# Design Approach and Mechanism Analysis for Cavitation-Tolerant Torque Converter Blades
## 2 Cavitation Simulation and Verification of HTC
### CFD Model and Validation  
The overall impeller and flow passage layout of the torque converter is shown in Figure 2. The purple parts in Figure 2 are the pump and the pump shell, the green parts are the turbine and the output shaft, the yellow part is the stator, and the cyan part is the hub. The pump is affixed to the engine flywheel and rotates at a rated speed of 2000 rpm. The turbine operates at different speed ratios with changes in the external load. The stator is fixed on the stationary hub. The torus diameter of the HTC is 375 mm. The detailed geometric parameters of the HTC cascade are shown in Table 1.  
Figure 2: HTC CFD model and grid independence study. The grid near the blade wall is refined to capture the transient cavitation flow behavior around the blade. The height of the first-layer grid is set to 0.015 mm to ensure that the y+ value does not exceed 1. Additionally, the grid growth rate is 1.2, the wall grid height is 0.3 mm, and the prism grid has 12 layers. A hexahedral structured grid model of the HTC is depicted in Figure 2. This structural grid is generated using the software Ansys ICEM CFD, and the CFD simulation is performed using the software Ansys Fluent. The full flow passage can be obtained from the geometric model of the torque converter through Boolean operations. The HTC is mainly composed of three computational domains: pump, turbine, and stator. The sliding mesh method is applied to deal with the real-time interaction between the upstream and downstream flows. Mesh interfaces are set up to enable the transmission of variables and parameters between adjacent impellers. The rotational speed of the pump is constant (\(n_{\text{P}}=2000\) rpm), whereas that of the turbine is varied from 0 to 1600 rpm at 200 rpm increments in accordance with the different operating conditions. The time step of the HTC is critical for the transient cavitation simulation. The rotor-stator interaction (RSI) between the pump and the turbine is highly evident, whereas that between the turbine and the stator is smaller [22]. Because the RSI of the turbine-pump (T-P) interface is the strongest, the time step is determined in this study based on the pump rotational speed. If the time step is too large, the transient cavitation will not be obvious or the CFD result will not converge. If the time step is too small, the calculation time will be too long. In this study, the time step is calculated using Equation (8) [23; 24]. Transient calculation is performed with a maximum of 15 loops for every time step, and the total time is 0.12 s, during which the pump can complete four revolutions. The time step is chosen to resolve the unsteadiness in one blade passage at the T-P interface with at least 10 time steps. \[\Delta t=\frac{1}{\omega_{\text{P}}}\times\frac{1}{N_{\text{P}}}\times\frac{1} {10}\geq 0.0001\text{ s} \tag{8}\]  
In Equation (8), \(\omega_{\text{P}}\) represents the revolution speed of the pump (r/s) and \(N_{\text{P}}\) represents the number of blades of the pump. The detailed CFD simulation parameter setting of the HTC is shown in Table 2. On the shell of the stator-pump interface, the pressure level is set to 0.8 MPa, which is identical to the charge pressure during the test. On the shell of the turbine-stator interface, the pressure level is set to 0.4 MPa, which is identical to the back pressure of the HTC. Figure 2 shows the grid independence study. The CFD results indicate that when the mesh number reaches approximately 5 million, further refining the grid size does not strongly affect the outcome but will considerably increase the computational cost. Considering the balance between computational cost and accuracy, 3 is set as the final global grid size in this study. The bench test of the torque converter is shown in Figure 3. The motor drives the pump and the turbine to rotate, and by adjusting different turbine rotational speeds, the torque converter is simulated to work under different working conditions.