Particle Dispersal of Granular Materials in High-Speed Compressible Flow

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This dissertation describes efforts to investigate particle dispersal of granular materials under high-speed flows using a recently proposed continuum model for dense granular materials. The model, based upon the kinetic theory of granular flows (KTGF), is known to perform well for high-speed, compressible flows over a wide range from dense to dilute particle volume fractions. The simulations solve the Euler equations of fluid dynamics and granular flow, and account for multiple particle types using a binning approach, where particles in each bin have their own uniform particle size and density. This model is then applied to two configurations (a) dust-lifting induced by shock waves, and (b) subsurface explosions in granular materials. These two examples are used to underpin a thorough discussion of particle motions under high-speed flow.

The first study discusses the phenomenon of dust lifting behind a moving shock wave in which the conditions are characteristic of what is found in a coal mine. Specifically, we are interested in the factors influencing the level of dust dispersion, and the particle segregation phenomenon between different types of particles within the dust layer. First, we investigated the case of a shock wave passing over a single dust layer containing two uniformly mixed particle types. Effects of particle size and density were studied in terms of the governing forces acting on each particle type. The results indicate that larger particles are lifted higher than smaller particles, and lighter particles are

lifted higher than heavier particles due to the differences in lift and drag forces. Then, simulations of a shock passing over stratified dust layers containing different types of particles were performed. We find that the larger particles placed in the lower layer can be lifted higher than the smaller particles placed in the upper layer when the two types of particles have large size differences. These results provide important information that can be used to determine how to prevent and mitigate a dust explosion in underground

coal mines.

The second study discusses particle ejections from a subsurface explosion in the conditions similar to that of a comet. A preliminary one-dimensional computation describes the structure of a granular shock formed from a spherical explosion. The two-dimensional axisymmetric calculations show that the explosion creates a cavity in the granular phase, and this cavity expands radially until it breaks through the surface. The blast wave created during the explosion initiates particle motions and forms a granular shock. The particles are initially entrained by the gas flow and then move by the granular shock. We demonstrate that there is a power-law relation between the explosion radius and time, and that this result is consistent with the blast-wave theory. At lower background temperatures, the velocities of both phases decrease, and this leads to more compact structures in the granular phase.