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Abstract In continuous casting process, there are many factors that could affect the cleanliness of molten steel. One of the important factors is the unsuitable operation. It is necessary to appraise the effect of variable operating conditions for cleanliness of molten steel. In this study, a mathematical model that can calculate the flow pattern in casting mold and the trajectory of inclusions for variable sizes will be developed. The numerical method used in this study is explicit finite difference including full mesh system and partial mesh system. The calculating scheme based on SOLA and SOLA-SURF is developed from Los Alamos Laboratory of USA. And the calculating scheme is expanded to three dimension and it can predict the trajectory of nonmetallic inclusions. For the choice of numerical test, a slab caster with simple geometry is selected to check the mathematical model first. And the submerged nozzle alters the immersed depths and rotated angles. And then the round billet in 160mm diameter including three kinds of submerged nozzles is simulated. The pathlines of nonmetallic inclusions are calculated to estimate the cleanliness of melt. The results are rather satisfied. The geometry contour is more match the real caster in partial mesh system. Finally, to compare between the mathematical mode and water model is used to verify the accuracy.
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