Search Results (48)

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

During frequent peak-regulation operation, pumped storage units inevitably operate under off-design conditions. Variations in draft tube flow structures under different load conditions may alter the hydraulic loading acting on the runner and shaft system. In this study, a model pump-turbine was investigated using unsteady numerical simulations combined with finite element structural analysis. Analyses were conducted under 70%, 100%, and 105% load conditions, representing typical part-load, rated, and overload operating states. The results show that under 70% load, the draft tube flow exhibits an eccentric structure with strong circumferential pressure non-uniformity. At the rated condition (100% load), the flow field is closest to axisymmetric with the most uniform pressure distribution. Under 105% load, a concentrated central vortex forms, and the degree of non-uniformity is intermediate. The hydraulic loads under different conditions lead to significant differences in the stress and deformation characteristics of the shaft system. The maximum equivalent stress increases from 1.84 MPa at the rated condition to 3.33 MPa under overload conditions, while more pronounced flow asymmetry and pressure non-uniformity occur at part-load operation. These findings clarify the relationship between load variation, draft tube flow structures, and the mechanical response of the shaft system. Full article

To investigate the characteristics of pressure pulsation induced by vortex ropes in the draft tube of a centrifugal pump under runaway conditions, a closed double-layer hydraulic test bench was established in this study. Runaway characteristic experiments were conducted, and pressure pulsation signals were acquired at heads of 7.6 m, 9.6 m, and 11.9 m. The measured pressure data were analyzed in the time–frequency domain using Fast Fourier Transform (FFT) and Wavelet Transform (WT). The results show that both the runaway rotational speed and the reverse flow rate increase with increasing head. Under all three heads, the dominant frequency upstream of the elbow section of the draft tube is 0.53 times the rotational frequency, confirming that the vortex rope in the draft tube serves as the primary excitation source of the flow field. As the vortex rope is conveyed by the main flow through the elbow, it undergoes impingement and fragmentation, causing the dominant frequency downstream of the elbow to decrease to 0.1 times the rotational frequency. The dominant frequency induced by the vortex rope remains continuous over time, whereas the frequency arising from the coupling between the vortex rope and rotor–stator interaction exhibits pronounced time-varying oscillations. These oscillations intensify with increasing head, and their frequency oscillation range broadens from 4 to 6 times the rotational frequency at low head to 2–8 times at high head. These findings provide a theoretical foundation for the preventive and protective design of centrifugal pumps under runaway conditions. Full article

Pump-turbines are critical for maintaining power grid stability, but they frequently suffer from flow instabilities induced by cavitation due to frequent operating condition changes. This study employs numerical simulations to systematically analyze the internal flow characteristics and changes in runner forces within a model pump-turbine under varying guide vane openings and cavitation coefficients. Results indicate that, under low opening conditions, a spiral vortex rope forms within the draft tube, inducing significant low-frequency pressure fluctuations. As cavitation intensifies, the vortex rope undergoes substantial expansion. At guide vane openings of 30.6 degrees and 37.3 degrees, the draft tube vortex rope exhibits a straight conical shape, with its dimensions increasing as flow rate rises. Additionally, the radial force on the runner is dominated by low-frequency fluctuations generated by the draft tube at low opening conditions, shifting to high-frequency characteristics caused by rotor–stator interaction at high opening conditions. Meanwhile, the expansion and contraction of the cavity volume induce low-frequency fluctuations in the axial force on the runner. These findings reveal the mechanism of vortex rope evolution on runner forces, emphasizing the impact of cavitation on the flow characteristics and force characteristics of the unit. Full article

Against the backdrop of the carbon peaking and neutrality (“dual-carbon”) goals and evolving new-type power system dispatch, the share of pumped-storage hydropower (PSH) in power systems continues to increase, imposing stricter requirements on units for higher cycling frequency, greater operational flexibility, and rapid, stable startup and shutdown. Focusing on the entire hot-standby-to-generation transition of a PSH plant, a full-flow-path three-dimensional transient numerical model encompassing kilometer-scale headrace/tailrace systems, meter-scale runner and casing passages, and millimeter-scale inter-component clearances is developed. Three-dimensional unsteady computational fluid dynamics are determined, while the surge tank free surface and gaseous phase are captured using a volume-of-fluid (VOF) two-phase formula. Grid independence is demonstrated, and time-resolved validation is performed against the experimental model–test operating data. Internal instability structures are diagnosed via pressure fluctuation spectral analysis and characteristic mode identification, complemented by entropy production analysis to quantify dissipative losses. The results indicate that hydraulic instabilities concentrate in the acceleration phase at small guide vane openings, where misalignment between inflow incidence and blade setting induces separation and vortical structures. Concurrently, an intensified adverse pressure gradient in the draft tube generates an axial recirculation core and a vortex rope, driving upstream propagation of low-frequency pressure pulsations. These findings deepen our mechanistic understanding of hydraulic transients during the hot-standby-to-generation transition of PSH units and provide a theoretical basis for improving transitional stability and optimizing control strategies. 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

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

This study presents a numerical investigation of the internal flow characteristics within the draft tube of a Kaplan turbine using computational fluid dynamics (CFD). The distribution and evolution of vortical structures, particularly the formation and development of vortex ropes under various operating conditions, are systematically analyzed. The study aims to explore the effects of blade angle and guide vane opening on the internal flow characteristics of the unit, thereby providing guidance for flow control strategies. The influence of guide vane opening and turbine head on vortex dynamics and flow stability is examined, with a focus on the pressure pulsations induced by vortex ropes through frequency-domain analysis. The results indicate that increased guide vane openings and higher heads lead to the expansion and downstream extension of the vortex rope into the elbow section, causing significant low-frequency pressure pulsations and enhancing flow instability. These findings contribute to a deeper understanding of unsteady flow behavior in Kaplan turbine draft tubes and provide a theoretical foundation for improving hydraulic stability and optimizing operational performance. Full article

In our previous research work, we investigated different methods to mitigate the vortex rope that appears in the draft tube of a Francis turbine when it operates at off-design operating points. The most promising results were obtained for a method involving an axial jet of water. The minor disadvantage of this method was the high value of the flow rate of the water jet. Our present work focuses on another method that decreases the value of the flow rate of the jet. In this sense, a new device has been developed that produces a pulsating water jet, which mitigates the pressure fluctuations associated with the swirling flows. The objective of this paper is to use our experimental test rig to validate the efficiency of a pulsating water jet in mitigating the vortex rope. To perform that, pressure measurements were carried out at four test levels to evaluate the pressure amplitude evolution when the pulsating jet was deployed. From preliminary investigations, the results indicate that this method leads to a decrease of the pressure amplitude of the vortex rope, with a lower value of the flow rate of the jet. Full article

Pumped storage units often deviate from the optimal operating conditions in the process of regulating new energy fluctuations. To effectively improve the performance of the units, the variable speed of the units is one of the more feasible means at present. This paper focuses on the part-load condition of turbine operation, with an emphasis on the internal flow characteristics and pressure pulsation characteristics of the pump turbine during the linear reduction of the rated speed. It is found that the streamlines in the runner become turbulent in the process of speed reduction, forming a vortex at the inlet of the runner, and the vortex scale gradually increases with the speed reduction. The vortex rope in the draft tube undergoes three types of changes during the speed reduction: helical eccentric vortex rope, vanishing vortex rope, and columnar vortex rope. Before the speed change, the low-frequency components with high amplitude exist in each flow-passing part, but gradually disappear with the speed reduction. Except for the runner, the frequency affected by rotor–stator interference of each flow-passing part increases with the decrease of speed, and the growth is most obvious in the vaneless region. The findings of this research can serve as a valuable reference for the variable speed operation of pumped storage units. Full article

Under partial load operating conditions, vortex rope generation in the draft tube of a Francis turbine is considered one of the main reasons for hydro unit vibration. In this paper, a Francis turbine HLA551-LJ-43 in the laboratory was taken as a prototype. Numerical simulations of the entire flow passage were carried out. Four different hydro-turbines were chosen to analyze the effect of vortex suppression, which were named the prototype turbine (N-J), the turbine with J-grooves installed on its conical section (W-J), the one with extending runner cone (C), and the one that considered the J-grooves and the extending runner cone at the same time (J+C). Under the part load conditions in which the vortex rope is easily generated (0.4–0.8 times design flow Q_BEP), the spectrum characteristics of pressure fluctuation, the morphology of vortex rope, and the energy dissipation based on the entropy production theory in the draft tube were studied. The results show that the three optimized structures W-J, C, and J+C could reduce the pressure pulsation in the conical section of the draft tube, weaken the eccentricity of the vortex rope, and decrease the energy losses in the runner and draft tube. It is worth mentioning that the turbine with a J+C optimized structure had the most potent effect on vortex suppression and energy dissipation. Primarily when operating in deep partial load (DPL) conditions, the efficiency of the turbine with a J+C optimized structure was increased by 13.7% compared to the prototype turbine, and the main frequency amplitude of the pressure pulsation in the draft tube was reduced to 32% of the prototype. Full article

Unstable flow in a pump-turbine can cause pressure pulsation, and the resulting vibration deteriorates the stability and operating safety of the unit. This study conducted three-dimensional numerical calculations of the overall flow passage of a pump-turbine with splitter blades under the small guide vane opening, and the unsteady flow characteristics of the turbine were investigated. The results showed that the pressure fluctuation was more severe at lower head operating conditions with lower efficiency, especially in the vaneless area (the runner blade passages). Under the lower head condition, the proportion of 12 times the rotational frequency (12 f/f_n) increased in the vaneless area, and the amplitude of 1 f/f_n as well as 2 f/f_n became larger in the runner blade channel, with more space occupied by vortices and reflux areas. A spiral vortex rope formed in the draft tube, increasing the proportion of 0.4 f/f_n and 0.7 f/f_n pressure pulses. Full article

In hydro turbines, the draft tube vortex rope is one of the most crucial impact factors causing pressure pulsation and vibration. It is affected by operating conditions due to differences in the flow rate and state and can be symmetric or asymmetric along the rotational direction. It may influence the stability of draft tube flow. To achieve a better understanding, in this work, dynamic mode decomposition is used in a draft tube case study of a simplification of a vortex rope. As the flow rate increases, the shape of the vortex rope becomes clear, and the flow rotation becomes more significant as the inlet flow rate increases. Dynamic mode decomposition was used to determine the relative frequencies, which were 0 (averaged), 0.7 times, and 1.4 times the features of the reference frequency. As the inlet flow rate increases, the order of high-energy modes and their influence on the vortex rope gradually increase, and this characteristic is exhibited further downstream of the draft tube. When the inlet flow rate is low, the impact of mode noise is greater. As the flow velocity increases, the noise weakens and the rotation mode becomes more apparent. Identifying the mode of the vortex flow helps extract characteristics of the vortex rope flow under different operating conditions, providing a richer data-driven basis for an in-depth analysis of the impact of operating conditions on the flow stability of a draft tube. Full article

Hydraulic vibrations in Francis turbines caused by cavitation profoundly impact the overall hydraulic performance and operational stability. Therefore, to investigate the influence of cavitation phenomena under high-load conditions, a three-dimensional unsteady numerical simulation is carried out for a Francis turbine with different head operating conditions, which is combined with the SST k-w turbulence model and two-phase flow cavitation model to capture the evolution of cavitation under high-load conditions. Additionally, utilizing entropy production theory, the hydraulic losses of the Francis turbine during cavitation development are assessed. Contrary to the pressure-drop method, the entropy production theory can quantitatively reflect the characteristics of the local hydraulic loss distribution, with a calculated error coefficient τ not exceeding 2%. The specific findings include: the primary sources of energy loss inside the turbine are the airfoil cavitation and cavitation vortex rope, constituting 26% and 71% of the total hydraulic losses, respectively. According to the comparison with model tests, the vapor volume fraction (VVF) inside the draft tube fluctuates periodically under high-load conditions, causing low-frequency pressure pulsation in the turbine’s power, flow rate, and other external characteristic parameters at 0.37 Hz, and the runner radial force fluctuates at a frequency of 1.85 Hz. Full article

Pump turbines operate under various off-design conditions, resulting in complex internal flow patterns. This study employs Reynolds-averaged Navier–Stokes (RANS) numerical methods to investigate the flow characteristics of a prototype pump turbine with a single draft tube pier in turbine mode, and then, the flow characteristics inside the draft tube are discussed with emphasis. Asymmetry between the pier-divided draft tube passage flows is inevitable due to the elbow section’s curvature. Most of the fluid flows out of one passage, while vortex motion dominates the interior of the other one, resulting in completely different pressure fluctuation characteristics for the two flow passages. The large-flow passage is mainly characterized by the wide band in the frequency domain, corresponding to the recirculation zone, while some of the measured points in the low-discharge passage exhibit frequency splitting under kinematic progression. Further analysis demonstrates a low-frequency peak corresponding to the complementary shape between the vortex rope and the recirculation zone. This work elucidates the effects of the pier on the flow behavior and pressure fluctuation characteristics inside the draft tube and fills the research gap on piers in the field of pump turbines. Full article