Hydrogen-oxygen reactions behind shock waves assisted by OH(2Σ+) formation

Article abstract of DOI:10.1016/S0009-2614(03)00875-3

The results of the OH(²Σ⁺) → OH(²Π) luminescence registration at 1000≤ T≤2500 K and 2.0≥p≥0.3 atm during the ignition-combustion process behind incident shock waves in (2H₂ + O ₂) + Ar mixtures were s

Full text of DOI:10.1016/S0009-2614(03)00875-3

Chemical Physics Letters 375 (2003) 413–418
www.elsevier.com/locate/cplett
Hydrogen–oxygen reactions behind shock waves assisted
þ
2
by OH( R ) formation
*
O.V. Skrebkov , S.P. Karkach, V.M. VasilÕev, A.L. Smirnov
Institute of Problems of Chemical Physics RAS, Chernogolovka 142432, Russia
Received 19 March 2003
Published online:
Abstract
2
þ
2
The results of the OH( R ) ! OH( P) luminescence registration at 1000 6 T 6 2500 K and 2:0 P p P 0:3 atm during
the ignition–combustion process behind incident shock waves in (2H + O ) + Ar mixtures were subjected to theoretical
analysis. Experiments are interpreted in terms of kinetic problem with account of the electronically excited particles
2
2
2
þ
1
1
OH( R ), O( D), and O
relaxation of O molecules exerts essential influence on the chemical transformation process through the chain
2 2 2
( D), and the vibrational nonequilibrium of initial H and O molecules. Slow vibrational
2
branching reaction H + O
observed ones.
2
!HO + O. The maximum luminescence moments calculated are in good agreement with
Ó 2003 Published by Elsevier Science B.V.
1
. Introduction
others electronically excited particles, such as
1
1
O* ¼ O( D) and O
2
* ¼ O
2
( D), possessing lower
The combustion of hydrogen (or hydro-
carbons) is accompanied by the emission of
ultraviolet light due to transitions of excited
excitation energies. Answers to these questions are
of importance for the search of alternative ap-
proaches to improve combustion, in particular,
for efficient ways of influencing the ignition pro-
cess [5]. On the other hand, the problems of
detailed understanding the hydrogen–oxygen re-
action remains one of central in modern com-
bustion chemical physics; in particular, the
mechanism of chain initiation and new develop-
ments in this field were discussed in recent publi-
cations [6–10].
2
þ
OH* ¼ OH( R ) radicals to their ground states
2
OH( P), and monitoring for this emission has
been used long ago in the investigation practice as
a method for determining the ignition-delay time
[
1–4]. Since the OH ! OH* excitation energy is
about 47 000 K, the question arise, what is the
formation mechanism for excited OH* radicals at
low temperatures ꢀ1000 K, and what is the role of
In this Letter, in continuation of the study
10], we focus on the physically adequate mech-
[
*
anism for ignition–combustion processes in hy-
drogen–oxygen mixture with allowance for
Corresponding author.
E-mail address: skreb@icp.ac.ru (O.V. Skrebkov).
0
009-2614/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V.
doi:10.1016/S0009-2614(03)00875-3

414
O.V. Skrebkov et al. / Chemical Physics Letters 375 (2003) 413–418
electronically excited OH*, O*, and O
and vibrational nonequilibrium for initial H
and O molecules. To rectify the kinetic scheme,
2
* particles,
2
2
results of ab initio analysis are widely used;
in particular, rate constants for essential reac-
tions were held near the theoretically suggestible
levels.
2
. Experimental
All experiments [10] were carried out in the
round 76 mm stainless steel shock tube. The high-
pressure chamber (1.5 m long) was separated from
the low pressure channel (4.5 m long) by the
0
.2 mm copper diaphragm. This channel had at its
Fig. 1. The temperatures T (solid) and pressures p (open) be-
hind shock wave in dependence of initial pressure p1 for the
following experiments: 1, 1.4%; 2, 2.5%; 3, 2.8%; 4, 5.0%; and 5,
end a measuring section (1 m long) with piezo-
electric pressure cells and quartz optical windows
5
2 2
.6% of (2H + O ) in Ar (driver gas is hydrogen). Dependencies
(
1 mm  10 mm). (Detailed description of the
6
–8 are used in subsequent kinetic calculations.
equipment is presented in [11].) The OH* ! OH
emission at k ꢁ 306 nm was monitored behind the
incident shock wave. The position of the lumi-
nescence maximum (in the laboratory coordinate
system) and the shock front are clearly distin-
guishable in all oscillogrammes. The shock wave
velocity was determined by the baseline method
3. Theory
Theoretical consideration involves the following
two aspects: (i) ab initio analysis intended to iden-
tification of some reactions as elementary ones and
to independent estimate for their rate constants,
and (ii) kinetic calculations including further re-
finement of some rate constants as a result of fitting
the calculated t* values to experimental ones.
For a number of systems, extensive ab initio
analysis was carried out with use of GAMESS
program package, employing complete active
space self-consistent field (CASSCF) method, in
various active spaces. Most accurate energy and
frequency estimates for use in frames of conven-
tional transition state theory (CTST) were per-
formed employing high-level post-SCF methods
from GAUSSIAN package, within the energy pre-
diction scheme proposed earlier [7]. This scheme
was also adapted to MCQDPT2 (multiconfigura-
tion quasi-degenerate perturbation theory, second
order) energy calculations. To a number of acti-
vationless reactions, CASSCF-based variational
transition state theory (VTST) was applied.
(
on 0.1 m base) with the aid of piezoelectric pres-
sure cells. Thermodynamic state of the gas mixture
behind a shock wave was calculated by standard
method from the wave velocity measured; see
Fig. 1.
Herein, we deal with stoichiometric (2H +
2
O
2
) + Ar mixtures containing small amounts (65%)
of reactive addition, this enables us to exclude the
1
thermal phenomena out of consideration . As a
driver gas, hydrogen was used. The principal ki-
netic characteristic, both measured and calculated,
was the time t* between the shock wave passing
and the moment of emission signal maximum.
1
At larger content of reactive 2H2 + O2 addition, gas-
dynamical and thermal phenomena come to foreground. To
derive kinetic characteristics from such experiments, it is
necessary to solve non-stationary problem on arising and
propagation of the detonation wave over the gas mixture heated
by initial shock.
General formulation of problem for the
chemically and vibrationally nonequilibrium flow
of multicomponent gas mixture has been given

O.V. Skrebkov et al. / Chemical Physics Letters 375 (2003) 413–418
415
previously [12,13]. Presently, the problem is sim-
plified to isothermal one because, for greatly di-
luted mixtures, the heat effects can be neglected.
For calculations, the coordinate system was at-
tached to the flow behind the shock wave (the gas
rests, T ¼ const, p ¼ const, t ¼ 0 when the shock
front is passing). Vibrational nonequilibrium was
taken into account for the initial H and O mol-
2
2
ecules; the influence of that on the chemical reac-
tion rates was estimated as following:
0
k ðT; T Þ ¼ j ðT; T Þ Á k rðTÞ;
ð1Þ
is the vibrational temperature of the kth
r
k
r
k
where T
k
0
mode; k ðT Þ is the equilibrium rate constant of the
r
rth reaction; j
estimated in frames of model [12,13].
r
ðT; T Þ is the nonequilibrium factor
k
The measured t* values were used for compar-
ison with calculated moments of the OH* con-
centration maximum. The latter is determined in
competition between the OH* producing and
quenching processes.
Fig. 2. Observed, 1–5, and predicted, curves 6–8, values of t* in
dependence of temperature behind incident shock wave: 1,
1
4
.4%; 2, 2.5%; 3, 2.8%; 4, 5.0%; 5, 5.6%; 6, 1.4%; 7, 2.7%; and 8,
.8% of (2H + O ) in Ar (driver gas is hydrogen).
2
2
results are used. Most essential processes deter-
mining the reaction mechanism on the whole and
the formation of OH* radicals are listed in Table 1.
4
. Results and discussion
The vibrational relaxation times used for initial H
and O molecules are given in Table 2.
2
The comparison of observed (1–5) and pre-
dicted (6–8) values for the maximum luminescence
time, t* is presented in Fig. 2. Theoretical curves
2
Because of obvious discrepancy between liter-
ary and recent theoretical data for initiating reac-
tions, they were analyzed carefully. Most
unambiguous is reaction (1) of Table 1 estimated,
with close results, both experimentally [8,14] and
theoretically [7,8]. At high temperatures and low
pressures, T > 2200 K, p < 0:6 atm, reaction (2)
becomes principal. In addition, our full kinetic
scheme involves the following initiating processes:
(
6–8) conform to calculations with temperatures
and pressures behind shock wave according to
dependencies (6–8) in Fig. 1. Experimental values
correspond to the compositions with various, from
1
.4% to 5.6%, amounts of (2H + O ) reactive ad-
2 2
dition. As it follows from Fig. 2, the theoretical
model is in agreement with the experiment; the
best coincidence being at small amounts of
(
2 2
2H + O ). At 5.6% and 5% of hydrogen–oxygen
(
i3) H
ki3 ¼ 2:1 Â 10 Â ðT =298Þ
 expðÀ33935=TÞ ðCTSTÞ;
2
+ O
2
! H
2
O + O,
addition, the effect of heating becomes consider-
able and manifests itself in a discrepancy with the
isothermal theoretical model, and in the experi-
mental data spread.
The kinetic scheme was destined for interpreta-
tion the experimental t* values in 1000 6 T 6 2500
K, 2:0 P p P 0:3 atm region. The full reaction set
includes 91 irreversible stages involving H
H
traditional reactions, most equilibrium rate con-
stants were found in [14], but in some cases newer
1
2
1:833
(
i4) H + O ! 2OH,
i4 ¼ 2:9 Â 10 Â ðT =298Þ
2
2
12
1:905
k
 expðÀ34377=TÞ ðCTSTÞ;
2 2
, O ,
2
O, HO , H, O, H , O , O *, O*, and OH*. For
2
2
2
O
2
3
(
i5) O
2
+ M!2O + M,
14
k
i5 ¼ 3:1  10  expðÀ58410=T Þ½14Š;

416
O.V. Skrebkov et al. / Chemical Physics Letters 375 (2003) 413–418
Table 1
The reactions in (2H
2
+ O
2
) + Ar mixture at 1000 6 T 6 2500 K, 2:0 P p P 0:3 atm
0
r
3
r
Reactions
k ðTÞ (in cm , mol, s)
References
Initiating
1
2
2:056
a
1
2
H
H
2
2
+ O
2
$ H + HO
2
2:2 Â 10 Â ðT=298Þ
 expðÀ27059=TÞ
15
+ M $ 2H + M
2:1  10  expðÀ50920=TÞ
[14]
Chain branching and others
HO + H O + H
$ H
+ O $ H + HO
H + O
$ HO + O
HO + H
! H
H + O
+ M $ HO
12
1:779
0:861
3:17
a
a
3
4
5
6
7
2
2
1:1 Â 10 Â ðT=298Þ
1:1 Â 10 Â ðT=298Þ
 expðÀ1558=TÞ
 expðÀ4648=TÞ
13
H
2
12
b
2
1:8  10  ðT=298Þ Â expðÀ7500=TÞ
[8,14]
[14]
12
2
2
2
O
2
+ H
(v) + M
2:6  10  expðÀ10750=TÞ
M ¼ H , O : 2:1 Â 10 Â ðT=298Þ
M ¼ Ar: 7:0 Â 10 Â ðT=298Þ À 0:8
À1:3
16
À0:8
2
2
2
2
15
[14]
13
8
O
2
+ O + M $ O + M
3
M ¼ H
2
, O
2
: 9:1 Â 10 Â ðT=298Þ
13
À1
M ¼ Ar: 4:9 Â 10 Â ðT=298Þ
[14]
[14]
[14]
[8]
13
0:486
0:330
2:7
9
0
1
2
HO
2
+ H!HO + OH
3:8 Â 10 Â ðT=298Þ
1:5 Â 10 Â ðT=298Þ
 expðÀ103=TÞ
 expð128=TÞ
13
1
1
1
O + HO !OH + O
HO + HO $ H O + O
H + OH + M $ H O + M
2
2
10
2
2:1 Â 10 Â ðT=298Þ Â expð1251=TÞ
1
7
À1:212
À1:212
À2
2
M ¼ H
M ¼ O
M ¼ Ar: 9:4 Â 10 Â ðT=298Þ
3:2  10  expðÀ23820=TÞ
3:1  10  expðÀ73=TÞ
1:3 Â 10 Â expð67=TÞ
2
: 1:3 Â 10 Â ðT=298Þ
 expð295=TÞ
 expð295=TÞ
16
2
: 3:1 Â 10 Â ðT=298Þ
[14]
16
17
13
14
15
H
2
O
2
+ M $ HO + OH + M
OH + HO O + O
!H
2HO + O
!H
Excitation and quenching
HO + H
[14]
[14]
[14]
13
2
2
2
12
2
2
O
2
2
15
À1:7
À1
b
b
b
16
17
18
2
2
$ OH* + H
2
O
3:0 Â 10 Â ðT=298Þ
 expðÀ19000=TÞ
15
O* + H + M!OH* + M
O + H + M!OH* + M
7:0 Â 10 Â ðT=298Þ
16
À1
M ¼ H
M ¼ H
2
, O
2
, Ar: 1:0  10  ðT=298Þ Â expðÀ12000=TÞ
1
1
0:18
À1
2
: 5:6  10  ðT=298Þ Â expðÀ4035=TÞ
1
5
M ¼ OH: 2:0 Â 10 Â ðT=298Þ
1
4
b
19
OH* + M $ OH + M
M ¼ H
2
O: 2:2  10  expðÀ276TÞ
[16,17]
1
2
12
M ¼ H
2
: 1.0 Â 10 ; M ¼ O
2
: 6.0 Â 10
1
1
0:5
M ¼ Ar: 1:3 Â 10 Â ðT=298Þ
13
0:5
b
2
2
2
2
2
2
2
2
2
2
a
0
1
2
3
4
5
6
7
8
9
OH* + O
2
$ O
O $ H
!H O + H
!HO + O
OH*!OH + hm
HO O + O*
+ H!H
O* + H
$ OH + H
3
+ H
4:0 Â 10 Â ðT=298Þ
[16,17]
[16,17]
12
b
OH* + H
OH* + H
2
2
2
O
2
+ H
7:5  10  expðÀ276=TÞ
13
0:5
b
2
8:8 Â 10 Â ðT=298Þ
[16,17]
[16,17]
[1]
13
0:5
b
OH* + O
2
2
2:0 Â 10 Â ðT=298Þ
6
1.4 Â 10
13
0:458
b
2
2
2:3 Â 10 Â ðT=298Þ
 expðÀ678=TÞ
[14]
[14]
13
2
8:7 Â 10 Â expð14=TÞ
14
11
11
O* + M!O + M
M ¼ H
2
: 1.0 Â 10 ; M ¼ O
2
: 2.0 Â 10 ; M ¼ Ar: 2.0Â10
[14]
a
11
1:671
H + HO
2
$ H
2
+ O
+ M
2
*
6:5 Â 10 Â ðT=298Þ
 expðÀ3162=TÞ
6
6
5
O
2
* + M $ O
2
M ¼ H
2
: 2.7 Â 10 ; M ¼ O
2
: 1.0 Â 10 ; M ¼ Ar: 3.0 Â 10
[14]
0
Present CTST estimation. Here and below, the double arrow means the brief writing for two reactions (forward, r, and reverse, r ).
Fitted; see text.
b
0 0
2
*, (28 ) followed (29 ),
(
i6) H
2
+ 2O
2
!2HO
2
,
ating process involving O
can be ignored.
1
7
k ꢁ 2  10  expðÀ13000=TÞ:
i6
The initiation is noticeably slowed down due to
slow vibrational relaxation of O molecules. This
For (i6), the rate constant is based on presently
available ab initio results and on data [14] for re-
verse reaction. In our experimental conditions,
reactions (i3)–(i5), as well as the two stage initi-
2
effect is increased with the gas temperature in-
crease (because of weaker Landau–Teller temper-
ature dependence for vibrational relaxation times

O.V. Skrebkov et al. / Chemical Physics Letters 375 (2003) 413–418
417
Table 2
Vibrational relaxation processes
v
Process
(1) + M $ H
p Á sðMÞ (atm s)
References
[18]
À9
À9
À9
À1=3
À1=3
À1=3
1
H
2
2
(0) + M
M ¼ H
2
: 1:55 Â 10 Â expð93 Â T
Þ
M ¼ O
2
: 3:76 Â 10 Â expð101 Â T
Þ
M ¼ Ar: 1:08 Â 10 Â expð104:5 Â T
Þ
Þ
À8
À9
À1=3
À1=3
À1=3
2
O
2
(1) + M $ O
2
(0) + M
M ¼ H
2
: 5:3 Â 10 Â expð49:7 Â T
Þ
M ¼ O
2
: 9:9:0 Â 10 Â expð138 Â T
Þ
M ¼ Ar: 2:0 Â 10 À 10 Â expð173 Â T
[18]
as compared to Arrenius dependence for rate
constants). Whereas at T < 1400 K the vibrational
relaxation has managed to come to the end within
the induction period, at T > 1800 K nearly the
whole combustion process proceeds in absence of
Eq. (1). Very likely, it is the disregard of the vi-
brational nonequilibrium effect that is a cause of
considerable discrepancies between experimental
results for k themselves, and with the calculated
5
ones [8,14,15].
The formation of electronically excited hy-
droxyl–radical OH* is caused by reactions (16)–
vibrational equilibrium, see Fig. 3. Slow O
2
vi-
brational relaxation exerts essential quantitative
influence on the process via the overwhelmingly
important chain branching reaction (5), see curve
0
0
0
(18) and (19 )–(21 ). The k value of Table 1 is
based on known data for quenching of OH* rad-
16
0
4
into account when the shock tube experiments are
for j ðT; T Þ in Fig. 3, and this should be taken
ical on H O molecules [16,17] having supposed the
2
5
2
0
reverse reaction (16 ) to be one of possible chan-
nels for such quenching. Also the superequilibrium
0
interpreted quantitatively. Note that the k value
of Table 1 is based on allowance for the vibra-
tional nonequilibrium effect in accordance with
5
vibrational excitation of HO
the bimolecular recombination (7) was supposed.
2
radical produced by
0
7
0
18
The k1 and k values were chosen on the basis of
ab initio analysis and kinetic fitting. There are the
following channels for OH* formation: (i) non-
adiabatic channel O* + H (17) having a high
transition probability, (ii) adiabatic one O + H (18)
with activation barrier about 12 000 K, (iii) the
third body specific (M ¼ H
2
) nonadiabatic channel
from O + H via the low-lying crossing of lowest
þ
2
2
OH( P) + H
2
2
term with OH( R ) + H one in the
linear HO–HH configuration. Very likely, similar
processes are possible (but not revealed yet) with
participation of another species, M ¼ O , H O, etc.
2
2
Reactions (21)–(23) are possible channels for
OH* quenching on H O, H , and O .
In our ab initio estimate, the known rate con-
2
2
2
stant value for HO
should be ascribed to k2 for HO
reaction which is the source of O* atoms. In spite
of their fast quenching, at T 6 1400 K this exerts,
via reaction (17), noticeable influence on OH*
formation. Reactions (25) and (26 ) followed with
fast O* quenching, are important for generation of
O atoms. The quenching of O* on hydrogen
2
+ H!H
2
O + O reaction [14]
O + O*
0
5
2
+ H ! H
2
2
Fig. 3. Calculated profiles of vibrational temperatures for H ,
0
0
0
curves 1 and 1 , and O
2
, 2 and 2 (the ratio to the equilibrium
one); H
2
concentrations, 3 and 3 (the ratio to the initial one);
0
0
and the j
5
ðT; T
2
Þ value, 4 . Cases: T ¼ 1100 K, p ¼ 1:96 atm
0
0
0
0
(
1, 2, and 3); T ¼ 2300 K, p ¼ 0:5 atm (1 , 2 , 3 , and 4 , dashed
curves). The composition is H :O
2
2
:Ar ¼ 1.8:0.9:97.3.

418
O.V. Skrebkov et al. / Chemical Physics Letters 375 (2003) 413–418
molecules (26) results in chain-branching. Reac-
0
[6] R. Blumenthal, K. Fieweger, K.H. Komp, G. Adomeit,
B.E. Gelfand, in: 20th International Symposium on Shock
Tubes and Waves, 1996, p. 935.
tion (28 ) is of interest as a tool for influencing the
ignition–combustion process by making an excess
of electronically excited molecular oxygen.
[
[
[
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1
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Acknowledgements
[
This work was supported by INTAS (Grant
No. INTAS-2000-00556) and RFBR (Grants No.
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