Vibrational degrees of freedom in the Total Collision Energy DSMC chemistry model

The Total Collision Energy (TCE) model is used to simulate chemical reactions in the Direct Simulation Monte Carlo method. Colliding particle pairs with total collision energy (translational plus internal energy) greater than an activation energy are accepted for reaction with a probability which depends on the amount of the collision energy in excess of the activation energy. Constants in the probability function are adjusted to match experimentally determined rates in an Arrhenius form under thermal equilibrium conditions. The model thus attempts to extrapolate equilibrium reaction rates to non-equilibrium conditions by using microscopic based information from colliding particle pairs. However, the number of active ‘degrees of freedom’ (DOF) in the vibrational energy mode contributing to the total collision energy must be specified for each collision pair; various methods have been proposed for this. It is shown that the different calculation methods can alter the equilibrium reaction rate returned by the TCE model, and can have significant effects throughout non-equilibrium flowfields. If we assume, as is usual, that all of the internal energy is available for the reaction, we consider that the most consistent and physically intuitive approach is to determine the number of active DOF from the local macroscopic temperatures in the cell.