A reduced order maximum entropy model for chemical and thermal non-equilibrium in high temperature co₂ gas

This paper presents a physics-based macroscopic model for thermal and chemical non-equilibriumin CO₂-Msystem. The starting point is the state-to-state model for vibrational excitation in CO₂ developed using modified SSH theory. A reduced order representation is formulated by dividing the vibrational states of CO₂ into macroscopic bins. The state population is reconstructed from macroscopic variables using bin-wise distribution func-tions based on the maximum entropy principle. A reduced system of governing equations is derived by taking successive moments of the fundamental microscopic equations without any ad-hoc simplifications. The impact of limited transition pathways that allow direct interactions only between specific states, is taken into account to improve the applicability of the coarse grained reduced model approach. Numerical results are obtained for CO₂ recombination and vibrational relaxation in an zero-dimensional homogeneous isothermal chemical reactor. The validity of the reduced order model is established by comparing solutions of the maximum entropy linear model with the exact numerical solutions of the microscopic master equations. A good prediction for the time evolution of both macro-scopic quantities and the microscopic state population distribution is obtained using the reduced order formulation.