## 4 Results and Discussion
### Flow Characteristics of Unsteady Cloud Cavitation  
In the above section, the steady and unsteady characteristics of sheet cavitation are mainly analyzed. In this section, the investigations are focused on the unsteady characteristics of cloud cavitation. The cloud cavitation is a complex physical phenomenon with obvious strong unsteady characteristics. Figure 8 shows the evolution of the cavity structure over time, with the experimental data and numerical results. Three cavitation models clearly captured the periodic process of the initial, development, shedding, and collapse of the bubbles, which is consistent with the experimental phenomena. The periodic evolution of the cavity structure can be divided into two processes. The first is the process of bubble development from \(t_{0}\) to \(t_{0}+12.5\) ms. During this process, bubbles attached to the leading edge of the hydrofoil and grew linear to the maximum length. The second is the process of the formation and development of the re-entrant jet from \(t_{0}+12.5\) ms to \(t_{0}+42.5\) ms. When the attached bubbles grow to their maximum length, the re-entrant jet begins to appear at the cavity tail, near the wall of the hydrofoil. As the re-entrant jet moves along the suction side toward the leading edge of the hydrofoil, the attached cavity is sheared and then separated from the suction side. When the re-entrant jet reaches the leading edge of the hydrofoil, the attached cavity breaks into two parts, which are named the separated cavity body and the attached cavity body. The separated cavity body moves along the mainstream in the form of a vortex. During this process, the attached cavity body stops growing, and disappears suddenly. Then, the separated cavity body moves downstream and collapses in the high-pressure area. By comparing the calculated results of the three cavitation models, it can be found that the different cavitation models predict different cycle scales. The cycle calculated by the Kunz model is  
Figure 7: Velocity vector field predicted by three cavitation models (\(\sigma=1.075\), \(\kappa=60^{\circ}\)). short; it is equal to 47.5 ms (\(t_{0}\) = 47.5 ms). The cycle calculated by the other two models is about 55 \(ms\) (\(t_{0}\) = 55 ms), which is agree well with the experimental data. The Kunz model predicts the fracture and shedding of bubbles prematurely. The Zwart model successfully predicts the unsteady details of the shearing action of the re-entrant jet on the attached cavity. However, it is not obvious enough to simulate the vortex characteristics for the cavity tail. For the full cavitation model (FCM), the cavity thickness that it predicted was thinner than the other two models, and the cavitation region had a higher vapor content. It simulated the interface of vapor and liquid more clearly, and accurately captured the unsteady details regarding the vortex motion and re-entrant jet, which is consistent with the experimental phenomena. The Kunz model calculated the maximum length and thickness of the bubbles out of the three cavitation models. However, the Kunz model could not predict the shearing action of the re-entrant jet on the attached cavity; it could only predict the shedding vortex of the cavity tail and the retraction of the attached cavity. Also, the Kunz model predicted the shedding of bubbles prematurely. Different cavitation models consider different mechanisms and methods, so different results were obtained. The Zwart model defined the evaporation and condensation source terms from the perspective of the difference between the vapor pressure \(P_{v}\) and the flow field pressure \(p\). It could not reflect the degree of turbulence in the flow field only from the perspective of pressure difference, so the Zwart model does not predict the vortex motion of the cavity tail. The Kunz model uses the cubic polynomial of the liquid volume fraction to define the condensation source term, which leads to the excessive prediction of the condensation potential. Thus, cavity bubbles separated in advance, and the cycle was short.