## 3 Verification and Validation of Condensation Heat Transfer Model
### Model Verification Using Traditional Containment Analysis Codes  
By utilizing the developed heat transfer calculation model of the internal heat structure of the containment, which is implemented in the autonomous integral analysis code, PISAA, the calculation is performed using a control volume coupled with a heat structure. If the coupling between the control volume and the heat structure is in a non-equilibrium state, the heat structure serves as a heat sink and transfers heat and mass with the internal fluid until the system reaches a steady state. During the process, parameters such as the composition and state of the fluid inside the control volume, and the position, direction and boundary conditions of the heat structure are all important factors that affect the system's ability to reach its final equilibrium state and should be taken into account, respectively, in calculation. Moreover, the developed computing code is validated by combining the parameters with the mainstream containment computing code and conducting the same case calculations. The conditions for the calculation are shown in Table 1 below. For the above case, calculations were carried out using traditional containment analysis codes, code A, code B and PISAA, respectively. The pressure and gas temperature in the control volume, as well as the wall temperature and heat transfer coefficient of the heat structure, were analyzed sequentially, and the comparison diagrams are shown in Figure 2 below. Figure 2 shows the variations in the pressure and gas temperature of the control volume, and the wall temperature of the heat structure when it is vertically placed inside the control volume. It can be observed from the figure that, after the process starts, heat transfer occurs between the fluid and the heat structure in the control volume due to the heat disequilibrium. The heat release from the high-temperature heat structure causes increases in the temperature and pressure of the gas inside the control volume, which gradually stabilize over time. Since the heat storage capacity of the gas in the control volume is much smaller than that of the heat structure, the temperature rise in the gas is much larger than the wall temperature of the heat structure. As can be seen from the figure, the temperature of the gas increases by about 40 K, while the wall temperature of the heat structure finally changes by less than 0.1 K. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Volume (m\({}^{3}\)) & 1000 \\ Elevation (m) & 0.0 \\ Control volume height (m) & 15.0 \\ Hydraulic diameter (m) & 9.2132 \\ Pressure (kPa) & 101.0 \\ Gas phase temperature (K) & 313.15 \\ Liquid phase temperature (K) & - \\ Relative humidity (\%) & 0.1 \\ Liquid phase fraction (\%) & 0.0 \\ Surface area (m\({}^{2}\)) & 552.0 \\ Elevation (m) & 0.0 \\ Heat structure height (m) & 5.0 \\ Thickness (m) & 0.3048 \\ Direction & Vertical \\ Boundary condition A & Convective \\ Boundary condition B & Convective \\ Initial temperature (K) & 353.15 \\ Calculation time (s) & 15,000.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial testing conditions of control volume coupled with heat structure. Figure 2: _Cont._  
The convective heat transfer coefficient increases significantly after the beginning of the process, because the temperature difference between the gas temperature and the wall temperature is the largest at the beginning. For the natural convection heat transfer process in a limited space, the corresponding Grashof number is the largest at this time. Meanwhile, since the qualitative temperature of the fluid is half of the sum of the gas temperature and the wall temperature of the heat structure, it is also the maximum value. As the temperature of the gas approaches the temperature of the heat structure, the heat transfer coefficient tends to be stable. As the system gradually approaches stability, there is a certain deviation in the calculation results of the convective heat transfer coefficient for three codes.