High-Performance Computing of Flow, Diffusion, and Hydrodynamic Dispersion in Random Sphere Packings

This thesis is dedicated to the study of mass transport processes (flow, diffusion, and hydrodynamic dispersion) in computer-generated random sphere packings. Periodic and confined packings of hard impermeable spheres were generated using Jodrey–Tory and Monte Carlo procedure-based algorithms, mass transport in the packing void space was simulated using the lattice Boltzmann and random walk particle tracking methods. Simulation codes written in C programming language using MPI library allowed an efficient use of the high-performance computing systems (supercomputers). The first part of this thesis investigates the influence of the cross-sectional geometry of the confined random sphere packings on the hydrodynamic dispersion. Packings with different values of porosity (interstitial void space fraction) generated in containers of circular, quadratic, rectangular, trapezoidal, and irregular (reconstructed) geometries were studied, and resulting pre-asymptotic and close-to-asymptotic hydrodynamic dispersion coefficients were analyzed. It was demonstrated i) a significant impact of the cross-sectional geometry and porosity on the hydrodynamic dispersion coefficients, and ii) reduction of the symmetry of the cross section results in longer times to reach close-to-asymptotic values and larger absolute values of the hydrodynamic dispersion coefficients. In case of reconstructed geometry, good agreement with experimental data was found. In the second part of this thesis i) length scales of heterogeneity persistent in unconfined and confined sphere packings were analyzed and correlated with a time behavior of the hydrodynamic dispersion coefficients; close-to-asymptotic values of the dispersion coefficients (expressed in terms of plate height) were successfully fitted to the generalized Giddings equation; ii) influence of the packing microstructural disorder on the effective diffusion and hydrodynamic dispersion coefficients was investigated and clear qualitative corellation with geometrical descriptors (which are based on Delaunay and Voronoi spatial tessellations) was demonstrated

Dynamic triangulations for efficient 3D simulation of granular materials

Granular materials are omnipresent in many fields ranging from civil engineering to food, mining and pharmaceutical industries. Often considered a fourth state of matter, they exhibit specific phenomena such as segregation, arching effects, pattern formation, etc. Due to its potential capability of realistically rendering these behaviors, the Distinct Element Method (DEM) is a very enticing simulation technique. Indeed it makes it possible to analyze and observe phenomena that are barely if at all accessible experimentally. DEM works by tracking every particle in the system individually, maintaining for each a trajectory influenced by external factors such as gravitation or contacts with boundary objects and by the interactions with other grains. The mathematical problem of identifying pairs of grains that interact and locating precisely where the contact occurs is highly dependent on the shape of the grains. We focus in this thesis on 3D spherical grains and use dynamic weighted Delaunay triangulations to track the collisions. The triangulation is built on the centers of the grains and evolves to follow their motion. We prove that all potentially colliding pairs of spheres are adjacent in the triangulation. As there are 6n to 8n edges for n spheres in most practical cases, the complexity of the collision detection becomes linear instead of quadratic in the number of particles, with a small overhead in maintaining the triangulation with efficient local operations. For the physical problem of realistically rendering the collision in a numerical contact model suitable for computer simulation, we have used widely accepted theories such as the viscoelastic model of Cundall, but have also tested some recent, more sophisticated developments in the field. The collision detection and contact models have been implemented in a modular DEM simulation code with advanced features in data structures storing the triangulation, in numerical robustness of the geometric computations, and in parallel processing on shared memory computers. Optimal packing of powders is important in many industrial processes, yet no theoretical result exists when dealing with grains of different sizes. We have performed simulations of such cases and could compare our results with experimental data. Preliminary results have been obtained regarding the relation between the size and proportion of grains and the density of the packing. Other simulations have also been performed, such as the granular flow through an hourglass. As no efficient simulation method is currently known for non-spherical 3D grains, we propose an intermediate approach of gluing spheres together into arbitrary shaped clusters and show some examples based on this approach

A Collective Dynamics-based Method for Initial Pebble Packing

ABSTRACT In the simulation of pebble flow in Pebble Bed Reactors (PBR), high-fidelity methods, such as Discrete Element Methods (DEM) and Computational Fluid Dynamics (CFD) methods, are usually employed to simulate the dynamic process of pebbles circulation, accounting for the pebble-to-pebble, pebble-to-reflector wall and pebble-to-fluid interactions. To obtain a realistic model of pebble distribution around dynamic equilibrium state of pebble flow, the simulation based on high-fidelity methods normally resists brute force computation. However, if an initial dense packing of pebbles can be provided, which is close to realistic packing at equilibrium state and can be easily implemented without much computational effort, the long time high-fidelity simulation can be considerably more efficient and take much less time to reach dynamic equilibrium state. In this paper, a collective arrangement method based on a dynamics model is developed to generate an initial pebble distribution at a quasi-equilibrium state. In the new method, pebble positions are generated firstly by a fast sequential process in the full core allowing overlapping, and then a simplified normal contact force model is adopted in the initialization for eliminating the pebble overlap. The adopted model provides an adaptive way to account for the situations in which multiple pebbles are overlapped and different contact forces should be applied for different ratios of overlapping depth and sphere size, thus speeding up the initialization without loss of reliability and making the approach feasible for variable size sphere packing. Moreover, an intermittent vibration function, as an optional process, can be provided to further densify the packing depending on different applications. Comparisons with other existing random packing methods for initialization are made. It is shown that the developed method not only exhibits unique significance and good computation efficiency in speeding up the pebble flow simulation, but also presents desirable potential in other applications as a general packing algorithm for packing uniform-or variable-size spheres in a large container

On the behavior of spherical and non-spherical grain assemblies, its modeling and numerical simulation

This thesis deals with the numerical modeling and simulation of granular media with large populations of non-spherical particles. Granular media are highly pervasive in nature and play an important role in technology. They are present in fields as diverse as civil engineering, food processing, and the pharmaceutical industry. For the physicist, they raise many challenging questions. They can behave like solids, as well as liquids or even gases and at times as none of these. Indeed, phenomena like granular segregation, arching effects or pattern formation are specific to granular media, hence often they are considered as a fourth state of matter. Around the turn of the century, the increasing availability of large computers made it possible to start investigating granular matter by using numerical modeling and simulation. Most numerical models were originally designed to handle spherical particles. However, making it possible to process non-spherical particles has turned out to be of utmost importance. Indeed, it is such grains that one finds in nature and many important phenomena cannot be reproduced just using spherical grains. This is the motivation for the research of the present thesis. Subjects in several fields are involved. The geometrical modeling of the particles and the simulation methods require discrete geometry results. A wide range of particle shapes is proposed. Those shapes, spheropolyhedra, are Minkowski sums of polyhedra and spheres and can be seen as smoothed polyhedra. Next, a contact detection algorithm is proposed that uses triangulations. This algorithm is a generalization of a method already available for spheres. It turns out that this algorithm relies on a positive answer to an open problem of computational geometry, the connectivity of the flip-graph of all triangulations. In this thesis it has been shown that the flip-graph of regular triangulations that share a same vertex set is connected. The modeling of contacts requires physics. Again the contact model we propose is based on the existing molecular dynamics model for contacts between spheres. Those models turn out to be easily generalizable to smoothed polyhedra, which further motivates this choice of particle shape. The implementation of those methods requires computer science. An implementation of this simulation methods for granular media composed of non-spherical particles was carried out based on the existing C++ code by J.-A. Ferrez that originally handled spherical particles. The resulting simulation code was used to gain insight into the behavior of granular matter. Three experiments are presented that have been numerically carried out with our models. The first of these experiments deals with the flowability (i. e. the ability to flow) of powders. The flowability of bidisperse bead assemblies was found to depend only on their mass-average diameters. Next, an experiment of vibrating rods inside a cylindrical container shows that under appropriate conditions they will order vertically. Finally, experiments investigating the shape segregation of sheres and spherotetrahedra are perfomed. Unexpectedly they are found to mix

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Self-assembly of granular particles

Granular particles are ubiquitous in nature and daily life, and have wide applications in various disciplines such as infrastructure engineering, architecture, agriculture, etc. Yet, their fundamentals have not been fully understood by scientists. This is mainly because the structure of granular particles, which determines their properties, is complicated and can experience critical changes from disorder to ordered state. In recent years, understanding the fundamentals of such critical structural transitions of granular materials has become a hot multidisciplinary research topic attracting both scientists and engineers. Generally the transition from disordered to ordered structure can be regarded as a self-assembly process, which happens at different scales. In the nucleation of crystals, atoms or molecules can self-assemble due to thermal energy. For such thermodynamics systems, the theory of self-assembly is well established and is dependent on the Gibbs free energy. However, granular particles are much bigger and can dissipate energy quickly with the collision between particles, so they are normally at athermal or low-thermal states. The granular packings are prone to be disordered in structure, whereas they can also self-assemble with the input of external energy via vibration or shear, which can densify the granular packings and hence improve their properties for different applications. This thesis is devoted to advancing the knowledge of the self-assembly of granular spheres, particularly in better understanding the effects of the energy input and the boundary shape. The thesis has revealed a rich and deep picture for the effect of various factors on the self-assembly of granular particles, including the vibration mode, the container shape, material properties, different wall motions and gravity. The obtained results can improve the current understanding of the structural evolution and phase transition of the granular packings with or without vibration. The findings of this study enhance the knowledge on the self-assembly of granular systems and help take a step forward toward stablishing the mechanism behind the phenomenon. Thorough comprehension of the structure of the granular particles are essential for controlling the behaviour and properties of the granular materials, which can be of paramount importance for both the science and technology and have sensible influence on the mankind’s life

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Towards the Glass Transition in Vibrated Granular Matter

Granular materials are large sets of macroscopic particles that interact solely via contact forces. The static behavior depends on the contact network and on the surface friction forces between grains; when they are set in motion (typically by vibrations) their dynamics is dominated by inelastic collisions. For these reasons granular media show an extremely rich phenomenology, ranging from fluid-like properties (if strongly vibrated), to "jamming", glassy, behavior (if weakly vibrated), to aging and hysteretical phenomena observed when they become trapped in frozen, amorphous states. The objective of this work is to study these states and transitions, and to characterize the analogies found between the dynamic behavior of vibrated granular media and the glass transition observed in thermal glass-formers. These analogies justify the interest in granular materials, because granular media can be seen as simplified model systems useful in the study of out of equilibrium thermodynamics, and, in general, to the larger framework known as "complexity". The granular materials considered here are composed of spheric, polished glass spheres. Since the surface state plays an important role in the grain-grain interaction, some measurements were also performed with acid etched beads, having different surface roughness. The samples are vertically vibrated to achieve vibrofluidization. Different kinds of vibration are used, to highlight different properties of the system. We first consider the transition between the fluid and the subcooled glassy phase, using different experimental techniques. The most important one is a torsion oscillator, that interacts with the granular media via immersed probes. The torsion oscillator can be used in forced mode. A torque is applied on the probe, and we measure the mechanical response function (complex susceptibility). In general, a relaxation is found and it is interpreted as the signature of the irreversible energy loss (damping) in granular collisions. This relaxation has an intrinsic time scale, and systematic analysis of it shows that a clear parallel can be traced to the behavior of "strong" glasses. In particular, it is found that (i) the relaxation time is a function of a unified control parameter, proportional to the square root of the average vibration, and phenomenologically equivalent to an effective temperature; (ii) the functional form with which the relaxation times approach the final "frozen" state has an Arrhenius, or Vögel-Fulcher-Tamman (VFT) behavior. The same torsion oscillator is employed in free mode. In this case, no external torque is applied, and the probe moves adapting its position under the effect of the continuous rearrangements in the sample. The system is studied by computing the power spectral density of the (angular position) time series. The resulting spectra represent a "configurational noise" as the system randomly hops from one configuration to the following. This allows to define, using a completely different approach, the same intrinsic time scale observed in forced mode measurements. The comparison of the two techniques allows to obtain a more complete and detailed picture of the dynamics in the jamming region. From this comparison, it was inferred that the system is also influenced by an effective vibration frequency, and that the relaxation time has indeed a non-Arrhenius behavior as a function of a control parameter defined as as = √ Γ/ωs. A model was developed combining rheological observations to a statistic approach describing extremal phenomena. This model justifies the appearance of both the control parameter and the VFT evolution of the relaxation. Furthermore, the model is predictive and exposes the effect of a few other rheologic properties of granular system. The effect of surface roughness are considered, showing that the static and dynamic surface friction coefficients are well described by the model. A second relevant part of this work is devoted to an explicit verification that macroscopic probes act as Brownian objects. This fact is often used to interpret experimental data (also in the present work) and to propose theoretical model. However, no explicit evidence has ever been discussed. This is hard to do, using a constrained system such as the torsion oscillator, because the restoring coefficient influences the dynamics of diffusion. To overcome the problem we built a different apparatus, called "Brownian motor", where the probes are mounted on ball bearings, so that they are free to turn without constraint. The properties of the time series of the position of the free turning probe and of the torsionally constrained oscillator can finally be analyzed and compared with simple simulations. The data show an overall diffusion-like behavior, that is influenced by the presence of constraints. Using fractal analysis we estimate the diffusion, or Hurst exponent. This allows to verify that a "macroscopic" object (the probe) immersed in the "microscopic" granular medium indeed behaves as a Brownian object, and that its dynamics can be studied in detail, showing that it undergoes anomalous diffusion. This work is concluded with a discussion on a few possible developments. The most promising idea is a novel approach to the study of the geometrical properties of the contact network of granular assemblies, that is responsible for many of the properties of the granular sample. By using Magnetic Resonance Imaging, the static 3-D structure of granular media can be reconstructed with unprecedented accuracy, resolution and ease of reproducibility. From the spatial information we can extract all the properties of static granular media: the compaction factor, the grain-grain correlation function, the free volume and other observables. Systematic studies could allow experimental confirmations of the many theoretical models that have been proposed in the last years and that still lack a thorough comparison with experiments. This idea does not conclude the perspectives of this work, that are vast and intriguing. A few promising subjects are reviewed more into detail in the corresponding Perspective section. To name a few we cite: measurements of induced aging in non-vibrated samples, the Brownian motor, stick and slip phenomena and their comparison with earthquakes