# The Development of an Optimized Impact Pad for a Six-Strand Tundish Using CFD Simulations
## 3 Numerical Modeling
### Geometry, Computational Mesh, and Boundary Conditions  
For the purpose of flow modeling, a model representing the internal volume of the tundish (5.7 m\({}^{3}\)) was created to simulate the fluid flow inside the tundish. The simulations were carried out for a casting speed of 1.3 m.min\({}^{-1}\) for a casting block of 280 \(\times\) 280 mm on a real continuous casting machine. The basic dimensions of the tundish with the \"KTHE/C\" impact pad are shown in Figure 5. Three different configurations were analyzed, namely configuration K for the \"KTHE/C\" impact pad (Figure 6), the SP-K2 configuration for the \"SPHERIC-K2\" impact pad (Figure 7), and the SP-K4 configuration for the \"SPHERIC-K4\" impact pad. The geometries were drawn using the DesignModeler environment of the Ansys 2023 R1 software package.  
A polyhedral computational mesh was generated for the simulation domain, as illustrated in Figure 8, comprising over 1.4 million mesh elements. The structured nature of the mesh was intended to enable the accurate resolution of velocity gradients, particularly within the boundary layer regions. Mesh quality was assessed using skewness and orthogonality metrics, yielding values of 0.32 and 0.99, respectively, which indicate a high-quality grid. Given the turbulent characteristics of the flow under investigation, boundary layer refinement was applied during mesh generation. In addition, specific regions corresponding to the inlet, outlet, and tundish walls were clearly defined to ensure the accurate implementation of the initial and boundary conditions in the simulation setup.  
Figure 5: A technical drawing of the analyzed 6-strand tundish.  
Figure 6: Geometry of the 6-strand tundish in the K Configuration—“KTHE/C”.  
Figure 7: Geometry of the 6-strand tundish in the SP-K2 Configuration—“SPHERIC-K4”.  
To verify the reliability of the computational mesh quality, a mesh independence analysis was performed. Three levels of mesh refinement--coarse (912,874 elements), medium (1,404,422 elements), and fine (1,895,970 elements)--were compared by evaluating output variables such as tracer concentration and temperature field distribution. The results of the analysis showed that while the coarse mesh exhibited noticeable deviations, the differences between the medium and fine meshes were less than 2%, indicating that the model results are mesh-independent, and that the medium mesh provides a good balance between accuracy and computational efficiency.  
The analysis was performed in transient modes, with a total of 8000 time steps and a maximum time step of 0.1 s. The calculation took into account the effect of gravity.  
The computational model used in the simulation was defined with a ladle shroud diameter of 80 mm, a molten steel depth of 930 mm, and a ladle shroud immersion depth of 334 mm. The total internal volume of the tundish was 5.7 m\({}^{3}\). The ladle shroud had an outside diameter of 80 mm.  
The material properties of the molten steel included an inlet temperature of 1813 K, a density of 7030 kg\(\cdot\)m\({}^{-3}\), a viscosity of 0.0067 kg\(\cdot\)m\({}^{-1}\cdot\)s\({}^{-1}\), a specific heat capacity of 751 J\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\), and a thermal conductivity of 41.5 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\). The heat flux applied was 15 kW\(\cdot\)m\({}^{-2}\).  
At the inlet, the mass flow rate of the molten steel was set to 11.36 kg\(\cdot\)s\({}^{-1}\), with a turbulent intensity of 3.48% and a hydraulic diameter of 0.08 m. Outlet conditions were defined with a pressure outlet set to 0, a turbulent intensity of 3.64%, and a hydraulic diameter of 0.055 m.  
Thermal boundary conditions at the tundish walls included a constant temperature of 1777 K. Heat losses were specified as 2.5 kW\(\cdot\)m\({}^{-2}\) through the wall and 15 kW\(\cdot\)m\({}^{-2}\) through the surface.  
For tracer-based flow analysis, the tracer was injected for a duration of 10 s.