Skip to main content
SpringerLink
Log in

A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

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

Abstract

A self similar method is used to analyze numerically the one-dimensional, unsteady flow of a strong cylindrical shock wave driven by a piston moving with time according to an exponential law in a plasma of constant density. The plasma is assumed to be a non-ideal gas with infinite electrical conductivity permeated by an axial magnetic field. Numerical solutions in the region between the shock and the piston are presented for the cases of adiabatic and isothermal flow. The general behaviour of density, velocity, and pressure profiles remains unaffected due to presence of magnetic field in non-ideal gas. However, there is a decrease in values of density, velocity and pressure in case of magnetogasdynamics as compared to non-magnetic case. It may be noted that the effect of magnetic field on the flow pattern is more significant in case of isothermal flow as compared to adiabatic flow. The effect of non-idealness, specific heat exponent and magnetic field strength on the variation of shock strength across the shock front is also investigated.

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

    MATH  Google Scholar 

  2. Wang KC (1964) Approximate solution of a plane radiating piston problem. J Fluid Mech 20:447–455

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  4. Finkleman D, Baron JR (1970) A characteristic approach to radiative gas dynamics. AIAA 8:87–95

    Article  Google Scholar 

  5. Singh LP, Sharma VD, Ram R (1989) Flow pattern induced by a piston moving in a perfectly conducting inviscid radiating gas. Phys Fluids B 1:692–699

    Article  ADS  Google Scholar 

  6. Gretler W, Regenfelder R (2005) Variable energy blast waves generated by a piston moving in a dusty gas. J Eng Math 52:321–336

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  8. 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 

  9. Ranga Rao MP, Purohit NK (1976) Self similar piston problem in non-ideal gas. Int J Eng Sci 14:91–97

    Article  MATH  Google Scholar 

  10. Wu CC, Roberts PH (1996) Structure and stability of a spherical implosion. Phys Lett A 213:59–64

    Article  ADS  Google Scholar 

  11. Madhumita G, Sharma VD (2004) Imploding cylindrical and spherical shock waves in a non-ideal medium. J Hyperbolic Differ Equ 1:521–530

    Article  MathSciNet  MATH  Google Scholar 

  12. Arora R, Sharma VD (2006) Convergence of strong shock in a van der Waals gas. SIAM J Appl Math 66:1825–1837

    Article  MathSciNet  MATH  Google Scholar 

  13. Vishwakarma JP, Nath G (2007) Similarity solutions for the flow behind an exponential shock in a non-ideal gas. Meccanica 42:331–339

    Article  MathSciNet  MATH  Google Scholar 

  14. Vishwakarma JP, Nath G (2009) A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles. Meccanica 44:239–254

    Article  Google Scholar 

  15. Korobeinikov VP (1976) Problems in the theory of point explosion in gases. American Mathematical Society, Providence

    Google Scholar 

  16. Shang JS (2001) Recent research in magneto-aerodynamics. Prog Aerosp Sci 31:1–20

    Article  Google Scholar 

  17. Lock RM, Mestel AJ (2008) Annular self- similar solution in ideal gas magnetogasdynamics. J Fluid Mech 74:531–554

    Google Scholar 

  18. 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 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. Lerche I (1979) Mathematical theory of one-dimensional isothermal blast waves in a magnetic field. Aust J Phys 32:491–502

    MathSciNet  ADS  Google Scholar 

  22. Lerche I (1981) Mathematical theory of one-dimensional cylindrical isothermal blast waves in a magnetic field. Aust J Phys 34:279–301

    MathSciNet  ADS  Google Scholar 

  23. Whitham GB (1974) Linear and non-linear waves. Wiley, New York

    Google Scholar 

  24. Landau LD, Lifshitz EM (1958) Course of theoretical physics, statistical physics. Pergamon Press, Oxford

    Google Scholar 

  25. Courant R, Friedrichs KO (1948) Supersonic flow and shock waves. Springer, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi, 221005, India

    L. P. Singh, Akmal Husain & M. Singh

Authors
  1. L. P. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akmal Husain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Akmal Husain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Singh, L.P., Husain, A. & Singh, M. A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics. Meccanica 46, 437–445 (2011). https://doi.org/10.1007/s11012-010-9325-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-010-9325-9

Keywords

Search

Navigation