# A Study on the Effect of O\({}_{2}\) Diffusion on the Retention Time of Inert Agents
## 4 Results  
### Experiment Analysis  
First, the experimental O\({}_{2}\) concentration data were measured by the height of the enclosure in order to obtain the interface slope \(\alpha\) and interface descending velocity \(\partial H_{i}/\partial t\). Therefore, O\({}_{2}\) concentration was measured for a total of 10 points at 0.1 m intervals from 1 to 1.9 m in height of the enclosure. The O\({}_{2}\) concentration data according to the measured height are shown in Figure 8. As explained in Chapter 2, Figure 8 shows the \(y\)-axis as the enclosure height (independent variable) and the \(x\)-axis as the O\({}_{2}\) concentration (dependent variable) to express the O\({}_{2}\) concentration data measured at the specified height. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Total Leakage** & **Inert** & **Density** & **Initial O\({}_{2}\)** & **Temperature** & **Temperature** \\  & **Area (cm\({}^{2}\))** & **Agent** & **(kg/m\({}^{3}\))** & **Concentration** & **Inside (K)** & **Outside (K)** \\ \hline
1-1 & 5.79 & IG-01 & 1.3988 & 0.120 & 290.5 & \\
1-2 & (Hole 8 ea) & IG-55 & 1.2920 & 0.119 & 290.5 & \\
1-3 & & IG-541 & 1.2978 & 0.120 & 289.5 & \\ \hline
2-1 & 8.68 & IG-01 & 1.3988 & 0.120 & 290.5 & \\
2-2 & (Hole 12 ea) & IG-55 & 1.2920 & 0.119 & 290.5 & \\
2-3 & & IG-541 & 1.2978 & 0.119 & 289.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: List of initial conditions inside and outside the enclosure taken for modeling. Figure 7: Mesh-sensitive study of the O\({}_{2}\) concentration: (**a**) Change in the O\({}_{2}\) concentration according to mesh sizes and elements; (**b**) comparison of the O\({}_{2}\) concentration between experimental and numerical results at the specified height \(H_{e}\)  
Figure 8a-c present the conditions with 8 leakage holes, and Figure 8d-f present the conditions with 12 leakage holes. The O2 concentration measurement with an increase in the leakage hole was measured to observe how species diffusion (diffusion flux \(J_{a}\)) changes with an increase in outflow volumetric flow \(\dot{V}_{o}\). Figure 8 shows how much O2 introduced from the outside diffuses into the z-direction over time. In this figure, it can be seen that the interface slope \(\alpha\) saturates after a certain period of time (approximately 200 s). In other words, it means that the O2 introduced from the outside diffuse through the z-direction with a constant diffusion flux \(J_{d}\) (i.e., diffusion velocity \(v_{d}\)). The interface slope \(\alpha\) appeared to differ depending on the type of inert agent used in the experiment. The interface slope \(\alpha_{541}\) of IG-541 was the smallest and \(\alpha_{55}\) of IG-55 was the largest. It can be seen that this is the same as the results of a previous study [3], that is, because the interface slope \(\alpha\) represents the z-direction diffusion flux \(J_{d}\), it was confirmed that the \(J_{d}\) of each inert agent presents different values. In addition, the interface slope \(\alpha\), that is, the diffusion flux \(J_{d}\), does not change significantly with the outflow volumetric flow \(\dot{V}_{o}\). This means that the diffusion flux \(J_{d}\) is an independent factor that is not affected by advection flux \(J_{a}\). Moreover, because the theoretical models for the retention time do not consider changes in temperature, the binary diffusion coefficient \(D_{ij}\) can be seen as a fixed value [24,25]. This means that by [PERSON]'s first law, the diffusion flux \(J_{d}\) can also be seen as a fixed value. Therefore, in the theoretical equation for retention time, the diffusion flux \(J_{d}\) can be calculated as a constant. The O2 concentration near the ceiling of the enclosure showed a tendency to increase rapidly. This is also the same as the results of a previous study [3]. This can be inferred from the turbulent mixing formed by the inflow volumetric flow \(\dot{V}_{i}\). Therefore, this part will be analyzed in detail through numerical analysis.