# 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  
The above analysis shows that the flame temperature significantly affects the thermal radiation release of the flame. The details of the weight coefficient optimization based on the temperature distribution along the flame axis are presented in Section 3.7. The temperature distribution along the \(y\)-axis of jet fires under different conditions is illustrated in Figure 13. It is evident that the temperature distribution follows a similar pattern across various conditions. Starting from the nozzle, the temperature along the flame's vertical axis initially rises and then falls, increasing from the initial temperature of hydrogen to the peak value of approximately 2300 K. The flame temperature at different points  
Figure 11: Thermal radiation distributions in \(x\)- and \(y\)-directions under different leakage diameters. Figure 12: Temperature distributions along the jet fire axis under different leakage diameters. along the axis shows minimal variation under different conditions, with the highest flame temperature consistently occurring at about 0.71 \(y\)-\(L_{\text{f}}^{-1}\). This pattern has been corroborated by experimental data [35]. Consequently, the thermal source weight coefficient in the thermal radiation prediction model can be optimized based on the temperature distribution along the jet flame axis. Figure 14 presents a comparison between the optimized and non-optimized weight coefficients. Utilizing the thermal radiation prediction model optimized by the flame axis temperature distribution, the thermal radiation of the hydrogen jet fire under the same experimental conditions of this study was predicted. Table 2 compares the experimental and predicted thermal radiation values of the jet flame. As shown in Table 2, the optimized thermal radiation model achieves a better predictive performance at lower flame heights. Specifically, compared with the thermal radiation predictions at a height of 0.75 m, the model's predictions at the 0.25 m and 0.5 m flame heights are closer to the experimental measurements. To more clearly illustrate the predictive effectiveness of the optimized model, the errors between the model predictions and experimental measurements under different conditions were calculated, as shown in Figure 15. In Figure 15, the horizontal axis represents the conditions sequentially numbered as in Table 2. It is observed that the thermal radiation prediction model performs satisfactorily at lower flame heights. For a flame height of  
Figure 14: Diagram of weighting coefficient distributions [25]. Figure 13: The temperature distributions along the flame axis under different conditions. 0.25 m, the minimum prediction error obtained is 2.52%, with an average error of 14.09%. At the height of 0.5 m, the minimum error is 2.05%, and the average error is 15.36%. However, at a height of 0.75 m, the minimum prediction error is only 18.57%, while the average error is 47.06%. Therefore, the thermal radiation prediction model close to the flame tip requires more factors to be considered. The accuracy of the current multi-point source thermal radiation model is inevitably constrained by the flame shape, resulting in certain prediction errors. At higher flame heights, the model predictions exhibit relatively larger errors. This discrepancy is probably due to the pronounced increase in oscillatory phenomena at higher flame positions. When hydrogen is released at high pressures from the leakage hole, the initial jet kinetic energy and turbulent Reynolds number are significantly higher, leading to noticeable oscillations in the flame. These oscillations cause the flame tip to move irregularly, leading to a quite unstable flame tip and, thus, higher uncertainty in the experimental measurements of the thermal radiation. Consequently, substantial deviations in radiation predictions could be