Skip to main content
SpringerLink
Log in

Similarity solutions for the flow behind an exponential shock in a non-ideal gas

  • Original Paper
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law are obtained. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compare to that of the adiabatic case. Effects of the non-idealness of the gas on the flow-field between the shock and the piston are investigated. The variations of density-ratio across the shock and the location of the piston with the parameter of non-idealness of the gas \({\overline{b}}\) are also obtained.

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. Parker EN (1963) Interplanetary dynamical processes. Interscience, New York

    MATH  Google Scholar 

  2. Lee TS, Chen T (1968) Hydromagnetic interplanetary shock waves. Planet Space Sci 16:1483–1502

    Article  ADS  Google Scholar 

  3. Rosenau P, Frankenthal S (1976) Equatorial propagation of axisymmetric magnetohydrodynamic shocks. Phys Fluids 19:1889–1899

    Article  MATH  ADS  Google Scholar 

  4. Director MN, Dabora EK (1977) Predictions of variable energy blast waves. AIAA J 15: 1315–1321

    Article  MATH  ADS  Google Scholar 

  5. Rogers MH (1958) Similarity flows behind strong shock waves. Q J Mech Appl Math 11:411–422

    Article  MATH  Google Scholar 

  6. Dabora EK (1972) Variable energy blast waves. AIAA J 10:1384–1386

    ADS  Google Scholar 

  7. Helliwell JB (1969) Self-similar piston problems with radiative heat transfer. J Fluid Mech 37:497–512

    Article  MATH  ADS  Google Scholar 

  8. Sedov LI (1959) Similarity and dimensional methods in mechanics. Academic, New York

    MATH  Google Scholar 

  9. Mirelsh H (1962) Hypersonic flow over slender bodies associated with power law shocks Adv Appl Mech 7. Academic, New York

    Google Scholar 

  10. Steiner H, Hirschler T (2002) A self-similar solution of a shock propagation in a dusty gas. Eur J Mech B/Fluids 21:371–380

    Article  MATH  MathSciNet  Google Scholar 

  11. Ranga Rao MP, Ramana BV (1976) Unsteady flow of a gas behind an exponential shock. J Math Phy Sci 10:465–476

    MATH  Google Scholar 

  12. Higashino F (1983) Characteristic method applied to blast waves in a dusty gas. Z Naturforsch 38a:399–406

    ADS  Google Scholar 

  13. Anisimov SI, Spiner OM (1972) Motion of an almost ideal gas in the presence of a strong point explosion. J Appl Math Mech. 36:883–887

    Article  Google Scholar 

  14. Wu CC, Roberts PH (1993) Shock-wave propagation in a sonoluminescing gas bubble. Phys Rev Lett 70: 3424–3427

    Article  ADS  Google Scholar 

  15. Roberts PH, Wu CC (1996) Structure and stability of a spherical implosion. Phys Lett A213:59–64

    Article  ADS  Google Scholar 

  16. Singh JB, Vishwakarma PR (1983) Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics. Astrophys Space Sci 95:111– 116

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Liberman MA, Velikovich AL (1989) Self-similar spherical expansion of a laser plasma or of detonation products into a low-density ambient gas. Phys. Fluids 1:1271–1276

    Article  Google Scholar 

  18. Korobeinikov VP (1976) Problems in the theory of point explosion in gases. In: Proceedings of the Steklov institute of mathematics. No.119. American Mathematical Society, Providence, RI

  19. Laumbach DD, Probstein RF (1970) Self-similar strong shocks with radiation in a decreasing exponential atmosphere. Phys Fluids 13:1178–1183

    Article  ADS  Google Scholar 

  20. Sachdev PL, Ashraf S (1971) Converging spherical and cylindrical shocks with zero temperature gradient in the rear flow-field. J Appl Math Phys (ZAMP) 22:1095–1102

    Article  Google Scholar 

  21. Ashraf S, Ahmad Z (1975) Approximate analytic solution of a strong shock with radiation near the surface of the star. J Pure Appl Math 6:1090–1098

    MATH  Google Scholar 

  22. Zhuravskaya TA, Levin VA (1996) The propagation of converging and diverging shock waves under intense heat exchange conditions. J Appl Math Mech 60: 745–752

    Article  MATH  MathSciNet  Google Scholar 

  23. Landau LD, Lifshitz EM (1958) Course of theoretical physics Statistical physics, vol 5. Pergaman Press, Oxford

    Google Scholar 

  24. Singh RA, Singh JB (1998) Analysis of diverging shock waves in non-ideal gas. Ind J Theor Phys 46:133–138

    Google Scholar 

  25. Ojha SN (2002)Shock waves in non-ideal fluids. Int J Appl Mech Eng 17:445–464

    Google Scholar 

  26. Chandrasekhar S (1939) An introduction to the study of Stellar structure. University Chicago Press, Chicago

    Google Scholar 

  27. Vishwakarma JP (2000) Propagation of shock waves in a dusty gas with exponentially varying density. Eur Phys J B 16:369–372

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, D.D.U. Gorakhpur University, Gorakhpur, 273009, INDIA

    J. P. Vishwakarma & G. Nath

Authors
  1. J. P. Vishwakarma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Nath
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Vishwakarma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vishwakarma, J.P., Nath, G. Similarity solutions for the flow behind an exponential shock in a non-ideal gas. Meccanica 42, 331–339 (2007). https://doi.org/10.1007/s11012-007-9058-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-007-9058-6

Keywords

Search

Navigation