# Study on Thermal Radiation Characteristics and the Multi-Point Source Model of Hydrogen Jet Fire
## 1 Introduction
Research on the thermal radiation characteristics of hydrogen jet fires has increasingly utilized numerical simulations with Computational Fluid Dynamics (CFD) software. [PERSON] et al. [17; 18] simulated hydrogen jet fires with leakage pressures of 0.5 MPa and temperatures of 48-82 K, comparing the simulated flame length and radiation heat flux data with experimental results, thus validating the accuracy of the CFD model. Additionally, [PERSON] et al. [19] simulated 90 MPa high-pressure hydrogen jet flames using ANSYS Fluent, achieving good agreement with the experimental results of [PERSON] [20]. [PERSON] et al. [21] used the FLACS program to analyze the hydrogen concentration, temperature, and thermal radiation distribution in confined spaces following high-pressure hydrogen leaks and ignitions. [PERSON] et al. [22] compared the thermal radiation released by hydrogen and propane jet flames, finding that the axial radiation rate of hydrogen was 3.5 times lower than that of propane under similar conditions. [PERSON] et al. [23] used CFD software to study large hydrogen jet fires under a leakage pressure of 16 MPa and a flow rate of 15.0 kg/s, finding that the thermal radiation could reach 100 kW/m\({}^{2}\) even 70 m from the jet fire source, posing serious risks to humans and facilities. [PERSON] et al. [24] conducted experimental studies on hydrogen thermal radiation release during low leakage and ambient temperature, finding that low-temperature hydrogen jet flames had a higher radiation heat flux density at certain mass flow rates compared with ambient-temperature jet flames. The multi-point source thermal radiation model, based on the weighted distribution of heat sources, performs well in predicting near-field and far-field thermal radiation. This model, proposed by [PERSON] et al. [25], uses a weighted superposition method based on the single-point source thermal radiation model. [PERSON] et al. [26] compared experimental data with predicted thermal radiation values under similar conditions, finding the model to have a good predictive performance. [PERSON] et al. [27] optimized the heat source-weighted coefficients along the jet flame axis using an inversion method. The predicted values of the optimized radiation model showed a smaller deviation from the experimental data, indicating that the improvement of the flame length prediction model and the weighted coefficients can significantly improve the accuracy of the weighted multi-point source model. [PERSON] et al. [28] predicted the thermal radiation of methane well blowout flames by the multi-point source prediction model and optimized the weighted coefficient by the inverse optimization method. Then, the predicted values were compared with the CFD simulation results. The results showed that the weighted coefficient optimization method can further improve the accuracy of the multi-source model for predicting the thermal radiation of methane jet fires. [PERSON] et al. [29] predicted the thermal radiation release from combustible materials, noting that rapid flame formation must account for flame shape changes in thermal radiation prediction. [PERSON] et al. [30] optimized the traditional multi-point source prediction model by considering the buoyancy effect on the flame centerline trajectory, improving the model's practical application accuracy. In the weighted multi-point source thermal radiation prediction model, the accurate calculation of weight coefficients significantly impacts the predictive accuracy of the model. In the classic multi-point source thermal radiation prediction model for methane jet fires proposed by [PERSON] et al. [25], the weighted coefficients were assumed to linearly increase from zero, reaching a maximum value at 75% of the flame length, and then linearly decrease to zero at the flame tip. Although this weighted multi-point source model has demonstrated practical utility in some applications, the underlying assumption for calculating these weights is overly simplistic, limiting the accuracy of the model.