## 3 Results and Discussion
### Effects of Divergent Length on Cavitation Characteristics  
#### 3.2.1 Analysis of Pressure and Vapor Volume Fraction  
Figures 7 and 8 depict the changes in the absolute pressure and vapor volume fraction for varying divergence lengths of Venturi tubes at inlet pressures of 0.4 MPa, 0.8 MPa, and 1.2 MPa. The results indicate that the absolute pressure variation profile is similar across all three operating conditions, characterized by a sudden drop in pressure, followed by the lowest pressure in the throat, and eventually rebounding to the outlet pressure. The aforementioned process was also reported in a study conducted by [PERSON] et al. (2018), who observed that the pressure flatness at the throat of the Venturi indicates the occurrence of a phase transition. However, our current study reveals that the influence of the divergence length on the absolute pressure is contingent upon the inlet pressure. Specifically, when the inlet pressure is 0.4 MPa, as depicted in Figure 7a, the curves representing the absolute pressure variation for the three different divergence lengths show a remarkable overlap, suggesting that the length of the divergence section has a negligible effect on the absolute pressure under these conditions. In Figure 7b,c, the effect of the length of the divergence section on the absolute pressure becomes more prominent when the inlet pressure is either 0.8 or 1.2 MPa. It is observed that shorter divergence sections in Venturi tubes result in longer low-pressure zones, which promote bubble formation. This distinction becomes increasingly apparent with higher inlet pressures. The rationale behind this phenomenon can be ascribed to the synergistic impact of two key factors: the inlet pressure and the expansion of the diameter in the diverging section. In the context of higher pressure conditions, the length of the low-pressure zone within the Venturi tube is not solely determined by the magnitude of the inlet pressure but is also influenced by the degree of diameter expansion in the diverging section. Venturi tubes with shorter diverging sections exhibit a relatively smaller increase in diameter. As a result, the velocity decay inside the tube is gradual, leading to an extended low-pressure zone. Figure 8 exhibits a rising trend in the vapor volume fraction within the Venturi's throat, which is aligned with the previously discussed pressure variation. These findings indicate that the low-pressure region in the throat plays a significant role in generating cavities. Furthermore, it has been observed that there exists a certain degree of overlap in the ascending segment of the  
Figure 6: Comparison of the distribution of vapor phase between the experiment and the numerical results. vapor phase curve under varying pressure conditions, suggesting that alterations in the length of the divergent section do not impact the cavitation characteristics of the throat. Moreover, at an inlet pressure of 0.4 MPa, the distribution of vapor volume fraction remains consistent across different divergence section lengths. However, at inlet pressures of 0.8 MPa and 1.2 MPa, this consistency is broken, and an increasing trend is observed in both the amplitude and coverage area of the vapor volume fraction with a decreasing divergence section length. This shows that shorter divergence section lengths under higher pressure circumstances are beneficial to enhance the cavitation effect in the Venturi tube. Figure 9 presents a comparison of the vapor volume fraction contours for three divergence lengths of the Venturi at various inlet pressures. The figure illustrates that vapor initially appears in the neck of the Venturi and then develops further in the divergence section. Furthermore, it is worth noting that the sensitivity of the vapor volume fraction exhibits variations under different pressure conditions. When the inlet pressure is 0.4 MPa, the cavity lengths of the Venturi with different divergence lengths are very similar, as demonstrated in Figure 9a.