Skip to main content
SpringerLink
Log in

Numerical Solution of the Problem of Hypersonic Flow past a Thin Plate

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

An Erratum to this article was published on 08 June 2022

This article has been updated

Abstract

The problem of hypersonic flow past an absolutely thin edge is considered. The solution is obtained using a model kinetic equation for polyatomic gases. The method of the problem solution, which makes it possible to distinguish the discontinuity of the molecule distribution in the velocity space, is described. The distribution of the normal stress over the plate surface and above it is calculated. The results obtained are in good agreement with the experimental data. It is shown that a disturbed flow region arises ahead of the thin edge of a plate in hypersonic flow

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

Change history

REFERENCES

  1. Buzykin, O.G. and Galkin, V.S., Modifications of gasdynamic equations of higher approximations of the Chapman–Enskog method, Fluid Dyn., 2001, vol. 36, no. 3, pp. 508–520.

    Article  Google Scholar 

  2. Galkin, V.S. and Rusakov, S.V., Transformation of the Burnett components of transport relations of gases, Fluid Dyn., 2014, vol. 49, no. 1, pp. 131–136.

    Article  MathSciNet  ADS  Google Scholar 

  3. Kogan, M.N., Rarefied Gas Dynamics, New York: Plenum, 1969.

    Book  Google Scholar 

  4. Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford: Clarendon, 1994.

    Google Scholar 

  5. Shakhov, E.M., Metod issledovaniya dvizhenii razrezhennogo gaza (Method for Investigating Rarefied Gas Flows), Moscow: Computer Center of the USSR Academy of Sciences, 1975.

  6. Becker, M. and Boyland, D.E., Flow field and surface pressure measurements in the fully merged and transition flow regimes on a cooled sharp flat plate / Rarefied Gas Dynamics, Suppl. 4, Vol. 2, Ed. by C.L. Brundin, New York: Academic, 1967, pp. 993–1014.

    Google Scholar 

  7. Dorrence, W.H., Viscous Hypersonic Flow, New York: McGraw-Hill, 1962.

    Google Scholar 

  8. Balashov, A.A. and Dudin, G.N., Flow past a plate in the strong interaction regime in the presence of mass transfer, Trudy MFTI, 2015, vol. 7, no 1.

  9. Balashov, A.A. and Dudin, G.N., Investigation of flow past a flat plate in the strong interaction regime, Fluid Dyn. 2018, vol. 53, no. 3, pp. 394–401.

    Article  MathSciNet  ADS  Google Scholar 

  10. Kuznetsov, M.M., Lipatov, I.I., and Nikol’skii V.S., Asymptotic analysis of the translational nonequilibrium effects in a hypersonic flow past a flat surface with sharp leading edge, Techn. Phys. Lett., 2008, vol. 34, no. 4, article 327.

  11. Kuznetsov, A.A. and Lunev, V.V., Heating of a sharp slender wedge in supersonic flow, Fluid Dyn., 2021, vol. 56, no. 1, pp. 116–120.

    Article  MathSciNet  ADS  Google Scholar 

  12. Egorov, I.V. and Erofeev, A.I., Continuum and kinetic approaches to the simulation of the hypersonic flow past a flat plate, Fluid Dyn., 1997, vol. 32, no. 1, pp. 112–122.

    Article  ADS  Google Scholar 

  13. Shershnev, A.A., Kuznetsov, A.N., and Bondar’, E.A., Numerical simulation of supersonic gas flow past a flat plate on the basis of kinetic and continuum models, Vychisl. Tekhnologii, 2011, vol. 16, no. 6, pp. 93–104.

    Google Scholar 

  14. Vyong Van Tien, Gorelov, S.L., and Rusakov, S.V., Effects of nonmonotonicity of the aerodynamic characteristics of a plate in a hypersonic rarefied gas flow, Trudy MAI, 2020, no. 110.

  15. Sumbatyan, M.A., Berdnik, Ya.A., and Bondarchuk, A.A., Iteration method for solving Navier–Stokes equations in the problem of viscous incompressible flow past a thin plate, Vestnik Tomsk. Univ., 2020, no. 66.

  16. Nikitchenko, Yu.A., Modeli neravnovesnykh techenii (Models of Nonequilibrium Flows), Moscow Aviation Institute, 2013.

  17. Nikitchenko, Yu.A., Model kinetic equation for polyatomic gases, Comput. Math. Math. Phys., 2017, vol. 57, no. 11, pp. 1843–1855.

    Article  MathSciNet  Google Scholar 

  18. Bhatnagar, P.L., Gross, E.P., and Krook, M., A model for collision processes in gases, Phys. Rev., 1954, vol. 94, no. 3.

  19. Holway, L.H., New statistical models in kinetic theory: methods of construction, Phys. Fluids, 1966, vol. 3, no. 3.

Download references

Funding

The study was carried out within the framework of the State Assignment of the Ministry of Education and Science of the Russian Federation no. FSFF-2020-0013.

Author information

Authors and Affiliations

  1. Zhukovski Central Aerohydrodynamic Institute (TsAGI), 140180, Zhukovsky, Moscow oblast, Russia

    M. E. Berezko & Yu. A. Nikitchenko

Authors
  1. M. E. Berezko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Nikitchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. A. Nikitchenko.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by M. Lebedev

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berezko, M.E., Nikitchenko, Y.A. Numerical Solution of the Problem of Hypersonic Flow past a Thin Plate. Fluid Dyn 57, 193–201 (2022). https://doi.org/10.1134/S0015462822020021

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462822020021

Keywords:

Search

Navigation