“Development of a Numerical Model for the Heat and Mass Transport in an Electric Arc Furnace Freeboard” From the Faculty of Georesources and Materials Engineering of the RWTH Aachen University Submitted by Dipl- Ing. Jacqueline Christina Gruber from Johannesburg, South Africa in respect of the academic degree of Doctor of Engineering approved thesis Advisors: Univ.-Prof. Dr.-Ing. Herbert Pfeifer Prof. Dr.-Ing. Klaus Krüger PD Dr. rer. nat. M. Kirschen Date of the oral examination: 09.12.2015 This thesis is available in electronic format on the university library’s website Jaqueline Christina Gruber Development of a Numerical Model for the Heat and Mass Transport in an Electric Arc Furnace Freeboard ISBN: 978-3-95886-087-2 1. Auflage 2016 Bibliografische Information der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Da- ten sind im Internet über http://dnb.ddb.de abrufbar. Das Werk einschließlich seiner Teile ist urheberrechtlich geschützt. Jede Verwendung ist ohne die Zustimmung des Herausgebers außerhalb der engen Grenzen des Urhebergesetzes unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Vertrieb: 1. Auflage 2016 © Verlagshaus Mainz GmbH Aachen Süsterfeldstr. 83, 52072 Aachen Tel. 0241/87 34 34 Fax 0241/87 55 77 www.Verlag-Mainz.de Herstellung: Druck und Verlagshaus Mainz GmbH Aachen Süsterfeldstraße 83 52072 Aachen Tel. 0241/87 34 34 Fax 0241/87 55 77 www.DruckereiMainz.de Satz: nach Druckvorlage des Autors Umschlaggestaltung: Druckerei Mainz printed in Germany D 82 (Diss. RWTH Aachen University, 2015) Acknowledgements This thesis was created during my time as a research associate at the Department of Industrial Furnaces and Heat Engineering (IOB) of the RWTH Aachen University in Germany. I would especially like to thank University Professor Dr.-Ing. Herbert Pfeifer and Dr.-Ing. Thomas Echterhof for giving me the opportunity to carry out the work concerning this dissertation and for their patience, guidance, encouragement and advice. I greatly appreciate the invaluable input, especially of Professor Pfeifer, during the phase when the results of the work done had to be consolidated, explained and clearly presented, resulting in this thesis. In addition, the constructive advice and correction suggestions made by both Prof. Dr.-Ing. Klaus Krüger and PD Dr. rer. nat. Markus Kirschen should be mentioned. I would like to thank both my advisors for their time and for their valuable input, giving me the benefit of advice based on many years of in-depth experience concerning the topic of steel production in an EAF. I would also like to thank all my colleagues at the IOB for their support. My special thanks goes to those who have become good friends and whose inspiration, advice, good cheer and company make working at the IOB a pleasure. Last, but not least, I would like to thank my family, my children and especially my husband, for their support and patience. i Content Nomenclature ................................................................................................................................ iii Abstract ....................................................................................................................................... viii Kurzfassung ................................................................................................................................... x 1 Introduction ............................................................................................................................. 1 1.1 EAF-Steelmaking ................................................................................................................ 1 1.1.1 Relevance of the EAF steel production route ............................................................... 1 1.1.2 Types of electric arc furnaces....................................................................................... 2 1.1.3 Description of the EAF steelmaking process ................................................................ 3 1.2 Problem definition, objectives and approach ...................................................................... 5 2 Current state of research ..................................................................................................... 10 2.1 Numerical models of the heat and mass transport in an EAF freeboard ........................... 10 2.2 Electric arc models............................................................................................................ 27 2.2.1 Magneto- fluid dynamic models .................................................................................. 27 2.2.2 Channel Arc Model (CAM) ......................................................................................... 36 2.2.3 Black-box models ....................................................................................................... 39 2.3 Experimental investigations .............................................................................................. 40 3 EAF model description ......................................................................................................... 45 3.1 Basic characteristics ......................................................................................................... 45 3.2 Arc model .......................................................................................................................... 46 3.3 Electrode model ................................................................................................................ 47 3.4 Thermal radiation model ................................................................................................... 48 3.5 Modelling of chemical reactions ........................................................................................ 52 3.6 Conservation equations and turbulence modelling ........................................................... 56 3.6.1 Mass, momentum and energy conservation ............................................................... 56 3.6.2 Turbulence ................................................................................................................. 58 3.6.3 Wall functions and wall surface roughness ................................................................ 61 4 Model implementation .......................................................................................................... 64 4.1 Geometry .......................................................................................................................... 64 4.2 Discretisation .................................................................................................................... 67 4.2.1 Influence of boundary conditions on convergence of simulations .............................. 67 4.2.2 Mesh sensitivity study ................................................................................................ 70 4.3 Material properties ............................................................................................................ 72 ii 4.3.1 Fluids .......................................................................................................................... 72 4.3.2 Solids ......................................................................................................................... 75 4.4 Boundary conditions ......................................................................................................... 76 4.4.1 Inflows, outflows and sources..................................................................................... 76 4.4.2 Electrodes .................................................................................................................. 79 4.4.3 Electric arc region ....................................................................................................... 79 4.4.4 Surfaces ..................................................................................................................... 81 5 Results ................................................................................................................................... 83 5.1 Overview of simulations .................................................................................................... 83 5.2 Arc region modelling ......................................................................................................... 85 5.2.1 Flow field .................................................................................................................... 85 5.2.2 Temperature distributions ........................................................................................... 91 5.2.3 Mass transfer and post-combustion ........................................................................... 96 5.2.4 Residence time ........................................................................................................... 99 5.2.5 Energy flows ............................................................................................................. 102 5.3 Slag layer height ............................................................................................................. 105 5.3.1 Flow field .................................................................................................................. 105 5.3.2 Temperature distributions ........................................................................................