Semi-analytical models of non-spherical particle shapes using optimised spherical harmonics

Abstract Determining particle shape is vital for many industrial processes such as those found in the pharmaceutical, agricultural, and bioenergy industries. With modelling being an essential tool to acquire an understanding of the behaviour of particulates in industrial processes, numerical methods such as DEM are needing numerical solutions to formulate and implement particle shape models that overcome current limitations. Whereas pharmaceutical particles have a regular shape, agricultural and biomass particles often are specific, irregular and non-analytic. Because the diversity of real shapes is enormous, a variety of methods for describing particle shapes currently exist. Recently, the series of spherical harmonics (SHs) has gained much interest through their application in many other fields. This paper focuses on the application of the semi-analytical SH technique and addresses the development of a universal modelling tool for describing different particle shapes using a finite number of SHs. The results obtained from modelling pharmaceutical, agricultural, and biomass particles prove the applicability of SHs to regular as well as irregular shapes. In this regard, their optimised description by minimising the number of non-zero expansion coefficients is demonstrated. To proceed with a smaller number of low-order SHs, surface segmentation is introduced. Sufficient accuracy in the shape description of the particles selected was achieved with less than 16 SHs.

[1]  Sergiy Antonyuk,et al.  Effect of the particle shape on the particle dynamics in a spheronization process , 2017 .

[2]  Lingzhi Liao,et al.  What is the “typical” particle shape of active pharmaceutical ingredients? , 2017 .

[3]  Rimantas Kacianauskas,et al.  Determining the shape of agricultural materials using spherical harmonics , 2016, Comput. Electron. Agric..

[4]  Edward J. Garboczi,et al.  Spherical harmonic-based random fields based on real particle 3D data: Improved numerical algorithm and quantitative comparison to real particles , 2011 .

[5]  Budi Zhao,et al.  Micromorphology characterization and reconstruction of sand particles using micro X-ray tomography and spherical harmonics , 2015 .

[6]  K. Pye,et al.  Particle shape: a review and new methods of characterization and classification , 2007 .

[7]  R. Cromarty,et al.  Relationship Between Iron Ore Granulation Mechanisms, Granule Shapes, and Sinter Bed Permeability , 2017 .

[8]  Alexander V. Potapov,et al.  A fast model for the simulation of non-round particles , 1998 .

[9]  Guilhem Mollon,et al.  Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials , 2012, Granular Matter.

[10]  G. Lu,et al.  Discrete element models for non-spherical particle systems: From theoretical developments to applications , 2015 .

[11]  Aibing Yu,et al.  DEM/CFD-DEM Modelling of Non-spherical Particulate Systems: Theoretical Developments and Applications , 2016 .

[12]  Harald Kruggel-Emden,et al.  Particle shape and Stefan flow effects on the burning rate of torrefied biomass , 2017 .

[13]  Baosheng Jin,et al.  CFD-DEM simulation of spouting of corn-shaped particles , 2012 .

[14]  Mohammad Hossein Abbaspour-Fard,et al.  Shape representation of axi‐symmetrical, non‐spherical particles in discrete element simulation using multi‐element model particles , 1999 .

[15]  Raphaëlle Chaine,et al.  Toward an efficient triangle-based spherical harmonics representation of 3D objects , 2008, Comput. Aided Geom. Des..

[16]  Rimantas Kačianauskas,et al.  Investigation of symmetric non-spherical particle shapes by applying low-resolution spherical harmonics , 2017 .

[17]  John R. Williams,et al.  SUPERQUADRICS AND MODAL DYNAMICS FOR DISCRETE ELEMENTS IN INTERACTIVE DESIGN , 1992 .

[18]  G. Lu,et al.  Critical assessment of two approaches for evaluating contacts between super-quadric shaped particles in DEM simulations , 2012 .

[19]  J. Bullard,et al.  Contact function, uniform-thickness shell volume, and convexity measure for 3D star-shaped random particles , 2013 .

[20]  Ingo Kock,et al.  Influence of particle shape on the frictional strength of sediments — A numerical case study , 2007 .

[21]  Carl Wassgren,et al.  Intra-tablet coating variability for several pharmaceutical tablet shapes , 2011 .

[22]  Rimantas Kačianauskas,et al.  Simulation of the normal impact of randomly shaped quasi-spherical particles , 2014 .

[23]  Mohammad Mehdi Ahmadi,et al.  How particle shape affects the flow through granular materials. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Wei Chen,et al.  Particle shape characterisation and its application to discrete element modelling , 2014 .

[25]  Edward J. Garboczi,et al.  The 3-D shape of blasted and crushed rocks: From 20 μm to 38 mm , 2012 .

[26]  B. Persson.  Contact mechanics for randomly rough surfaces , 2006, cond-mat/0603807.

[27]  Li Yaoming,et al.  DEM simulation and physical testing of rice seed impact against a grain loss sensor , 2013 .

[28]  Stefan Pirker,et al.  Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework , 2017, CPM 2017.

[29]  Fernando Alonso-Marroquin,et al.  Spheropolygons: A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies , 2008 .

[30]  Volker Schmidt,et al.  Structural characterization of particle systems using spherical harmonics , 2015 .

[31]  John R. Williams,et al.  A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries , 1995 .

[32]  Jianfeng Wang,et al.  Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis , 2017 .

[33]  Álvaro Ramírez-Gómez,et al.  Research needs on biomass characterization to prevent handling problems and hazards in industry , 2016 .

[34]  H. J. Herrmann,et al.  Influence of particle shape on sheared dense granular media , 2006 .

[35]  Lin Ma,et al.  Influence of particle shape and internal thermal gradients of biomass particles on pulverised coal/biomass co-fired flames , 2011 .

[36]  Álvaro Ramírez-Gómez,et al.  Low-resolution spherical harmonics models in application to quasi-quadric particle shapes , 2016 .

[37]  Dallas N. Little,et al.  Computations of particle surface characteristics using optical and X-ray CT images , 2005 .

[38]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[39]  Bo Zhou,et al.  Discrete element modeling of crushable sands considering realistic particle shape effect , 2017 .

[40]  K. Soga,et al.  Particle shape characterisation using Fourier descriptor analysis , 2001 .

[41]  W. Ketterhagen,et al.  Modeling the motion and orientation of various pharmaceutical tablet shapes in a film coating pan using DEM. , 2011, International journal of pharmaceutics.

[42]  Shumiao Chen,et al.  Experimental and numerical determination of mechanical properties of polygonal wood particles and their flow analysis in silos , 2013 .

[43]  Carlos Henrique Ataíde,et al.  Physical characterization of sweet sorghum bagasse, tobacco residue, soy hull and fiber sorghum bagasse particles: Density, particle size and shape distributions , 2013 .

[44]  Hans-Georg Matuttis,et al.  Discrete Element Simulation for Polyhedral Granular Particles , 2011 .

[45]  Josué Sznitman,et al.  Transport of ellipsoid fibers in oscillatory shear flows: Implications for aerosol deposition in deep airways , 2017, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[46]  Scott M. Johnson,et al.  Sub-discretized surface model with application to contact mechanics in multi-body simulation , 2008 .

[47]  Edward J. Garboczi,et al.  Computing elastic moduli on 3-D X-ray computed tomography image stacks , 2015 .

[48]  Paul W. Cleary,et al.  Modelling spray coating using a combined CFD–DEM and spherical harmonic formulation , 2013 .

[49]  Wei Zhou,et al.  Macroscopic and Microscopic Behaviors of Binary Mixtures of Different Particle Shapes and Particle Sizes , 2017 .

[50]  E. Garboczi.  Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: Application to aggregates used in concrete , 2002 .

[51]  Mahmood A. Khwaja,et al.  An ellipse-based discrete element model for granular materials , 1993 .

[52]  A. Munjiza,et al.  The modelling of particle systems with real shapes , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[53]  Edward J. Garboczi,et al.  Three dimensional shape analysis of JSC-1A simulated lunar regolith particles , 2011 .

[54]  Jidong Zhao,et al.  3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors , 2014 .

[55]  M. Molenda,et al.  Parameters and contact models for DEM simulations of agricultural granular materials: A review , 2016 .

[56]  Burak Felekoğlu,et al.  A new approach to the characterisation of particle shape and surface properties of powders employed in concrete industry , 2009 .

[57]  Rimantas Kačianauskas,et al.  Modelling Soil Particles by Low-resolution Spherical Harmonics☆ , 2017 .

[58]  J. Bullard,et al.  Defining shape measures for 3D star-shaped particles: Sphericity, roundness, and dimensions , 2013 .