# Study on Thermal Radiation Characteristics and the Multi-Point Source Model of Hydrogen Jet Fire
## 4 Results and Discussion
### Thermal Radiation  
The relationship between the thermal radiation and the leakage pressure at different flame heights and different leakage diameters is shown in Figure 8. The height at the nozzle is defined as zero. Each figure represents thermal radiation data at different measurement heights for specific leakage diameters and radial distances.  
It is observed that the thermal radiation at various heights increases with increasing leakage pressure, displaying almost a linear relationship. This is primarily because a higher leakage pressure results in an increased hydrogen leakage rate, leading to a higher thermal power of the hydrogen jet flame. A linear relationship exists between the thermal radiation and the flame thermal power. For most conditions, the maximum thermal radiation is observed at a flame height of 0.25 m. The thermal radiation decreases with the increase in the flame height, with the minimum thermal radiation measured at a height of 1.0 m. However, for the condition of a leakage diameter of 2.0 mm, a different trend is observed. When the leakage pressure exceeds 0.55 MPa, the maximum thermal radiation is at a flame height of 0.5 m. This is because flame length increases at higher leakage diameters  
Figure 7: Variations in flame shape parameters under various leakage conditions.  
and pressures, resulting in an upward shift of the maximum radiation position along the axis. Under this condition, the flame height of 0.5 m has a higher local radiation emission coefficient compared with the height of 0.25 m. As the pressure decreases, the flame length decreases, and the maximum thermal radiation returns back to a 0.25 m height. Thus, the thermal radiation at different flame heights is significantly influenced by the flame length.  
Figure 8: Variation in flame thermal radiation with different parameters.  
Comparing Figure 8a,c,e, it is found that as the leakage diameter increases from 1.2 mm to 2.0 mm, the thermal radiation rapidly increases. For the radial measurement distance of 0.23 m, the maximum thermal radiation is 952.8 W\(\cdot\)m\({}^{-2}\) for a diameter of 1.2 mm, and 3378.1 W\(\cdot\)m\({}^{-2}\) for a diameter of 2.0 mm, which is 3.5 times the thermal radiation value for 1.2 mm. It is evident that the diameter of the leakage hole significantly affects the thermal radiation emitted by the jet fire. Compared with the smaller leakage hole, the thermal radiation increases much more rapidly for the larger leakage hole. As a consequence, the heat source power of hydrogen jet fire is higher. This is because the relationship between the hydrogen leakage rate and the leakage diameter is not linear. Therefore, when the leakage diameter increases from 1.2 mm to 2.0 mm, the thermal radiation exhibits dramatic changes and is much stronger.  
Additionally, the variation in the thermal radiation in the different radial distances of the hydrogen jet flame was investigated. Comparing Figure 8a-f, it is found that as the radial distance from the flame axis increases from 0.23 m to 0.5 m, the thermal radiation at the same height decreases. For example, under the condition of a 1.5 mm leakage diameter and a leakage pressure of 0.6 MPa, the maximum thermal radiation at the distance of 0.23 m is 1360.5 W\(\cdot\)m\({}^{-2}\), while this value is only 412.1 W\(\cdot\)m\({}^{-2}\) at a radial distance of 0.5 mm, less than one-third of the value at 0.23 m. Moreover, in the measured thermal radiation density at a flame height of 1.0 m, relatively obvious oscillation characteristics are observed. This is related to the greater strength of the oscillations at the flame head. These oscillations are more pronounced at higher leakage pressures, mainly due to the stronger turbulence intensity of the hydrogen jet at higher outlet pressures, causing the hydrogen jet flame, especially the flame front, to oscillate. This oscillation leads to irregular fluctuations in the thermal radiation flux density measured at specific locations.