Kinetic Modeling for Chemiluminescent Radicals in Acetylene Combustion

Uma modelagem cinética foi avaliada para reproduzir a quimiluminescência experimental dos radicais excitados OH*, CHO*, CH* e C 2 * formados na combustão de C 2 H 2 /O 2 em uma câmara fechada. Um mecanismo reacional com 37 espécies e 106 reações elementares foi validado para a combustão de C 2 H 2 /O 2 com Φ=1.00 e Φ=1.62, através das medidas de quimiluminescência. Para isso foram incluídas reações de formação e de decaimento dos radicais excitados. As simulações foram realizadas com o pacote KINAL; o programa DIFF foi utilizado para resolver as equações diferenciais ordinárias e o programa ROPA para realizar a análise das velocidades de produção. Houve uma boa concordância entre os perfis de quimiluminescência experimental e simulado de todos os radicais e para ambas reações. Os resultados mostraram que o CH tem um papel central na formação dos radicais. As reações: H + O 2 = OH* + O; CH + O = CHO*; C 2 H + O 2 = CH* + CO 2 e CH 2 + C = C 2 * + H 2 são as principais rotas reacionais para reproduzir os perfis experimentais.


Introduction
2][3] Acetylene plays a role in processes like polycyclic aromatic hydrocarbons (PAH), soot and prompt-NO formation, and chemiionization and chemiluminescence in combustion chemistry, due to its oxidation products, which are highly reactive small radicals, such as CHCO, CH 2 , CH and C 2 H. [1][2][3] Consequently, the oxidation chemistry of acetylene has a significant influence on mechanisms involved in heavier hydrocarbon flames and, thus, the kinetic modeling of acetylene combustion is of great significance.
][11] Kinetic modeling results usually describe concentration profiles of stable species and free radicals in the ground electronic states that can be validated by experimental data, which have been generally obtained using molecular-beam mass spectrometry and laser induced fluorescence. 5,6,10,12,13lthough the chemiluminescent radicals are minor species, they are probes of the combustion processes since they are intermediate species with short lifetimes that characterize the reaction zones, where the reagents are principally consumed.Thus, they are suitable to use in following the chemistry of small species and other features of the combustion reactions.
In this work, a mechanism is proposed and validated for acetylene combustion in a small closed chamber, where fixed C 2 H 2 /O 2 premixed amounts at a given initial pressure were ignited, using chemiluminescence data.To validate the proposed mechanism the reactions for excited radical formation and decay are considered and the simulated and experimental chemiluminescence profiles resulting from decay of excited radicals were compared.Based on the analysis of production rates of the kinetic modeling established, the key reaction paths for the production of the excited radicals are also identified.

Experimental setup
The combustion system used to obtain the experimental chemiluminescence profiles of OH*, CHO*, CH* and C 2 * excited radicals is the same as that previously reported 14 and thus, will be described briefly.
The combustion reactions were carried out in a closed chamber with constant small volume (ca.200 ml).The gaseous mixtures were prepared using a vacuum manifold to introduce acetylene and oxygen directly into the combustion chamber at a fixed initial composition and pressure.The combustible mixture was ignited by a spark plug at the center of the combustion chamber.
The light emitted from the reaction inside the whole chamber was analyzed by a monochromator (Oriel, 77200), detected simultaneously by a photodiode and a photomultiplier (Burle, 1P28A) and recorded by an oscilloscope (Nicolet, 450).Once the combustion of the fixed mixture amount is initiated, the large number of species produced reacts among themselves and with the original components of the initial mixture, until the reaction rate falls off, while exhibiting a defined chemiluminescence time behavior.
The total chemiluminescences produced in the stoichiometric (Φ=1.00) and fuel-rich (Φ=1.62)C 2 H 2 /O 2 flames at 140 torr were measured setting the diffraction grating of the monochromator to reflect the light emitted from these processes ( , where S.R. is the Chemiluminescence profiles as a function of time from our previous work 14 for each emitter at the heads of the emission bands for OH* (A 2 Σ → X 2 Π), CHO* (A 2 Π → X 2 A'), CH* (A 2 ∆ → X 2 Π) and C 2 * (A 3 Π → X 3 Π) excited radical transitions, for both stoichiometric and fuel-rich flames, are also presented.

Calculation methods
6][17][18] The kinetic model can be expressed by a set of coupled ordinary differential equations.The equation system is described as: dYi/dt = f(Yi(t),...,Yj(t),t,k), where Yi represents the chemical species i and k represents the vector of the kinetic parameters.In this work, we have used the KINAL program package, 19 which is a public domain program based on the Runge-Kutta-4-semiimplicit method. 20The system of coupled ordinary differential equations are automatically generated and solved by the DIFF program of the KINAL package.
The classic method for the study of the reaction relevance is the production rate analysis 21,22 and this was carried out by the ROPA program of the KINAL package.The production rate analysis requires calculation of the Pij matrix elements, which show the contribution of reaction j to the rate of production of species i. 23,24

Reaction mechanism
The proposed reaction mechanism for C 2 H 2 /O 2 homogeneous combustion developed in this study consists of 37 species and 106 elementary reactions, as listed in Table 1.These were proposed in order to reproduce the experimental chemiluminescences of OH*, CHO*, CH* and C 2 * excited radicals obtained in an earlier study for stoichiometric and fuel-rich C 2 H 2 /O 2 combustion in a closed chamber at 140 torr. 14he starting mechanism was based on the studies of Eraslan and Brown 9 and Hidaka et al. 10 with the addition of a set of reactions involving electronically excited species (formation reactions, radiative decay and collisional deactivation reactions and reactions between excited radicals and other species).The initial mechanism also included reverse reactions.They were each inserted, as new reactions, since the KINAL package only works with forward reactions.
Reactions of electronically excited species and their kinetic parameters are limited in the literature, except for the CH* radical.41] In this way, some of the reactions used in our model do not have established kinetic parameters and it was necessary to estimate them.The Arrhenius parameters for these formation reactions of excited species were estimated from similar reactions, which lead to the same species in their ground states, as well as those used for our earlier simulation of ethanol combustion. 42This approach was based on activatedcomplex theory 16,43 and in the fact that reagent species for the formation reactions of the excited species are diatomic and/or atomic.
In the simulated combustion processes, soot particle formation is negligible as our previous study of soot temporal evolution by laser extinction measurements reported. 44Hence, elementary reactions for the production of polycyclic aromatic hydrocarbon (PAH) and soot were not included in the initial reaction mechanism.
The proposed reaction mechanism displayed in Table 1 is very different from the initial one described above.To obtain it, the initial model was optimized through the reduction procedure based on ROPA results and later by applying kinetic parameters from other studies, those that better fitted to the experimental chemiluminescence curves of the excited radicals.
The temperature of the combustion processes, in this study, was a parameter adjusted by running the kinetic modeling at different temperatures until to reproduce the experimental chemiluminescence temporal scales.Simulations with 50 K higher or lower than 1350 K resulted in chemiluminescence temporal scales very different from those experimentally observed.
The proposed reaction mechanism (Table 1) was fitted to 1350 K to reproduce the observed experimental chemiluminescence time of about 2.5 ms in the stoichiometric C 2 H 2 /O 2 combustion (Φ = 1.00) at 140 torr initial pressure.The same reaction mechanism was applied to fuel-rich C 2 H 2 /O 2 (Φ = 1.62) combustion at the same initial pressure (140 torr) and the temperature parameter was adjusted to 1375 K to reproduce the observed experimental chemiluminescence time of about 3.5 ms.
It is well known that the principal path of acetylene oxidation is the reaction of acetylene with atomic oxygen, producing CHCO and CH 2 radicals as primary products: 1,11,45 (r4) (r5) However, there are still polemics about the branching ratio, k 5 /k C2H2+O and the reported determinations show a wide variation.In this work, the branching ratio k 5 /k C2H2+O = 50%, used by Miller and Melius, 8 was adopted.This value is within the range of the reported determinations and it is that which best fit our experimental chemiluminescence profiles.Frank et al. 46 cited by Peeters et al., 26 reported a branching ratio of (64 ± 15)% in favor of CHCO at 1500 K to 2500 K and Baulch et al. 25 deduced k 5 /k C2H2+O = (70 ± 20)% for the temperature range of 295-2500 K.There are also some studies 1,11,45 suggesting a CHCO-yield of 80% from the C 2 H 2 + O reaction, and possibly as high as 95% over a wide range of temperatures.
One of products of the C 2 H 2 + O reaction is the radical CH 2 , which is of great importance in acetylene chemistry.This radical can form in both the triplet CH 2 ( 3 B 1 ) and the singlet CH 2 ( 1 A 1 ) electronic states.CH 2 ( 3 B 1 ) is preferentially produced via C 2 H 2 + O (r5) and the CHCO + H reaction (r31) is the principal channel of CH 2 ( 1 A 1 ) formation. 1,11Although the reactions for production of both singlet and triplet CH 2 radicals are commonly included in the reaction mechanisms, only CH 2 ( 3 B 1 ) was considered here, since there is a fast conversion of singlet to triplet CH 2 radical (CH 2 ( 1 A 1 ) + M = CH 2 ( 3 B 1 ) + M) and, thus, it is predominantly formed, as reported in the literature. 1,46H 2 radicals are mainly reduced by reaction with C 2 H 2 to produce C 3 H 3 + H in the proposed reaction mechanism.][49] In this work, only the reaction CH 2 ( 3 B 1 ) + C 2 H 2 = C 3 H 3 + H with k = 1.74 X 10 13 mol cm 3 s -1 was considered.This rate coefficient is very similar to those used recently by Frenklach and co-workers. 48,49for production of propargyl radical via CH 2 ( 1 A 1 ) to simulate polyaromatic and soot formation.

Initial considerations
Figures 1a and 1b show the temporal behavior of the total chemiluminescence (light signal detected by the photomultiplier, setting the monochromator to have total reflection) from the C 2 H 2 /O 2 combustions with equivalence ratios (Φ) equal to 1.0 and 1.62, respectively.The experimental data show a short time interval to reach maximum chemiluminescence intensity (around 0.55 ms and 0.65 ms after starting the increase, respectively, in Figure 1a and in Figure 1b), followed by an intensity decay to zero during a longer time interval (around 2.0 ms in Figure 1a and ca.3.0 ms in Figure 1b).
Based on this temporal behavior, an approximation to the combustion process may be proposed which occurs as two different events.Flame propagation throughout the chamber is the dominant process in the first part of the chemiluminescence process.This part of the combustion process is strongly affected by dynamic factors that are related to the flame propagation phenomenon.After the chemiluminescence reaches its maximum emission intensity, the reagent consumption is the predominant process in the reaction throughout the chamber.
Theoretical and experimental studies are reported in the literature for C 2 H 2 /O 2 combustion under different conditions: shock tubes, open burners, etc. 5,6,50,51 The results indicate that the combustion shows an initial step, where the intermediate species are formed and the initial reagents are partially consumed.After the initial step, reagent consumption increases and the reaction goes to completion with the formation of stable species.
Since the chemiluminescence temporal behavior is faster in the first process than in the second, the observed chemiluminescence in the second process, where turbulence makes the reaction fairly homogeneous, is considered to be emitted from the entire reacting chamber volume.In the second, slow process, the turbulence results in stirring within the reaction zone, which increases heat transfer and radical diffusion.As some studies 50,51 have reported that the reagents are only partially consumed in the initial step and the KINAL is a software package for the analysis of homogeneous gas-phase chemical kinetics (it does not include fluid dynamic factors related to the flame propagation, as most of the software package is for combustion kinetic simulations), a better approach is to use the slower second process to describe the combustion reaction as a guideline to validate the model in simulation studies of acetylene combustion in a closed chamber.
This work proposes a mechanism for acetylene combustion including formation reactions for electronically excited species.The simulated temporal behavior of the chemiluminescence originating from the radiative decay of the excited species is compared with the second step of the experimental chemiluminescence, which is used as a criterion for mechanism optimization.
To obtain the simulated chemiluminescence displayed in Figures 2 and 3, the photons emitted, hν OH* , hν CHO* , hν CH* and hν C2* , from each corresponding excited radical (r64, r67, r72, r78) were inserted as "species" in the reaction mechanism.The computer simulation results in growth curves of "photon concentration" as a function of time and the differentials of these curves produce the photon production rates as a function of time, which can be associated with the experimental data.The temporal behavior of experimental chemiluminescence can represent the production rate of these excited radicals (number of photons / s) as a function of time, because self-absorption of OH, CHO, CH and C 2 is negligible 36,52 and the total emission time (milliseconds) recorded was a thousand times larger than the lifetimes (microseconds) of excited radicals. 14o compare the experimental chemiluminescent profiles with the simulated chemiluminescent profiles, the first part of all curves (which represents the fast flame propagation through the whole chamber) was removed and the curves were normalized to make the first point coincide with zero on the abscissa and with unity on the ordinate.This procedure does not produce any deformation in the curves and allows comparison between the different groups of results.Thus, the simulated and experimental production rates of the excited radicals can be properly compared, since the comparison between the emission intensities (number of photons / s) and the differentials of the "photon concentrations" (generated in the simulation procedure), are not directly possible.Similar approaches were done to simulate the formation of the chemiluminescent species in ethanol combustion produced in the same combustion system. 42

Mechanism for OH* (A 2 Σ + ) radical formation
The temporal decay of the experimental and simulated chemiluminescence of OH*, presented in Figures 4 (a   Gaydon 36 originally suggested reaction (r60) and Gaydon and Wolfhard 53 proposed reaction (r62) for hydrogen flames for OH* chemiluminescence.Both reactions (r60) and (r62) are exothermic enough to produce OH* in the excited electronic state, around 159 kcal mol -1 and 101 kcal mol -1 , respectively.
Reaction (r61), in spite of being slightly endothermic (16 kcal mol -1 ), 54 was proposed by Shuler 55 for hydrogen flames.Shuler 55 based on analysis of potential energy surfaces, showed OH* production through a [HO 2 ] complex intermediate.Two reaction paths are possible, one from excited O 2 * and another from O 2 in the ground state.However, none of these authors supplied the reaction kinetic parameters.For both reactions (r61) and (r62), kinetic parameters were obtained from similar reactions that produce OH in the ground electronic state. 11,25Since in the first case, the activated complex is the same for both reaction paths to production of ground OH (X 2 Π) and excited OH* ( 2 Σ + ), this approach is valid.In the second, the recombination reaction (r62) would need a third body (M) (to transfer the excess energy) to produce OH in the ground state, so the same rate constant without M in the reaction is suitable.
The reaction (r60) has usually been attributed to OH* chemiluminescence.For this reason the rate constant used by Berman et al., 28 that gives the higher value, was adopted in this work, to test the other possible reactions for OH* chemiluminescence.In this way, the rate constant for reaction (r60) is about hundred times higher than that for reaction (r61) at the temperatures used.The simulated chemiluminescence profiles without (r61) in the reaction mechanism did not fit the experimental chemiluminescence profiles very well.
In this study, the radiative rate for OH* (A 2 Σ + ) radical was 1.70x10 6 s -1 , the same value adopted by Berman et al., 28 and the collisional quenching rate was taken from Tamura et al. 29 ROPA analysis indicated that, in the purposed reaction mechanism, reaction (r61) is the principal route for OH* formation and it contributes to about 90% of the total amount of OH*.The other reactions (r60 and r62) together are responsible for around 10% of OH* production.

Mechanism for CHO* (A 2 Π) radical formation
There is also a good fit between the simulated and experimental chemiluminescence data for the CHO* radical for both stoichiometric and fuel-rich C 2 H 2 /O 2 combustion, as shown in Figures 4 (b) and 5 (b).
To reproduce the experimental chemiluminescence of CHO*, only a single formation reaction of this radical was found in the literature, suggested by Gaydon, 36 and it was inserted in the reaction mechanism.

CH + O = CHO* (r65)
According to Sappey and Crosley, 32 the CHO* (A 2 Π) lifetime is 30 ps and presents a low quantum fluorescence yield.In spite of this, the radical CHO* shows several emission bands in the UV-Visible region from 250 nm to 400 nm that are features of hydrocarbon flames. 32,36inetic parameters for reaction (r65) were not found in the literature, the rate coefficient established 25 for a similar reaction, CH + O = H + CO (exothermic, 57-65 kcal mol -1 ), 56 was applied to this reaction.

Mechanism for CH* (A 2 ∆) radical formation
Experimental and simulated chemiluminescences of the CH* radical are shown in Figures 4 (c) and 5 (c).Again the model reproduces the experimental data with good agreement for both stoichiometric and fuel-rich C 2 H 2 / O 2 combustion.
Although the mechanism of CH* formation has not yet been definitely established, it is one of the most studied excited radicals.Most of these studies, the reaction between C 2 H and O was found to be the main source of CH* radical. 33,37o reproduce the experimental chemiluminescent profile of CH* radical, the reactions proposed initially by Hand and Kistiakowsky 56 (r68 and r69) and reaction (r70), suggested by Gaydon, 36 were tested.
Kinetic parameters for reactions (r68) and (r70) were taken from Eraslan and Brown 9 and the kinetic parameters for the latter reaction are the same as those adopted by Grebe and Homann. 37For reaction (r69), the kinetic parameters were from Devriendt and Peeters. 33The CH* (A 2 Δ) radical lifetime is (0.56±0.06) μs 34 and its nonradiative rate was taken from Tamura et al. 29 ROPA analysis indicates that only reaction (r68) is important in this reaction mechanism for CH* production, in order to fit the simulated chemiluminescence of this radical to its experimental chemiluminescence.The other two reactions (r69) and (r70) were discarded by ROPA analysis.Grebe and Homann 37 also discard reaction (r70), due to the low concentration of C 2 radical in the ground state and our results support their conclusion.

Mechanism for C 2 (A 3 Π g ) radical formation
The temporal decay of experimental and simulated chemiluminescence of C 2 *, presented in Figures 4 (d Four formation reactions for C 2 * radical were inserted in the reaction mechanism to try to reproduce its experimental chemiluminescence.Reactions (r73) and (r76) were originally proposed by Gaydon. 36Miller and Palmer 57 proposed reaction (r74) and Fergunson 58 suggested reaction (r75). of the formation reactions of excited radicals have almost no influence on the simulated chemiluminescence profiles.However, the simulated chemiluminescence profiles are strongly affected by changes in the rate coefficients of reactions that lead to the main precursors (CH 2 and CHCO) of most of the excited radicals.
The most important reactions for production and consumption of each species inserted in the reaction mechanism were determined through production rate analysis by ROPA. Figure 6 shows the reaction scheme built from ROPA analysis results at t = 0.05 ms.ROPA analysis was also carried out at t = 0.50 ms to verify the changes in the importance of different reactions with temporal evolution.As there is practically no change in a reaction's importance as a function of reaction time, the scheme in Figure 6 can properly represent the reaction paths of acetylene oxidation over the whole reaction period.
The proposed reaction mechanism shows three main routes to acetylene oxidation (Figure 6).The first leads to the formation of C2 and C3 species through production of the propargyl radical (C 3 H 3 ) and contributes about 20% to acetylene oxidation.Another route results in oxygenated species such as formaldehyde, water and hydrogen peroxide, via CH 2 CO formation; this route also contributes about 20% to acetylene oxidation.The third is the main route that contributes approximately 60% to acetylene consumption and gives the CH 2 and CHCO primary radicals, which are the precursors of most of the excited radicals.
Both primary radicals, CH 2 and CHCO, take part in the production of CH radical in the ground electronic state.CH radical has a meaningful role in the formation of excited radicals, despite neither always being directly involved in the production of these species.CH radicals are directly linked to OH* and CHO* formation from

Figure 1 .
Figure 1.Total chemiluminescence as a function of time for C 2 H 2 /O 2 combustion in a closed chamber (a) Φ = 1.00 and (b) Φ = 1.62. )

Figure 2 .
Figure 2. Stoichiometric C 2 H 2 /O 2 combustion.(a) Experimental chemiluminescence profiles of excited radicals obtained from reference 14 and (b, c, d, e, f) simulated chemiluminescence profiles of excited species as indicated.

Figure 3 .
Figure 3. Fuel-rich C 2 H 2 /O 2 combustion.(a) Experimental chemiluminescence profiles of excited radicals obtained from reference 14 and (b, c, d, e, f) simulated chemiluminescence profiles of excited species as indicated.

Table 1 .
Optimized reaction mechanism for C 2 H 2 /O 2 combustions.Reaction rate coefficients are presented in the form k = A T n exp(-Ea/RT) and units are in cm 3 , mol, s, K and kcal mol -1 , respectively

Table 1 .
(cont.)Therate constants for these reactions were estimated using the same rate constant parameters of similar reactions, where the species are formed in the ground electronic state.The references indicate the rate coefficients for the formation reactions of species in the ground state; b The rate coefficients were obtained from the literature for the quenching of the excited species by O 2 (M = O 2 ).However, in the simulations k'= k [M] where [M] = [C 2 H 2 ] 0 + [O 2 ] 0is the initial reagent concentrations for each combustion process studied; c The rate coefficients were the inverse of excited species' lifetime. a