MATHEMATICAL MODELING OF METAL FLOW IN CRYSTALLIZER AT ITS SUPPLY FROM SUBMERSIBLE NOZZLE WITH ECCENTRIC HOLES

Flow of liquid melt in the crystallizer is a little-studied process. Analytical solutions of melt flow in general case refer to complex mathematical problems, therefore numerical methods are used to model it. The purpose of this work is to use numerical method proposed by Professor V.I. Odinokov, based on finite-difference representation of the initial system of equations. This method has been successfully used in mechanics of continuous media, in foundry industry in mathematical modeling of strained deformed state of shell molds on investment models,
as well as in other technological works, which indicates its universality. In the present study, the object of research is hydrodynamic flows of liquid metal during steel casting into a rectangular section mold when fed from a submerged nozzle with eccentric holes, and the result is a spatial mathematical model describing the flows of liquid metal in the crystallizer. To simulate the processes occurring in the crystallizer, the software complex “Odyssey” was used. The theoretical calculation is based on fundamental equations of hydrodynamics and approved numerical
method. Solution of differential equations system formulated
in the work was carried out numerically. Investigated area was divided into elements of finite dimensions, for each element the resulting system of equations was written in the difference form. The result of the solution is velocity field of metal flow in crystallizer volume. To solve the system of algebraic equations obtained, a numerical scheme and a calculation algorithm were developed. Based on developed numerical scheme and algorithm, a computation program was compiled in Fortran-4. Mathematical model makes it possible to vary geometric dimensions of the crystallizer and cross-section of metal exit openings from the immersion nozzle, and it can also help to understand the flow pattern of the cast metal that affects heat dissipation of crystallizer walls and to find the optimal parameters for liquid metal outlet from the gravy glass at various casting modes. As an example it is given calculation of steel casting into a rectangular mold with a height of 100 cm and a section of 2000×40 (cm) in plan. Casting was carried out from immersion nozzle eccentrically in both sides in a horizontal plane. The calculation results are presented in graphical form. The movement of liquid metal flows is shown, their magnitudes and intensity are determined. 

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