## 3 Results and Discussion
### 2D-PIV Measurement  
In order to clarify the influence of ball panels and grooves in the critical region, 2D-PIV measurements were performed. Tables 2-5 show the results of Evopower, Vantaggio, Jabulani, and Teamgeist measured in the subcritical, critical, and supercritical flow regions. The ball is painted black to reduce the reflection of the PIV laser. The flow around the ball is influenced by the complex three-dimensional groove geometry and is considered to have a three-dimensional structure. Therefore, in order to obtain three-dimensional information about the flow around the ball, the flow was measured at three locations with different positions of the measurement surface. The lines drawn in the pictures of balls a, b, and c indicate the plane measured by the PIV. The structure of the surface grooves on each surface depends on the bonding status of the panels. In the images of the PIV measurements, the separation point and flow direction from the separation position are shown as white circles and solid lines. Figure 14: The results of the oil film experiment to show the separation point on the panels. Figure 15: The relationship between the \(C_{D}\) values in the supercritical region and the separation position of the oil film experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & \begin{tabular}{c} **Panel Orientation** \\ **and Laser Position** \\ \end{tabular} & \begin{tabular}{c} **Subcritical (5m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Critical (14m/s)** \\ \end{tabular} &
\begin{tabular}{c} **Supercritical (20m/s)** \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The PIV results of Jabulani with the different panel orientations and flow velocity. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & \begin{tabular}{c} **Panel Orientation** \\ **and Laser Position** \\ \end{tabular} & \begin{tabular}{c} **Subcritical (6m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Critical (8m/s)** \\ \end{tabular} &
\begin{tabular}{c} **Supercritical (15m/s)** \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The PIV results of Evopower with the different panel orientations and flow velocity. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & \begin{tabular}{c} **Panel Orientation** \\ **and Laser Position** \\ \end{tabular} & \begin{tabular}{c} **Subcritical (9m/s)** \\ \end{tabular} & \
\begin{tabular}{c} **Critical (12.5m/s)** \\ \end{tabular} &
\begin{tabular}{c} **Supercritical (20m/s)** \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The PIV results of Vantaggio with the different panel orientations and flow velocity. In both the subcritical and supercritical regions, the flow direction at the separation point and the wake were almost the same for the same type of ball in any measurement plane. In the subcritical region, the flow separation occurred at around 90\({}^{\circ}\) for all the balls when the residence point was set to 0\({}^{\circ}\). The \(C_{D}\) in this region was relatively large, about 0.5. The fast separation of the laminar flow increased the width of the wake, which resulted in higher pressure drag. Next, in the supercritical region, the \(C_{D}\) was smaller, about 0.2, because the flow transitioned to turbulence with the increase of the Reynolds number, and the detachment was delayed. As a result, the wake became narrower, and the pressure drag became small. The location of flow detachment in the supercritical region was generally consistent with the location of the detachment shown by the oil film experiments in Figure 11.  
Finally, for the flow in the critical region, the position of the separation point and the direction of the wake varied depending on the position of the measured surface. For example, in the Vantaggio measurement planes a and c in Table 3, the separation position of the critical region flow was behind the ball and showed the same trend as the results for the supercritical region.