A Mathematical Modeling Study of Tracer Mixing in a Continuous Casting Tundish
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ng tundish represents an intermediate vessel placed between a discontinuous teemingladle and a mould to enable a continuous casting of CHAO CHEN, Ph.D. Student, is with the Division of Applied Process Metallurgy, Department of Materials Science and Engineering, KTH-Royal Institute of Technology, Brinellva¨gen 23, SE-100 44 Stockholm, Sweden, also with the State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, P.R. China and also with Department of Ferrous Metallurgy, School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing. Contact e-mail: [email protected] LAGE TORD INGEMAR JONSSON, Professor, is with the Division of Applied Process Metallurgy, Department of Materials Science and Engineering, KTH-Royal Institute of Technology, and also with the Division of CBRN Defence and Security, FOI, Swedish Defence Research Agency, SE-901 82 Umea˚, Sweden. ANDERS TILLIANDER, Docent, and PA¨R GO¨RAN JO¨NSSON, Professor, are with the Division of Applied Process Metallurgy, Department of Materials Science and Engineering, KTH-Royal Institute of Technology GUOGUANG CHENG, Professor, is with the State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing. Manuscript submitted August 29, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS B
steel. In addition, the tundish has been developed to carry out metallurgical operations such as inclusions removal, temperature and chemical composition homogenization, and alloy trimming as summarized by Mazumdar and Guthrie.[1] Overall, the fluid flow in a tundish has been widely studied using a concept of residence time distribution (RTD), which was first developed by Danckwerts[2] in the Chemical Engineering Science field. A detailed explanation and discussion of RTD can be found in Reference 3. In the steelmaking industry, two categories of RTD have been investigated,[4] i.e., (1) a continuous addition of tracers (step input)—F diagram which can be used to describe the chemical composition mixing during grade change operations; (2) an instantaneous addition of tracer (pulse input)—C diagram which has been used to roughly describe the fluid flow in a tundish, and further to optimize flow control devices such as weirs, dams, and baffles in a tundish. Besides, the most important use for RTD studies is to determine a mathematical model that represents the behavior of flow and mixing realistically enough to yield useful information for system design and analysis.[5] The mathematical modeling study
A kinematic equation of the height function was used to represent the free surface configuration. The breakthrough time, mean residence time data were used for validation. Water and steel were studied by the same method. The density of mixture fluid as a function of tracer mass concentration was coupled in the governing equations. § The two-fluid model assumed that the system were consisted of two fluids i.e., turbulent and non-turbulent fluid. Transport equations were solved for the variables of each
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