# Study on Thermal Radiation Characteristics and the Multi-Point Source Model of Hydrogen Jet Fire
## 4 Results and Discussion
### Optimization of Thermal Radiation Prediction Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Diameter/mm** & **Radial Distance/m** & **Height/m** & **Measurement/W\(\cdot\)m\({}^{-2}\)** & **Prediction/W\(\cdot\)m\({}^{-2}\)** & **Error\%** \\ \hline \multirow{4}{*}{1.2} & & 0.25 & 944.2 & 1002.2 & 6.14 \\  & & 0.50 & 630.9 & 547.6 & 13.2 \\  & & 0.75 & 420.6 & 128.3 & 69.5 \\ \cline{2-6}  & & 0.25 & 409.8 & 250.2 & 38.95 \\  & & 0.50 & 373.3 & 200.7 & 46.24 \\  & & 0.75 & 309.0 & 107.2 & 65.31 \\ \hline \multirow{4}{*}{1.5} & & 0.25 & 1905.6 & 2233.7 & 17.22 \\  & & 0.50 & 1783.3 & 1878.4 & 5.33 \\  & & 0.75 & 1343.3 & 561.3 & 58.21 \\ \cline{2-6}  & & 0.25 & 626.6 & 610.8 & 2.52 \\  & & 0.50 & 0.50 & 605.2 & 574.4 & 5.09 \\  & & 0.75 & 555.8 & 344.7 & 37.98 \\ \hline \multirow{4}{*}{2.0} & & 0.25 & 2540.8 & 2815.4 & 10.81 \\  & & 0.50 & 3019.3 & 3635.2 & 20.40 \\ \cline{1-1}  & & 0.75 & 2581.5 & 2102.1 & 18.57 \\ \cline{1-1} \cline{2-6}  & & 0.25 & 1006.4 & 916.6 & 8.92 \\ \cline{1-1}  & & 0.50 & 0.50 & 1081.5 & 1059.3 & 2.05 \\ \cline{1-1}  & & 0.75 & 1195.3 & 803.1 & 32.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between experimental and predicted results of flame thermal radiation. Figure 15: Error rate between experimental measurements and model predictions. generated at higher flame positions. Furthermore, in the near-field range of the flame, the influence of the flame width cannot be neglected. Therefore, modeling the jet flame as several thermal source points distributed along the flame axis lines inevitably introduces certain errors. Furthermore, to demonstrate the effectiveness and accuracy of the present optimized thermal radiation prediction model, we compared the predictions of our optimized model with those from the original thermal radiation prediction model against experimental jet fire results [12]. Under the six comparative conditions, the leakage diameters range from 4.2 mm to 6.4 mm, with leakage pressures varying between several tens of MPa. The radial measurement positions range from a 2.9 m to 30.5 m distance to the flame axis. Table 3 presents the comparative predictive performance under different conditions. In this table, the prediction data from our optimized model are denoted as \(q_{\text{mod,new}}\), while the prediction data from the model of [PERSON] et al. [25] are denoted as \(q_{\text{mod,old}}\). As shown in Table 3, the predictions of the present optimized model are generally closer to the experimental values, indicating a higher predictive accuracy. Additionally, the prediction errors of the two thermal radiation models under different conditions are compared and presented in Figure 16. It is observed that the optimized model proposed in this study exhibits an overall better predictive performance. For the six experimental conditions, the minimum error of the optimized model in this study is 5.6%, and the maximum error does not exceed 21.7%. The average error of the optimized model across the six conditions is 13.9%, which is an improvement over the 19.5% average error of the old model. The optimized multi-point source model demonstrated a better predictive performance. This improvement is mainly attributed to the current study not retaining the simplified assumptions of the original model that the weight coeffici  
Figure 16: Comparison of new and old models for flame thermal radiation prediction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **P/MPa** & **_d/mm_** & **_R/m_** & **_qexp_/W\(\cdot\)m\({}^{-2}\)** & **_qmod_new_/W\(\cdot\)m\({}^{-2}\)** & **_q_mod_old/W\(\cdot\)m\({}^{-2}\)** \\ \hline
1 & 1.83 & 6.35 & 2.9 & 1557 & 1729 & 1990 \\
2 & 20.79 & 6.35 & 13.09 & 1557 & 1298 & 2045 \\
3 & 51.81 & 4.23 & 13.27 & 1557 & 1470 & 1863 \\
4 & 51.81 & 6.35 & 12.46 & 4732 & 3707 & 4181 \\
5 & 51.81 & 6.35 & 21.58 & 1557 & 1303 & 1877 \\
6 & 103.52 & 6.35 & 30.46 & 1557 & 1364 & 1653 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prediction effects of different models on jet fire experiment. along the axis and then decrease linearly.