Mathematical modelling vacuum degassing of steel in argon-stirred ladle
Keywords:вакууматор камерного типу, дегазація металевого розплаву, суцільне багатоскладове середовище, рівняння Нав’є-Стокса
The article presents a mathematical model of a non-stationary process of denitrogenation and dehydrogenation of steel melt in vacuum chamber with argon stirring. Vacuum degassing is a technology that is widely used in metallurgical plants to achieve extremely low concentrations of hydrogen and nitrogen in the metal melt, which is needed to improve the quality of steel products. According to the well-known hypothesis, initially the gas in the melt is in the dissolved state. Hydrogen and nitrogen bubbles are formed from a solution on the surface of the ladle lining provided that the pressure of metal melt is sufficiently low. The pressure required for the bubble to appear is determined in accordance with Sieverts' law. To a large extent, the degassing is also affected by the argon stirring, when bubbles collect hydrogen and nitrogen in their paths, floating through the melt and flying off the free surface. It is also important to reduce the duration of degassing to keep the melt temperature at a sufficiently high level, as well as to speed up overall process. Conducting numerical studies of the above process on a mathematical model reduces the cost of time and financial resources, so building a model is an actual task. The description of the melt flow and gases in the ladle is based on the mass and impulse conservation laws for a continuous medium, which is justified by the small size of the bubbles and their large number. Given the complexity of finding the analytic solution of nonlinear differential equations in partial derivatives in three-dimensional formulation, it is proposed to use the central difference method, which is sufficiently accurate and widely used for similar problems. It is proposed to implement the mathematical model in a C# computer program, because that language has sufficient programming capabilities, including parallelization of computation. The software application will allow evaluating the influence of the intensity of argon stirring, as well as the depth of the melt, on the degree of degassing, which can be used in the implementation of technological recommendations in the production of steel.
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