Random-walk approach to granular flows

Subdiffusion model for granular discharge in a submerged silo

Silo discharge has been extensively studied for decades although questions remain regarding the nature of the velocity field, particularly for submerged systems. In this work, fluid-driven granular drainage was performed in a quasi-two-dimensional silo with grains submerged in fluid. While the observed Gaussian velocity profiles were generally consistent with current diffusion models, the diffusion length was found to significantly decrease with height in contrast to the increases previously seen in dry silos. We propose a phenomenological anomalous diffusion model for the spreading of the flow upwards in the cell, with the fluid-driven flows we study here falling in the category of subdiffusive behavior. As the viscous characteristics of the system were amplified, the diffusion length increased and the shape of the flowing zone in the silo changed, deviating further from the parabolic form predicted by traditional normal diffusion models, in effect becoming more subdiffusive as quantified by a decreasing diffusion exponent.

Some Movement Mechanisms and Characteristics in Pebble Bed Reactor

The pebblebed-type high temperature gas-cooled reactor is considered to be one of the promising solutions for generation IV advanced reactors, and the two-region arranged reactor core can enhance its advantages by flattening neutron flux. However, this application is held back by the existence of mixing zone between central and peripheral regions, which results from pebbles’ dispersion motions. In this study, experiments have been carried out to study the dispersion phenomenon, and the variation of dispersion region and radial distribution of pebbles in the specifically shaped flow field are shown. Most importantly, the standard deviation of pebbles’ radial positions in dispersion region, as a quantitative index to describe the size of dispersion region, is gotten through statistical analysis. Besides, discrete element method has been utilized to analyze the parameter influence on dispersion region, and this practice offers some strategies to eliminate or reduce mixing zone in practical reactors.

Molecular dynamics simulation for PBR pebble tracking simulation via a random walk approach using Monte Carlo simulation

Using a Monte Carlo (MC) simulation, random walks were used for pebble tracking in a two-dimensional geometry in the presence of a biased gravity field. We investigated the effect of viscosity damping in the presence of random Gaussian fluctuations. The particle tracks were generated by Molecular Dynamics (MD) simulation for a Pebble Bed Reactor. The MD simulations were conducted in the interaction of noncohesive Hertz-Mindlin theory where the random walk MC simulation has a correlation with the MD simulation. This treatment can easily be extended to include the generation of transient gamma-ray spectra from a single pebble that contains a radioactive tracer. Then the inverse analysis thereof could be made to determine the uncertainty of the realistic measurement of transient positions of that pebble by any given radiation detection system designed for that purpose.

Physical test of a particle simulation model in a sheared granular system

We report a detailed comparison of a slow gravity-driven sheared granular flow with a discrete-element simulation performed in the same geometry. In the experiments, grains flow inside a silo with a rectangular cross section and are sheared by a rough boundary on one side and smooth boundaries on the other sides. Individual grain position and motion are measured using a particle index-matching imaging technique where a fluorescent dye is added to the interstitial liquid which has the same refractive index as the glass beads. The simulations use a Cundall-Strack contact model between the grains using contact parameters that have been used in many other previous studies and ignore the hydrodynamic effects of the interstitial liquid. Computations are performed to understand the effect of particle coefficient of friction, elasticity, contact model, and polydispersity on mean flow properties. We then perform a detailed comparison of the particle fluctuation properties as measured by the displacement probability distribution function and the mean square displacement. All in all, our study suggests a high level of quantitative agreement between the simulations and experiments.

Diffusion and mixing in gravity-driven dense granular flows

We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Péclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with long-lasting contacts but not thermal collisions, as in normal fluids.

Size segregation of granular matter in silo discharges

We present an experimental study of segregation of granular matter in a quasi-two-dimensional silo emptying out of an orifice. Size separation is observed when multisized particles are used with the larger particles found in the center of the silo in the region of fastest flow. We use imaging to study the flow inside the silo and quantitatively measure the concentration profiles of bidisperse beads as a function of position and time. The angle of the surface is given by the angle of repose of the particles, and the flow occurs in a few layers only near the top of this inclined surface. The flowing region becomes deeper near the center of the silo and is confined to a parabolic region centered at the orifice which is approximately described by the kinematic model. The experimental evidence suggests that the segregation occurs on the surface and not in the flow deep inside the silo where velocity gradients also are present. We report the time development of the concentrations of the bidisperse particles as a function of size ratios, flow rate, and the ratio of initial mixture. The qualitative aspects of the observed phenomena may be explained by a void filling model of segregation.

Physics of the Granular State

Granular materials display a variety of behaviors that are in many ways different from those of other substances. They cannot be easily classified as either solids or liquids. This has prompted the generation of analogies between the physics found in a simple sandpile and that found in complicated microscopic systems, such as flux motion in superconductors or spin glasses. Recently, the unusual behavior of granular systems has led to a number of new theories and to a new era of experimentation on granular systems.