## 5 Evaluation of Bubble Size Correlation with CFD Code
### Evaluation of the New Bubble Size Model  
The proposed bubble size correlation was applied to the benchmark calculation of the CFD code against experiments. Figures 5-8 show a comparison of the local two-phase flow parameters, such as the void fraction, bubble diameter, and phase velocities predicted with the proposed bubble size correlation and experimental data. Of the four experiments used to evaluate the correlation, the first three experiments listed in Table 5 were used to determine the coefficients of the correlation when developing the correlation; however, VAWL data were not used. The existing correlations investigated in Section 2 were also implemented in the CFD code and evaluated. Figure 4: Results of grid sensitivity study for the Hibiki experiment. Figure 3: (**a**) Flow domain with boundary conditions, (**b**) grid near the outlet, and (**c**) cross-section of the grid. \begin{table}
\begin{tabular}{c c c} \hline
**Experiments** & **Radial** & **Axial** \\ \hline DEDALE & 25 & 1200 \\ Hibiki & 25 & 612 \\ Kalkach-Navarro & 30 & 700 \\ VAWL & 30 & 1000 \\ \hline \end{tabular}
\end{table} 
Table 5: Grids used in the benchmark calculation of each experiment. Figure 5: Comparison of the predicted two-phase parameters with the DEDALE experiment: (**a**) void fraction, (**b**) bubble diameter, (**c**) liquid velocity, and (**d**) gas velocity. Figure 6: Comparison of the predicted two-phase parameters with the Hibiki experiment: (**a**) void fraction, (**b**) bubble diameter, (**c**) liquid velocity, and (**d**) gas velocity. Figure 8: Comparison of the predicted two-phase parameters with the VAWL experiment: (**a**) void fraction, (**b**) bubble diameter, (**c**) liquid velocity, and (**d**) gas velocity. Figure 7: Comparison of the predicted two-phase parameters with the Kalkach-Navarro experiment: (**a**) void fraction (Cases 1–4), (**b**) void fraction (Cases 5–8), (**c**) bubble diameter (Cases 1–4), and (**d**) bubble diameter (Cases 5–8). As illustrated in Figure 5, the numerical calculation result for the DEDALE experiment shows a flat void fraction distribution at the center of the pipe and a rapid increase in the vicinity of the wall with reasonable accuracy. Moreover, the bubble size and phase velocity are well predicted against the experimental data. For the four cases of Hibiki experiments, the peak void fraction in the channel center was well predicted, as depicted in Figure 6a. Additionally, the prediction of the phase velocities shows good agreement, as shown in Figure 6c,d. In Case 3 of the Hibiki experiment, the local void fraction for r/R \(<\) 0.7 exceeds 0.25 and, thus, the appearance of a slug bubble is expected [49]. Therfore, the relatively large bubbles at the center of the pipe could not be accurately predicted, even though their profiles closely followed the tendency of the bubble size, as shown in Figure 6b. For the Kalkach-Navarro experiment, the data on the velocity of the liquid and gas phase are not provided; only the void fraction and the bubble size are shown in Figure 7. Simulation results show that large bubbles, which appeared in the center in Cases 1-4, were not well predicted, similar to those in the Hibiki experiment. Furthermore, the increase in bubble size near the wall was not predicted in Cases 5-8. Thus, a second group bubble size model for large bubbles is required for better prediction. Nevertheless, the overall value and tendencies of the void fraction and bubble size were predicted with reasonable accuracy. Finally, the new bubble size model was evaluated for the VAWL experiment, which was not used for determining the correlation coefficients. Figure 8 shows a comparison of the simulation results and experimental data for the local two-phase flow parameters, such as the void fraction, bubble diameter, and phase velocities. The VAWL data show both the core and wall peaks, where bubbles are concentrated at the center and near the wall, respectively, according to the experimental conditions. These phenomena were well predicted by the calculations.