As the core hydraulic component of hybrid pumped storage station, the mixed-flow pump (MFP) frequently experiences speed rise process (SRP) to respond to changing operating demands. However, the coupling between hydraulic excitation and rotor dynamic response during SRP can generate strong hydraulic excitation vibration on MFP, posing potential risks to operational stability (OS) and system safety. To enhance the OS of the pump during SRP, shaft vibration (SV) and pressure pulsation (PP) signals were acquired under various speed rise strategies (SRSes). Their characteristics are subsequently analyzed using innovative nonlinear signal processing methods. On this basis, an OS assessment system driven by multi-source data is established, and the mathematical relationship between SRS and OS is established. The results indicate that among the 21 SRSes established, the Mode-P4 with the speed rise time (SRT) of 6 s is the most effective in mitigating vibration shock. The increase of SRT can also alleviate the hydraulic coupling shock on the MFP. Assessment results revealed that among the 21 SRSes investigated, the Mode-P4 with SRT of 6 s exhibited the highest OS. Within the parameter variation range given in this study, the optimal SRS obtained based on the mathematical relationship is achieved with the SRT of 6 s and the power exponential of 3.631. The results can provide theoretical support for improving the operational reliability of hybrid pumped storage station.

Variable-speed operation of pump-turbines enhances efficiency and grid stability in renewable-rich power systems. However, the internal complex flow and energy dissipation mechanisms during speed regulation, particularly throughout complete speed increase and decrease cycles, are not well understood, posing challenges to operational safety and efficiency optimization. This study systematically investigates and compares the internal flow and energy dissipation under linear speed increase and decrease processes in pump mode using high-fidelity numerical simulation, experimental validation, and entropy generation theory. The results indicate that variable-speed operation significantly affects the internal flow structure and energy distribution: although the speed increase process locally improves the flow pattern at the stay vanes, the total system entropy generation increases by 17.9% compared to constant-speed operation, indicating intensified flow disturbance; during the speed decrease process, velocity distribution at runner outlet becomes more uniform, the velocity gradient decreases significantly, effectively suppressing flow separation and vortex dissipation in areas of runner and guide vanes, leading to a significant 12.6% reduction in total system entropy generation compared to constant-speed operation and improved energy efficiency. The runner and double-row cascades remain the primary sources of energy loss, accounting for over 62.7% of entropy generation. Entropy gradients are strongest near the runner crown, while the spiral casing exhibits nonlinear loss and the draft tube remains stable. These findings, derived from a direct comparison of bidirectional speed regulation, fill a gap in understanding transient loss mechanisms and provide a theoretical basis for the optimized design and safe operation of variable-speed pump-turbines.

Addressing the limitations of the Time Series Generative Adversarial Network (TimeGAN), such as training instability, inattention to critical time steps, and low training efficiency, an improved TimeGAN model is proposed to generate high-quality time series data. This model is applied to fault diagnosis of pumped storage units under limited data scenarios. Firstly, the Jensen-Shannon (JS) divergence in the original adversarial loss function was replaced with the Wasserstein distance, combined with a gradient penalty mechanism, to provide smoother gradient signals and mitigate gradient vanishing.Secondly, a temporal attention (TA) mechanism was incorporated into the generative adversarial network to direct the model's focus to critical temporal regions within the data.Finally, the Adam optimizer was replaced with the Rectified Adam (RAdam) optimizer, thus accelerating network convergence and enhancing training efficiency.Experimental validation of the proposed method was conducted using data collected from a pumped storage power station. The analysis results demonstrate that the time series data generated by the improved TimeGAN model achieved superior quality assessment metrics. Specifically, the similarity between the generated data and the original data reached 0.9831, outperforming the SMOTE method (0.8579), the original TimeGAN (0.9054), and other comparative improved TimeGAN models.In the fault diagnosis task, the proposed method outperformed other approaches across all three evaluation metrics: accuracy, recall, and F1-score. With only 50 real samples, the accuracy of the proposed method significantly increased from 67.32% to 98.02%, demonstrating a substantial improvement over both the SMOTE and the original TimeGAN models. These results validate its effectiveness and superiority in few-shot learning scenarios.

Frequent start-stop operations of pumped storage power stations subject pump-turbine units to high-amplitude water hammer pressures at small guide vane openings, thereby compromising operational stability and service life. This study numerically simulates the pump mode start-up process of a prototype pump-turbine under three heads, with a focus on runner forces and internal flow dynamics. Results show that the x-direction component of runner hydraulic thrust exhibits minimal head dependence, whereas the y-component decreases by 28.2 % at 220.05 m relative to 175.4 m. At 220.05 m head, the force magnitude increases significantly, and rotor eccentricity intensifies. During small guide vane openings, reverse flow develops in the vaneless space between stay and guide vanes, driven by reverse blockage and forward blockage. Additionally, significant flow maldistribution persists in stay vane passages throughout the start-up process. The absolute radial hydraulic thrust on guide vanes decreases with increasing guide vane opening and head, achieving a maximum reduction of 75.4 %. These findings establish a dual-blockage theoretical framework for understanding transient instabilities, providing critical guidance for stability optimization in high head pumped-storage power plant designs.

Deepwater oil and gas reservoirs are characterized by great depth, high temperature and pressure, leading to viscosity variations of crude oil across different reservoir types. When multiphase pumps convey media of different viscosities, internal flow patterns become unstable, readily triggering pressure pulsations and shaft vibrations, thereby affecting the stability of the transportation system. The effects of liquid viscosity on pressure pulsations and force characteristics during gas–liquid transport in a pump are systematically investigated, based on four liquid media of different viscosities, including water (1.01 mPa·s), light oil (4.42 mPa·s), medium oil (12.46 mPa·s), and heavy oil (39 mPa·s), together with air (0.018 mPa·s). Numerical simulations combined with signal analysis methods such as variational mode decomposition and comprehensive evaluation index (CEI) were employed. Results show that both the head and efficiency of the pump decrease as medium viscosity increases. Pressure pulsation characteristics and axial force behavior inside the pump are jointly influenced by rotor‑stator interaction and viscosity. With rising viscosity, the peak‑to‑peak pressure at the impeller outlet increases, reaching 2.1 times the value under water conditions at high‑viscosity oil conditions, where macroscale energy becomes dominant, eliminating the broadband pulsations observed under water conditions. Additionally, the average axial force is 8% higher than under water conditions. As viscosity increases, the CEI of the pump’s radial force decreases, reaching its lowest value under heavy‑oil conditions, where the radial force performance is relatively optimal. The findings provide valuable insights for enhancing the stability and optimizing the design of multiphase pumps.

The variation of inlet gas volume fraction (IGVF) intensifies bubble breakup and coalescence behaviors, and the resulting evolution of gas pockets may directly impact the energy performance and stability of multiphase pumps. In this work, effects of IGVF on performance parameters, energy characteristics and flow instability are investigated by ANSYS CFX software. Bubble breakup and coalescence dynamics, along with their associated gas–liquid interfacial entropy production under high IGVF conditions are considered. Results show that predicted values of pressure increment, pressure fluctuation, and gas distribution characteristics agree well with experimental data. With the increase of IGVF, the pressure increment decreases while gas volume fraction (GVF) in the impeller and diffuser increases. When the IGVF rises from 5% to 15%, gas pockets form on the diffuser suction sides, accompanied by a sharp decline in pressure increment and rapid increase in GVF and average bubble diameter, ultimately triggering surge phenomena. The increasing IGVF accelerates bubble coalescence, leading to a higher proportion of large bubbles in the flow passages. Consequently, both the number and size of gas pockets increase, resulting in enhanced gas–liquid interfacial entropy production. Furthermore, pressure fluctuation characteristics are thoroughly analyzed, which can provide a reference for the energy loss analysis and optimal design of multiphase pumps.

Marine hydraulic components are typically subjected to the coupled effect of flow-driven erosion and corrosion, which is the primary failure cause, and preventive coatings are crucial for extending their service life. In this work, the multi-physics coupled damage behavior of laser-clad Ni-Fe coating in liquid-solid flow of marine environments is investigated. The complex interactions involving fluid shear stress, particle erosion, ion transport, and electrochemical reactions are systematically studied in a rotating liquid-solid flow system. The synergistic erosion-corrosion mechanism and damage evolution are clarified through weight loss analysis, electrochemical testing, and microstructure characterization. The results suggest that the erosion-corrosion mechanism exhibits phased shifts with flow velocity. At low flow velocities, corrosion dominates the material degradation, where low-energy particles only locally disrupt the corrosion product film but still promote localized corrosion extension. At medium flow velocities, stronger particle impact and fluid shear induce significant rupture of the corrosion product film, producing a positive feedback cycle between erosion and corrosion that rapidly intensifies the synergistic effects. At high flow velocities, corrosion-accelerated erosion dominates, as localized selective dissolution mechanically weakens the surface and destabilizes the interface, greatly accelerating material degradation. During this stage, the synergistic effects peak, and the material loss rate exhibits a nonlinear and rapid increase. These findings suggest that, for Ni-Fe coatings operating under high flow velocities, mitigating corrosion-accelerated erosion requires prioritizing high surface hardness together with stable passivation behavior, thereby suppressing surface mechanical weakening and film breakdown under aggressive flow. This study demonstrates that flow velocity plays a key role in controlling erosion-corrosion synergy, providing a scientific basis for designing and improving erosion-corrosion resistant coatings.

During the transient start-up process (SUP) of mixed-flow pumps (MFP), pressure pulsation (PP) and principal shaft vibration (PSV) in MFP are two main indicators for analyzing failure types and evaluating operational stability. To investigate the effect of start-up mode (SUM) on the stability of MFP, the PP and PSV of MFP under nonlinear and linear SUM were collected. And the stability of MFP under different SUMs was quantitatively evaluated by the proposed WF-SampEn method which combining two-dimensional (2D) sample entropy and wavelet fusion diagram. Then, the relationship between the SUM and the stability of the MFP were studied. Experimental results indicate that the energy distribution of PSV in the frequency domain can be improved by the concave exponential function (CCEF) SUM. And the CCEF SUM can suppress the shock vibration of the shaft and reduce the duration of high-amplitude (HA) PSV, thereby decreasing the probability of shaft instability failure. Specifically, 2D sample entropy of the PSV and PP are the lowest when the MFP start-up in CCEF SUM, and the stability of MFP in CCEF SUM is 39.9% and 22.8% higher than that in Linear and CVEF SUM. The results provide a quantitative theoretical criterion and a practical diagnostic tool for designing start-up strategy and preventing instability-induced failures in fluid machinery.

The hydraulic machinery in marine environment is vulnerable to the synergistic damage by high-speed rotating flow, chloride-induced corrosion, and sand particle erosion, which has become the major threat to its safe and efficient operation. In this study, the erosion-corrosion behavior of HVOF-sprayed WC-4Co-58Cr coating is investigated in artificial seawater containing 3.5 wt.% quartz sand with an average particle size of about 400 μm at 25 °C. The flow velocity ranges from 3 to 9 m/s. Based on the coupling analysis of multi-component weight loss, electrochemical behavior and micro-damage morphology, the multi-scale coupling process of fluid flow, particle-surface impact, ion mass transfer and interface electrochemistry is revealed. The results show that the erosion-corrosion mechanism transfers with the flow velocity. At low velocities, corrosion is the dominant factor in material degradation. At 3 m/s, the total loss rate is 0.069 mm/y, in which pure corrosion accounts for 46.38% of the total damage, while the synergistic component contributes 37.68%. As the velocity increases, the synergistic effect intensifies and eventually becomes the dominant damage mechanism. At 9 m/s, the total loss rate increases to 0.310 mm/y, and the synergistic component reaches 47.42%. In particular, the corrosion-accelerated erosion component accounts for 28.39%. This transition stems from turbulent shear stress enhancing the mass transfer of corrosive medium, combined with localized breakdown of the passive film due to high-speed particle impact. Their interaction creates a positive feedback mechanism. The WC-4Co-58Cr coating with high Cr content forms a composite protective film primarily composed of Cr2O3, enriched with hydroxyl compounds on the outer layer, demonstrating strong resistance to synergistic erosion-corrosion. The study elucidates the intrinsic relationship among hydrodynamic effects, particle impact behavior, ion mass transfer processes, and material damage evolution, which contributes to the optimal design of erosion-corrosion resistant materials based on flow-induced damage mechanisms.

Medium viscosity is a core factor exerting a critical influence on the energy efficiency and operational stability of multiphase pumps (MPs). To better approximate actual working conditions, this study uses fluids with viscosities of 1.01 mPa center dot s (water), 4.42 mPa center dot s, 12.46 mPa center dot s, and 39 mPa center dot s to examine the impacts of liquid viscosity on hydraulic characteristics and energy conversion within MPs via ANSYS CFX. A comparison between calculated and measured head/efficiency for water cases confirms the model's accuracy, and the predicted pressure rise for water-gas cases also agrees well with experimental data. As medium viscosity increases, both head and efficiency exhibit a gradual decline. Nevertheless, the pump exhibits poorer performance in water compared to a more viscous medium when the inlet gas volume fraction reaches 40%, which is confirmed by flow field analysis. The diffuser exhibits diminished low-speed regions, less gas aggregation, and a lower void fraction. Furthermore, entropy generation rate distribution under varying viscosity conditions is thoroughly analyzed, which can provide insights for optimizing pump designs toward cleaner and more energy-efficient deep-sea hydrocarbon production. This work advances the understanding of high-viscosity multiphase flows and supports sustainable offshore resource extraction.

The presence of tip clearance can generate a leakage vortex, which complicates the cavitating flow characteristics and significantly affects the energy loss. This study numerically investigates the cavitating flow around a National Advisory Committee for Aeronautics 0009 hydrofoil with a tip clearance. Based on velocity gradient tensor (VGT) decomposition and entropy production (EP) theory, the fluid motion patterns and the sources of vortices in hydrofoil cavitating flow are investigated; furthermore, the energy losses and their underlying mechanisms are revealed. The results show that pure shear (PS) is the predominant deformation in hydrofoil cavitating flow, while rigid rotation accounts for a relatively small proportion. The vortices can be divided into three categories based on their causes, including cavity growth induced vortex, cavity shedding induced vortex, and cavity collapse induced vortex. The detached cavity moves downstream with internal rotation rather than a simple translation. With increasing tip clearance, the energy loss presents a declining trend. The turbulence dissipation EP serves as the primary contributor, constituting over 90% of the total. The changes in cavity volume and EP exhibit opposite trends during one cycle. The distributions of EP rates exhibit a strong correlation with those of VGT components. The energy loss predominantly arises from the PS and compression/stretching (CS) deformation. Among them, direct dissipation EP mainly comes from CS, and turbulent dissipation EP is mainly caused by PS.

When a centrifugal pump is used to transport gas-liquid two-phase flow, the surge at high gas volume fraction leads to head and efficiency decrease, as well as cause strong vibrations in the pump system. To improve the transport performance of centrifugal pumps, the closed impeller is redesigned into a semi-open impeller. The effect of the blade tip clearance size on the head and efficiency is explored. The similarities and differences in the internal gas distribution patterns between closed and semi-open impellers are analyzed. The suppression mechanism of the tip leakage flow on surge is clarified. At 5% inlet gas volume fraction, the closed impeller exhibits significant gas accumulation characteristics on the pressure surface, forming gas pocket flow patterns and gas vortex. Additionally, some gas bypasses the blade leading edge, forming gas leading edge overflow, and re-accumulates at adjacent blades, further exacerbating the gas pocket flow patterns. This results in high gas phase distribution zones and low liquid phase velocity zones, inducing surge. There is a proper tip clearance, which provides an additional flow path for the gas in the flow passage. The liquid and gas mixed tip leakage flow impacts and suppresses the gas accumulation. The gas pocket flow pattern and gas vortex are disrupted. The liquid and gas mixed fluids can smoothly flow out of the impeller. The surge is suppressed and the performance of gas-liquid mixed transport is significantly improved. The optimal tip clearance size of 1 mm increased the head and efficiency by 16.2% and 13.1% respectively under surge condition.

Semi-open centrifugal pumps play a crucial role in the fluid transportation and energy conversion for renewable energy systems, due to their flexible structure, adaptability to complex fluids and high energy efficiency. However, in the transportation of solid-liquid two-phase flow, the interaction between particles and fluid will change the particle migration trajectory and the vortex characteristics, thereby affecting the flow stability and erosion damage, unfortunately this effect is difficult to be quantified. Therefore, this paper introduces the Stokes number (St) to quantitatively analyze the influence of particle-fluid interaction on the hydraulic performance and erosion behavior of centrifugal pumps. A four-way coupled Euler-Lagrangian method is adopted, coupled with the SST k-omega turbulence model and the Finnie's erosion model, to resolve the solid-liquid two-phase flow field in a semi-open centrifugal pump. The results indicate that, for St < 1, particles exhibit a stronger ability to follow fluid motion, and are more dispersed within the impeller. A significant influx of particles into the tip clearance impacts leakage vortices, resulting in fragmentation and shedding of vortex structures, accompanied by significant high-amplitude, low-frequency pressure pulsations. For St >= 1, the motion of particles is dominated by inertial forces, with pronounced accumulation near the blade pressure surfaces and rear shroud, intensifying erosion on the blade pressure sides and the rear shroud adjacent to the blade leading edges. As the St increases, erosion rates on all flow components rise. In particular, when St > 0.6, the increase of erosion rate on the blade surface and rear shroud noticeably accelerates. This study provides a new insight into the effect of solid-liquid interaction on the semi-open centrifugal pump performance.

Cavitation is a major hydraulic excitation in Kaplan turbines, posing a serious threat to their operational stability. However, the coupling mechanisms between vibration and pressure fluctuation under cavitation conditions remain poorly understood. In this study, synchronous measurements of runner vibration and draft tube pressure fluctuation were conducted on a Kaplan turbine under varying cavitation states using a Laser Doppler Vibrometer and high-frequency pressure measurement techniques. A multiscale nonlinear analytical framework based on multifractal detrended cross-correlation analysis was constructed to elucidate the pressure-vibration interaction during cavitation development. The results show that cavitation selectively amplifies vibration across frequency bands: the high-frequency component (48f(n) < f < 192f(n), where fn is the runner rotating frequency), associated with bubble collapse shocks, exhibits the most pronounced growth, whereas low-frequency vibration remains nearly unchanged. Pressure fluctuations are consistently identified as the dominant excitation source of runner vibration across all cavitation states, with cavitation markedly strengthening the hydraulic driving effect. Moreover, cavitation drives the fluid-structure interaction mechanism from a weakly coupled state toward a strongly nonlinear, multiscale coupled regime. As cavitation intensifies, the nonlinear cross-correlation strength increases by over 50%, indicating a substantial enhancement of scale heterogeneity and nonlinear pressurevibration interaction intensity. These findings provide a theoretical foundation for operational stability assessment of the turbines.

Surge in gas-liquid two-phase centrifugal pumps under high inlet gas volume fractions (IGVF) will lead to performance degradation and vibration increase, and threaten safe and stable operation. A novel method is proposed to suppress surge with radial grooves in a semi-open centrifugal pump. A parametric study on the circumferential coverage ratio, depth, and number of radial grooves was conducted, and the gas-liquid mixing characteristics, radial velocity, streamline, and vortex were quantitatively analyzed. The results show that the gas-liquid transportation performance of the centrifugal pump is optimal when the circumferential coverage ratio, depth, and number of radial grooves are 0.125, 3 mm, and 12, respectively. The maximum increases in the head and efficiency were 23.9%, and 6.9%, respectively. Gas accumulation in the flow channel forms high-gas volume fraction (GVF) regions. With an increase in the IGVF, the gas accumulation phenomenon becomes more obvious, and GVF becomes larger. The fluid enters the radial groove from the high-pressure side and flows out from the low-pressure side at a relatively high speed, impacting the gas accumulation and gas pocket flow, improving the flow state at the blade inlet, and reducing GVF in the impeller and the scale of the vortex, thereby increasing the mixing degree of the gas-liquid two phases. The mixing coefficient increased by 9.8%.

To solve stall-induced flow instability and performance degradation in axial flow waterjet pumps, an active stall recovery method integrating stall warning and end wall injection is proposed. Experimental tests were conducted to evaluate the recovery performance of end wall injection under stall-locked and dynamic stall modes, coupled with full-annulus unsteady numerical simulations to clarify the underlying mechanism. The results demonstrate that the proposed method can restore pump stability within 3 s, with the stabilized pump head increasing by over 25% compared to the stalled state. Specifically, the stall warning criteria exert negligible influence on the recovery efficacy under the stall-locked mode. The critical minimum injection flow rate for stall recovery is 6% of the design flow rate, and the optimal injection flow rate is 8%. In dynamic stall mode, earlier stall warning yields superior recovery performance, and the stall warning should be triggered before the pump enters deep stall. Mechanistic analysis reveals that forward spillage of the tip leakage vortex (TLV) interacts with the passage vortex (PV), inducing large-scale tip blockage that evolves into a rotating stall cell. End wall injection mitigates TLV-PV interactions, driving disordered vortex clusters to evolve into helically twisted TLVs. This enhances the tip through-flow capacity and blade tip loading, thereby enabling stall recovery. This study provides a reliable active control strategy for stall recovery in axial flow waterjet pumps, offering technical support for the safe operation of hydraulic engineering equipment.

Efficient transportation of gas–liquid mixtures is essential for geothermal energy exploitation, whereas geothermal multiphase pumps operating under surge conditions suffer from severe gas accumulation, flow instability, and degraded pressure boosting capability. To address these issues, a multi-objective impeller optimisation method is developed by combining an orthogonal experimental strategy with an improved TOPSIS approach incorporating Mahalanobis distance for comprehensive performance assessment. Four key impeller geometric parameters were selected as optimisation variables, and the optimal configuration was identified through comprehensive multi-objective evaluation. The results show that blade number is the dominant factor affecting pump performance. Relative to baseline impeller, optimised design adopts a four-blade configuration with inlet and outlet blade angles adjusted to 80.6° and 14.8°, respectively, together with a blade thickness ratio of 0.8. This redesigned impeller achieves a 23.84% increase in head and a 2.71% improvement in hydraulic efficiency under surge conditions. Moreover, the optimised impeller produces a more uniform pressure distribution, suppresses gas accumulation, reduces bubble size and flow angle fluctuations, and significantly enhances gas–liquid transport stability. The relative closeness coefficient obtained from the improved TOPSIS evaluation increases by 84.09%, verifying the feasibility and reliability of the developed optimisation framework. The present work provides an effective strategy for the hydraulic characteristics of geothermal multiphase pumps subjected to complicated gas–liquid operating scenarios.

Deepwater oil and gas reservoirs are typically characterized by considerable depth, high temperature, and high pressure, which lead to variations in crude oil viscosity across different reservoir types. When multiphase pumps transport media with different viscosity conditions, the internal flow patterns become unstable, readily inducing pressure pulsations and shaft vibrations, thereby compromising the stability of the transportation system. This study systematically investigates the influence of liquid viscosity on pressure pulsations and force characteristics during gas-liquid transport in a multiphase pump. Four liquid media with distinct viscosity conditions, water (1.01 mPa s), light oil (4.42 mPa s), medium oil (12.46 mPa s), and heavy oil (39 mPa s), were used, along with air (0.018 mPa s) as the gas phase. Numerical simulations were conducted in conjunction with signal analysis techniques, including variational mode decomposition and the comprehensive evaluation index (CEI). The results indicate that both the pump head and efficiency decrease with increasing medium viscosity. The pressure pulsation characteristics and axial force behavior inside the pump are jointly governed by rotor-stator interaction and viscosity. As viscosity rises, the peak-to-peak pressure at the impeller outlet increases, reaching 2.1 times that observed under water conditions when heavy oil is used. Under such high-viscosity conditions, macroscale energy becomes dominant, and the broadband pulsations observed with water are eliminated. Furthermore, the average axial force is 8% higher than that under water conditions. With increasing viscosity, the CEI of the pump's radial force declines, reaching its minimum under heavy-oil conditions, where the radial force performance is optimal. These findings contribute to the enhancement of operational stability and the optimal design of multiphase pumps.

Semi-open centrifugal pumps often experience hydraulic instabilities under low-flow conditions, manifested as the hump phenomenon in the head-flow curve. This instability arises from tip leakage vortices (TLV) and inlet recirculation (IR), which disturb the impeller inlet and cause energy losses. Although casing treatment has been widely applied in centrifugal compressors to suppress similar instabilities, its application in centrifugal pumps remains limited. To address this gap, the present study investigates slotted endwalls as a passive flow-control strategy to stabilize internal flow and suppress low-flow instabilities in semi-open impeller pumps. Three-dimensional simulations based on the Reynolds-averaged Navier-Stokes (RANS) equations and the shear stress transport (SST) k-ω (k denotes turbulent kinetic energy, ω denotes specific dissipation rate) turbulence model were performed and validated against experimental data with good agreement. Three slot configurations, namely arc, inclined polyline, and inclined slot, were designed to assess the geometric effects on TLV and IR. Results show that all designs effectively mitigate the hump phenomenon and extend the stable operating range, with the inclined slot achieving the best performance. It effectively eliminates the hump region and enhances the efficiency at both design and high-flow rates. Further analyses reveal that slotted endwalls promote smoother reentry of leakage flow and reduce energy dissipation. Orthogonal optimization identifies slot position as the dominant factor influencing performance. These findings confirm that slotted endwall modification is an effective and practical passive design approach for improving flow stability and hydraulic efficiency in semi-open centrifugal pumps.