# Study on Thermal Radiation Characteristics and the Multi-Point Source Model of Hydrogen Jet Fire
## 1 Introduction  
Global climate change is a pressing issue that has garnered significant attention worldwide. Hydrogen energy, known for its high calorific value, cleanliness, pollution-free nature, widespread availability, and diverse utilization forms, is considered one of the most promising alternative energy sources for the future [1]. Several countries, including the United States and Europe, have elevated hydrogen energy to the level of national strategic planning, establishing initial industrial systems spanning from hydrogen production to utilization [2]. However, the density of hydrogen is only 0.089 g/L under standard conditions, making the development of efficient and safe storage and transportation technologies crucial for improving hydrogen energy utilization efficiency [3]. Currently, there are several methods for large-scale hydrogen transportation, including high-pressure tankers, liquid hydrogen transport, pipeline transport, etc. Compared with high-pressure tankers and liquid hydrogen transport, pipeline transport is an economical and efficient method, making it more suitable for long-distance scenarios. Various countries are developing hydrogen pipeline networks, with notable examples in the United States and parts of Europe. Currently, the US has constructed several thousand kilometers of hydrogen pipelines, with the longest network reaching 965 km [4]. However, hydrogen has certain hazardous properties. Under high pressure, hydrogen's wide flammability limits, low ignition energy, and fast combustion rate can lead to large-scale fires and explosions following a leak [5]. Additionally, the \"hydrogen embrittlement\" effect in hydrogen pipelines increases the likelihood of leakage accidents. Hydrogen jet fires are a common and severely harmful type of disaster [6; 7]. Upon leakage, hydrogen can form jet fires that produce continuous intense thermal radiation and can also motivate chain reactions, leading to secondary or even higher-level accidents [8]. Therefore, addressing the safety issues of hydrogen pipelines is of utmost importance. It is urgent and necessary to focus on the characteristics of jet fires formed by hydrogen pipeline leaks and the thermal radiation hazards they cause and to establish more comprehensive thermal radiation prediction models. In recent years, many scholars have conducted a series of studies on the flame size and thermal radiation characteristics of hydrogen jet fires following leaks in medium- and high-pressure pipelines [9]. Regarding the size of hydrogen jet fires, the visible flame length is an important parameter closely related to the range and severity of thermal radiation. [PERSON] et al. [10] studied the transition characteristics of jet flames from buoyancy-dominated to momentum-dominated, introducing the dimensionless Froude number to describe the normalized flame length based on the nozzle diameter. [PERSON] et al. [11] redefined the Froude number and validated the flame length model across infrared, visible, and ultraviolet spectra. Subsequently, [PERSON] et al. [12] calculated nominal nozzle parameters using a virtual nozzle model, combining these with the flame length model to account for hydrogen's non-ideal behavior at high pressures. [PERSON] et al. [13] conducted small-diameter hydrogen jet fire experiments, finding that the ratio of the flame width to length was approximately 0.18. [PERSON] et al. [14] analyzed extensive experimental data on hydrogen jet flame lengths, using new parameter groups to more accurately describe the dimensionless relationships of the flame length. [PERSON] et al. [15] conducted an experimental study on the stability and size characteristics of hydrogen jet flames, finding that the stability and length of the jet flame are proportional to the fuel injection velocity. [PERSON] et al. [16] measured hydrogen jet flame lengths under various leakage pressures and temperatures, discovering that the flame length and width increased with a higher release pressure and a lower release temperature.