# A Simplified Analysis to Predict the Fire Hazard of Primary Lithium Battery
## 3 Results and Discussion
The ignition gap of two batteries cannot exceed 30 s according to the experiment results:  
\[0\leq T_{ignition\ gap}\leq\ 30 \tag{10}\]  
Figure 4: Heat release rate (HRR) experimental results of the ignition two batteries. Considering the exponential relationship of energy, Equation (5) can be written as:  
\[\dot{q}_{n}=n^{a}.b.t^{2} \tag{11}\]  
By introducing a time variable and combining the t\({}^{2}\) fire model and the heat release rate growth model, the HRRs of one, two, four, and nine batteries were simulated and compared with the experimental results, as shown in Figure 5. The ignition time gap was random so the HRR curve was not unique. The battery combustion curve in the experiment was also not unique. The calculation results were close to the experimental results under the same ignition time gap condition. According to the results, the overall simulation trend was close to the experimental results, and the values of maximum HRR and total heat release (THR) were close to each other, as shown in Table 2. Therefore, this simulation can be used as a preliminary analysis to simulate the scale of a lithium battery fire, providing a reference for the simulation of foreseeable disasters. When a large number of batteries burned, as the combustion scale increased, several batteries ignited at the same time. This process is more likely to occur after the flame increases. It is necessary to assume that several batteries ignite simultaneously at a certain time when simulating a large number of batteries burning. The ignition gap at this time is not simply between two batteries, but the ignition interval of the battery pack. Applying the simulation analysis to a fire with more batteries, the comparison results of a 6 \(\times\) 6 and 10 \(\times\) 10 test are shown in Figure 3:0 The changing trends in the simulation curves are consistent with the experimental curves. Obtained by the figure, the simulation THR data from 6 \(\times\) 6 and 10 \(\times\) 10 were calculated as 2802 kJ and 10,388 kJ, respectively. The energies of the three groups of 6 \(\times\) 6 experiments were 2925 kJ, 2800 kJ, and 2834 kJ; and 10,080 kJ, 9985 kJ, and 10,290 kJ for 10 \(\times\) 10 tests. These results feasibly aligned with the fitting line. There was a small difference in reaction time between simulation and experimental results for the 10 \(\times\) 10 test. The reason for this difference is that both the reaction time of the experiment and simulation were not a fixed value. These simulation curves conformed well to the experimental ones. As a result, this HRR simulation analysis is suitable for simulation of CR123A battery fires. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No. of**} & \multicolumn{2}{c}{**Maximum HRR (kW)**} & \multicolumn{2}{c}{**THR (kJ)**} & \multirow{2}{*}{**Difference in**} \\ \cline{2-2} \cline{4-5}
**Batteries** & **Experiment** & **Simulation** & **Experiment** & **Simulation** & **THR** \\ \hline
1 & 2.51 & 2.51 & 32.4 & 33.6 & 3.7\% \\
2 & 5.12 & 5 & 68.5 & 73.6 & 7.4\% \\
4 & 7.71 & 7.12 & 164.6 & 166.9 & 1.4\% \\
9 & 13.53 & 14.86 & 495.2 & 463.8 & \(-\)6.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum HRR and THR of experimental and simulated one, two, four, and nine batteries. Figure 5: (**a**) Simulated and (**b**) experimental HRR results of one, two, four, and nine batteries. Based on the analysis methodology, primary lithium battery fire could be predicted. Firstly, the curve of the HRR for a single primary lithium battery was plotted. The curve provides a simplified analysis to create the heat release rate curve of a primary lithium battery based on t\({}^{2}\) fire model in Equations (5)-(8) and using MATLAB software for mathematical curve construction. The required data for t\({}^{2}\) fire were obtained experimentally (Table 1).