Regression models for calculating state-to-state coefficients of the rate of vibrational energy exchanges

Authors

  • Andrey A. Isakov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Viacheslav I. Gorikhovskii St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Maksim Yu. Melnik St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2024.207

Abstract

The paper proposes an effective algorithm for solving problems of nonequilibrium gas dynamics taking into account detailed state-to-state vibrational kinetics. One of the problems of traditional methods is their high computational complexity, which requires a lot of time and memory. The work explored the possibilities of using relaxation rate prediction to improve the performance of numerical simulations of nonequilibrium oxygen flows instead of direct calculations. For this purpose, an approach based on nonlinear regression analysis was used, which made it possible to obtain computationally efficient approximation formulas for the energy exchange rate coefficients in the model of a forced harmonic oscillator, taking into account free rotations (FHO-FR), to significantly increase the calculation speed while maintaining accuracy, and to construct an optimized model FHO-FR-reg. Using the obtained regression formulas, numerical modeling was carried out, which made it possible to validate the model for the problem of oxygen flow behind an incident and reflected shock wave. A comparison between the forced harmonic oscillator (FHO) and FHO-FR models is not possible due to the high computational complexity of the second model. With the advent of a common approximation model, it became possible to compare simulation results for these models. Numerical calculations have shown that the FHO-FR-reg model gives values of gas-dynamic parameters close to the FHO model. The developed regression models make it possible to speed up the solution of the problem of modeling oxygen relaxation several times compared to other models of similar accuracy.

Keywords:

vibrational relaxation, state-to-state kinetics, shock wave, optimization of numerical calculations, nonlinear regression, machine learning

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References

Литература

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7. Adamovich I., Rich J. Three-dimensional nonperturbative analytic model of vibrational energy transfer in atom-molecule collisions. J. Chem. Phys. 109, 7711-7724 (1998). https://doi.org/10.1063/1.477417

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9. Gimelshein S. F., Wysong I. J., Adamovich I. V. Application of the 3D Forced Harmonic Oscillator Model in the DSMC Method. J. Thermophys. Heat Transf. 32 (4), 882-891 (2018). https://doi.org/10.2514/1.T5228

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13. Ibraguimova L. B., Sergievskaya A. L., Levashov V. Yu., Shatalov O. P., Tunik Yu. V., Zabelinskii I. E. Investigation of oxygen dissociation and vibrational relaxation at temperatures 4000-10800 K. J. Chem. Phys. 139, 034317 (2013). https://doi.org/10.1063/1.4813070

14. Streicher J. W., Krish A., Hanson R. K. Coupled vibration-dissociation time-histories and rate measurements in shock-heated, nondilute O2 and O2-Ar mixtures from 6000 to 14000 K. Phys. Fluids. 33, 056107 (2021). https://doi.org/10.1063/5.0048059

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16. Streicher J.W., Krish A., Hanson R. K. High-temperature vibrational relaxation and decomposition of shock-heated nitric oxide. I. Argon dilution from 2200 to 8700 K. Physics of Fluids 34, 116122 (2022). https://doi.org/10.1063/5.0109109

References

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3. Campoli L., Kunova O., Kustova E., Melnik M. Models validation and code profiling in state-to-state simulations of shock heated air flows. Acta Astronautica 175, 493-509 (2020). https://doi.org/10.1016/j.actaastro.2020.06.008

4. Kravchenko D. S., Kustova E. V., Melnik M. Yu. Modeling of state-to-state oxygen kinetics behind reflected shock waves. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9 (67), iss. 3, 426-439 (2022). https://doi.org/10.21638/spbu01.2022.304 (In Russian) [Eng. transl.: Vestnik St. Petersburg University. Mathematics 55, iss. 3, 281-289 (2022). https://doi.org/10.1134/S1063454122030104].

5. Schwartz R. N., Slawsky Z. I., Herzfeld K. F. Calculation of vibrational relaxation times in gases.J. Chem. Phys. 20 (10), 1591-1599 (1952). https://doi.org/10.1063/1.1700221

6. Adamovich I., Macheret S., Rich J., Treanor C. Vibrational energy transfer rates using a forced harmonic oscillator model. J. Thermophys. Heat Transf. 12 (1), 57-65 (1998). https://doi.org/10.2514/2.6302

7. Adamovich I., Rich J. Three-dimensional nonperturbative analytic model of vibrational energy transfer in atom-molecule collisions. J. Chem. Phys. 109, 7711-7724 (1998). https://doi.org/10.1063/1.477417

8. Adamovich I., Rich, J. Three-dimensional analytic model of vibrational energy transfer in molecule-molecule collisions. AIAA Journal 39 (10), 1916-1925 (2001). https://doi.org/10.1063/1.477417

9. Gimelshein S. F., Wysong I. J., Adamovich I. V. Application of the 3D Forced Harmonic Oscillator Model in the DSMC Method. J. Thermophys. Heat Transf. 32 (4), 882-891 (2018). https://doi.org/10.2514/1.T5228

10. Baluckram V. T., Fangman A. J., Andrienko D. A. Simulation of Oxygen Chemical Kinetics Behind Incident and Reflected Shocks via Master Equation. J. Thermophys. Heat Transf. 37, 198-212 (2022). https://doi.org/10.2514/1.T6522

11. Bushmakova M. A., Kustova E. V. Modeling vibrational relaxation rate using machine learning methods. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9 (67), iss. 1, 113-125 (2022). https://doi.org/10.21638/-spbu01.2022.111 (In Russian) [Eng. transl.: Vestnik St. Petersburg University. Mathematics 55, iss. 1, 87-95 (2022). https://doi.org/10.1134 /S1063454122010022].

12. Gorikhovskii V. I. Efficient Computational Approaches to Modeling Carbon Dioxide Kinetics: PhD thesis in Physics and Mathematics. St. Petersburg, St. Рetersburg State University (2022).

13. Ibraguimova L. B., Sergievskaya A. L., Levashov V. Yu., Shatalov O. P., Tunik Yu. V., Zabelinskii I. E. Investigation of oxygen dissociation and vibrational relaxation at temperatures 4000-10800 K. J. Chem. Phys. 139, 034317 (2013). https://doi.org/10.1063/1.4813070

14. Streicher J. W., Krish A., Hanson R. K. Coupled vibration-dissociation time-histories and rate measurements in shock-heated, nondilute O2 and O2-Ar mixtures from 6000 to 14000 K. Phys. Fluids. 33, 056107 (2021). https://doi.org/10.1063/5.0048059

15. Gimelshein S. F., Wysong I. J., Bykova N. G., Shatalov O. P., Zabelinskii I. E. Improved Analysis of O2 Ultraviolet Absorption Spectra Under Nonequilibrium Shock Conditions. AIAA Journal 58 (10), 4451-4460 (2020). https://doi.org/10.2514/1.J058961

16. Streicher J.W., Krish A., Hanson R. K. High-temperature vibrational relaxation and decomposition of shock-heated nitric oxide. I. Argon dilution from 2200 to 8700 K. Physics of Fluids 34, 116122 (2022). https://doi.org/10.1063/5.0109109

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Published

2024-08-10

How to Cite

Isakov, A. A., Gorikhovskii, V. I., & Melnik, M. Y. (2024). Regression models for calculating state-to-state coefficients of the rate of vibrational energy exchanges. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(2), 332–346. https://doi.org/10.21638/spbu01.2024.207

Issue

Vol. 11 No. 2 (2024)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.