The dynamics of dense particle clouds subjected to shock waves. Part 1. Experiments and scaling laws

Abstract

We quantify experimentally the dispersal characteristics of dense particle clouds in high-speed interactions with an atmosphere. Focused on the fundamentals, the experiments, conducted in a large-scale shock tube, involve a well-characterized ‘curtain’ of (falling) particles that fully occupies the cross-sectional area of the expansion section. The particle material (glass) and size (${\sim}$1 mm) are fixed, as is the curtain thickness (${\sim}$30 mm) and the particle volume fractions in it, varying from ${\sim}$58 % at the top of the curtain to ${\sim}$24 % near the bottom. Thus, the principal experimental variable is the impacting shock strength, with Mach numbers varying from 1.2 to 2.6, and flow speeds that cover from subsonic ($M_{IS}\sim 0.3$) to transonic and supersonic ($M_{IS}\sim 1.2$). The peak shock pressure ratio, 7.6, yields a flow speed of ${\sim}\!630~\text{m}~\text{s}^{-1}$, and a curtain expansion rate at ${\sim}$20 000 g. We record visually (high-speed, particle-resolving shadowgraphic method) the reflected/transmitted pressure waves and the transmitted contact wave, as well as the curtain displacements, and we measure the reflected/transmitted pressure transients. Data analysis yields simple rules for the amplitudes of the reflected pressure waves and the rapid cloud expansions observed, and we discover a time scaling that hints at a universal regime for cloud expansion. The data and these data-analysis results can provide the validation basis for numerical simulations meant to enable a deeper understanding of the key physics that drive this rather complex dispersal process.