**2. Methodology**

The EAF refining process is a complex, high-temperature physicochemical process. Theoretically it may be feasible to directly conduct the CFD simulation of the entire EAF refining process, however, obvious limitations can be found including the numerical instability of simulation and the extremely high computational costs. Therefore, the attempt of using a fully-coupled CFD model to concurrently capture the multi-physical phenomena, such as the combustion flame, the supersonic compressible flow, the jet penetration and the multiphase reacting flow, is difficult as expected.

To avoid the aforementioned difficulties, the complex phenomena during the refining stage can be classified into three major categories based on their major physical principles, including (1) the supersonic coherent jet above the liquid steel bath; (2) the interaction between the coherent jet and the liquid steel; (3) the stirring and the chemical reactions inside the liquid steel bath. The present study modeled each part separately and then made the overall integration to predict the entire refining process. This methodology can greatly ensure the simulation accuracy of each part with acceptable computational time, meanwhile facilitate the targeted control and analysis of various key parameters at the same time. The methodology of developing the proposed 3D integrated model is given in Figure 1 and the details are described below:


**Figure 1.** Methodology of developing the 3D integrated model for electric arc furnace (EAF) steel refining simulation.

The CFD simulation of part 1 and part 3 mentioned above is based on solving the appropriate Navier-Stokes equations with the required source terms of the specific phenomenon and incorporating them into the finite volume method (FVM) of Patankar [12]. A commercial software ANSYS® FLUENT 19.1 (ANSYS Inc., Washington County, PA, USA, 2019) [13] was adopted for the simulation.

This 3D integrated model can eliminate the compatibility issue of different CFD models during multi-physics simulations, especially for the consideration of the interaction between multi phases. Besides, the adoption of the current model makes the three-dimensional modeling of the decarburization process possible, which provides the way for a more comprehensive analysis of the chemical reaction rate and the species distribution inside the liquid steel bath. The complete model will be detailed in the next section.
