# Evaluation and Validation of Viscous Oil Cavitation Model Used in Torque Converter
## 2 Materials and Methods
### CFD Settings  
The parameter study on torque converter cavitation is carried out according to the flow chart shown in Figure 4. The internal flow of torque converter is three-dimensional, viscous and turbulent. The full flow model of torque converter was firstly established and then the meshing and mesh independence analysis were carried out, the mesh around the blade surface was refined and its Yplus should be less than 2. Figure 4: Flow chart for the torque converter cavitation calculation using CFD. Figure 3: Mesh model and independence analysis results of torque converter. The CFD calculation was divided into four steps to improve the accuracy and the convergence of the simulation, and the results of previous calculations were used as the initial value of next simulation because the convergence of solution is directly affected by initial value. Firstly, the characteristics of torque converter ignoring cavitation were solved by a steady-state model with the upwind advection scheme, then the non-cavitation steady-state CFD model was performed by high-resolution advection scheme and turbulence numerics to provide accurate flow field status. Thirdly, the steady-state cavitation behavior was simulated using the high-resolution scheme and default cavitation parameters based on the non-cavitation model results. Lastly, a series of steady-state CFD cavitation models with cavitation empirical parameters were carried out using the steady-state non-cavitation outputs as its initial condition to study the influence of cavitation model parameters. After the calculation, the results were processed and the effects of cavitation parameters were analyzed. The detailed CFD model settings are listed in Table 2. The pressure setting in the torque converter has no inlet or outlet boundaries because of the closed-loop flow. Therefore, a pressure value of 0.4 MPa was set at the charge oil inlet which is located at the interface between pump and stator corresponding to the test. The internal fluid fields of the torque converter under stall operating condition were calculated with non-cavitation and cavitation models, and then the pump torque (\(T_{\text{P}}\)), turbine torque (\(T_{\text{T}}\)), and other performance indices were derived from the CFD results. In addition, there are seven parameters in the torque converter cavitation model. \(P_{\text{V}}\) is the saturated vapor pressure, and the vapor pressure of automatic transmission oil is very low, it was set to be 110 Pa in our previous studies [13]. \(F_{\text{cond}}\) is the cavitation condensation coefficient whose default value is 0.01 as condensation usually occurs slowly. \(F_{\text{vap}}\) is the cavitation vaporization coefficient with a much higher default value (50) to represent the growth (vaporization) rate of the cavitation bubbles. \(R_{\text{B}}\) is the mean radius of cavitation bubble, and the default value of 2 \(\times\) 10\({}^{-6}\) m is considered reasonable. \(MDR\) is the maximum density ratio of oil and oilvapor which is used to clip the vapor density for all terms except the cavitation source term itself, its default value is 1000. \(NVF\) is the volume fraction of the nucleation sites with a default value of 5 \(\times\) 10\({}^{-4}\). \(CRRF\) is the cavitation rate under relaxation factor, and its default value is 0.25 [22; 27; 28]. In order to further study the cavitation model, the performance of torque converter with different cavitation parameters was calculated to analyze the sensitivity of each parameter. Herein the parameter study was conducted by varying each parameter while keeping the rest at their default level. The value ranges of the parameters were confirmed