# Design Approach and Mechanism Analysis for Cavitation-Tolerant Torque Converter Blades
## 2 Cavitation Simulation and Verification of HTC
### CFD Model and Validation
The rotational speed and torque of the pump and the turbine are obtained through the torque and rotational speed sensors on both sides of the pump and the turbine, and then the hydrodynamic performance of the torque converter can be obtained through calculation. \begin{table}
\begin{tabular}{c c c c} \hline
**Element** & **Inlet Angle (\({}^{\circ}\))** & **Outlet Angle (\({}^{\circ}\))** & **Number of Blades** \\ \hline Pump & 123 & 64 & 29 \\ Turbine & 32 & 157 & 24 \\ Stator & 120 & 33 & 22 \\ \hline \end{tabular}
\end{table} 
Table 1: Structural parameters of HTC. \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 & \(\rho_{v}\)= 2.1 kg m\({}^{-3}\), \(\mu_{v}\) = 1.2 \(\times\) 10\({}^{-5}\) Pa s \\ Turbulence model & SST \(k\)-\(\omega\) \\ Advection scheme & High resolution \\ Convergence target & RMS 1 \(\times\) 10\({}^{-4}\) \\ Charge pressure & 0.8 MPa \\ Back pressure & 0.4 MPa \\ Pump status & Fixed at 2000 rpm \\ Turbine status & Varied within 0–1600 rpm \\ Stator status & Stationary \\ Pressure–velocity coupling & SIMPLE \\ Transient formation & Second–order implicit \\ Other term spatial discretization & Second–order upwind \\ Time step & 0.0001 s \\ Boundary details & No slip and smooth wall \\ Vapor pressure (\(p_{v}\)) & 110 Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed CFD model parameter setting. Figure 3: Test rig for the HTC (1—drive dynamometer meter, 2—drive dynamometer, 3, 14—fluted disc, 4, 15—speed transducer, 5, 7, 11, 13—coupler, 6, 12—torque transducer, 8—oil inlet, 9—oil outlet, 10—torque converter, 16—dynamometer, 17—dynamometer meter, 18—mechanical brake, 19, 26—speed meter, 20, 25—torque meter, 21, 23—pressure meter, 22, 24—temperature meter). After the simulation, the torque of each component is obtained; both noncavitation and transient cavitation CFD results are compared with the test data (Figure 4). The calculation formula for the hydrodynamic performance of the HTC is in [25; 26]. The hydrodynamic performance of the torque converter is defined by the following operating parameters. The torque values of each impeller are averaged, and the hydrodynamic performance of the torque converter is calculated. \[SR\ (\text{speed \ ratio})=\frac{n_{\text{T}}}{n_{\text{P}}} \tag{9}\]  
\[K\ (\text{torque \ ratio})=\frac{T_{\text{T}}}{T_{\text{P}}} \tag{10}\]  
\[\eta\ (\text{efficiency})=K\times SR \tag{11}\]  
\[T_{\text{bg}}\ (\text{capacity factor})=\frac{T_{\text{P}}}{\rho gn_{\text{P}}^{ 2}D^{5}} \tag{12}\]  
where \(n_{\text{P}}\) and \(n_{\text{T}}\) are the rotational speed (rpm) and \(T_{\text{P}}\) and \(T_{\text{T}}\) are the torque (Nm) of the pump and the turbine, respectively; \(D\) is the diameter of the torus (mm); and \(T_{\text{bg}}\) is the capacity of the power transmission (\(10^{-6}\text{min}^{2}r^{-2}\text{m}^{-1}\)). When speed ratio (\(SR\)) > 0.3, the two CFD results are consistent in terms of the capacity factor. When \(SR\leq 0.3\), the capacity factor of the test data increases with \(SR\). The noncavitation result does not exhibit this trend, and a maximum error of 13.23%  
Figure 4: Comparison of CFD results with test data under various \(SR\) conditions. (**a**) \(K\) and \(K\) absolute; (**b**) \(T_{\text{bg}}\) and \(T_{\text{bg}}\) absolute error. occurs under stall operating condition. On the contrary, the transient cavitation result achieves accurate prediction, with an error of less than 5% at a low \(SR\). However, both the noncavitation and cavitation models overpredict the capacity factor under high-\(SR\) (\(SR>0.3\)) operating conditions; this can be attributed to the disregard for the flow leakage at the shell and core in the HTC. When \(SR>0.3\), the \(K\) values of the two models are consistent with the trend of the capacity factor. When \(SR\leq 0.3\), the error of \(K\) considering the cavitation effect is less than 4%; by contrast, the \(K\) error without cavitation is up to 8%.