## 4 Results
### Cavitation  
The cavitation of the proposed cylinder-in-ball valve was evaluated quantitatively using the results from the multi-phase CFD analysis. Figure 9 shows the obtained results for the contours of the pressure and the vapor volume fraction, _VVF_, at an opening rate of 20%. The pressure did not change significantly for the entire streamline, where the range of pressure changes was only from 101.05 to 102.77 kPa, as shown in Figure 9a. By  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Technical Specification of Flow Test Facility**} \\ \hline Max. pressure of pump & 15 bar \\ Capacity of water reservoir & 107.25 m\({}^{3}\) \\ Measurement range of digital pressure gauge & 0–1000 kPa \\ Test standard & KS B 2101 \\ \hline \multicolumn{2}{c}{**Results of experimental and numerical analysis**} \\ \hline \hline \multicolumn{2}{c}{Experiment} & Analysis \\ Flow rates & 72.0 m\({}^{3}\)/h & 80.78 m\({}^{3}\)/h \\ _CV_ & 97.3 & 109.87 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Technical specifications of flow test facility and results of experimental and numerical analysis for the fully opened proposed cylinder-in-ball valve.  
Figure 8: Experimental equipment and test set-up for _CV_ measurement.  
Figure 7: Prototype of the proposed cylinder-in-ball valve.  
substituting the results obtained from the pressure distribution into the Rayleigh-Plesset equation, the cavity size, such as the radius of the vapors, \(R_{B}\), was calculated, and then the _VVF_ was evaluated, as shown in Figure 9b. No meaningful _VVF_ was found. In general, the occurrence of cavities was defined as when the _VVF_ reached \(10^{-5}\), but it was reasonable to regard a level of 0.5 or more, which could cause noticeable damage to the valve [19]. Therefore, cavitation did not occur in the proposed cylinder-in-ball valve even with a small opening rate, and the irregular flow characteristics that commonly occur when using a conventional ball valve were avoided.  
Meanwhile, the cavitation of the V-port ball valve with a V-port angle of \(90^{\circ}\) was estimated at the same opening rate. Figure 10 shows the contours of the velocity of streamlines and the _VVF_. The valve opening starts from the side and causes the flow path to change rapidly, as shown in Figure 10a. The velocity in the streamlines changed remarkably from 0.168 to 8.657 m/s. This change caused a drastic pressure drop, and the _VVF_ reached 1.0, as shown in Figure 10b. The possibility of damage in a piping system due to cavitation is expected.  
In this section, quantitative evaluations of the cavitation in the cylinder-in-ball valve and the V-port valve at a small opening rate of 20% were carried out. The coaxial counter-rotating motion of the ball and cylinder in the cylinder-in-ball valve was able to stabilize the flow path in the flow fields and significantly reduce the occurrence of vortices. This sophisticated flow control mechanism improved the irregular flow characteristics that appear frequently in the conventional ball valve. In addition, the cavitation that was one of the drawbacks of the V-port valve was avoided.  
Figure 10: Contour plots of the velocity and vapor volume fraction for a V-port ball valve at an opening rate of 20%: (**a**) velocity of streamlines; (**b**) vapor volume fraction.  
Figure 9: Contour plots of the pressure and vapor volume fraction for the proposed cylinder-in-ball valve at an opening rate of 20%: (**a**) pressure; (**b**) vapor volume fraction.