The electric arc furnace is the main process unit in scrap‐based steelmaking. Owing to its importance, numerous mathematical models for predicting the course of the electric arc furnace process have been developed. This article reviews mathematical process models proposed in the literature, identifying the most common modeling approaches, and uses mathematical descriptions for the main phenomena. Furthermore, the validation of such models is discussed in detail. Finally, the article identifies gaps in the existing knowledge and provides suggestions for the further development of mathematical process models.

Hot metal desulfurization serves as the main unit process for removing sulfur in blast‐furnace based steelmaking. The available body of literature on modeling hot metal desulfurization is reviewed to provide an in‐depth analysis of the approaches used and results obtained. The mathematical models for reaction kinetics have evolved from simplistic rate equations to more complex phenomenon‐based models that provide useful information on the effect of physico‐chemical properties and operating parameters on desulfurization efficiency. Data‐driven approaches with varying levels of phenomenological basis have also been proposed with the aim of achieving better predictive performance in industrial scale applications. Bath mixing has been studied using physical and numerical modeling to optimize mixing conditions in ladles and torpedo cars. The coupling of gas‐particle jets and their penetration into the liquid have been a focal point of physical and numerical modeling. In recent years, the fluid flow phenomena in mechanically stirred ladles has been studied extensively using physical and numerical modeling. These studies have focused on the fluid flow field, reagent dispersion, and bubble dispersion.

A simulation model for inclusion precipitation kinetics during solidification of steel was proposed in this work. With the aim to calculate the inclusion size distribution during solidification of steel, the microsegregation calculation combined with the Kampmann–Wagner numerical (KWN) model for nucleation and growth of inclusion was incorporated into the present simulation model for calculating the evolution of inclusion size distribution during solidification of steel. The inclusion agglomeration due to Brownian collisions was also taken into account. The present simulation model was first applied in simulating precipitation of MnS during steel solidification and validated by the experimental data available in the literature. The effects of cooling rates and sulfur concentrations on the precipitation of MnS were investigated by the model calculations. Then, the present simulation model was applied in simulating the precipitation of TiN inclusions during steel solidification. The calculated mean size was found to be in good agreement with data available in the literature. Finally, the model was employed for studying the effects of interfacial tension between TiN and steel due to sulfur concentration change and cooling rates on the inclusion precipitation kinetics. It was found that interfacial tension between TiN and steel has a crucial influence on the precipitation of TiN. With an increase of the cooling rate, the size distribution of TiN transforms from the lognormal distribution to the bimodal distribution.

In secondary steelmaking, the optimal size and position of open‐eye is important for effective alloying practice. In the current work, the effect of the top layer thickness and density on the formation of open‐eye in a gas stirred ladle was investigated. A one‐fifth scale water model of 150‐ton ladle was established with single and dual plug configurations for the physical modeling measurements. Air, water and three different oils were used to simulate the argon, liquid steel and slag in the water model, respectively. A transient Computational Fluid Dynamics (CFD) model based on Eulerian Volume of Fluid (VOF) approach was developed for numerical modeling of the fluid flow behavior. The physical modeling results show that the relative open‐eye area decreases from 46.7 to 5.6% when top layer thickness was increased from 0.75 to 7.5 cm using a gas flow rate of 7.5 NL min⁻¹. The effect of the number of plugs on the open‐eye area for the same range of top layer thickness mentioned above was also studied. The relative open‐eye area generated due to the gas injection through the dual plugs decreased from 49.9 to 5.8%. To study the effect of top layer properties, rapeseed oil, castor oil and paraffin oil were employed for studying the effect of density and dynamic viscosity on the open‐eye formation. The results revealed that a larger open‐eye is formed when the density is increased. Furthermore, it was found out that the density of the upper phase dominates the open‐eye formation while dynamic viscosity has only minor effect. The results obtained from numerical simulations and physical modeling were found to be in good agreement.

In ladle metallurgy of steelmaking, the role of gas injection into the metal bath is been studied to a great extent as it improves the quality of steel. The size of the open‐eye is associated with higher emulsification of top slag, which intensifies metal–slag reactions, and information about the position and size of the open‐eye is important for effective alloying practice. Moreover, the open‐eye has an effect on the energy balance since it increases heat losses. In this work, experimental measurements and numerical simulations are performed to study the effect gas flow rate on the formation of the open‐eye in a steelmaking ladle. A one‐fifth scale water model is constructed for studying gas injection with single and dual plug configurations. For the numerical modeling, the Multiphase Volume of Fluid (VOF) model is used for simulating the system including the behavior of the slag layer. The physical modeling results show that the open‐eye area changes from 9.22 to 198.34 cm² when the gas flow rate varies from 0.75 to 15 SLM using a single plug. The effect of the number of plugs on the open‐eye area for the same range of flow rates mentioned above is also studied. The two open‐eye areas generated due to the gas injected through the dual plugs change from 37.59 to 231.1 cm² when the gas flow rate is increased from 0.75 to 7.5 SLM for each plug in the physical modeling. The numerical simulation results of the open‐eye area are found to be in good agreement with the experimental data obtained from the water model. During the gas stirring process, the slag layer is deformed such that the thickness of the slag becomes thick near to the wall and thin near the slag eye at high gas flow rates. In dual plug system, the two open‐eyes tends to merge and form a huge open‐eye at high flow rates that suits for better alloying purposes. The high‐flow velocity near the surface, which could damage the ladle refractory, tends to be reduced in dual plug system when compared to single plug system.