Similarity solution for laser-driven shock waves in a particle-laden gas

Abstract

A similarity solution has been obtained for a laser-driven strong shock wave propagating in a mixture of gas and small solid particles. It is assumed that the equilibrium-ow condition is maintained and the variable laser energy is completely absorbed at the shock front according to a time-dependent power law. The similarity solution is valid for adiabatic ow as long as the e ect of the counter pressure is neglected. The e ects of a parameter characterising the various energy input of the blast wave on the similarity solution as well as on its limits have been examined. The computations have been performed for various values of mass concentration of the solid particles and for the ratio of density of solid particles to the constant-initial density of gas.

Similarity Solution of Spherical Shock Waves -Effect of Viscosity

“…This behaviour remains unaltered with the value of K > 0.349. (8) We conclude that with the non-idealness parameters and with the introduction of artificial viscosity (K = 0.00349, 0.0349 and 0.349) the excitation of oscillations in the molecules dampen and the smoothness in the profiles increases.…”

“…The viscosity term suggested by is included into the hydrodynamic equations for spherically symmetric flow in magnetogasdynamics regime, can be written in Eulerian form [8,14,20,25,26,27] where r and t are independent space and time coordinates ρ, u, p, q and e are density, velocity, pressure, artificial viscosity and internal energy per unit mass respectively and h = µH 2 2 is the magnetic pressure, H and µ being magnetic field strength and the magnetic permeability respectively. The shock position is given by R s (t) and its velocity D = dR s (t)…”

Similarity solution for laser-driven shock waves in a dust-laden gas with internal heat transfer effects

“…Results are obtained for a spherical variable-energy wave over the complete physical range of possibilities for the energy-input parameter, from ÿ = 0 to an upper limit. Some of these results are compared with the adiabatic solutions presented in our previous paper (Gretler and Regenfelder, 2001).…”

“…Narasimhulu Naidu et al (1985) Laumbach and Probstein (1969). Recently, Gretler and Regenfelder (2001) provided a similarity solution for a laser-driven strong shock wave in a mixture of gas and small solid particles for adiabatic ow. As in the present study, this radiation-driven shock wave can be generated by a number of lasers focused on a common plane, line or point; a sudden breakdown at the centre of the irradiated region then causes an exploding plane, cylindrical or spherical shock wave.…”

Numerical study of shock waves in non-ideal magnetogasdynamics (MHD)

“…The non-steady one dimensional flow is a function of two independent variables the time t and the space coordinate r. The conservation equations governing the flow can be written as [12,[16][17][18][19][20] @q @t þ u @q @r þ q @u @r þ ðm À 1Þqu r ¼ 0 ð1Þ @u @t þ u @u @r þ q À1 @p @r þ @h @r ¼ 0 ð2Þ @p @t þ u @p @r À a 2 @q @t þ u @q @r ¼ 0 ð3Þ…”