Advanced models for vibrational–chemical coupling in multi-temperature flows

Consistent kinetic-continuum dissociation model. II. Continuum formulation and verification

In this article, we implement a recently developed non-equilibrium chemical kinetics model [N. Singh and T. Schwartzentruber, J. Chem. Phys. 152, 224302 (2020)] based on ab initio simulation data and perform verification studies. Direct molecular simulation data are used to verify the predictive capabilities of the model. Using the model, dominant physics, such as the need for a rotational energy equation, and the quantitative role of non-Boltzmann effects are identified. Based on the analysis and reasonable assumptions, a simplified model for implementation into large-scale computational fluid dynamic simulations is proposed. Without incurring additional computational cost, the model can be used in existing flow solvers to analyze hypersonic flows.

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.

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is developed for compressible thermal reactive flows. A unified Boltzmann equation set is solved for hydrodynamic and thermodynamic quantities as well as higher order kinetic moments. The collision, reaction, and force terms are uniformly calculated with a matrix inversion method, which is physically accurate, numerically efficient, and convenient for coding. Via the Chapman-Enskog analysis, the DBM is demonstrated to recover reactive Navier-Stokes (NS) equations in the hydrodynamic limit. Both specific heat ratio and Prandtl number are adjustable. Moreover, it provides quantification of hydrodynamic and thermodynamic nonequilibrium effects beyond the NS equations. The capability of the DBM is demonstrated through simulations of chemical reactions in the free falling process, sound wave, thermal Couette flow, and steady and unsteady detonation cases. Moreover, nonequilibrium effects on the predicted physical quantities in unsteady combustion are quantified via the DBM. It is demonstrated that nonequilibrium effects suppress detonation instability and dissipate small oscillations of fluid flows.

Calculation of Vibrational Relaxation Times Using a Kinetic Theory Approach

In the present work, a method for computation of vibrational relaxation times based on a kinetic theory definition is utilized to calculate vibrational relaxation times of molecules present in air (N₂, O₂, and NO) in collisions with air species particles. An overview of available experiment VT relaxation time measurements, as well as quasi-classical trajectory (QCT) calculation results, and various empirical models, is given. Different inelastic cross-section models are used for the computation of the relaxation times, and their parameters are adjusted to fit the available experimental data and QCT results. It is shown that the proposed method of calculation can give a quantitative and qualitative agreement with the available data in a wide range of temperatures; the obtained interaction parameters may be used not only for vibrational relaxation time calculation within a multitemperature framework but also for development of state-specific models for use in CFD and DSMC codes.

Mutual effect of vibrational relaxation and chemical reactions in viscous multitemperature flows

We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of N(2) and N, and O(2) and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.