## 3 Model Test Validation
### Verification by Experiment  
At Wuhan University of Technology, model tests were carried out in the towing tank to verify the correctness of the numerical calculations. The towing tank has a total length of 132 m and a width of 10.8 m; the depth can be adjusted as needed, and the maximum depth is 2 m. The experimental model and the computer model were identical. The water depth for the deep water state experiment was set at 1.8 m following the actual circumstances of the towing tank, which corresponds to a depth-to-draft ratio of 5.29 and satisfies the deep water navigation standard established by The World Association for Waterborne Transport Infrastructure (PIANC), Which states that the shallow water effect can be disregarded when the depth to ratio is greater than 3.0 [26]. The experimental water depth for the shallow water state was chosen at 0.4 m, or a depth-to-draft ratio of 1.18, to ensure uniformity between the experimental and computational circumstances. Model resistance tests were carried out at various speeds and water depths while taking into account the two typical states of fully saturated and non-saturated jetting. The approach outlined in the reference [14] was used to determine the saturated airflow rate. Figure 6 presents a photograph of the experimental ship model. The pictures of the model tank experiment are shown in Figure 7. Figure 7a is the schematic diagram of the installation of the model for the tank experiment, and Figure 7b is the schematic diagram for the installation of the jet devices. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Deep Water**} & \multicolumn{3}{c}{**Shallow Water (\(h/T_{m}\) = 1.18)**} \\ \cline{2-7}  & **Number of Grids** & **Total Resistance** & **Change Rate** & **Number of Grids** & **Total Resistance** & **Change Rate** \\  & **(Million)** & **(N)** & **(Million)** & **(N)** & **(N)** & **(N)** \\ \hline
1 & 1.4 & 18.16 & / & 2.6 & 41.36 & / \\
2 & 1.8 & 17.70 & 2.54\% & 3 & 40.07 & 3.12\% \\
3 & 1.9 & 17.60 & 0.56\% & 3.2 & 39.86 & 0.51\% \\
4 & 2.2 & 17.51 & 0.50\% & 3.7 & 39.69 & 0.43\% \\
5 & 3.5 & 17.48 & 0.18\% & 5.1 & 39.58 & 0.27\% \\
6 & 6 & 17.46 & 0.11\% & 7.9 & 39.53 & 0.14\% \\ \hline \end{tabular}
\end{table} 
Table 3: The effect of the mesh number on the model resistance. For non-jet and fully saturated jet situations under two distinct water depth scenarios, Tables 4 and 5 compare the simulated and experimental values of the total model resistance. As seen in Tables 4 and 5, the computed values of the total model resistance for the non-jet situation are reasonably close to the experimental findings, with the greatest error being within 5%. The computed values of the total model resistance for the jet condition differ from the experimental values less than those for the non-jet condition, with some examples showing errors of more than 6%. The inability of the model testing to accurately regulate the jet airflow rate, which might vary due to fluctuations in different speeds and residual pressure in the air cylinder, may be the cause of this mismatch. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\(\mathbf{F_{r}}\)} & \multicolumn{4}{c}{**Resistance for Non-Jet (N)**} & \multicolumn{4}{c}{**Resistance for the Fully Saturated Jet (N)**} \\ \cline{3-8}  & & **Simulated** & **Experimental** & **Error** & **Simulated** & **Experimental** & **Error** \\ \hline
1 & 0.045 & 3.765 & 3.637 & 3.52\% & 2.894 & 2.83 & \(-2.26\%\) \\
2 & 0.057 & 5.080 & 5.224 & \(-2.76\%\) & 3.838 & 3.98 & \(3.57\%\) \\
3 & 0.068 & 7.854 & 7.537 & 4.21\% & 5.842 & 5.59 & \(-4.51\%\) \\
4 & 0.079 & 10.383 & 10.101 & 2.79\% & 7.801 & 7.29 & \(-7.01\%\) \\
5 & 0.091 & 12.160 & 12.691 & \(-4.18\%\) & 9.580 & 9.02 & \(-6.21\%\) \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of simulated and experimental values of resistance under different jetting conditions in deep water. Figure 6: Photos of the experimental ship model. (**a**) model appearance; (**b**) model bottom.