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The Francis turbine stability is impacted significantly by the flow characteristics in its draft tube. In the case of a Francis turbine in a hydropower plant, numerical simulations were undertaken at the maximum and rated heads, respectively, under three output scenarios of 20%, 100%, and 120%. The flow characteristics in the turbine draft tube and the evolution mechanism of flow pattern were assessed, as well as the impact of opening on vortex rope. The results demonstrate that with the increasing of the guide vane opening, a progressive transformation is noted for the random large vortex rope located in the conical section at the draft tube inlet into uniformly distributed one. The opening influences the velocity and pressure greatly, and as the opening enlarges, enhancement of the flow pattern is noted in the draft tube. Meanwhile, as the head increases, the influence scope of the vortex rope becomes larger. This research can reveal the operating conditions not suitable for the Francis turbine, thereby offering guidance for ensuring the stability of power station operation.

Abstract To address the measurement accuracy challenges posed by the internal flow complexity in atypical circular bend pipes with short turning sections and without extended straight pipe segments, this study designed an experimental circular “S”-shaped bent pipe with a diameter of 0.4 m and a bending angle of 135°. Numerical analysis was used to determine the stable region for velocity distribution within the experimental segment. Furthermore, a novel evaluation method based on the coefficient of variation was proposed to accurately locate the optimal position for installing thermal mass flow meters on the test cross section. Additionally, a formula for calculating the pipeline flow rate based on velocity differences was derived. This formula considers pipeline flow as the dependent variable and uses the velocity at two points in the test cross section as the independent variable. Experimental validation on a primary standard test bench demonstrated that the flow rate calculated by this method had an error controlled within 0.625% compared to the standard flow rate, thus effectively verifying the method’s high accuracy and engineering applicability. This research provides a new testing methodology and practical basis for flow measurement in complex pipeline systems, offering significant guidance for research and applications in related fields.

During the flood season, Francis turbines often operate under low-head and full-load conditions, frequently experiencing significant pressure pulsations, posing potential threats to the safe and stable operation of the units. However, the factors contributing to substantial pressure pulsations in Francis turbines are multifaceted. This paper focuses on a mixed-flow hydroelectric generating unit at a specific hydropower station. Field tests were conducted to investigate abnormal vibrations and hydraulic pressure pulsations under low-head and full-load conditions. Utilizing the Navier–Stokes equations and the RNG k-ε turbulence model, the unsteady flow field within the turbine under these conditions was calculated. The results indicate that the abnormal pressure pulsations detected in the bladeless zone between the wicket gates and the turbine inlet are due to operational points deviating from the normal operating range of the turbine. When water flows at a large inflow angle, striking the turbine blade heads, it leads to significant flow separation and vortex formation at the back of the blade inlet edges, causing severe vibrations in the hydroelectric generating unit. These findings provide a basis and assurance for the safe and stable operation of the power station.

Bubble flow can be simulated by the two-fluid model and the multi-fluid model based on the Eulerian method. In this paper, the gas phase was further divided into several groups of dispersed phases according to the diameter by using the Eulerian-Eulerian (E-E) multi-fluid model. The diameters of bubbles in each group were considered to be the same, and their distributions were reorganized according to a specific probability density function. The experimental data of two kinds of bubble flow with different characteristics were used to verify the model. With the help of the open-source CFD software, OpenFOAM-7.x (OpenFOAM-7.0, produced by OpenFOAM foundation, Reading, England), the influences of the group number, the probability distribution function, and the parameters of different bubble diameters on the calculation results were studied. Meanwhile, the numerical simulation results were compared with the two-fluid model and the experimental data. The results show that for the bubble flow with the unimodal distribution, both the multi-fluid model and the two-fluid model can obtain the distribution of gas volume fraction along the pipe radius. The calculation results of the multi-fluid model agree with the experimental data, while those of the two-fluid model differ greatly from the experimental data, which verifies the advantage of the multi-fluid model in calculating the distribution of gas volume fraction in the polydisperse bubble flow. Meanwhile, the multi-fluid model can be used to accurately predict the distribution of the parameters of each phase of the bubble flow if the reasonable bubble diameter distribution is provided and the appropriate interphase force calculation model is determined.

The flow inside axial-flow type multi-phase pumps is unstable at the conditions of high-speed and high gas volume fractions. The transient dynamic characteristics induced by the unstable flow will lead to pump vibration. Using the standard k–ε turbulence model, the standard wall equation, and the structured grid division technology, the transient dynamic characteristics of the pump at different gas volume fractions were computed by the SIMPLEC algorithm. The axial force and radial force on the pump were calculated by applying integral to the surface area of the computational domain. The results show that the pressurizing performance of the impeller degrades, the dynamic reaction on the blades decreases, while the force acting on the hub increases with the increasing of gas volume fractions. If the gas volume fraction reaches to a certain value, the direction of axial force on the multi-phase pump will change. The radial forces on the first- and last-stage impellers are non-uniformly distributed, and the pressure fluctuation is obvious, while the radial forces on the second-stage impeller and guide vanes are uniformly distributed, and the fluctuation amplitude is small. With the increasing of gas volume fractions, the radial forces on various components decrease gradually.

In order to investigate the mechanism and the characteristics of the noise induced by unstable flow in a centrifugal pump, the internal flow characteristics in the pump were numerically researched, and the acoustic pressure fluctuations at the pump inlet and outlet were experimentally investigated. Obvious corresponding relationships between the flow instabilities, the cavitation and the noise were established. It was found that the rotating stall, the backflow, the hump, the occurrence of unstable flow and the cavitation in such a centrifugal pump were effectively detected through the noise, which could help to provide fundamental information on flow instabilities and guarantee safe and steady operating conditions for the system. The recirculation and prewhirl regions in the pump upstream pipe, which were caused by the backflow and the rotation of the impeller, presented the circumferential movement with a spiral shape, causing apparent broadband fluctuations at low frequency band of the acoustic pressure. The backflow and rotating stall could also result in broadband fluctuations of the pump outlet noise, which was distributed from 100 Hz to 150 Hz. Meanwhile, the broadband fluctuations of the pump outlet acoustic pressure distributed in the low frequency range, which was produced by the occurrence of cavitation, moved to the lower frequency band as the flow rate increased. The enhanced broadband fluctuations of the pump inlet and outlet noise distributed from 1 kHz to 6 kHz were caused by the coupling between the cavitation-induced noise and the system-produced noise. The broadband fluctuations of the pump inlet noise distributed between 6 kHz and 9 kHz were regarded as the typical frequency band of cavitation in the centrifugal pump.

A combined numerical and experimental method study was performed to detect the inner flow state for a type of centrifugal pump. It was found that the inlet attack angles of blades in an impeller have a great influence on the flow instabilities in a centrifugal pump. The mechanism of the rotating stall in the impeller channel was explained. Meanwhile, flow state identification with vibration (FSIV) was proposed to detect the flow instabilities in a centrifugal pump. The relationship between the external vibration and the inner flow state has been established by FSIV. The characteristics and mechanism of the vibration produced by the flow instabilities in a centrifugal pump were investigated. It was found that the hump, the rotating stall, the backflow, the occurrence of unstable flow, and the cavitation in the centrifugal pump can be effectively detected by applying the vibration signals, which helps to obtain safe and steady operating conditions for the system.