• Kyrylo Serhiiovych Krasnikov
Keywords: intermediate ladle, argon melt blowing, solid multilayer medium, convection-diffusion equation, Navier-Stokes equations


The article is devoted to the mathematical description of the process of filling an intermediate ladle (tundish) with argon, which is blown into the melt stream falling from the steel casting ladle, which is common at metallurgical plants. Metallurgical plants use an intermediate ladle to reliably supply a continuous casting machine for the melt. Also important for the tundish is the removal of non-metallic inclusions using argon. The good distribution of argon bubbles in the tundish significantly influences the removal of unwanted melt components such as hydrogen and nitrogen. Given the need for gas to escape, the melt speed in the intermediate ladle should be sufficiently low, especially near outflow holes, where melt needs to be homogeneous and slow for a high–quality casting. Conducting experiments during the operation of a metallurgical plant is undesirable, costly and is accompanied by difficulties associated with high temperature and opacity of the melt. Therefore, the experiments are often carried out in laboratories on the so-called cold models, where the melt is replaced by water, argon – by air, and the tundish – by the transparent container of the rectangular shape under the conditions of similarity. Despite the obvious advantages of such cold modeling, today most experiments are still conducted on mathematical models, which are a much cheaper and low-erroneous way of predicting the development of a given process under different conditions. Mathematical modeling of melt motion helps to select the optimal geometry of the tundish, as well as the required amount of argon and usefulness of barriers on a way of melt streams. The article proposes to use the convection-diffusion equation for the argon field and the Navier-Stokes equations – for the velocity field. The numerical solution using finite volume method is well tested and provides sufficient accuracy. In addition, this method is easily parallelized to speed up computing on modern multi-core processors. A graphical user interface software application allows you to display the status of the system on the screen for further review and adoption decisions.


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