Converging spherical and cylindrical shock waves

Abstract

The self-similar solutions for converging spherical and cylindrical strong shock waves in a non-ideal gas satisfying the equation of state of the Mie-Gruneisen type are investigated. The equations governing the flow, which are highly non-linear hyperbolic partial differential equations, are first reduced to a Poincar6-type ordinary differential equation with suitable approximation. Such an approximation helps in obtaining the self-similar solutions and the similarity exponent numerically by phase-plane analysis.

Imploding shocks in a non-ideal medium

“…Using the Mie-Gruneisen coefficient given by (28) we recovered the solutions of the problem discussed in [13] for 1-'o = 5, u = 2. In a perfect gas, for which F(G) = 3' -1, the values of oL for different values of 7 are calculated and they are found to be in close agreement with the results obtained by Guderley. This numerical technique is applicable for the Mie-Gruneisen coefficient used by Ramu and Ranga Rao [7] and also for any coefficient satisfying the condition (18).…”

“…A power-series solution for the converging strong shock waves in a perfect gas was developed by Hafner [4]. Ramu and Ranga Rat [7] have presented the self-similar solutions for strong shock waves in a non-ideal medium satisfying the equation of state of the Mie-Gruneisen type. But they have put a condition on the Mie-Gruneisen coefficient so that the phase-plane analysis could be applied for solving the problem.…”

Interaction between Weak Discontinuities and Shocks in a Dusty Gas

“…Let us assume the flow to be a gas mixture obeying to the equation of state of Mie-Grüneisen type [7,8] …”

Quasi-similar solution of the strong shock wave problem in non-ideal gas dynamics

“…The propagation of blast waves establishes a problem of great interest to researchers in a variety of fields such as astrophysics, nuclear science, plasma physics and geophysics. A number of analytical solutions for the blast wave propagation have been obtained by Rogers (1957), Sakurai (1953Sakurai ( , 1954, Madhumita andSharma (2003, 2004), Arora and Sharma (2006), Sedov (1959), Lin (1954) and Taylor (1950aTaylor ( , 1950b. Anisimov and Spiner (1972) studied the problem of point explosion in a non-ideal gas by taking the equation of state in a simplified form to describe the behavior of the medium.…”

“…In recent years, many theoretical and experimental studies have been performed on the strong shock waves as an energy source for the generation of very high pressures and temperatures. Ramu and Ranga Rao (1993) studied the self-similar solutions for the converging spherical and cylindrical strong shock waves in a non-ideal gas satisfying the equation of state of the MieGruneisen type. Wu andRoberts (1995, 1996) investigated the similarity solutions and the stability for strong spherical implosions for both ideal and van der Waals gases.…”