Skip to main content
SpringerLink
Log in

Entropy Value on the Surface of a Non-Symmetric Convex Bow Part of a Body in the Supersonic Flow

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

In this study, using the Euler equations, we investigate 3D stationary flows behind a detached bow shock produced in a supersonic flow around a body with a smooth convex bow. The supersonic free stream was considered to be uniform. Maximal entropy on the body surface is substantiated. The streamline that ends at the front stagnation point on the body (the stagnation streamline) is shown to cross the bow shock at the point where the plane tangent to it is perpendicular to the free stream direction. This means that the entropy value on the body surface is calculated by the free stream parameters and is equal to the entropy value behind a normal shock at the point of the stagnation streamline onset.

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. Ladyzhenskii, M.D., Prostranstvennye giperzvukovye techeniya gaza (Spatial Hypersonic Gas Flows), Moscow: Mashinostroenie, 1968.

    Google Scholar 

  2. Shifrin, E.G., On the extremal properties of entropy on a critical streamline, J. Appl. Math. Mech., 1967, vol. 31, no. 3, pp. 618–620.

    Article  Google Scholar 

  3. Batchelor, G.K., An Introduction to Fluid Dynamics, CUP, 1970.

    Google Scholar 

  4. Von Mises, R., Mathematical Theory of Compressible Fluid Flow, New York: Academic, 1958.

    MATH  Google Scholar 

  5. Prim, R. and Truesdell, C., A derivation of Zorawski’s criterion for permanent vector-lines, Proc. Amer. Math. Soc., 1950, vol. 1, pp. 32–34.

    MathSciNet  MATH  Google Scholar 

  6. Kochin, N.E., Kibel, I.A., and Roze, N.V., Theoretical Hydromechanics, New York: Wiley, 1964.

    MATH  Google Scholar 

  7. Golubkin, V.N. and Sizykh, G.B., Some general properties of plane-parallel viscous flows, Fluid Dyn., 1987, vol. 22, no. 3, pp. 479–471.

    Article  ADS  Google Scholar 

  8. Markov, V.V. and Sizykh, G.B., Vorticity evolution in liquids and gases, Fluid Dyn., 2015, vol. 50, no. 2, pp. 186–192.

    Article  MathSciNet  Google Scholar 

  9. Sizykh, G.B., Evolution of vorticity in swirling axisymmetric flows of a viscous incompressible fluid, TsAGI Sci. J., 2015, vol. 46, no. 3, pp. 209–217.

    Article  Google Scholar 

  10. Pontryagin, L.S., Ordinary Differential Equations, London: Pergamon, 1962.

    MATH  Google Scholar 

  11. Sedov, L.I., Mechanics of Continuous Media (in 2 Vol.), Singapore: World Sci., 1997.

    Book  Google Scholar 

  12. Munk, M. and Prim, R., On the multiplicity of steady gas flows having the same streamline pattern, Proc. Nat. Acad. Sci. USA, 1947, vol. 33, pp. 137–141.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia

    G. B. Sizykh

Authors
  1. G. B. Sizykh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. B. Sizykh.

Additional information

Russian Text © The Author(s), 2019, published in Prikladnaya Matematika i Mekhanika, 2019, Vol. 83, No. 3, pp. 377–383.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sizykh, G.B. Entropy Value on the Surface of a Non-Symmetric Convex Bow Part of a Body in the Supersonic Flow. Fluid Dyn 54, 907–911 (2019). https://doi.org/10.1134/S0015462819070139

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462819070139

Keywords

Search

Navigation