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Modeling Granular Material Mixing and Segregation Using a Multi-Scale Model Yu Liu, Prof. Marcial Gonzalez, Prof. Carl Wassgren School of Mechanical Engineering, Purdue University, West Lafayette, IN Motivation Granular material mixing and segregation • Granular material mixing and segregation plays an important role in many industries ranging from pharmaceuticals to agrochemicals • Predictive engineering design of industrial powder blenders remains underdeveloped due to the lack of quantitative modeling tools Objective Develop a predictive model of granular material mixing and segregation for industrial equipment • Quantitatively predict the magnitude and rate of powder mixing and segregation • Be capable of modeling industrial-scale equipment • Demonstrate understanding to regulators in particle mixing and segregation Multi-Scale Model Diffusion correlations (3-D) • is an anisotropic tensor instead of an isotropic value • Off-diagonal components and are an order of magnitude smaller than the diagonal components and Utter et al. (2004, Phys Rev Lett, Vol. 69); Hsiau et al. (1999, J. Rheol, Vol. 43) • = 1 2 + 2 ( + ) 2 2 = 1.9 1 according to Utter et al. (2004 , Phys Rev Lett, Vol. 69) 1 can be calibrated from DEM simulations or experiments Segregation correlations (2-D) • Percolation is one of the most important mechanisms causing segregation • acts in the direction of gravity • According to Fan et al. (2014, J. Fluid Mech, Vol. 741): , = (1 − ) & , = − (1 − ) can be calibrated from DEM simulations or experiments FEM Model Model implementations • The commercial FEM package Abaqus V6.14 is used to perform the simulations • The Coupled Eulerian-Lagrangian (CEL) approach in Abaqus is applied to handle highly deformable material elements • Within the Eulerian domain, the material stress-strain behavior is modeled using the Mohr-Coulomb elastoplastic (MCEP) model • Material properties can be measured from independent, standard tests Bulk internal friction angle and cohesion => Shear test Bulk wall friction angle => Shear test Young’s Modulus and Poisson’s ratio => Uniaxial compression test FEM simulation results – velocity profile • Rotating drum • Conical and wedge-shaped hopper • V blender and Tote blender 3-D Tote blender - mixing • Compared with published experiments of binary mixing of glass beads in an industrial- scale Tote blender from Sudah et al. (2005, AIChE J., Vol. 51) • All the parameters were calibrated from independent experiments • Predictions of the mixing rate (relative standard deviation, RSD) from the multi-scale model compare well quantitatively to the published experimental data 2-D rotating drum - segregation • Compared with published DEM simulations of binary segregation in a lab-scale rotating drum from Schlick et al. (2015, J. Fluid Mech, Vol. 765) • All the parameters were derived directly from the published work • Predictions compare well quantitatively to DEM results 2-D conical hopper - segregation • Compared with published experiments of binary segregation of glass beads in different conical hoppers from Ketterhagen et al. (2007, Chem Eng Sci, Vol. 62) • All the parameters were calibrated directly from the published work • Predictions from the multi-scale model compare well quantitatively to experiments Macroscopic scale model • Predicts: advective flow field • Depends on: system geometries material bulk properties boundary conditions • Method used: FEM Microscopic scale model • Predicts: local diffusion / segregation rates • Depends on: particle properties local material concentration local shear rate and and solid fraction • Method used: DEM / Experiments Advection-diffusion-segregation equation = − ∙ +∙ −∙ • Predicts: global material concentration • Depends on: advective velocity (macro scale) diffusion and segregation rates (micro scale) Conical Wedge-shaped FEM simulations Conical Wedge-shaped DEM simulations FEM simulation DEM simulation V blender Tote blender Initial loading conditions Side-Side Top-Bottom Results 2-D rotating drum - mixing • Compared with DEM simulations of binary mixing in a lab-scale rotating drum • All the parameters were derived from published work by Fan et al. (2015, Phys Rev Lett, Vol. 115) • Predictions of concentration profiles from the multi-scale model compare well quantitatively to DEM results Multi-scale model predictions FEM simulations Concentration of red particles Concentration of small particles DEM simulation Multi-scale model Concentration of red particles Concentration of small particles Concentration of small particles B. Utter, R.P. Behringer, Self-diffusion in dense granular shear flows, Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 69 (2004) 1–12. O.S. Sudah, P.E. Arratia, A. Alexander, F.J. Muzzio, Simulation and experiments of mixing and segregation in a tote blender, AIChE J. 51 (2005) 836–844. S.-S. Hsiau, Y.-M. Shieh, Fluctuations and self-diffusion of sheared granular material flows, J. Rheol. (N. Y. N. Y). 43 (1999) 1049–1066. C.P. Schlick, Y. Fan, P.B. Umbanhowar, J.M. Ottino, R.M. Lueptow, Granular segregation in circular tumblers: Theoretical model and scaling laws, J. Fluid Mech. 765 (2015) 632–652. Y. Fan, C.P. Schlick, et al., Modelling size segregation of granular materials: The roles of segregation, advection and diffusion, J. Fluid Mech. 741 (2014) 252–279. Y. Liu, M. Gonzalez, C. Wassgren, Modeling Granular Material Blending in a Rotating Drum using a Finite Element Method and Advection-Diffusion Equation Multi-Scale Model, AIChE J. (2018). doi:10.1002/aic.16179. Y. Fan, P.B. Umbanhowar, J.M. Ottino, R.M. Lueptow, Shear-Rate-Independent Diffusion in Granular Flows, Phys. Rev. Lett. 115 (2015) 1–5. Y. Liu, A.T. Cameron, M. Gonzalez, C. Wassgren, Modeling granular material blending in a Tote blender using a finite element method and advection-diffusion equation multi-scale model, Powder Technol. (under review).
