Dependence of Shock Characteristics on Droplet Size in Supersonic Two-Phase Mixtures

Abstract

In a dispersed two-phase flow, the mixture chokes at a velocity well below the vapor choking velocity, as shown by the velocity at the throat of a converging-diverging, two-phase, supersonic nozzle. The formation and abruptness of a normal shock wave in a two-phase mixture depends strongly on the coupling between phases, particularly upon droplet size. As droplet size becomes small, the mixture behaves as a continuum, and sharp discontinuities can occur at velocities above the two-phase choking velocity but below the vapor sonic velocity. An approximate analysis is performed to incidate the droplet size at which continuum behavior might be expected to occur. A numerical model, which includes the drag, buoyancy, Basset force, and the force associated with the virtual mass effect, is used to show droplet-size dependence in two-phase normal shock waves. For the examples presented, continuum behavior apparently is approached at droplet diameters between 1 and 2 μm, even through normal shock waves.