Search Results (167)

The accurate reconstruction and real-time prediction of transient three-dimensional flow fields in hydraulic turbines are critical for ensuring operational stability under renewable energy-driven variable-load conditions, yet conventional computational fluid dynamics (CFD) approaches remain too computationally expensive for digital twin applications. This paper proposes a hybrid framework that integrates Proper Orthogonal Decomposition (POD) with Long Short-Term Memory (LSTM) networks to reconstruct and predict the unsteady flow field within the draft tube of a Francis turbine using only four sparse wall-mounted pressure sensors. The methodology begins with high-fidelity Large Eddy Simulation (LES) to establish a comprehensive flow field database under Part Load (PL), Best Efficiency Point (BEP), and High Load (HL) conditions. POD is subsequently applied to extract dominant coherent structures and their temporal coefficients, achieving a low-dimensional representation of the high-dimensional flow field. A comparative analysis between standard POD and weighted POD reveals that under the PL condition characterized by a strong double-helical vortex rope, the weighting effect is significant—standard POD captures 90% of the total energy with the first 2 modes, while weighted POD requires up to 8 modes to reach the same threshold. Under the BEP and HL conditions, the energy distributions of the two methods are nearly identical, yet weighted POD still yields cleaner spatial modes with sharper vortex boundaries and fewer spurious wall-region vortices. An LSTM network is then trained to establish a mapping between time-series signals from the four sensors and the POD temporal coefficients. The results demonstrate that LSTM prediction performance is governed by the spatial correlation between each mode and the sensor locations rather than by temporal regularity. Modes that project strongly onto the sensor locations—PL Modes 1–2 (R² = 0.85 and 0.513), BEP Mode 1 (R² = 0.96), and HL Mode 1 (R² = 0.92)—are reliably predictable, while PL Mode 3 and HL Mode 2, despite their regular temporal oscillations, yield strongly negative R² values (−3.366 and −186.6) because their spatial structures are concentrated away from the wall. With a condition-adaptive strategy predicting only sensor-correlated, energetic modes, the reconstructed pressure fields achieve mean L2 relative errors of 17.01% (PL), 7.17% (BEP), and 12.91% (HL). Because the mean flow dominates total pressure energy (86.66–98.07%), the effective absolute error is substantially lower. The proposed POD-LSTM framework successfully bridges the gap between high-fidelity CFD and real-time monitoring, enabling full-field flow state estimation from sparse sensor measurements without the computational expense of online simulations. This capability is particularly valuable for digital twin applications in hydraulic turbines operating under rapidly varying renewable energy conditions. Full article

The rapid increase in the penetration of renewable energy has imposed more stringent requirements on the regulation capacity and response speed of Francis turbines in modern power grids. Vortex-induced energy loss significantly constrains the energy performance and hydraulic stability of giant Francis turbines. However, the formation mechanisms of vortex-induced hydraulic loss near the operating boundary remain insufficiently understood. Based on numerical simulations and parameter validation under 30 representative operating conditions, three 50% rated load conditions located near the operating boundary were strategically selected for detailed investigation. By integrating rigid vorticity analysis with entropy production theory, the vortex dynamics and hydraulic loss characteristics were systematically quantified and visualized. The results indicate that entropy production rates caused by turbulent dissipation and wall shear constitute the primary components of hydraulic loss, among which entropy production rate caused by turbulent dissipation (EPRT) is more sensitive to variations in external operating conditions and dominates both the magnitude and spatial distribution of energy dissipation. Distinct loss evolution patterns are observed in the runner and the draft tube. Recirculation and separation flows along the blade surfaces alter the normal blade loading distribution in the runner. In the draft tube, hydraulic loss is mainly governed by the energy dissipation associated with the interaction between the main flow region and the reverse flow region, while the intensity of hydraulic loss is not directly related to the specific vortex morphology. Overall, shear vorticity remains the key mechanism responsible for the increase in EPRT. This study provides theoretical insights and practical evidence for understanding the mechanisms of vortex-induced energy loss in giant Francis turbines and for quantitatively evaluating the distribution and evolution of hydraulic loss. Full article

Francis turbines are renowned for their high efficiency and adaptability across a wide range of head and discharge conditions. However, internal mechanical friction losses (IMFLs), resulting from rotational frictional resistance between the rotating runner and the surrounding fluid, remain a significant obstacle to further performance optimisation. This study introduced a CFD-derived integral friction torque framework, validated through theoretical analysis, that enables the spatially resolved quantification of IMFLs in Francis turbine runners. Building on this framework, a comprehensive computational approach was established to quantify IMFLs in a Francis turbine runner using a CFD-derived integral torque method combined with a theoretical verification model. Three runner configurations were analysed: the original runner model (ORM), a modified runner (RM1) with selective exit height reduction, and a modified runner (RM2) with uniform exit height reduction. Transient simulations were conducted at the best efficiency point (BEP) using the shear stress transport (SST) k–ω turbulence model and a sliding mesh approach. The numerical results were verified using the theoretical model and systematically evaluated to assess IMFL mechanisms and runner performance. The findings demonstrate that variations in runner geometry significantly influence internal frictional resistance and turbine efficiency. Compared with ORM, both RM1 and RM2 reduced the rotational friction torque, with RM2 exhibiting the greatest improvement: a 2.83% reduction in total friction resistance torque, a 14.74% reduction in total power losses, and a 1% absolute increase in efficiency. These improvements are primarily attributed to reduced wall shear stress and a more uniform pressure distribution across the runner surface. Full article

The precessing vortex core (PVC) is a major source of low-frequency harmful pressure pulsations that constrain the stable operating range of Francis turbines under part-load regimes. This study presents an experimental demonstration of active frequency control for the PVC in an aerodynamic turbine model (at Reynolds number 1.5 × 10⁴), employing a resonant forcing strategy grounded in linear stability theory. Low-energy air injection with a momentum flux coefficient in the range of approximately 0.06% to 1.56% was applied via rotating actuators positioned within the flow region of highest receptivity. The core finding is the observation of frequency, where the PVC’s natural precession frequency synchronizes with that of the rotating actuator. A comparative analysis of actuator geometry revealed that a single-jet configuration achieves a significantly greater frequency shift, up to 22%, and a wider lock-in range than a dual-jet actuator (8% shift). This enhanced performance is attributed to the higher momentum flux density and more spatially coherent forcing generated by the single jet, which couples more effectively with the global instability mode. The results validate the successful adaptation of a highly efficient, physics-based control paradigm from reacting flows to hydraulic machinery, offering a promising approach to mitigate vortex-induced vibrations and expanding turbine operational flexibility. Full article

This study proposes an analytical redundancy method that combines empirical models with a Kalman filter to ensure the reliability of measurements from axial deformation sensors in a turbine head-cover bolt-monitoring system. This integration enables the development of predictive models that optimally estimate the dynamic deformation of each bolt during turbine operation at full and partial load. The test results of the models under conditions of outliers, measurement noise, and changes in turbine operating mode, evaluated using accuracy and sensitivity metrics, confirmed their high accuracy (Acc ≈ 0.146 µm) and robustness (S_A < 0.001). The evaluation of the models’ responses to simulated sensor faults (offset, drift, precision degradation, stuck-at) revealed characteristic residual patterns for faults with magnitudes > 5 µm. These findings establish the foundation for developing a fault detection and isolation algorithm for continuous monitoring of these sensors’ operational health. For practical implementation, the models require validation across all operational modes, and maximum admissible deformation thresholds must be defined. Full article

Flexible grid regulation necessitates Francis turbines to operate at heads of 120–180 m (compared to the rated head of 154.6 m), breaking the designed rotational symmetry and inducing hydraulic instabilities that threaten structural integrity and operational reliability. This study presents extensive field measurements of pressure pulsations in a 600 MW prototype Francis turbine operating at heads of 120–180 m and loads of 20–600 MW across 77 operating conditions (7 head levels × 11 load points). We strategically positioned high-precision piezoelectric pressure sensors at three critical locations—volute inlet, vaneless space, and draft tube cone—to capture the amplitude and frequency characteristics of symmetry-breaking phenomena. Advanced signal processing revealed three distinct mechanisms with characteristic pressure pulsation signatures: (1) Draft tube rotating vortex rope (RVR) represents spontaneous breaking of axial symmetry, exhibiting helical precession at 0.38 Hz (approximately 0.18 f_n, where f_n = 2.08 Hz) with maximum peak-to-peak amplitudes of 108 kPa (87% of the rated pressure p_rated = 124 kPa) at H = 180 m and P = 300 MW, demonstrating approximately 70% amplitude reduction potential through load-based operational strategies. (2) Vaneless space rotor-stator interaction (RSI) reflects periodic disruption of the combined C₂₄ × C₁₃ symmetry at the blade-passing frequency of 27.1 Hz (N_r × f_n = 13 × 2.08 Hz), reaching peak amplitudes of 164 kPa (132% p_rated) at H = 180 m and P = 150 MW, representing the most severe symmetry-breaking phenomenon. (3) Volute multi-point excitation exhibits broadband spectral characteristics (4–10 Hz) with peak amplitudes of 146 kPa (118% p_rated) under small guide vane openings. The spatial amplitude hierarchy—vaneless space (164 kPa) > volute (146 kPa) > draft tube (108 kPa)—directly correlates with the local symmetry-breaking intensity, providing quantitative evidence for the relationship between geometric symmetry disruption and hydraulic excitation magnitude. Systematic head-dependent amplitude increases of 22–43% across all monitoring locations are attributed to effects related to Euler head scaling and Reynolds number variation, with the vaneless space demonstrating the highest sensitivity (0.83 kPa/m, equivalent to 0.67% p_rated/m). The study establishes data-driven operational guidelines identifying forbidden operating regions (H = 160–180 m, P = 20–150 MW for vaneless space; H = 160–180 m, P = 250–350 MW for draft tube) and critical monitoring frequencies (0.38 Hz for RVR, 27.1 Hz for RSI), providing essential reference data for condition monitoring systems and operational optimization of large Francis turbines functioning as flexible grid-regulating units in renewable energy integration scenarios. Full article

This paper reviews key parameters which may cause unacceptable water hammer loads in Francis-turbine hydropower schemes. Water hammer control strategies are presented for this context including operational scenarios (closing and opening laws), surge control devices, redesign of the pipeline components, or limitation of operating conditions. Theoretical water hammer models and solutions are outlined and discussed. Case studies include simple and complex new and refurbished hydropower systems including headrace and tailrace tunnels, surge tanks of various designs, and different penstock layouts. The case studies in this paper cover the application of both commercial and in-house software packages for hydraulic transient analysis. Two-stage guide vane closing law, increased unit inertia and surge tank(s) are used in the cases considered to keep the water hammer within the prescribed limits. Typical values for the maximum pressure head at the turbine inlet and the maximum unit speed rise during normal transient regimes were in the range of 10 to 35% of the maximum gross head and 35 to 50% above the nominal speed, respectively. The agreement between computational results using both software packages, and field test results is well within the limits of ±5% accepted in hydropower engineering practice. Full article

Establishing a mathematical model of a Francis turbine is the foundation for the simulation of hydropower station operation and is of great significance for the analysis of the hydropower station’s transient process. Currently, in engineering practice, the model is often established based on the comprehensive characteristic curves of the Francis turbine provided by the manufacturer, using the external characteristic method. Traditional modeling methods mostly adopt manual reading of points or the use of dedicated numerical software for curve tracing to discretely sample the comprehensive characteristic curves of the turbine. This method is labor-intensive, inefficient, and relies on manual experience, with a small sample size, which, to some extent, affects the accuracy and reliability of the numerical processing results and cannot meet the needs of transient process simulation analysis. To address these shortcomings, this paper proposes a refined modeling method based on image numerical processing and an RBF neural network. Taking the HLA685 Francis turbine as an example, the method first uses image processing to achieve large-scale automated discrete sampling of the turbine’s high-efficiency zone characteristic data, then reasonably extends the small-opening and low-speed regions, and finally uses the RBF neural network method for interpolation and extrapolation to obtain the full characteristic data. This method can effectively improve the efficiency and accuracy of comprehensive characteristic modeling of the turbine and has good reference significance for the comprehensive characteristic modeling of blade-type machinery. Full article

The transition toward renewable-dominated power systems is increasingly constrained by the shortage of flexible regulation resources. Hydropower, with its rapid response and strong load-adjustment capability, remains a cornerstone for enabling large-scale integration of intermittent wind and solar energy. Splitter-blade runners are widely employed in medium- and high-head conventional hydropower plants and pumped-storage stations due to their broad high-efficiency operating range and superior stability. In this study, based on a runner replacement project at an existing hydropower station, refined computational fluid dynamics (CFD) simulations were carried out to design a splitter-blade runner under strict dimensional constraints. The optimized runner expanded the unit’s stable operating range from 50–100% to 0–100% rated power, while also improving overall efficiency and reducing pressure pulsations. The optimized splitter-blade runner improved efficiency by 1–2%, reduced pressure pulsations in the draft tube by ≈25%, and decreased the runner radial force by ≈12% compared with the baseline configuration. Importantly, this work demonstrates for the first time that splitter-blade runners can be successfully applied at head ranges below 100 m, thereby extending their applicability beyond traditional limits. The results provide both theoretical and practical guidance for flexibility retrofits of existing Francis turbine units in China, offering a feasible pathway to support the adaptability of future renewable energy systems. Full article

Erosion caused by sediment-laden flow significantly affects the efficiency and durability of Francis turbines. In this study, the Euler–Lagrange multi-phase flow model was employed to simulate solid-liquid two-phase flow with different sediment particle sizes to analyze erosion characteristics in turbine components. The results show that the maximum erosion rate of the runner blades is positively correlated with particle impact velocity, confirming that impact velocity is the dominant factor influencing local material removal. The total erosion rate of the runner blades, guide vanes, and draft tube corresponds closely with vorticity, indicating that vortex-induced flow separation accelerates particle–wall collisions and intensifies erosion. Both vorticity and erosion exhibit a nonlinear variation with particle size, reaching a minimum at 0.05 mm. These findings establish clear qualitative and quantitative relationships between erosion and key flow parameters, providing theoretical guidance for understanding and mitigating sediment-induced wear in Francis turbines. Full article

The lack of detailed design information in legacy hydropower plants creates challenges for modernising their ageing turbine components. This research advances a digitalisation approach which combines inverse design methodology (IDM) with multi-objective genetic algorithms (MOGA) and computational fluid dynamics (CFD) to digitally reconstruct and optimise the Bérchules Francis turbine runner and guide vane geometries using limited available legacy data, avoiding invasive techniques. A two-stage optimisation process was conducted. The first stage of runner blade optimisation achieved a 22.7% reduction in profile loss and a 16.8% decrease in secondary flow factor while raising minimum pressure from −877,325.5 Pa to −132,703.4 Pa. Guide vane optimisation during Stage 2 produced additional performance gains through a 9.3% reduction in profile loss and a 20% decrease in secondary flow factor and a minimum pressure increase to +247,452.1 Pa which represented an 183% improvement. The CFD validation results showed that the final turbine efficiency reached 93.7% while producing more power than the plant’s rated 942 kW. The sensitivity analysis revealed that leading edge loading at mid-span and normal chord proved to be the most significant design parameters affecting pressure loss and flow behaviour metrics. The research proves that legacy turbines can be digitally restored through hybrid optimisation and CFD workflows, which enables data-driven refurbishment design without needing complete component replacement. Full article

Francis turbines are widely used due to their large capacity and broad head adaptability, placing higher demands on the internal flow characteristics and runner performance of the units. In this paper, numerical simulations of a Francis turbine model were conducted using ANSYS CFX 2022 R1. The SST turbulence model, ZGB cavitation model, and VOF multiphase flow model were selected for the calculations. The internal flow characteristics and pressure pulsations in the runner and draft tube under different operating conditions were analyzed, and the variations in normal and tangential forces acting on the runner blades during operation were investigated. The results indicate significant differences in the internal flow within the runner and draft tube under various guide vane opening conditions. The pressure pulsation in the unit is influenced by both the internal flow in the draft tube and the rotation of the runner. The mechanical load on the runner blades is affected by multiple factors, including the wake from upstream fixed guide vanes, rotor–stator interaction, and downstream vortex ropes. Under low-flow conditions, the variation in forces acting on the runner blades is relatively small, whereas under high-flow conditions, the runner blades are prone to abrupt force fluctuations at 0.6–0.8 times the rotational frequency. This is manifested as periodic abrupt force changes in both the X and Y directions of the runner blades under high-flow conditions. The normal force in the Z-direction of the runner blades increases instantaneously and then decreases immediately, while the tangential force decreases instantaneously and then increases promptly. Full article

Francis turbines operating in sediment-laden flows experience efficiency loss and reduced service life due to abrasive wear. To enhance wear resistance, this study optimized the turbine at Mupo Hydropower Station in Sichuan Province. Using the Plackett–Burman design, three runner parameters were identified as most influential: blade number, inlet setting angle, and outlet setting angle. A central composite design based on response surface methodology was then applied to these factors. Multiple regression models linking the parameters to turbine head, efficiency, and wear rate were established, revealing a trade-off between hydraulic performance and wear resistance. Multi-objective optimization, a method that simultaneously addresses and balances multiple competing goals, was performed to minimize wear rate while maintaining the original head. The optimal parameter combination was obtained as follows: blade number Z₃ = 17, inlet setting angle ${\alpha }_1$ = 65°, and outlet setting angle ${\alpha }_2$ = 22°. Numerical results demonstrate a 32.3% reduction in runner wear under these parameters, with the head requirement satisfied, confirming a significant improvement in overall turbine performance. Full article

This study utilizes the Standard k-ε turbulence model and ANSYS CFX software to tackle silt erosion in the top cover clearances of guide vane of the Francis turbine at Genda Power Station (Minjiang River Basin section, 103°17′ E and 31°06′ N) under sediment-laden flow conditions. A numerical simulation of a solid–liquid two-phase flow along the whole flow route was performed under rated operating circumstances to examine the impact of varying guide vane end clearance heights (0.3 mm, 0.5 mm, and 1.0 mm) on internal flow patterns and sediment erosion characteristics. The simulation parameters employed an average sediment concentration of 2.9 kg/m³ and a median particle size of 0.058 mm, indicative of the flood season. The findings demonstrate that augmenting the clearance height intensifies leaky flow and secondary flow, resulting in a 0.49% reduction in efficiency. As the gap expanded from 0.3 mm to 1.0 mm, the leakage flow velocity notably increased to 40 m/s, exacerbating flow separation, enlarging the vortex structures in the vaneless space, and augmenting the sediment velocity gradient and concentration, consequently heightening the risk of erosion. An experimental setup was devised based on the numerical results, and the dynamic resemblance between the constructed test section and the prototype turbine was confirmed for flow velocity, concentration, and Reynolds number. Tests on sediment erosion revealed that the erosion resistance of the anti-sediment erosion material 04Cr13Ni5Mo markedly exceeded that of the base cast steel, especially in high-velocity areas. This study delivers a systematic, quantitative analysis of clearance effects on flow and erosion, along with an experimental wear model specifically for the Gengda Power Station, thereby providing direct theoretical support and engineering guidance for its wear protection strategy and maintenance planning. Full article

The low-pressure edge of a pump-turbine runner blade is more prone to cavitation than other parts. The installation angle of the blade’s low-pressure edge is one of the key parameters affecting the cavitation performance of the pump-turbine. Based on the installation angle of the blade’s low-pressure edge obtained by the principle of normal outflow of the turbine runner, two other installation angles of the low-pressure edge are constructed by increasing the installation angle of the low-pressure edge toward the band direction. Three types of blades are designed based on the parametric design program of the pump-turbine runner. The Zwart cavitation model is adopted to carry out full-channel steady numerical simulations for the three runners. The efficiencies and internal flow fields of the draft tube under turbine operating conditions are compared. The cavitation characteristics in pump mode, the distribution of the turbulent flow field, and the pressure distribution on the blade surface are analyzed. The influence laws of the installation angle of the blade’s low-pressure edge on pump-turbine performance is summarized. A design method for anti-cavitation of Francis pump-turbine runners has been explored. The results show that the LP1 blade can achieve normal outflow under the turbine’s rated operating condition, but due to the large inflow attack angle under pump operating conditions, the cavitation performance in pump mode is very poor. By increasing the installation angle of the blade’s low-pressure edge toward the band direction, the efficiencies and cavitation performances of the pump mode can be improved. The LP3 blade reduces the inflow attack angle while optimizing the pressure distribution on the blade’s suction surface, thereby reducing the superimposed effect of two phenomena under large-discharge pump operating conditions with low cavitation numbers: flow separations on the pressure surface caused by inflow impact, and flow separations on the suction surface of adjacent blades caused by cavitation. As a result, the cavitation performance of the LP3 blade is significantly better than that of the LP1 and LP2 blades. The proposed anti-cavitation design method is simple and effective and can be applied to the research and modification design of Francis pump-turbine runners. Full article