An Analytical and Numerical Study of Granular Flows in Hoppers PDF Download
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Languages : en
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This work investigates the characteristics of a steady state flow of granular material, under the influence of gravity, in two and three dimensional hoppers of simple geometry. Simulations of such flows are of particular interest to various industries, such as the foodand mining industries, where the handling of large quantities of granular materials in hop-persand silos is routine. While understanding and simulation of time-dependent phenomenaare the ultimate goals in this field, those phenomena are still poorly understood and thustheir study is beyond the scope of this research. It has been observed that steady flowscan provide reasonable approximations, and the corresponding steady state model has con-sequentlybeen the focus of a great deal of research. Historically, these steady state modelshave been approached using only smooth radial fields, and even today most practical hop-perdesign uses these fields as their basis. Our work represents the first time that qualitynumerical methods have been brought to bear on the model equations in their original form, without assuming smoothness of the resulting fields. Two different, yet related, models forstress/velocity consisting of systems of hyperbolic conservation laws and algebraic relationsare considered and discussed. The radial stress and velocity fields, and the stability of thosefields, are studied briefly with both analytical and numerical results presented. More im-portantly, a Runge-Kutta Discontinuous Galerkin method is implemented and applied tovarious boundary value problems involving perturbed stress and velocity fields arising fromdiscontinuous changes in parameters such as hopper wall angle or hopper wall friction.
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Languages : en
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Book Description
This work investigates the characteristics of a steady state flow of granular material, under the influence of gravity, in two and three dimensional hoppers of simple geometry. Simulations of such flows are of particular interest to various industries, such as the foodand mining industries, where the handling of large quantities of granular materials in hop-persand silos is routine. While understanding and simulation of time-dependent phenomenaare the ultimate goals in this field, those phenomena are still poorly understood and thustheir study is beyond the scope of this research. It has been observed that steady flowscan provide reasonable approximations, and the corresponding steady state model has con-sequentlybeen the focus of a great deal of research. Historically, these steady state modelshave been approached using only smooth radial fields, and even today most practical hop-perdesign uses these fields as their basis. Our work represents the first time that qualitynumerical methods have been brought to bear on the model equations in their original form, without assuming smoothness of the resulting fields. Two different, yet related, models forstress/velocity consisting of systems of hyperbolic conservation laws and algebraic relationsare considered and discussed. The radial stress and velocity fields, and the stability of thosefields, are studied briefly with both analytical and numerical results presented. More im-portantly, a Runge-Kutta Discontinuous Galerkin method is implemented and applied tovarious boundary value problems involving perturbed stress and velocity fields arising fromdiscontinuous changes in parameters such as hopper wall angle or hopper wall friction.
Author: John V. Matthews
Publisher:
ISBN:
Category :
Languages : en
Pages : 77
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Keywords: Granular flows, Hyperbolic, Partial differential equations, Discontinuous Galerkin, Runge-Kutta.
Author: Feng Wang
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 142
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Languages : en
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We study elastoplastic transitions in solutions of the antiplane shear model of granular flow, and describe a time-periodic solution that arises when the antiplane shear model is discretized in space. The antiplane shear model is a simplification of the continuum equations representing the flow of granular materials. The modeling of granular flow has many applications, from agricultural silos to geomechanics: improved accuracy in modeling will lead to safer and more economical designs for silos and industrial hoppers, and make oil drilling a more efficient process. We construct approximate solutions to the antiplane shear model with piecewise linear initial data, which feature transitions between elastic and plastic states. These transitions travel with fixed speed. Numerical simulations demonstrate that the same elastoplastic transitions are the prominent features of the numerical solution. The periodic solution of discretized antiplane shear appears at a critical value of the elasticity parameter for antiplane shear. The bifurcation to a periodic solution appears to be a Hopf bifurcation. The periodic solution contains elastoplastic transitions, as well as a shear band that appears over part of the period. Away from the shear band, the periodic solution has four distinct regions, three elastic and one plastic. Refinement of the spatial discretization further resolves these states.
Author: Shirin Shiri
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Languages : en
Pages :
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Book Description
Granular materials are abundant in nature and industries, and their flow has been subjected to various experimental, analytical and numerical studies over the last decades. The granular flow applications is extended from sorting, packing, and transporting grains and pharmaceutical particles to the study of avalanches and soil erosion. Most of the studies focused on spherical grains. However, most grains in actual applications are geometrically ellipsoidal. Despite being common, the behaviour of the ellipsoidal grains and their response to the flow remain challenging to predict since their ellipsoidal shape brings the effect of the grain orientation to their mechanical response, which has been ignored in most studies. To study the tendency of ellipsoidal grains to align, this work first investigates the performance of a kinematic model that relates the flow to the evolution of the grain alignment. This is done by performing a numerical analysis for discharging ellipsoidal grains in a flat bottom hopper with various opening sizes. After that, two model parameters that can determine the tendency to align and the misalignment of the grains due to collision are generalized according to the shape of the grains and the level of the mutual alignments that is called the ordering factor. These two model parameters should be used along with the model to capture the effect of the grain orientation. The validity of the generalized model is supported by applying it in discharging prolate (rice) and oblate (lentil) grains from a flat bottom hopper and then comparing the outcome with the available experimental results. To reveal the improvement of the generalized model compared to the original model, the differences of the calculated orientational fields are quantified and visualized for the studied grains and conditions. The outcome of this work indicates that the generalized model is in a better agreement with experimental results in capturing the orientational flow of the ellipsoidal grains. This work also advances the capability of the model in capturing the flow type.
Author: James M. Hill
Publisher: Springer Science & Business Media
ISBN: 1402041837
Category : Science
Languages : en
Pages : 320
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Book Description
Granular or particulate materials arise in almost every aspect of our lives, including many familiar materials such as tea, coffee, sugar, sand, cement and powders. At some stage almost every industrial process involves a particulate material, and it is usually the cause of the disruption to the smooth running of the process. In the natural environment, understanding the behaviour of particulate materials is vital in many geophysical processes such as earthquakes, landslides and avalanches. This book is a collection of current research from some of the major contributors in the topic of modelling the behaviour of granular materials. Papers from every area of current activity are included, such as theoretical, numerical, engineering and computational approaches. This book illustrates the numerous diverse approaches to one of the outstanding problems of modern continuum mechanics.
Author: C. A. Mota Soares
Publisher: Springer Science & Business Media
ISBN: 1402053703
Category : Technology & Engineering
Languages : en
Pages : 861
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Book Description
III European Conference on Computational Mechanics: Solids, Structures and Coupled Problem in Engineering Computational Mechanics in Solid, Structures and Coupled Problems in Engineering is today a mature science with applications to major industrial projects. This book contains the edited version of the Abstracts of Plenary and Keynote Lectures and Papers, and a companion CD-ROM with the full-length papers, presented at the III European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering (ECCM-2006), held in the National Laboratory of Civil Engineering, Lisbon, Portugal 5th - 8th June 2006. The book reflects the state-of-art of Computation Mechanics in Solids, Structures and Coupled Problems in Engineering and it includes contributions by the world most active researchers in this field.
Author: Nan Gui
Publisher: Elsevier
ISBN: 0128163992
Category : Science
Languages : en
Pages : 388
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Book Description
Gas-Particle and Granular Flow Systems: Coupled Numerical Methods and Applications breaks down complexities, details numerical methods (including basic theory, modeling and techniques in programming), and provides researchers with an introduction and starting point to each of the disciplines involved. As the modeling of gas-particle and granular flow systems is an emerging interdisciplinary field of study involving mathematics, numerical methods, computational science, and mechanical, chemical and nuclear engineering, this book provides an ideal resource for new researchers who are often intimidated by the complexities of fluid-particle, particle-particle, and particle-wall interactions in many disciplines. - Presents the most recent advances in modeling of gas-particle and granular flow systems - Features detailed and multidisciplinary case studies at the conclusion of each chapter to underscore key concepts - Discusses coupled methods of particle and granular flow systems theory and includes advanced modeling tools and numerical techniques
Author: R. Garcia-Rojo
Publisher: CRC Press
ISBN: 1000006735
Category : Technology & Engineering
Languages : en
Pages : 1510
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Book Description
This volume contains the proceedings of the Fifth International Conference on the Micromechanics of Granular Media, Powders and Grains 2005. Powders and Grains is an international scientific conference held every 4 years that brings together engineers and physicists interested in the micromechanics of granular media.The book is a guide to the hotte
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Languages : en
Pages : 7
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Book Description
This project has led to significant progress on several critical questions related to granular flows. First, a high order code based on Discontinuous Galerkin method has been produced to study granular in axisymmetric hoppers. Before that, only ad hoc discretization methods were used. This led to the discovery of several new phenomena (such as shock formation and propagation). Several weaknesses of established models were also brought to the fore. Second, the effect of the geometry of the hopper on the flow were analyzed. Secondary circulation and resonance phenomena were observed in the models. This too is new. Third, advances were made in the analysis of sound propagation in sand and the importance of wall friction in the process. Fourth, a model of powder consolidation has been proposed, analyzed and discretized, leading to an industrial code. Fifth, a robust method for the volume determination of granular heap in complicated geometries has been proposed and implemented. The project has also yielded results not directly related to granular materials, such progress in long time integration of Discontinuous Galerkin methods and study of Partial Differential Algebraic equations.
