecting axial corresponding to a Gaussian distribution were diffusion in a laminar flow we can describe the modeled statistically in turn. The end having a coordinate y l = 0 at an instant of time t = 0 was process by the equation 7 described by the distribution p ( V ) = ( l x / ~ V) exp ( - v2/2iz2), and the value t~'l,0) was determined. For ?nj ?2nj (VII) U ?x =DJ ~v ~ the adjacent point having a coordinate Y2 and separated from the former by the distance Ay2= where U is the axial velocity, which is constant over Y2 - Y l , we calculated the space correlation coefficient the cross-section and length, D i is the molecular by the approximation formula RAy,= exp(-- Ay2/L). diffusion coefficient, n~ is the concentration of the The value of the fluctuating velocity (y,,0) was j-th substance 0"=0,1), and x and y are the co- defined by a Gaussian distribution; in doing so, the ordinates. mean velocity was taken to be RAy2v(.v~,O) and the Substituting ~x/U = ?t, Eq. (VII) can be rewritten standard deviation was F2(1-R2y2), through the point m. In a time interval At~ we specified new m (gF/j ?2F/j (VIII) random points distributed uniformly over (0,Y3) ?~ = D j ?v ~ and modeled statistically the values v(v,At,) in each of them. For the end having a coordinate y ~ = 0 With an assumption of "one-dimensional" turbuwe evaluated the fluctuating velocity with a correllence, ~92 in order to describe the mixing process in a ation coefficient R~,, = e x p ( - A t t / r ) , mean velocity quasi-stationary approximation, we must introduce Rag(y],0) and standard deviation F2(1 -R2,~ ). At the into the equation a convective term involving the successive point: having coordinate y~, separated fluctuating velocity: from the first point by the distance A,y2~--,v~'2-Y~, the fluctuating velocity v(y~,Atl) was calculated in accor~nj = D t~2nj ?viii (IX) dance with the correlation coefficient Rau "Ray!, ?t ?y2 ?y with the standard deviation F 2 ( 1 - R a , "R,,y~) and where t is the projection of the fluctuating velocity the mean value equal to on the y-axis. The convective term is related to the ~[_R,,,, v(_v~,O)+R,,,,, v(_v],At, )+ Rag Ra,~ v(y~,O)]. variation in the concentration due to the difference between the flows through the left and the right The value of vO:,t) between the statistically modeled points was determined by linear interpolation. boundary layer (volume). The assumption of oneAn example of the solution for the case of dimensional turbulence is in conflict with the conhydrogen-air mixing is given in Fig. 20. The figure tinuity equation for an incompressible liquid 2.4.1. Physical characteristics

-------0

1.5

?y

and it can be justified only because of the substantial simplification of the problem under this assumption. To describe the mixing of hydrogen and air with the following initial and boundary conditions t=0 v=O: Y3

(nil0=0 f o r y = 0 - Y x , Y2-Y3, (nj)l ~---/'/1 f o r y = YI-Y2 ?nj?y= 0

,"1 ~..

• I

n=. -

-

~,i It

~"

/

I

I

tl /

I

~i ,,I

|~n

.I/~

I

c o.~- g

we can employ the following procedure for modeling the random field of turbulent velocity fluctuations

r= r(y,t). The value of the velocity v0',t) was obtained by modeling statistically its value for specified rootmean-squre fluctuating velocities P', Euler length scale L, and Lagrangian time scale r, which are the same for any value of y and t. The latter condition,

y (era)

FIG; 20. Concentration profiles in the mixing of hydrogen and air To=293 K. P=0.5 atm.. v-= 130 cm/sec, L = 1.5 cm, t = t 0 msec, nj--initial profile (t=0); for t = 9 msec; n-instantaneous concentration, ~--average value (averaging over 10 realizations), nr---experiment.

228

V. YA. BASEVlCH

shows that the presence of a convective term fitting the mass and heat transfer by an instantaneous fluctuating velocity markedly increases the calculated mixing rate and yields results close to the experimental data. 2.4.1.2. Flame propagation: one-dimensional approximation. The procedure described above has been employed to describe the propagation of a turbulent flame. 29'* The reaction rate was approximated by a single Arrhenius formula W = nA e x p ( - E / R T ) , with empirical values of the pre-exponential factor A and activation energy E. The reaction rate was expressed in this form for the sake of simplicity. This expression may be used when a detailed chemical mechanism is not important and the expression for W fits the heat generation rate. The latter circumstance can be verified by comparing the reaction rate calculated using the empirical expression with that obtained from a detailed kinetics mechanism under the same conditions. In our case, the expression for W has been established using the kinetics calculation results on flame propagation for hydrogen-air mixtures obtained in Refs 18, 19, 195. It is found that A=2.26. 106sec - t and E = l l kcal/mol. The energy and material balance equations can be written in the form 194'196

~cT

__

~

(n~)o=no, T = T O fory=0-Y~, Y2-Y3 T = T I for3'= Yt-Y,_,

at t = 0

(njh =nx,

a t y = 0 , Y3

x~

where Uk stands for the projections of the instantaneous fluctuating velocity on the coordinate axis x, which are interrelated by the continuity equation

apu,,.= 0 .

?y

=p

g(n/p)r . , --=u. cy

F.

any/p ~. WiJ+ E ~ Dip ani/P - ~ a(njlp)pu, ?xk

i~cTr

1,1T~ l,tnT T ,

(x)

~ axk

P

The turbulent velocity field has been modeled in a way similar to that for the above-mentioned mixing process. Calculations were done for hydrogen-air combustion where, [H2]o = 8.5-11 °,,, P=0.1~).5 atm., Y= 0-190 cm" sec- ~, L = 4.2 cm, and ~ = 3.2 msec. It is evident from the calculations that the width of the turbulent reaction zone is close to that of a laminar flame (for r=0). This observation suggests that the so-called "'wrinkled flame" model of the turbulent flame applies to the calculation conditions. This conclusion is consistent with the numerous experimental data on the validity of the wrinkled flames model. We have also established the reaction zone velocity in a turbulent flame U,r (normal to the combustion surface). The value u,r is contained in a wellknown expression, which is valid for the wrinkled flame model of turbulent combustion

2 aT _ ~ acTpu~

U

Po ~-t-t=7

In this case, system (X) consists of two equations, one for T and the other for n. Let us seek the solution for the initial and boundary conditions:

(XI)

where u r is the flame velocity, F, and F are the instantaneous combustion surface area distorted by turbulent fluctuations and the arbitrary mean surface area of half-conversion of the initial fuel. The surfaces F, and F cannot be defined within a onedimensional approximation. Figure 21 plots U,r against the root-mean-square fluctuating velocity E This relationship can be assumed from general physical considerations as the effect of small-scale turbulence.

k CXk

Preliminary numerical calculations have revealed that the error due to the violation of the continuity equation in a one-dimensional description of turbulence is minimal if the convective terms are cast in the form

?,cTu P t?x~-

and

P

?(n/p)u t?x~-

In a one-dimensional approach, the coordinate axisx coincides with the y-axis. Let us consider the combustion of a homogeneous mixture in a turbulent flow with a jet flame stabilization, Fig. 15. A high-temperature gas jet emerges from the internal channel and mixes with a fresh fuel-air mixture supplied by the external channel. In the mixture zone, the mixture is ignited and the combustion process propagates over the entire channel.

2.4.1.3. Flame propagation: two-dimensional approximation. Even a one-dimensional approximation provides a solution for the equations of the mixing and combustion processes. A two-dimensional ap-

SG

rain

I

1(30

J

2O0

0 (cmlsec) FIG. 21. Hydrogen-air flame velocity ",r vs i:.~94 [H2]o= 8.5 °~i,To= 293 K, P=0.5 atm., L=4.2 cm. r=3.2 msec.

Chemical kinetics proximation, however, provides a much more realistic analysis of the phenomenon, although it involves more complex calculations. The last term in Eqs (X) represents the contribution to convective heat and mass transfer by turbulent fluctuations. It can be simplified as follows. The difference between the material input and output per unit volume, with due reference to (XI) is

229

ever increasing effect on the process inside it. Therefore, the calculation regibn taken was sufficiently wide, the effect of convective motion along the flame propagation was considered in the form of a correction, and the calculation time was limited. The field of instantaneous fluctuating velocities U I . o ( X I , X 2 , t ) and U2,o(X~,X2,t) was simulated, as previously, by modeling statistically possible values of velocity for specified characteristics of turbulence. ?(n/p)puk cn/'p + n ~ ~P~kk ~P Simulation of the field of fluctuating velocities is an 2 -Z- . . . . P 2 u, pZUk extremely important operation that affects the results k ('Xk k ('Xk r° k CXk obtained. It is desirable that the resulting fields resemble realistic fields. The calculations were based where Uk refers to a medium of density p. Then, on an approximate procedure: statistical modeling under the assumption that for turbulent fluctuations was carried out for the whole field at an initial the following equality density Po, for specified root-mean-square fluctupUk = PO"Uk.0 (XII) ation velocity, Euler length scales: longitudinal L' holds, the form of the convective term becomes (Uk.o correlated along the axis Xk) and transverse L" simpler, where uk.0 pertains to a medium of density (Uk.o correlated in the direction normal to the axis x k) P0. In a similar way, we can express the term in the as well as Lagrangian time scale r, which are identical for any Xk and t. The latter point is heat balance equation. Now let us consider combustion of a homogeneous consistent with the assumption of isotropic, uniform, mixture in a turbulent flow with jet flame stabiliz- quasi-stationary turbulence and of the lack of an ation, see Fig. 15. The cross-section of the plane B effect of combustion on the turbulence parameters. perpendicular to the flow axis is depicted on the right Variations in the turbulence level throughout combustion are defined by Eq. (XII). side of Fig. 15. To calculate the main parameters of turbulent The solution has been obtained for boundary conditions in which the initial position of the plane combustion, some values obtained in the solution B corresponds to the section plane of the central of equations for instantaneous parameters must be averaged. However, no averaging has been perchannel: formed and we must content ourselves with a single t=0 n = n o, T = T o beyond the central channel realization due to the large machine-time requiren = n l , T = TI for the central channel ments. The characteristics of combustion determined while on the boundaries of tff~eexternal channel we in this way can be at variance with the mean values for specific cases. have The calculated effect of root-mean-square velocity on ~T ~n/p the turbulent combustion velocity are presented in Fig. ?x~ ?xk 22 and Table 13. In this series of calculations, [H2]0 = We will assume a uniform motion of the plane B at 17.5°,~, the pressure was 0.5 atm., the molecular a velocity U along the x-axis (Fig. 15): the distance diffusion coefficient was D.=0.795 cm2/sec, and the travelled will be x = U t . In a two-dimensional heat conductivity was ),. = 6.25- 10- 5cal/cm. sec- deg. approximation (k=2). we assume that exchange As ~ increases, the value of u r increases at first, along the x-axis and occurrence of convective and molecular exchange in the plane B are negligible. Some time after ignition the flame reaches the walls of the external channel and the combustion products 70 fill the entire cross-section. Preliminary calculations have demonstrated that 6O the required integration step with respect to space cannot be achieved in view of the complex calculations and insufficient speed and memory of the u computer employed. To partially resolve this problem, 1we selected a calculation region B~ in the plane B 40 ldesignated by the dashed line in Fig. 15), and the boundary conditions were related just to this region. 3C This restriction on the calculation region gives rise to I [ 0 5O I00 errors. In practice, in the course of time, the values of (cm/sec) ~7 and T on the boundaries will change as the combustion process develops and heat and mass transfer FIG. 22. Turbulenl velocity of a hydrogen-air flame u-~ xs through the boundaries of the region will have an turbulence level.I°'' [H2],= 17.5°,,. T,,= 293 K. P=0.5 atm.

230

V. YA. BASEVICH TABLE 13. Characteristics of turbulent hydrogen-air flames [H:]o= 17,5 %. T=293 K, P=0,5 atm. 196 cm/sec u, cm/sec u+rcm/sec Ur/U, 6. cm 6nr cm F~/F u.r cm/sec 0 45 90 150 190

29,5 -----

-39,5 65,5 29,7 19,4

-1,33 2,22 1,01 0,66

goes through a maximum and then decreases. This behavior is in qualitative agreement with experimental data. 197 Initially, enhancement of heat and mass transfer will accelerate the flame velocity; but, too high intensity of mixing with the cool fresh gas tends to lower the temperature in the reaction zone and prevents further development of chemical reaction. Checking the reproducibility of the results, we have established that there is a relatively small spread of values for low fluctuating velocities, 5 < 90 cm/sec, and that the spread in the combustion characteristics may be fairly large for high velocities ~. For instance, with ~=190cm/sec, the instantaneous values of Ur were as high as 94.7 cm/sec, although the mean value of ur is smaller. This indicates that an increase in ~ and the imminence of flame blow-off are contributing factors to the standard deviation of the numerical characteristics. In experiments, the flame blows off at much higher values of ~ (200-600 cm/sec). This may be attributed to a somewhat over-predicted velocity fluctuation when Eq. (XII) is used. For TI we have the ratio Po/Pt = u~.l/Uk.o ~- 5.6. The calculated ratio ur/u, and the rate of its initial growth are consistent with those observed experimentally: ur/u . ~ 1.5--4 for u, = 10-100 cm/sec and 5 = 100 cm/sec (Ref. 197 at atmospheric pressure: the value of Ur/U~ is expected to decrease at lower pressures). It follows from predictions that the values of 6,r and F , / F markedly increase with 5. No experimental data on these parameters are available. The absolute value of the combustion zone thickness, 6,r, however, remains sufficiently small: hence, the wrinkled flame model of turbulent combustion is still valid for the calculation conditions. It is seen in Fig. 23 that the turbulent flame velocity, ur, considerably exceeds the laminar velocity, u,, at 1 atm., decreases with decreasing pressure for ~ = 190 cm/sec; but, it increases for 5 = 90 cm/sec and for laminar flow (the latter circumstance is the result of the increased molecular diffusion coefficient, higher thermal diffusivity and lower density). As the pressure is reduced, the combustion zone thickness, 6~r, increases less in the turbulent case and more in the laminar case. The thicknesses are comparable at P=0.1 atm. The ratio of the instantaneous surface of combustion to the mean value

0,17 -----

-0,17 0,172 0,179 0+31

-1,06 1.19 1.37 1,48

-38,3 55,0 20,7 13.1

IZ" Ill

I0(

--"

" A-2

i X

0-3

I

O.S

I

P toLm)

FIG. 23. Characteristics of a turbulent hydrogen-air flame vs pressure.J98 [H2]o= 17.5 0/,,,~i,cm/sec: 1-0, 2-90, 3-190.

F J F is smaller for low pressures (it is equal to unity for a laminar flame). These results are qualitatively consistent with experimental data on the relationship between ur and u,=J(P) 199 and can be conveniently explained within the following framework. For the wrinkled flame mechanism of turbulent combustion, ur ~ F,/F. The value of F, is dependent on the characteristics of turbulence and on the ratios of turbulence length scales to the value of 6hr. If the length scale corresponding to a certain fluctuation frequency is less than 6,r, it no longer contributes to the surface development, while it does affect the value of 6,r by increasing the latter. Thus, an increase in the value of 6,r due to the decreased pressure will decrease the value of F,. Figure 24 compares calculated results for mixtures with low molecular diffusion coefficients and viscosity (mixture 1, diluent=At) to those with high

Chemical kinetics

FnT F

, / "

*

"

o.z V

~ I P

l

E

) 4,g /

?

/ :,s!

!?i i

I00

(cm/sec)

I

i

200

FtG. 24. Characteristics of a turbulent hydrogen-oxygen diluent flame vs root-mean-square pulsation velocity for several diluents. ~98 [H2]o= 17.5 %, P=0.5 atm. l--mixture {diluent = Art 1: 2--mixture {diluent = He) 2, A = 0.0345 cm; 3--mixture 2, A =0.1 cm.

values (mixture 2, d i l u e n t = He). The value of u T is always higher for mixture 2 than for mixture I, but the relative increase of ur is greater in the latter case. Thus, when ~ = 190 cm/sec the ratio UT/U, is 1.75 for mixture 2 and it is 3.35 for mixture 1. In the absence of turbulence, the reaction zone is wider for mixture 2 than for mixture 1, whereas the ratio F , / F is, in contrast, larger for mixture 1 : for mixture 2 it is close to unity. With due reference to the increased thermal scale A = v 3!4 resulting from a higher viscosity v 2°° of mixture 2, the observed affects are more pronounced (in the calculation, the value of A is specified as a mean distance between the points at which velocities are statistically modelled in the simulation of turbulent fluctuations). The predictions agree qualitatively with the experimental data. ~9; An increase in the value of 6,7", with high coefficients of heat and mass transfer and of viscosity, will decrease the value of F, and cause a relative decrease in the value of u r. The rise in v and accordingly in A will reduce further the contributions of small-scale heat and mass transfer as well as the value of u.r. As the value of ~ increased the value of u r increases at a relatively slower rate for viscous mixtures with high values of the molecular transfer coefficients, and vice versa. Thus, the suggested approach for description of turbulent combustion proves to be correct both in the main physical relationship and in detailed specific features.

231

2.4.2. Kinetics characteristics The main feature of the calculation method concerned is that it offers an opportunity for employing a detailed kinetics mechanism of any complexity to describe a chemical process in a turbulent medium without involving empirical relations for the reaction rate. The satisfactory qualitative description of the physical characteristics of a turbulent flame, outlined in the foregoing discussion, has offered hope of a satisfactory description of its chemical characteristics as well. This prox, ision has been verified in a one-dimensional approximation, by calculating the combustion characteristics of h y d r o g e n - a i r mixtures with jet flame stabilization, Fig. 15. 2°1 The calculation results are compared below with experimental data for hydrogen and methane. The reaction scheme used for the terms 2~j W~j and 2~rhuWu of the system of Eq. (X) is taken from Table 1, forward and reverse reactions, 1, 4, 6-9, 11-13, 17, 28, 29a. Figure 25 gives concentration and temperature profiles in the combustion zone of a turbulent flame. The curves in 25a represent the distributions of instantaneous values T for a time of 10 msec on the left of the ordinate and for the mean 'F (the number of realizations is 10) for t = 0 , 2, 4, 6, 8, and 10 msec on the right. The curves in 25b show the corresponding distributions of instantaneous con-

T,?,K

(O)

6

t*-IOy

8

3C~

°

C

/-.\ n,fi,%

{b)

\I -2:o y/\

2

22

24

26

2.8

y (cm)

I

I

32

3.4

I~---B,vl2----~. 36

-1 .

3 8

4

FIG. 25. Temperature and composition profiles for a turbulent hydrogen air flame. "~1 [H , ] , - 8.5 ",,. T. = 293 K. P=0.5atm.. T 1=1823K. [O]1..=0.05°,,. U=190cm,sec. O = 8.6 ram.

232

V. YA. BASEVICH 125C

10OC

I--

-'."~q~..

3

..... ...

7'50 • %.. ......

% .....

~00

O.T', - -

4 ......

....,...

..'

• "' " " . - " " "

T(K)

/

FIG. 26. Turbulent flame velocity vs temperature: (a) calculated 2°1 U~T([H2]o=8.5%, P=0.5 atm.,/i= 190 cm/sec) and (b) experimental 2°' u,4[CH,]o= 9.5 %, P=latm., Re= 50,000, inverted cone stabilization, no correction for reaction product expansion).

tHZl

0"O~"

.'"' I"

I

m

.'/ . . . . . .

t .z3, 02".

~

~

s

- 3

:,/

I'

, 25

5

75

t (rnsec)

centrations n(j) (j= H2, 02, OH, H, O, HO2, H202, and H20) and of the mean values n(H2). As the initial temperature of the mixture is raised from 293 to 500 K, Fig. 26, the value of ur is observed experimentally to increase by a factor of more than 2 (a mixture of 9.5 ~o methane with air, P = 1 atm., the R e number is 50,000). It follows from calculations that once the initial temperature T Orises from 293 to 450 K, the value of U,r goes up by a factor of about 1.35 (in accordance with the above expression u r " U,r since U~r has not been measured). An adequate description of the turbulent flame structure does not require criteria for determining the flame blow-off limits. Flame blow-off shows up as extinction behind a stabilizer. Approximate as it is, the suggested method of calculation of turbulent combustion allows us to determine flame blow-off by temperature and concentration profiles. Although Eqs (X) do not contain explicitly the flow rate at which the flame is blown off, its absolute value determines the characteristics of turbulence and particularly the value of root-mean-square fluctuation velocity ~. It us known from experiments that when the diameter of a stabilizer is enlarged, the stabilization limits may be extended. According to the results of experiments 9s carried out with 8.5% of H 2 and P = 10 kPa, a limiting blow-off velocity on a 7.5 mm dia active jet stabilizer (the jet containing atomic products) is 8 m/see. Predictions show that a flame of a 5 % hydrogen mixture is stabilized on a 8.6 mm dia active jet stabilizer (with O-atoms addition), as can be seen from the behavior of the temperature and hydrogen concentration on the axis of a combustion chamber, Fig. 27 (curve 1). For the same mixture, other conditigns being equal, the flame extinguishes on a smaller diameter (3.7 mm) stabilizer (curve 2). The temperature decreases and the hydrogen concentration on the chamber axis increases to a high value. Let us examine the effect of turbulence upon the parameters of the chemical reactions involved in com-

FIG. 27. Temperature and hydrogen concentration profiles on the combustion chamber axis.-'°~ T,~=293, P=0.1 atm.. if= 190 cm/sec. I-H_,],,, o, l

5

2 3 4

8.5 5 8.5

[ 0 ] , .... °,,

~b.mm

3.4 3.4 3.4 5.6' I0 -~'

8.6 3.7 3.7 3.7

bustion. The turbulence-induced increase in the heat and mass transfer lowers the maxima and gradients of intermediates, including the active centres. At the same time, the most favorable conditions for the reaction may establish themselves, regarding component proportions and temperature. In principle, this problem can be solved using numerical analysis of chemical kinetics• The calculations below have been done for mixtures of hydrogen and methane and air. 2°3 For the sake of simplicity, only those reactions that contribute significantly to the reaction under particular calculation conditions have been taken into account. The kinetics scheme selected on the basis of preliminary calculations includes 18 species (O2, H2, OH, H, O, HO2, H20, ["t202, CHa, CH3, H2CO, CHv HCO, CO, CO2, N2, NO and N) and 35 forward and reverse reactions (35 x 2). The calculation results differ depending upon the fuel type and temperature of the stabilizing jet Tt (in all the calculations, the jet is air containing 0.05 ?'~iof oxygen atoms). As the root-mean-square velocity increases, the calculations are more time-consuming, and the more complex the reaction kinetics scheme, the higher the machine-time requirements. For this reason, the calculations for the hydrogen-air flame were carried out up to a maximum value if= 190 cm/sec, while the calculations of the methane-air flame include a maximum value ~ = 90 cm/sec.

Chemical kinetics

233

TABLE 14. Conditions and results of turbulent flame calculations 2''3 Maximum 7",,

T I

No.

H2

CH,~

K

K

1 2 3 4 5 6 7 8 9

8.5 8.5 8,5 8.5 8.5 17.5 17.5

----

980 980 980 980 980 1640 1640 1920 1920

1823 1823 1823 980 980 1640 1640 1920 1920

-

-

-7,5 7,5

P

It

l In 1

concerltrations.

atm. cm/sec cm:sec

cm

OH

H

O

0.5 0.5 0.5 0,5 0.5 0.5 0,5 0.25 0,25

0.65 0.69 0.71 0,53 0,84 0.43 0.58 0,79 0,96

0.274 0.227 0.179 0.020 0,054 0.335 0,410 0,496 0.462

0.081 0.078 0.074 0.078 0.119 0,57 1.28 0,638 0,610

0.511 0,375 0.264 0.122 0.195 0.32 0.56 1.46 1.36

45 100 190 45 190 45 190 22,5 90

19 26.4 36.4 6.7 12,5 28,5 66,5 8,9 15.9

"

~n t

NO* CO

H2

0.27 0.40 2,60 2.94 0.203 2.24 3.07 0.218

J rel.un.

[4 m

tool I" sec

0.126

155

0.126

I 48

0.0724 0.0344 0,0845 0,66 2.6

093 0.485 0.846 5.55 10.63 0.40 0.49

*Volume proportions × 10".

In the calculation of the h y d r o g e n - a i r flame, the h y d r o g e n c o n t e n t was taken to be 8.5 a n d 17.5 04, at a pressure P = 0.5 atm. T w o cases were considered. In the first case, the t e m p e r a t u r e of the stabilizing jet is h i g h e r t h a n the a d i a b a t i c flame t e m p e r a t u r e (Ta), T 1 > T a. T h e values of U,r, 6 , r a n d the concent r a t i o n of all the p r o d u c t s were calculated for Ta = 1823 K, [H2] o = 8.5 '~o (Ta= 930 K), r o o t - m e a n - s q u a r e velocity ~ = 4 5 a n d 190 cm/sec. T a b l e 14, cases 1-3, lists m a x i m u m c o n c e n t r a t i o n s of the m a i n active centers, i.e. O H , H, a n d O, which c o r r e s p o n d to a final calculation time of 10 msec (the p o s i t i o n s of the m a x i m a on the ),-axis do n o t coincide). It is evident from the table that the conc e n t r a t i o n s of the O a n d H a t o m s a n d of the O H radical are h i g h e r at lower intensity levels. T h e local rate of the c o m b u s t i o n reaction varies a l o n g the coo r d i n a t e y a n d it can be c h a r a c t e r i z e d by its maxim u m value, 147=, at each i n s t a n t of time. T h e latter is calculated as the rate of h y d r o g e n c o n s u m p t i o n by c o n s i d e r i n g the c o n t r i b u t i o n s of only those elem e n t a r y reactions involving O H a n d O with H2:

W = k, [ O H ] . [H2] + k_ 6 [ 0 ] . [ H 23., where k I a n d k_ 6 are the rate c o n s t a n t s of the a b o v e reactions. T h e value of W,, also is h i g h e r at lower intensity levels. T h e calculated values of W,, for t = 10 msec are given in T a b l e 14: the values are averaged over two m a x i m a - - o n the left a n d right axes of the comb u s t i o n c h a m b e r . T h e same table presents the value of the p r o d u c t of c o n c e n t r a t i o n s J = [ O ] . [ H ] which is a p p r o x i m a t e l y p r o p o r t i o n a l to the intensity of hydroxyl emission: :°4 this value is also an average over the two maxima. In the second case. TI = TQ. T h e calculations were carried out for [ H 2 ] 0 = 8 . 5 a n d 17.5°,, T a b l e 14. cases 4-7. Here the turbulence exerts an o p p o s i t e effect u p o n the c o n c e n t r a t i o n s of the m a i n active species, upon the emission a n d rate of h y d r o g e n combustion: they increase in the range i i = 4 5 - 1 9 0 cm/sec. F o r m e t h a n e - a i r flames, the calculations were based on an initial m e t h a n e c o n t e n t [ C H 4 ] o = 7.5 oo, a pressure of 0.25 atm. a n d T~ = TQ. T h e h i g h e r the

turbulence level, the lower the c o n c e n t r a t i o n s of the m a i n active centers a n d the faster the rate of the combustion reaction defined by the e q u a t i o n c o n s i d e r i n g only c o n t r i b u t i o n s of the reactions of m e t h a n e with O H , H a n d O [two reaction channelsl: W=k3~[OH].[CHa]

+k33[H].[CH.~ ]

+(k3~ + k3~)[O]. [ C H , ] , where k31, 1<33, k3s a n d /<3,) are the rate c o n s t a n t s of the relevant reactions. Thus, for m e t h a n e at T1 = T , , an increase in the turbulence level causes the c o n c e n t r a t i o n s of the active species to fall r a t h e r t h a n rise, which was the case with hydrogen. T h e v a r i a t i o n s in the active species c o n c e n t r a t i o n s with turbulence level m a y be u n d e r s t o o d in terms of increased heat a n d mass transfer u n d e r the c o n d i t i o n s of accelerated flucfuation velocity. Let us c o m p a r e the c o m b u s t i o n of h y d r o g e n a n d methane. F o r h y d r o g e n at T1 > T~ Ithe case with an active stabilizert, lowering of the t e m p e r a t u r e in the reaction zone b e h i n d the stabilizer results in a decreased c o n c e n t r a t i o n of the m a i n active species: the h i g h e r the turbulence level, the faster the decrease. T h i s is the principal cause of the decrease in the m a x i m u m rate of c o m b u s t i o n . Sufficiently far d o w n stream from the stabilizer, the temperature approaches the a d i a b a t i c value, the b e h a v i o r is identical to the case T1 = T,. T h e case with T~ = T, is the most c o m m o n a n d c o r r e s p o n d s to c o n v e n t i o n a l stabilization c o n d i t i o n s (buff-body, l o w - c o n s u m p t i o n pilot burner). The temperature a r o u n d the c h a m b e r axis is not elevated, a n d turbulence will produce an increased heat a n d mass exchange. T h e heat a n d the main active species. n a m e l y O a n d H a t o m s a n d the radical m o v e towards the fresh mixture at a faster rate. thereby ensuring a h i g h e r local reaction rate, W, a n d a larger value of the p r o d u c t J. It is well-known that an increasing turbulence level c o n t r i b u t e s to the emission per unit of the reacted fuel 2°5 a n d it is consistent with the calculation results on the effect of u u p o n J. T h e o p p o s i t e is found in the calculation of active species c o n c e n t r a t i o n s for m e t h a n e c o m b u s t i o n (TI =

234

V. YA. BASEVlCH

T=). The difference in the behavior of hydrogen and methane can be attributed, in a qualitative fashion, to the following. In the two cases, the branching chain reaction involves mainly hydrogen, and the process is most rapid in the presence of hydrogen H2 and reaction intermediates H, O and OH. The hydrogen fuel and intermediates are separated in space in a hydrogen mixture. Hence, the turbulenceinduced exchange facilitates the branching process. In methane combustion, the fresh mixture is devoid of hydrogen. It forms at the reaction site. So, the intensified removal of the active species due to turbulence is not compensated for by the concurrent chain branching. The concentration of active centers drops, although the maximum reaction rate is somewhat higher as a result of the raised local concentration of methane. It is evident from experiment that in methane combustion the emission per unit of the reacted fuel decreases with increasing turbulence level. 19°'2°s In the case of methane, emission is due primarily to the chemiluminescence of the excited radicals C~ and CH °. Their concentrations have not been calculated; but, we can anticipate that they vary with the concentrations of the main active species, as those of other radicals do. Experiments 2°6"2°~ indicate a decreased concentration of O atoms with increasing root-mean-square fluctuating velocity, Fig. 28. The atomic oxygen concentration was determined by the method outlined in Ref. 208 from the emission of the reaction O + N O = N O z +hr. To this end, a small amount of NO was added to the combustible mixture and the emission was measured photometrically. The other two main active species, i.e. the H atoms and OH, are expected to behave in a similar way, since their concentrations are interrelated and rise or fall simultaneously in a particular mixture. It is noted that the authors of Ref. 209 observed increased concentrations of OH and O with turbulence level in a methane-air mixture in a stirred reactor. This may be accounted for by an increase in the flame temperature at higher turbulence levels recorded in their experiments. According to experimental investigations,z97 at high fluctuating velocities t300-600 cm/secl the reactions in turbulent flames tend to slow down and

C

t--

-0.2

-0.4

I

I0

I

2O

r

3O

U (m/see)

l

I

P 60

(cm/sec)

Fx(i. 28. Logarithm of the methane air flame emission intensity with added NO vs velocily.-~"7[CH,t].=6.5 7.5 ",, T,,=293 K. P=0.25 atm.

subsequently cease. It is reasonable to argue that the decrease of the concentrations of the main active species in a turbulent flame with increasing turbulence displayed by methane in calculations and experiments at low turbulence levels, is responsible for this tendency. We can hypothesize that with hydrogen these processes will occur at higher values of ~. The leveling off and drop of the turbulent flame velocity at high fluctuating velocities manifest themselves in two-dimensional calculations. 196 The general consistency of experimental and theoretical findings indicates that the suggested method of modeling chemical reactions involved in turbulent combustion is correct, at least qualitatively. Using higher-speed computers, this method can be employed for practical calculations. To the best of our knowledge, there is only one other study 2~° in which the Monte Carlo method is used to calculate the characteristics of turbulent combustion. 2.5. Promotion of Combustion This section provides a somewhat more detailed description of the experiments and calculations related to combustion promotion (by acceleration due to additives), since they directly display the role of the rate of a chemical reaction in the combustion processes. The promotion effect has both applied and theoretical aspects and deserves to be discussed separatel y.9a.21 t In the operation of many practical combustors, the combustion products mix with a fresh mixture (recirculation, afterburners, gasifiers, etc.) resulting in higher concentrations of the active species, free atoms and radicals O, OH and H in the initial mixture. These species are expected to affect the combustion process. It is also essential to clarify the possibility for accelerating the combustion process in a flame by introducing combustion products either into a fresh mixture or into the reaction zone. The effect of small additives--reaction promoters and inhibitors--on the low-temperature oxidation of hydrocarbons has been the object of numerous investigations. A qualitative explanation is given in terms of the theory of branching reactions. In hightemperature combustion, where active centers are generated relatively fast and where they can sometimes be transported to the reaction zone by diffusion, the possible effect of additives has been open to disscussion. In fact, as the temperature rises (T>90OK), the effect of peroxides, aldehydes, and NO 2 is reduced even in the case of self-ignition, as shown in Refs 161, 212. It is reported in Ref. 103 that an addition of 1.45 o~, of H2CO to a methane-oxygen mixture at temperatures ranging from 1330 to 1820 K will not reduce the induction period. In Ref. 213, additives of this kind were not observed to affect chemically the flame propagation limits or flame stabilization.

Chemical kinetics

235

of active species, free atoms, and radicals over a wide range of operating conditions as well as to undertake a kinetics description of the process. T M ' 2 1 1 . 2 2 3 Experiments with an air flow heated by a hydrogen diffusion flame show that there is super-equilibrium concentration of hydroxyl immediately behind the diffusion flame zone. 224 The hydroxyl concentration falls with increasing distance from the combustion zone. The first report of a super-equilibrium concentration of active species (H atoms) in the reaction products behind the combustion zone was made in Ref. 225. The existence of super-equilibrium concentrations has subsequently received numerous confirmations. We measured hydroxyl concentrations and found them to be of the order of 101L1013cm -3. Later measurements show that the concentrations of oxygen atoms were of the same order of magnitude. The concentration was determined by the relative amount of hydrogen burnt and by the distance from the burner. These measurements were carried out in a flow which was heated by burning hydrogen to a high temperature (900-1800 K) and which contained a sufficient amount (8-16 %) of oxygen for subsequent combustion. The concentration, n, of the hydroxyl OH and oxygen atoms decreased in accordance with the law 1/n=k[M]t+l/no (n and no being the current and the initial concentrations, respectively, t--the recombination time, [ M ] - - t h e bulk concentration of the gases, k - - a constant~ The value of k was 1.5- 1011 12/mol2" sec for OH and 1.14.101112/tool 2, sec for O (assuming a termolecular reaction). The concentration of H atoms has not been determined. To vary the concentrations of active particles, the fuel was introduced at various distances downstream from the H2-diffusion burner. The temperature and the composition of the stable components (02, N2, H20) were maintained constant at the site of fuel introduction in all the experiments. Ignition experiments on this type of apparatus have revealed 224 that the ignition delay time for injected

The lack of direct observations of promotion of combustion of mixtures of hydrocarbons and hydrogen with air and oxygen upon addition of stable substances is due to the fact that at high temperatures the difference between the rates of initiating reactions involving additives and the main fuel is small. Also the difference in the rates of reactions involving active centers that diffuse out of the flame zone is less pronouced. Therefore, in the self-ignition and combustion processes at high-temperatures, the promotion effects may show up only upon rapid introduction into the combustion zone of highly reactive substances, such as O, H and OH. 2a 4 Isolated observations of such processes in hydrocarbon combustion were reported earlier. In Ref. 215 the limits of stabilization of a propane-air flame on a laboratory burner were extended if the combustion zone was exposed to radioactive Au. According to the results, 2~6 the limiting stabilization velocities increase by 40 % when a corona discharge (1 kHz, 800 W) occurs between the stabilizer and the combustion chamber wall. In Ref. 217 a propane-air mixture highly pre-irradiated with radioactive Au had a flame velocity which was nearly twice that of the unradiated mixture. The flame velocity was also found 2~8 to be affected profoundly by ozone added to the combustible mixture. It is safe to claim that in all the above-mentioned experiments the action of electric discharge, radiation, and ozone contributes ultimately to the formation of active species which accelerate the combustion process. It is noteworthy that the direct reaction of hydrocarbons with O, H atoms at low pressures is well known and is observed in atomic flames. 219 The effect of O and H atoms upon hydrogen ignition was investigated in Refs 220-222, where the ignition limits were found to extend. The objective of our work was to study experimentally the feasibility of promoting combustion of hydrocarbons and hydrogen by direct introduction

10 3

V~ 20C

O,E; ]

o

t I

/

-:

,

o.[I

0,| I

~:) (]F"

0

x

I

I~:30 MIO0 1300

,I)~

I

I:DO0

~e r

I

IlO0

•

I

...f

, ,,/.-"

m

-.--

I ~00

rI,Z I

I

I

~ilO0

800

I

~FO0

I

60~

I

~Sil40

T(*C)

FIG. 29. M e t h a n e ignition delay times for various temperatures vs distance (ram) between the active species source and the fuel inlet site: P = 1 atm. 224

236

V. YA. I]ASE'vlCH

TAaLE 15. Ignition delay times of stoichiometric methaneair mixtures, msec T,K Concentration x I0-14 i'OH]0 cm-' [0]. Calculation 3° Experiment ~°9

o-I

1523 1338 1223 1048 0,51 0.85 1.2 5

0,85 1.3 1,31 1.95 1,7 3,2 5 5

2.1 3.02 5,4 5

O.Z

" •O.l~ o [1.

methane (Fig. 29) and higher hydrocarbons in a turbulent flow at a pressure of 1 atm. and temperatures ranging from 900 to 1800 K were 2-200 msec and they reduced by an order of magnitude or even more in the presence of increased concentrations of active species (OH, O, H) at the same temperature. For identical delay times, the ignition temperature was reduced by a factor of two in the presence of active particles and the effective activation energy decreased from 71 to 19 kcal/mol. The kinetics calculation 3° shows that the observed and the calculated ignition delay times are consistent in order of magnitude, Table 15. The authors of Ref. 226 studied spark ignition, pilot flame, and heated body and discovered that if the initial concentration of active species is increased, the lean flammability limit is appreciably extended. Similar experiments were made using atomized liquid fuel (kerosene). In this case, the limits of ignition from a pilot flame are extended at relatively higher temperatures than with gas mixtures 223 containing an appreciable amount of fuel vapor in the flow. The limits of flame stabilization on a bluff-body have been studied with homogeneous mixtures 224 and atomized liquid fuel (kerosene and cetane) over temperatures ranging from 400 to 723 K. In the case of homogeneous mixtures, both the lean and the rich limits were extended at high concentrations of active species. For an atomized liquid fuel, only the lean limit was investigated and it was found to be extended, too. The latter also '~,as observed at relatively higher temperatures. In some of our work we used a glow-discharge tube as a source of active species (primarily oxygen atoms and molecular excited oxygen) and conducted experiments at lower pressures. The concentrations of atomic products were controlled by the current and were close to those given above for the hydrogen diffusion flame (1013+1016 cm-3}. At pressures >0.01 atm., the jet of the glow discharge products proved to be markedly heated. Hence, care was taken to separate the effects of the jet temperature and the active centers concentrations on the combustion process. Thus, experiments were set up with a view to stabilizing a hydrogen-air flame (7.5-17.5 !';) in a turbulent flow at pressures 0.0684).5 atm. Provision was made to determine the limits of blow-off of the hydrogen-air flame with stabilization by an active jet and by a disk stabilizer upon preliminary intro-

01 I

P

I

f

H2 (°/.]

FIG. 30. Limiting pressures of turbulent flame stabilization on a disk vs composition of a hydrogen-air mixture. To=293 K . 95 1 - without atomic oxygen addition, 2 -with atomic oxygen addition.

duction into the flow of oxygen atoms from the discharge. Addition of oxygen atoms to the initial combustible mixture, other conditions being equal, appreciably lowers the stabilization pressure (Fig. 30}. See also Refs 227, 228. The kinetics calculations of flame stabilization using Eqs (VII with no allowance for turbulence (using the experimental criterion r/~>0.95, see the foregoing discussion) permit quantitative estimations of the stabilization limits and of their extension. For stabilization by an active jet, the relative errors of the calculated flame blow-off pressure p=

Pc=l - Pcxp

Pexp and of the consumption

Q= ~cal

--

Qexp

Qexp

did not exceed 36 0;,. The use of a heated stabilizing jet of oxygen atoms reduced the limiting blow-off pressure from 0.136 to 0.068 atm. The calculations for a disk stabilizer yield larger discrepancies in comparison with experiment. They confirm the substantial promotion effect of the oxygen atoms present in the initial mixture for a disk stabilizer, too. The higher the flow temperature, the greater the relative growth of the blow-off velocity AU/U, see Table 16. The quantitative calculations allowing for turbulence give the same evidence. Thus. with a smalldiameter (3.7 mm) active stabilizer, the flame of a 5 o, hydrogen mixture can be still maintained, according to the predictions, by the stabilizer, Fig. 27 (curves 3): although the temperature is moderate, it goes through a minimum and increases slightly, whereas the hydrogen concentration goes through a maximum and decreases. The main stabilizing factor proves to be

Chemical kinetics TAI3Lt: 16. C M c u l a t e d

r e s u l t s 21] o n

[O],,.cm 3 10 ~'' 5 101' 7.5" 10 la

10 ~" 10 ~" 5.10 ~3

40

the relative extension of

the flame stabilization velocit.~ (At_' U)and relative increase of laminar flame velocit) tAu,,u,I. Hydrogen air mixtures. [H2].= 10",,. P=0.22 arm. T.,. K

A t t'. ",,

293 293 293 293 452 452

0 3 24 55 0 6.2

Au.

u..

237

_

•

3o-

ql'

T M

• i~..........I

",,

0 1.9 8.1 182 0 3.3

a high content of atomic oxygen [O]a = 3 . 4 % . An oxygen jet containing an equilibrium concentration of atoms [O]~ = 6 - 1 0 - ~ ' ° , , is not capable of maintaining the 8.5 o,, Hz.flame: the temperature suddenly falls and the hydrogen concentration around the axis rises considerably (curve 4). The effect of p r o m o t i o n of laminar flame velocity was investigated at pressures from 0.032 to 0oll atm.] s.195.229 The oxygen passed through a discharge tube and a nozzle to a reservoir, while hydrocarbon or hydrogen was supplied by means of a tube mounted concentrically with the nozzle. After the mixture had been spark-ignited, the flame propagation velocity was recorded by a scanning method or with a quick-response resistance thermometer. The flame velocity increases appreciably in the presence of the glow discharge products (Fig. 31]. P r o p a n e - b u t a n e oxygen mixtures required relatively high discharge currents, compared to hydrogen mixtures. In the latter case, at relatively low temperatures the p r o m o t i o n effect of O2(1A) formed in the discharge was observed. ~95"23° The p r o m o t i o n effect is more pronounced with lean rather than with stoichiometric or rich mixtures. The calculations of the flame velocity for a hydrogen-oxygen mixture have shown that u, also increases if atomic oxygen is present in the fresh mixture, but the relative increases of the velocity, Au,/u, is smaller than that of blow-off of a stabilized flame, see Table 16. The absolute velocities u, prove to be close to the values obtained in laminar flame experiments. When active species were produced in the diffusion combustion of hydrogen, consideration was given to their effect on the flame propagation in a turbulent flow. 2°2 As their concentrations were raised, the emission of the torch was enhanced. It has been shown that the characteristics of the turbulence remain practically constant, with active species present or absent. It is evident from experiment that a higher content of chemically active species in the fresh mixture contributes considerably to the flame velocity ur. Introduction of superequilibrium concentrations of OH. O and H at initial temperatures of 293 to 473 K raises the value of UT by a factor of up to 1.5, Fig. 32, a. 2°-' The curve b in this figure represents the

to

0

IO0

I

200

J

300

I

400

500

u(ma)

FIG. 31. Apparent velocity of a laminar propane butane flame vs current i in a glow-discharge tube serving as a source of active species. -'2" Equivalence ratio 7=3. P= 0.058arm. Outlet of the discharge products: I direct. 2 through the oxygen atom recombination grid. (o) I° a

[H2]o(:/o)

21

t9

17

I

I

I

zs > i ~ . n

2z~

t.~

1

175

•

I

2 iR

15 []

I I

I

•

2

!

I

2.25

2$

4o

v 3O

O.2 0.4 0.6 m [OH*H +0} ('7.)

FIG. 32. Effect of the initial concentration of active species on the velocity of a hydrogen-air flame, a. Experiment: 2°2 To=453 K, P= 1 atm., Re= 70,000 (l --with no active particles, 2--with active particles), b. Calculation: TM [ H , ] . = 8.5 %. To=293 K, P= 1 atm., u= 190 cm/sec. calculated value of U.T increasing with the concentration of introduced active centers for the same initial temperature T o = 2 0 ° C . As indicated earlier, calculations on the basis of detailed kinetics mechanism are possible for the time being only in a one-dimensional approximation, and we can define only the value of U.r to which Ur is proportional. The active species cor.centrations correspond roughly to their experimental values, as does their ratio In(OH)0 : n(Ot0 : n(H)0 ~0.03:0.3 : 1 ). The plotted values of U.r have been averaged over a time 10 msec. In short times (under 3 msec) the concentration-induced increase of u. r is far greater and amounts to tens of per cent. In the course of time, the active species concentrations in front of the flame drop due to recombination and, accordingly, the value of U.r decreases. There are a number of studies reporting the accelerating effect of atoms and radicals introduced

238

V. YA. B^SEWCn

into the fresh mixture upon the combustion processes. Thus, in Ref. 231, the limiting velocity of methaneflame blow-off is increased with decreasing distance between the burner and the source of active particles. The ignition delay times in an oblique shock wave were measured and calculated in Ref. 232, and a conclusion was drawn that the observed and the predicted ignition delay times are in accord only with the allowances for the initial concentrations of the O, H atoms and hydroxyl provided by a heater (temperature 1389 K, pressure 0.35 atm.L A similar conclusion is made in Ref. 233 where ignition delay time in a normal compression wave and hydroxyl concentration prior to the normal compression wave in a stationary combustion of hydrogen in a supersonic flow (M = 5) were measured. The above considerations indicate that promotion of combustion by active species is rather common. It has been observed in various combustion processes, in turbulent and laminar flows, at atmospheric and lower pressures, over a wide temperature range, with homogeneous mixtures and atomized liquid fuel, in air and oxygen mixtures. Thus, there is every reason to extend the phenomenon of chemical reaction promotion to hightemperature combustion processes. The promoters in the latter case must be highly reactive. Ag"l~dicated earlier, the detailed kinetic model calculations do describe, at least qualitatively, the promotion effects observed.

2.6.

Chemi-ionization

It is common knowledge that a superequilibrium ionization of nonthermal origin occurs in hydrocarbon combustion. 7 The mechanism of chemiionization and subsequent recombination is reported in Refs 234-236 to occur as follows: CH + O---~CHO + + e CHO + + H20---.CO + H3 O+ H3 O+ + e ---.H20 + H. The rate constants of the above reactions at flame temperatures are about 10 -12 , 10 -11 and 2.1.10 - 7 cm3/sec, respectively. The detailed kinetics model for methane oxidation was employed in a study s° of chemi-ionization. The mechanism was simplified and reduced to 41 reactions (processes 1-14, 17, 19, 21, 24, 26-31, 33, 35, 40, 42--46a, 54, 57, 59, 66, 70, 83, 86). Along with the above reactions, the mechanism also included five reactions responsible for the production and consumption of the CH radical, Table 1: CH2 + OH---*CH + H 2 0 CH 2 + H---*CH + H 2 CH2 + O---*CH + OH CH + OH ---*CO+ H2 CH + O--*CO+ H.

(95) (96) (97) (98) (99)

I / / / / / ,o,

c

O5

_

! 1

--~

I

0.2

I

0.4

0,6

08

(msec)

FIG. 33. Logarithm of electron concentration, n cm-3 vs combustion time of stoichiometric fuel-air mixtures. T,,= 293 K: P=0.5. 1.0, 1.5 and 2 atm. Shaded region--experiment.23~ [ C 3 H s ] o =4.2 %~,,curves---calculation.5° [CH,~]o= 9.5 °(,.

The rate constants of these reactions have been estimated very roughly. These estimates have been used in the discussion of the detailed kinetics mechanism for the H - C - N - O system. An electron concentration in isothermal ignition was calculated using a standard kinetics program. The calculation was performed for the conditions of experiments 237 in which the electron concentration was measured for a stoichiometric propane--air mixture for various pressures; however, the calculations were performed for methane--air at an identical stoichiometry. The temperature was assumed to be equal to the flame temperature 2130 K. The calculation results are given in Fig. 33. The shaded region represents the experimentally measured maximum concentratin of electrons, n. In the flame, the temperature rises from a low initial temperature to a final value in a time equal to about 1 msec. Since in the calculations the temperature is assumed to be its maximum value from the very outset of the process, the reaction is over in 0.1 msec; during the remaining time, recombination processes

occur.

At a later time, data became available 23s on the measured concentrations of electrons and ions in the methane flame at 1 atm. T = 1150-1467 K. For T = 1453 K and [CH4]o=6.5 %, the calculated concentration of positive ions is n,,o. =4.3.1011 cm-3; in the experiment nmz=2.65.1011 cm -3. It is reported in Ref. 239 that measured electron concentrations, [e], in shock-induced methane ignition were higher than those in the flame. This fact is consistent with the

Chemical kinetics excess of the calculated value of [e] over the experimental value in the flame, which is attributable to diffusion. In a later work, 24° calculations were carried out for ionization in self-ignition of methane mixtures in shock waves. 2.7. Technolo#): Methane-Based Production oJ Acetylene and Synthesis Gas The kinetics mechanism underlying hydrocarbon combustion consists of a large number of elementary reactions. Some of these reactions are essential in order to calculate for the flame velocity and the reaction product yield, while others determine certain other features of the combustion process, such as acetylene production. Production of acetylene in the combustion of stoichiometric or near-stoichiometric mixtures of hydrocarbons with air or oxygen is negligible and reactions involving acetylene have only a small effect on the rate of the main combustion process. This also is the case in the combustion of very rich mixtures despite the increased yield of acetylene and even though the production reactions are basic to the manufacturing process. This permits a kinetic description of acetylene production in the combustion of methane-oxygen mixtures by drawing on the methane combustion mechanism. The industrial process route to acetylene, described as oxygenolysis, seems similar to flame propagation in very rihch methane-oxygen mixtures. To analyze the reaction kinetics in this case, it is convenient to use the calculation procedure assuming a step-like temperature rise in the combustion zone. Preliminary calculations of flame propagation in rich methane-oxygen mixtures have revealed that the main features typical of the combustion of rich mixtures are predicted correctly: large amounts of H 2 and CO form and the intermediates, CH 3 and H, exhibit maximum concentrations. Since H2, CH3 and H are the products of thermal pyrolysis, the methane combustion reaction scheme was supplemented with the reactions characteristic of methane thermal pyrolysis (the reactions not involving oxygen, Table 1, reactions 3b, 5b, 8b, lc, 2c, 4c, 25c, 29c, le-7e). The latter were suggested earlier by various

239

authors and one variation of the mechanism is discussed most comprehensively in Ref. 60. The scheme considered here relies on the familiar assumption of the sequence of the reactions involved in pyrolysis CH4---*C2H6----~C2H4---*C2H2. It is understood that the reaction mechanism and elementary reactions have been selected somewhat arbitrarily. For this reason, the calculation results should be treated as tentative and subject to further verification and more exact definition. The Arrhenius parameters of the reactions are taken from literature sources or have been estimated. Calculations by the assumption of a step-like temperature rise were carried out using a system of 21 equations (j= OH, H, O, HO 2, HCO, CH 3, CH2, H2, H20. H202. CO, CO 2, H2CO, C2H. C2H3. C2H5, 0 2, CHa, C2H2, C2H6, C2H4) for the experimental conditions 241 in which detailed information on the product composition in a flat flame was available. In the experiments, the initial concentrations were [CH4]0 = 56 o,, [02]0 =44 %, P = 1 atm., T = 1700 K, u,=7.4 cm/sec, the zone width 1=2 cm Table 17 (Case I I compares the calculated and the experimental concentrations of the main stable products at the end of the combustion zone. They are evidently in a satisfactory agreement. An analysis of the calculation results shows that in oxygenolysis reactions of hydroxyl and molecular oxygen may become important, especially in the early stages of the reaction. The OH concentration is only an order of magnitude lower than the H concentration, and the 02 concentration does not decrease very rapidly. Therefore, in subsequent calculations allowance was made for some of their possible reactions (Table 1, reactions 2d, 3d, 2b, 7b, 9b, 3c, 24c, 8e). Table 17 (Case 2~ lists experimental and predicted concentrations of the main stable products formed at the end of the combustion zone. They are satisfactorily consistent although calculated concentrations in this case differ from those obtained previously. From this calculation, we can examine the contributions of certain reactions to acetylene production. The conclusions following from this examination naturally depend, to a large extent, on the selected reactions and rate constants. But, even in this case, they are of definite interest.

7A,U: 17. Species concentrations in the combustion products, o. In calculations P= 1 atm.. t= 10 msec.5'~ Species

H.,

CO

H:O

CO~

CH4

C2H2

Experiment 2.~t Calculation Case I Case 2

42 40.3 42

26 20 25

20 28 24

5.0 4.4 4.4

5.0 2.2 2.8

3.3 4.8 2,0

Experiment 2"2 Calculation Case 3

40-40.5 44

19 23.1

28* 20

2-3 2.2

3-4 6.8

5.4 5.9 3.9

*Pyrogenetic moisture.

02

C2H4

<1 <1 <1

0.5 0.36 0,16

<0.15 0.24

0.22 0.2

240

V. YA. BASEVICH

Contributions of particular elementary reactions will be estimated by the value of integral (V). The reactions making the most substantial contributions are summarized below. The carbon bond C - C forms in two parallel reactions: 2CH3---*C2H6 and CH 3 +CH4---+CzHs+H2. In the reactions C2H6+H---* C2H5 + H2 and C2H6 + OH---,C2Hs + H20, ethane is converted into ethyl radical. Ethyl reacts mainly with H and OH: C2H5 + H---*C2H4+H2 and C2H5 + O H ---*C2H4+H20. The ethylene formed in these reactions decomposes by C2H4---,C2H2+H2. This is the principal acetylene formation step in the scheme. The reverse reaction is important in order to maintain the established ratio of C2H4 and C2H2 concentrations. Acetylene is consumed in the last reaction (reverse) as well as in its reaction with hydroxyl: C2H2 +OH---+CH3 + C O . The contributions of the remaining competing reactions for these conditions are at least an order of magnitude smaller. The methane combustion reactions have been omitted in the present discussion. For the specified conditions of acetylene 'production in combustion the reaction scheme may be simplified, particularly by eliminating reactions of H202 whose contribution at temperatures > 1200 K is not significant. The lack of experimental data on the concentrations of unstable products for the specified conditions does not permit a more detailed comparison of the calculations and the observations, which is necessary in order to estimate the reliability of the mechanism. The conditions for acetylene production in the chemical industry normally combined with synthesisgas manufacture differ from those of combustion in a flat flame. For example, provision is made for gas preheating and reaction zone stabilization by a pilot flame. In addition, there is a short process time due to products quenching and nonuniform, turbulent flow. The calculations may, therefore, only yield a very general qualitative description of the phenomenon. With these reservations, the calculation was carried out for typical conditions of acetylene production: 242 the initial concentrations of [CH4]o=62.8°~,, of [O2]o= 37.5 0~il,P = 1 atm., T = 2 1 0 0 K. In this calculation, the velocity was arbitrarily taken to be the same as in the previous case. The zone length /=0.074 cm is chosen to correspond to a process time of 10 -2 sec. The calculation results and the experimental data are summarized in Table 17 (Case 3). The general qualitative agreement of the predictions and observations implies that the flow conditions do not affect markedly the yield of the reaction products, although the physical conditions of the reaction in the two cases greatly differ. Similar calculations were made in Ref. 24 for various temperatures, pressures, mixture compositions, reaction times and flow rates. 2.8. Ecological A.~pects oJ Combustion Processes Kinetics may be used to analyze pollutant formation in combustion, to find out possible ways for

reducing the concentrations of harmful products formed in combustion/NO, CO, hydrocarbons/. In the pioneer work, 16s two main reactions were identified, which led to the production of nitric oxide from nitrogen of the air O+N2~NO+N N+O2~NO+O.

(1.12) (1.13)

In Ref. 244 it is stated that the reaction Nz+O2=2NO

-1.14)

is orbital-symmetry-forbidden and it exhibits a high activation energy. Hence, this reaction is significant only at high temperatures. The mechanism suggested in Ref. 168 is often combined with the fast reaction N+OH=NO+H

(1.15)

and in this form it is referred to as extended Zerdovich mechanism. The contribution of Eq. (1.15) to the production of NO, as shown by calculations, is frequently larger than that of Eq. (1.13). 245 Under practical conditions, very high N O concentrations can be produced (due to relatively high temperatures and long residence times (>0.1 sec) at high temperatures). The extended Zel'dovich mechanism is principal N O formation process in the absence of fuel nitrogen. In many laboratory flames, with relatively low temperatures (-,,<2000 K) and short residence times (10-20 msec), the assumptions underlying theory t 6s are insufficiently valid, thereby giving rise to a discrepancy between calculated and observed N O concentrations. For these conditions, equilibrium cannot be established and the actual concentrations of atomic oxygen may exceed markedly the thermodynamic equilibrium values. The detailed kinetics calculations show that in this case more NO is produced. 246-24s (The occurrence of superequilibrium concentrations of active species--atoms and radicals--in the combustion zone has already been mentioned.) Quantitative kinetics calculations of ignition of hydrogen mixtures with a mechanism that models reactions in the flame and assumes an isothermal reaction with a temperature equal to the final combustion temperature show overshoot of the atomic oxygen concentration and a jump in NO production. However, kinetics calculations using the equation for hydrogenair flame propagation do not predict any jump ~s3 and give support for the theoretical and experimental findings t6s that the reaction zone can be eliminated from consideration. It is also evident from the calculations that the amount of N O formed in the flame zone itself is very small, due to the short residence time, up to pressures of 100 atm. and even at initial temperatures of 600 K This situation is different in combustion of hydrocarbons, especially for rich mixtures. The earliest experimental observation of the prompt production of nitric oxide dates back to Ref. 245, where it was

Chemical kinetics TABLI: 18. Concentration of NO in the post-flame gas. T=2873 K. P=I atm.. t---1.5 msec Composition. o,, [CH,~]o [02](, 45.7 44 22.2 21.5

50.3 49 74.6 72.7

NO. o,

[N,],, Experiment2~{' Calculation 2'.6 4 7 3.2 5.8

0.008 0.01 0,13 0.27

0,0003 0.0005 0.054 0.096

found that for rich mixture combustion NO production occurred in two stages: a rapid stage in the reaction zone and a slow stage taking place in the flame gases. The two stages may be explained in part by Eqs (1.12-1.15), where the O atom concentrations are in superequilibrium. In Ref. 249, a conclusion is made to the effect that for hydrogen the mechanism involving Eqs (1.12-1.15) fits lean mixtures (the equivalence ratio :t= 1/tp~> 1.3). However, it has been reported in the literature (see, for instance, Table 18 with experimental data 25° and calculations 246) that there is a large discrepancy between the predicted and observed NO concentrations for rich mixtures. This discrepancy attests to the fact that the N O formation mechanism is more complex and is not restricted solely to Eqs (1.12-1.15). Specific experiments have been run to compare the NO yields at identical temperatures in hydrogen-oxygen-nitrogen flames, either pure or with admixed acetylene. In the latter case, the yield of NO is higher. T M Hence, its production can be ascribed to the reactions between hydrocarbon radical and nitrogen (see the detailed kinetic mechanism for the H - C - N - O system in the foregoing discussion), although these routes to nitric oxide have been studied insufficiently up to now. The value of the "prompt" NO concentration does not exceed 100-120 ppm, see Ref. 252, where the authors optimized the experimental conditions in order to arrive at a maximum yield of NO. Finally, there is one more source of nitric oxide production in combustion. This is nitrogen contained in a molecule of a fuel or an additive. It has been demonstrated experimentally 2~3 that 10-90% of fuel nitrogen is converted to nitric oxide, depending on the combustion conditions and composition of the combustible mixture; the remaining proportion (in rich mixtures) is converted into ammonia and HCN as well as molecular nitrogen, see the above scheme for H - C - N - O and the relevant calculations. The reaction scheme accounting for production of N O from fuel nitrogen should be developed in further detail and better substantiated. The possible important role of the N atoms in this process, showing up in Ref. 69, is also mentioned in Ref. 172. The features of N O production as well as of CO and hydrocarbons in turbulent combustion are considered in Refs 203, 206, 207, 254. As indicated earlier, the experimental investigation of hydrocarbon flames at reduced pressures 2°7 has revealed JPECS 13-3-F

241

a decreasing concentration of oxygen atoms with increasing root-mean-square fluctuating velocity. Since the concentrations of O, OH and H in the reaction of hydrocarbons vary together, this may exert influence on pollutant formation in a turbulent flame. It is evident that under the same experimental conditions the NO concentration tends to go down as the level of turbulent is raised, Fig. 34. 206 in these experiments, an inverted flame cone was used so that the heat loss was minimal. There are opposite conclusions in the literature, too. For instance, Ref. 255 reports that NO is produced in the reaction zone of turbulent flame at a faster rate than in laminar flame. This contradiction might arise because the authors of Ref. 255 compare the results obtained under different conditions. It is also difficult to give a clear-cut explanation of the inconsistency with the "findings. 2s6'2s~ To be sure, the flow rates and the Reynolds numbers were much higher, the pressure was 1 atm. The authors do not mention the combustion efficiency attained, nor do they say anything of the measures taken to reduce the heat loss at low flow rates (it is not clear whether or not the temperature in the reaction zone was maintained at a constant level). According to experimental data, 2°~ the concentration of carbon monoxide tends to increase with root-mean-square fluctuating velocity, with the combustion efficiency held fixed, Fig. 35. However, the authors of Ref. 257 found that the CO yield increased (and the N O yield decreased, see earlier) with increasing flow rate. However, it is problematic to compare CO yields for various flow rates in the absence of information about the temperature and composition of the combustion products If in experiments the temperature rose at l'/igh flow rates, the increase in N O with flow rate and the corresponding reduction in CO are quite consistent.

==

~

o

o

7

,0.-I o-2

8

[ ella]O(°/.) FIG. 34. Yield of nitric oxide in a methane-air turbulent flame.2°6 P=0.25 atm.. U m/see (~ cm/secl: 10(20) and 201"401.

242

V. YA. BASEVICH CCHd 1.0 - -

[ CH4]o(*/.} 6.5

~.~

"r/= I (I)

[CH4]o

0.74

n

0.'9 0.8

1,0 --

(2)

0.86

.

0.9 0.11 0.7 I

[C.H,,,] = ~ {([C,H,,,] - [C,H,,,_]')/[C,H,,,.]' --

O.g

o

0.7

I

I

I

IO

l

20

30

U ( m/sec ) 1

I

20

dO

.

I

60

0 (cm/mc)

FIG. 35. Yield of CO in a methane-air turbulent flame vs velocity. To=293 K. P=0.25 atm. z°7 Combustion [CH,Jo, ~,,, efficiency, q 6.5 7.O 7.5

0.74 0.86 0.93

Production of hydrocarbons in combustion processes and ways for its prevention are the subjects of much study. Production of the hydrocarbons in combustion (specifically in internal-combustion engines) is related to the existence of volumes and slots where flame propagation is rendered difficult, to the fuel adsorption and desorption on surfaces in the compression-expansion and to the flame extinction near cool walls, see, for example Ref. 258. To elucidate the causes of hydrocarbon production and of their increased levels in the reaction products, experimental and theoretical modeling is often performed for laminar flames. As will be shown below, however, another cause should be considered, namely efficiency of combustion of the initial fuel and the higher extent of hydrocarbon production in the combustion zone, induced by turbulence. Hydrocarbon experiments 254 used the same setup to study a turbulent flame as was employed in experiments with N O and CO. Combustible mixtures with an initial content of [CH4]o of 5.5--8.5 Vo at a pressure of 0.25 atm. were used. The absolute mean concentrations of hydrocarbons produced in combustion (ethane, propane, heavier hydrocarbons as well as ethylene and acetylene) at first increase, go through a maximum, and then fall. The same is true of the concentration of hydrogen formed as an intermediate product. The relevant concentrations were observed to attain the following maximum values: [C2H6] =0.014 %, [C2H,,] = 0.0023 %, [C2H2] =0.0014 ~o, [C3H8] =0.001 ~o and [Hz] =0.25 ~,,,. Of particular interest to us is the hydrocarbon

}/N

N

0.93,,,,,,,o

O.g

I 2 3

concentration [C,H,,] for a specified methane concentration and, hence, combustion efficiency for various intensity levels, i.e. for various values of rootmean-square fluctuating velocity (this was achieved by varying the mean flow rate). The experimental data obtained were then used to derive a relative concentration

where [C,H,,] stands for the measured hydrocarbon concentration, the prime refers to a minimum flow rate and, hence, to a minimum fluctuating velocity (U=7.5 m/see, ~ = 1 5 cm/sec, [C,H,,,]-=0), N is the number of measurements. Figure 36 summarizes all the data obtained for [CH4]o=6.5, 7.0 and 7.5 %. They do not differ within the experimental uncertainty. The vertical line represents the value of standard deviation. Evidently, [C2H6]---[C3Hs]---0. The values of [ C : H 4 ] and [C2H2] increase with increasing flow rate. Moreover, hydrocarbon concentrations [C,H.,] were determined for a particular flow rate and efficiency of methane combustion but for various amounts of added hydrogen. The data were subsequently reduced to a dimensionless concentration [C,H,,], Fig. 37 (referred to the case of no hydrogen additive, [H2]o=0). One can see that, as previously, [C2H6] ~ [ C 3 H s ] ~ 0 , whereas the values of [ C , H 4 ] and [C2H2] decrease with increasing concentration of [H2] 0.

0.4 --"C

0:41 --

t t,

-04' --

~

0"4t_ ~

'~

o.4[-

'1"

0 -x

!

,%

°Jf-

I

10

I

20

I

I

t

I

20 U (m/sac)

30

aO

60

I

I

(cm/sec)

FIG. 36. Relative variations in the hydrocarbon concentrations [C,H,,], hydrogen [Hz], and emission logarithm Ig I in a turbulent flame vs velocity.254 [CH4]0=6.5-7.57/,,, q = 0.74-0.93.

Chemical kinetics

~oo2 I-

_o3_

02i-~'¢ Og

I~

OIF

0.05

oo

-00~I 0

I

05 [ t..12]0 (°/oJ

FiG. 37, Relative variations in the concentratmn of hydrocarbcn [C, Hm] and emission logarithm Ig I in a turbulent flame vs hydrogen concentration [H2]o.2s'~[CH4]o = 7.5 °,,, r/= 0.93: U = 30 m/sec, h = 60 cm/sec. Here there are also represented the corresponding values of dimensionless variation in the luminescence level logarithm upon addition of nitric oxide, which indicates the relative behavior of the concentration of O-atoms. The luminescence level rises upon addition of [H2] 0. A numerical analysis using equations for instantaneous parameters in conjunction with statistical modeling of the turbulence allows, in principle, a quantitative explanation of the results of the experiments. The calculations carried out in a onedimensional approximation for a methane-air flame do indicate that the yield of nitric oxide N O decreases while the concentrations of CO and H 2 increase with an increasing turbulence level, see above Table 14. As for nitric oxide, it should be borne in mind that the kinetics scheme used contains the so-called thermal nitric oxide formation mechanism (Eqs 1.12-1.15). 168 The contribution of these reactions is small, which is attributed to the relatively low temperatures for which the calculations were made. This is evident from the values of the calculated N O concentrations. In actual conditions, a more substantial contribution is likely to come from the "prompt" NO mechanism, where the reactions of CH and CH2 with N 2 are important. But, they have been omitted from this already sophisticated calculation. It is expected, however, that once the concentration of OH, H and O decrease the yield of "prompt" N O will also decrease. Hydroxyl taking part in Eqs (1) and (21) facilitates the conversion of H 2 into H 2 0 and CO into COx. Hence, with insufficient OH concentrations, the maximum concentrations of hydrogen and carbon monoxide in the reaction zone prove to be higher

243

and larger amounts of them remain in the combustion products. Presently, we cannot carry out rigorous kinetics calculations of hydrocarbon yields in a turbulent medium, since these calculations would consume too much machine time. But it is easy to calculate the kinetics without diffusion and turbulence. This implies an approximate semi-quantitative modeling of a single chemical aspect of the observed phenomenon. This has been accomplished on the basis of the kinetics mechanism for oxidation of hydrocarbons C~-C2. 64 Thought was given only to the effect of hydrogen additives, which is, as pointed out earlier, the reciprocal of the fluctuating velocity effect, whereas the turbulence-induced decrease of the concentration of active centers is impossible to model by such calculations. The initial compositions of a combustible mixture corresponded to the actual experimental conditions, the temperature was taken to be equal to an adiabatic temperature of combustion. Calculations for [CH4]o= 7.5 o/~,,have established that combustion efficiency ~/=0.98 with respect to methane correspond the following concentrations of oxygen atoms and amounts of products (in ~,,,): [H2]0 0 0.55 1.1

[O] 0.51 0.56 0.76

[C2Ho] 0.004 0.007 0.0093

[C2H4] 0.0046 0.00095 0.0006

[C2H2"I 0.0018 0.00036 0.00024.

Thus, the calculation yields the same qualitative pattern as does the experiment, with the only difference being that the theoretical pattern is defined more clearly: on addition of hydrogen, the O-atom concentration is raised, which causes a sharp lowering of the concentrations of [C2H4] and [C2H~] (by a factor of 7.5), along with a relatively slight (by a factor of 2.3) increase in the concentration of [C~H6"]. It appears that a decrease in the radical concentrations due to higher turbulence levels is a contributing factor to the increased yields of unsaturated hydrocarbons. Hydrogen additives prevent reduction of the radical concentration and, hence, tend to reduce the yield of unsaturated hydrocarbons. Summarizing, as the turbulence level is raised, the concentrations of the radicals in a turbulent hydrocarbon-air flame decrease. This situation results in the reduction of the nitric oxide yield and in increased concentrations of CO, C2H4, C2H2 and hydrogen. Since C2H4 and particularly C2H2 are likely to be intermediate products in the process of soot production and in the formation of polycyclic aromatic hydrocarbons, hydrogen may be added for the purpose of their reduction. In conclusion, we note that it is common knowledge that an increase in the turbulence level can be useful for accelerating the flame velocity. It is reasonable, however, to increase the turbulence so as to achieve the required flame velocity, but not so much as to produce a marked increase in the yields of CO and unsaturated hydrocarbons.

244

V. YA. BASEVICH CONCLUSIONS

To describe the combustion processes of hydrogen and hydrocarbons C~-C2, we employed a detailed kinetics mechanism which is represented reasonably accurately in Table 1. One of the tasks of the present work was to elucidate how satisfactory and how accurate this description can be if one uses the available kinetic information included in the mechanism. A comparison of the findings yields a conclusion that this accuracy can be estimated on the average to be a factor of 2-5. In certain instances, a higher degree of accuracy is reported elsewhere, but this is often related to optimization aimed at describing a particular experiment or a set of experiments and does not ensure the same accuracy over a wide range of conditions. The main source of uncertainties is insufficient knowledge of elementary reactions and relevant rate constants. The available kinetic data are scattered in numerous journals and partially compiled in some review papers. 55'259 A great deal of research should be undertaken here. Hence, it seems premature to state a preference for any one of the reported mechanisms for hydrocarbon combustion. It is obvious that in the near future with further development of computers, it will not b~ necessary to use semiempirical expressions in the modeling of kinetics, and application of detailed kinetics mechanisms for estimation of characteristics, parameters, and properties of physico-chemical processes related to combustion will be normal. Kinetics calculations require well-developed computer programs. 26° F o r description of self-ignition processes at a constant pressure, constant volume (as is generally the case with various kinetics experiments), with or without reference to heat removal it is best to run standard programs, say, of the type reported in Refs 30, 46, 261, 262. It also proves helpful to use standard programs for a propagating flame, of the type in Ref. 263. In addition special programs may be used in the description of a chemical process in the flow and in complex-shaped volumes. O f particular importance to kinetics calculations are programs permitting selection of the principal reactions, thereby markedly simplifying the calculation. Different principles of selection exist, among them those outlined in Refs 46, 240, 264. The accuracy of a particular simplified mechanism can be verified by c o m p a r i n g the calculation results obtained for complete and simplified kinetics. The principal conclusion from the above considerations is that at this time it is quite feasible to develop a realistic detailed kinetics mechanism of the oxidation of small molecules in the H - C - N - O system, which can fit extensive and various experimental data either in general outline or in detail and which is suitable for prediction. The first stage of development of this detailed kinetics mechanism has clarified its potential and estimated the accuracy provided by its application.

In the next development stage, we have to analyze thoroughly particular elementary reactions to achieve a higher degree of accuracy in the estimation of rate constants. The goal of this stage is to go from today's qualitative estimations to exact a priori calculations. REFERENCES

1. SEMYONOV,N. N.. Some Problems oJ Chemical Kinetics and ReactiviO', USSR Acad. Sci.. Moscow (1958). 2. KONDRAT'YEV,V. N. and NIKITIN, E. E.. Kinetics and Mechanism oJ Gas-Phase Reactions. Nauka. Moscow (1974). 3. KONDRAT'VEVV. N., NIKVnN, E. E., REZNIKOV.A. N. and UMANSKY, S. Ya., Thermal Bimolec,dco" Reuction,~ in Gases, Nauka, Moscow 11976). 4. GLASSTONE,S., LMDLER, K. J. and EYRING, H.. The Theory of Rate Processes, New York and London (1941). 5. BENSON S.. Thermochemical Kinetics. IRuss. transl.). Mir, Moscow (1971). 6. SEMYONOV,N. N., Chain Reactions, Goskhimtekhizdat. Leningrad (1934). 7. KONDRAT'YEV, V. N., Kinetics of Chemical Gas Reactions, USSR Acad. Sci.. Moscow (1958). 8. NALBANO'YAN,A. B. and VOEVOOSKY, V. V., Mechanism of Oxidation and Combustion of Hydroyen, USSR Acad, Sci., Moscow (1949). 9. NALBAND'YAN,A. B. and MANTASH'YAN,A. A.. Elementary Processes of Slow Gas-Phase Reactions, Erevan (Armenian SSR) (1975). I0. EMANUEL, N. M. and KNORRE, D. G.. Course oJ Chemical Kinetics, Visshaya Shkola, Moscow (1984). 1I. HINSHELWOOD,C. S. and WILLIAMSON,A. T., Reaction between Hydro(len and Oxygen, London (1934). 12. LEWIS,B. and YON ELBE, G., Combustion, Flames and Explosions of Gases, (Russ. transl.) IL (1948). 13. LEwis, B. and yon ELRE.G., Combustion, Flames and Explosions of Gases. Academic Press Inc.. New York and London (1961). 14. ZAGUHN, A. V., KOVAL'SKY.A. A., KOPP, I. D. and SEMYONOV.N. N., Zh. [i=. Khim I. 263 (1930). 15. KOVALSKn,A.. Phys. Z. So~] Un 4, 723 (1933). 16. ZEL'DOVICH,YA. B., BARENBLAT,G. I., L1BROV1CH,V. B. and MAKHVILADZE, Mathematical Theory of Combustion and Explosion, Nauka, Moscow (1980). 17. DUFF, R. E., J. Chem. Phys. 28, 1193 (1958). 18. BASEXqCH,V. YA. and KOGARKO,S. M., Kinet. Katal. 6, 23 (1965): Pyrodynamics 7, 41 (1966). 19. BASEVlCrl,V. YA. and KOGARKO,S. M., Fi= goreno'a Vzrvva 3, No 1,98 (1967). 20. DIXON-LEWIS,G., WILSON. W. E. and WESTENBERG,A. A., J. Chem. Phys. 44, 2877 (1966). 21. AZAT'YAN,V. V., VOEVONSKY.V. V. and NALBAND'YAN, A. B., Kinet. Katal. 2, 340 (1961). 22. BASEVICH. V. YA. and KOGARKO. S. M., l-v. Akad. Nauk SSSR, Set. Khim No. 7, 1504 (1980). 23. KAUFMAN,F. and DEL GRECO, F. P., 9th Strop. Ilnt.) Combu.~tion, p. 659, Academic Press, New York (1963). 24. DXXON-LEWIS,G., SUTTON, M. M. and WILLIAMS.A., Discuss. Faraday Sot., 33. 205 (1962). 25. MORGEN,J. E. and SCHIFF. H. I., J. chem. Phys. 38. 1495 (1963). 26. RIPLEY,D. L. and GARDINER,W. C., J. chem. Phys. 44, 2285 (1966). 27. BASEVICH,V. YA., KOGARKO,S. M. and FURMAN,G. A., 17.v. Akad Nauk. SSSR, ser khim. No. 1.7 (1975). 28. BASEV1CH, V. YA. and KOGARKO, S. M., l:v. Akad. Nauk SSSR, Ser. Khim. No. 7, 1503 (1980). 29. HACK, W., WAGNER,H. G.. and HOVERMANN,K., Ber. Bunsemles. phys. Chem. 82, 713 (1978). 30. BASEVlCH,V. YA., KC'~ARKO,S. M. and FURMAN,G. A.,

Chemical kinetics I.-r. Akad. Nauk SSSR, Ser Khim. No. 7, 1406 11971 ). 31. GRBNER. N. R., d. phys. Chem. 72,406 11968). 32. ALBERS, E. A.. HOYERMANN, K., WAGNER. H. G. and WOLFRUM, J., 13th Syrup. (Int.) on Combustion, p. 81, Combust. Inst. Pittsburgh 11971 ). 33. BASEVlCH, V. YA.. KOGARKO, S. M. and BEREZXN, O. Yu., 1-r. Akad. Nauk SSSR, Ser. Khim. No. 9, 1986 11979). 34. KONDRATIEV. V. N.. 7th Symp. (Int.) on Combustion, p. 41, Butterworths, London 11959). 35. VARDAN'YAN.I. A., DANGH'YAN,G. M., SAK'YAN,G. A. and NALBAND'YAN. A, B.. Dokl. Akad. Nauk SSSR 205, 619 11973). 36. STEACIE. E. W. R_ Atomic and Free Radical Reactions, Academic Press, New York 11954). 37. BASF!VICH.V. YA.. KO~ARKO, S. M. and FURMAN, G. A., l-r. Akad Nauk SSSR, Ser. Khim. No. 10, 2139 11972). 38. HERRON. J. T. and PENZHORN, R. D., J. phys. Chem. 73, 191 11969). 39. SCHf~CKI-R. H. G. and JOST, W., Bet'. Bunsenpe.~. phy.~. ChenL 73, No 6. 521 (1969). 40. WASHXDA. N., MARZnNZ, R. Y. and BARES, K. D.. Z. NaturL 290(2). 251 (1974). 41.WESTENBER(;. A. A. and HAAS. N., d. phys. Chem. 76. 2215 (1972). 42. AVRAMENK(XK. I. and LORENTSO, R. V., Zh. fit. Khim. 21, 1135 (1947). 43. FENIMORL, C. P. and JONES, G. W., d. phys. Chem. 65, 2200 ( 1961 ). 44. AVRAMI?NKO.L 1.. KOLESNIKOVA.R. V. and KUZNETSOVA, N. L., lzr. Akad. Nauk SSSR. O K h N , 620 (1963). 45. HARTIG. R.. TROE, J. and WAGNER, H. G., 13th Syrup. (Int.t on Combustion, p. 147, Combust. Inst., Pittsburgh 11971 ). 46. BASiVICH. V. YA.. KOGARKO, S. M. and NEYGAUS, M. G.. Izc. Akad. Nauk SSSR. Set. Khim. No. 1,42 11976). 47. DIAX. A. M. and KIS'nAKOWSKY. d. chem. Phys. 54, 17181t971). 48. FFNIMORI. C. P. and JoNliS, G. W.. d. ph.t's. Chem. 65. 1532 (1961 }. 49. BASI:Xq('H. V. YA., KCXiARKO. S. M. and POSVYANSKY, V. S.. Fi c, qoreni)', | - r v r a 12. N o 2. 217 (1976). 50. BASI!V1CH.V. YA., K(KIARKO, S. M. and FURMAN, G. A., l:r. Akad. Nauk SSSR, Ser Khim. No. 1,197 11974). 51. BASt:VlCH. V. YA.. KOGARKO. S. M. and FURMAN, G. A., l:r. Akad. Nauk SSSR, Set. Khim. No. 5, 1035 11975). 52. OGANES'Y,\N. K. T., NALP,AND'YAN. A. B. and PARSAM'YAN. N. 1., DokL Akad. Nauk Armenian SSSR 40, No 3, 159 (1965). 53. SPINDI,IR. K. and WAGNER. H. G., Bet'. Bunsen¢le~. phys. ChenL 8 6 2 119821. 54. WESTENBER(;, A. A. and HAAS, N., J. phys. Chem. 73, 1181 (19691. 55. KONDRAT'YEV. B. N.. Rate Constant.s of Ga.s-Phase Reactions. Nauka . Moscow (19701. 56. BAStVlCH. V. Y-x. and KOGARKO. S. M., Fit. yoreniva l-rvra 14. No. 1.46 11978). 57. BASEV1CH, V. YA.. KOGARKO. S, M. and POSVYANSKY. V. S.. Fi-. :/oreniva I/--rvt'a 13, N o 2. 193 11977). 58. GREJNER, N. R.. J. chenl. Phys. 53, 1284 (1970). 59. KOZLOX. G. I. and KNORRE. V. G., Kinet. katal. 4. 189 11963). 60. GARDIXER. W. C.. OWEN. J. H. and CLARK. T. C. et al., 15th Syrup. (Int.) on Comhustihon, p. 857, Combust, lnsL. Pittsburgh 11975). 61, CLARK. T. C.. IZOD. T. P. J. and KZSTIAKOWSKY.O. B. J (hem. Phr~. 54. 1295 (1971). 62. IZOD. T. P. J.. d. chenl. PIU'.s. 55.4425 (19711. 63. AZ,XT'YAN. V. V. and ROMANOVICH. L. B., Izr. Akad. XauL SSSR. Set. Khinl., No 5. 941 (1971). 64, BASI!XlCH.V. YA. and KO(;ARKO. S. M. l-c. Akad. Nauk SSSR. Scr. Kllim.. No 8. 1728 (1977). 65. PR \T7. G. and \'At TMAN. J.. d. chem. Sot'. Farad. Tran.~.

245

1, 1841 11974). 66. KNIGHT, C. M.. NIKI, H. S. and WEINSTOCK. J, t h e m Phys. 47, 5129 11967). 67. CADLE. R. D. and POWERS, J. W., J. phy.s. Chem. 71, No 6, 1702 11967). 68. Baldwin, R. R. and WALKER, R. W., 14th Syrup. (Int.)on Combustion, p. 241, Combust. lnst. Pittsburgh 11973). 69. BASEV1CH,V. YA., KOGARKO,S. M. and TYUaaN, A. N., Khim. fit. 2, N o 1.113 11983). 70. ATraNSON. R., PERRY, R. A. and P1TTS, J, N., d. t h e m Phys. 66, 1578 11977). 71. BLUMENBERG, B. and WAGNER, H. C., Z. Bunsem/e.~. phys. Chem. 77, 253 11973). 72. TSANG. W.. Int. d. chem. Kinetic,x 10,41 (1978). 73. DOVE. J. E. and NxP, W. S.. Can. d. Chem. 52, No 7, 1171 (1974). 74. WONG. E. L. and POTTER. A. E., d. chent. Phys. 43, 3371 (1965). 75. LESCLAUXR., KHL, P. V., DEZAUZIER, P. and SOULI(iNAC. J. C.. Chem. Phy.~. Lett. 35, 493 (1975). 76. HACK, W., HOYERMANN, K. and WA(;NER. H G.. Bet'. Bunsenges. phys. Chem. 78, 386 (1974). 77. DUXBURY, J. and PRATT, N. H., 15th Syrup. (Int.) on Combustion, p. 843. Combust. Inst. Pittsburgh (1975). 78. ALBERS, E. A., HOYERMANN. K., WA(;NER, H. G. and WOt, FRUM. J., 12th Syrup. (Int.)on Combu,stion. p. 313, Combust. Inst. Pittsburgh 11969). 79. ZETZSCH. C. and HAKSEN, J., n(,r. Bun:~t'n(l('.',. phys. Chem. 82, No 8,830 (1978). 80. ARMSTRONG,D. A. and WINKI.ER. C. A.. Ctln. J. Chent. 33, 1649 11955). 81. Rorrl. P. and JUST. TH.. Ber. Bzmsenqe,~. phys. Chem. 8. N o 2 . 171 (1976). 82. ALBERS, E. A.. HOYERMANN, K.. S('HA('KE. H.. SCHMATJKO, K. J., WAGNER. H. G. and WOLFRUM, J,, 15th Syrup. (Int.)on Combustion. p. 765. Combust. Inst. Pittsburgh (1975). 83. R o m , P., LOHR, R. and HERMANNS. H. D., Ber. Bunsenge.~. phys. Chem. 84, 835 (1980),. 84. LAM, L. and DUGAN. C. H., d. chem. Phv.s. 69, 2877 11978). 85. BODEN, J. C. and THRUSH, B. A.. Pro('. R. Soc. A365, 107 (19681. 86. BLAUWENS, J., SMETS, B. and PEETERS, J., 16th Syrup. tint. Ion Combu.~tion, p. 1055, Combust. Inst. Pittsburgh (1977). 87. BUTLER. J. E. and FLEMING, J M., Chem. Phv.s. 56. 355 11981 ). 88. BASEXaCH. V. YA. and KOGARKO, S. M., l-r. Akad. Nauk SSSR, Set. Khim. No. 10, 2250 (1978). 89. BUTT. P. K. and LEVITT, B. P.. d. chem. Soc. Faradal' Tran.~. 1,69. 1957 (1973). 90. GL)~NZER. K. and TROtZ. J.. Bet'. Bun~enue.~. phr.~. Chem. 78, 182 11974). 91. FREEDMAN. E. and DAIBER, J. W.. d. chem. Phv.~. 34. 1271 (1961). 92. CAMBELL, J. M. and THRUSH, B. A.. Tran.~. Faraday Sot'. 64. 1265 11968). 93. ZELLNER. K. and SMITH. J. W. M.. Chem. Phv.s. Lett. 26. 72 11974). 94. BASEXaCH, V. YA. and KO(iARKO. S. M.. l-c. Akad. Nauk SSSR, Set'. Khim. No 12. 2658 (1982). 95. BDLDWIN. P. P and WALKER. R. V_ Col, Chentical Kinetics and Chain Reaction~. (Russ. transl.). 243. Nauka, Moscow\ 11966). 96. BASEV1CH.V. YA,, KOGARKO. S. M. and DINABUR(3. E I.. Fi-. qoreniya l - r r r a 4, No 2,220 (1968t 97. BASI~VaCH.V. YA.. KOGARKO. S. M. and FURMAN, G. A.. Proc. 2 N ationtd Sympos. on Cmnbu.stion (tnd E'~l,lo.~ion. 92. Institute of Chem. Phys. USSR Academ) of Sciences. Moscow (1969). 98. BASEVlCH. V. YA.. Doctorate. Inst. c h c m Phys. Acctd. SCL USSR. Moscow 119691.

246

V. YA. BASEVICH

99. BASEWCH,V. YA., KOGARKO, S. M. and FURMAN,G.A., 137. WESTBROOK, C. K.. Combust. Flame 46. 191 (1982). lzv. Akad. Nauk, SSSR. Set. Khim.. 2191 (1971). 138. KATO, A. and CVETONOWC, R. J., Can. J. Chem. 46, 235 (1968). 100. SOLOtWdtIN. R. N.. Fiz..qoren(ja Vzrvva, 2, 12 (1966). 101. SrdNNEa, B. G. and RINGROSE,G. H., J. chem. Phys. 43, 139. LEFEVRE, H. F., MEAGHER, J. F. and TIMMONS, R. B., Int. J. chem. Kinetics 4, 103 (1972). 4129 (1965). 102. HAw'r'HORNE, R. D. and NIXON, A. C., A I A A J. 4, 166 140. AVRAMENKO,L. I., KOLESNIKOVA,R. V. and KUZNETSOVA, N. L., Izr. Akad. Nauk SSSR, OKhN, 599 (1961). (1966). 103. As^a^, T., YOKEDA, K., KArdHARA, N. and HIrdTA, T., 141. ADERS, W. K., Eur. Syrup. Combustion, p. 19, Academic Press, New York (1973). 9th Syrup. (Int.) on Combustion, p. 193, Academic Press, New York (1963). 142. DovE, J. E. and WARNATZ, J., Bet. Bunsenges. phys. Chem. 8% 1040 (1983). 104. SOLOUKHIN, R. S., !Oth Syrup. (Int.) on Combustion, p. 521, Combust. Inst., Pittsburgh (1965). 143. WESTBROOK, C. K. and DRYER, F. L., Combust. Flame 37. 171 (1980). 105. Bomsov, A. A., KOG^RKO, S. M. and LYumMov. A. V., Dokl. Akad. Nauk SSSR 149, 869 (1963), 144. GARDINER, W. C. and WALKER, B. F., J. chem. Phys. 48. 5279 (1968). 106. MI~'AM^, H. and T^KEY^MA T.. J. chem. Phys. 40, 2049 (1964). 145. BROWN, W. G., PORTER, R. P.. VERLIN, J. D. and CLARK. A. H., 12th Syrup. (Int.) on Combustion, p. 1035, 107. GLASS, G. P,, KISTIAKOWSKY,G. B.. MICHAEL,J. V. and Combust. Inst., Pittsburgh (1969). NIKI, H., lOth Syrup. (int.) on Combustion. p. 513, Combust. Inst., Pittsburgh (1965). 146. BRADLEY, J. N. and TSE, R. S., Trans. Faraday Sot'. 65. 2685 (1969). 108. MULUMS,B. P.. Fuel 32, 211,343 [1953). 109. KOGARKO,S. M., DEVlSHEV, M. I. and BASEVlCH, V. 147. EBERIUS, K. H.. HOYERMANN,K. and WAGNER. H. G., 14th Syrup. (Int). on Combustion, p. 147, Combust. Inst., YA., Zh. fiz. khim. 33, 2345 (1959). Pittsburgh (1973). 110. HOARE, D. E. and WALSH. A. D., 5th Syrup. (int.) on Combustion, p. 474, Reinhold, New York (1955). 148. PEETERS, J. and VINCKIER, C., 15th Syrup. (Int.) on Combustion, p. 185, Combust. Inst., Pittsburgh (1975). 111. KARt~LOVA,L V., Er,aKOLONOV,N. S. and N^LBANO'YAN. A. B., Zh. fiz. khim. 31,851 (1957). 149. HIDAKA, Y., EUBANK. C. S.. GAROINER, W. C. and HWANG. S. M., J. phys. Chem. 88. 1096 (1984). IIZ KAgmLOVA, L .V., ENIKOLONOV,N. S. and NALBAND'YAN, A. B., Zh. fiz. khim. 34, 550 (1960). 150. MILLER, J. A., MITCHELL. R. E.. SMOOKE. M. D. and KEE, R, J., 19th Syrup. (Int.) on Combustion, p. 181, 113. TROE, J., Ber. Bunsenoes. phys. Chem. 73, No 10, 946 Combust. Inst., Pittsburgh (1983). (1969). 114. DII~TROV, V. J., React. Kinet. Catal. Left. 7, No 1, 81 151. PEETERS,J. and MAHNEN,G., Eur. Syrup. Combustion, p. 53, Academic Press. New York (1973). (1977). 115. DIXON-LEwIS, G., Combust. Sci. Teehnol. 34, No 1-6, 1 152. CVETANOVlC, P. J., J. chem. Phys, 23, 1375 (1955). (1983). 153. PRUSS, F. J.. SLAGLE, J. R. and GUTMAN, D., J. phys. Chem. 78, 663 (1974). 116. WARNATZ, J., Bet. Btmsenqes. phys, Chem. 82, 643 (1978). 154. LEVY, J. M., TAYLOR, B. R., LONGWELL, J. P. and SAROOM, A. F., 19th Syrup. {Int.) on Combustion, p. 167, 117. WARN^TZ, J., Ber. Bunsen qes. phys. Chem. 87, 1008 Combust. Inst., Pittsburgh (1983). (1983). 118. SHTERN, V. Y^.. Mechanism of Hydrocarbon Oxidation 155. WESTBROOK, C. K., DRYER, F. L. and SCHUG, K. P., Comhust. Flame 52. 299 (1983). in the Gas Phase, USSR Acad. Sci., Moscow (1960). 119. KARI~LOVA,L. V.. ENIKOLONOV,N. S. and NALBAND'YAN, 156. BOWMAN, C. T., Combust. Sci. Technol. 2, 161 (1970). A. B., Zh. liz. Khim. 34, 990 (1960). 157. COOKE, D. F. and WILLIAMS, A., 13th Syrup. (Int.) on Combustion, p. 757, Combust. Inst., Pittsburgh {1971 ). 120. KARMILOVA,L. V., ENIKOLONOV,N. S., NALBAND'YAN. A. B. and SEMVONOV, N. N., Zh. f i - Khim. 34, 1177 158. PAPANDOPOULOS,C.. ASHMORE, P. G. and TYLER, B. J.. (1960). 13th Syrup. (Int.) on Combustion, p. 281, Combust. Inst.. Pittsburgh (1971). 121. WESTENBERG, A. A. and F~USTROM, R. M.. J. phys. Chem. 65, 591 (1961). 159. KANE. G. P., CHAMBERLAIN,G. H. N. and TOWNEND, D. T. A., J. chem. Soc., 436 (1937). 122. FENIMORE, C. P., Chemistry oJ Premixted Flames, Pergamon. New York (1964). 160. OGANES'YAN.E. A., VARDAN'YAN,I. A. and NALBAND'YAN. A. B., Dokl. Akad. Nauk SSSR 212. No 1. 153 (1973). 123. FRISTROM, R. M., 9th Syrup. (Int.) on Combustion. p. 560, Academic Press, New York (1963). 161. TOWNEND, D. and CHAMBERLAIN, E., Proc. R. Sot'. AI54, 95 (1936). 124. CHIMITZ. W. A.. I~l.rodynamics, 3, No 3~,, 197 (1965). 125. BUgHMAN, F. A., MELAMED, V. G. and POLAK. L.S., 162. BURCAT. A., CROSSLEY, R. W.. SCHELLER. K. and SKINNER, G. B., Combust. Flame 18, 115 (1972). Khimiya visokikh enerqhii 2, No 5, 395 (1968). 126. HIGGINS. R. M. R. and WILLIAMS, A., 12th Syrup. [Int.) 163. SMETS. B. and PEETERS,J., 2 Symp. Era'. Combustion, p. 38, Combust. Inst., Orleans (1975). on Combustion, p. 105, Combust. Inst., Pittsburgh (1969). 164. KULICH, D. M., TAYLOR. J. E., Int. J. chem. Kinetii's 7, 895 (1975). 127. GURVICH, L. V. et al.. Thermodynamic Properties t~] Individual Substances, USSR Acad. Sci. (1962). 165. LEV1TSKY. A. A.. MOSHKINA, R. N., POLAK, L. S. and POLYAK. S. S.. Kinet. Katal. 20, I l l l (1979). 128. BASEVlCH, V. YA., KOGARKO, S. M. and POSVYANSKY. V. S., Fi:. yoreni.va Vzo'va ! I, No 2, 242 (1975). 166. GURVlCH, L. V., KARACHEVTSEV,G. V. et HI., Chemical Bond Breakaffe Ener¢liex, Nauka. Moscow (1974). 129. PEETER$, J. and MAHNEN, G., 14th Syrup. (Int) on Combustion, p. 133, Combust. Inst. Pittsburgh (1973). 167. FENIMORE, C. P., Comhust. Flame 26. 249 (1976). 130. VANPEE, M.. C. R. Aeud. Sei. 243, 804 (1956). 168. ZEL'DOVlCH, YA. B., SAOOVNIKOV, R. YA. and FRANKKAMENETSKY,D, A., Nitroffen Oxidation in Combustion, 131. OLSON, D. B. and GARt~NER, W. C., J. phys. Chem. 81. USSR Acad. Sci., Moscow (1947). 2514 (1977). 132. B^SEVICH. V. YA. and KOGARKO, S. M.. I:v. Akad. 169. FOSTER, D. E. and KECK, J. E., Comhust. Flame 38. 199 (1980L Nauk SSSR, Set. Khim., No. 6, 1404 (1979). 133. COFFEE,T. P,, Combust. Flame 55. No 2, 161 (1984}. 170. LYON, R. K. and BENN. D., 17th Syrup. (Int.) on Combustion. p. 60. Combust. Inst,, Pittsburgh (1979). 134. B^RISOV, A. A., DRAGALOVA. E. V. et HI., Khim. ]/z. I, No 4, 536 (1982). 171. DI~AN, A. M., HARDY. Y. E. and LYON. R. K.. 19th Syrup. (Int.) on Combustion. p. 97, Combust. Inst., 135. SMoor, L .D., Comhust. Flame 31,325 (1978). Pittsburgh (19831. 136. TSATSARONIA.G.. Combust. Flame 33, 217 (1978L

Chemical kinetics 172. MILLER, J. A,, SMOOKE, M. D., GREEN, R. M.and KEE, R. J.. Combust. Sci. Technol. 34, 149 (1983). 173. HARmSON, H., JOHNSTON, H. S. and HARDWICK, E. R., J. Am, Chem. Sot'. 84, 2478 (1962). 174. GHERS~ENZON YU. M., DEM~T'YEV, A. P. and NALB^ND'YAN, A. B., Dokl. Akad. Nauk SSSR 210, No. 2, 381 1,1973). 175. SHNAIDER, !. A., lVANOV, O. A. and NALB^ND'YAN, A. B., Dokl. Akad. Nauk SSSR 168, 626 (1968). 176. JOSIE, J., SCHLIDER, J. A. and VOLANSCHI, Revue roum. ehim. 15, 1827 (1970). 177. GONTKOVSKAYA, V. T.. GORtX)POLOVA, P. S. and BASEVICH, V. YA., Fi:. ~toreniya Vzo'va 17, No 1, 64 (1981). 178. LEwls, B. and ELBE, G., d. chem. Phys. 2. 537 1,1934). 179. ZEL'DOVlCH,YA. B. and SEMYONOV.N. N., Zhurn, eksp. i teor. tiz.. 10. No 12, 1427 0940). 180. LOV^CHEV, L .A., BASEVlCH,V. YA., KOGAN, A. M. and POSVYANSKY, V. S., lzt'. Akad. Nauk SSSR, Ser. Khim. 1256 (1970). 181. LOVACHEV,L. A., B^SEVICrl, V. YA., KOGAN, A. M. and POSVYANSKY. V. S., l=t'. Akad. Nauk SSSR, Ser. Khim. No. 4. 881 1,1971). 182. BASEVICH,V. YA., VOLODIN, V. P., KOGARKO, S. M. and PEREGUDOV. N. 1.. Fiz. ooreniya Vzrvva 16, No 2, 126 (1980). 183. BASEVlCH,V. YA. and B~YAEV,A. A., Khim. liz. 4, No 3, 421 (1985). 184. KOKUSHKIN, N. V., Izt'. Akad. Nauk SSSR, OTN, No. 8, 3 (1958). 185. BASEVICH, V. YA. and KOGARKO, S. M., I-v. Akad. Nauk SSSR, OTN, ener#, avtom. No. 2, 13 (1959); A R S Jl. 29, 756 (1959). 186. KOZLOV, S. N., BASEVICH, V. Y^ and KOGARKO, S. M., Teor. osn. khim. tekhnol. 7, N o 4, 614 (1973). 187. BASEVWH, V. YA. and KOGARKO, S. M., Arehwm termod)~, spalaniu 6, No 1, 95 1"1975). 188. DAMKOHLER.G., Z. Elektroehem. 46, 601 (1940). 189. SHCHELKIN,K. I., Zh. tekh.//:. 13, No 9-10, 520 (1943). 190. SUMMERnELD, M., REITER, S. H., KEBELY, V. and MASCOLO, R. W., Jet Propul. 25, 377 (1955). 191. BASEVICH, V. YA. and KO(iARKO, S. M., Dokl. Akad. Na,tk SSSR 203, No 1,144 (1972). 192. BURGERS. I. M., Advances Appl. Mech., 171, Academic Press, New York, (1948), 193. B^SEVICH, V. Y^.. KOGARKO, S. M. and DINAnURG. E. I., Teor. osn. khim. tekhnol. I0, N o 1,155 (1976). 194. BASEVICH.V. YA., VOLODIN, V. P., KOGARKO,S. M. and PEREGUDOV, N. I., Fiz, ooreniya Vzryva 14, No 5, 48 (1978): Combust. Flame 36, 19 1,1979). 195. BASEVICH.V. Y^. and KOGARKO, S. M., Kinet. katal. 7, 393 (1966). 196. BASt~VlCH,V. YA., VOLODIN, V. P.. KOGARKO,S. M. and PEREGUDOV. N. I., Khim, fiz. I. No 8, 1130 (1982). 197. KARPOV. V. P. and SEVERIN. E. S., Fi:..qoreniya Vz,3"va, 16, No 1.45 (1980). 198. BASI!VWH.V. YA.. VOLOD1N,V. P., KOGARKO.S. M. and PEREGUDOV. N. I.. Fi:. ooreniya Vz,Tra 19. No 4, 24 (1983). 199. FINE, B., Comhust. Flame 2, 109 (1958). 200 KOLMOGOROV.A. N., Dokl. Akad. Nauk SSSR 30. N o 4. 299 (1941). 201. BASEVICH,V. YA., VOLODIN, V. P., KOGARKO, S. M. and PEREGUDOV, N. I., Fi:. ooreniya Vzo'va 16, No 4, 7 (1980). 202, BASEVICH, V. Y^.. DEVlSHEV, M. I. and KOG^RKO, S. M., Icy. Akad. Nauk SSSR. OTN, ener O. avtom. N o 3. 138 1,19601: ARS Journ.. 32. 133 (1962). 203 BASEVlCH,V. YA., VOLODIN. V. P., KOGARKO. S. M. and PEREGUDOX, N. I.. Fi:. goreniya Vzrvt'a 22, No 3. 44 ~1986). 204. GgYDON. A. G.. The Spectroseop.v oJ Flames. London t19591.

247

205. KOGARKO, S. M. and BASEV1CH, V. YA., Zh. [i:. Khtm. 35, 1794 (1961). 206. B^SEVlCH, V. YA.. KOGARKO, S. M., P^SnKOV, V. Yc. and TVURIN, A. N , Khim.//z. 1, No 11, 1557 1,1982). 207. BASEWCH,V. YA., KOGARKO, K M. and SHAKHBAZ'YAN. A., Khim. fi:. 4, No 2, 289 1,1985). 208. KARMILOVA, L. V. and KONDRAT'YEV. V. N., Zh. fi.7. khim. 25, 312 (1951). 209. MALTE, P. C., SCHMIDT, S. C. and PRA'Vr, D. T., 16th Syrup. (int.) on Combustion, p. 209, Combust. Inst., Pittsburgh (1977). 210. ASHURST, W, T. and B^RR, P. K., Comhust. Sei. Teehnol. 34, 227 (1983). 211. BASEVICH, V. YA. and KOGARKO, S. M., Fi:. ~loreniya Vzo'va 5, No 1, 99 (1969). 212. LEVlNSON,G. S., Combust. Flame 9, 65 (1965). 213. EGERTON, A. and TABET, S. K., Proe. R. Sot'. 211,445 (1952). 214. BAmSOV, A. A.. GELFAND, B. E. et ul.,Khim.//z. 2, No 6, 838 (1983). 215. CULLEN, R. E. and GLUCKSTEIN, M. E., 5th Syrup. (Int.) on Combustion, p. 569, Reinhold. New York (1955). 216. MITCHNER, M. and GROSS, R. A., J. aeronaut. Sci. 23, 607 (19561. 217. CHURCHILL, WEIR A., GEALER, R. L. and KELLEY, R. J., Ind. Era.In#. Chem. 49, 1419 1,,1957). 218. CHEREDNICHENKO, V. M., POSPELOVA, !. N. and PSHEZHETSKY, S. YA., Zh. fiz. Khim. 32, 2673 1,19581. 219. HARTECK, P. and KoPscH, U., Z. phys. Chem. Bl2, 327 1,1931). 220. SEMYONOV,N. N.. DUBOVITSKY,F. 1. and NALBAND'YAN, A. B., Tran,~. Far^dr O" Sot'. 29, 606 (1933). 221. NALBANJAN,A. B., Phy.s.Z. SmvjUn. 4, 747 (1933). 222. NALBANDJAN, A. B.. Aeta Phy.~.-chem. URSS I, 305 (1934). 223. KOGARKO, S. M. and BASEVlCH, V. YA., Fi:. goreniya V:rvva, 13, No 2, 275 (1977). 224. KOG^RKO, S. M.. DEvlsnev. M. I. and B^sEwcrt, V. YA.. Dokl. Akad. Nauk SSSR 127, 137 (1959). 225. JAMES. C. G. and SUGDEN, T. M , Proc. R. Sot'. A227. 312 [1955). 226. KOGARKO, S. M., MIKHEEV, V. V. and BASEVlCH. V. YA.. Zh. fi:. Khim. 35. 2341 (1961). 227. VAV1LOV.A. N.. KOGARKO,S. M. and BASEVlCH,V. YA., Fi:. goreniya Vzrvva 2. No 2, 107 (1966). 228. BASEVICH, V. YA. and KOGARKO, S. M., Fi:. ,qoreniyu Vzryva 8. No 4, 582 1,1972). 229. BASEVICH, V. YA. and KOGARKO, S. M., Dokl. Akad. Nauk SSSR 141, No 3,659 (1961). 230. BASEVICH.V. YA. and V~,DENEEV,V. 1., Khim. f/-. 4, No 6 (1985). 231. CHOULIS. D. and WILSON, M. J. G., Comhust. Flame 7. 4, 369 (1963). 232. RUmNS, P. M. and RHODES, R. P., AIAA JI I. No 12, 2778 (1963). 233. RICHMOND.J. K. and SHREEVE, R. P.. AIAA JI 5. 1777 (1967). 234. SUGDEN,T. M., lOth Syrup. (Int.) on Combustion, p. 539, Combust. Inst., Pittsburgh (1965). 235. BASCOMaE. K. N , GREEN, J. A. and SUGDEN. T. M., Adv, Mass-speetrom. 2, 66 (1962). 236. CALCOTE, H F, and JENSEN,D. E., Advd. Chem. Set. 58, 291 (1966). 237. SEMYONOV,E. S. and SOKOLIK. A. S., Zh. teor. Fiz. 32, 1074 (1962). 238. DEFLAU. J. L. and BARASSIN, A.. C. R. Aead. Sci. C273, No 12. 689 (1971L 239. DASSER. A., 3rd Int. Syrup. Comb. Processe.s. Abstracts, p. 10. Polish Acad. Sci., Kazimier (1973). 240. ARAVlN, G. S.. VLASOV, P. A., KARASEVlCH. Yt:. K. et al., Fi:. om'eni)'a Vzo'va 18, No 1,49 (19821. 241. DILESSIO, A., LORENZO. A.. BERETTA. F. and VENTOZZI.

248

242. 243.

244. 245. 246. 247. 248. 249. 250. 251. 252. 253. 254.

V. YA. BASEVICH C., 14th Syrup. (Int.) on Combustion, p. 941, Combust. Inst., Pittsburgh (1973). ANTONOV, V. N. and LAPIDUS, A. S., Manujacture of Acetylene, Khimiya. Moscow (1970). BASEVtCH,V. YA., KOGARKO,S. M., GONTKOVSKAYA,V. T. and DUBOWTSKY.V. A., Teor. osn. khim. tekhnol. 15, No 3,449 (1981). PEARSON. R. G., Symmeo 3" Rules Jbr Chemical Reactions, Wiley-lnterscience Publ., N. Y. (1977). FENIMORE, C. P., 13th Syrup. (Int.) on Combustion, p. 373, Combust. Inst., Pittsburgh (1971). BASEWCH,V. YA., KOGARKO,S. M, and FURMAN,G. A.. Izr. Akad. Nauk SSSR, ser. khim. No 10, 2371 (1972). KOGARKO, S. M. and BASEVlCH.V. YA., Fiz..qoreniva Vcryra 17, No 5, 3 (1981). SAROFIM, A. F. and POHL, J. H., 14th Syrup. (int.) on Combustion, p. 739, Combust. Inst., Pittsburgh (1973). BACHMAIER,F., EBERIUS,K. H. and JUST. TH., Comhust. Sei. Teehnol. 7, 77 (1973). L1VESEY, J. B.. ROaERTS, A. L. and WtLLtAMS, A., Combust. Sci. Teehnol. 4. 9 (1971). HAYHURST,A. N. and MCKEAN, H. A. G., Nature 251, No 5473. 303 (1975). HAYI-IURST,A. N. and VINCE, I. M., Comhust. Flame 50, 41 (1983). CORLETT, R. C., MONTEITH, L. E.. HALGREN,C. A. and MALTE, P. C., Comhust. Sci. Technol. 19, 95 (1979t BASEVlCH.V. YA. and KOGARKO,S. M., Fic. ,qoreniya V--t3'ra 21, No 5, 12 (1985).

255. SEMERJIAN, H. and VRANOS. A., 16th S.vmp. (Int.) on Combustion, p. 169, Combust. Inst., Pittsburgh (1977). 256. TALANTOV,A. V., SrwHUrdN, V. A. and VALIEV,F. M., Col. Combustion in the Flow. No 2, 3, Kazai. Kazan (1978). 257. NAZAROV, I. P.. NAUMOV, S. V., NOVIKOV, S. S. and PROSTOV, V. N.. 8th Int. Colloquium on Gasdvnamies Explosions. p. 41. Minsk. 258. LORUSSO, J. A.. KAISER. E. W. and LAVOtE. G. A.. Comhust. Sci. Teehnol. 33, 75 (1983). 259. BAULCH,D. L. DRYSOALE,D. D., HORNE. D. G. and LLOYD, A. G., Eraluated Kinetic Data Jot HighTemperature Reactions, vol. 1-2, Butterworths, London (1973). 260. POLAK, L. S., GOL'DENBERG, M. YA. and LEVITSKY, A. A., Computational Methods in Kinetics. USSR Acad. Sci.. Moscow (1984). 261. RUSXN, L. Yu., FURMAN. G. A. and PAVLOV, B. V.. Kinet katal. 8, 887 (1967). 262. AZAT'YAN,V. V., KOGAN. A. M.. NEUGAUS.M. G. et al., Kinet. katal. 16, 577 (1975). 263. BASEVICH, V. YA., BELYAEV,A. A. and POSVYANSKY. V. S., Khim.[i:. i, No 6. 842 (1982). 264. GONTKOVSKAYA. V. T., MERZHANOV, A. G. and OZERKOVSKAYA, N. I., Col. Chemical Physics of the Combustion and Explosion Processes, Institute of Chemical Physics of the USSR Acad. Sci., Chernogolovka (1977).