A Reduced Order Maximum Entropy Model for Chemical and Thermal Non-equilibrium in High Temperature CO₂Gas

Abstract

This paper presents a physics-based macroscopic model for thermal and chemical nonequilibrium in CO2 -M system. 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 functions 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 macroscopic quantities and the microscopic state population distribution is obtained using the reduced order formulation.

Kinetic study of low-temperature CO2plasmas under non-equilibrium conditions. I. Relaxation of vibrational energy

“…This leads to a total of ∼9000 different CO 2 vibrational states, and very high computational costs when considering all the possible vibrational energy transfers. Other research work has been devoted to reducing the complexity of CO 2 kinetics through the: (i) development of lumped-levels models [20]; (ii) formulation of bin-wise distribution functions [21]; and (iii) assumption of a continuum of vibrational levels [6,22]. Despite the high relevance of all of these studies, the disparity of formulations raises the question concerning the advantages and disadvantages of each approach.…”

Assessment of Machine Learning Methods for State-to-State Approach in Nonequilibrium Flow Simulations

“…The price for such high level of detail description is the computational cost, which is often prohibitive. This led several researchers to investigate various energy binning approaches, in the framework of traditional CFD (Computational Fluid Dynamics) and DSMC (Direct Simulation Monte Carlo) methods [5][6][7][8][9][10][11], as well as MPI-CUDA approaches [12].…”

Assessment of machine learning methods for state-to-state approaches

“…For strongly nonequilibrium flows, the STS description, provides the most accurate results and the best agreement with experimental data [1,2,3,4], nevertheless in many cases it is prohibitively computationally expensive. This led several researchers to investigate various energy binning approaches, both for CFD (Computational Fluid Dynamics) and DSMC (Direct Simulation Monte Carlo) simulation methods [5,6,7,8,9,10,11], as well as MPI-CUDA approaches [12].…”