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Direct Molecular Simulation of Nitrogen and Oxygen at Hypersonic Conditions

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Direct Molecular Simulation of Nitrogen and Oxygen at Hypersonic Conditions Direct Molecular Simulation of Nitrogen and Oxygen at Hypersonic Conditions A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Maninder S. Grover IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Thomas E. Schwartzentruber, Adviser February, 2018 © Maninder S. Grover 2018 ALL RIGHTS RESERVED Acknowledgements A number of people have earned my gratitude for their support, guidance and patience during the course of my graduate career. Firstly, I would like to thank my adviser, Prof. Tom Schwartzentruber for his sup- port, and mentorship, and for affording many opportunities of personal and professional growth throughout my graduate career. Tom has been a great teacher and a source of inspiration for the past four and half years. His enthusiasm and passion for research constantly provided motivation to work hard. I will not forget the overall kindness and support he has shown over the years. Tom will definitely be a role model for me for years to come. I am grateful for the guidance of Dr. Rich Jaffe of NASA's Ames Research Center, for many valuable discussion and teaching moments that he shared during our collaboration. Working with Rich has been one of the highlights of my time as a graduate student and I am honored and humbled to have had this opportunity. I would like to thank Dr. David Hash for his mentorship, support and encouragement through the years. I would also like to thank Dr. David Schwenke, Dr. Michael Barnhardt, and Dr. Brett Cruden at NASA Ames Research Center for enabling the collaboration between the University of Minnesota and NASA, and for valuable inputs during my time as an intern at Ames Research Center. I would like to thank my collaborators at the University of Illinois at Urbana Cham- paign: Prof. Marco Panesi, Robyn Macdonald, and Simone Venturi. Working with them has certainly been an immense learning experience. I am thankful to my collab- orators in the Chemistry Department at the University of Minnesota : Prof. Donald i Truhlar, Dr. Zoltan Varga, and Dr. Yulia Paukku for providing the potential energy surfaces that most of my work is based on and for always being there to clarify any queries and questions that I had regarding the chemistry aspect of this project. I would like to thank Prof. Graham Candler, Prof. Joseph Nichols, and Prof. Steven Girshick for being a part of my committee and the thesis reviewing process. A special thanks to my colleagues Paolo, Savio, Ross, and Narendra for spirited and valuable discussions that we have had over the years and for all the feed-back they have given about my work. I am grateful to my parents and my sister for always cheering me on and supporting me throughout this endeavor. I am grateful to my friends, here in Minnesota for making me feel at home even when I was half a planet away. Finally, I would like to express my gratitude to the Air Force Office of Scientific Research (AFOSR) and the Doctoral Dissertation Fellowship (DDF) for supporting my graduate research. ii \ Far and away the best prize that life has to offer is the chance to work hard at work worth doing. " - Theodore Roosevelt iii Abstract The objective of this thesis is to characterize the gas-phase thermochemical non-equilibrium that occurs during hypersonic flight for nitrogen and oxygen gases. This thesis uses the direct molecular simulation (DMS) method in conjunction with potential energy surfaces (PESs) to provide an in-depth molecular level analysis of inter- nal energy excitation and dissociation of molecular nitrogen due to N2 +N2 and N2 +N interactions. Characteristic vibrational excitation times and non-equilibrium dissocia- tion rate coefficients are calculated using the ab−initio PESs developed at NASA Ames Research Center. Comparison of these rate coefficients and non-equilibrium vibrational energy distributions is carried out against prior work done with nitrogen using an inde- pendently developed ab − initio PES at the University of Minnesota. Good agreement was found between properties predicted by the two PESs. Furthermore, comparative studies were carried out for the nitrogen system between the DMS method and the state-to-state method. The results obtained by the two different methods, are found to be in good agreement. The DMS method is used to calculate benchmark data for vibrational energy exci- tation and non-equilibrium dissociation due to O2 + O interactions. O2 + O interactions are modeled using nine PESs corresponding to. 11A0, 21A0, 11A00, 13A0, 23A0, 13A00 15A0, 25A0 and 15A00 states, which govern electronically adiabatic (ground-electronic- state) collisions of diatomic oxygen with atomic oxygen. This is the first data set in the aerospace community that incorporates all nine PESs for the O2 + O system and fully describes the dynamics of ground state interactions of diatomic oxygen with atomic oxy- gen. Characteristic vibrational excitation times are calculated over a temperature range iv of T = 3000K to T = 15000K. It is observed that the characteristic vibrational exci- tation time for O2 + O interactions is weakly dependent on temperature and increases slightly with increasing temperature. Vibrational excitation is slowest for interactions in the quintet spin state, with the 15A00 state having the slowest excitation rate, and vibrational excitation is fastest on the 11A0 potential energy surface. Non-equilibrium dissociation rate coefficients are calculated over a temperature range of T = 6000K to T = 15000K during quasi-steady state (QSS) dissociation, and the results agree well with experimental data. For the O2 + O2 system interactions can occur over singlet, quintet and triplet spin states. An in-depth analysis of excitation and dissociation on the quintet and singlet surfaces is provided and bench-mark data for excitation using all three PESs for O2 + O2 interactions is presented for a temperature range of T = 5000K to T = 12000K . Finally, this thesis explores internal energy exchange processes in oxygen and nitro- gen. Probability distribution functions for vibrational energy change during collisions are presented (due to N2 + N2 non-reactive collisions, N2 + N2 exchange reactions, N2 + N non-reactive collisions, N2 + N exchange reactions, O2 + O non-reactive col- lisions, and O2 + O exchange reactions). It is shown that non-reactive collisions are less efficient in vibrational energy redistribution when compared to exchange reactions. Furthermore, it is observed that the probability distribution functions for vibrational energy change (for both oxygen and nitrogen) are self-similar and may be modeled by simplified functional forms. v Contents Acknowledgementsi Dedication iii Abstract iv List of Tables ix List of Figuresx 1 Introduction1 1.1 Challenges of Hypersonic Flight.......................1 1.2 Contemporary work.............................4 1.3 Introduction to Direct Molecular Simulation................5 1.4 Outline....................................6 2 Potential Energy Surfaces8 2.1 Introduction..................................8 2.2 Spin multiplicity and spatial symmetry................... 12 2.3 Potential energy surfaces for nitrogen.................... 15 2.3.1 Ab-initio potential energy surfaces................. 16 2.3.2 Site-to-site potential energy surface................. 20 2.4 Potential energy surfaces for oxygen.................... 22 2.4.1 Potential energy surfaces for O3 interactions............ 22 vi 2.4.2 Potential energy surfaces for O4 interactions............ 26 3 Physical Model and Numerical Method 28 3.1 Introduction.................................. 28 3.2 Direct molecular simulation......................... 30 3.2.1 Numerical method.......................... 30 3.2.2 Trajectory calculations and parallel implementation....... 33 3.2.3 Validation with molecular dynamics................ 40 3.3 Code implementation............................. 43 3.3.1 Normal shock waves......................... 43 3.3.2 Multidimensional flows........................ 45 3.3.3 Chemically reacting isothermal systems.............. 46 4 Rovibrational Coupling in Normal Shocks 52 4.1 Introduction.................................. 52 4.2 Rovibrational coupling in normal shock waves............... 53 5 Direct Molecular Simulation of Nitrogen 57 5.1 Introduction.................................. 57 5.2 Effect of PES on the N2 + N2 system.................... 58 5.2.1 Vibrational energy excitation.................... 58 5.2.2 Nonequilibrium dissociation..................... 59 5.3 Effect of numerical method on the N2 + N2 system............ 64 5.3.1 Internal energy excitation...................... 66 5.3.2 Nonequilibrium dissociation..................... 68 5.4 Effect of PES on the N2 + N system.................... 71 5.4.1 Vibrational energy excitation.................... 71 5.4.2 Non-equilibrium dissociation.................... 76 5.5 Effect of numerical method on the N2 + N system............ 80 5.5.1 Internal energy excitation...................... 81 5.5.2 Nonequilibrium dissociation..................... 83 vii 5.6 Comparison of N4 system to N3 + N4 system............... 85 5.7 Comparison of ab − initio results for the full nitrogen system...... 87 5.8 Conclusions.................................. 88 6 Direct Molecular Simulation of Oxygen 92 6.1 Direct molecular simulation of O2 + O interactions............ 92 6.1.1 Introduction............................. 92 6.1.2 Simulation of O2 + O interactions................. 93 6.1.3 Vibrational energy excitation by O2 + O interactions....... 97
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