Two-dimensional comprehensive mathematical model for electroslag remelting process with pipe electrode

Taking the electroslag remelting with pipe electrode (ESR-PE) and electroslag remelting with solid electrode (ESR-SE) as the research objects, a two-dimensional steady-state mathematical model of coupled electromagnetic field equation, energy equation, and flow equation was established. The distribution of its current density, Joule heat, flow field, and temperature field was compared and the difference of their molten metal pool was analyzed. The results show that compared with those of ESR-SE, current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip, while the Joule heat generated in the central area of the slag pool is less. In the ESR-PE, the slag flows from the outside of the electrode to the hollow area of the electrode, which makes the temperature distribution in the slag pool is more uniform. Affected by the Joule heating area and flow field, the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery. However, in the ESR-PE, the heat is concentrated near the inner and outer walls of the electrode tip, and the heat is transferred from the periphery to the center of the slag pool. The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m. Compared with that of ESR-SE, the molten metal pool of ESR-PE is shallower and flatter.