# The Development of an Optimized Impact Pad for a Six-Strand Tundish Using CFD Simulations
## 3 Numerical Modeling  
### Description of the CFD Model  
The study was performed using computational fluid dynamics (CFD) simulations within Ansys Fluent (ANSYS Inc., Canonsburg, PA, USA). The simulation process was based on three-dimensional models. To analyze turbulent flow behavior, the most widely applied approach in engineering practice is the Reynolds-Averaged Navier-Stokes (RANS) method. This approach involves time-averaging the flow variables to represent the effects of turbulence, which significantly reduces computational demands while still maintaining reliable accuracy. Within this framework, the RANS equations incorporate the impact of velocity fluctuations through turbulence models. Depending on the selected RANS formulation, additional transport equations are introduced to approximate turbulent characteristics. Models such as k-\(\epsilon\) and k-\(\omega\) incorporate the Boussinesq approximation, which allows for the calculation of turbulent viscosity based on the mean flow field [24; 25; 26; 27]. The k-\(\omega\) (k-\(\omega\)) turbulence model is a widely used model to capture the effect of turbulent flow conditions. The k-\(\omega\) SST model provides a better prediction of steel flow than most RANS models and accounts for its good behavior under adverse pressure gradients. It can account for the transfer of principal shear stress in adverse pressure gradient boundary layers. The k-\(\omega\) SST model is the most commonly used model in the industry due to its high accuracy and cost ratio. The k-\(\omega\) SST model combines the robustness and accuracy of the k-\(\omega\) model near walls with the suitability of the k-\(\epsilon\) model in regions further from the walls. This makes it more advantageous for various types of flow [24; 25; 26; 27; 28; 29]. Turbulent viscosity was calculated using Equation (2):  
\[\mu_{t}=\frac{\rho k}{\omega}\frac{1}{max\Big{[}\frac{1}{\mathrm{k}^{\alpha}},\frac{\mathrm{SF}_{\mathrm{c}}}{\mathrm{a}_{1}\omega}\Big{]}} \tag{2}\]  
where \(\rho\) represents the fluid's density [kg\(\cdot\)m\({}^{-3}\)]; k denotes the turbulent kinetic energy; \(\omega\) is the specific rate of turbulence dissipation (approximately \(\varepsilon/\)k); S refers to user-defined source terms; \(\alpha^{*}\) is a damping coefficient affecting turbulent viscosity; a stands for the inverse of the effective turbulent Prandtl number; F indicates the internal body force per unit volume [N\(\cdot\)m\({}^{-3}\)]; and \(\alpha_{1}\) is a constant specific to the SST k-\(\omega\) turbulence model. For the simulations, the k-\(\omega\) SST model was utilized based on these facts (Table 2). Thermal conditions for walls refer to the boundary conditions related to heat transfer at the surfaces (walls) of a physical system. These conditions define how heat interacts with the walls, influencing the overall temperature distribution and heat flow within the system. In computational simulations and thermal analysis, specifying accurate thermal conditions for walls is crucial for achieving realistic and reliable results. Heat flux is a measure of the rate of heat energy transfer through a given surface per unit area. It is a vector quantity, indicating not only the magnitude of heat transfer but also its direction. In practical applications, heat flux is crucial for understanding how materials behave under thermal loads, for designing thermal management systems, and for evaluating the efficiency of heat exchangers, among other things. The heat transfer equation used in Ansys Fluent is based on the general form of the heat conduction equation.