*5.4. Static Pressure Distributions*

Figures 14–16 compare the static pressure distribution on the same diameter section in the pump flow channel of different blade configurations. It can be seen that the static and dynamic interference between the diffuser and the impeller makes the pressure field periodically change. At the impeller outlet, the blade is no longer working on the fluid, the flow rate begins to decline, flow separation appears gradually, and two different regions appear at the pressure fields of the impeller outlet. A low-pressure area is located at the outlet of the impeller blades, while the other one is in the mainstream area downstream from the blade pressure surface, which is also known as the wake-jet, as shown in Figure 14. Wake changes gradually along with the rotating impeller, while the location of the

vortex core remains unchanged, and always appears at the exit of the blades. The generation of static and dynamic interference process can be attributed to the jet and wake flow that then flows into the diffuser vanes.

**Figure 14.** Static pressure distribution of the six-vane configuration.

**Figure 15.** Static pressure distribution of the seven-vane configuration.

**Figure 16.** Static pressure distribution of the eight-vane configuration.

As shown in Figure 15, with the increase of diffuser vane number from six to seven, the flow channel area of diffuser decreases. Accordingly, the frequency of the dynamic and static interference between impeller blades and diffuser vanes increases, and the amplitude of pressure fluctuation increases obviously. Meanwhile, Figure 16 shows that the evolution period of static pressure in the flow channels of three configurations is about 72 degrees, which is the same as the rotation period of the impeller blades. When the outlet side of impeller blade converges with the inlet side of the diffuser vanes, the rotor-stator interaction is the most intense. Simultaneously, there is an obvious low-pressure zone at the outlet of impeller blade, which is close to the pressure surface. With the rotation of the impeller, when the outlet side of the impeller blade is gradually close to the inlet side of the diffuser vanes, the low pressure zone begins to diffuse from the pressure surface of the impeller blade to the suction surface of the diffuser. Then with the interleaving between the impeller channel and the diffuser channel, wake, and jet at the impeller outlet flows into the diffuser vanes successively, the static pressure distribution in the diffuser has a periodic evolution, the area of the low pressure region also changes with the rotation of the impeller blades. When the inlet of the diffuser vanes overlaps with the outlet of impeller blade, the area of low-pressure region generated by the wake is the smallest, and the pressure fluctuation amplitude inside the diffuser is the smallest.

#### **6. Conclusions**

This paper introduces the basic theory and research methods of the pressure fluctuation, and the unsteady numerical simulation under multi-working conditions of three different configurations of a centrifugal pump corresponding to different numbers of diffuser vanes. The unsteady pressure fluctuation in the transient flow is obtained, and the frequency domain and the time domain distribution are analyzed and compared by means of Fast Fourier Transform. With the increase of the number of diffuser vanes, the amplitude of each monitoring point in the diffuser increases gradually, which indicates that the velocity of the fluid is converted to pressure due to the operation of diffuser. The lower number of diffuser vanes is beneficial to obtain the weaker pressure fluctuation intensity. It can be clearly seen that with the static pressure gradually increasing, the effects of the impeller blade passing frequency decay gradually, and the effect of the diffuser vanes increases gradually. The results could supply a basis for further design improvement of the pump body structure and working reliability.

**Author Contributions:** Conceptualization, L.B., L.Z. and Y.Z.; Methodology, L.Z.; Resources: W.S.; Writing-Original Draft Preparation, L.B.; Writing-Review & Editing, C.H.; Supervision, L.Z.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 51609106 and 51805214), China Postdoctoral Science Foundation (Grant No. 2015M581737 and 2017T100331), and Jiangsu Province 333 Projects (Grant No. BRA2017353).

**Conflicts of Interest:** The authors declare no conflict of interest.
