## 2 Methodology
### Simulation Setup  
Many researchers employed the single flow passage to develop the cavitation flow field of the torque converter, and the internal flow field was always in highly developed transient turbulence. The rotor-stator interaction and turbulence between the impellers make the flow field distribution of a single flow passage no longer have rotational symmetrical characteristics. Obviously, the CFD model establishment is incorrect. The torus meridian view and the single flow passage are shown in Figure 2, which indicates the layout of the six domains of the torque converter in this paper. Except for pressure inlet (charge pressure, Figure 2a is displayed with a cyan line), pressure outlet (backpressure, Figure 2a is displayed with a cyan line), adjacent domains are connected by an interface, and the remaining boundaries are walls. Figure 3 is a cross-sectional view of the torque converter. According to the sectional view of the torque converter, the full-flow transient passage model was implemented in our study to increase the prediction accuracy for the hydrodynamic torque converter. The charge pressure and backpressure were set at 0.8 and 0.4 MPa, respectively, for the S-P and T-S clearances near the shell (Figure 4).  
Figure 2: Flow passage layout of the hydrodynamic torque converter. (**a**) torus meridian view and (**b**) single flow passage (1-pump domain, 2-turbine domain, 3-stator domain, 4-P-T clearance domain, 5-T-S clearance domain, and 6-S-P clearance domain).  
Figure 4: Structural mesh model of the hydrodynamic torque converter.  
Figure 3: Hydrodynamic torque converter cross-section view (1-pump, 2-turbine, and 3-stator).  
torque converter models with different grid densities were carried out under stall operating condition. Setting the same boundary conditions, algorithms, and convergence criteria, the CFD results under different grid elements are shown in Figure 5. The results indicated that refining the grid had a small effect on the torque when the global grid element size was 3 mm. The commercial software ANSYS FLUENT was used to simulate CFD models comprising 4.48 \(\times\) 10\({}^{6}\) grid elements with a global grid element size of 3 mm.  
Compared with single-phase simulation, converging a multiphase simulation is very challenging. To improve the convergence and accuracy, the time step of the multiphase-flow simulation was reduced five times compared with that of the single-phase flow simulation. The Zwart-Gerber-Belamri cavitation model was employed, which is more stable than that of [PERSON] et al. cavitation model [25]. The time step was taken as 0.0001 s. In total, 1200 time steps were calculated, during which time, the pump completed at least four revolutions. Table 2 presents the details of the CFD model parameters.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Analysis Type** & **Transient** \\ \hline Fluid properties & \(\rho_{l}\) = 860 kg m\({}^{-3}\), \(\mu_{l}\) = 0.0258 Pa s \\ Vapor properties & \(\rho_{o}\) = 2.1 kg m\({}^{-3}\), \(\mu_{o}\) = 1.2 \(\times\) 10\({}^{-5}\) Pa s \\ Turbulence model & SST \(k\)-\(\omega\) \\ Advection scheme & High resolution \\ Convergence target & RMS 1 \(\times\) 10\({}^{-4}\) \\ Pump status & Fixed at 2000 rpm \\ Turbine status & Variable within 0–1600 rpm \\ Stator status & Stationary \\ Charge pressure & 0.8 MPa \\ Backpressure & 0.4 MPa \\ Transient formulation & Second-order upwind \\ Other term spatial discretization & Second-order upwind \\ Time step & 1 \(\times\) 10\({}^{-4}\) s \\ Boundary details & No slip and smooth wall \\ Vapor pressure (\(p_{o}\)) & 110 Pa \\ \hline \hline \end{tabular}
\end{table}
Table 2: Detailed computational fluid dynamics (CFD) model settings.  
Figure 5: Predicted torque results under variant element density (speed ratio (\(SR\)) = 0).