## 1 Introduction
Extensive research on refrigerant leakage and diffusion has been conducted by domestic and foreign scholars, encompassing both theoretical and experimental approaches. In terms of theory, [PERSON] et al. [19] comprehensively investigated the refrigerant leakage within pipelines and its subsequent diffusion in confined spaces. They developed a leakage-diffusion model for real refrigerant gases, dividing the leakage process into three stages: transportation, primary throttling, and secondary expansion. The diffusion process within the confined space was similarly categorized into two stages: localized expansion and compression near the leak source, followed by turbulent diffusion in the far field. By incorporating the thermophysical properties of real refrigerants, the model reveals that transonic flow conditions are reached during the throttling and expansion phases. Upon entering the external space, the refrigerant continues to expand and compress, generating complex excitation waves within the near-field region. These waves, forming Mach loops,induce substantial variations in the temperature, pressure, and velocity of the refrigerant. The presence of the Mach ring hinders efficient refrigerant diffusion, significantly increasing the localized high-concentration areas formed by the leaked refrigerant. Based on their previous work, [PERSON] et al. [20,21] explored the effects of the initial leakage pressure, leakage hole diameter and hole shape, refrigerant thermophysical parameters, velocity, and concentration fields after refrigerant leakage. The diffusion process and concentration distribution characteristics of the refrigerant in the confined space were analyzed, and the boundaries of the flammability area where the refrigerant leaked into the confined space under different conditions were divided. It was found that due to the differences in the thermophysical properties of the refrigerant, the temperature field, velocity field, and concentration field in a confined space showed large differences. Among them, the density, viscosity, and diffusion coefficient of the refrigerants were found to have a significant effect on the concentration field. When two refrigerants have similar densities, the Schmidt number (Sc) can be used to comprehensively evaluate the combined effects of viscosity and diffusion coefficient on their diffusion. In addition, [PERSON] et al. [22] numerically simulated the diffusion process of R290 when it leaks from the heat exchanger elbow in the indoor unit of a split air conditioner and analyzed the refrigerant concentration distribution within the room. [PERSON] et al. [23] simulated the scenario of R32 leaking from the indoor heat exchanger in a rooftop air conditioning system, and found that the refrigerant concentration in most areas of the air supply duct exceeded the flammability limit. [PERSON] et al. [24] studied several of these parameters, including refrigerant charge size, leakage mass flow, leakage direction, height of refrigerant-containing components, cabinet doors, condensing unit housings, air flow, and room clogging, by simulating R290 leaks. The simulation results were used to understand the meaning of device leaks and possible structural characteristics that help limit the development of high concentrations. [PERSON] et al. [25] studied the R290 leakage scenario in a multi-split air conditioning system, analyzing the variations in refrigerant concentration under different ventilation conditions within the confined space. [PERSON] et al. [26] performed CFD simulations of the dispersion of HC-290 leaks for a variety of scenarios, including leakage rate, IDU installation height, IDU fan on or off, and furniture type. [PERSON] et al. [27] used computational fluid dynamics to simulate major leaks from a 2640 kW (750 TR) chiller, evaluating a range of refrigerant leak rates and different alarm trigger ventilation rates to understand the dilution requirements to prevent a significant fuel buildup.