Mixed-flow pumps are characterized by their wide operating range and high-efficiency region in the fields of agricultural irrigation, hydropower engineering, and urban water supply systems. The stability of the transient processes, such as start-up and shutdown, has drawn great attention to the increasing capacity and impeller diameter of mixed-flow pumps in the industrial field. Particularly, the start-up process of a mixed-flow pump is an extremely complex transient process. The mixed-flow pumps can experience shock loading, hydraulic vibrations, and cavitation damage during the start-up process, leading to a negative impact on the stable operation of the pump. The evolution of noise characteristics at the pump section is of great significance for stability monitoring during the start-up process of mixed-flow pumps. This study aims to investigate the variation and influencing factors of noise under different start-up modes. An acoustic vibration test system was selected to collect the noise, shaft vibration, and pressure fluctuation signal of mixed-flow pumps under linear and non-linear starting modes. Then, the collected noise signals were analyzed using acoustic signal processing, including the energy entropy ratio analysis, spectral chart analysis, and A-weighted sound pressure calculation. A systematic analysis was made to clarify the influence of start-up on the sound pressure level and spectral characteristics of noise. The energy intensity in the noise was also analyzed. A coherence analysis was then implemented to determine the correlation among the impeller outlet pressure fluctuation, shaft vibration, and pump noise during the start-up process. The results showed that there was a concentrated region in the high amplitude sound pressure of the noise starting at the end of the start-up process in the three start-up modes. The shortest time scale was achieved in the high amplitude noise region under the concave exponential function start-up mode, indicating the least persistent impact on the environment. There was a relatively minimal impact noise generated by the concave exponential function start-up mode, indicating that this start-up mode was beneficial to avoid the severe mechanical impact during start-up. In addition, the formant analysis of the noise spectrogram showed that there was the lowest probability of mixed-flow pump’s instability induced by the concave exponential function start-up mode among the three start-up modes. The highest A-weighted sound pressure level of the noise generated by the pump was located at the frequency band with the center frequency of 250 Hz. The maximum A-weighted sound pressure level and the total effective sound pressure level of the noise generated by the pump under the linear start-up mode were less than those of the other two start-up modes. Compared with the linear start-up mode, the concave exponential function start-up mode improved the sound pressure level of the medium- and low-frequency noise. The wavelet partial coherence analysis showed that the impeller outlet pressure fluctuation was the main factor affecting the dominant sound pressure level (center frequency was 250 Hz) of the noise during the start-up process. The radial vibration of the shaft only affected the noise at the very low-frequency band.

Pumping stations can serve as crucial hydraulic facilities in various applications. However, their operating conditions can often lead to the presence of suction vortices in the sump. There are some serious impacts on the safe and stable operation of the pumping station. This study aims to explore the effect of the suction vortex morphology and its evolution on the stability of the centrifugal pumps under different operating conditions. A full-channel test platform was constructed for the vertical centrifugal pump. The research object was taken as the suction pipe on the horizontal side. The volume of fluid (VOF) was used to simulate the flow characteristics. A systematic analysis was made to explore the effects of the unsteady flow on the steady operation of a centrifugal pump during the evolution of the suction vortex at high flow rates. The results show that the steady duration of the suction vortex increased with the flow rate increased during testing. The shape of the vortex was greatly varied from the surface depression to the continuous suction. The strength and diameter of the suction vortex increased continuously at the high flow rates. The whole observation time was in the continuous phase of the suction vortex. Among them, the projected area remained at a high value. At the same time, the shedding of the large-scale bubble also caused the projected area to fluctuate violently. Excellent agreement was found in the development paths of the suction vortices that were captured by numerical simulations and the experimental ones (Q=15.6 m³/h). The suction vortices first appeared near the wall of the tube, then broke off into the suction tube under the action of the incoming flow after being destroyed, and flowed along the bottom of the suction tube to form two air paths and large bubble clusters at the inlet of the centrifugal pump. The air moved constantly toward the centrifugal pump at the high flow rates, as the suction vortex evolved. The content of air then reached a peak in the flow passage components during the continuous phase. As the suction vortices evolved from the development phase to the continuous phase, the void fraction rapidly increased, and the bubbles clustered in the flow channel of the impeller, leading to a sudden change in the pressure pulsation on the suction surface of the blades. The pulsation range of pressure in the continuous phase was 2 times that of the development phase. The main frequency of the pressure pulsation was shifted from f_n（rotating frequence）to 2f_n. While the amplitude of the pulsation at 2f_n increased along the flow direction. The gas action was also enhanced dramatically by the non-uniform inflow. Large-scale vortices were observed within the channel of the impeller. The greatest velocity of the gas was observed at the leading edge of the blade near the suction pipe side. In the rest of the channel, the gas velocity varied from increasing first to decreasing, leading to the increasing amplitude of the radial force on the impeller and the radial force vector to eccentric. The gas was distributed unevenly in the impeller flow passage and then converged at the outlet of the volute after rotating. The high peak-and-peak values of the pressure pulsations were found in the three specific regions (vaneless region, guide vane, and volute) of the centrifugal pump. The peak-to-peak values of pressure pulsations exhibited the most significant increase near the volute tongue, with increments of 59%, 57%, and 58% observed in the vaneless space, guide vane, and volute respectively. Furthermore, the bubble moved with the main flow towards the tongue in the continuous phase of the suction vortex. The density of the gas was much lower than that of the liquid. The bubble cluster was prevented from a pressure gradient to occupy the flow channel. There was a significant increase in the turbulent pulsation. The region was then expanded into the highly turbulent kinetic energy. Consequently, there was an increase in the peak-to-peak value of the pressure pulsation at the tongue, thus affecting the operational stability of centrifugal pumps.

The variation of inlet gas volume fraction (IGVF) intensifies bubble breakup and coalescence behaviors, and the resulting evolution of gas pockets may directly impact the energy performance and stability of multiphase pumps. In this work, effects of IGVF on performance parameters, energy characteristics and flow instability are investigated by ANSYS CFX software. Bubble breakup and coalescence dynamics, along with their associated gas–liquid interfacial entropy production under high IGVF conditions are considered. Results show that predicted values of pressure increment, pressure fluctuation, and gas distribution characteristics agree well with experimental data. With the increase of IGVF, the pressure increment decreases while gas volume fraction (GVF) in the impeller and diffuser increases. When the IGVF rises from 5% to 15%, gas pockets form on the diffuser suction sides, accompanied by a sharp decline in pressure increment and rapid increase in GVF and average bubble diameter, ultimately triggering surge phenomena. The increasing IGVF accelerates bubble coalescence, leading to a higher proportion of large bubbles in the flow passages. Consequently, both the number and size of gas pockets increase, resulting in enhanced gas–liquid interfacial entropy production. Furthermore, pressure fluctuation characteristics are thoroughly analyzed, which can provide a reference for the energy loss analysis and optimal design of multiphase 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.

Speed conversion has posed a significant impact on the stability of the mixed flow pump in the operation of variable speed. Taking the mixed flow pump as the research object, this study aims to collect the displacement signals of shaft vibration and pressure pulsation inside the pump under different speed conversion modes using a synchronous acquisition system. A systematic analysis was made to clarify the influence of speed conversion modes on the stability of mixed-flow pumps. The results show that the position of the shaft center was inconsistent with before the start of speed conversion at the end of speed conversion. There was the smallest offset distance of the quartic power speed conversion, which was 0.075 mm. The vortex motion of shaft vibration was the most stable under the speed conversion to the quartic power, compared with the rest. In the quartic power speed conversion, the ratio of S_(p-p) to ∆D was only greater than 0.33 at the end of the speed conversion. The maximum kurtosis of the two-dimensional joint was 5.67 (quarter power), 5.61 (linear), and 5.4 (quartic power), respectively, for the three-speed conversion modes. Among them, the proportion of positive joint kurtosis for the shaft vibration was 70% (quarter power), 44% (linear), and 4% (quartic power), respectively. The quartic power speed conversion effectively improved the mechanical impact of shaft vibration. The main frequency of shaft vibration was the rotational frequency f_n under different speed conversion modes. The proportion of high amplitude region was 87.5%, 62.5%, and 12.5% in the descending order of the index under the speed conversion mode. The high amplitude and high-order harmonic frequencies of shaft vibration were concentrated mainly in 2f_n among the three-speed conversion modes. Phase resonance caused the amplitude of higher-order harmonics of pressure pulsation inside the impeller to be stronger than f_BPF(passing frequency of impeller blades) during speed conversion. The proportions of high amplitude areas in 12f_n under the three-speed conversion modes were 75%, 50%, and 5% in the descending order of their indices. The main frequency of shaft vibration velocity still remained in the time-frequency of pressure pulsation inside the pump during speed conversion, indicating the high impact of shaft vibration on pressure pulsation. Finally, the improved TOPSIS was used to quantitatively evaluate the operational stability of mixed-flow pumps under speed conversion modes. The results showed that the operational stability of the mixed flow pump gradually deteriorated, as the speed increased. There was the smallest stability index of the quartic power speed conversion. The mixed flow pump has the best stability during the quartic power speed conversion, only considering shaft vibration and pressure pulsation. The findings can provide a strong reference to improve the stability of mixed flow pumps during speed conversion.

Cavitation is one kind of complex multiphase flow. Unstable cavitation flow can often induce a high amplitude of pressure pulsation, leading to the vibration of the pump body inside the centrifugal pump. A threat can also be posed to the safety and stability of pump operation. This study aims to explore the variation in the radial force and the pressure pulsation of the impeller, as the cavitation developed. A closed centrifugal pump was taken as the research object. Unsteady numerical simulation was carried out to investigate the cavitation flow in the centrifugal pump under a given flow rate. The homogeneous Eulerian-Eulerian two-fluid model was used to simulate the cavitation flow. Two-equation SST (shear stress transmission) k-ω model was adopted as the turbulence model to close the URANS (unsteady reynolds averaged navier-stokes) equations. The Schnerr-Sauer cavitation model was used to solve the volume fraction of the vapor phase. The reliability of the model and numerical simulation was verified to compare with experimental values. A systematic analysis was made to determine the influence of vapor bubbles on radial force and pressure pulsation. The research results indicated that the time-averaged radial force on the impeller first slightly decreased and then suddenly increased as the cavitation developed. The turning point was observed in the condition that the sheet cavitation appeared near the shroud. Furthermore, the time-averaged radial force reached as high as 60.5 N under complete cavitation, which was 1.4 times higher than under non-cavitation. And the peak value of radial force reached the maximum of 120 N, which was 1.69 times that of no cavitation stage. The high amplitude radial force caused the pump body more prone to instantaneous large vibration. The presence of bubbles disrupted the symmetry of pressure distribution, resulting in a polygonal distribution of radial force. The frequency of radial force variation was dominated by the impeller rotational frequency and its multiplication under different cavitation states. Once the cavitation was developed to the critical value, there was no variation in the amplitude of radial force corresponding to the impeller rotational frequency, while the amplitude of its multiplication increased only. When the net positive suction head was 1.9 m, the amplitude of radial force corresponding to the impeller rotational frequency was 41 N, which was about 1.4 times that under non-cavitation. The amplitude of radial force was 10 N corresponding to the sub-frequency of 2 times the impeller rotational frequency, which was 1.7 times that under non-cavitation. The influence of the breaking of vapor bubbles on pressure fluctuations shared a certain degree of global significance. This influence also depended on the relative position of the monitoring points and bubble clusters. The pressure pulsation coefficient and standard deviation were basically 0 when the monitoring point was located inside the bubble cluster. There was a significant increase and then a decrease, as the vapor bubbles were broken and aggregated when the monitoring point was located near the bubble clusters. The pressure wave generated by the breaking of vapor bubbles was also found downstream along the flow direction. The main frequency of pressure pulsation at each monitoring point was the impeller rotational frequency under different cavitation. The slow evolution of bubble clusters in the impeller induced the low-frequency pressure pulsations of 0.5 times the impeller rotational frequency during the complete cavitation. Consequently, the main frequency amplitude of radial force in the pressure pulsation was more suitable for evaluating the development of the cavitation flow field. The findings can also provide theoretical references to monitor and identify the cavitation in centrifugal pumps.