Mathematical modeling of the influence of the place of delivery of electrode metal drops on the metal bath depth during electroslag remelting

The article analyzes ways to influence the process of electroslag remelting in order to reduce the depth of the liquid metal bath. Painful depth of the liquid metal bath is the reason that prevents the use of electroslag remelting for obtaining multilayer castings. The method of remelting with rotation of the consumable electrode, which allows to change the place of delivery of electrode metal droplets into the metal bath, thus contributing to reducing its depth, is proposed. A mathematical model is proposed, which makes it possible to estimate the effect of changing the place of delivery of electrode metal droplets into the liquid metal bath on its depth. Achieving quasi-stationary thermal regime of the metal bath is achieved by using the transition from the initial to the steady-state thermal state, by solving the non-stationary problem of thermal conductivity, taking into account the phase transition with specific boundary conditions. Temperature distribution in the solid, two-phase and liquid regions of the bath is described by the general thermal conductivity equation. To obtain an approximate solution, the finite difference method was used. Results of mathematical modeling show the change in the position of liquidus and solidus lines for alloys of a given chemical composition depending on changes in the place of delivery of electrode metal droplets during remelting with rotation of the consumable electrode. Changing the place of delivery of droplets from the subelectrode zone closer to the wall of the crystallizer leads to a decrease in the depth of the metal bath. The reason for the decrease in the depth of the metal bath is the redistribution of heat flows in the slag and metal baths. Mathematical model was the basis for creating a computer program "Thermal state of the crystallizing billet in the electric arc furnace".The study was carried out at the expense of Russian Science Foundation’ grant № 22-29-20049, https://rscf.en/project/22-29-20049/.