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

Alonso-Marroquin, 2005, The incremental response of soils. An investigation using a discrete-element model, Journal of Engineering Mathematics, 52, 11, 10.1007/s10665-004-6675-0 Anderson, 1967, A fluid mechanical description of fluidized beds-equations of motion, Industrial and Engineering Chemistry Fundamentals, 6, 527, 10.1021/i160024a007 Babic, 1997, Average balance equations for granular materials, International Journal of Engineering Science, 35, 523, 10.1016/S0020-7225(96)00094-8 Campbell, 1993, Boundary interactions for two-dimensional granular flows. Part 1. Flat boundaries, asymmetric stresses and couple stresses, Journal of Fluid Mechanics, 247, 111, 10.1017/S0022112093000400 Campbell, 1993, Boundary interactions for two-dimensional granular flows. Part 2. Roughened boundaries, Journal of Fluid Mechanics, 247, 137, 10.1017/S0022112093000412 Campbell, 2006, Granular material flows—An overview, Powder Technology, 162, 208, 10.1016/j.powtec.2005.12.008 Chen, 1993, Modeling of solid flow in moving beds, ISIJ International, 33, 664, 10.2355/isijinternational.33.664 Christoffersen, 1981, A micromechanical description of granular material behavior, Journal of Applied Mechanics—Transactions of the ASME, 48, 339, 10.1115/1.3157619 Cundall, 1979, A discrete numerical-model for granular assemblies, Geotechnique, 29, 47, 10.1680/geot.1979.29.1.47 Di Felice, 1994, The voidage function for fluid–particle interaction systems, International Journal of Multiphase Flow, 20, 153, 10.1016/0301-9322(94)90011-6 Dong, 2007, Modelling of multiphase flow in a blast furnace: Recent developments and future work, ISIJ International, 47, 1553, 10.2355/isijinternational.47.1553 Drescher, 1972, Photoelastic verification of a mechanical model for the flow of a granular material, Journal of the Mechanics and Physics of Solids, 20, 337, 10.1016/0022-5096(72)90029-4 Enwald, 1996, Eulerian two-phase flow theory applied to fluidization, International Journal of Multiphase Flow, 22, 21, 10.1016/S0301-9322(96)90004-X Fan, 2010, Transient behavior of burden descending and influence of cohesive zone shape on solid flow and stress distribution in blast furnace by discrete element method, ISIJ International, 50, 946, 10.2355/isijinternational.50.946 Feng, 2003, Numerical study of gas–solid flow in the raceway of a blast furnace, Steel Research International, 74, 523, 10.1002/srin.200300229 Feng, 2004, Discrete particle simulation of gas fluidization of particle mixtures, AIChE Journal, 50, 1713, 10.1002/aic.10169 Feng, 2004, Assessment of model formulations in the discrete particle simulation of gas–solid flow, Industrial and Engineering Chemistry Research, 43, 8378, 10.1021/ie049387v Feng, 2007, Microdynamic modelling and analysis of the mixing and segregation of binary mixtures of particles in gas fluidization, Chemical Engineering Science, 62, 256, 10.1016/j.ces.2006.08.015 German, 1989 Gidaspow, 1994 Glasser, 2001, Scale dependence, correlations, and fluctuations of stresses in rapid granular flows, Physics of Fluids, 13, 407, 10.1063/1.1338543 Goldenberg, 2002, Force chains, microelasticity, and macroelasticity, Physical Review Letters, 89, 10.1103/PhysRevLett.89.084302 Goldhirsch, 2010, Stress, stress asymmetry and couple stress: From discrete particles to continuous fields, Granular Matter, 12, 239, 10.1007/s10035-010-0181-z Gremaud, 2000, Similarity solutions for granular materials in hoppers, 255, 79 Gutfraind, 1996, Study of the origin of shear zones in quasi-static vertical chute flows by using discrete particle simulations, Mechanics of Materials, 24, 273, 10.1016/S0167-6636(96)00040-3 Heyes, 2004, Discrete-element method simulations: From micro to macro scales, Philosophical Transactions of the Royal Society of London Series A—Mathematical Physical and Engineering Sciences, 362, 1853, 10.1098/rsta.2004.1420 Ho, 1990, On the flow of granular material in a model blast furnace, Powder Technology, 63, 13, 10.1016/0032-5910(90)80003-H Ho, 2009, Experimental and numerical investigations of gouge formation related to blast furnace burden distribution, Minerals Engineering, 22, 986, 10.1016/j.mineng.2009.03.004 Hutter, 1994, On flows of granular materials, Continuum Mechanics and Thermodynamics, 6, 81, 10.1007/BF01140894 Inada, 2003, Behavior of stress field in packed bed of Kokura No. 2 blast furnace during filling and after blow-in, ISIJ International, 43, 1376, 10.2355/isijinternational.43.1376 Ishii, 1975 Jaeger, 1996, Granular solids, liquids, and gases, Reviews of Modern Physics, 68, 1259, 10.1103/RevModPhys.68.1259 Janssen, 1895, Versuche über getreidedruck in silozellen, Zeitschrift des Vereines deutscher Ingenieure, 39, 1045 Jenike, 1973, Bin loads. Part 2: Concepts, Part 3: Mass flow bin, Journal of Engineering for Industry—Transaction of the ASME, 95, 1, 10.1115/1.3438100 Jop, 2006, A constitutive law for dense granular flows, Nature, 441, 727, 10.1038/nature04801 Kanatani, 1981, A theory of contact force distribution in granular-materials, Powder Technology, 28, 167, 10.1016/0032-5910(81)87039-8 Kawai, 2004, 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, ISIJ International, 44, 1140, 10.2355/isijinternational.44.1140 Khodak, 1971, Velocity and pressure distributions of moving granular materials in a model of a shalt kiln, Powder Technology, 4, 187, 10.1016/0032-5910(71)80034-7 Langston, 1995, Discrete element simulation of granular flow in 2d and 3d hoppers—Dependence of discharge rate and wall stress on particle interactions, Chemical Engineering Science, 50, 967, 10.1016/0009-2509(94)00467-6 Langston, 1995, Discrete element simulation of internal-stress and flow-fields in funnel flow hoppers, Powder Technology, 85, 153, 10.1016/0032-5910(95)03009-X Latz, 2010, Hydrodynamic modeling of dilute and dense granular flow, Granular Matter, 12, 387, 10.1007/s10035-010-0187-6 Lätzel, 2000, Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell, Granular Matter, 2, 123, 10.1007/s100350000048 Lätzel, 2001, From discontinuous models towards a continuum description, 215 Li, 2000, Compromise and resolution—Exploring the multi-scale nature of gas–solid fluidization, Powder Technology, 111, 50, 10.1016/S0032-5910(00)00238-2 Luding, 2001, From discrete element simulations to a continuum model, Computer Methods in Applied Mechanics and Engineering, 191, 21, 10.1016/S0045-7825(01)00242-0 Luding, 2008, The effect of friction on wide shear bands, Particulate Science and Technology, 26, 33, 10.1080/02726350701759167 Lun, 1984, Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield, Journal of Fluid Mechanics, 140, 223, 10.1017/S0022112084000586 Makse, 2002, Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment, Nature, 415, 614, 10.1038/415614a 1993 Mio, 2009, Effect of chute angle on charging behavior of sintered ore particles at bell-less type charging system of blast furnace by discrete element method, ISIJ International, 49, 479, 10.2355/isijinternational.49.479 Moreea, 1996, Exact stress and velocity distributions in a cohesionless material discharging from a conical hopper, Chemical Engineering Science, 51, 3931, 10.1016/0009-2509(96)00248-5 Nedderman, 1992 Nogami, 2004, Raceway design for the innovative blast furnace, ISIJ International, 44, 2150, 10.2355/isijinternational.44.2150 Nouchi, 2005, Effects of operation condition and casting strategy on drainage efficiency of the blast furnace hearth, ISIJ International, 45, 1515, 10.2355/isijinternational.45.1515 1999 Oda, 2000, Study on couple stress and shear band development in granular media based on numerical simulation analyses, International Journal of Engineering Science, 38, 1713, 10.1016/S0020-7225(99)00132-9 Ooi, 1997, Finite element analysis of wall pressure in imperfect silos, International Journal of Solids and Structures, 34, 2061, 10.1016/S0020-7683(96)00138-2 Potapov, 1996, Computer simulation of hopper flow, Physics of Fluids, 8, 2884, 10.1063/1.869069 Pouliquen, 1996, Stress fluctuations and shear zones in quasistatic granular chute flows, Physical Review E, 53, 552, 10.1103/PhysRevE.53.552 Rothenburg, 1981, A micromechanical definition of the Cauchy stress tensor for particulate media, 469 Rotter, 1998, Silo pressure predictions using discrete element and finite element analyses, Philosophical Transactions of the Royal Society of London Series A—Mathematical Physical and Engineering Sciences, 356, 2685, 10.1098/rsta.1998.0293 Savage, 1998, Analyses of slow high-concentration flows of granular materials, Journal of Fluid Mechanics, 377, 1, 10.1017/S0022112098002936 Seville, 1997 Standish, 1985, Comparison of stop start and continuous sampling methods of studying segregation of materials discharging from a hopper, Chemical Engineering Science, 40, 2152, 10.1016/0009-2509(85)87036-6 Takahashi, 1993, Cold model study on burden behavior in the lower part of blast-furnace, ISIJ International, 33, 655, 10.2355/isijinternational.33.655 Takahashi, 1996, Burden descending behaviour with renewal of deadman in a two dimensional cold model of blast furnace, ISIJ International, 36, 1354, 10.2355/isijinternational.36.1354 Tordesillas, 2002, Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media, Powder Technology, 124, 106, 10.1016/S0032-5910(01)00490-9 Tsuji, 2007, Multi-scale modeling of dense phase gas-particle flow, Chemical Engineering Science, 62, 3410, 10.1016/j.ces.2006.12.090 Tüzün, 1982, The flow of granular-materials. II. Velocity distributions in slow flow, Chemical Engineering Science, 37, 1691, 10.1016/0009-2509(82)80042-0 Villermaux, 1996, New horizons in chemical engineering, 16 Walton, 1986, Stress calculations for assemblies of inelastic spheres in uniform shear, Acta Mechanica, 63, 73, 10.1007/BF01182541 Walton, 1986, Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks, Journal of Rheology, 30, 949, 10.1122/1.549893 Wright, 2011, Gas–solid flow in an ironmaking blast furnace. Part I: Experimental studies, Powder Technology, 208, 86, 10.1016/j.powtec.2010.12.006 Xu, 1997, Numerical simulation of the gas–solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chemical Engineering Science, 52, 2785, 10.1016/S0009-2509(97)00081-X Xu, 2000, Numerical simulation of the gas–solid flow in a bed with lateral gas blasting, Powder Technology, 109, 13, 10.1016/S0032-5910(99)00223-5 Yagi, 1993, Mathematical modeling of the flow of four fluids in a packed bed, ISIJ International, 33, 619, 10.2355/isijinternational.33.619 Yang, 2000, Computer simulation of the packing of fine particles, Physical Review E, 62, 3900, 10.1103/PhysRevE.62.3900 Yuu, 2005, Prediction of stable and unstable flows in blast furnace raceway using numerical simulation methods for gas and particles, ISIJ International, 45, 1406, 10.2355/isijinternational.45.1406 Yuu, 2010, Large scale simulation of coke and iron ore particle motions and air flow in actual blast furnace, ISIJ International, 50, 962, 10.2355/isijinternational.50.962 Zaimi, 2000, Validation of a blast furnace solid flow model using reliable 3-D experimental results, ISIJ International, 40, 332, 10.2355/isijinternational.40.332 Zhang, 1998, Modelling of the solids flow in a blast furnace, ISIJ International, 38, 1311, 10.2355/isijinternational.38.1311 Zhang, 1992, The interface between fluid-like and solid-like behaviour in two-dimensional granular flows, Journal of Fluid Mechanics, 237, 541, 10.1017/S0022112092003525 Zhou, 1999, Rolling friction in the dynamic simulation of sandpile formation, Physica A, 269, 536, 10.1016/S0378-4371(99)00183-1 Zhou, 2005, Discrete particle simulation of solid flow in a model blast furnace, ISIJ International, 45, 1828, 10.2355/isijinternational.45.1828 Zhou, 2008, Discrete particle simulation of gas–solid flow in a blast furnace, Computers and Chemical Engineering, 32, 1760, 10.1016/j.compchemeng.2007.08.018 Zhou, 2009, Particle scale study of heat transfer in packed and bubbling fluidized beds, AIChE Journal, 55, 868, 10.1002/aic.11823 Zhou, 2011, Gas–Solid flow in an ironmaking blast furnace. II: Discrete particle simulation, Powder Technology, 208, 72, 10.1016/j.powtec.2010.12.005 Zhou, 2010, Discrete particle simulation of particle-fluid flow: Model formulations and their applicability, Journal of Fluid Mechanics, 661, 482, 10.1017/S002211201000306X Zhou, 2010, Numerical investigation of the transient multiphase flow in an ironmaking blast furnace, ISIJ International, 50, 515, 10.2355/isijinternational.50.515 Zhu, 2001, Weighting function in the averaging method of granular materials and its application to hopper flow, Bulk Solids Handling, 21, 53 Zhu, 2002, Averaging method of granular materials, Physical Review E, 66, 021302, 10.1103/PhysRevE.66.021302 Zhu, 2003, The effects of wall and rolling resistance on the couple stress of granular materials in vertical flow, Physica A, 325, 347, 10.1016/S0378-4371(03)00143-2 Zhu, 2004, Steady-state granular flow in a 3D cylindrical hopper with flat bottom: Microscopic analysis, Journal of Physics D: Applied Physics, 37, 1497, 10.1088/0022-3727/37/10/013 Zhu, 2005, Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper, Journal of Engineering Mathematics, 52, 307, 10.1007/s10665-004-6011-8 Zhu, 2005, Steady-state granular flow in a 3D cylindrical hopper with flat bottom: Macroscopic analysis, Granular Matter, 7, 97, 10.1007/s10035-004-0191-9 Zhu, 2006, Numerical investigation of steady and unsteady state hopper flows, Powder Technology, 170, 125, 10.1016/j.powtec.2006.09.001 Zhu, 2007, Discrete particle simulation of particulate systems: Theoretical developments, Chemical Engineering Science, 62, 3378, 10.1016/j.ces.2006.12.089 Zhu, 2009, Averaging method of particulate systems and its application to particle-fluid flow in a fluidized bed, Chinese Science Bulletin, 54, 4309, 10.1007/s11434-009-0500-0 Zhu, 2009, Stress fields of solid flow in a model blast furnace, Granular Matter, 11, 269, 10.1007/s10035-008-0123-1