The Q-K model for gas-phase chemical reaction rates

Abstract

The quantum-kinetic, or Q-K, model is based on the quantum vibration model that is employed in the computation of gas flows at the molecular level by the direct simulation Monte Carlo (DSMC) method. The Q-K procedure for dissociation is physically realistic within the context of the vibration model in that the reaction occurs upon the selection of the vibrational level that corresponds to dissociation. An analogous, but entirely phenomenological, procedure has been presented for endothermic exchange and chain reactions. These procedures for the endothermic reactions have been well validated, but the existing procedures for the corresponding exothermic reactions have proved to be problematic. This paper presents new procedures for the exothermic reactions that are computationally efficient and provide a near exact match with the equilibrium constant of statistical mechanics. The Q-K model does not depend on the availability of continuum rate coefficients. Instead, the simplicity of the new DSMC procedures allows analytical expressions to be written down for the corresponding rate coefficients in an equilibrium gas. These are used to validate the Q-K model for reactions in high temperature air and in hydrogen-oxygen combustion. The development of the Q-K model has been driven by the need for efficient reaction procedures in DSMC applications that often involve the computation of billions of simulated collisions. It is not intended to compete with the modern theories for gas-phase chemical reactions that employ more accurate physical representations of real reactions. At the same time, the degree of validation of the model is such that the analytical expressions for the rate coefficients that correspond to the model should be useful in their own right.