A stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation

Analysis of Granular Flow in a Pebble-Bed Nuclear Reactor

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 degrees or 60 degrees. 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.Comment: 18 pages, 21 figure

Second All-Union Seminar on Hydromechanics and Heat and Mass Exchange in Weightlessness, summaries of reports

Abstracts of reports are given which were presented at the Second All Union Seminar on Hydromechanics and Heat-Mass Transfer in Weightlessness. Topics include: (1) features of crystallization of semiconductor materials under conditions of microacceleration; (2) experimental results of crystallization of solid solutions of CDTE-HGTE under conditions of weightlessness; (3) impurities in crystals cultivated under conditions of weightlessness; and (4) a numerical investigation of the distribution of impurities during guided crystallization of a melt

Study on SPH Viscosity Term Formulations

For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified

Numerical investigation of freak wave effects on offshore structures

The freak wave is extremely dangerous to offshore structures due to its unexpected high wave height and strong nonlinearity. Although increasingly more attention is paid to the investigations of freak wave, the principle of its generation mechanism and the factors that contribute to its occurrence remain unclear. Also, few efforts were exerted to investigate the interactions between offshore structures and a freak wave such as wave run-up and slamming force. In this present work, both the two dimensional (2D) and three dimensional (3D) numerical wave tanks are established based on Navier-Stokes equations for viscous, incompressible fluid by CFD commercial software FLUENT.;At first, the regular waves are generated numerically. Two different wave generation methods, paddle wave making method and the source function wave making method, are introduced. The paddle wave-making method is a physical wave generation technology which is to imitate the wave makers in the laboratory. The source function wave-making method is discussed later and the empirical formulas of the source size and source intensity are introduced. The numerical wave elevations are compared with the linear analytical results.;Second, the freak waves are generated numerically. According to Longuet-Higgins wave model theory, the wave free surface can be represented by the linear sum of the individual wave components with different frequencies and random phases. Improving this wave model, the wave components have their phase adjusted, so that a large amount of energy is located at the focus position at a given time. Then two more efficient and realistic freak wave models are presented, combining wave models and phase modulation wave models, respectively. Finally, the numerical results of the shift of freak wave train focusing position and focusing time are analysed, and the time history of wave elevations are compared with the analytical results.;Third, a 3-D numerical wave tank is established to perform the interactions between a freak wave train and a single cylinder or a pair of two cylinders. How the focused wave parameters, including wave steepness, frequency bandwidth, focused position and the distance between the two cylinders, affect the freak wave run-up and total slamming forces on the cylinders are investigated.;Finally, the hydrodynamic behaviour of a rectangular body in roll motions under both freak wave excitation and internal flow sloshing is investigated in a CFD numerical wave tank. In this study, three different freak wave conditions are considered, and two different water levels are investigated.;The comparisons of numerical regular wave elevations and first order analytical results show that the current CFD numerical wave tank based on computational fluid dynamic commercial software FLUENT has a good capacity in sea water waves simulation. The focused wave parameters, such as frequency bandwidth and input wave steepness, have an obvious effect on the nonlinear behaviour of a focused wave group.;This nonlinear behaviour will not only downstream shift the focused position and focused time, but also change the wave elevation at the focused position largely. The increased nonlinear behaviour of a focused wave group will increase the wave run-up along a fixed vertical cylinder at the incident wave facing direction largely. The bigger nonlinear behaviour of a focused wave group can result in larger rolling motion amplitude for a floating rectangular body, however the anti-rolling behaviour is obvious for the low filling case.The freak wave is extremely dangerous to offshore structures due to its unexpected high wave height and strong nonlinearity. Although increasingly more attention is paid to the investigations of freak wave, the principle of its generation mechanism and the factors that contribute to its occurrence remain unclear. Also, few efforts were exerted to investigate the interactions between offshore structures and a freak wave such as wave run-up and slamming force. In this present work, both the two dimensional (2D) and three dimensional (3D) numerical wave tanks are established based on Navier-Stokes equations for viscous, incompressible fluid by CFD commercial software FLUENT.;At first, the regular waves are generated numerically. Two different wave generation methods, paddle wave making method and the source function wave making method, are introduced. The paddle wave-making method is a physical wave generation technology which is to imitate the wave makers in the laboratory. The source function wave-making method is discussed later and the empirical formulas of the source size and source intensity are introduced. The numerical wave elevations are compared with the linear analytical results.;Second, the freak waves are generated numerically. According to Longuet-Higgins wave model theory, the wave free surface can be represented by the linear sum of the individual wave components with different frequencies and random phases. Improving this wave model, the wave components have their phase adjusted, so that a large amount of energy is located at the focus position at a given time. Then two more efficient and realistic freak wave models are presented, combining wave models and phase modulation wave models, respectively. Finally, the numerical results of the shift of freak wave train focusing position and focusing time are analysed, and the time history of wave elevations are compared with the analytical results.;Third, a 3-D numerical wave tank is established to perform the interactions between a freak wave train and a single cylinder or a pair of two cylinders. How the focused wave parameters, including wave steepness, frequency bandwidth, focused position and the distance between the two cylinders, affect the freak wave run-up and total slamming forces on the cylinders are investigated.;Finally, the hydrodynamic behaviour of a rectangular body in roll motions under both freak wave excitation and internal flow sloshing is investigated in a CFD numerical wave tank. In this study, three different freak wave conditions are considered, and two different water levels are investigated.;The comparisons of numerical regular wave elevations and first order analytical results show that the current CFD numerical wave tank based on computational fluid dynamic commercial software FLUENT has a good capacity in sea water waves simulation. The focused wave parameters, such as frequency bandwidth and input wave steepness, have an obvious effect on the nonlinear behaviour of a focused wave group.;This nonlinear behaviour will not only downstream shift the focused position and focused time, but also change the wave elevation at the focused position largely. The increased nonlinear behaviour of a focused wave group will increase the wave run-up along a fixed vertical cylinder at the incident wave facing direction largely. The bigger nonlinear behaviour of a focused wave group can result in larger rolling motion amplitude for a floating rectangular body, however the anti-rolling behaviour is obvious for the low filling case

Modeling the wind circulation around mills with a Lagrangian stochastic approach

This work aims at introducing model methodology and numerical studies related to a Lagrangian stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian stochastic downscaling method that we have introduced in [3] and [4] to the atmospheric boundary layer and we introduce here a Lagrangian version of the actuator disc methods to take account of the mills. We present our numerical method and numerical experiments in the case of non rotating and rotating actuator disc models. We also present some features of our numerical method, in particular the computation of the probability distribution of the wind in the wake zone, as a byproduct of the fluid particle model and the associated PDF method