Coupling of state-resolved rovibrational coarse-grain model for nitrogen to stochastic particle method for simulating internal energy excitation and dissociation

We propose to couple a state-resolved rovibrational coarse-grain model to a stochastic particle method for simulating internal energy excitation and dissociation of a molecular gas. A coarse-grained model for a rovibrational reaction mechanism of an ab initio database developed at the NASA Ames Research Center for the N₂-N system is modified based on variably spaced energy bins. The thermodynamic properties of the modified coarse-grained model allow us to closely match those obtained with the full set of rovibrational levels over a wide temperature range, while using a number of bins significantly smaller than the complete mechanism. The chemical-kinetic behavior of equally and variably spaced bin formulations is compared by simulating internal energy excitation and dissociation of nitrogen in an adiabatic, isochoric reactor. We find that the variably spaced formulation is better suited for reproducing the dynamics of the full database at conditions of interest in the Earth atmospheric entry. Also in this paper, we discuss the details of our particle method implementation for the uniform rovibrational collisional bin model and describe changes to the Direct Simulation Monte Carlo (DSMC) collision algorithm, which become necessary to accommodate our state-resolved reaction mechanism for excitation and dissociation reactions. The DSMC code is then verified against equivalent master equation calculations. In these simulations, state-resolved cross sections are used in analytical form. These cross sections verify micro-reversibility relations for the rovibrational bins and allow for fast execution of the DSMC code. In our verification calculations, we obtain very close agreement for the concentrations profiles of N and N₂, as well as the translational and rovibrational mode temperatures obtained independently through both methods. In addition to macroscopic moments, we compare discrete internal energy populations predicted at selected time steps via DSMC and the master equations. We observe good agreement between the two sets of results within the limits imposed by statistical scatter, which is inherent to particle-based DSMC solutions. As future work, the rovibrational coarse-grain model coupled to the particle method will allow us to study 3D reentry flow configurations.