# A Study on the Effect of O\({}_{2}\) Diffusion on the Retention Time of Inert Agents
## 4 Results
### Summary of the Experimental and Numerical Analysis Results  
Through experiments and numerical analysis, information regarding the interface slope \(\alpha\), interface thickness \(\omega\), leading edge of the interface \(H_{i}\), turbulence mixing zone, and z-direction diffusion velocity \(v_{d}\) was obtained. Therefore, the results of this study can be expressed in Figure 14 and Table 7. Table 7 summarizes the results obtained through experiments and numerical analysis, and Figure 14 shows the newly proposed model as a figure based on the experiment and numerical analyses. Figure 14: Schematic diagram of O\({}_{2}\) concentration distribution profile reflecting the experimental and numerical analysis results. Figure 13: Schematic diagram of turbulence mixing zone and interface descending zone. First, the interface slope \(\alpha\) has a unique constant value for each agent. As presented in Equation (8), this value is eventually proportional to the z-direction diffusion flux \(J_{d}\). Therefore, the greater the interface slope \(\alpha\), the faster the O\({}_{2}\) diffusion and the faster the retention time. The interface slope \(\alpha_{55}\) of IG-55 is the largest with \(\alpha_{55}=0.083\), and it has values of \(\alpha_{01}=0.071\) and \(\alpha_{541}=0.062\). The interface slope \(\alpha\) is ultimately determined by the concentration difference between air and the agent-air gas mixture; thus, it will have a constant value regardless of the enclosure height. Therefore, if the composition of the agent-air gas mixture does not change, the interface slope \(\alpha\) has a fixed value. Second, using the interface slope \(\alpha\) and the specified height \(H_{e}\), the leading edge of the interface \(H_{i}\) can be calculated using Equation (12). Therefore, if the leading edge of the interface \(H_{i}\) can be calculated, the retention time considering species diffusion can also be calculated. Third, the diffusion velocity \(v_{d}\) can also be taken as a fixed value. This is because the interface slope \(\alpha\) is proportional to the diffusion flux \(J_{d}\), and the diffusion velocity \(v_{d}\) is also proportional to the diffusion flux \(J_{d}\). Therefore, if temperature is not considered, \(v_{d}\) can also be taken as a fixed value when calculating the theoretical retention time. Finally, it was confirmed that there was a turbulence mixing zone at the top of the enclosure; it cannot be interpreted as a z-direction descending interface model, because this area induces mixing of the air and the agent-air gas mixture by advection of the air introduced from the outside. Therefore, when calculating the retention time, it was confirmed that more accurate results were obtained when the turbulence mixing zone was excluded. Based on the results thus far, Table 7 presents the calculated retention time using the theoretical equation proposed in the previous chapter. The diffusion velocity was \(v_{d,541}=-3.40\times 10^{-4}\), \(v_{d,55}=-4.40\times 10^{-4}\), and \(v_{d,01}=-4.18\times 10^{-4}\). These results were the same as those for the interface slope \(\alpha\). The measured and calculated retention times for all the inert agents present errors within 2.8%. This part is considered to be due to the turbulence mixing zone and the average error of the calculated factors. However, the retention time considering species diffusion proposed in this study is significantly more accurate than the retention time of the existing models. This can be seen in more detail in Figure 15. That is, this figure compares the retention time according to the height measured in the experiment with the retention time of the existing theoretical models, including the theoretical method proposed in this study. A comparison of the existing theoretical model was conducted in _the sharp descending interface model_ and _the wide descending interface model_.