# A Study on a Modified Model for the Hold Time of a Clean Extinguishing Agent
## 5 Conclusions  
In this study, a theoretical equation for predicting the hold time of the CEA was proposed by modifying it from the viewpoint of advection. Conventionally, when the leakage exponent \(n\) is applied as 0.5, there is no difference in the hold time predicted by the existing and modified theoretical models. However, if variable \(n\) is applied, the difference in hold time predicted by the existing and modified theoretical equations increases as \(n\) increases. This shows a bigger difference as \(\rho_{mix}\) becomes bigger. Validation of the modified theoretical equation was done through direct comparison with the outflow volumetric flow \(\dot{V}_{o}\) and hold time \(t_{h}\) observed in the test enclosure. The outflow volumetric flow \(\dot{V}_{o}\) observed in the test enclosure showed more similar results to the outflow volumetric flow \(\dot{V}_{mo}\) predicted by the modified equation than the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Open** & **Leakage** & \(\dot{V}_{o}\)/\(\dot{V}_{vo}\) & \(\triangle\) & \(t_{h}\)/\(t_{vh}\) & \(t_{h}\)/\(t_{mh}\) & \(\triangle\) \\  & **Holes** & **Exponent** & **(Mean/StDev)** & **(\%)** & **(Mean/StDev)** & **(Mean/StDev)** & **(\%)** \\ \hline  & 4 & 0.526 & 0.924/0.041 & 0.3\% & 1.113/0.031 & 1.109/0.031 & \(-0.4\%\) \\ _IG_ & 8 & 0.767 & 0.890/0.024 & 3.5\% & 1.172/0.028 & 1.127/0.027 & \(-4.5\%\) \\ _01_ & 12 & 0.609 & 0.937/0.039 & 1.5\% & 1.130/0.033 & 1.112/0.032 & \(-1.8\%\) \\  & 16 & 0.834 & 0.891/0.047 & 4.5\% & 1.143/0.034 & 1.089/0.033 & \(-5.5\%\) \\ \hline  & 4 & 0.526 & 0.968/0.017 & 0.7\% & 1.10/0.035 & 1.094/0.035 & \(-0.7\%\) \\ _HFC_ & 8 & 0.767 & 0.905/0.017 & 6.9\% & 1.18/0.034 & 1.098/0.032 & \(-8.4\%\) \\ _125_ & 12 & 0.609 & 0.949/0.015 & 2.8\% & 1.13/0.035 & 1.097/0.034 & \(-3.2\%\) \\  & 16 & 0.834 & 0.888/0.015 & 8.6\% & 1.21/0.036 & 1.105/0.033 & \(-10.7\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of theoretically predicted and experimentally observed results. outflow volumetric flow \(\dot{V}_{v0}\) predicted by the existing theoretical equation. For the case of leakage exponent \(n=0.834\), compared to the observed \(\dot{V}_{o}\), the existing model's \(\dot{V}_{v0}\) showed an error of approximately 11% for both _IG-01_ and _HFC-125_. However, the modified model's \(\dot{V}_{mo}\) showed an error of approximately 6% for _IG-01_ and approximately 3% for _HFC-125_. This result shows an improvement effect of approximately 4.5% for _IG-01_ and approximately 8.6% for _HFC-125_. The hold time also showed similar results to the outflow volumetric flow. For the case of leakage exponent \(n=0.834\), compared to the observed \(t_{h}\), the existing model's \(t_{bh}\) showed approximately 11.4% and 21% errors for _IG-01_ and _HFC-125_, respectively. However, the modified model's \(t_{mh}\) showed an error of approximately 8.9% for _IG-01_ and approximately 10.5% for _HFC-125_. This shows an improvement effect of approximately 5.5% for _IG-01_ and approximately 10.7% for _HFC-125_. These results show that differences in hold time can occur depending on the interpretation of advection. It was also verified that the modified theoretical equation can predict the hold time more accurately than the existing theoretical equation. Therefore, it was decided that the modified theoretical equation could be more useful in fire-safety engineering. The authors declare no conflict of interest. * (13) [PERSON] Analysis of vapor density effects on hold times for total flooding clean extinguishing agents. In Proceedings of the Halon Options Technical Working Conference, 16 th Proceedings, HOTWC 2006, Albuquerque, NM, USA, 16-18 May 2006; pp. 1-12. Available online: [[https://www.nist.gov/system/files/documents/el/fire_research/R0601297.pdf](https://www.nist.gov/system/files/documents/el/fire_research/R0601297.pdf)]([https://www.nist.gov/system/files/documents/el/fire_research/R0601297.pdf](https://www.nist.gov/system/files/documents/el/fire_research/R0601297.pdf)) (accessed on 23 September 2021).