## 1 Introduction  
Massive commercial refrigeration systems are highly susceptible to having loose components and refrigerant leakages. These systems have many complex pipes. Any improper installation, maintenance or tightening can result in loose or broken fittings, which weaken connection points and allow for leaks [1]. The mechanics of a refrigerator, which operates by expanding and contracting refrigerant under pressure, adversely affects the integrity of seals. In fact, vibration and regular wear and tear, itself, can exacerbate leakages. For these reasons, it is nearly impossible to have a system that will never leak in its lifetime. Refrigeration and air conditioners have a very wide range of applications around the world. They usually contain mechanical moving parts, long pipelines, small parts, etc. During long-term operation, due to the continuous vibration of pipelines, friction and corrosion of working fluids, weathering of external space, or external forces, etc., cracks, holes or gaps often appear in the pipeline, which in turn lead to the occurrence of refrigerant leakage events [2, 3]. [PERSON] et al. [4] found that the annual leakage rate of the commercial refrigeration system of a supermarket chain in the United States was close to 30%. [PERSON] et al. [5] mentioned that among the more than 4000 residential air conditioners surveyed in California, the refrigerants leaked from approximately 62% of the systems. When these high GWP (global warming potential) gases and, in some instances, still ODS (ozone depleting substance), inevitably leak, they pose a direct threat to our climate and environment. Moreover, with the surge in the application of refrigeration and air-conditioning equipment year by year, the impact of leaked refrigerant on the climate increases significantly [6]. Therefore, the replacement of refrigerants should be further implemented to reduce the application of refrigerants with high GWP. Refrigerants with potential to replace high GWP hydrofluorocarbons (HFCs) mainly include natural working fluids, hydrofluoroolefins (HFOs), ethers (HFEs), low GWP HFCs and mixed refrigerants, and some alternative refrigerants have different flammable limits [7]. When the flammable refrigerant leaks from the refrigeration system to the external space, if it is not diffused in time, the concentration of the leaked refrigerant in the local area exceeds its lower flammable limit (LFL) and a flammable area is formed, which threatens the safety of the external space [8]. Therefore, in order to promote the application of alternative refrigerants with superior environmental performance, a large number of theories on the leakage characteristics, the diffusion process and concentration distribution characteristics of flammable alternative refrigerants in local areas have been carried out. The hole model and pipeline leakage model, established by [PERSON] and [PERSON] et al. [9; 10] to describe the gas leakage in pipelines, appeared earlier, which could be used to calculate the leakage and diffusion characteristics for a very small hole area and a completely broken pipeline, respectively. Later, [PERSON] et al. [11] established a more general medium/low pressure pipeline gas leakage model, also known as the big-hole model. On the basis of the three models, some revised models were proposed to further improve their calculation accuracy for gas leakage and diffusion process. For example, [PERSON] et al. [12] analyzed the heat loss in the gas flow process in the pipeline, and a steady-state leakage model under non-isothermal conditions was established, and the gas temperature at the center point within the pipeline above the leak hole was closer to the actual temperature. [PERSON] et al. [13] introduced a correction factor for pressure drop due to the frictional losses along the pipeline and proposed a simplified model for estimating the leakage rate of high-pressure gas pipelines, which slightly overestimated the leakage rate. [PERSON] et al.