Pebble-bed nuclear reactor technology, which is currently being revived around the world, raises fundamental questions about dense granular flow in silos. A typical reactor core is composed of graphite fuel pebbles, which drain very slowly in a continuous refueling process. Pebble flow is poorly understood and not easily accessible to experiments, and yet it has a major impact on reactor physics. To address this problem, we perform full-scale, discrete-element simulations in realistic geometries, with up to 440,000 frictional, viscoelastic 6cm-diameter spheres draining in a cylindrical vessel of diameter 3.5m and height 10m with bottom funnels angled at 30• or 60• . We also simulate a bidisperse core with a dynamic central column of smaller graphite moderator pebbles and show that little mixing occurs down to a 1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local ordering and porosity (from Voronoi volumes), the residence-time distribution, and the effects of wall friction and discuss implications for reactor design and the basic physics of granular flow.

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow-no-flow boundary is determined for piles of varying heights over a range of inclination angles θ. Three angles determine the phase diagram: θr, the angle of repose, is the angle at which a flowing system comes to rest; θm, the maximum angle of stability, is the inclination required to induce flow in a static system; and θmax is the maximum angle for which stable, steady state flow is observed. In the stable flow region θr < θ < θmax, three flow regimes can be distinguished that depend on how close θ is to θr: i) θ >> θr: Bagnold rheology, characterized by a mean particle velocity vx in the direction of flow that scales as vx ∝ h 3/2 , for a pile of height h, ii) θ > ∼ θr: the slow flow regime, characterized by a linear velocity profile with depth, and iii) θ ≈ θr: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming. 46.55.+d, 45.70.Cc,

Simulated granular packings with different particle friction coefficient are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P( f ) are computed and compared with existing experimental data. Here f ϵF/F is the contact force F normalized by the average value F . P( f ) exhibits exponential-like decay at large forces, a plateau/peak near f ϭ1, with additional features at forces smaller than the average that depend on . Additional information beyond the one-point force distribution functions is provided in the form of the force-force spatial distribution function and the contact point radial distribution function. These quantities indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three-dimensional, unloaded packings.

The structure and stresses of static granular packs in cylindrical containers are studied by using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth independent for deep piles and we compare these stress depth profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen, while particle-particle contacts in the bulk are far from the Coulomb criterion. In addition, we show that a linear hydrostaticlike region at the top of the packings unexplained by the Janssen theory arises because most of the particle-wall tangential forces in this region are far from the Coulomb yield criterion. The distributions of particle-particle and particle-wall contact forces P(f) exhibit exponential-like decay at large forces in agreement with previous studies.