Abstract
Self-similar solutions of the second kind for the unsteady one-dimensional flow behind converging spherical and cylindrical strong shocks in a non-ideal medium are studied. The equation of state of the medium is assumed to be in the form of the Mie-Gruneisen type. A simple numerical technique is developed to find the similarity exponent. Detailed studies are carried out for a different non-ideal medium such as a dusty gas, condensed matter and c,s medium. The solutions for an ideal gas are recovered as a particular case. A comparative study of the numerical and some approximate solutions is also made.
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G. Guderley, Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19 (1942) 302–312.
K.P. Stanyukocich, Unsteady motion of continuous media. London: Pergamon Press, (1960) 417–489.
Ya.B. Zeldovich and Yu.P. Raizer, Physics of shock waves and high temperature hydrodynamic phenomena. New York: Academic Press, Vol. II (1966) 785–806.
P. Hafner, Strong convergent shock waves near the center of convergence: a power series solution. SIAM. J. Appl. Math 48 (1988) 1244–1261.
Y. Fujimoto and E.A. Mishkin, Analysis of spherically imploding shocks. Phys. Fluids 21 (1978) 1933–1938.
G.B. Whitham, Linear and non-linear waves, New York: John Wiley & Sons, Inc., (1974) 270–271.
A. Ramu and M.P. Ranga Rao, Converging spherical and cylindrical shock waves. J. Engrg. Math. (1973) 411–417.
M. Yousaf, Imploding spherical and cylindrical shocks. Physics of fluids 29 (1986) 680–684.
S.I. Pai, S. Menon and Z.Q. Fan, Similarity solutions of a strong shock wave propagating in a mixture of a gas and dusty particles. Int. J. Engrg. Sci. 18 (1980) 1365–1373.
A.V. Bushman and V.E. Fortov, Model equation of state. Sov. Phys-USPEKHI. 26 (1983) 465–496.
S.I. Anisimov and V.A. Kravchenko, Shock wave in condensed matter generated by impulsive load. Z. Naturforsch. 40a (1984) 8–13.
J.M. Walsh, On non-linear plane waves in metal plates. General Atomic Report, GAMD-2115 (1960) 5–7.
R.A. Axford and D.D. Holm, Spherical Shock collapse in a non-ideal medium. Proc. 2 nd Int. Symp. on Group Theory Methods in Mechanics Novosibirsk, USSR, (1978) 47.
N.H. Patel and M.P. Ranga Rao, Shock waves due to impulsive load. To be published.
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Patel, N.H., Ranga Rao, M.P. Imploding shocks in a non-ideal medium. J Eng Math 30, 683–692 (1996). https://doi.org/10.1007/BF00042788
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DOI: https://doi.org/10.1007/BF00042788