A Model for Scrap Melting in Steel Converter
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NTRODUCTION
SCRAP is commonly used in steel converters to keep the melt temperature in a suitable range during carbon oxidation. Predicting the melting rate of the scrap is an important part of the converter process modeling. The surrounding liquid hot metal has a high carbon content compared with the steel scrap. Carbon is transported from the liquid iron to the surface of the solid scrap which causes the melting point of the material to decrease. Therefore, melting of solid scrap is greatly affected by the mass transfer of carbon in addition to heat transfer. In the literature several authors[1–6] have developed 1-D scrap melting models. These models have either an analytical or numerical fixed-grid approach. These models use constant material parameters for the entire temperature range from room temperature to the melting point. The same material parameters are used even for the steel and solidified pig iron layer. The numerical fixed-grid methods have a varying amount of active nodes that are linearly dependent on the thickness of the scrap. So when the thickness of the scrap is small during melting, a very low amount of nodes is used in the calculations. Also one of the fixed-grid methods[1] gives a jagged shape on the melting curve, which is undesirable. In this paper the material data for heat capacity, thermal conductivity, and diffusion coefficient are temperature and carbon concentration dependent. Especially for the heat capacity the model requires special attention to achieve the dependencies. Namely the enthalpy method[7] is used to take into account the temperature- and concentration-dependent heat caARI KRUSKOPF, Doctoral Student, is with the Research Group for Metallurgy, Department of Materials Science and Engineering, Aalto University, Vuorimiehentie 2, PO Box 16200, 00076 Espoo, Aalto, Finland. Contact e-mail: ari.kruskopf@aalto.fi Manuscript submitted November 21, 2014. Article published online March 12, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS B
pacity. This method can take into account the sudden changes in heat capacity related to phase changes. This increases the usability and accuracy of the model compared with the models in literature. The current model also enables the use of different material properties for steel and the solidified iron. The 1-D equations for enthalpy and carbon concentrations are discretized with a control volume method into a moving grid with implicit Crank–Nicolson method. The control volume method in the 1-D case makes it simple to change the coordinate system from Cartesian to cylindrical or spherical system. The moving grid expands and contracts according to the movement of the solidus point indicating solidification or melting, respectively. The moving grid makes it possible to achieve smooth and accurate melting rate curve with a low spatial and temporal resolution. Using moving grid the same resolution in the mesh is available during the entire process, which is not the case with fixed-grid approach. The implicit discretization method is more stable than explicit meth
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