# A Study on a Modified Model for the Hold Time of a Clean Extinguishing Agent
## 4 Results  
The hold time of the CEA was predicted through a theoretical equation that was interpreted as a function of the height of the enclosure. The theoretical model was based on the leakage characteristics measured through an EIT and the outflow volumetric flow calculated through the leakage exponent, to predict the hold time according to the height. In a previous section, the leakage exponent and leakage characteristics were evaluated according to the number of leakage holes (Table 1). These values can be used to predict the existing outflow volumetric flow \(\dot{V}_{vo}\) and the modified outflow volumetric flow \(\dot{V}_{mo}\). The outflow volumetric flow at different enclosure heights predicted by Equations (6) and (18) is shown in Figure 5.  
Different values of leakage exponent \(n\) were evaluated according to the number of leakage holes. The leakage exponent \(n\) was at its largest when there were 16 leakage holes and at its smallest when there were 4 leakage holes. Therefore, the outflow volumetric flows \(\dot{V}_{mo}\) and \(\dot{V}_{vo}\) calculated by Equations (6) and (18) can be expressed as in Figure 5.  
The predicted outflow volumetric flow becomes smaller as the specified height \(H_{e}\) decreases. This is a result of the neutral plane \(\dot{H}_{np}\) decreasing as time passes and the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Open** & **Leakage Exponent \(n\)** & **Leakage Characteristics \(k\)** & \\
**Holes** & **(-)** & **(\(l\)/s/Pa\({}^{\star}\))** & **r-sq** \\ \hline
4 & 0.526 & 1.275 & 0.992 \\
8 & 0.767 & 1.705 & 0.997 \\
12 & 0.609 & 2.354 & 0.999 \\
16 & 0.834 & 3.025 & 0.999 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured leakage exponent and leakage characteristics. Figure 5: Outflow volumetric flow at different enclosure heights according to the number of leakage holes predicted by the existing and proposed theoretical equations: **(a)**_IG-01_; **(b)**_HFC-125_. pressure difference \(\Delta P_{LL}\) inside and outside the enclosure becomes smaller. This predicts the same result for both \(\dot{V}_{vv}\) and \(\dot{V}_{mo}\). The difference between \(\dot{V}_{vo}\) and \(\dot{V}_{mo}\) increases as leakage exponent \(n\) increases. When the number of leakage holes is 4, the difference between \(\dot{V}_{vv}\) and \(\dot{V}_{mo}\) is the smallest because \(n\) is the smallest as 0.526. When the number of leakage holes is 16, \(n\) is the largest value (0.834), and at this time, the difference between \(\dot{V}_{vv}\) and \(\dot{V}_{mo}\) is also the largest. This difference is more pronounced for _HFC-125_ than _IG-01_. This happens because the agent-air mixture's density \(\rho_{mix}\) of _HFC-125_ is larger than that of _IG-01_. Therefore, it is decided that this difference will be larger in the _HFC_ series, which has a larger \(\rho_{mix}\) than the _IG_ series. As mentioned in the previous section, it is difficult to directly experimentally measure the outflow volumetric flow of the test enclosure. Therefore, outflow volumetric flow was estimated by measuring the height and time at which the concentration of the agent-air mixture inside the enclosure became \((c_{mix}+c_{air})/2\). The concentration distribution inside the enclosure according to the enclosure height is shown in Figure 6.  
Figure 6 shows the concentration data for each height measured through the experiment. At this time, the concentration data were values converted based on the oxygen concentration measured inside the enclosure. Figure 6a-d shows the concentration value of _IG-01_, and Figure 6e-h shows the concentration value of _HFC-125_. From these values, it can be observed that the higher the measured height is, the faster the concentration decreases. This confirms that air is coming in from the upper leakage area and is descending to the bottom. As the number of leakage holes increases, the decrease in concentration becomes faster, and it can be seen that the decrease in concentration of _HFC-125_ with a large density of agent-air mixture is faster.