Skip to main content
SpringerLink
Log in

Flow Behind an Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas with Conduction and Radiation Heat Flux

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

A self-similar model for one-dimensional unsteady adiabatic flows behind a cylindrical shock wave driven out by a piston moving with time according to an exponential law in non-ideal gas in the presence of conductive and radiative heat fluxes is discussed in a rotating atmosphere. The ambient medium is assumed to have axial, azimuthal and radial component of fluid velocities. The axial and azimuthal component of fluid velocity in the ambient medium is assumed to be varying according to exponential laws. The initial density and angular velocity of the ambient medium are taken to be constant for the existence of the similarity solutions. It is shown that increase in the parameter of non-idealness of the gas and the conductive or radiative heat transfer parameters have decaying effect on the shock wave. It is obtained that the parameter of non-idealness of the gas and heat transfer parameters have same effects on shock strength, density, pressure, axial and azimuthal component of fluid velocity and vorticity vector.

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

Similar content being viewed by others

References

  1. Sedov, L.I.: Similarity and Dimensional Methods in Mechanics. Academic Press, New York (1959)

    MATH  Google Scholar 

  2. Marshak, R.E.: Effect of radiation on shock wave behavior. Phys. Fluids 1, 24–29 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  3. Elliott, L.A.: Similarity methods in radiation hydrodynamics. Proc. R. Soc. Lond. Ser. A 258, 287–301 (1960)

    Article  MathSciNet  Google Scholar 

  4. Wang, K.C.: The piston problem with thermal radiation. J. Fluid Mech. 20, 447–455 (1964)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. NiCastro, J.R.: Similarity analysis of the radiative gas dynamic equations with spherical symmetry. Phys. Fluids 13, 2000–2006 (1970)

    Article  Google Scholar 

  7. Ghoneim, A.F., Kamel, M.M., Berger, S.A., Oppenheim, A.K.: Effect of internal heat transfer on the structure of self-similar blast waves. J. Fluid Mech. 117, 473–491 (1982)

    Article  MATH  Google Scholar 

  8. Chaturani, P.: Strong cylindrical shocks in a rotating gas. Appl. Sci. Res. 23, 197–211 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sakurai, A.: Propagation of spherical shock waves in stars. J. Fluid Mech. 1, 436–453 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  10. Nath, O., Ojha, S.N., Takhar, H.S.: Propagation of a shock wave in a rotating interplanetary atmosphere with increasing energy. J. Magnetohydrodyn. Plasma Res. 8, 269–282 (1999)

    Google Scholar 

  11. Ganguly, A., Jana, M.: Propagation of shock wave in self-gravitating radiative magnetohydrodynamic non-uniform rotating atmosphere. Bull. Calcutta Math. Soc. 90, 77–82 (1998)

    MATH  Google Scholar 

  12. Rao, M.P.R., Ramana, B.V.: Unsteady flow of a gas behind an exponential shock. J. Math. Phys. Sci. 10, 465–476 (1976)

    MATH  Google Scholar 

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

    Article  Google Scholar 

  14. Rao, M.P.R., Purohit, N.K.: Self-similar piston problem in non-ideal gas. Int. J. Eng. Sci. 14, 91–97 (1976)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  16. Nath, G.: Propagation of a cylindrical shock wave in a rotational axisymmetric isothermal flow of a non-ideal gas in magnetogasdynamics. Ain Shams Eng. J. 3, 393–401 (2012)

    Article  Google Scholar 

  17. Wu, C.C., Roberts, P.H.: Shock-wave propagation in a sonoluminescing gas bubble. Phys. Rev. Lett. 70, 3424–3427 (1993)

    Article  Google Scholar 

  18. Roberts, P.H., Wu, C.C.: Structure and stability of a spherical implosion. Phys. Lett. A 213, 59–64 (1996)

    Article  Google Scholar 

  19. Levin, V.A., Skopina, G.A.: Detonation wave propagation in rotational gas flows. J. Appl. Mech. Tech. Phys. 45, 457–460 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nath, G.: Magnetogasdynamic shock wave generated by a moving piston in a rotational axisymmetric isothermal flow of perfect gas with variable density. J. Adv. Space Res. 47, 1463–1471 (2011)

    Article  Google Scholar 

  21. Vishwakarma, J.P., Nath, G.: Similarity solutions for unsteady flow behind an exponential shock in a dusty gas. Phys. Scr. 74, 493–498 (2006)

    Article  MathSciNet  Google Scholar 

  22. Gretler, W., Wehle, P.: Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation. Shock Waves 3, 95–104 (1993)

    Article  MATH  Google Scholar 

  23. Vishwakarma, J.P., Nath, G.: Propagation of shock waves in an exponential medium with heat conduction and radiation heat flux. Model. Meas. Control B 77, 67–84 (2008)

    Google Scholar 

  24. Pomroning, G.C.: The Equations of Radiation Hydrodynamics, International Series of Monographs in Natural Philosophy, vol. 54. Pergaman Press, Oxford (1973)

    Google Scholar 

  25. Vishwakarma, J.P., Nath, G.: Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux. Commun. Nonlinear Sci. Numer. Simul. 17, 154–169 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  26. Laumbach, D.D., Probstein, R.F.: A point explosion in a cold exponential atmosphere. Part 2. Radiating flow. J. Fluid Mech. 40, 833–858 (1970)

    Article  Google Scholar 

  27. Nath, G.: Similarity solutions for unsteady flow behind an exponential shock in an axisymmetric rotating non-ideal gas. Meccanica 50, 1701–1715 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  28. Moelwyn-Hughes, E.A.: Physical Chemistry. Pergamon Press, London (1961)

    Google Scholar 

  29. Freeman, R.A., Craggs, J.D.: Shock waves from spark discharges. J. Phys. D 2, 421–427 (1969)

    Article  Google Scholar 

  30. Igra, O., Falcovitz, J., Reichenbach, H., Heilig, W.: Experimental and numerical study of the interaction between a planar shock wave and a square cavity. J. Fluid Mech. 313, 105–130 (1996)

    Article  Google Scholar 

  31. Igra, O., Wu, X., Falcovitz, J., Meguro, T., Takayama, K., Heilig, W.: Experimental and theoretical study of shock wave propagation through double-bend ducts. J. Fluid Mech. 437, 255–282 (2001)

    Article  MATH  Google Scholar 

  32. Falcovtiz, J., Alfandary, G., Ben-Dor, G.: Numerical simulation of the headon reflection of a regular reflection. Int. J. Numer. Methods Fluids 17, 1055–1077 (1993)

    Article  MATH  Google Scholar 

  33. Falcovitz, J., Ben-Artzi, M.: Recent developments of the GRP method. JSME Int. J. Ser. B. 38, 497–517 (1995)

    Article  Google Scholar 

  34. He, J.H.: Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178, 257–262 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  35. He, J.H.: Variational iteration method- a kind of non-linear analytical technique: some examples. Int. J. Non-linear Mech. 34, 699–708 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, Uttar Pradesh, 211004, India

    G. Nath & P. K. Sahu

Authors
  1. G. Nath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. K. Sahu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to G. Nath or P. K. Sahu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nath, G., Sahu, P.K. Flow Behind an Exponential Shock Wave in a Rotational Axisymmetric Non-ideal Gas with Conduction and Radiation Heat Flux. Int. J. Appl. Comput. Math 3, 2785–2801 (2017). https://doi.org/10.1007/s40819-016-0260-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40819-016-0260-x

Keywords

Search

Navigation