In this study, a numerical simulation method based on Eulerian–Eulerian model and population balance model (PBM) (i.e., computational fluid dynamics (CFD)–PBM coupling model) was developed to investigate the gas–liquid two-phase performance of centrifugal pump under bubble inflow. The realizable k–ε model turbulence model was implemented in ansysfluent solver. The air and water were employed as the working fluids, which was consistent with the experiment. The water head and pressure increment obtained by the experiment were used to validate the numerical method. The results show that the CFD–PBM coupling model is superior to the Eulerian–Eulerian model, particularly in the “surging” conditions. Using the CFD–PBM coupling model, the influences of parameters, such as inlet gas volume fraction, liquid phase flowrate, and rotational speed, on the head and efficiency of the centrifugal pump were investigated. Under the design condition, when the inlet gas volume fraction increases from 3% to 5%, the bubbles form air mass and stagnate in the impeller channel. The stagnated air mass can hardly be discharged with the liquid phase. Thus, the pump head drops suddenly, i.e., the surging occurs. The two-phase performance of centrifugal pump can be improved under the surging condition by increasing the liquid flowrate and the rotational speed to a certain value. The results contribute to an alternative simulation method to investigate the characteristics of bubble flow in pump and shed new lights on the understanding of the performance of centrifugal pumps under two-phase flow conditions.

The accurate identification of the gas–liquid two-phase flow pattern within the impeller of a centrifugal pump is critical to develop a reliable model for predicting the gas–liquid two-phase performance of the centrifugal pump. The influences of the inlet gas volume fraction, the liquid phase flow rate and the pump rotational speed on the flow characteristics of the centrifugal pump were investigated experimentally. Four typical flow patterns in the impeller of the centrifugal pump, i.e., the bubble flow, the agglomerated bubble flow, the gas pocket flow and the segregated flow, were obtained, and the corresponding flow pattern maps were drawn. After oversampling based on the SMOTE algorithm, a four-layer artificial neural network model with two hidden layers was constructed. By selecting the appropriate network super parameters, including the neuron numbers in the hidden layer, the learning rate and the activation function, the different flow patterns in the centrifugal pump impeller were identified. The identification rate of the model increased from 89.91% to 94.88% when the original data was oversampled by the SMOTE algorithm. It is demonstrated that the SMOTE algorithm is an effective method to improve the accuracy of the artificial neural network model. In addition, the Kappa coefficient, the Macro-F1 and the Micro-F1 were 0.93, 0.95 and 0.95, respectively, indicating that the model established in this paper can well identify the flow pattern in the impeller of a centrifugal pump.

The behaviors of bubbles in a vortex pump play a crucial role in its performance when handling gas–liquid flows. However, not much research has been done on the distribution of the gas–liquid phases and the characteristics of bubble breakage and aggregation in vortex pumps. This lack of understanding hinders the improvement of pump performance in gas–liquid flow transport. This study aims to investigate the bubble characteristics in a vortex pump using the population balance model, focusing on the variation of bubble size and the influence of the inlet gas volume fraction (IGVF) on bubble breakage and aggregation. The results show that as the IGVF increases, the gas volume fraction in the impeller becomes larger than that in the bladeless chamber. The majority of bubbles in the impeller are concentrated near the hub, while they also remain in the circulating-flow zone of the bladeless chamber. Under low IGVF conditions, the average diameter of bubbles decreases from the pump inlet to the outlet. The bladeless chamber has a larger average bubble diameter and a higher percentage of large bubbles compared to other parts of the pump. Moreover, the bubble number density at the pump outlet increases with the IGVF, indicating the production of more bubbles, while the increase in IGVF also results in an increase in the percentage of large bubbles. The study also discusses the mechanism of bubble breakage and aggregation in vortex pumps. It suggests that the effective breakage frequency and effective aggregation frequency are responsible for bubble breakage and aggregation in the vortex pump. The gas volume fraction and turbulent dissipation rate are identified as important parameters affecting the effective breakage and aggregation frequency. These findings provide new insights into understanding the characteristics of bubble breakage and aggregation in vortex pumps.

The flow in mixed-flow pumps under gas–liquid operating conditions is complex, involving special phenomena such as secondary flow and bubble breakup and coalescence. As a result, its pressure fluctuation characteristic is far different from that under pure water conditions. In this work, the energy performance, pressure fluctuation characteristics, and flow pattern under different inlet gas volume fractions (IGVFs) are studied through a visualization test in a mixed-flow pump. The air pocket forms easily close to the suction side of diffuser vanes, where two pressure fluctuation monitoring points are set up. The pressure increment decreases continuously when the IGVF increases, and the flow pattern shows a transition from bubble, condensed bubble, and air pocket to separated flow. Moreover, the pressure fluctuation amplitude and peak-to-peak values increase. The main frequency under different IGVFs is maintained as the blade passing frequency. When the IGVF increases to 15%, the peak-to-peak amplitude at P1 reaches the maximum, which is 2.24 times that of the pure water condition. Some amplitudes at one frequency fluctuate at different times when the IGVF is higher than 10%. The findings contribute theoretical support in improving the stability of multiphase pumps.

The cone meter has been paid increasing attention in wet gas measurement, due to its distinct advantages. However, the cone sensor, which is an essential primary element of the cone meter, plays a role in the measurement of wet gas flow that is important, but not fully understood. In this article, we investigate the gas-liquid annular flow through a cone sensor by experiment and numerical simulation. Emphasis is put on the influences of pressure recovery characteristics and flow structure, and how they are affected by the cone sensor. The results show that the vortex length is shortened in gas-liquid annular flow, compared with that in single-phase gas flow. The pressure recovery length is closely related with the vortex length, and shorter vortex length leads to shorter pressure recovery length. The gas-liquid distribution suggests that flow around the apex of back-cone is very stable, little liquid is entrained into the vortex, and no liquid appears around the low pressure tapping, which makes a more stable pressure at the apex of cone sensor feasible. This finding highlights the importance of obtaining the low pressure from the back-cone apex, which should be recommended in the multiphase flow measurement. Our results may help to guide the optimization of the cone sensor structure in the wet gas measurement.