## 4 Confirmation of Flow Data According to Dynamic Characteristics  
In this study, FVM analysis was performed to obtain the flow data of the softened base material by considering the dynamic characteristics of the welding tool. The FVM analysis confirmed the velocity distribution and data generated around the welding tool pin. These data were then used to determine the uniformity of mixing of the base material. FVM is a conservative method that solves the skewness effect of a lattice by calculating it as a flux passing through a finite volume surface. Because the purpose is to check the velocity data along the periphery of the pin by considering the dynamic characteristics of the welding tool, the FVM analysis was performed over a short span of 50 mm. The FVM-generated cell reflected the material in the softened state when the physical properties presented in Table 10 were applied. All domain cells along the path through which the welding tool passed were applied to the softened material, which made it possible to compare the velocity data around the pin by considering the dynamic characteristics of the welding tool. Because frictional heat was set as a factor affecting the deflection of the base material, it was not applied in the FVM analysis, where the physical properties of the material in its softened state were used. In addition, because the base materials targeted in this study were thin (2 mm), tilting the welding tool was not considered to ensure adequate friction bridge welding. When tilting is applied to a welding tool and the base material is thin, the base material tears, which makes it difficult to supply an adequate amount of heat \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Base Metal (Aluminum)** \\ \hline Density (kg/m\({}^{3}\)) & 2350 \\ Kinematic Viscosity (m\({}^{2}\)/s) & \(2.34\times 10^{-7}\) \\ Surface Tension Coefficient (N/m) & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Base material properties in softened state. Figure 20: +Z directional deflection image of each point. because of the small friction component. Therefore, in this study, the data were compared and analyzed by conducting a case run in which the rotation and progression velocity were considered, as summarized in Table 11, for the same welding tool shape. The cell interval for the FVM was set to 0.1 mm, and the velocity data were measured at the periphery of the pin. As shown in Figure 21, a data box offset by 0.3 mm from the pin was created, and the velocity was dataized in the box. In the 0-0.5 s period, the rotation and progress velocity of the welding tool increased to the set value. After that, the welding tool was transferred by 50 mm from 1 s. Therefore, the data were secured from 1 s for uniform data comparison in the analysis. The velocity data were calculated along the Y direction with respect to the traveling direction of the welding tool and the X direction perpendicular to the traveling direction of the welding tool. In the scenario where the rotational velocity changed while the progression velocity did not, the velocity distribution around the pin is shown in Figure 22. The higher the rotational velocity of the welding tool, the wider was the velocity distribution generated around the pin. Moreover, a high RPM was more effective for FSW than a low RPM under the same conditions. In addition, as the progress velocity of the welding tool increased, the velocity distribution generated around the pin diminished. Based on Figure 22, the maximum value over time for each velocity distribution was calculated, as shown in Figure 23. As the rotational velocity of the welding tool increased, the velocity generated around the pin increased. Figure 24 shows the correlations between the progress velocity and rotation velocity. As the progress velocity increased, the difference in the velocity generated along the periphery of the pin was not large, but it did increase marginally.