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Pumps as turbines (PATs) are used in petroleum and chemical industries to recover high-pressure residual energy. Multistage PATs allow for a wider energy recovery interval and wider range of applications. However, because multistage centrifugal pumps were not originally designed for turbine conditions, complex pressure fluctuations occur, impacting the stable operation and performance of multistage PAT. Pressure fluctuation is essentially a wave, and by analogy with the wave intensity definition, pressure fluctuations were quantified using the pressure wave energy flow density, and the pressure fluctuation patterns at different stages were investigated. The findings reveal significant differences in the intensity of pressure fluctuations at different locations within the multistage PAT. Specifically, the pressure fluctuation intensity is significantly higher from the second to the final stage, compared to the first stage. The difference in inlet flow conditions is the main reason for this difference in pressure fluctuations between stages. The inlet inflow from the second to the final stage is subject to rotational effects that exacerbate the difference in pressure fluctuation intensity between stages. Pressure fluctuations are found to be negatively related to the distance from the source of fluctuations and positively related to the flow state. Different flow conditions and interaction regions of the impeller affect the distribution of pressure fluctuation intensity and the distribution of pressure fluctuation energy across different frequency domains within the guide vanes. The main source of fluctuations in the shaft frequency and four times the shaft frequency is the impeller inlet interaction region, whereas the fluctuations in the blade passing frequency originate from the impeller outlet interaction region. This paper provides a reference for improving the stable operation of multistage PATs. [ABSTRACT FROM AUTHOR]

A five-stage centrifugal pump is utilized to investigate the interstage flow characteristics of the multistage centrifugal pump as turbine (PAT). The simulation results of performance are verified by comparing with the experimental results. Owing to the distinct structural attributes, significant differences in flow occur between the first stage and the other stages of the multistage PAT. To enhance the understanding of these disparities and explore their repercussions, this study focuses on analyzing the flow within the impellers in the first and second stages by a deterministic analysis. The main conclusions are as follows: The discrepancies in the inflow conditions are the major reason for the dissimilarities in the flow of impellers between stages. The impact loss generated by the misalignment between the positive guide vane outlet angle and the impeller inlet angle leads to flow deviation between impeller passages and affects the internal flow pattern. The unsteadiness under low flow rates is mostly produced by the spatial gradient of the blade-to-blade nonuniformities, which is relevant to the relative position between blades and the positive guide vanes. At high flow rates, especially in the second-stage impeller, the pure unsteady term is the primary cause of flow unsteadiness as a result of the flow separation induced by interactions between the blades and the positive guide vanes. This study can provide some references for the practical operation and performance optimization of the multistage PATs in the future. [ABSTRACT FROM AUTHOR]

Numerical simulations of multiphase flows with both interfaces and discrete particles are challenging because they possess a wide range of length and time scales. Meanwhile, the volume of fluid (VOF) method is suitable for resolving the interface, while the discrete particle model (DPM) under the Lagrangian frame better simulates unresolvable particles; a multiscale VOF–DPM combined model is urgently needed for multiscale multiphase flows. The present work implements a VOF–DPM solver that includes a two-way transition algorithm to model the transformation between discrete and continuous phases for bubbles or droplets using OpenFOAM. The interface-capturing scheme in the solver is based on the interIsoFoam solver, which supports the geometric reconstruction of the interface and adaptive mesh refinement. A connected component labeling approach is used for particle detection and VOF-to-DPM transition for discrete bubbles or droplets produced by interface breakup. Conversely, a DPM-to-VOF transition algorithm for particles touching the interface is incorporated to achieve a two-way transition. In addition, phase change modeling between continuous phases and bubble dynamic modeling for cavitating flow cases are also implemented in the solver. Test simulations are performed for validation, including the gas–liquid two-phase dam break and cavitating flow in a convergent–divergent test section. The results demonstrate that the solver is reasonably accurate and can adequately represent the complex phase structure, including the interface and discrete particles. [ABSTRACT FROM AUTHOR]

High-speed centrifugal pumps are widely used in the aerospace and chemical industries. However, the large axial thrust of a rotor due to high rotating speeds exacerbates the device operation instability. Herein, the axial thrust characteristics of a high-speed centrifugal pump under variable speed conditions are analyzed via numerical simulations and experiments. Results show that at high rotating speeds, although the dynamic reaction of the impeller and axial force on the inducer blade only account for a small proportion of the axial thrust, they are the main sources of axial thrust instability. Moreover, axial thrust exhibits a linear relation with the axial force acting on the front and back surfaces of the impeller, and the values of these parameters are very close. However, huge errors are afforded when these two parameters are interchanged, and many axial thrust estimation models ignore this. Therefore, considering the influence of the impeller dynamic reaction and the axial force of the inducer blade on axial thrust, this study proposes an estimation theory for predicting axial thrust. Comparison of the prediction results of the estimation theory and the numerical simulation results reveals that the maximum and minimum relative errors of these two parameters are 11.1% and 2.6%, respectively, under different rotational speeds, thereby suggesting that the prediction results of the estimation theory are sufficiently accurate. The estimation theory can greatly reduce the calculation cost, shorten the design cycle of the centrifugal pump, and provide certain reference for engineering practice. [ABSTRACT FROM AUTHOR]

Cavitating flows always include micro-bubbles and macro-cavities over a wide range of length scale, and understanding the vorticity force evolution induced by cavitation is also a challenging issue. In the present work, a hybrid multiscale cavitation model incorporated with the large eddy simulation approach is applied for comprehensively revealing the unsteady cavitating flow features. The macroscale cavities are captured by the volume of fluid (VOF) method while the microscale bubbles are modeled using a discrete bubble model (DBM) in the Lagrangian way. Simulations of the cavitating flow on a twist hydrofoil are performed and validated against the experimental result. Good agreement in terms of cavity morphology and shedding frequency is obtained. Applying the multiscale cavitation model, the microscale cavitation bubbles that are unable to be predicted by the VOF method are well represented especially in the region near the trailing edge. To investigate the vorticity force evolution, the force element method is adopted to quantitatively analyze the change of force elements along with the evolution of the cavity. The overall effect of cavitation on the lift and drag forces is also investigated. Finally, the superiority of the multiscale VOF-DBM model is attested compared with the original VOF method. [ABSTRACT FROM AUTHOR]

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied. [ABSTRACT FROM AUTHOR]

For the tip-leakage cavitating flow, the existence of both interface and microbubbles at scales separated by orders of magnitude makes it difficult to be comprehensively reproduced by numerical modeling. This work aims to develop a multiscale model that directly resolves the large-scale cavities and models small discrete bubbles. The volume of fluid (VOF) method and the Schnerr–Sauer cavitation model are first adopted to represent the phase field of water and vapor from a macroscale point of view. A discrete bubble model (DBM) based on the Lagrangian formulation is then developed to simulate the microscale cavitation bubbles that are smoothed in the macroscale model due to the limited mesh resolution. The transition between DBM and VOF is also implemented to achieve the multiscale simulation. For modeling of the turbulence, the scale adaptive simulation approach is used. The tip-leakage cavitating flows induced by the NACA0009 hydrofoil under the conditions with different gaps according to the reported experiment are simulated. Results show that, using the proposed multiscale model, better agreements can be obtained compared with the macroscale model, and specific phenomena can be well revealed including the bubble nucleation, growth and collapse, the interaction between discrete bubbles and large-scale cavities. [ABSTRACT FROM AUTHOR]