Pumps as turbines (PATs) are widely applied in micro-hydropower stations and chemical industries as economical and efficient energy recovery devices. This study used numerical simulations and entropy dissipation theory to investigate the influence of four draft tube diffusion angles (β0, β1, β2, and β3) on the hydraulic performance and energy losses of a double-suction centrifugal PAT. The results show that the diffusion angle exhibits a complex nonlinear effect on head, efficiency, and shaft power across different flow rates. Under low-flow conditions (0.6Qd), β2 reduces efficiency by 9.27%, whereas under high-flow conditions (1.4Qd), β3 improves efficiency by 1.01%. Entropy analysis reveals that total entropy generation follows an approximately parabolic trend with flow rate, reaching its minimum near the design condition. Among the schemes, β1 and β3 effectively reduce total entropy generation, with β3 achieving a 5.51% reduction under high-flow conditions. The impeller is identified as the dominant source of energy loss (approximately 53% of entropy production), followed by the draft chamber (approximately 30%). Further analysis indicates that entropy generation in the draft chamber primarily arises from turbulent dissipation and wall friction and is highly sensitive to the diffusion angle. Under high-flow conditions, β3 reduces draft chamber entropy production by 7.44%, whereas under low-flow conditions, larger diffusion angles increase entropy production. Thus, optimizing the diffusion angle not only improves impeller flow conditions but also effectively reduces system energy losses, particularly under high-flow and off-design operating conditions. This work provides theoretical insights and engineering guidance for the optimized design of PAT draft tubes.

Although previous studies have demonstrated the potential of a hydraulic barrier in draft tube spout-fluid bed (DTSFB) systems to reduce gas bypassing under fixed operating conditions, a systematic understanding of how design and operating parameters influence bypass behavior, pressure drop, and spouting requirements in DTSFB systems with a barrier is still lacking. A modified DTSFB with a hydraulic barrier was experimentally investigated in this study to obtain fundamental hydrodynamic data essential for understanding, optimizing, and applying this type of gas–solid contactor. To this end, spherical glass particles were used in the experiments, and air was used as a spouting and aeration fluid. The effect of the aeration fluid flow rate, draft tube diameter, and height of the entrainment zone on the pressure drop, minimum spouting flow rate, and fluid distribution between the annulus and draft tube was investigated. The results indicated that the hydraulic barrier effectively avoided the aeration fluid from bypassing into the draft tube over a wide range of operating conditions, with only a minor bypass observed at the maximum aeration fluid flow rate. The amount of aeration fluid bypassing into the draft tube increased with increasing draft tube diameter and decreasing height of the entrainment zone. This behavior contrasted with conventional systems without a barrier, wherein the aeration fluid strongly affected spouting behavior. The study identified the optimal design and operating conditions for completely suppressing the bypassing of aeration fluid, thereby demonstrating that this configuration offers stable operation and considerable potential for practical applications.

The development of renewable energy and the increasing demand for electricity underscore the importance of pumped storage for grid stability. Under low-flow pump operating conditions, pump-turbines frequently exhibit hump characteristics, causing severe hydraulic instability and strong pressure pulsations. This study investigates the formation of a hump using full-channel numerical simulations based on the Scale-Adaptive Simulation turbulence model. The numerical flow–head characteristics were validated against the available experimental H–Q data, while the pressure pulsation results were used for qualitative mechanism analysis. The results reveal three major mechanisms: pre-swirl and spiral backflow in the draft tube, non-uniform runner inflow, and vortex flow-induced separation in the wicket gates. An analysis of entropy production reveals that vortex dissipation is responsible for as much as 71% of hydraulic losses in the hump region. In order to mitigate these effects, four stabilizing fins were installed inside the draft tube. The simulations indicate that the fins possess the capability to inhibit swirl and backflow, confine the vortices within the fin–runner interface, improve inflow uniformity and reduce overall hydraulic losses. As a result, the structural modification significantly attenuates the pressure pulsation amplitudes at key monitoring points and visibly shortens the recovery periods. The region of the hump and positive slope of the performance curve are considerably reduced while the head near the region of the hump is increased. Although the intrinsic hump characteristic is still present, the fin-based flow-control strategy can effectively improve the performance and stability of the pump-turbine, which can guide the design and optimization of high-efficiency pumped-storage plants.

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.

The structural complexity of hydropower units and the intricate nature of internal flow make it challenging to analyze and resolve abnormal noise issues in hydropower stations. This paper investigates an abnormal noise problem in a specific hydropower unit through a combination of tests and computational fluid dynamics simulations. By analyzing the on-site measured noise spectra, vibration spectra, and pressure fluctuation spectra, potential sources such as draft tube vortex, runner-stator interaction (RSI), inter-blade vortex, and air supply valve vibration were systematically excluded. The abnormal noise source was ultimately identified as resonance triggered by Karman vortex shedding from the turbine runner, based on the analysis of the locked-in phenomenon and the calculation of vortex shedding frequency. After thinning the trailing edges of the runner blades on site, the abnormal noise, along with the associated vibration and pressure fluctuation, was effectively eliminated. Noise and vibration near the runner were significantly reduced under all load conditions, with the maximum noise energy in the turbine chamber reduced by 95.2% and the vibration amplitude at the main frequency in the draft tube reduced to only 2% of its original value. This work provides a method for quickly analyzing and resolving flow-induced abnormal noise issues, offering theoretical and practical support for addressing abnormal noise problems in hydro-turbines.

The pump-turbine, as the core equipment of pumped storage power stations, must frequently pass through the S-shaped characteristic region during operation, which severely impacts the stability of the unit. To enhance the operational stability of the pump-turbine in the S-shaped characteristic region, a new runner with C-shaped blades was designed based on an existing runner model. A systematic comparison was conducted on the flow and pressure pulsation characteristics within the S-shaped characteristic region between the flow passage of the C-shaped blades and the original design. The results demonstrate that under braking conditions, the C-type runner exhibits optimal flow stability, with a more uniform streamline distribution in the guide vane and runner domains, and minimal influence from draft tube backflow. Vortex analysis indicates that the C-type runner possesses superior vortex control capability in the guide vane domain, vaneless region, and draft tube compared to the original model. Under reverse pump conditions, the pressure pulsation of the C-type runner is significantly improved; the growth of pulsation amplitude within the blade passage slows, and the maximum pulsation amplitude in the draft tube is reduced by 28% compared to the original model, with an average reduction of 9.8% across all monitoring points. This indicates that the C-type runner can effectively suppress flow instability and pressure pulsation under complex operating conditions. The findings provide an effective technical approach for improving the stability of pump-turbines in the S-shaped characteristic region.

This study addresses the challenges of risk control and parameter compliance during large fluctuation transients in the diversion power generation system of Sri Lanka’s Moragahakanda Reservoir Project. Based on a mathematical model of unsteady flow in pressurized pipelines and the method of characteristics, we investigate the impact of wicket gate opening and closing laws on key parameters, including metal volute pressure, unit speed, and draft tube pressure. Numerical simulations are conducted under various extreme conditions, such as load rejection, load increase, and extreme water levels. The results demonstrate that the optimized straight-line closing and opening laws effectively regulate the system's transient response. The maximum metal volute pressure, maximum speed rise rate, and minimum draft tube pressure all meet the design requirements with significant safety margins, thereby verifying the project's safety and reliability. This research provides a critical reference for the design and operation of similar multi-objective hydropower stations.

Boosting CO2 mineralisation reaction with a spiral internal draft tube reactor: from concept to continuous operation

The Palamuru Ranga Reddy Lift Irrigation Scheme (PRLIS) is a major lift irrigation project in Telangana, India. It includes lifting 90 TMC of water from the Srisailam reservoirs back water to higher elevations for irrigation and drinking purposes. This study focuses on the engineering geological characterization and the subsequent support system design for five draft tube tunnels within Package-16 of the PRLIS. Rock mass conditions were evaluated using the Q-System of classification, integrated with three-dimensional geological mapping and the Norwegian Method of Tunneling (NMT) to develop site-specific support strategies. The tunnels generally exhibited fair to good rock mass quality, with Q-values ranging from 5.10 to 23.8. However, intersecting joint sets introduced localized instability, necessitating targeted reinforcement measures. The adopted support system comprising rock bolts, steel-fibre-reinforced shotcrete, and steel ribs were optimized for structural safety, cost-effectiveness, and long-term durability. Draft tube tunnel-1 required additional reinforcement due to diverse geological complexities. Findings highlight the necessity of adaptive support design in granitic terrains and provide practical insights for tunnel construction in comparable geological settings.

Centrifugal pump as turbine (PAT) is a crucial technology for recovering and utilizing liquid pressure energy, but its cavitation behavior remains insufficiently understood. To investigate the cavitation performance of a specific pump operating as turbine, this study systematically analyzed its behavior across varying flow rates using computational fluid dynamics (CFD) based on the Schnerr-Sauer cavitation model. The results show that the incipient and critical cavitation margins reach their minimum values at the optimal flow rate, closely matching those under low flow conditions. When flow rate exceeds the optimal point, both margins increase significantly. At optimal and high flow rates, the cavity volume inside the impeller first increases and then decreases as cavitation evolves, peaking at the critical cavitation point. The impeller cavity volume grows with increasing flow rate, while draft tube cavity volumes continuously expand as cavitation progresses.

The pump as turbine (PAT), utilizing high-speed centrifugal pumps, boasts technical advantages such as low cost, compact structure, and broad flow adaptability. The present work is a numerical simulation study of the internal flow fields of the volute, runner, and draft tube of a PAT using CFX flow field analysis software. The findings reveal that the maximum energy loss in the PAT runner amounts to 11.5%, accounting for 49.67% of the total loss. The energy loss in the volute section follows closely at 10.6%, constituting 45.79% of the total loss, while the loss in the draft tube is minimal at 1.05%. The PAT volute exhibits significant velocity variations at the inlet section, accompanied by rapid changes and suboptimal internal pressure distribution. Within each flow passage of the runner, the velocity distribution is uneven, with vortices present on the suction side of the blades. The pressure distribution at the center of the runner is nonuniform, characterized by large and multiple small vortices. In the draft tube, the pressure distribution is uneven, with vortex bands at the center causing some energy loss; however, the overall internal flow characteristics remain favorable.

This paper presents a simplified design methodology for Francis turbine components for the low-head micro-hydropower applications. The runner is developed using the Bovet method, while the remaining components are designed taking the runner as the reference. For the design ofa free vortex-type of spiral casing with circular cross-section, the guidelines provided by UNIDO are considered. Likewise, the guide vanes aremodeled using the NACA airfoil profile, and the draft tube adopts a Bend-Spacer-diffuser arrangement to enhance pressure recovery. CFD simulations are performed in ANSYS FLUENT to analyze flow characteristics, pressure distributions, and performance metrics across the distributor,runner, and draft tube. The distributor shows favorable pressure and velocity distributions with a minor head loss of 0.46 m. The runner produces a power output of 17.11 KW with a hydraulic efficiency of 92%, though it operated in off-design conditions, while the draft tube achieveseffective pressure recovery despite a major head loss of 1.26 m. The turbine attains an overall efficiency of 83.5%, highlighting the feasibility ofa simplified and cost-effective design for small-scale hydropower systems.

Nowadays, hydraulic turbines are more often operated under off-design conditions due to the increase in intermittent energy production (wind and solar). In these operating conditions, dynamic phenomena in hydraulic circuit are observed, such as flow instabilities, secondary flows, vortex rope developed in the draft tube etc. These phenomena can lead to pressure pulsations and structural vibrations of the hydraulic turbine structure, that affect the hydraulic turbine performance and its lifespan. In the present paper a wall model, developed by Manhart et al. (2008), is used with the k-ω SST turbulence model to study numerically the pulsating flows which can occur in a hydraulic turbine during part load operation. The Manhart wall model considers the adverse pressure gradient and has the advantage of being used on a coarser mesh (dimensionless distance, y+, can result in values up to 5), leading to smaller simulation time and computational demands when compared to the general approaches. The numerical analysis is carried on using the open-source software, Code_Saturne, and considers a geometry that is similar to the draft tube of a hydraulic turbine.

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.

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 fn, where fn = 2.08 Hz) with maximum peak-to-peak amplitudes of 108 kPa (87% of the rated pressure prated = 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 (Nr × fn = 13 × 2.08 Hz), reaching peak amplitudes of 164 kPa (132% prated) 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% prated) 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% prated/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.

Abstract Under the influence of unstable wind power and other renewable energy sources, hydropower stations frequently perform peak regulation and frequency modulation to meet dynamic grid demands, leading to prolonged operation of hydraulic turbines under low-load conditions. In such scenarios, the flow patterns within the draft tube become highly complex, potentially inducing abnormal pressure pulsations and causing unit vibrations. This study conducted three-dimensional numerical simulations on six low-load operating conditions of a large hydropower unit. The flow states and vortex rope structures in the draft tube under varying loads were investigated, with a focus on analysing pressure pulsations at critical locations. The results reveal that vortex ropes with distinct morphologies form in the draft tube across all low-load conditions. As the load decreases, the vortex ropes gradually evolve into spiral shapes with increased eccentricity, while their interference with central backflow weakens. Influenced by the periodic rotation of the vortex ropes, pressure pulsations in the straight conical section of the draft tube exhibit dominant low-frequency, high-amplitude frequency components. These pulsations may propagate to the runner, altering its hydrodynamic characteristics. The findings provide a foundational basis for subsequent analyses of hydraulic excitation mechanisms in turbine runners.

Modeling the turbulent flow within different draft tube configurations in a cost-effective way is essential for efficient turbine optimization and exploring the underlying flow mechanics. In this study, a convolution neural network (CNN) based surrogate model was proposed to predict local flow parameters within different inclined Francis turbine draft tubes. Three symbolic representations denoting the complex geometry and boundary conditions were set as the input, and pressure and velocity were the output. The adopted CNN framework consists of the U-Net architecture with a contracting path and four expansive paths. Six representative hyperparameters were considered to analyze their influence on the performance and generalization ability of the CNN model. The results show that the predicting accuracy of the CNN model with a U-Net network is 7.53% higher than the traditional CNN model, as skip connections improve image segmentation accuracy. The CNN model with a larger convolution kernel can more comprehensively capture the main features of the flow field. The model with three input variables improves prediction accuracy by 2.4% as more geometrical features correlate with the key flow patterns. For the four different image resolutions, the model with a resolution of 200 × 400 performs exceptionally well. In addition, appropriately increasing the number of convolutional layers or blocks can significantly improve the prediction accuracy of the CNN model. The proposed innovative surrogate model is useful for facilitating the optimization of hydraulic turbine components.

Abstract The pump-turbine is the core equipment of the pumped storage system. The dynamic coupling effect between the flow channel and the water delivery system during variable-speed operation is a crucial factor that contributes to flow instability. This paper investigates the effects of water pipelines on the variable-speed operation of pump-turbines. Based on a 1D-3D unsteady numerical simulation method, the unsteady flow evolution characteristics of the entire flow passage under variable-speed conditions are studied. By integrating the SST k - ω turbulence model, the focus is on revealing the influence of the water pipeline on the flow pattern inside the runner and the vortex in the draft tube. Research indicates that the water pipeline substantially enhances the stability of the variable-speed process through the effects of inertial compensation and damping. The efficiency of the system utilizing piping is enhanced by 2.6% in comparison to a single unit, while the flow gradient has been decreased by 12%. Extend the propagation path of pressure waves to mitigate torque pulsation energy. It is essential to avoid the risks associated with structural resonance. By optimizing the speed distribution of the runner outlet surface, the disorderly development of the meridional velocity component is suppressed. This achieves the purpose of improving the vortex in the draft tube. This study systematically elucidates the effects of water pipelines on variable-speed processes, offering theoretical support for the operational optimization of variable-speed pump-turbines.

Abstract Pump as Turbine (PAT), utilizing high-speed centrifugal pumps, boasts technical advantages such as low cost, compact structure, and broad flow adaptability. This research undertakes a numerical simulation study on the internal flow fields of the volute, runner, and draft tube for the flow passage components of PAT using the flow field analysis software CFX. The findings reveal that the maximum energy loss in the PAT runner amounts to 11.5%, accounting for 49.67% of the total loss. The energy loss in the volute section follows closely at 10.6%, constituting 45.79% of the total loss, while the loss in the draft tube is minimal at 1.05%. The PAT volute exhibits significant velocity variations at the inlet section, accompanied by rapid changes and suboptimal internal pressure distribution. Within each flow passage of the runner, the velocity distribution is uneven, with vortices present on the blade’s suction side. The pressure distribution at the runner’s center is non-uniform, characterized by large and multiple small vortices. Inside the draft tube, the pressure distribution is uneven, with vortex bands at the center causing some energy loss; however, the overall internal flow characteristics remain favorable.

Abstract The swirling flow with cavitation can cause the cavitation volume fluctuation in a draft tube of a hydro turbine at full load condition, causing pressure fluctuation with flow rate fluctuation known as cavitation surge. Although the cavitation surge characteristic has been investigated in previous studies, the detailed mechanism has not yet been established. In this study, the effect of the pipe length on the cavitation surge was investigated using the venturi tube simulating a draft tube. While the cavitation surge frequency was changed with the pipe length at large cavitation coefficient, it was not so changed at small cavitation coefficient. It is assumed that the flow fluctuation upstream the venturi tube was small at small cavitation coefficient so the effect of changing the upstream pipe length was small. Furthermore, the occurrence condition and frequency of pressure amplitude peak was changed with the pipe length. It was clarified that the pressure amplitude peak occurs in correlation with the cavitation volume fluctuation by CFD results.