Jae Gang Kim

Master Equation Study and Nonequilibrium Chemical Reactions for H + H2 and He + H2

Complete sets of state-to-state cross sections and rate coefficients for the transition of 348 (v,j) rotational and vibrational states ofthe electronic ground state of the hydrogen molecule for H and He collisions were evaluated using quasi-classical trajectory calculations based on the latest potential energy surfaces. The state-to-state cross sections for the rotational and vibrational energy transitions were validated by comparing the results with those of quantum mechanical calculations and other quasi-classical trajectory calculations. The state-to-state rate coefficients were fed into a master equation, and the rotational and vibrational number densities were numerically evaluated. In this master equation study, relaxation of the rotational and vibrational temperatures, number density relaxation, and average rotational and vibrational energy losses due to dissociation were examined in heating and cooling environments. From the results of the state-to-state rate coefficients and the master equation study, dissociation and recombination rate coefficients were calculated under a quasi-steady-state assumption for a temperature range between 1000 and 32,000 K. These rate coefficients were validated by comparing the results with existing experiments. The reaction rates expressed by a two-temperature model based on translational and vibrational temperatures were also proposed upon collision with H and He, respectively.

Monte Carlo simulation of nitrogen dissociation based on state-resolved cross sections

State-resolved analyses of N + N2 are performed using the direct simulation Monte Carlo (DSMC) method. In describing the elastic collisions by a state-resolved method, a state-specific total cross section is proposed. The state-resolved method is constructed from the state-specific total cross section and the rovibrational state-to-state transition cross sections for bound-bound and bound-free transitions taken from a NASA database. This approach makes it possible to analyze the rotational-to-translational, vibrational-to-translational, and rotational-to-vibrational energy transfers and the chemical reactions without relying on macroscopic properties and phenomenological models. In nonequilibrium heat bath calculations, the results of present state-resolved DSMC calculations are validated with those of the master equation calculations and the existing shock-tube experimental data for bound-bound and bound-free transitions. In various equilibrium and nonequilibrium heat bath conditions and 2D cylindrical f...

State-resolved thermochemical nonequilibrium analysis of hydrogen mixture flows

The complete sets of state-to-state transition rate coefficients for both target and projectile molecules of hydrogen are derived from the predicted response surface designed by the ordinary Kriging model. A system of master equations is constructed for bound-bound and bound-free transitions with these designed transition rate coefficients, and the rovibrational number densities are numerically evaluated by implicitly integrating a system of master equations. In these master equation studies, relaxation of rotation and vibration modes, number density relaxation, reaction rate coefficients, and average rotational and vibrational energy losses due to dissociation are each considered in strong nonequilibrium conditions. A system of master equations is coupled with one-dimensional flow equations to analyze the relaxations of hydrogen in post-normal shock and nozzle expanding flows. In post-normal shock flows, at high temperature, the relaxation of the rotational mode is similar to the relaxation of the vibrat...

A High Temperature Elastic Collision Model for DSMC Based on Collision Integrals

A new elastic collision model for use in direct simulation is proposed for the temperature range of 2,000 to 100,000K, where the existing models are inaccurate. For this purpose, collision integrals „ › (l;s) ’s are expressed in terms of the soft-sphere scattering parameter and four total cross-section parameters. These results in an expression that consists of two

State Resolved Thermochemical Modeling of Nitrogen Using DSMC

State-resolved analyses of N+N2 are performed using the direct simulation Monte Carlo (DSMC) method. In describing the elastic collisions in a state-resolved method, a statespecific total cross section is proposed. The state-resolved model is constructed from the state-specific total cross section and the state-to-state transition cross sections for boundbound and bound-free transitions taken from a NASA database. This approach makes it possible to analyze the rotation-to-translation, vibration-to-translation, and rotation-tovibration energy transfer and the chemical reactions without relying on a phenomenological model. In nonequilibrium heat bath and 2-D cylindrical flow, the DSMC calculations by the state-resolved model are compared with those obtained with previous DSMC models and master equation calculations. In these previous DSMC models, the VSS, phenomenological LB, QK, and TCE models are considered. From these studies, it is concluded that the present state-resolved model more accurately describes the rotational and vibrational relaxation and chemical processes than the other previous DSMC models.

Master Equation Analysis of Post Normal Shock Waves of Nitrogen

One-dimensional post normal shock flow calculations are carried out using state-of-the-art thermochemical nonequilibrium models. Two-temperature, four-temperature, and electronic master equation coupling models are adopted in the present work. In the four-temperature model, the rotational nonequilibrium is described by Parker and modified Park models. In the electronic master equation coupling model, recently evaluated electron and heavy-particle impacts and radiative transition cross-sections are employed in constructing the system of electronic master equations. In analyzing the shock-tube experiments, the results calculated by the state-of-the-art thermochemical nonequilibrium models are compared with existing shock-tube experimental data. The four-temperature and electronic master equation coupling models with rotational nonequilibrium described by the modified Park model approximately reproduce the measured rotational, vibrational, and electronic temperatures.

Thermochemical nonequilibrium modeling of electronically excited molecular oxygen

The thermochemical nonequilibrium of the three lowest lying electronic states of molecular oxygen, O2(X Σg , a ∆g, b Σg ), through interactions with argon is studied in the present work. The multi-body potential energy surfaces of O2+Ar are evaluated from the semiclassical RKR potential of O2 in each electronic state. The rovibrational states and energies of each electronic state are calculated by the quantum mechanical method based on the present inter-nuclear potential of O2. Then, the complete sets of the rovibrational stateto-state transition rates of O2+Ar are calculated by the quasi-classical trajectory method including the quasi-bound states. The system of master equations constructed by the present state-to-state transition rates are solved to analyze the thermochemical nonequilibrium of O2+Ar in various heat bath conditions. From these studies, it is concluded that the vibrational relaxation and coupled chemical reactions of each electronic state needs to be treated as a separate nonequilibrium process, and rotational nonequilibrium needs to be considered at translational temperatures above 10,000 K.

Master Equation Study of Hydrogen Relaxation Using Complete Sets of State-to-state Transition Rates

The complete sets of state-to-state transition rate coefficients for both target and projectile molecules are derived from the predicted response surface designed by the ordinary Kriging model. A system of master equations is constructed for bound-bound and bound-free transitions with these designed transition rate coefficients, and the rovibrational number densities are numerically evaluated by implicitly integrating a system of master equations. In these master equation studies, relaxation of rotation and vibration modes, number density relaxation, reaction rate coefficients, and average rotational and vibrational energy losses due to dissociation are each considered in strong nonequilibrium conditions. A system of master equations are coupled with one-dimensional flow equations to analyze the relaxations of H 2 in post-normal shock and nozzle expanding flows. In post-normal shock flows, the relaxation of the rotational mode is slightly faster or almost similar to the relaxation of the vibrational mode. In nozzle expanding flows, the relaxations of both rotational and vibrational modes seem to be frozen. Nomenclature A area, cm 2 c dissociation of molecule i D dissociation energy of rovibrational state i, erg i e rovibrational energy of state i, erg r e , v e averaged rotational and vibrational energies, respectively, erg ( ) r e i , ( ) v e i rotational and vibrational energies of rovibrational state i, respectively, erg � r e , � v e averaged rotational and vibrational energy losses, respectively, erg tr E relative translational energy, erg h enthalpy, erg/g f h formation energy, erg/mol ij m g l , ij g l , ijm g , ij g parameter to prohibit the multiple count e g statistical multiplicity of electronic state s g nuclear spin degeneracy

Master Equation Analysis of Thermochemical Nonequilibrium of Nitrogen

Using a NASA database of state-to-state transition rates for N+N2, master equation studies are performed for various nonequilibrium heat bath conditions. In these master equation studies, relaxation of the rotational and vibrational modes, time variation of chemical composition, reaction rate coefficients, and average rotational and vibrational energy losses due to dissociation are each considered in strong and weak nonequilibrium conditions. A system of master equations is coupled with one-dimensional flow equations to analyze the relaxation of N2 in post-normal shock flows. From the results of master equations and the post-normal shock calculations, it is recommended that the rotational nonequilibrium of N2 should be treated as a nonequilibrium mode in hypersonic re-entry calculations.

Nonequilibrium modeling of oxygen in reflected shock tube flows

The nonequilibrium modeling of reflected shock tube flows is investigated, motivated by hypersonic vehicle design. Oxygen nonequilibrium behavior is the focus of the work due to its contribution to modeling uncertainty, specifically the vibrational-translational energy transfer process of the O2-Ar system. Two levels of vibrational nonequilibrium modeling fidelity are evaluated. The lower fidelity model is the two-temperature model that uses Millikan-White vibration relaxation rates to capture the vibrational nonequilibrium process at the macroscopic level. The higher fidelity model is the state-resolved master equation method that uses vibrational state-to-state rates to explicitly calculate the vibrational state distribution throughout the analysis. The vibrational state-to-state rates are evaluated using the forced harmonic oscillator (FHO) model and a detailed quasi-classical trajectory (QCT) analysis. The nonequilibrium models are implemented in two flow solvers to analyze reflected shock tube experiments. First, a simple method is employed of chaining two post-normal shock analyses together to simulate the vibrational nonequilibrium behavior of a particular parcel of fluid in the reflected shock tube. Second, the nonequilibrium models are implemented in a 1-D unsteady flow solver to capture the entire behavior of the reflected shock tube. Comparisons are provided between results obtained with the two different flow solvers, and the three different physical models, for two different shock tube conditions.