**1. Introduction**

Electric arc furnace (EAF) steelmaking featuring high efficiency and energy saving has become one of the major steelmaking methods in the world. The steel refining stage is seen as a final period to improve the thermal homogenization of the bath and adjust the metallurgical parameters of the steel grade. During this period, oxygen injection is desired to help to stir the molten bath, remove impurities and further improve the quality of the liquid steel. In the 1990s, Praxair, Inc. introduced the supersonic coherent jet technology (Cojet®) for oxygen injection in EAF [1], which significantly improves the jet performance and makes the jet to have deeper penetration depth, less splashing and, most importantly, more oxygen delivered to the molten bath. Therefore, this technology has been widely-used in EAF operation. Generally, the oxygen carried by jet will dissolve and generate numerous in-bath bubbles and the turbulence created by those bubbles will result in the intensive stirring effect. Meanwhile, the bubbles containing the oxygen will effectively react with the carbon in the bath to form the CO bubbles, which achieves the purpose of the decarburization and the further bath stirring. Except for the carbon, other impurities including phosphorus, sulfur, aluminum, silicon and manganese may also be dissolved in the molten bath. Therefore, oxygen is also responsible for removing those impurities during the refining stage. The carbon and impurity removal process involves different exothermic oxidation reactions leading to the consistent rising of the in-bath temperature. Once the carbon content is reduced to a critical value and the bath temperature reaches the desired temperature, the liquid steel is ready for tapping.

Among the research of the EAF refining process, most researchers choose to conduct the study separately for either the gas phase or the liquid phase, namely the supersonic coherent jet part or the molten bath part. For the supersonic coherent jet part, Anderson et al. [2] designed an experiment aimed to generate the supersonic coherent jet and measured the corresponding characteristics of the jet. Alam et al. [3] developed a numerical model with a revised *k* − ε turbulence model to simulate the

supersonic coherent jet and validated the model by comparing the measurement from Anderson's experiment. Liu et al. [4] experimentally and numerically studied the effect of different ambient temperatures and different oxygen preheating temperatures on jet performance. Li et al. [5] investigated the jet performance using different shrouding flame created by different types of fuel. As for the molten bath part, previous works can be further subdivided into the study of molten bath dynamics and the study of in-bath chemical reactions. Cafeery et al. [6] and Li [7] simulated the stirring process for both top-blown and bottom-blown EAF to investigate the mixing efficiency and the bath homogeneity. Ramirez et al. [8] compared different operation conditions of the furnace in the refining process in order to eliminate the flow dead zones in the bath and improve the heat dissipation of the arc. On the other hand, Szekely et al. [9] developed a mathematical model to predict the stainless steel decarburization process. Zhu [10] further analyzed the bath reaction mechanism to study the effect of different carbon contents on deoxidizer consumption.

The research mentioned above separately provide useful information for modeling the EAF refining from two perspectives but still lack a complete mathematical description of this process. Theoretically, the numerical simulation based on the finite element or finite difference method could be a feasible way to achieve the goals but considering that the simulation of such a complex process (high-speed jet interacting with the liquid phase, post-combustion, in-bath multiphase chemical reactions, etc.) may lead to either unaffordable computational time or numerical convergence issues, no related research using this method have been reported so far. In fact, some researchers, like Memoli et al. [11], attempted to adopt a jet cavity to connect both the top-blown jet part and the molten bath part for modeling the EAF refining process, which makes it possible to establish a mathematical model that contains the complete phenomena in the process. However, their models only considered the refining using the top-blown supersonic conventional jet (without the shrouding flame), which obviously makes a difference in the case using the top-blown supersonic coherent jet. In addition, the calculated 3D jet cavity was only used to provide the effective contact area with the molten bath for decarburization simulation. Therefore, the proposed decarburization simulation is still based on a zero-dimensional mathematical model in essence, which cannot provide a detailed 3D information of the molten bath.

Based on the previous statement, the study of the EAF refining process presented in this paper focuses on using the computational fluid dynamics (CFD) technique to simulate the top-blown supersonic coherent jet decarburization process. A complete 3D integrated model with good accuracy has been proposed, which can be used to predict the complete phenomena in the refining process and provide detailed 3D distribution of in-bath substances as well as the flow characteristics for further investigation. More information of the methodology for this 3D integrated model will be illustrated below.
