Effects of particle volume on the structure of a partly dispersed normal shock wave in a dusty gas

The structure of a partly dispersed shock wave in a steady, one-dimensional flow of a dusty gas is studied in depth, including the frozen flow just behind the leading gas shocks, nonequilibrium flow in the relaxation zone, and final equilibrium flow. Particle volume effects, which are normally important only if the particles are numerous and/or have a low density, are included more fully in the present analysis than in previous studies. As an example, the effects of virtual mass of the particles is included and assessed for the first time. Including the effects of particle volume more completely has yielded a new equation for the frozen sound speed, a better definition of the frozen shock Mach number, and a more accurate dividing line between fully and partly dispersed shock waves in dusty gases. Also, simpler and more elegant expressions have been obtained for the equilibrium-flow properties, in a more classic form as modified Rankine-Hugoniot equations.