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A three-dimensional transient multi-physical field model with comprehensive reduction reaction consideration has been developed to capture the complex processes of a three-phase submerged arc furnace. The multi-physics model integrates electromagnetic, fluid flow, reduction reaction, and thermodynamics phenomenon in unison computational framework. The furnace internal structure consists of arc and furnace charge, for which the physical properties include temperature dependence. Aiming to search the optimum design for more efficient industrial operation, the electrode insertion depth is investigated. The predicted temperature distribution of high temperature is in agreement with the measurement and simulation results. The result shows that the temperature of arc zone is maximum, which is 5897.17 K. The high-temperature area of furnace charge is near the arc zone. The temperature distribution is similar with current density. With the increase of electrode insertion depth, the average voltage drop of three arc zones is 11.43, 11.12, 10.83, and 10.35 V, respectively. When the electrode insertion depth is 1.99 and 1.79 m, the maximum magnetic field intensity around the electrode bottom is of 0.068 and 0.063 T. Cr2O3 mainly reacts under the arc bottom, while iron oxides are reduced less in the same location. An optimum electrode insertion depth exists according to the simulation results.

An inhomogeneous Multiple Size Group (MUSIG) model based on the Eulerian–Eulerian approach has been developed to describe the polydispersed bubbly flow inside the continuous-casting mold. A laboratory scale mold has been simulated using four different turbulence closure models (modified k − ɛ, RNG k − ɛ, k − ω, and SST) with the purpose of critically comparing their predictions of bubble Sauter mean diameter distribution with previous experimental data. Furthermore, the influences of all the interfacial momentum transfer terms including drag force, lift force, virtual mass force, wall lubrication force, and turbulent dispersion force are investigated. The breakup and coalescence effects of the bubbles are modeled according to the bubble breakup by the impact of turbulent eddies while for bubble coalescence by the random collisions driven by turbulence and wake entrainment. It has been found that the modified k − ɛ model shows better agreement than other models in predicting the bubble Sauter mean diameter profiles. Further, simulations have also been performed to understand the sensitivity of different interfacial forces. The appropriate drag force coefficient, lift force coefficient, virtual mass force coefficient, and turbulent dispersion force coefficient are chosen in accordance with measurements of water model experiments. However, the wall lubrication force does not have much effect on the current polydispersed bubbly flow system. Finally, the MUSIG model is then used to estimate the argon bubble diameter in the molten steel of the mold. The argon bubble Sauter mean diameter generated in molten steel is predicted to be larger than air bubbles in water for the similar conditions.

A population balance model based on the multiple-size-group (MUSIG) approach has been developed to investigate the polydispersed bubbly flow inside the slab continuous-casting mold and bubble behavior including volume fraction, breakup, coalescence, and size distribution. The Eulerian–Eulerian approach is used to describe the equations of motion of the two-phase flow. All the non-drag forces (lift force, virtual mass force, wall lubrication force, and turbulent dispersion force) and drag force are incorporated in this model. Sato and Sekiguchi model is used to account for the bubble-induced turbulence. Luo and Svendsen model and Prince and Blanch model are used to describe the bubbles breakup and coalescence behavior, respectively. A 1/4th water model of the slab continuous-casting mold was applied to investigate the distribution and size of bubbles by injecting air through a circumferential inlet chamber which was made of the specially-coated samples of mullite porous brick, which is used for the actual upper nozzle. Against experimental data, numerical results showed good agreement for the gas volume fraction and local bubble Sauter mean diameter. The bubble Sauter mean diameter in the upper recirculation zone decreases with increasing water flow rate and increases with increasing gas flow rate. The distribution of bubble Sauter mean diameter along the width direction of the upper mold increases first, and then gradually decreases from the SEN to the narrow wall. Close agreements between the predictions and measurements demonstrate the capability of the MUSIG model in modeling bubbly flow inside the continuous-casting mold.