Linking discrete particle simulation to continuum process modelling for granular matter: Theory and application

Abstract Two approaches are widely used to describe particle systems: the continuum approach at macroscopic scale and the discrete approach at particle scale. Each has its own advantages and disadvantages in the modelling of particle systems. It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches. Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory. This paper introduces an averaging method, including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.

[1]  Runyu Yang,et al.  Computer simulation of the packing of fine particles , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Shinichi Yuu,et al.  Predicition of Stable and Unstable Flows in Blast Furnace Raceway Using Numerical Simulation Methods for Gas and Particles , 2005 .

[3]  Hiroshi Nogami,et al.  Raceway Design for the Innovative Blast Furnace , 2004 .

[4]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[5]  Hiroshi Nogami,et al.  Modeling of Solid Flow in Moving Beds. , 1993 .

[6]  Aibing Yu,et al.  Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics , 1997 .

[7]  M. Ishii Thermo-fluid dynamic theory of two-phase flow , 1975 .

[8]  Fernando Alonso-Marroquin,et al.  The incremental response of soils. An investigation using a discrete-element model , 2005 .

[9]  N. Standish,et al.  Comparison of stop-start and continuous sampling methods of studying segregation of materials discharging from a hopper , 1985 .

[10]  Paul Zulli,et al.  Modelling of the Solids Flow in a Blast Furnace , 1998 .

[11]  Jun-ichiro Yagi,et al.  Mathematical Modeling of the Flow of Four Fluids in a Packed Bed. , 1993 .

[12]  Kumbakonam R. Rajagopal,et al.  On flows of granular materials , 1994 .

[13]  T. B. Anderson,et al.  Fluid Mechanical Description of Fluidized Beds. Equations of Motion , 1967 .

[14]  Shinroku Matsuzaki,et al.  Effect of chute angle on charging behavior of sintered ore particles at bell-less type charging system of blast furnace by discrete element method , 2009 .

[15]  A. Yu,et al.  Rolling friction in the dynamic simulation of sandpile formation , 1999 .

[16]  Hideki Kawai,et al.  Solid Behavior in Shaft and Deadman in a Cold Model of Blast Furnace with Floating-Sinking Motion of Hearth Packed Bed Studied by Experimental and Numerical DEM Analyses , 2004 .

[17]  Takanobu Inada,et al.  Behavior of Stress Field in Packed Bed of Kokura No. 2 Blast Furnace during Filling and after Blow-in , 2003 .

[18]  Paul Zulli,et al.  Discrete Particle Simulation of Solid Flow in a Model Blast Furnace , 2005 .

[19]  Wolfram Volk,et al.  From discrete element simulations to a continuum model , 2000 .

[20]  A. Yu,et al.  Discrete particle simulation of particle–fluid flow: model formulations and their applicability , 2010, Journal of Fluid Mechanics.

[21]  J. R. Johanson,et al.  Bin Loads—Part 2: Concepts , 1973 .

[22]  Aibing Yu,et al.  The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow , 2003 .

[23]  S. Nemat-Nasser,et al.  A Micromechanical Description of Granular Material Behavior , 1981 .

[24]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[25]  H. Jaeger,et al.  Granular solids, liquids, and gases , 1996 .

[26]  Masao Satake,et al.  Mechanics of Granular Materials , 1989 .

[27]  Jonathan Seville,et al.  Processing of Particulate Solids , 1997 .

[28]  A. Yu,et al.  Gas–solid flow in an ironmaking blast furnace — I: Physical modelling , 2011 .

[29]  S. Savage,et al.  Analyses of slow high-concentration flows of granular materials , 1998, Journal of Fluid Mechanics.

[30]  Pieter A. Vermeer,et al.  Continuous and Discontinuous Modelling of Cohesive-Frictional Materials , 2010 .

[31]  R. Nedderman Statics and Kinematics of Granular Materials: Euler's equation and rates of strain , 1992 .

[32]  Nobuyuki Komatsu,et al.  COLD MODEL STUDY ON BURDEN BEHAVIOUR IN THE LOWER PART OF BLAST FURNACE , 1993 .

[33]  A. Yu,et al.  Stress fields of solid flow in a model blast furnace , 2009 .

[34]  Masanobu Oda,et al.  Study on couple stress and shear band development in granular media based on numerical simulation analyses , 2000 .

[35]  J. R. Johanson,et al.  Bin Loads—Part 3: Mass-Flow Bins , 1973 .

[36]  Paul Zulli,et al.  Particle scale study of heat transfer in packed and bubbling fluidized beds , 2009 .

[37]  Aibing Yu,et al.  Numerical investigation of steady and unsteady state hopper flows , 2006 .

[38]  Aibing Yu,et al.  Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper , 2005 .

[39]  D. Jeffrey,et al.  Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield , 1984, Journal of Fluid Mechanics.

[40]  Jin Y. Ooi,et al.  Silo pressure predictions using discrete–element and finite–element analyses , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[41]  C. Campbell Boundary interactions for two-dimensional granular flows. Part 1. Flat boundaries, asymmetric stresses and couple stresses , 1993, Journal of Fluid Mechanics.

[42]  A. Tordesillas,et al.  Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media , 2002 .

[43]  Yuqing Feng,et al.  Assessment of model formulations in the discrete particle simulation of gas-solid flow , 2004 .

[44]  Jinghai Li,et al.  Compromise and resolution - Exploring the multi-scale nature of gas-solid fluidization , 2000 .

[45]  O. Pouliquen,et al.  Study of the origin of shear zones in quasi-static vertical chute flows by using discrete particle simulations , 1996 .

[46]  A. B. Yu,et al.  Weighting function in the averaging method of granular materials and its application to hopper flow , 2001 .

[47]  Paul Zulli,et al.  Numerical Study of Gas‐Solid Flow in the Raceway of a Blast Furnace , 2003 .

[48]  A. Yu,et al.  Discrete particle simulation of particulate systems: Theoretical developments , 2007 .

[49]  Aibing Yu,et al.  Experimental and numerical investigations of gouge formation related to blast furnace burden distribution , 2009 .

[50]  R. D. Felice,et al.  The voidage function for fluid-particle interaction systems , 1994 .

[51]  Stefan Luding,et al.  The Effect of Friction on Wide Shear Bands , 2007 .

[52]  H. Enwald,et al.  Eulerian two-phase flow theory applied to fluidization , 1996 .

[53]  X. F. Dong,et al.  Modelling of Multiphase Flow in a Blast Furnace: Recent Developments and Future Work , 2007 .

[54]  J. Kurchan,et al.  Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment , 2002, Nature.

[55]  Aibing Yu,et al.  Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis , 2005 .

[56]  Yutaka Tsuji,et al.  Multi-scale modeling of dense phase gas–particle flow , 2007 .

[57]  Charles S. Campbell,et al.  Boundary interactions for two-dimensional granular flows. Part 2. Roughened boundaries , 1993, Journal of Fluid Mechanics.

[58]  Tatsuro Ariyama,et al.  Transient Behavior of Burden Descending and Influence of Cohesive Zone Shape on Solid Flow and Stress Distribution in Blast Furnace by Discrete Element Method , 2010 .

[59]  Aibing Yu,et al.  Microdynamic modelling and analysis of the mixing and segregation of binary mixtures of particles in gas fluidization , 2007 .

[60]  L. Z. Khodak,et al.  Velocity and pressure distributions of moving granular materials in a model of a shalt kiln , 1971 .

[61]  A. Latz,et al.  Hydrodynamic modeling of dilute and dense granular flow , 2010 .

[62]  R. L. Braun,et al.  Stress calculations for assemblies of inelastic speres in uniform shear , 1986 .

[63]  P. A. Langston,et al.  Discrete element simulation of granular flow in 2D and 3D hoppers: Dependence of discharge rate and wall stress on particle interactions , 1995 .

[64]  Alexander V. Potapov,et al.  Computer simulation of hopper flow , 1996 .

[65]  Yuqing Feng,et al.  Discrete particle simulation of gas fluidization of particle mixtures , 2004 .

[66]  H. P. Zhu,et al.  Discrete particle simulation of gas-solid flow in a blast furnace , 2008, Comput. Chem. Eng..

[67]  R. M. Nedderman,et al.  Exact stress and velocity distributions in a cohesionless material discharging from a conical hopper , 1996 .

[68]  J. Y. Ooi,et al.  Finite element analysis of wall pressure in imperfect silos , 1997 .

[70]  A. Drescher,et al.  Photoelastic verification of a mechanical model for the flow of a granular material , 1972 .

[71]  R. L. Braun,et al.  Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks , 1986 .

[72]  U Tüzün,et al.  Discrete–element method simulations: from micro to macro scales , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[73]  Aibing Yu,et al.  Steady-state granular flow in a three-dimensional cylindrical hopper with flat bottom: microscopic analysis , 2004 .

[74]  Anita Mehta,et al.  Granular Matter: An Interdisciplinary Approach , 2011 .

[75]  A. Yu,et al.  Averaging method of particulate systems and its application to particle-fluid flow in a fluidized bed , 2009 .

[76]  Tomohiro Akiyama,et al.  Validation of a Blast Furnace Solid Flow Model Using Reliable 3-D Experimental Results , 2000 .

[77]  Guy T. Houlsby,et al.  The flow of granular materials—II Velocity distributions in slow flow , 1982 .

[78]  Ye-Mon Chen,et al.  On the flow of granular material in a model blast furnace , 1990 .

[79]  Benjamin J. Glasser,et al.  Scale dependence, correlations, and fluctuations of stresses in rapid granular flows , 2001 .

[80]  Stefan Luding,et al.  Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell , 2000 .

[81]  Stefan Luding,et al.  From discontinuous models towards a continuum description , 2001 .

[82]  Charles S. Campbell,et al.  Granular material flows – An overview , 2006 .

[83]  O. Pouliquen,et al.  Stress fluctuations and shear zones in quasistatic granular chute flows. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[84]  I. Goldhirsch,et al.  Stress, stress asymmetry and couple stress: from discrete particles to continuous fields , 2010 .

[85]  Michitaka Sato,et al.  Effects of Operation Condition and Casting Strategy on Drainage Efficiency of the Blast Furnace Hearth , 2005 .

[86]  Randall M. German,et al.  Particle packing characteristics , 1989 .

[87]  Paul Zulli,et al.  Gas–solid flow in an ironmaking blast furnace-II: Discrete particle simulation , 2011 .

[88]  C Goldenberg,et al.  Force chains, microelasticity, and macroelasticity. , 2002, Physical review letters.

[89]  M. Babić,et al.  AVERAGE BALANCE EQUATIONS FOR GRANULAR MATERIALS , 1997 .

[90]  K. Kanatani A theory of contact force distribution in granular materials , 1981 .

[91]  Aibing Yu,et al.  Numerical Investigation of the Transient Multiphase Flow in an Ironmaking Blast Furnace , 2010 .

[92]  Yi Zhang,et al.  The interface between fluid-like and solid-like behaviour in two-dimensional granular flows , 1992, Journal of Fluid Mechanics.

[93]  A. Yu,et al.  Averaging method of granular materials. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[94]  Paul Zulli,et al.  Numerical simulation of the gas-solid flow in a bed with lateral gas blasting , 2000 .

[95]  Jiro Katayama,et al.  Burden Descending Behaviour with Renewal of Deadman in a Two Dimensional Cold Model of Blast Furnace , 1996 .

[96]  P. A. Langston,et al.  Discrete element simulation of internal stress and flow fields in funnel flow hoppers , 1995 .