Interactions often occur between particle impact, leakage vortex production, and particle trajectory in a semi-open centrifugal pump. These interactions can aggravate the complexity of erosion under solid-liquid two-phase flow condition. In this research, the two-way coupling Euler-Lagrange and Finnie erosion model was proposed to determine the solid-liquid two-phase flow field under different particle volume concentrations in semi-open centrifugal pump. A systematic investigation was conducted to clarify the influence of particle volume concentration on the structure characteristics of leakage vortex, particle migration trajectory, and erosion. The correlation analysis was utilized to reveal the specific mechanism between particle volume concentration, tip clearance leakage vortex, and the erosion of flow passage components. The results show that the pressure gradually increased from the impeller inlet to the outlet under the solid-liquid two-phase condition. Compared with the clear water condition, there was the increase in the pressure for the accumulation of particles in the flow passage, where the maximum pressure increased by 4%. Once the particle volume concentration was less than 1%, there was the similar structure and characteristics of tip leakage vortex, tip separation vortex, and passage vortex in the impeller passages. A few particles inhibited the flow separation at the boundary layer. Correspondingly, the low-pressure area was reduced near the blade leading edge, which was conducive to the improvement of pump hydraulic performance. Particles with a diameter of 0.5 mm were belonged to the large size and mass particles, indicating the low fluid ability to carry them. As a result, most particles were remained the original direction of axial movement after entering the impeller. The obstruction effect was found to combine with the tip clearance leakage vortex. Particles were easy to impact the leading edge near the blade bottom and the suction surface near the blade tip, which were in the severe erosion and more outstanding spot erosion. The particles were frequently impacted on the surface of flow passage components, as the particle volume concentration increased, leading to the serious erosion of the hub and inlet edge of blade pressure surface. Meanwhile, the serious crowding among particles in the flow passage caused some particles to deviate from the running track, and then impact the blade suction surface with the fluid. Therefore, the linear erosion appeared near the blade bottom at the outlet edge of suction surface, and then the erosion range was gradually extended to the inlet. Once the particle volume concentration was greater than 3%, the average erosion rate of the hub increased faster and eventually greater than the blades. The number of particles increased to flow into the tip clearance layer with the increase of particle volume concentration. The frequent impact of particles on the tip leakage vortex led to their breakdown, separation, and refusion, which was aggravated the flow unsteadiness. In addition, more collision and friction between particles caused the increase of the energy consumption and hydraulic loss of fluid transport particles, indicating the significantly reduced pump head and efficiency. This finding can provide the theoretical references for the optimal design and safe operation of semi-open centrifugal pump under solid-liquid two-phase conditions.

Axial flow pumps can serve as the core equipment for waterjet propulsion and water diversion. However, the flow separation-induced stall can cause the hump-shaped characteristics in the head-flow curves under low-flow conditions. Such unstable flow can pose significant operational risks to the pump. In this study, a flow control strategy was proposed with the endwall injection to suppress the rotating stall in an axial flow pump. Experimental studies were conducted in terms of the steady-state and pulsed endwall injection for the axial flow pump. A systematic investigation was made on the influence of the injected flow rate, injector numbers, and pulsed injection frequency on the performance of the axial flow pump. The injected flow rate was normalized against the design flow rate of the axial flow pump. The injected flow rate was tested in the range from 2.6% to 10.48% in the experiment. The number of the injectors varied between 1 and 6. The frequency of the pulsed injection covered a range of 0.05 to 0.5 Hz. The pressure pulsation test revealed that the endwall injection improved the stability of the axial flow pump. A test rig of the closed-loop axial flow pump was carried out at the State Key Laboratory of Water Engineering Ecology and Environment in Arid Area, Xi’an University of Technology, Shanxi Province, China. The test pump was designed with a flow rate of 168 m³/h, a head of 3.12 m, and a rotational speed of 1 800 r/min. The results indicate that the injected mass flow rate, injector number, and pulsed injection frequency shared a significant impact on the performance of the axial flow pump. In the steady-state endwall injection, the stall margin of the axial flow pump increased with the increase of the injected mass flow rate and the number of injectors. The pump efficiency exhibited negligible sensitivity to the injected mass flow rate when the injected mass flow rate was below 5% of the design. The measurable efficiency was enhanced significantly when the injected mass flow rate exceeded 8.4%. Parametric studies revealed that there was a non-monotonic relationship between the injector number and pump efficiency, indicating peaking at four injectors. The optimal injector number was four, considering both the stall margin and the efficiency under the design point. The pump efficiency and the stall margin were improved by 1.83% and 39.4% at an injection flow rate of 5.6%. Experimental studies were conducted on the pulsed endwall injection using six injectors. The greater stability was achieved by reducing the injected flow in the pulsed endwall injection, compared with the steady-state one. The frequency of the injection significantly impacted the pump performance. The stall margin generally increased as the injection frequency rose. However, there was little influence of the increasing injection frequency on the pump stability when the injection frequency exceeded 0.25 Hz. The injection frequency was elevated to significantly improve the pump efficiency. Once the critical threshold of the injection frequency was beyond 0.17 Hz, there was a negligible influence of the injection frequency on the pump efficiency. Both the pump efficiency and stall margin of the axial flow pump were balanced at the injection frequency over 0.25 Hz. Once the injection frequency was 0.50 Hz, the superior stability was enhanced in the pulsed endwall injection, compared with the steady-state one. The injection flow rate of 4.2% and the efficiency under the design point were also improved by 53.9% and 3.52% in the stall margin of the axial flow pump, respectively. Mechanistic analysis revealed that the head declined to initiate with the rotating stall onset, where the propagation velocity of the stall cell reached 72% of the impeller rotational speed. Endwall injection effectively delayed the stall inception caused by the rotating stall. The optimal parameters fully suppressed the rotating stall. Thereby, the operational stability was improved significantly to eliminate the associated hump-shaped characteristics in the head-flow curves. In conclusion, the endwall injection demonstrated the dual-benefit capability to maintain the pump efficiency under the design point. While the operational stability was enhanced significantly. A critical flow control strategy can be expected for the high-efficiency and high-stability operation in the axial flow pumps.

Centrifugal pumps are widely used in industrial fields due to their simple structure and reliable operation. In industrial sites, valves are usually arranged in the inlet pipe of centrifugal pumps to cut off water flow during maintenance. However, the valve wake causes inflow distortion of the centrifugal pump, and the wake vortex also has a strong unsteady effect. These characteristics contradict the assumed stable and uniform inflow conditions during the design stage of the centrifugal pump, resulting in a deviation between the actual performance of the centrifugal pump and its design performance and reducing its stability. Therefore, conducting research on the impact of valve for maintenance on the performance of centrifugal pumps is of great significance for optimizing the design of inflow pipelines and improving the operational stability of centrifugal pumps. The research object of this article is a Tri-eccentric butterfly valve and a semi-open centrifugal pump, aiming to study the unsteady wake characteristics induced by the valve and its impact mechanism on the operating characteristics of centrifugal pumps under high flow conditions. The Tri-eccentric maintenance valve is placed at the position of one pipe diameter before the inlet of the centrifugal pump as the inflow distortion condition, and the situation without the valve is used as the uniform inflow condition. The external characteristics of the centrifugal pumps under uniform and distorted inflow conditions are compared through experiments. Numerical simulation is used to study the flow characteristics of valve plate wake vortices and their impact on the unsteady internal flow field of the centrifugal pump. The radial force of the impeller induced by valve plate wake vortices is analyzed. The results show that under the two conditions of uniform inflow and distorted inflow, the numerical simulation and experimental results of the external characteristics are in good agreement, with errors within 5%, and the accuracy of the numerical simulation used to reflect the flow characteristics of the centrifugal pump is verified. When water flows through the valve, complex vortices are generated, and the vortices that have a significant impact on the centrifugal pump mainly come from the boundary layer separation and suction on one side of the valve plate. This vortex results in a 9.15% decrease in efficiency and a 1.2 m decrease in head under high flow conditions. The shedding frequency of the valve plate wake vortex is 1.9 times rotational frequency, and a pressure pulsation of the same frequency is generated at the inlet of the centrifugal pump. The periodic inflow of wake vortices leads to an increase in the maximum relative flow angle of two blade leading edges from 30° to 43° and 39°, which exacerbates the flow separation of pressure surfaces of the two blades. Due to the influence of flow separation, a gradually dissipating stall vortex is generated in the impeller channel. The mismatch between the period of the stall vortex and the wake vortex results in the blade being subjected to complex non-stationary excitation forces, but the main frequency of the excitation force is still 2 times the rotational frequency, corresponding to the development period of the stall vortex. The periodic suction of wake vortices and the development of stall vortices cause the average radial force acting on the impeller to increase to about 4.5 times that of uniform inflow, and the maximum radial force to reach about 7 times that of uniform inflow, while the radial force vector shifts. The frequency spectrum of radial force fluctuation is mainly composed of the development frequency of stall vortices and the shedding frequency of wake vortices. The radial force vector shifts will exacerbate the risk of centrifugal pump shaft failure. The conclusions obtained can provide a judgment basis for the operating status of centrifugal pumps under inflow distortion conditions and a theoretical basis for improving the operational stability of centrifugal pumps.