Simulation of unsteady flows by the DSMC macroscopic chemistry method

In the Direct Simulation Monte Carlo method, a combination of statistical and deterministic procedures applied to a finite number of ‘simulator’ particles are used to model rarefied gas-kinetic processes. Traditionally, chemical reactions are modelled using information from specific colliding particle pairs. In the Macroscopic Chemistry Method (MCM), the reactions are decoupled from the specific particle pairs selected for collisions. Information from all of the particles within a cell is used to determine a reaction rate coefficient for that cell. MCM has previously been applied to steady flow DSMC simulations. Here we show how MCM can be used to model chemical kinetics in DSMC simulations of unsteady flow. Results are compared with a collision-based chemistry procedure for two binary reactions in a 1-D unsteady shock-expansion tube simulation. Close agreement is demonstrated between the two methods for instantaneous, ensemble-averaged profiles of temperature, density and species mole fractions, as well as for the accumulated number of net reactions per cell. The Macroscopic Chemistry Method is applicable to any general DSMC code using any viscosity or non-reacting collision models and any non-reacting energy exchange models. MCM can be used to implement any reaction rate formulations, whether these be from experimental or theoretical studies.