Thermochemical nonequilibrium modeling
in stateresolved high fidelity method
Motivation
Shockwave angle and shape is one of the important factors to design a reentry vehicle and hypersonic aircraft because the shockshape changes the center of aerodynamic force of the hypersonic vehicles. In compressible flow, this shockshape is mostly affected by the specific heat ratio of real gas, and this specific heat ratio is determined from the internal energy population of gas species. Such internal energy populations of gas species are mainly occurred by the energy transitions and chemical reactions due to electron and heavyparticle collision and radiative transitions in the nonequilibrium states. The other important factor in designing a hypersonic vehicle is the heat transfer on the vehicle surface by the aerodynamic heating. Such aerodynamic heating is mostly caused by the nonBoltzmann radiation and the nonequilibrium chemical reactions. The nonequilibrium populations of the internal energies are closed related to these nonBoltzmann radiation and nonequilibrium chemical reactions behind a strong shock wave. Hence, the improvement of thermochemical nonequilibrium modeling in predicting the nonequilibrium population of the internal energies is needed in the accurate aerodynamic analysis of the hypersonic vehicles.
In previous hypersonic researches, the aerothermodynamic analyses were carried out by lowfidelity and empirical thermochemical models based on the experimental data from hypersonic facilities. In 1970’s to 1990’s, Apollo projects and space shuttle program led these hypersonic thermophysics researches, and the outcomes was enough to perform the United States space program. In the recent years, the remaining hypersonic work involves the space explorations, hypersonic commercial vehicles, and unsolved hypersonic problems. However, these remaining hypersonic works are somewhat different to the previous Apollo and space shuttle programs. In the space exploration, we need to analyze the aerodynamic characteristics of highspeed return capsule into Earth and the outer planets. In these reentry cases, the previous thermochemical nonequilibrium model has limitations in estimating the shockdistance and measured nonequilibrium temperatures. In hypersonic commercial vehicles, the accuracy of thermochemical nonequilibrium model must be improved for the safety of passengers. In the last, the unsolved hypersonic problems are mainly related to the uncertainties of the previous thermochemical nonequilibrium models. In resolving such arising and future difficulties, the improvement of thermochemical nonequilibrium models is needed. In carrying out these new projects, the aerospace engineers need to understand the atomic and molecular structures from quantum mechanical view, need to improve the collisional and radiative transition cross sections by quasi and semiclassical and quantum mechanical calculations, and need to derive the highfidelity thermochemical nonequilibrium models from the microscopic calculations.
Research subjects
The research of our group is related to such improvement of thermochemical nonequilibrium models. In carrying out the thermochemical modeling work, we need five steps. 1) abinitio electronic structure calculations, 2) designing a potential energy surface in hyperdimensional space by the results of the abinitio quantum calculation, 3) obtaining the complete sets of the statetostate transition cross sections from trajectory calculations by quasi/semiclassical or quantum mechanical methods, 4) master equation analysis in observing the thermochemical nonequilibrium phenomena, and 5) constructing the hydrodynamic equations and applications in continuum and rarefied flows. In performing each step, there exist a lot of difficulties coming from the complication of the molecular physics and the limitation of computational resources. The target species of present research is H2, He, N2 and O2. H2 and He are the main atmospheric gas of the outer planets and N2 and O2 are the main gas of Earth.

Evaluation of the complete sets of rovibrational statetostate transition cross sections by quasi/semiclassical trajectory calculations
Master equation analysis by the complete set of rovibrational statetostate transition rates
High fidelity thermochemical analysis by statetostate kinetics behind a strong shock wave and in expanding flows using a 1D continuum solver
High fidelity thermochemical nonequilibrium modeling of electron and heavyparticle collisional and radiative transitions behind a strong shock wave using a 1D continuum solver
Total cross section modeling, nonphenomenological energy transitions, and detailed chemical reactions in DSMC
Acknowledgement
Funding from Air Force Office of Scientific Research Grant FA95501110309 and FA95501210483Publications
[1] Kim, J. G. and Boyd, I. D., “Master Equation Study of Hydrogen Relaxation Using Complete Sets of Statetostate Transition Rate,” AIAA 2012362, 50th AIAA Aerospace Sciences Meeting, Nashville, TN, Jan. 910, 2012.
[2] Kim, J. G. and Boyd, I. D., “State Resolved Thermochemical Modeling of Nitrogen Using DSMC,” AIAA 20122991, 43rd AIAA Thermophysics Conference, New Orleans, LA, June 2528, 2012.
[3] Kim, J. G. and Boyd, I. D., “Master Equation Analysis of Thermochemical Nonequilibrium of Nitrogen,” AIAA 20123305, 43rd AIAA Thermophysics Conference, New Orleans, LA, June 2528, 2012.
[4] Kim, J. G. and Boyd, I. D., “Stateresolved Analysis of Thermochemical Nonequilibrium for H2 and N2,” 1st International Symposium on Hypersonic Aerothermodynamics–Recent Advances, Bangalore, India, December 913, 2012. (Invited from India Institute of Science)
[5] Kim, J. G. and Boyd, I. D., “Stateresolved Thermochemical Nonequilibrium Analysis of Hydrogen Mixture Flows,” Physics of Fluids, Vol. 24, No. 8, 2012, pp. 086102.
[6] Kim, J. G. and Boyd, I. D., “Modeling of Rotational Nonequilibrium in PostNormal Shock Flow Analyses,” AIAA 20130191, 51th AIAA Aerospace Sciences Meeting, Grapevine (Dallas/Ft. Worth), TX, Jan. 710, 2013.
[7] Kim, J. G. and Boyd, I. D., “Stateresolved Master Equation Analysis of Thermochemical Nonequilibrium of Nitrogen,” Chemical Physics, In Press, 2013. DOI: http://dx.doi.org/10.1016/j.chemphys.2013.01.027
[8] Kim, J. G. and Boyd, I. D., “State Resolved Thermochemical Modeling of N+N2 in DSMC,” Submitted in Physics of Fluids