## 4 Results and Discussion  
### Flow Characteristics of Sheet Cavitation  
#### 4.1.1 Steady Characteristics  
Figure 3 shows the cavity structures observed by the experimental and numerical results, which were calculated by using the three different cavitation models. Note that the experimental data were obtained from YU and LUO [22]. Comparing the experimental data and numerical results from Figure 3, it is indicated that the Zwart model and Kunz model can predict similar distributions of vapor bubbles around the hydrofoil with the experimental data using the modified simulation method. The structure of the vapor appears to be attached to the hydrofoil NACA0015. The calculated cavity length is about \(0.36c\) for the Kunz model and \(0.37c\) for the [PERSON] model, while in the experiment, it was about \(0.39c\). The major difference between the Zwart model and the Kunz model is in the closure region of the cavities. The trailing edge of the cavity calculated by the Zwart model is narrow and long. The cavity structure predicted by the full cavitation model (FCM) is a very thin layer vapor attached to the leading edge of the hydrofoil, which is quite different from the cavity structure observed in the experiment. It is indicated that the full cavitation model (FCM) cannot predict the formation of sheet cavitation accurately. Figure 1: Computational domain and boundary conditions for NACA0015. Figure 2: Mesh around NACA0015 at an angle of attack \(\alpha=6^{\circ}\) (middle); close view of the leading edge region (left); close view of the trailing edge region (right). Figure 4 shows the distribution of the evaporation and condensation rate by using different cavitation models. It can be found from Figure 4 that the leading edge of the hydrofoil is the evaporation area, and the second half of the cavity is the condensation area. The value of the evaporation source term reflects the degree of the transition from liquid to vapor in the flow field region. The vapor phase is generated at the distribution area of the evaporation source term. Likewise, the value of the condensation source term reflects the degree of the transition from vapor to liquid in the flow field region. It is indicated that both the Zwart model and the Kunz model simulate the evaporation and condensation areas clearly. Meanwhile, the full cavitation model only simulates the small range of the evaporation area attached to the leading edge of the hydrofoil, and does not calculate the existence of the condensation area. Combined with Figure 3, it can be found that the evaporation region is about half of the entire cavity in the Zwart model. In the Kunz model, the evaporation region accounts for about two-thirds of the length of entire cavity. The difference between the two distributions is due to the different definitions of the evaporation and condensation source terms in the Zwart and Kunz models. Both the Zwart model and the Kunz model use the same method to define the evaporation source term. The evaporation source term \(\dot{m}^{-}\) of the Zwart model is proportional to half of the power difference between the bubble pressure \(P_{\rm v}\) and the flow field pressure \(p\), while the evaporation source term in the Kunz model is proportional to the difference between the bubble pressure \(P_{\rm v}\) and the flow field pressure \(p\). Therefore, the results show that Zwart model and Kunz model predict similar evaporation regions. The difference between the two models is mainly in the condensation area. The [PERSON] model performs the same method to define the evaporation and condensation source terms, and so the calculated evaporation area and condensation area account for about half of the cavity. The [PERSON] model uses different methods to define the evaporation and condensation source terms, and the condensation source term \(\dot{m}^{+}\) is a cubic polynomial based on the liquid volume fraction.