## 1 Introduction  
Cavitation, a common fluid mechanics phenomenon, refers to the microbubbles' (also known as nuclei) explosive growth resulting from liquid evaporation caused by local low pressure (i.e., the pressure is lower than the saturated vapor pressure at the corresponding temperature) in a liquid flow system, which is particularly common among various hydraulic turbines, pumps, and ship propellers [1; 2; 3]. Tip vortex cavitation, the earliest type of cavitation that occurs on real ship propellers due to the scale effect [4], will lead to significant pulsating pressure and strong radiation noise, degrading the ship's stealth performance significantly [5; 6]. Studies [7; 8; 9; 10] have shown that constant saturated vapor pressure alone cannot be used as a discrimination criterion, because the motion and growth of nuclei in the water have a considerable influence on the occurrence of TVC. Therefore, research on the discrimination method for propeller TVC inception based on the bubble dynamics models that take into account the effect of nuclei is of great significance in accurately predicting the TVC inception of warships. In [11; 12; 13], the authors determined propeller TVC inception mainly by visual observation during experiments, that is, they use means such as high-speed cameras and stroboscopes to capture the transient behavior of cavitation inception and made an intuitive judgment on cavitation inception through image acquisition with high temporal-spatial resolution. However, this method is heavily dependent on the observer's own experience because the faint TVC usually cannot be detected by the naked eye. Experimental results show that the inceptive cavitation number obtained using visual discrimination methods tends to be lower than that obtained using the acoustics criterion [14]. Moreover, the explosive growth and rapid contraction collapse processes of microscopic nuclei, which are difficult to observe and generate strong pulse acoustic pressure, tend to occur before the cavitation is observed. Such impulsive acoustic signals are also difficult to measure due to the limitations in the accuracy of experimental measurement instruments and the background noise. Therefore, the experimental prediction method for propeller cavitation inception is not only expensive but also tends to underestimate the occurrence of cavitation to a certain extent. In recent years, with the rapid development of high-performance computers, there has been an increasing number of studies investigating propeller TVC inception with the help of computational fluid mechanics (CFD) [15; 16; 17]. At present, the most common numerical prediction method for cavitation inception is the minimum pressure coefficient method based on the Eulerian framework, which predicts the cavitation number of cavitation inception based on the minimum pressure of a global flow field [18; 19]. However, the occurrence of cavitation is caused by the interaction between nuclei and the local pressure field in essence; this method obviously neglects the influence of the growth and collapse effect of nuclei on cavitation inception and only can make a relatively accurate prediction for the weak water with larger-sized nuclei (approximately 400 \(\upmu\)m in diameter), but cannot make a relatively accurate prediction for the strong water with smaller nuclei [15]. Furthermore, existing experimental measurement results show that the size of nuclei in the water is mainly distributed between 40 \(\upmu\)m and 60 \(\upmu\)m, which is closer to the strong water. Therefore, the traditional minimum pressure coefficient method is incapable of making an accurate prediction. [PERSON]'s research team [20] investigated the cavitation inception mechanism of a ducted propeller--David Taylor Propeller 5206--through experiments and found that TVC inception did not occur in a minimum pressure region, and the occurrence of cavitation at early stage might be caused by the strong interaction between vortexes.