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Yang J, Li J, Li J, Li J. Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O 2 Collision Dissociation Reactions. J Phys Chem A 2024; 128:4966-4975. [PMID: 38869143 DOI: 10.1021/acs.jpca.4c01445] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2024]
Abstract
Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.
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Affiliation(s)
- Jiawei Yang
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Chemical Theory and Mechanism, Chongqing University, Chongqing 401331, China
| | - Jia Li
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Chemical Theory and Mechanism, Chongqing University, Chongqing 401331, China
| | - Junhong Li
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Chemical Theory and Mechanism, Chongqing University, Chongqing 401331, China
| | - Jun Li
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Chemical Theory and Mechanism, Chongqing University, Chongqing 401331, China
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Macdonald RL. State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules. J Chem Phys 2024; 160:134307. [PMID: 38568944 DOI: 10.1063/5.0195238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2023] [Accepted: 02/26/2024] [Indexed: 04/05/2024] Open
Abstract
Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by ab initio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.
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Affiliation(s)
- Robyn L Macdonald
- Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado 80303, USA
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Zhang T, Lu Y, Cheng X. State-Specific Dynamic Study of the Exchange and Dissociation Reaction for O(3P) and O2($${}^{3}\Sigma _{g}^{ - }$$) Collision by Quasi-Classical Trajectory. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2022. [DOI: 10.1134/s0036024422040331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Kondur C, Stephani KA. Rate constants and molecular recombination pathways of oxygen from quasi-classical trajectory simulations of the O3 system. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2021.111357] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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Pan TJ, Stephani KA. Rovibrationally state-specific collision model for the O 2(Σg-3) + O(P3) system in DSMC. J Chem Phys 2021; 154:104306. [PMID: 33722033 DOI: 10.1063/5.0027411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A rovibrationally state-specific collision model for the O2(Σg-3)+O(P3) system is presented for direct simulation Monte Carlo, including rotation-vibration-translation energy transfer, exchange, dissociation, and recombination processes. The two-step binary collision approach is employed to model recombination reactions. Two available cross section databases by Andrienko/Boyd and Esposito/Capitelli are employed for the rovibrationally resolved model (rv-STS) and vibrationally resolved model (v-STS), respectively. The difference between rv-STS and v-STS comes from two contributions: the multisurface factor of dissociation (fMS) and the rotational averaging process. The dissociation cross section with the constant fMS is typically larger than with the variable fMS, especially for the low vibrational energy states. On the other hand, the cross sections resulting from the rotationally averaged database are found to underpredict the dissociation rate coefficient at low temperatures. In the rovibrational heating case, the rv-STS predicts faster relaxation than the v-STS, which also shows a lower quasi-steady-state temperature than v-STS. In the rovibrational cooling case, the rv-STS shows a faster relaxation than v-STS, which also presents a thermal non-equilibrium between rovibrational and translational mode during the cooling process.
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Affiliation(s)
- Tzu-Jung Pan
- Center for Hypersonics and Entry Systems Studies, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kelly A Stephani
- Center for Hypersonics and Entry Systems Studies, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Hong Q, Sun Q, Pirani F, Valentín-Rodríguez MA, Hernández-Lamoneda R, Coletti C, Hernández MI, Bartolomei M. Energy exchange rate coefficients from vibrational inelastic O 2(Σg-3) + O 2(Σg-3) collisions on a new spin-averaged potential energy surface. J Chem Phys 2021; 154:064304. [PMID: 33588556 DOI: 10.1063/5.0041244] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new spin-averaged potential energy surface (PES) for non-reactive O2(Σg-3) + O2(Σg-3) collisions is presented. The potential is formulated analytically according to the nature of the principal interaction components, with the main van der Waals contribution described through the improved Lennard-Jones model. All the parameters involved in the formulation, having a physical meaning, have been modulated in restricted variation ranges, exploiting a combined analysis of experimental and ab initio reference data. The new PES is shown to be able to reproduce a wealth of different physical properties, ranging from the second virial coefficients to transport properties (shear viscosity and thermal conductivity) and rate coefficients for inelastic scattering collisions. Rate coefficients for the vibrational inelastic processes of O2, including both vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy exchanges, were then calculated on this PES using a mixed quantum-classical method. The effective formulation of the potential and its combination with an efficient, yet accurate, nuclear dynamics treatment allowed for the determination of a large database of V-V and V-T/R energy transfer rate coefficients in a wide temperature range.
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Affiliation(s)
- Qizhen Hong
- State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, 100190 Beijing, China
| | - Quanhua Sun
- State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, 100190 Beijing, China
| | - Fernando Pirani
- Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, via Elce di Sotto, 8 - 06183 Perugia, Italy
| | - Mónica A Valentín-Rodríguez
- Centro de Investigaciones Químicas-IICBA, Universidad Autónoma del Estado de Morelos, Cuernavaca 62210, Morelos, Mexico
| | - Ramón Hernández-Lamoneda
- Centro de Investigaciones Químicas-IICBA, Universidad Autónoma del Estado de Morelos, Cuernavaca 62210, Morelos, Mexico
| | - Cecilia Coletti
- Dipartimento di Farmacia, Università G. d'Annunzio Chieti-Pescara, via dei Vestini, 66100 Chieti, Italy
| | - Marta I Hernández
- Instituto de Física Fundamental - CSIC, C/Serrano 123, Madrid, Spain
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Venturi S, Sharma MP, Lopez B, Panesi M. Data-Inspired and Physics-Driven Model Reduction for Dissociation: Application to the O 2 + O System. J Phys Chem A 2020; 124:8359-8372. [PMID: 32886505 DOI: 10.1021/acs.jpca.0c04516] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
This work presents an in-depth discussion on the nonequilibrium dissociation of O2 molecules colliding with O atoms, combining quasi-classical trajectory calculations, master equation, and dimensionality reduction. A rovibrationally resolved database for all of the elementary collisional processes is constructed by including all nine adiabatic electronic states of O3 in the QCT calculations. A detailed analysis of the ab initio data set reveals that for a rovibrational level, the probability of dissociating is mostly dictated by its deficit in internal energy compared to the centrifugal barrier. Because of the assumption of rotational equilibrium, the conventional vibrational-specific calculations fail to characterize such a dependence. Based on this observation, a new physics-based grouping strategy for application to coarse-grained models is proposed. By relying on a hybrid technique made of rovibrationally resolved excitation coupled to coarse-grained dissociation, the new approach is compared to the vibrational-specific model and the direct solution of the rovibrational state-to-state master equation. Simulations are performed in a zero-dimensional isothermal and isochoric chemical reactor for a wide range of temperatures (1500-20,000 K). The study shows that the main contribution to the model inadequacy of vibrational-specific approaches originates from the incapability of characterizing dissociation, rather than the energy transfers. Even when constructed with only twenty groups, the new reduced-order model outperforms the vibrational-specific one in predicting all of the QoIs related to dissociation kinetics. At the highest temperature, the accuracy in the mole fraction is improved by 2000%.
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Affiliation(s)
- S Venturi
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - M P Sharma
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - B Lopez
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - M Panesi
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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