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.

This work aimed to study the bubble distribution in a multiphase pump. A Euler-Euler inhomogeneous two-phase flow model coupled with a discrete particle population balance model (PBM) was used to simulate the whole flow channel of a three-stage gas-liquid two-phase centrifugal pump. Comparison of the computational fluid dynamic (CFD) simulation results with experimental data shows that the model can accurately predict the performance of the pump under various operating conditions. In addition, the liquid phase velocity distribution, gas-phase distribution, and pressure distribution of the second stage impeller at a 0.5 span of blade height under three typical working conditions were compared. Results show that the region with high local gas volume fraction (LGVF) mainly appears on the suction surface (SS) of the blade. With the increase in inlet gas volume fraction (IGVF), vortices and low velocity recirculation regions are generated at the impeller outlet and SS of the blade, the area with high LGVF increases, and gas–liquid separation occurs at the SS of the blade. The liquid phase flows out of the impeller at high velocity along the pressure surface of the blade, and the limited pressurization of fluid mainly happens at the impeller outlet. The average bubble size at the impeller outlet is the smallest while that at the impeller inlet is the largest. Under low IGVF conditions, bubbles tend to break into smaller ones, and the broken bubbles mainly concentrate at the blade pressure surface (PS) and the impeller outlet. Bubbles tend to coalesce into larger ones under high IGVF conditions. With the increase in IGVF, the bubble aggregation zone diffuses from the blade SS to the PS.

Integrated systems required for renewable energy use are under development. These systems impose more stringent control requirements. It is quite challenging to control a pumped storage system (PSS), which is a key component of such power systems. Because of the S-characteristic area of the PSS pump turbine, traditional proportional-integral-derivative (PID) control induces considerable speed oscillation under medium and low water heads. PSSs are difficult to model because of their nonlinear characteristics. Therefore, we propose a machine learning (ML)-based model predictive control (MPC) method. The ML algorithm is based on Koopman theory and experimental data that includes PSS state variables, and is used to establish linear relationships between the variables in high-dimensional space. Subsequently, a simple, accurate mathematical PSS model is obtained. This mathematical model is used via the MPC method to obtain the predicted control quantity value quickly and accurately. The feasibility and effectiveness of this method are simulated and tested under various operating conditions. The results demonstrate that the proposed MPC method is feasible. The MPC method can reduce the speed oscillation amplitude and improve the system response speed more effectively than PID control.

Since variational mode decomposition (VMD) was proposed, it has been widely used in condition monitoring and fault diagnosis of mechanical equipment. However, the parameters K and α in the VMD algorithm need to be set before decomposition, which causes VMD to be unable to decompose adaptively and obtain the best result for signal decomposition. Therefore, this paper optimizes the VMD algorithm. On this basis, this paper also proposes a method of multi-domain feature extraction of signals and combines an extreme learning machine (ELM) to realize comprehensive and accurate fault diagnosis. First, VMD is optimized according to the improved grey wolf optimizer; second, the feature vectors of the time, frequency, and time-frequency domains are calculated, which are synthesized after dimensionality reduction; ultimately, the synthesized vectors are input into the ELM for training and classification. The experimental results show that the proposed method can decompose the signal adaptively, which produces the best decomposition parameters and results. Moreover, this method can extract the fault features of the signal more completely to realize accurate fault identification.

To study the energy loss characteristics of a semi-open mixed-flow multiphase pump, an improved entropy generation theory considering the slip velocity was established to locate local areas with high energy loss. The relationships among local entropy generation, phase interface entropy generation, wall entropy generation, and unstable flow were analyzed for each component. The results showed that magnitude of interface entropy generation was similar to turbulent entropy generation and wall entropy generation, which could not be ignored. The interface entropy generation was mainly distributed at the leading edge, trailing edge, hub, and blade tip clearance. With an increased inlet gas volume fraction, the proportion of interfacial entropy production loss to total entropy production loss increased. As the inlet gas volume fraction increased to 30%, the interface entropy generation loss accounted for 70% of the local entropy generation loss at leading edge and 63% at trailing edge. The high interface entropy generation zone at the tip clearance region began to extend from the pressure side of the blade to the suction side of the blade. During the evolution of tip leakage vortex, the generation, unstable stretching, and breakup–regeneration stages were accompanied by a large loss of interface entropy generation.