Variable-energy Blast Waves Generated by a Piston Moving in a Dusty Gas

Abstract

This paper presents a similarity solution for strong blast waves of variable energy propagating in a dusty gas. It is assumed that the equilibrium-flow condition is maintained and the variable energy input is supplied by a driving piston or surface according to a time-dependent power law. Three cases have been investigated: Case I corresponds to a decelerated piston, Case II to a piston of constant velocity, and Case III to a continuously accelerated piston starting from rest. Except in the case of constant front velocity, the similarity solution is valid for adiabatic flow as long as the effect of the counter-pressure is neglected. The effects of a parameter characterizing the various energy input of the blast wave on the similarity solution 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. Tables and graphs of numerical results are presented and discussed.

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

“…The value M = 5 of the shock Mach-number is appropriate, because we have treated the flow of a non-ideal gas and a pseudo-fluid (small solid particles) at a velocity and temperature equilibrium. The assumption of velocity and temperature equilibrium may be a good approximation for strong shock waves, because the thickness of the relaxation zone behind the shock front becomes very small for higher Mach-numbers [52]. The set of values d C = 1, d R = 2 is the representative of the case of high-temperature, low-density medium [17].…”

On the Strong Spherical Shock Waves in a Two-Phase Gas–Particle Medium

“…In our investigation the total energy of the flow-field behind the shock front is time dependent and varying according to a power law [11,12,16,17] corresponds to the case in which the total energy increases with time. The nondimensional form of the conservation equations governing an unsteady, spherically symmetric flow-field between spherical shock front and inner expanding surface moving in a two-phase gas-particle medium can be expressed as [11]:…”

“…Gretler and Regenfelder [11] presented a similarity solution for strong blast waves of variable energy propagating in a dusty gas.…”

“…In this paper, the problem studied by Gretler and Regenfelder [11] has been revisited and the solutions for spherical shock wave with time dependent variable energy propagating in two-phase gasparticle medium has been presented in the form of power series. The power series solutions have been obtained in terms of 2 − M , wheres M is the upstream shock Mach number, taking into consideration the power series solution technique [4,12].…”

A Priori Estimates and Analytical Construction of Radially Symmetric Solutions in the Gas Dynamics

“…Very often only the case of a perfect polytropic gas satisfying the sate law pv = RT is considered. However, in numerous phenomenon such as cavitation or sonoluminescence [2,4] or considering a dusty gas [7,9,19,24,25], it seems more adapted to consider at least a Van der Waals gas satisfying p(v − b) = RT . We prove results in this more general framework.…”