A shock wave which is incident onto a gas-particle mixture or initiated within such a mixture needs a certain distance to reach a constant velocity. This effect is due to the inertia and the heat capacity of the particles. In general the shock wave is decelerated and the frozen pressure jump is decaying.

The unsteadiness of shock waves propagating through gas-particle mixtures

The flow resulting from the passage of a shock wave through a dusty-gas layer is studied theoretically. On the basis of an idealized equilibrium-gas approximation, the criteria for the wave reflexion at the contact surface separating the pure gas from the dusty-gas layer are obtained in terms of the properties of the gas and the dusty gas. For the cases treated here, a shock wave is reflected at the first contact surface and a shock wave stronger than the incident one is transmitted into the dusty-air layer. Subsequently, a rarefaction wave is reflected at the second contact surface and the shock wave transmitted into the free air is weakened by this nonlinear interaction. The induced rarefaction wave reflects later at the first contact surface as a compression wave, which runs through the layer to overtake the transmitted shock wave in air. The final emergent shock wave from the dusty air has almost the same strength as the original shock wave entering the layer. The time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator-splitting technique.

On the passage of a shock wave through a dusty-gas layer

On the passage of a shock wave through dusty-gas layer

Analytical and numerical methods were used to investigate the flow in­duced by a shock wave in a shock-tube channel containing air laden with suspended small solid particles. Exact results are given for the frozen and equilibrium shock-wave properties as a function of diaphragm-pressure ratio and shock-wave Mach numbers. The driver contained air at high pressure. A modified random-choice method together with an operator-splitting technique show clearly both the decay of a discontinuous frozen shock wave and a contact discontinuity, and the formation of a stationary shock structure and an effective contact front of finite thickness. The effects of particle diameter, particle-number density and diaphragm- pressure ratio on the transitional behaviour of the flow are investigated in detail. The alteration of the flow properties owing to the presence of particles is discussed thoroughly and compared with classical shock-tube flows.

On a dusty-gas shock tube

The flow resulting from the impulsive motion of a piston moving at constant speed in a dusty gas is studied analytically and numerically. An idealized equilibrium-gas approximation is used to discuss the effects of piston speed and mass concentration of dust particles on the eventually formed shock wave. The detailed time-dependent change of the flow structure is studied by solving the equations of motion numerically. A partly dispersed shock-wave structure is formed at a high piston speed and a fully dispersed shock at a low piston speed. Two situations are considered, where the particles striking the piston experience an elastic collision, or where they stick to its surface. Significant effects on the flow produced by particles that reflect from the piston surface are discussed and clarified.

Development of the Flow Induced by a Piston Moving Impulsively in a Dusty Gas

The structures and the behaviors of shock waves propagating through a gas and solid particle mixture are studied by shock-tube experiments and by two methods of wave analysis. The shock waves concerned are incident on the mixture dispersed uniformly in downstream part of the driven section. Pressures and shock velocities are measured under the condition that the particle loading ratio and the shock Mach number are both less than two. The final equilibrium pressures behind the waves and the velocities of the fully decayed shock fronts agree well respectively with the results of the usual shock theory on the mixture and those of the model analysis on a perfect "effective" gas. The analysis by the method of characteristics is satisfactorily applied to give a good explanation of the observed process whereby a shock wave decays to a weak wave with continuous wave form. And, the authors point out some problems relating to the relaxation process and some inconsistencies of the "effective" gas theory when analyzing the unsteady wave motions.

Hiroomi Morii

Papers

Experiments and Analyses on Shock Waves Propagating through a Gas-Particle Mixture