Vortices are fundamental coherent structures whose statistical characteristics reveal essential properties of turbulence. Previous studies on open-channel flows (OCF) have predominantly focused on the characteristics of spanwise vortices within two-dimensional planes, whereas the behaviors of streamwise and vertical vortices, as well as the true three-dimensional scale characteristics of vortices, remain largely unexplored. This study employs direct numerical simulation (DNS) to compare the two-dimensional and three-dimensional spatial statistical characteristics of vortices in OCF and closed-channel flow (CCF) at a friction Reynolds number of Reτ= 500, revealing the influence of the free surface on vortex characteristics in OCF. Prograde and retrograde vortices (i.e., spanwise vortices whose rotation is aligned with or opposite to the mean-shear-induced rotation), together with streamwise and vertical vortices, are identified via the λci criterion. Vortex radii and circulations are extracted based on the intrinsic properties of the vortices, and the VATIP algorithm is utilized to reconstruct three-dimensional vortex topologies for scale analysis. The results show that the vortex statistics exhibit distinct depth-dependent variations. In the region 0 <y/h< 0.10, the radius trends differ among vortex types. Meanwhile, the circulations of prograde and vertical vortices decrease rapidly, whereas the circulation of streamwise vortices increases. This increase is consistent with the interaction between near-wall streaks and quasi-streamwise vortices. The radius-circulation relationship of prograde vortices and the spanwise energy-flux distribution further suggest that vortex-intensity enhancement associated with an inverse-energy-cascade-like process may occur under strong mean shear. In the region 0.10 <y/h< 0.80, the mean radii of different vortex types gradually increase, which may be associated with interactions or merging among neighboring rotating structures away from the wall; however, their mean circulations generally decrease. In the region 0.80 <y/h< 1.0, compared with CCF, the radii and circulations of spanwise and streamwise vortices in OCF decrease more rapidly, which is consistent with the wall-normal constraint imposed by the free surface, whereas vertical vortices exhibit an increase in radius. The three-dimensional scale analysis further shows that, in the region 0.70 <y/h< 0.95, vortices exhibit a tendency toward flattening, characterized by a decrease in the wall-normal scale and increases in the streamwise and spanwise scales. Pressure-strain redistribution near the free surface provides a possible statistical explanation for this anisotropic deformation.

Water-sediment swirling flow is ubiquitous in rotating machinery. The centrifugal field drives the liquid outward and generates intense azimuthal shear, which in turn enhances the relative motion between water and sediment. The influence of the rotational effect on the velocity distribution of the two phases, particularly the relationship between vortex intensity and interphase slip velocity, has not yet been fully clarified. Based on PIV (particle image velocimetry) experiments, measurements were conducted on a dilute water-sediment two-phase flow with a magnetic stirrer rotating at 400-800 r/min and sediment particles ranging in size from 20 to 150 mu m. The experimental results indicate that in the water-sediment swirling flow system, under the same rotational speed and particle size, the circumferential distribution of the time-averaged velocity of the water-sediment two-phase flow exhibits strong uniformity across the azimuth, while the radial distribution shows a trend of first increasing and then decreasing with increasing r/R. Overall, the slip velocity decreases with increasing r/R, and larger values typically appear in the regions with a larger rotation-rate tensor magnitude or higher fluid velocity. The peak time-averaged velocity and St (Stokes number) of the two phases increase with increasing rotational speed and particle size, and the turbulence intensity of the particle phase is higher than that of the liquid phase. Furthermore, there is a significant positive correlation between & Vert;Omega & Vert;(2)(F), which characterizes the vortex strength, and the relative slip velocity, indicating that greater vortex strength tends to enhance the relative motion between particles and the fluid.

Image velocimetry has gained significant attention for flow measurement in field rivers, with recent efforts combining satellite videos with various image velocimetry techniques to enhance cost-effectiveness, resolution, and public accessibility. However, challenges remain, including lower image resolution and frame rates compared to conventional methods, as well as pixel offsets caused by continuous satellite motion. Moreover, the accuracy of satellite-based flow measurement has yet to be systematically evaluated due to the difficulty of obtaining instantaneous and precise surface flow fields in large rivers. This study applied three mainstream image velocimetry methods, namely space-time volume velocimetry (STVV), optical flow methods (OFM), and large-scale particle image velocimetry (LSPIV), to analyze satellite video footage of the Chongqing section of the Yangtze River. A hydrodynamic simulation was conducted to generate reference instantaneous flow fields corresponding to the video acquisition date. Results indicated that all three methods can derive large-scale flow fields with acceptable accuracy (the root mean square errors of velocity magnitude for STVV, OFM, and LSPIV were 0.3218 m/s, 0.8131 m/s, and 0.8003 m/s) when measurement parameters were appropriately adjusted, demonstrating the feasibility of satellite-based river velocity monitoring. Among them, STVV achieved the best performance, with regression lines closely aligned with y=x. The coefficients of determination were 0.86 for flow direction and 0.82 for velocity magnitude, with a relative error of 14.24

Hydraulic machinery is commonly employed to transport a solid-liquid two-phase flow with fine particles in chemical and hydraulic engineering, and the inner flow pattern is characterized by a strong swirling turbulence carrying massive amounts of fine particles. The classic two-fluid model (TFM) can completely describe the dynamic characteristics of each phase and their interactions. However, the multitude of coupled equations limits the prediction efficiency for large-scale engineering computations. Two alternative simplification methods are available: the first is the mixture model (MM), which treats the solid and liquid phases as a blended mixture, while the second is a quasi-single-phase model based on the suspended load diffusion equation. However, both struggle to balance high accuracy and flexibility, presenting an incompatibility between accurate velocity field computation and on-demand coupling with the concentration field. To address this issue, the partially-algebraic two-fluid model (PATFM) combining the strengths of both methods is proposed as a compromise solution. Its core ideas are as follows. (1) Based on D'Alembert's principle, the particle velocity is obtained by using a pseudo-transient algebraic expression, avoiding the higher computational cost of discretizing and solving the solid-phase partial differential equation. (2) According to engineering requirements, the flexible coupling between the velocity and concentration fields is achieved by an additional suspended-load diffusion equation, avoiding the forced coupling in reducible cases. (3) The interphase interaction effects on the primary carrier phase are applied through an additional momentum source term. This integration yields a partially-algebraic closure scheme. Practical applications demonstrate that PATFM can significantly reduce computational costs while accurately predict the key flow characteristics of each phase, thereby offering an efficient solution for large-scale engineering computations of solid-liquid two-phase flows in hydraulic machinery and its systems.

The SST k-w turbulence model (SST), widely used in hydro-energy machinery for rotating separation flows, is limited in prediction accuracy due to the Bradshaw constant assumption. To address this limitation, in a previous study, the strategy of introducing dynamic Bradshaw coefficient (DBC) into the turbulence kinetic energy dissipation term has proven to be effective. However, this strategy still suffers from over-modelling issues, characterized by underestimating the lift and overestimating the drag for hydro-energy machinery. To further optimize this strategy, a study on the functional mechanism and optimization strategy of DBC in SST is conducted. First, the influences of DBC on flow prediction are revealed. The primary effects of DBC occur in the nearwall region, including the thickening of wall shear layer, increase of eddy viscosity, and advancement of flow separation. Second, a generalized DBC based on the slope-peak factors is developed according to the correlation between the wall shear layer and the DBC layer. The functional mechanism of the slope factor and peak factor is to significantly affect the variations of mixing length and velocity gradient, respectively. Third, an optimization strategy for the generalized DBC is proposed, and its application effectiveness is validated. The generalized DBC optimization strategy provides a novel approach to enhancing the applicability of SST for rotating separation flows in hydro-energy machinery, thereby better supporting efficient engineering computations.

Compressors function as critical energy conversion units in Compressed Air Energy Storage (CAES) systems. Yet their operational stability and efficiency are adversely affected by pressure pulsations induced by the complex rotor-stator interaction (RSI). Since conventional FFT-based methods cannot reveal the correlation between pressure spectra and actual flow structures, Dynamic Mode Decomposition (DMD) is employed as an initial step to separate the flow field and characterize spatial structures corresponding to representative frequencies. To address the limitations of traditional DMD in analyzing the spatiotemporal evolution of pressure pulsations, a Phase-driven Low-order Coherent Structures Analysis (PLOCS-Analysis) method is further proposed by integrating DMD with phase-feature extraction to systematically investigate the physical mechanisms of pressure pulsations. Unsteady simulations of the ERCOFTAC model were performed to extract dominant pressure pulsation modes and their phase evolution, with emphasis on excitation and propagation mechanisms in the RSI region. Results clearly show that the impeller blade-passing frequency dominates pressure pulsations in the diffuser, whereas the diffuser blade-passing frequency dominates those in the impeller, consistent with existing RSI-induced structural response findings. The pressure propagation criterion based on phase gradient reveals the reflection, superposition and attenuation of pressure pulsations near the impeller-diffuser interface, confirming this region as the primary excitation source. PLOCS-Analysis uncovers the full excitation-propagation-dissipation cycle of pressure pulsations at different frequencies, providing a foundation for mitigating multi-frequency pulsations. By overcoming the spatiotemporal interpretive limitations of conventional DMD, the proposed method offers a new pathway for advancing unsteady flow research and vibration control strategies for high-performance CAES equipment.

In open-channel flows, a notably higher spanwise vortex density near the free surface compared to other wall-bounded turbulent flows has been observed, termed the additional vortex phenomenon. Two hypotheses explain this phenomenon: The free-surface accumulation hypothesis, suggesting slower vortex dissipation in open-channel flows leading to vortex accumulation in the outer region, and the free-surface generation hypothesis, proposing that free surface restrictions on vertical motions enhance vortex generation, increasing vortex density near the surface. To elucidate the dominant origin mechanism of the additional vortex phenomenon, this study conducts direct numerical simulation (DNS) of open-channel flows and closed-channel flows at a friction Reynolds number Reτ = 500. Using the λci - criterion, the spanwise, streamwise, and vertical vortex densities variations with distance from the wall are identified and quantified for both flows, and the presence of the additional vortex phenomenon near the free surface in the open-channel DNS data is confirmed again. Furthermore, the vortex birth-death density is defined to elucidate the dominant origin mechanism of the additional vortex phenomenon. Through the analysis of the vortex birth-death density profiles, the exact birth location of the additional vortices can be pinpointed. The result reveals significant positive values for spanwise and streamwise vortices near the wall and free surface in open-channel flow, indicating substantial vortex generation, while small negative values in the central region suggest vortex dissipation. The results of the vortex birth-death density analysis support the free-surface generation hypothesis for the additional vortex phenomenon in open-channel flows.

Despite widespread interest in variable-speed pump-turbines, the effects of rotational speed on runner modal characteristics remain unclear. This study models the runner as a rotating disk and experimentally investigates its natural frequencies and hydrodynamic damping behaviours over 0–720 r/min. Nodal diameter (ND) modal families and coupled nodal diameter-nodal circle (ND-NC) hybrid modes of the disk were identified, with mode splitting into co-rotating and counter-rotating components observed exclusively in ND families. For all ND modes, the natural frequency of co-rotating modes exhibited a monotonic decrease with increasing rotational speed, whereas counter-rotating modes showed an opposite trend. The resulting frequency gap exhibited a linear dependence on rotational speed, and the center frequency gradually drifted downward with increasing rotational speed. When the reduced frequency is adopted as the independent variable, the natural frequencies of co-rotating and counter-rotating modes were distributed almost symmetrically with respect to the center frequency, for which a second-order polynomial regression model was proposed to characterize this unified behavior. Rotational speed was also found to exert a strong influence on hydrodynamic damping ratios: counter-rotating modes exhibited up to 54.07

Large-scale vertical centrifugal pumps are widely used in the water diversion projects in China, and the pumping stations often operate in the river environments with suspended sediments. The problem of impeller wear caused by sediment-laden flow is very prominent, seriously affecting the safety, stability, and efficient operation of the units. The sediment-laden flows in large-scale vertical centrifugal pumps exhibit the features of high volumetric concentration and small particle size (huge number of particles per unit volume). Under these service conditions, the characteristics and mechanisms of impeller wear are still not fully understood. This study takes a vertical centrifugal pump model as an example and conducts research in combination with hydraulic model experiments. First, a new Eulerian-Eulerian two-phase flow model suitable for high concentration and fine particle water-sand two-phase flows in centrifugal pumps is established. Second, a new wear model applicable to the base material of the impeller wall of a centrifugal pump is calibrated. Third, the water-sand two-phase flows in the vertical centrifugal pump under the conditions of different fine particle sizes are simulated, and the characteristics of erosion rate, particle impact velocity, and particle impact angle in the impeller are quantified. Moreover, based on the dynamic balance relationship of the relative motions, the mechanism behind the impeller wear under this condition is revealed, which originates from the special balance between the potential rothalpy gradient, the Coriolis force, and the drag force. In summary, the above results can provide valuable guidance for the anti-wear protection of large-scale vertical centrifugal pumps.

This study aims to elucidate the rotor-stator interaction (RSI) mechanism in a centrifugal pump by employing high-fidelity stress-blended eddy simulation (SBES) turbulence modeling combined with reduced-order techniques [dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD)]. The core objective extends beyond confirming the dominant frequency characteristics, to quantifying the energy hierarchy of RSI-induced flow and resolving the energy cascade in a coupled space-time-frequency domain. The present work investigates the RSI in a pump based on the European Research Community on Flow, Turbulence and Combustion standard through three-dimensional, unsteady computational fluid dynamics simulations. Initially, the SBES and scale-adaptive simulation turbulence models were compared. It was observed that the SBES model had good predictive accuracy compared to the experimental data for the pressure coefficient, velocity profiles, and pressure fluctuations in the vaneless region. Further transient study using SBES showed that blade passing frequency (fBPF) and its second harmonic are the predominant frequencies in terms of pressure pulsations. Also, the energy variability of frequencies was distinct across the flow path. Reduced-order analysis showed low-dimensional features of the flow. DMD's isolation of the first four dominant modes, corresponding to fBPF and its harmonics, was successful, with their spatial structures visualizing the large-scale periodic wakes and associated small-scale vortex shedding from RSI. A reconstruction based only on the first 5 DMD modes is able to capture the essential dynamics of the actual flow field in the study. POD analysis confirmed previous results for the energetic behavior. It clearly indicates that the first four modes contain more than 66% of the total energy. Moreover, the corresponding spectra of modal coefficients perfectly align with the DMD frequencies. This synergy of results confirms that periodic wakes from RSI are the primary energy-driving mechanism. This work seeks to reveal how the transient vortex structures influence pressure and Reynolds stress fluctuations, thereby providing physical insights beyond conventional spectral analysis for flow-induced vibration and noise control, and offers a basis for optimizing fluid machinery design.

Hybrid unsteady Reynolds-averaged Navier-Stokes/large eddy simulation (URANS/LES) models are progressively being applied to compressible flow study due to the capability to balance computational cost with simulation accuracy, and have demonstrated significant prospect for future applications. As a recently developed hybrid URANS/LES model, the adaptive time-scale driven (ATSD) model is particularly suited for resolving rotating turbulence of turbomachinery owing to its adaptive time-scale-driven modelling strategy. However, when applied to compressible flows, such as in compressor rotors, the ATSD turbulence model may exhibit numerical instability and insufficient predictive accuracy stemming from the strong compressible effects. To address these limitations, this study proposes a novel ATSD-ρ (ρ denotes density) turbulence model, which incorporates the following enhancements specifically designed for compressible flows: (1) An implicit eddy viscosity adjustment strategy is used to enhance numerical stability. (2) Turbulence diffusion effect of density is considered to improve prediction accuracy. (3) An optimized characterization of the resolved time scale is utilized to reflect compressible flow adaptability. This new model is validated in two canonical transonic axial compressor rotor test cases, National Aeronautics and Space Administration (NASA) Rotor 67 and NASA Rotor 37, and the results demonstrate that the ATSD-ρ model improves the prediction accuracy of rotor aerodynamic performance while enhancing the resolution of finer-scale turbulent vortical structures, thereby providing an efficient solution for engineering computation of compressible turbulence.

Against the backdrop of the global low-carbon and renewable energy transition, the large-scale grid integration of wind and photovoltaic power poses challenges to grid stability. As a key grid regulation facility, pumped storage power stations rely on the safe and stable operation of their core equipment—pump-turbines. Pump-turbines frequently switch between pump and turbine operating conditions, and the pump mode shutdown process is prone to unit vibration, pressure pulsation and other hazards due to energy transfer interruption, abrupt water flow changes and hydro-mechanical coupling effects. Taking the pump mode shutdown process of a pump-turbine as the research object, this study systematically investigates the process via CFD numerical simulation, combined with entropy production theory and wavelet transform technology. First, a 3D model of the pump-turbine was established with clear definition of key parameters. Simulation calculations were performed after grid independence verification, and the numerical results were compared with experimental data from a hydraulic laboratory to verify simulation reliability. The study focuses on the entire shutdown process and analyzes the flow field evolution law at six characteristic moments. From the pressure field perspective, the stable period presents a uniform gradient distribution, with local pressure drops in the transition stage and reverse gradient formation in the early reversal stage. The velocity field decreases uniformly in the stable period, while local high-velocity zones and reverse velocity components emerge in the initial transition stage. High entropy production areas are mainly concentrated at guide vanes and runner blades. Meanwhile, the wavelet transform was used to analyze pressure pulsations at five key monitoring points (DT01, DT02, Gv-Sv01, Runner-Gv01, Vo101), revealing phased variations in pulsation amplitude and frequency with operating condition switching. In addition, pressure pulsation is the most intense in the runner-guide vane and guide vane transition regions, and the most stable in the volute region. This study clarifies the dynamic evolution law of the pump-turbine pump mode shutdown process, and provides a theoretical basis and technical support for improving the safety and economy of unit shutdown.

Pumping stations serve as critical hydraulic infrastructure for water conveyance and irrigation. Sediment deposition in forebays can deteriorate intake flow conditions, increase hydraulic losses, reduce pumping efficiency, and consequently impair the long-term operational performance of pumping systems. To accurately predict sediment deposition in complex three-dimensional flow fields, we developed a dynamics-driven boundary-responsive numerical model that integrates sediment particle dynamics with real-time bed evolution. This model adopts the near-bed vertical velocity of sediment particles as the deposition discrimination criterion and dynamically updates bed topography via a mass-conservation-based boundary response strategy. The proposed method was validated against open-channel experimental data. The simulated flow structures, deposition patterns, and temporal variations in deposition thickness agreed well with the measurements, with average deviations below 4%. Compared with conventional static-boundary numerical methods, the proposed model reproduces the coupled evolution of sediment transport, flow redistribution, and bed deformation with higher fidelity. The developed framework provides an effective numerical tool for sediment deposition prediction and offers practical support for hydraulic structure optimization, maintenance scheduling, and energy-efficient operation of pumping stations with sediment-laden flow.

Vortices near hydraulic intakes degrade hydraulic machinery performance, adversely affecting the operational efficiency and stability of tidal power plants or pumping stations. In this study, large-eddy simulations of vertical intake system based on a source-sink model are performed. The formation process of the wall-normal vortex and its velocity distribution characteristics are elucidated. The evolution process can be classified into the vortex-pairing and single-vortex stages, and an empirical model that more accurately characterizes its velocity distribution is proposed based on canonical vortex model. Velocity perturbations in the streamwise and spanwise directions dominate the turbulent kinetic energy due to the intense streamwise-spanwise momentum exchange triggered by vortex interactions during the vortex-pairing stage and vortex meandering during the single-vortex stage. Turbulent kinetic energy production in the vortex-pairing stage is driven by the coupling u and du/dx, while in the single-vortex stage, it is sustained by the coupling of w'w' and u'w' with dw/dz and dw/dx, respectively. The meandering phenomenon of vortex occurs in single-vortex stage, and the meandering spatial scope conforms to a joint Gaussian probability density function. Further proper orthogonal decomposition analyses of the velocity and vorticity fields reveal that the in-plane meandering of wall-normal vortex is driven large-scale coherent structures and that these coherent structures originate from streamwise and spanwise turbulent velocity fluctuations. Moreover, the helical structures extracted from the decomposed vertical turbulent velocity fluctuations reveal the spatial structural characteristics of the wall-normal vortex. These are manifested as the three-dimensional distortion induced by axial stretching effects and as the spiral topology associated with the twisting and writhing of the vortex lines.

With the large-scale development of renewable energy such as wind, solar and ocean energy, the demand for energy storage is more urgent. Pumped hydro energy storage (PHES) is one of the fundamental solutions to the problem of intermittent supply of renewable energy. The large-capacity/low-head pumped hydro energy storage (LL-PHES) system with the use of tubular pump turbine is a beneficial extension of traditional PHES systems owing to large flow rate and cheaper civil structures. However, the continuous competition between the “static water pressure difference caused by gravity” and the “pressure increase caused by accelerated impeller rotation” leads to prominent instability in the start-up process of the LL-PHES system under pump conditions. An explicit coupling algorithm is proposed for analyzing the transient characteristics in the start-up process of the LL-PHES system under pump conditions. This algorithm is based on the idea of dimensional transformation, and performs 3D flow calculations and 2D rigid body dynamics equation solution in the pump domain and the flap gate domain, respectively. This algorithm avoids the problems of high computational cost and poor convergence that exist in existing fully three-dimensional coupling algorithms and ensures the efficiency of transient hydraulic characteristic calculation. A comprehensive analysis of the transient characteristics of the LL-PHES system during pump start-up process is conducted using the proposed new algorithm. The entire process of the increase in rotational speed, valve opening, flow rate, and the continuous evolution of blade surface pressure during the start-up process is quantitatively described. The amplitude and spectral characteristics of the alternating pressure on multiple blades are clarified. The evolution law of blade load during the stage of severe pressure fluctuations during the start-up process is explained. The load distribution characteristics of “high in the leading and trailing edge areas and low in the middle” in the blade stream direction is presented. The research results have a direct guiding role in improving the hydraulic design and enhancing the operational stability of LL-PHES systems.

To explore the degree and mechanism of damage inflicted by cavitation bubbles in the vicinity of the wall, stainless steel was chosen as the wall material in this study. Laser-induced bubbles were then generated at a specific distance above the stainless steel wall. The surface damage morphology of the material was analyzed using scanning electron microscopy (SEM) and a three-dimensional contour scanner. We observed the phenomenon of shockwave self-focusing that occurs when cavitation bubbles collapse near the wall. This shockwave self-focusing is identified as the decisive mechanism underlying cavitation erosion. Additionally, the results indicate that the projection of the bubble center on the material surface does not overlap with the cavitation erosion region, implying that the microjet is not the main cause of cavitation erosion. Cavitation bubble collapse causes significant erosion on the surface when the stand-off distance gamma is less than 0.5. Finally, we conducted a quantitative analysis of the energy density of the collapse shockwave, the number of bubble collapses, and the volume loss of the cavitation erosion area. It is found that the cavitation erosion volume follows an exponential relationship with the product of the number of bubble collapses and the shockwave energy density.

The precessing vortex rope and associated energy dissipation in draft-tube flows arise from the interaction among residual swirl, adverse pressure gradients, and separated shear-layer dynamics. Their numerical prediction is sensitive to modeled turbulent momentum transfer, but the resulting influence on vortex-rope coherence and dissipation localization remains insufficiently understood. This study investigates this coupling in the Timisoara Swirl Generator at one part-load benchmark condition. The generalized k–ω (GEKO) turbulence model is employed within an unsteady Reynolds-averaged Navier–Stokes framework. The GEKO separation coefficient CSEP is constrained using laser Doppler velocimetry (LDV) profiles, while Liutex-based vortex identification and entropy-production analysis examine the predicted vortex structure and modeled loss distribution. As modeled eddy-viscosity diffusion is reduced, the predicted flow evolves from an over-damped and nearly axisymmetric vortex core to a coherent eccentric helical vortex rope, and subsequently to premature separation accompanied by fragmented and grid-aligned structures under insufficient modeled damping. For this benchmark, the intermediate CSEP setting yields the lowest LDV-based normalized sum of squared errors among the numerically evaluated cases. It also preserves a continuous precessing vortex rope without the excessive smoothing observed at lower settings or the grid-aligned fragmentation observed at higher settings. The corresponding modeled turbulent entropy-production field is more strongly concentrated near the Liutex-identified vortex-boundary region, whereas the lower and higher settings produce broader or more scattered distributions. These results show that modeled turbulent momentum transfer strongly influences the predicted coupling among separated-shear-layer coherence, vortex-rope morphology, and entropy-production localization in the present swirling draft-tube flow.

Under the dual background of global energy transformation and environmental protection, pumped storage is a key energy storage technology to maintain the reliable operation of power systems. As the core component of pumped storage power plants, the operation stability of pump-turbine is of great importance. However, frequent operating condition transitions can trigger rotating stall in pump-turbine under off-design conditions, which seriously affects the energy conversion efficiency and stable operation of the unit. In this study, the pump-turbine model of a certain power plant is taken as research object. A combination of experiment and unsteady simulation is used to thoroughly investigate the mechanism of rotating stall in pump-turbine under pump mode. The circumferential evolution law of rotating stall and the reasons for its disappearance are analyzed in detail. The associated energy conversion characteristics are also elucidated, including pressure fluctuations, turbulent kinetic energy, and entropy production rate. The results show that rotating stall mainly occurs in the guide vane. As the flow rate decreases, the location of rotating stall shifts towards the guide vane inlet and the number of stall cells generally shows a decreasing trend. The circumferential evolution of rotating stall is primarily due to the blockage of stalled channels, which induces flow deflection and alters the adverse pressure gradient within the channels. This drives the front end of stall vortices to move along the runner rotation direction into the next non-stalled channel, while the rear end of the stall vortices exits the stalled channel, resulting in the formation of rotating stall. Additionally, from the perspective of energy loss, the uneven flow state distribution at the runner outlet is an important reason for the disappearance of rotating stall under the valley condition Op3 in hump region. This study further expands the understanding of the mechanism of rotating stall in pump-turbines, and provides important bases for optimization design and operation control of pump-turbines.

The cavitation bubble precipitation refers to the formation process of the spherical cavities, known as cavitation bubbles, as the ambient pressure of water decreases. In the fields of hydraulic machinery, the saturated vapor pressure of clean water is often used as the pressure threshold for cavitation occurrence. However, the engineering practice has demonstrated that, the incipient cavitation pressure may be significantly higher than the saturated vapor pressure, especially in sand-laden water conditions. Therefore, to determine a reasonable cavitation pressure threshold and ensure the accurate cavitation flow simulations and effective assessment of cavitation risks for hydraulic machinery operating in sand-laden water conditions, an experimental investigation is conducted. First, a high-precision experimental setup based on the vacuum pump, high-frequency pressure sensor and high-speed camera is constructed. This setup allows for the continuous pressure reduction in water, acquisition of high-precision pressure data and tracking of the entire cavitation bubble precipitation process. Second, based on the experiments in clean water conditions, the relationship between the cavitation bubble precipitation degree and pressure is established, and two key states of incipient cavitation and boiling cavitation are defined. Third, based on the experiments in sand-laden water conditions, it is observed that the numerous cavitation nuclei on sand surfaces make both the incipient and boiling cavitation pressure in sand-laden water higher than those in clean water. The quantitative relationship between the sand concentration and diameter, and the cavitation pressure is established, providing a more reasonable cavitation pressure threshold. This investigation enhances the understanding of cavitation bubble precipitation in sand-laden water and supports the development of more accurate cavitation models for hydraulic machinery operating in sand-laden water conditions.