An extended methodology for automated calculations of non-Boltzmann kinetic sequences: H + C 2 H 2 + X and combustion impact
It is generally assumed in phenomenological kinetic models that bimolecular reactions only occur between species whose rovibrational energy follows a Boltzmann (thermal) distribution. That is, any complexes initially formed in non-Boltzmann distributions are assumed to be thermalized by energy-transferring collisions prior to bimolecular reactions. Given the high mole fractions of reactive species, X, in combustion environments, reactive collisions of the complexes with X often occur on the same timescale as energy-transferring collisions – yielding sequences proceeding through non-Boltzmann intermediates across multiple potential energy surfaces. Recent studies have shown that such non-Boltzmann kinetic sequences can have substantial impact on the global reactivity in combustion systems. Simulations of these non-Boltzmann reaction sequences, which can be described in phenomenological kinetic models via chemically termolecular reactions, require that rovibrational excitation from one potential energy surface be carried over to the next. Here this paper presents an extended theoretical and computational methodology that couples multiple master equations and derives rate constants for phenomenological reactions describing the conversion of thermal reactants to thermal products for use in phenomenological kinetic schemes. The methodology is then implemented using in-house scripts for non-Boltzmann sequences involving C2H$^*_3$ + X (with X = O 2 , H, and OH) where C 2 H$^*_3$ is formed via H + C 2 H 2 association – which were identified as having strong potential for influencing combustion predictions in a recent study. The results reveal that non-Boltzmann reaction sequences for X = O 2 (the primary focus of this paper) significantly alters the total conversion rate from H + C 2 H 2 to products and product branching fractions from those of thermal sequential pathways. Furthermore, the present results demonstrate that non-Boltzmann reaction sequences have significant impact – as high as an order of magnitude – on predicted ignition delay times. Similarly, they yield significantly different dependence of ignition delay times with temperature and O 2 mole fraction – yielding signatures that are likely observable experimentally.