**6. Details of the Model Setup**

For CFD studies, the three-dimensional, transient state, turbulent fluid flow was modeled using Fluent software (14.5, Ansys, Inc., Canonsburg, PA, USA, 1970). The code is based on the finite volume method (FVM) [18]. The simulation domain chosen to carry out this research study had the following dimensions, length (0.195 m), height (0.016 m), and width (0.05 m), as shown in Figure 4. The semi-implicit method for pressure linked equations (SIMPLE) was used for coupling pressure and velocity in the governing equations. More details can be found in the literature [19]. To improve on the accuracy, the advection terms were discretized using a 2nd-order upwind scheme over the entire simulation domain, whereas the diffusion term was approximated by the central differencing scheme. To stabilize the interactive process, an under-relaxation factor of 0.7 for the velocity and 0.3 for the pressure, were used. The solution process was iterated until the residuals of governing equations reduced to 1 <sup>×</sup> <sup>10</sup><sup>−</sup>7. Different grids were tested until mesh-independent results were achieved. Finally, 2,867,541 hexahedral cells were identified as being an accurate, but less computationally intensive, exercise for obtaining the desired results. The molten metal was treated as a Newtonian, incompressible fluid, and all the physical properties were assumed to be constant (Tables 2 and 3).


**Table 2.** Physical properties of the Phases used in the model.

**Figure 4.** (**a**) Simulation domain containing hexahedral meshes (3D), (**b**) Mesh refinement at the nozzle outlet, edges and the quadruple region, (**c**) A closer look on the hexahedral mesh system at the inclined refractory plane. The dimensions are in meters


**Table 3.** Operating parameters and assumptions made in the model [2,13].
