On different contributions to the heat flux and diffusion in non-equilibrium flows

Two-temperature thermochemical nonequilibrium model based on the coarse-grained treatment of molecular vibrational states

Although the high-fidelity state-to-state (StS) model accurately describes high-temperature thermochemical nonequilibrium flows, its practical application is hindered by the prohibitively high computational cost. In this paper, we develop a reduced-order model that leverages the widely used two-temperature (2T) framework and a coarse-grained treatment of molecular vibrational states to achieve accuracy comparable to the StS model while ensuring computational efficiency. We observe that the multigroup coarse-grained model (CGM), lumping vibrational energy levels into several groups, yields results close to the StS model for the high-temperature postshock oxygen flows, even using only two groups. However, the one-group CGM (CGM-1G), equivalent to the 2T model but using the StS kinetics, fails to approximate the StS results. Analysis of microscopic group properties reveals that the failure of the CGM-1G stems from the inability to capture the non-Boltzmann effects of mid-to-high vibrational levels, overestimating apparent dissociation rates and vibrational energy loss in the dissociation-dominated region. We then propose an analytical distribution function of vibrational groups by incorporating Treanor-like terms and an additional linear term (addressing the dissociation depletion of high-lying levels). Building upon this algebraic group distribution function and reconstructing vibrational levels within each group using the vibrational temperature, we develop a new 2T model called CG2T, which demonstrates accuracy much closer (than the CGM-1G) to the StS results for the postshock oxygen flows with varying degrees of thermochemical nonequilibrium. Moreover, a fullyconnected neural network is pretrained to substitute the module for the mass and vibrational energy source terms to enhance computational efficiency, achieving about 30-fold speedup in the CG2T model without sacrificing accuracy.

State-Resolved Dissociation and Exchange Reactions in CO2 Flows

State-resolved chemical reactions in CO₂ are studied by taking into account excitation of all vibrational modes and preferential reaction mechanisms. The effect of several parameters on the reaction rate coefficients is discussed; it is shown that the nonequilibrium factor in the expression for the rate coefficients of exchange reactions is much less sensitive to the number of accounted vibrational states and model parameters than that of dissociation. On the other hand, the choice of thermal equilibrium Arrhenius law parameters is crucial for the correct prediction of rate coefficients for both reactions. Developed models are implemented to the one-dimensional boundary layer code for coupled state-to-state simulations of nonequilibrium CO₂ flows under Mars entry conditions. Vibrational distributions, mixture composition, flow variables, and heat flux are studied for several kinetic schemes and different models of chemical reactions. Whereas including the exchange reactions weakly affects the flow, switching between the Park and McKenzie sets of parameters results in significant modification of the kinetic mechanisms; for the McKenzie model, recombination near the wall is a dominating reaction, whereas for the Park model, chemical reactions are frozen. Different contributions to the heat flux are evaluated and a satisfactory agreement with experiments is shown.

Effect of Asymmetric Mode on CO2 State-to-State Vibrational-Chemical Kinetics

Coupled state-to-state vibrational-chemical kinetics, gas dynamics, and heat transfer in the five-component mixture of dissociated CO₂ are studied using the complete three-mode kinetic model and the reduced scheme involving mainly the vibrational states of the asymmetric mode. The emphasis is on the effect of asymmetric vibrations on the rate of dissociation, fluid dynamic variables, and heat flux. It is shown that intermode vibrational energy transitions between CO and CO₂ asymmetric mode may considerably decrease the rate of dissociation; the presence of CO in the mixture quickly depletes high vibrational states and thus inhibits dissociation at low temperatures. The reduced model overpredicts populations of highly located states of the asymmetric mode, especially when intermode VV transitions are neglected; therefore, using the simplified model in flows with dominating dissociation may yield overestimated dissociation rate. In the hypersonic flow along the stagnation line, the influence of asymmetric vibrations on the fluid dynamics and heat transfer is weak; the main role belongs to chemical reactions and VT transitions in the bending mode. In this case, the computationally efficient simplified model can be used to predict macroscopic variables and heat flux without significant loss of accuracy.

Quantum and quasi-classical collisional dynamics of O2-Ar at high temperatures

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.