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Image of Journal of Applied Nonlinear Dynamics
ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Direct Simulation Monte Carlo Procedure for Molecular Collision Energy Transfer in Quantum Nature

Journal of Environmental Accounting and Management 11(3) (2023) 285--296 | DOI:10.5890/JEAM.2023.09.003

Jie Liang$^{1,2}$, Zhihui Li$^{3,4}$, Ming Fang$^{1,2}$, Xiaowei Tang$^{1,2}$

$^1$ Hypervelocity Aerodynamics Institute, CARDC, Mianyang, SiChuan, 621000, China

$^2$ Laboratory of Aerodynamics in Multiple Flow Regimes, CARDC, Mianyang, SiChuan, 621000, China

$^3$ National Lab. for Computational Fluid Dynamics, CARDC, Beijing 100191, China

$^4$ Beijing Aerohydrodynamic Research Center, Beijing 100011, China

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Abstract

In order to precisely simulate the thermodynamic nonequilibrium feature in hypervelocity streaming and plume expansion flows, the discrete energy transfer procedure considering quantum effect in direct simulation Monte Carlo method is presented. The formulas of rotational energy for non-rigid rotator model and vibrational energy for anharmonic oscillator model on diatomic molecules are given. The calculation of quantum energy levels at equilibrium distribution is described. The energy transfer models of rotation-translation and vibration-translation as well as their implementation are derived. Two dimensional hypersonic flow around a cylinder of Nitrogen with different flight speeds is computed and analyzed. The comparison of the thermodynamic nonequilibrium process between continuous and discrete energy modes indicate the necessity of energy transfer model considering quantum effect for precise simulation of the thermodynamic nonequilibrium feature in high temperature flow field. The simulation of vacuum plume expansion also demonstrates the significant quantum effect of rotation mode.

Acknowledgments

This work is supported by the projects of the manned space engineering technology (ZS2020103001), the National key basic research project (2022-JCJQ-ZD-206-00), the National Basic Research Program of China (``973'' Program) (Grant No.2014CB744102), and~the National Science Foundation for Distinguished Young Scholars of~China under Grants No. (11325212, 91530319). The authors are particularly thankful to the reviewers and editor for their valuable comments and suggestions, which greatly improved the quality of the manuscript.

References

  1. [1]  Freno, B.A., Carnes, B.R., and Gregory Weirs, V. (2021), Code-verification techniques for hypersonic reacting flows in thermochemical nonequilibrium, Journal of Computational Physics, 425, 109752.
  2. [2]  Schouler, M., Pr'evereaud, Y., and Mieussens, L. (2020), Survey of flight and numerical data of hypersonic rarefied flows encountered in earth orbit and atmospheric reentry, Progress in Aerospace Sciences, 118, 100638.
  3. [3]  Kim, J.G., Kang, S.H., and Park, S.H. (2019), Thermochemical nonequilibrium modeling of oxygen in hypersonic air flows, International Journal of Heat and Mass Transfer, 148, 119059.
  4. [4]  Li, Z.H., Peng, A.P., Zhang, H.X., and Yang, J.Y. (2015), Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations, Progress in Aero-space Sciences, 74, 81-113.
  5. [5]  Votta, R., Schettino, A., and Bonfiglioli, A. (2013), Hypersonic high altitude aerothermodynamics of a space re-entry vehicle, Aerospace Science and Technology, 25, 253-265.
  6. [6]  Surzhikov, S.T. (2012), Radiative-Collisional Models in Non-Equilibrium Aerothermodynamics of Entry Probes, Journal of Heat Transfer, 134, 031002.
  7. [7]  Jo, S.M., Kwon, O.J., and Kim, J.G. (2019), Electronic-state-resolved analysis of high-enthalpy air plasma flows, Physical Review E, 100, 033203.
  8. [8]  Tsai, C.Y., Chue, R., Nicholson, C., and Tyll, J. (2009), Hypervelocity capability of hypulse shock tunnel for radiative heat transfer measurements at lunar reentries, AIAA, 2009-1516.
  9. [9]  Titarev, V., Dumbser, M., and Utyuzhnikov, S. (2014), Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions, Journal of Computational Physics, 256, 17-33.
  10. [10]  Wang, P., Wu, L., Ho, M.T., Li, J., Li, Z.H., and Zhang Y.H., (2020), The kinetic Shakhov-Enskog model for non-equilibrium flow of dense gases, Journal of Fluid Mechanics, 883(A48), 1-22.
  11. [11]  Mieussens, L. (2000), Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equation in Plane and Axisymmetric Geometries, Journal of Computational Physics, 162(2), 429-466.
  12. [12]  Yang, L.M., Shu, C., Wu, J., and Wang, Y. (2016), Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes, Journal of Computational Physics, 306, 291-310.
  13. [13]  Li, Z.H. and Zhang, H.X. (2004), Study on gas kinetic unified algorithm for flows from rarefied transition to continuum, Journal of Computational Physics, 193, 708-738.
  14. [14]  Li, Z.H., Peng, A.P., Zhang, H.X., and Yang, J.Y. (2015), Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations, Progress in Aerospace Sciences, 74, 81-113.
  15. [15]  Kolobov, V.I., Arslanbekov R.R., Aristov V.V., Frolova, A.A., and Zabelok, S.A. (2007), Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement, Journal of Computational Physics, 223, 589-608.
  16. [16]  Xu, K. and Huang, J.C. (2010), A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows. Journal of Computational Physics, 229, 7747-7764.
  17. [17]  Zhu, L.H., Guo, Z.L., and Xu, K. (2016), Discrete unified gas kinetic scheme on unstructured meshes, Computers and Fluids, 127, 211-225.
  18. [18]  Bird, G.A. (1994), Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford.
  19. [19]  Borgnakke, C. and Larsen, P.S. (1975), Statistical collision model for Monte Carlo simulation of polyatomic gas mixtures. Journal of Computational Physics, 18, 405-420.
  20. [20]  Gimelshein, S.F., Gimelshein, N.E., Levin, D.A., Ivanov, M.S., and Markelov, G.N. (2002), Modeling of rarefied hypersonic flows over spacecraft in Martian atmosphere using the DSMC method, AIAA, 2002-2759.
  21. [21]  Wu, Q.F. and Chen, W.F. (1999), DSMC procedure for high temperature rarefied thermochemical nonequilibrium flows (in Chinese), National University of Defense Technology Press.
  22. [22]  Ivanov, M.S., Markelov, G.N., and Gimelshein, S.F. (1998), Statistical simulation of reactive rarefied flows: numerical approach and applications, AIAA Paper, 98-2669.
  23. [23]  Gimelshein, S.F., Boyd, I.D., and Ivanov, M.S. (1999), DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows, AIAA Paper, 99-3451.
  24. [24]  Haas, B.L. (1992), Models of energy-exchange mechanics applicable to a particle simulation of reactive flow, Journal of Thermophys, 6, 200-207.
  25. [25]  Bergemann, F. and Boyd, I.D. (1995), New-discrete vibrational energy model for the direct simulation Monte Carlo method, Progress in Aeronautics and Astronautics, 158, 174-183.
  26. [26]  Lumpkin, F.E., Haas, B.L., and Boyd, I.D. (1991), Resolution of differences between collision number definitions in particle and continuum simulations, Physics of Fluids, A3(9), 2282-2284.

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