# Design Approach and Mechanism Analysis for Cavitation-Tolerant Torque Converter Blades
## 4 Discussion  
### Quantitative Analysis of Cavitation Threat with Slot Designs  
The cavitation number is a dimensionless number that is essential for describing the threat of cavitation. The smaller the cavitation number, the greater the risk of cavitation. The equation is  
\[\sigma=\frac{p_{ref}-p_{v}}{0.5\rho_{l}v_{ref}^{2}} \tag{17}\]  
In Equation (17), \(p_{ref}\) is the reference pressure, \(p_{v}\) is the vapor pressure, \(\rho_{l}\) is the fluid density, and \(v_{ref}\) is the reference velocity. In this study, the toroidal velocity is considered the reference velocity, and it is expressed as  
\[v_{t}=\frac{\dot{m}}{\text{B}\rho_{l}} \tag{18}\]  
where \(\dot{m}\) is the fluid mass flow rate and B is constant for a given design (in this case B = 2.56 \(\times\) 10\({}^{-2}\) m\({}^{2}\)).  
The hydrodynamic performance of the four suppression slots is calculated. The \(T_{\text{bg0}}\) of Plan 4 deteriorates the most severely (6.81%). The \(K_{0}\) of Plan 4 is reduced the most (3.23%). Despite the hydrodynamic performance degradation, the application of suppression slots  
Figure 11: Velocity distribution in stator domain under stall operating condition for various suppression slots (\(t\) = 0.12 s).  
greatly suppresses the stator cavitation process in the HTC. Additionally, no unstable shedding cavitation is observed in the flow field of the HTC with the suppression slot blades, which can reduce noise and strong erosion caused by cavitation.  
As seen in Figure 12, the cavitation number increases with \(SR\), which indicates that low \(SR\)s lead to a high risk of cavitation. Additionally, the cavitation number of the baseline configuration is the smallest. After the slotted blade is used, the cavitation number can be greatly increased, and the cavitation threat around the blade is greatly decreased. The cavitation numbers of Plan 3 and Plan 4 are basically the same when \(SR\leq 0.3\), and they are also the blades with the most obvious increase in cavitation numbers. Plan 1 shows the worst improvement of the cavitation number, which means that its improvement effect of cavitation suppression is unsatisfactory.  
The load distribution of the stator suction blade with the different suppression slots is shown in Figure 13. These findings are used to investigate the cavitation suppression effect of the different suppression slots under stall operating condition. The torque exerted by the fluid on the blade is identical to the integral of the product of the pressure on the blade and the radius. Therefore, it is directly identical to the pressure difference between the pressure surface and the suction surface of the blade. As shown in Figure 13, because of the accelerated flow of fluid near the leading edge of the stator suction surface, the pressure drop in this region is very noticeable, which is conducive to cavitation. When the baseline is near S0.1, the absolute pressure is close to 0, which means that the baseline configuration undergoes heavy cavitation. Additionally, the placement of the suppression slot increases the absolute pressure near the leading edge of the stator suction surface to varying degrees and reduces the cavitation effect in this region. The absolute pressure increase of Plan 4 is the most significant (the lowest absolute pressure is >3.0 \(\times\) 10\({}^{5}\) Pa), thus fully suppressing the stator cavitation. On the contrary, the method of slotting only the suction side (Plan 1) is not highly effective in suppressing the stator cavitation. Additionally, it causes the blade load to fluctuate drastically, which is not conducive to power transmission.  
Figure 12: Distribution of cavitation threat characteristics for various suppression slots.