Real-time simulation of heat transfer in continuous casting
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I.
INTRODUCTION
THE careful control of the strand cooling and the shell growth along the machine is of central importance in continuous casting operation. These have a considerable influence on the formation of cracks and other defects which can be formed in the cast material. To ensure defectfree products, the strand is to be cooled down according to a pattern which depends on steel grade, product dimension, casting speed, and machine design. On the other hand, the control of the liquid pool length is a key element in optimizing the casting speed with respect to good productivity. So, the heat transfer plays a very important role in continuous casting, especially when casting cracksensitive steel grades. To study the thermal state of a continuously cast strand, two methods can be used: empirical correlation of numerous experimental results and mathematical simulation models supported by experimental results. It is difficult and inaccurate to measure, at least inside the spray chamber, the strand temperatures or the shell thickness during casting. Moreover, the empirical models cannot be used to extrapolate the results outside the experimental range and generally they cannot be used for simulation of transient casting conditions. Mathematical models, on the other hand, once verified are easy to use and comprehensive in simulating the thermal state of the strand. In recent years, many mathematical heat-transfer models for continuous casting have been developed, t~-2~l However, most of the models can be used only for simulation of steady state casting operations in off-line. They give the strand temperature field as a function of casting parameters, such as the casting speed, superheat, mold heat removal, spray water flow rates, steel grade, and strand geometry. The numerical approximation of the model is usually done by the finite difference or finite element method. Heat-transfer models are being increasingly used to improve the existing cooling systems, to improve casting practices, and for process control. SEPPO LOUHENKILPI, Senior Teaching Assistant, is with the Laboratory of Metallurgy, Helsinki University of Technology, 02150 Espoo. Finland. ERKKI LAITINEN, Associate Professor, and RISTO NIEMINEN, Researcher, are with the Department of Mathematics, Jyv~iskylfi University, 40100 Jyv~iskyl~i, Finland. Manuscript submitted October 13, 1992. METALLURGICAL TRANSACTIONS B
Although the steady state models offer important knowledge for the operational limits of the continuous casting machine, they are not valid for simulation of transient casting conditions which occur rather frequently. For better control of heat transfer over the whole continuous casting cycle, more attention has recently focused on developing real-time simulation models which are valid under transient casting conditionsJ ~6-211 In the real-time simulation, many practical requirements will be set for the simulation model. The computing time must, for instance, be short enough and the special process conditions, such as the start and the end of ca
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