Nonequilibrium reaction rates in the macroscopic chemistry method for direct simulation Monte Carlo calculations

Abstract

The direct simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the macroscopic chemistry method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the MCM in both equilibrium and nonequilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal nonequilibrium are determined from a zero-dimensional Monte Carlo sampling procedure which simulates “intramodal” nonequilibrium; that is, equilibrium distributions in each of the translational, rotational, and vibrational modes but with different temperatures for each mode; (2) the 2D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the nonequilibrium reaction rate is a simple means by which information contained within nonequilibrium distribution functions predicted by the DSMC method can be included in the macroscopic chemistry method.