Time evolution of discontinuities at the wave head in a non-equilibrium two-phase flow of a mixture of a gas and dusty particles

Abstract

The behavior of weak discontinuities in a non-equilibrium flow of a mixture of a gas and small dusty particles is analysed using the singular surface theory. The propagation velocity of these weak waves, “a”, is determined and is shown to agree with the ordinary gasdynamic results in a limit of vanishingz, the volume fraction of the solid particles in the mixture. The differential equation governing the growth and decay of weak discontinuities is derived and solved both analytically and numerically. Using a representative set of data for the upstream flow, it is shown that all expansive waves are ultimately damped, whereas not all compressive waves grow into shock waves. The effect of the volume fraction of the solid particles and the wave front curvature are to enhance the flattening rate of an expansive wave and to diminish the steeping rate of a compressive wave.