Thermochemical nonequilibrium widely exists in supersonic combustion, cold plasma and hypersonic flight. The effect can influence heat transfer, surface ablation and aerodynamic loads. One distinct feature of it is the coupling between internal energy excitation and chemical reactions, particularly the vibration-dissociation coupling. The widely used models are empirical and calibrated based on limited experimental data. Advances in theories and computational power have made the first-principle calculation of thermal nonequilibrium reaction rates by methods like quasi-classical trajectory (QCT) almost a routine today. However, the approach is limited by the uncertainties and availability of potential energy surfaces. To the best of our knowledge, there is no study of thermal nonequilibrium transport properties with this approach. Most importantly, non-trivial effort is required to process the QCT data and implement it in flow simulation methods. In this context, the first part of this work establishes the approach to compute transport properties by the QCT method and studies the influence of thermal nonequilibrium on transport properties for N₂-O molecules. The preponderance of the work is the second part, a comprehensive study of the development of a new thermal nonequilibrium reaction model based on reasonable assumptions and approximations. The new model is as convenient as empirical models. By validating against recent QCT data and experimental results, we found the new model can predict nonequilibrium characteristics of dissociation reactions with nearly the same accuracy as QCT calculations do. In general, the results show the potential of the new model to be used as the standard dissociation model for the simulation of thermochemical nonequilibrium flows.

The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.