# A Study on the Effect of O\({}_{2}\) Diffusion on the Retention Time of Inert Agents
## 4 Results
### Numerical Analysis
Therefore, when the retention time is calculated using the theoretical equation, the z-direction diffusion velocity \(v_{d}\) for each inert agent can be calculated by substituting a fixed value. From Table 6, it can be seen that the difference in species diffusion for each inert agent occurs clearly. Based on the optimized numerical analysis results, the turbulent mixing zone of the upper part of the enclosure that could not be analyzed in the experiment was analyzed. Experiments have shown that this turbulent mixing region can cause distortion in the interface slope \(\alpha\) and the theoretical retention time. As mentioned in the experimental study, a turbulence mixing zone is created near the ceiling of the enclosure due to incoming air. Therefore, turbulent mixing occurs between air and air-agent mixture gas in this zone by the driving force of the inlet volume flow \(\dot{V}_{i}\). This is shown in detail in Figure 13. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Inert** \\ **Agent** \\ **(kg/m3)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Descending interface** \\ **Velocity**\(\partial\dot{H}_{j}\partial t\) **(m/s)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Averaged Advection** \\ **Velocity**\(v_{a}\) **(m/s)** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Diffusion Velocity** \\ **\(v_{d}\) **(m/s)** \\ \end{tabular} } \\ \cline{2-7}  &
\begin{tabular}{c} **\(P_{mix}\)** \\ **(kg/m3)** \\ \end{tabular} & **8 Holes** & **12 Holes** & **8 Holes** & **12 Holes** & **8 Holes** & **12 Holes** \\ \hline IG-541 & 1.292 & \(-8.32\times 10^{-4}\) & \(-1.07\times 10^{-3}\) & \(-4.92\times 10^{-4}\) & \(-7.32\times 10^{-4}\) & \(-3.40\times 10^{-4}\) & \(-3.41\times 10^{-4}\) \\ IG-55 & 1.294 & \(-9.38\times 10^{-4}\) & \(-1.21\times 10^{-3}\) & \(-5.02\times 10^{-4}\) & \(-7.68\times 10^{-4}\) & \(-4.36\times 10^{-4}\) & \(-4.43\times 10^{-4}\) \\ IG-01 & 1.399 & \(-1.08\times 10^{-3}\) & \(-1.41\times 10^{-3}\) & \(-6.68\times 10^{-4}\) & \(-9.87\times 10^{-4}\) & \(-4.12\times 10^{-4}\) & \(-4.23\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the z-direction advection velocity \(v_{a}\) and the z-direction diffusion velocity \(v_{d}\) for each inert agent. Figure 13 presents the cross-sectional area of the enclosure for each inert agent at \(t=10\) s. The arrow in the figure represents the species flow field inside the enclosure; air introduced from the outside in the turbulence mixing zone is mixed in all directions by advection. Therefore, it is not possible to interpret this part simply by the z-direction descending interface. Rather, this area can be considered as if mixing occurs in all areas of the turbulence mixing zone, similar to _the continuous mixing model_. Therefore, the turbulent mixing area may be interpreted as a region having a single concentration rather than a concentration gradient in the z-direction. It can be interpreted that the starting point of the interface is not \(H_{max}\) when calculating the retention time, but \(H_{t}\), which is the boundary between the turbulent mixing region and the interface descending region. In addition, it can be expected that \(t_{0}\), the starting time of the retention time measurement, should be approximately 10 s instead of 0 s. Therefore, it can be seen that the distortion of the interface slope \(\alpha\) and the theoretical retention time occur in this zone. In addition, the error between the calculated retention time and the measured retention time can be seen as being caused by this zone.