# Numerical Investigation of Methodologies for Cavitation Suppression Inside Globe Valves
## 3 Results and Discussion
### Effects of the Working Temperature and Outlet Pressure  
When the outlet pressure and the working temperature vary, the total pressure drop or the saturated vapor pressure changes, thus leading to the variation of cavitation intensity. In this section, the effects of the working temperature and the outlet pressure are studied and compared. Figures 7 and 8 show the water vapor volume distribution in the two-cage globe valve under different outlet pressures and different working temperatures. The working temperature for Figure 7 is 80 \({}^{\circ}\)C, and the outlet pressure for Figure 8 is 0.1 MPa. The water vapor volume decreases with the increase in the outlet pressure or the decrease in the working temperature. Based on the water vapor volume distributions, one can find that increased outlet pressure has more positive effects on cavitation intensity than the working temperature. Figure 6: Comparison of cavitation number and loss coefficient for the globe valve with a different number of cages. Figure 7: Water vapor distribution in two-cage globe valve with different outlet pressure: (**a**) 0.15 MPa; (**b**) 0.20 MPa; (**c**) 0.25 MPa. To investigate the effects of the outlet pressure and the working temperature quantitatively, the cavitation number and the loss coefficient are compared in Figure 9, where the straight line stands for cavitation number, and the dash line stands for the loss coefficient. It can be found that the cavitation number increases with the increase in the outlet pressure and the decrease in the working temperature, which is consistent with the above results. Cavitation number almost has a linear relationship with the outlet pressure. When the outlet pressure increases by 0.05 MPa, the cavitation number increases nearly by 0.4. While the increment of the cavitation number decreases with the decrease in the working temperature. When the working temperature decreases from 80 \({}^{\circ}\)C to 60 \({}^{\circ}\)C, the average increment of cavitation number is 0.134, and the average increment of cavitation number is 0.0538 if the working temperature decreases from 40 \({}^{\circ}\)C to 20 \({}^{\circ}\)C.  
The loss coefficient barely changes with varying outlet pressure which is because the loss coefficient is affected by the pressure difference between the valve inlet and valve outlet shown in Equation (5). However, with the increase in the working temperature, the loss coefficient decreases firstly then increases rapidly, and when the working temperature is 80 \({}^{\circ}\)C, the loss coefficient has the maximum value. The difference of the loss coefficient may be caused by the cavitation phenomenon inside valves. Figure 8: Water vapor volume distribution in two-cage globe valve with different working temperature: (a) 20 \({}^{\circ}\)C; (b) 40 \({}^{\circ}\)C; (c) 60 \({}^{\circ}\)C.  
Figure 9: Cavitation number and loss coefficient of two-cage globe valve with different outlet pressure and working temperature. In the numerical simulation applied in this study, the finite volume method is used. Thus, the water vapor volume in valves can be calculated based on the water vapor fraction and the discrete volume, and the expression is shown below. \[V=\sum_{1}^{n}\alpha_{v}dV \tag{6}\]  
here \(V\) stands for the total water vapor volume in a valve, \(n\) stands for the total number of the discrete volume, \(dV\) stands for the volume of a discrete volume, \(\alpha_{v}\) stands for the water vapor fraction in a discrete volume. The water vapor volume in the investigated two-cage globe valve under different outlet pressures and the different working temperatures is shown in Figure 10. It can be found that when the outlet pressure is larger than 0.2 MPa, the variation of water vapor volume under different working temperatures is small. While the outlet pressure is smaller than 0.2 MPa, the water vapor volume increases with the increase in the working temperature and the outlet pressure, and the higher the working temperature, the greater the influence of the outlet pressure on water vapor volume.