Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

Abstract

The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.

Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimuthal or Axial Magnetic Field

“…The governing equations which describe unsteady, onedimensional cylindrically or spherically symmetric adiabatic flow of an electrically conducting dusty gas in which an azimuthal or axial magnetic field is permeated and heat conduction, as well as viscous stress, are negligible, have the form (c.f. Nath and Sahu [14], Anisimov and Spiner [15], Pai et al [23], Vishwakarma and Nath [30], Pai [31], Sahu [20,34], Vishwakarma and Lata [36])…”

“…Across the shock front, the Rankine-Hugoniot conditions, i.e.,the jump conditions at the magnetogasdynamic shock wave, are given by the conservation of mass, magnetic flux, momentum, and energy, namely (c.f Nath and Sahu [14], Pai et al [23], Vishwakarma and Nath [30], Pai [31], Sahu [20,34], Vishwakarma and Lata [36])…”

“…To obtain the similarity solutions, we write the unknown variables in terms of the dimensionless functions of y (Anisimov and Spiner [15], Pai et al [23], Vishwakarma and Nath [30], Pai [31], Sahu [20,34]…”

“…The situation very much of the same kind may prevail during the formation of a cylindrical spark channel from exploding wires. Besides, in the usual cases of spark break down, time-dependent energy input is a more realistic assumption than instantaneous energy input (see Sahu [20], Freeman and Craggs [49]).…”

“…Due to the extremely high pressure or low temperature that prevails in most of the problems especially associated with blast waves, the gas deviates from the ideal gas law and behaves like a real gas (non-ideal gas). The real gas effects are exemplified, in particular, by [15][16][17][18][19][20][21] among others. Since the presence of real gas effects increases the strength of the blast waves and comes into post-blast conditions, these effects need to be accounted for in theoretical and experimental studies.…”