The dynamics of dense particle clouds subjected to shock waves. Part 1. Experiments and scaling laws
2016
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.
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