Skip to main content
SpringerLink
Log in

On the Relaxation of Molecules’ Rotational Energy in the Direct Simulation Monte Carlo Method

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

Rotational-translational energy exchange simulation in the direct simulation Monte Carlo method is considered for the problem of the entry of hypersonic space vehicles in the atmosphere of the Earth, Mars, Venus, Titan, and gas giants. The diatomic and polyatomic molecules’ discrete quantum energy levels are systematized. The energy exchange Larsen-Borgnakke algorithm is described for the molecules with discrete rotational energy levels. The parameters of the model of hard spheres of variable diameters (VHS) are derived for molecules present in the atmospheres from the experimental data on the viscosity of gases and calculation of cross sections of clashing molecules elastic. Analogously, the parameters in Parker’s formula, describing the rotational-translational relaxation, are chosen from the experimental data on the times of relaxation of the rotational energy of the molecules. Close agreement between The calculated and experimental data are in close agreement for moving away and the width of the shock wave before the sphere in nitrogen gas. This means that the used models and their parameters are adequate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. N. Zalogin, “Rotational relaxation of nitrogen in a viscous shock layer at low Reynolds numbers,” Fluid Dyn. 12, 629–632 (1977).

    Article  MATH  Google Scholar 

  2. V. V. Ryabov, “Numerical investigation of the flow of nitrogen past a sphere with allowance for rotational relaxation,” Fluid Dyn. 15, 320–324 (1980).

    Article  Google Scholar 

  3. V. I. Vlasov and A. B. Gorshkov, “Comparison of the calculated results for hypersonic flow past blunt bodies with the OREX flight test data,” Fluid Dyn. 36, 812–819 (2001).

    Article  MATH  Google Scholar 

  4. A. L. Kusov, “Comparison of the calculation heat flux with OREX flight data,” Fiz.-Khim. Kinet. Gaz. Din. 17 (1), 4 (2016).

    Google Scholar 

  5. M. J. Wright, J. Olejniczak, L. Walpot, E. Raynaud, T. Magin, L. Caillaut, and B. R. Hollis, “A code calibration study for huygens entry aeroheating,” in Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 9–12, 2006, Reno, NV, AIAA Paper No. 2006-382, pp. 1–16.

  6. C. Park, “Viscous shock layer calculation of stagnation-region heating environment in neptune aerocapture,” in Proceedings of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Jan. 4–7, 2011, Orlando, FL, AIAA Paper No. 2011-248, pp. 1–7.7.

  7. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989, 4th ed.; Pergamon, New York, 1977, 3rd ed.).

    Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980).

    Google Scholar 

  9. A. S. Davydov, Quantum Mechanics (Pergamon, Oxford, 1965; Nauka, Moscow, 1973).

    Google Scholar 

  10. S. F. Gimelshein, I. D. Boyd, and M. S. Ivanov, “Modeling of internal energy transfer in plume flows of polyatomic molecules by the DSMC method,” in Proceedings of the 37th Aerospace Sciences Meeting and Exhibit, Jan. 11–14, 1999, Reno, NV, AIAA Paper No. 99-0738, pp. 1–9.

    Google Scholar 

  11. Thermodynamical Properties of Individual Substances, The Handbook, Ed. by V. P. Glushko (Nauka, Moscow, 1978), Vol. 1, pt. 1 [in Russian].

  12. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).

    Google Scholar 

  13. A. L. Kusov, “Numerical simulation of the flow around cylinder with sphere nose using direct simulation Monte-Carlo method,” Mat. Model. 27 (12), 33–47 (2015).

    MathSciNet  MATH  Google Scholar 

  14. A. L. Kusov and V. V. Lunev, “Use of Monte-Carlo direct static modeling method for solving problem of nonstationary rarefied gas dispersion when evaporating from overheated material surface in vacuum,” Kosmonavt. Raketostroen., No. 1 (58), 36–45 (2010).

    Google Scholar 

  15. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).

    MATH  Google Scholar 

  16. Physicochemical Processes in Gas Dynamics. Computer Handbook, Vol. 1: Dynamics of Physicochemical Processes in Gas and Plasma, Ed. by G. G. Chernyi and S. A. Losev (Mosk. Gos. Univ., Moscow, 1995) [in Russian].

    Google Scholar 

  17. M. J. Wright, D. Bose, G. E. Palmer, and E. Levin, “Recommended collision integrals for transport property computations, Part 1: Air species,” AIAA J. 43, 2558–2564 (2005).

    Article  Google Scholar 

  18. M. J. Wright, H. H. Hwang, and D. W. Schwenke, “Recommended collision integrals for transport property computations, Part 2: Mars and Venus entries,” AIAA J. 45, 281–288 (2007).

    Article  Google Scholar 

  19. Physical Values, The Handbook, Ed. by I. S. Grigorev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991) [in Russian].

    Google Scholar 

  20. A. L. Kusov, “On the possibility of the oxygen dissociation modeling in the shock wave using classical models of the direct simulation Monte Carlo method,” Fiz.-Khim. Kinet. Gaz. Din. 17 (1), 5 (2016).

    Google Scholar 

  21. J. G. Parker, “Rotational and vibrational relaxation in diatomic gases,” Phys. Fluids 2, 449–462 (1959).

    Article  MathSciNet  Google Scholar 

  22. I. D. Boyd, “Rotational and vibrational nonequilibrium effects in rarefied hypersonic flow,” J. Thermophys. 4, 478–484 (1990).

    Article  Google Scholar 

  23. I. D. Boyd, “Rotational-translational energy transfer in rarefied nonequilibrium flows,” Phys. Fluids A 2, 447–452 (1990).

    Article  Google Scholar 

  24. Y. V. Stupochenko, S. A. Losev, and A. I. Osipov, Relaxation in Shock Waves (Springer, Berlin, Heidelberg, 1967; Nauka, Moscow, 1965).

    Google Scholar 

  25. A. V. Bogdanov, G. V. Dubrovskii, A. I. Osipov, and V. M. Strelchenia, Rotational Relaxation in Gases and Plasma (Energoatomizdat, Moscow, 1991) [in Russian].

    Google Scholar 

  26. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, New York, 1968; Nauka, Moscow, 1973).

    Google Scholar 

  27. I. M. Sobol’, A Primer for the Monte Carlo Method (CRC, Boca Raton, FL, 1994; Nauka, Moscow, 1973).

    MATH  Google Scholar 

  28. D. A. Russell, “Density disturbance ahead of a sphere in rarefied supersonic flow,” Phys. Fluids 11, 1679 (1968).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Central Research Institute of Machine Building, Korolev, Moscow oblast, Russia

    A. L. Kusov

Authors
  1. A. L. Kusov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. L. Kusov.

Additional information

Original Russian Text © A.L. Kusov, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 8, pp. 95–109.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kusov, A.L. On the Relaxation of Molecules’ Rotational Energy in the Direct Simulation Monte Carlo Method. Math Models Comput Simul 10, 237–248 (2018). https://doi.org/10.1134/S2070048218020084

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048218020084

Keywords

Search

Navigation