*4.1. Cavitation Characteristics of Impeller in Waterjet Propulsion Pump*

The propulsion pump is the core component of the waterjet propulsion pump system. Therefore, to ensure that the pump system has better anti-cavitation capability, it is necessary to require the pump itself to have excellent anti-cavitation performance. The analysis and research on the cavitation characteristics of the propulsion pump can provide reference for the study of the cavitation performance of the whole waterjet pump system. This paper predicts the cavitation characteristics of the impeller by analyzing the cavitation form, cavitation occurrence region and development trend of the impeller, and the influence of cavitation on head and efficiency of the propulsion pump. As shown in Figure 6, the propulsion pump inlet is extended for a distance to guarantee the accuracy and convergence of the calculation, and the outlet section is connected to the nozzle. The inlet of the extension section is chosen as the inlet of the overall calculation domain, and the nozzle outlet is the outlet of the overall calculation domain. The setting of the boundary conditions is not changed.

**Figure 6.** Three-dimensional schematic diagram of the waterjet propulsion pump.

Based on the calculation results of the performance curve, the design flow rate *Qbep* corresponding to the highest efficiency point was chosen for the simulation calculation of the cavitation flow. During the process of gradually reducing the total pressure of the inlet section from 0.5 atm to 0.1 atm, the pressure distribution of the working surface and suction surface of impeller blade and the change of the area of the cavitation region were simulated. The pressure distribution on the suction surface of the impeller under different *NPSHa* is shown in Figure 7. The blue region represents the lowest air content region, and the red region represents the highest air content region. The air content represents the number of vacuoles per unit volume on the blade surface. In the figure, the blue region represents the low pressure region and the red region represents the high pressure region. It can be seen from the figure that when the value of *NPSHa* is greater than 1.87 m, the low pressure region is mainly concentrated at the leading edge of the blade. When the *NPSHa* value decreases, the area of the low pressure region along the edge of the airfoil gradually increases, indicating that the area and possibilities of the cavitation occurrence become larger.

**Figure 7.** *Cont*.

**Figure 7.** Pressure distribution on suction surface of blade with different net positive suction head-available (*NPSHa*) values.

Pressure distribution on pressure surface of blade with different *NPSHa* values as shown in Figure 8. When the *NPSHa* value is less than 0.96 m, the region on the pressure surface of the blade which is lower than the vaporization pressure begins to appear and the region becomes larger gradually. As the *NPSHa* value decreases, the low pressure region on the pressure surface of the blade gradually develops from the hub near the blade leading edge to the rim.

**Figure 8.** Pressure distribution on pressure surface of blade with different *NPSHa* values.

Figure 9 shows the vapor volume fraction distribution of suction surface of propulsion pump blade in different cavitation stages. The overall distribution trend of vapor volume fraction is consistent with the pressure distribution curve, and cavitation occurs in the low pressure region. The red region indicates the existence of the largest vapor volume fraction in this region, while the blue region indicates the existence of the smallest vapor volume fraction in this region. It can be seen from the figure that the cavitation of the impeller in the propulsion pump first appears around the leading edge of the blade suction surface. The flow pattern at the inlet of the impeller has a great effect on the cavitation performance. When the *NPSHa* value is equal to 1.87 m, the cavitation mainly collects on the leading edge of the blade suction surface near the rim of the impeller. The vapor volume fraction near the rim is the largest. With the decrease of the total pressure, the vapor region gradually spreads along the blade trailing edge and hub direction. When the *NPSHa* value is equal to 1.38 m, cavitation begins to appear in the middle of the surface of the blade, and the cavitation area accounts for about half of the area of the suction surface of the blade. In the process of reducing the *NPSHa* value from 2.41 to 0.76, the maximum vapor volume fraction appeared at the leading edge of the blade near the rim, and as the *NPSHa* value decreased, the maximum vapor volume fraction area gradually expanded toward the blade trailing edge along the water flow direction. As the total pressure of the inlet further decreases, the vapor region gradually spreads to the entire blade. At the same time, the maximum vapor volume fraction area is gradually moving towards the outlet side of the blade. From Figure 9h, it can be seen that when the *NPSHa* value is reduced to 0.76 m, the suction surface of impeller blade is basically covered by bubbles, and cavitation has been fully developed. As shown in Figure 10, when suction surface cavitation develops completely, bubbles begin to propagate towards the trailing edge of the blade pressure surface. When the cavitation develops completely, the cavitation occupies almost the entire blade surface. At this time, the cavitation will block the flow passage and destroy the continuity of liquid flow in the impeller, resulting in the decrease of pump efficiency and head. In summary, according to the classification of cavitation types in the pump, it can be seen that the main type of blade cavitation shown in the figure is airfoil cavitation.

**Figure 9.** *Cont*.

(**g**) *NPSHa* = 0.96 m (**h**) *NPSHa* = 0.76 m

**Figure 9.** Vapor volume fraction distribution on suction surface of blade.

**Figure 10.** Vapor volume fraction distribution on pressure surface of blade.

Figure 11 presents the static pressure distribution along the chord on the suction and pressure surfaces of the blades under three spans at different *NPSHa* values. As can be seen from the figure, the static pressure on the hub side is lower than that on the rim side, and the pressure distribution at the span of 0.9 times shows that the rim produces a lower pressure zone lower than the vaporization pressure (*Pv* = 3574 Pa) earlier than the hub. As the value of *NPSHa* decreases, the continuous development of cavitation causes the velocity and pressure distribution in the impeller passage to change, resulting in a decrease in the pressure of the blade working face and an increase in the area of the low pressure region.

**Figure 11.** *Cont*.

**Figure 11.** Static pressure distribution at different spans on blade surface.

Figure 12 shows the pressure variation from hub to rim with different *NPSHa* values. The calculation results show that the pressure close to the hub edge is less than the rim edge. The pressure at the same point of the blade surface increases as the value of *NPSHa* increases.

**Figure 12.** Pressure variation from hub to rim with different *NPSHa* values.

As shown in Figure 13, the figure presents the distribution of the vapor volume fraction in the impeller passage (facing the incoming flow direction). The figure shows that the vapor in the impeller flow passage first appears at the rim. Moreover, the vapor mainly occurs on the leading edge of the blade, and the vapor gradually extends toward the trailing edge as the value of *NPSHa* decreases. As shown in Figure 13c–e, the vapor at the hub first appears near the trailing edge of the airfoil root, and its gas content is significantly higher than the rim. When the value of *NPSHa* is 0.76m, the maximum vapor volume fraction of the rim is about 51.69%, and the maximum value of the gas content of the hub is 97.11%. The reason may be due to the large distortion of the blade root airfoil and the flow separation of the water flow, resulting in a local low pressure region.

(**e**) *NPSHa* = 0.76 m

**Figure 13.** Vapor volume distribution of impeller rim and hub.

The pump efficiency η, shaft power *N*, and head *H* were used to define the hydraulic characteristics of the waterjet propulsion system. The calculation formula is as follows:

$$
\eta = \frac{30\rho gQH}{\pi nM} \times 100\% \tag{11}
$$

where *T* is the torque of blades, N·m, *n* is the rotating speed of the impeller, r/min, *Q* is the flow rate, m3/s, and *N* is the shaft power, kW.

The cavitation performance curve of the pump under the designed flow rate is shown in Figure 14. As shown in Figure 10, the main type of blade cavitation is airfoil cavitation. When the *NPSHa* value decreases from 2.41 m to 1.47 m, cavitation can be found on the blade surface of the impeller. However, compared with Figure 14, it is found that the head and efficiency curves do not decrease sharply but increase slightly in this process, which is caused by the complexity and instability of cavitation flow. When the pump operates between the initial cavitation condition and the critical cavitation condition, the lift coefficient of the supercavitation will increase slightly as *NPSHa* gradually decreases toward the critical value, and the development of blade cavitation will lead to a certain degree of increase of the pump head before the breakdown cavitation condition. However, the increase of lift and the development of cavitation will also cause cavitation oscillation and damage the flow passage parts of the pump. Hence, pumps are generally not allowed to operate between these two conditions. As shown in Figure 14, the *NPSHa* corresponding to the critical cavitation point K is 1.29 m, and the head decreases by 3.28%. In fact, when the value of *NPSHa* is 1.27 m, it can be seen from the vapor fraction distribution of Figure 9 that cavitation has developed to a certain extent. When the value of *NPSHa* is less than 1.29 m, the head and efficiency of the pump drops sharply as the total pressure at the inlet decreases further. When the *NPSHa* value is reduced from 1.29 m to 1.21 m, the pump head is reduced by 23.23%. When the *NPSHa* value is less than 1.29 m, with the further decrease of *NPSHa* value, the cavitation rapidly covers the suction surface of the blade and gradually extends to the pressure surface, thus blocking the impeller passage and making the pump unable to work normally.

**Figure 14.** Cavitation characteristic curve of pump under design flow condition.
