DOCTORAL T H E SIS Department of Engineering Sciences and Mathematics Division of Mechanics of Solid Materials Particle Methods for Modelling ISSN 1402-1544 Simon Larsson Material Methods for Modelling Granular Particle Flow ISBN 978-91-7790-332-1 (print) ISBN 978-91-7790-333-8 (pdf) Granular Material Flow Luleå University of Technology 2019 Simon Larsson Solid Mechanics Particle Methods for Modelling Granular Material Flow Simon Larsson Division of Mechanics of Solid Materials Department of Engineering Sciences and Mathematics Lule˚aUniversity of Technology Lule˚a,Sweden Doctoral Thesis in Solid Mechanics Particle Methods for Modelling Granular Material Flow c Simon Larsson (2019) This document is freely available at http://www.ltu.se This document may be freely distributed in its original form including the current author's name. None of the content may be changed or excluded without permission of the author. Printed by Lule˚aUniversity of Technology, Graphic Services 2019 ISSN 1402-1544 ISBN 978-91-7790-332-1 (print) ISBN 978-91-7790-333-8 (pdf) Lule˚a2019 www.ltu.se ii Preface The work presented in this thesis has been carried out during the years 2015{2019 within the Solid Mechanics group at the Division of Mechanics of Solid Materials, Department of Engineering Sciences and Mathematics, Lule˚aUniversity of Technology, Lule˚a,Sweden. Financial support was provided by the European Commission through the Horizon 2020 project "Development of smart and flexible freight wagons and facilities for improved transport of granular multimaterials", project id: 636520, and by KIC RawMaterials through the project "HARSHWORK", Project Agreement No. 17152. Many people have contributed to the completion of this thesis. First of all, I would like to express my gratitude to my supervisors Prof. P¨arJons´en,Prof. Hans-Ake˚ H¨aggblad and Assoc. Prof. Gustaf Gustafsson, for their invaluable scientific guidance and support through the course of this work. Thanks also to all my present and former colleagues at the Division of Mechanics of Solid Materials, for contributing to a very inspiring and pleasant work environment. Especially, I want to thank my friend and colleague Samuel Hammarberg, a better office mate is hard to find. Thanks also to all my friends outside the academic world, you have given me much happiness during my leisure time. And thank you Emelie, for your encouragement and love through this final phase of my PhD studies. Finally, I want to express my deepest gratitude to my family, my parents Thord and Madeleine and my brothers Anton, Isak and Gustav. Thank you for your unconditional love and support. Without you, the completion of this thesis would not have been pos- sible. Lule˚a,April 2019 Simon Larsson iii iv Abstract Granular materials are very abundant in nature and are often used in industry, where the dynamics of granular material flow is of relevance in many processes. There are strong economic and environmental incentives for increased efficiency in handling and transporting granular materials. Despite being common, the mechanical behaviour of granular materials remains challenging to predict and a unifying theory describing gran- ular material flow does not exist. If the ambition is an efficient industrial handling of granular materials, increased knowledge and understanding of their behaviour is of ut- most importance. In the present thesis, particle-based numerical methods are used for modelling granular material flow. In this context, particle-based methods refer to the use of particles as a discretization unit in numerical methods. Particle-based modelling can be divided in two main approaches: discrete and continuum. In a discrete approach, each physical particle in the granular mass is modelled as a discrete particle. Newton's second law of motion combined with a contact model governs the behaviour of the granular mass. In a continuum approach, the granular material is modelled using a constitutive law re- lating stresses and strains. As a discrete approach, the discrete element method (DEM) is used and as a continuum approach the smoothed particle hydrodynamics (SPH) method and the particle finite element method (PFEM) are used. Furthermore, an experimental methodology able to capture the flow behaviour of granular materials is developed. The methodology is based on digital image correlation and it is used to obtain the in-plane velocity field for granular material flow. This thesis covers experimental measurements and numerical modelling of granular material flow in a number of applications. In pa- per A, an experimental powder filling rig is used to study the flow of sand. With this rig, a methodology for obtaining the in-plane velocity field of a granular material flow is developed. This methodology is applied in paper B, to quantify the flow of a tungsten carbide powder. The powder is modelled using the SPH method, with good agreement to experimental results. In paper C, the flow of potassium chloride fertilizers is modelled using the SPH method, and in Paper D the PFEM is explored for modelling of granular material flow. The numerical models are validated against experimental results, such as in-plane velocity field measurements. In paper E, coupled finite element, DEM and PFEM models are used to model the physical interactions of grinding media, slurry and mill structure and in a stirred media mill. The findings in the present thesis support the establishment of particle-based numerical methods for modelling granular material flow in a number of different applications. Furthermore, a methodology for calibration and validation of numerical models is developed. v vi Thesis This is a compilation thesis consisting of a synopsis and the following scientific articles: Paper A: S. Larsson, G. Gustafsson, A. Oudich, P. Jons´enand H.-A.˚ H¨aggblad. Experimental methodology for study of granular material flow using digital speckle photography. Chem- ical Engineering Science 155, pp. 524-536, 2016. Paper B: S. Larsson, G. Gustafsson, P. Jons´enand H.-A.˚ H¨aggblad. Study of powder filling us- ing experimental and numerical methods. In: World PM 2016 congress and exhibition, Hamburg, Germany, EPMA, Shrewsbury, UK, ISBN:978-1-899072-47-7. Paper C: S. Larsson, G. Gustafsson, H.-A.˚ H¨aggbladand P. Jons´en.Experimental and numerical study of potassium chloride flow using smoothed particle hydrodynamics. Minerals En- gineering 116, pp. 88-100, 2018. Paper D: S. Larsson, J.M. Rodriguez Prieto, G. Gustafsson, H.-A.˚ H¨aggbladand P. Jons´en.The particle finite element method for transient granular material flow: modelling and vali- dation. To be submitted. Paper E: S. Larsson, B. P˚alsson,M. Parian and P. Jons´en. A novel approach for modelling of physical interactions between slurry, grinding media and mill structure in stirred media mills. To be submitted. vii viii Contents Synopsis 1 Chapter 1 { Introduction 3 1.1 Objective and research question . 3 1.2 Background and motivation . 3 1.3 Scientific background . 4 1.4 Scope and limitations . 11 Chapter 2 { Modelling and experimental methods 13 2.1 Discrete modelling approach . 13 2.2 Continuum modelling approach . 16 2.3 Experimental methods . 24 Chapter 3 { Summary of appended papers 27 Chapter 4 { Discussion and conclusions 31 Chapter 5 { Outlook 33 References 35 Appended Papers 45 Paper A 47 Paper B 73 Paper C 85 Paper D 119 Paper E 157 ix x Synopsis 1 2 Chapter 1 Introduction The aim of this introductory chapter is to provide the reader with the objective, back- ground and motivation of the present work, and also the general context which the present work aims to contribute to. 1.1 Objective and research question The present work is concerned with the use of particle-based numerical methods for mod- elling granular material flow. The objective is to develop, improve and evaluate strategies for modelling granular media and granular material flow at dissimilar loading conditions, with adequate accuracy and at a tolerable computational cost. Another objective is the development of experimental approaches for calibrating and validating numerical models with improved accuracy. On a fundamental level, the aim is to contribute to increasing the knowledge and understanding of granular material flow and its impact on industrial processes. The following research question can be formulated: "How can particle-based numerical methods be used to model granular material flow, and how can they be cali- brated and validated with adequate accuracy?" 1.2 Background and motivation Granular materials are very abundant in nature and are often used in industry, where they are the second most used material, only surpassed by water (Richard et al., 2005). In the chemical industry, it has been estimated that about one-half of the products and three-quarters of the raw materials are in granular form (Nedderman, 1992). Granular materials are an important part of the pharmaceutical and agricultural industry, where e.g. the processing of powders in the manufacture of pills, and the transportation of grains, seeds and fertilizers are important processes. Or in the powder metallurgy indus- try, where components are manufactured by compacting granular materials in the form of metal powder mixtures. Components whose quality is affected to a large extent by the 3 4 Introduction handling of the loose powders (German, 1994; Zenger and Cai, 1997). Furthermore, gran- ular materials are handled on a large scale in the mining and in the mineral processing industry. For instance, the Swedish mining company LKAB ships millions of tonnes of iron ore products annually in granular form (iron ore pellets) from Narvik in Norway and Lule˚ain Sweden to customers all over the world. Such quantities of granular materials entail enormous costs and environmental effects associated with handling and transporta- tion. Granular materials also cause wear and damage to handling and transport systems, and products in granular form, such as iron ore pellets, degrade during handling and transportation resulting in a less effective use of natural resources (Gustafsson et al., 2017).