## 1 Introduction  
The spiral groove mechanical seal is a typical non-contact mechanical seal. The liquid film between the end faces can not only provide opening force, but also reduce end face wear. It has been successfully applied to equipment such as pumps, steam turbines, and reactors [1]. Currently, volatile or easily vaporized liquid media are more frequently used in the fluid industry. When the pump is running, the temperature rise of the mechanical seal face causes the liquid film between the seal faces to vaporize, thus changing the seal face fluid film to a vapor-liquid mixed state [2, 3]. Because the fluid film is in a two-phase state, its full sealing film stability is relatively poor. Therefore, the liquid film phase transition impacts the operational stability and reliability of the seal. The aforementioned may even result in seal failure [4]. Although the phase transition may improve the film carrying capacity, reduce leakage, and reduce interfacial friction torque, it also may cause adverse effects [5, 6, 7]. For example, vaporization may cause the integrity of the seal face liquid film to be damaged, thus ensuring the contact between the separated dynamic and static ring seal faces. Consequently, seal face wear, cavitation damage, seal face thermal cracking, or other forms of seal failure may occur. Recently, numerous researchers have carried out relevant research on the phase transition of liquid film mechanical seals. The Rayleigh-Plesset equation, Zwart-Gerber-Belanri model [8], Schnerr-Sauer model [9], and Singhal model [10] have been proposed to solve the cavitation phase transition problem. To address the vaporization phase transition problem, [PERSON] [11], [PERSON] [12], and [PERSON] [13] have proposed different types of Thermal LB models based on the lattice Boltzmann method. The Lee model [14] is generally used for computational fluid dynamics (CFD) analyses to simulate the condensation or the boiling process. This model has the advantages of a simple form, relatively easy calculation, and high reliability. [PERSON] et al. [15; 16; 17] established a vaporization phase transition calculation model based on the viscosity-temperature effect. The saturation temperature with the pressure change equation, fluid internal friction effect, and the phase transition mechanism of the spiral groove liquid film seal were analyzed and discussed. The effect of operating condition parameters on vaporization characteristics of the liquid film and the sealing performance parameters were studied. Based on the evaporation and condensation model in Fluent, [PERSON] [18] and [PERSON] [19] analyzed and calculated the vaporization distribution law of the seal surface liquid film and the phase transition radius. [PERSON] [20; 21; 22], [PERSON] [23; 24], and [PERSON] [25] established the spiral groove and other liquid film phase transition models. Moreover, the authors calculated the flow field and seal pressure distribution in the sealing gap. In addition, they analyzed the influence of operating conditions and structural parameters on the phase transition of the liquid film. Finally, the authors studied the influence of the phase change area on the sealing performance. Based on the finite volume method, [PERSON] [26] established a fluid model to analyze and study the coexistence of cavitation and vaporization. However, in related studies, the mass transfer equation in the Lee model has a mass transfer coefficient whose value is usually based on the researcher's experience. This value lacks a theoretical basis, and the values in different documents are inconsistent [27; 28; 29]. The mass transfer coefficient is generally taken as a default value when studying the phase transition of a non-contact mechanical seal liquid film. [PERSON] et al. [30] proposed that when CFD is used to simulate the vaporization phase transition, a larger value can be selected for the mass transfer coefficient. The larger the value, the higher the calculation accuracy.