## 3 Transient Cavitation Behavior in a Hydrodynamic Torque Converter
### Validation of the CFD Model
Figure 7 depicts the periodic behavior of stator cavitation under the stall operating condition, which indicates vapor shedding and confirms that the reentrant jet shedding mechanism was captured well using the CFD models. The cavitation shedding was triggered by a reentrant jet, which formed upstream of the reattachment point of the reverse flow and was then driven by the reverse pressure gradient to move upstream toward the leading edge. The attached cavitation cloud finally detached, and the process repeated. Figure 6: Comparison of computational fluid dynamics (CFD) results against test data under various operating conditions. The height of the attached cavitation cloud at the leading edge increased with cavitation development, which can aggravate its unsteadiness. O-shaped cavitation was predicted at the peak of the attached cavitation near the stator leading edge, which has not previously been discovered by other researchers studying cavitation in hydrodynamic torque converters. [PERSON] and [PERSON] at Wuhan University and the Beijing Institute of Technology, respectively, have similarly been researching hydrofoil cavitation, and they predicted shedding horseshoe cavitation and U-type cavitation [27,28]. With the further development of the reentrant jet, the O-type cavitation broke, and the attached cavitation was cut off. The occurrence of stator cavitation was determined by the circulation flow rate and incidence angle. When the circulation flow rate approached the threshold for cavitation inception, the attached cavitation was predicted in the hydrodynamic torque converter. Cavitation then became unstable with increasing mass flow rate, and the reentrant jet driven by the reverse pressure gradient moved towards the stator nose. The jet then lifted and cut off the attached cavitation, which triggered the shedding cycle. O-type cavitation could be predicted at the stator leading edge when the mass flow rate fulfilled certain conditions. The stator cavitation showed three forms depending on the reentrant jet, i.e., attached, O-type, and shedding cavitation. Four stages, i.e., inception, development, shedding, and collapse were observed. The \(Q\) criterion was introduced to capture the vortex structure in the internal flow field [29], which is defined by  
\[Q=\frac{1}{2}\Big{(}\|\Omega\|^{2}-\|S\|^{2}\Big{)}, \tag{17}\]  
where \(\Omega\) (vortex tensor) and \(S\) (strain rate tensor) are the antisymmetric and symmetric portions, respectively, of the velocity gradient tensor. Figure 7: Unsteady cavitation process in the stator domain under \(SR=0\) condition. (**a**) \(t=0.125\) T, (**b**) \(t=0.25\) T, (**c**) \(t=0.375\) T, (**d**) \(t=0.5\) T, (**e**) \(t=0.625\) T, (**f**) \(t=0.75\) T, (**g**) \(t=0.875\) T, and (**h**) \(t=1\) T. (1-attached cavity, 2-cavity development, 3-”O” type cavity, 4-”O” type cavity break, 5-shedding cavity, and 6-scatter cavity (collapse)). Figure 8 depicts the vortex structure near the turbine and stator blades. The details of the turbulent flow are given under non-cavitation and cavitation conditions. The attached cavitation at the turbine leading edge induced a large-scale shedding vortex and significantly modified the structure of the local vortex. The fluid velocity on the leading edge of turbine was greater without cavitation than with cavitation. It indicated that the flow velocity without cavitation effects was overestimated. It is the result of blockage of the flow passage caused by cavitation bubbles. Because of the fully developed turbulence, the vortex structure of the turbine was scattered and chaotic when cavitation effects were not included, as shown in Figure 8a. As shown in Figure 8c, a measurable separation vortex was predicted at the turbine leading edge due to the attached cavitation, and the largest-scale vortex structure appeared at the maximum camberline location of the turbine blade.