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Review

A Brief Review of Recent Research on Reversible Francis Pump Turbines in Pumped Storage Plants

by
Xiuli Mao
1,2,3,4,*,
Jiaren Hu
1,3,
Zhongyong Pan
4,5,
Pengju Zhong
1,3 and
Ning Zhang
1,3
1
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China
2
Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, China
3
Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling 712100, China
4
School of Fundamental Science and Engineering, Waseda University, Tokyo 169-8555, Japan
5
National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China
*
Author to whom correspondence should be addressed.
Energies 2025, 18(2), 394; https://doi.org/10.3390/en18020394
Submission received: 19 December 2024 / Revised: 3 January 2025 / Accepted: 14 January 2025 / Published: 17 January 2025
(This article belongs to the Section B: Energy and Environment)
Browse Figures
Versions Notes

Abstract

:
As the core for energy conversion in pumped storage plants, the pump turbine is also a key component in the process of building a clean power grid, owing to its fast and accurate load regulation. This paper introduces the current status of research and development of pump turbines from the perspectives of significance, design and optimization, operational performance, advanced research methods, etc. Internal and external characteristics such as transient flow evolution, structural vibration, flow-induced noise, etc., not only reflect operational performance (hydraulic, cavitation, sediment abrasion, and stability performance, etc.) but also directly affect the safe and efficient operation of the system. It is worth mentioning that the space-time evolution of internal and external characteristics is an emerging research direction, the results of which can be used to predict the operational conditions of pump turbines. Moreover, the development and application of intelligent condition monitoring and fault diagnosis aim to prevent failures and accidents in pumped storage plants.

1. Introduction

Pumped storage plants (PSPs) make a great contribution to the safe and stable operation of power grids, especially for integrated functions such as peak shifting, valley filling, etc., which provide further means of consumption of renewable energy in the grid. China’s 14th Five-Year Plan accelerated the construction of pumped storage projects, promoting the large-scale development of new energy sources like wind and photovoltaic systems. It is expected that by 2030, the capacity of PSPs in China will be about 120 million kilowatts, and the installed capacity of PSPs will reach 200 million kilowatts in 2035. Table 1 lists the PSPs under construction and proposed for construction in Shaanxi province, where the authors’ workplaces are located [1,2]; some other representative pumped storage plants can be found in [3]. Currently, commissioned PSPs are primarily consist of reversible units; pump turbines (PTs) play a key role in the the systems of PSPs and can respond accurately to the dynamic demand of the power grid by switching operating conditions quickly and frequently, then building a smart grid with new energy sources and further helping to realize the goal of “double carbon” [4,5].
The peaks and valleys of parallel power loads require PTs to work in transient conditions [4,6], wherein the switching processes are inevitably accompanied by drastic changes in vibration, noise, pressure pulsation, etc. These fluctuations pose significant risks to system safety and compromise the effectiveness of energy regulation [7,8]. In the transient of PTs, issues such as output swing, unit lifting, structural vibration, noise radiation, component abrasion, cavitation damage, etc., can be mainly attributed to the turbulent flow field. Hydrodynamic challenges under variable-condition operation not only affect the safe and efficient operation of the unit but also further affect the stability of the power grid [6,9]. Therefore, studying the internal and external dynamics of PTs is essential for enhancing the safe and reliable operational performance of PSPs, as well as for meeting the need for efficient use of clean energy and supporting the coordinated smart development of the power grid [10,11].

2. Design and Optimization of Pump Turbine

2.1. Traditional Design Methods for Flow Domains

In order to apply the methods of mathematics and fluid dynamics to study the movement of water flow, certain assumptions are typically made—for example, that parameters of water-flow motion remain constant over time. This approach allows for the use of simplified, more regular flow approximations to represent complex movement in the runner [12,13]. Thus, according to the different assumptions and simplifications of the flow situation, there are three methods for the hydraulic design of a mixed-flow runner: the unitary theory, the binary theory, and the ternary theory design methods, in which the water flow is assumed to be an ideal fluid [14,15]. These methods are mainly used to design the rotating runner, wherein the unitary and binary theories assume an infinite number of blades in the Francis turbine or pump, allowing the flow on any axis to represent the flow on other axes. However, axial turbines or pumps have a small number of blades, so the assumption that the number of blades is infinite cannot be made. The unitary and binary theories are unable to calculate the respective parameters of the pressure and suction sides of blades; this is a disadvantage of the infinite blade assumption. The ternary design method starts from the study of finite blades in the runner; hence, the water flow is not axisymmetric, which is theoretically closer to the flow condition in the runner near the best efficient point (BEP). More detailed introductions of the unitary theory, the binary theory, and the ternary theory design methods for turbine can be found in [16], and an introduction to pumps can be found in [17]. Francis pump turbines are widely used in PSPs globally. Here, we consider a Francis PT as an example to explain the relative theories involved in the volute, stay/guide vane, and draft tube. Two kinds of definitions are commonly used in volute design at present [18,19]. The first assumes that the tangential velocity ( v u ) at any point within the volute is a constant ( v u = constant). The second assumes a constant velocity moment ( v u · r = constant), and the flow in the volute is ideally represented as axisymmetric flow (Figure 1).
PTs of currently operating PSPs contain both stay vanes and guide vanes, except for some small PTs in laboratories and pumps as turbines (PATs), only have guide vanes. A radial guide apparatus is housed in Francis PTs, neglecting the effect of friction loss, while flow in the vaneless space between the guide vane and runner can be viewed as potential flow; therefore, the change in circumferential velocity obeys the momentum conservation law. Figure 2 shows three different profiles of vanes, wherein a 0 is vane opening and is generally regarded as an operating parameter of the guide vane and α is the inlet angle of vane. α d ′ , α d ″ , and α d ‴ are outlet angles of a negative-curvature vane, symmetric vane, and positive curvature vane, respectively; these outlet angles affect Q significantly. In the case of a turbine operating near the BEP, positive-curvature guide vanes have the effect of reducing circulation, making them suitable for high-specific-speed turbines. On the contrary, for low-specific-speed turbines, guide vanes with negative curvature are often used to increase the circulation before the runner [20,21]. Positive-curvature guide vanes are also suitable for Francis pumps with low specific speed (high H and small Q), and negative-curvature guide vanes perform better with high-specific-speed pumps (small H and large Q) [18,22]. The movement of the guide vanes regulates the flow in different modes, and adjusting their movement changes the load of the PSP system; hence, symmetric vanes are preferred in PTs due to the need for bidirectional flow control [23,24]. The principle of minimum loss should be considered in the design of vane domains; therefore, it is common to assume that t a n δ = constant in stay vane design, wherein δ is the angle between the incoming flow velocity and the circumferential direction [25,26].
Elbow draft tubes are widely used in Francis PTs because they can reduce the amount of underwater excavation and can increase the energy recovery factor compared with straight draft tubes [27,28]. Determination of the geometrical parameters of an elbow draft tube should not only consider the performance of the PT but also the practicalities of the PSP. On one hand, draft tube design requires a high energy index (i.e., a high recovery factor), which brings long-term economic benefits to PSPs. On the other hand, minimizing civil engineering work is necessary in order to reduce the initial investment in PSP construction. These two requirements are contradictory and should be considered comprehensively, for example, increasing the height of the draft tube results in an improved recovery factor but also demands more extensive excavation and concrete work [29,30]. Moreover, assuming the water flows uniformly and axially into the draft tube is necessary in its hydraulic design [31,32].

2.2. Inverse Design Method (IDM)

Today’s PT designs integrate multiple disciplines, including hydraulic engineering, mechanical engineering, electrical engineering, fluid dynamics, materials science, etc. Although the motion of an ideal fluid does not vary with time, we assume that fluid in the runner is axisymmetric and the blade is infinitely thin [17,22]. With continuous improvements in theory and design methods for reversible hydraulic machinery, high-head, large-capacity, and high-speed PTs are applied in PSPs to improve economic efficiency [33,34]. Most PTs are designed in pumping mode and calibrated in generating mode for two main reasons: the high-efficiency region in pumping mode is narrow, and the design boundary at the highest head requires a certain head allowance. The lowest head in pumping mode should be limited to the maximum entry force; cavitation is controlled under the premise of meeting the pumping volume requirement. Normally, generating mode is used to verify the runner that designed in pumping mode, although some PTs are designed in turbine mode and calibrated in pump mode [35,36]. In fact, effective energy matching between pumping and generating modes is essential to fully utilize the generator’s capacity [37,38]. The IDM applied to PTs in China was proposed by Qi Xueyi from Lanzhou University of Technology in 1980; later, computational fluid dynamics (CFD) were used by Liu weichao and Yang lin in 2003 and 2005 to design and optimize PTs, respectively [39,40]. IDM designs the runner in generating mode; the velocity is decomposed into circumferentially averaged and periodically pulsating components along the flow direction. The blade shape is determined iteratively to satisfy the flow boundary conditions. The blade’s contribution to the flow field is replaced with a source–sink vortex on the blade’s center plane. Two-way flow characteristics of the pump and turbine are comprehensively taken into account. Consequently, IDM focuses on hydrodynamic parameters rather than structural parameters, making it a more physically intuitive method for reaching the desired flow field [41,42]. IDM is also used in other turbomachinery, applied in combination with genetic algorithms, multi-objective optimization, and other methods, contributing significantly to efficient design work [43,44]. Ref [45] provides further examples of IDM applications in engineering. Figure 3 shows the optimization of hydraulic efficiency and load distribution on the blades of one PT designed by IDM in previous work by the authors. The design process begins with determining key hydraulic design parameters, such as rotating speed, mass flow, water head, efficiency, output and input requirements, etc., which are typically specified in pumping mode. The second step is calculating the main structural parameters of the flow domains, like diameter, height, and the profile of each flow part, based on the optimization of hydrodynamic parameters with IDM in the flow field. The last part is the broadening of high-efficiency zones that take into account the two-way modes, as well as bidirectional feedback on hydraulic design and fluid stability (pressure fluctuations, vortex evolution, flow-induced noise, hydraulic excitation, etc.) [38,46,47].

2.3. Multi-Objective Optimization Method (MOM)

The MOM is an optimization technique for finding the optimal equilibrium among multiple conflicting objectives; its specific research methods mainly consider linear weighting, the principal objective, ideal point, Pareto solution set, genetic algorithm, particle swarm optimization, simulated annealing, gradient descent, etc. [49,50]. The application of the MOM in PT primarily includes the following aspects: determining the objective function, with the aim of increasing hydraulic efficiency and improving operational performance (especially for system stability of S characteristics) [51,52]; calculating hydraulic and structural parameters; and using the orthogonal test method (OTM) to build a parameter library, which further determined the influence weights of each parameter by intuitive, indirect, and extreme variance analyses. This allows for sensitivity analysis of optimization variables, highlighting their impact on PT performance and guiding subsequent design adjustments [53,54]. Selecting an appropriate algorithm is important to design work from the perspectives of accuracy, workload, and time, in addition to having a direct impact on the quality of optimization results [55,56]. Moreover, the MOM can be combined with the IDM to comprehensively consider multi-type performance of PTs in the design work. For instance, previous work by the authors integrated the MOM with the IDM to evaluate both hydraulic and sediment abrasion performance, as shown in Figure 4.

2.4. Pump Turbine with Variable Speed

Variable-speed and constant-frequency power generation motors enable PTs to operate with variable speed and greater flexibility during transitions [57,58]. The development and application of PTs with variable speed (PTvs) are still in early stages; China has reached a capacity of 300 MW, which will be used in the Zhaoqinglangjiang and Huizhouzhongdong PSPs [59]. In pumping mode, PTvs focus on the power adjustment range at the minimum and maximum heads, which are designed to break through the power adjustment range of variable speed, limited by the secondary flow at the blade inlet, the blade cavitation, and the maximum power. This effectively broadens the pump’s linear energy characteristic curve of a fixed-speed PT into a multi-dimensional energy characteristic surface. In generating mode, PTvs overcome the issue of the operating range of fixed-speed PTs being far away from the optimal zone, as well as the limitation of runner-blade deflux in the primordial line. By allowing for variable speeds, PTvs can extend the power range for stable operation to cover the optimum zone. Consequently, PTvs improve the energy efficiency of the generation model in both directions, i.e., energy conversion efficiency (measured as weighted average efficiency) and a broader operational range (characterized by the operating range area) [60,61,62]. However, there is no publicly available theoretical system of PTvs design and operation as yet.

2.5. Newer Structure of Flow Domains

Francis PTs, tabular PTs, Kaplan PTs, and diagonal PTs, are mainly distinguished by their structure and are suitable for different occasions. Francis PTs are widely used in engineering, especially for large and medium-sized PSPs [63,64]. The following are some representative structures from several Francis PTs. (1) The application of splitter blades reduces rotor–stator interaction, thereby enhancing fluid stability and dispersing water shock into pressure fluctuation. Splitter blades create back-pressure at the wide mouth edge, which helps to decrease the negative-pressure area and improve cavitation performance. Furthermore, a runner with long and short blades exhibits a wider working range with higher efficiencies and a more reasonable stress distribution; this corresponds to better structural strength and flexible adjustment [65,66,67]. (2) Symmetrical guide vanes for the bi-directional flow of PTs offer better flow stability and efficiency; specifically, they can reduce impingement losses and vortex generation in the guide-vane domain. In addition, symmetrical guide vanes have a relatively simple structure and a mature manufacturing process, which facilitate mass production and quality control [68,69,70]. (3) Volutes with trapezoidal, oval, and circular cross-sections require consideration of dimensions, materials, forces etc., which are more dependent on the actual requirements of projects rather than only considering the flow pattern. Variable functions of the cross-sectional area need to be matched with the volute outlet area in order to achieve uniform outflow/inflow. Hence, the ratio of long and short axes is an important measurement parameter [19,71,72]. (4) According to the traditional types of draft tube mentioned in Refs. [16,73], it is feasible to change the height and length of the draft tube to improve hydraulic efficiency, but this results in increased foundation work. Some scholars have proposed new structures of draft tubes; for example, an inclined conical diffuser for a Francis turbine was proposed to eliminate the vortex rope and mitigate the associated pressure fluctuations [74]. (5) PAT is a technically and economically effective technology to utilize small/mini/micro/pico hydropower, especially in rural areas [75,76]. However, the application of PAT still faces problems such as unstable operation, a narrow high-efficiency area, and insufficient structural strength [77,78].

3. Operational Performance of PTs

3.1. Hydraulic Performance

Efficiency, overflow capacity, head, power/output, vibration, noise, etc., are the main indicators of hydraulic performance, wherein profiles and flow angles of blades, multi-stage runners, variable-speed operation, etc., are studied to ameliorate the hydraulic performance of PTs [4,16]. Some of the main directions of hydraulic performance are listed as follows. (1) In general, volumetric and mechanical losses of PTs are constant values, whereas hydraulic loss depends on operational conditions (along-track loss, localized loss, impingement loss, vortex loss, etc.). Optimization of flow passages, the use of drag-reducing materials, adjustment of operating parameters, regular maintenance, etc., are the main paths to reducing losses at present. In recent years, the entropy production loss method has been combined with differential kinetic energy balance equation to solve the hydraulic loss from the thermodynamic point of view [79,80], which provides a new research insight for hydraulic machinery. (2) Rotor–stator interaction is caused by guide vanes and runner blades under steady conditions, while rotor–rotor interaction appears at transitions of PTs. If the dynamic and static interference frequencies are the same or close to the self-oscillation frequencies of structures, system resonance occurs, potentially seriously endangering the operational stability of PTs. Consequently, a large amount of studies have been carried out to explain the interference principle [81,82,83], but no systematic theory has been developed to comprehensively explain and respond to interventions among guide vanes and runner blades. (3) Flow-induced oscillation is inevitable in the operation of PTs, and long-term fatigue vibration can easily lead to structural damage. Current public research is committed to revealing the vibration generation mechanism and exploring effective vibration reduction measures, in which the fluid–solid coupling method is integrated with fluid mechanics, solid mechanics, computational mechanics, and other fields to analyze the interaction mechanism between fluid and solid structures. Collecting experimental data such as structural deflections, bearing and shaft vibrations, etc., and comparison with numerical modeling results to study the external characteristics of flow-excited vibrations presently represent the main approaches [84,85,86]. (4) Dynamic turbulence, vortex evolution, pressure fluctuations, etc., are the sources of flow-induced noise. The flow velocity, flow-channel structure, flow characteristics, etc., have direct impacts on the noise level. Because noise-affecting factors are difficult to qualitatively consider in PSPs, an assumption of boundary closure is necessary in research on flow-induced noise, wherein acoustic coupling methods can be used to solve the dynamic behavior of the acoustic wave and structural vibration under different conditions [87,88]. Furthermore, it has been found that optimizing the structural design, using noise-reducing materials, and improving the working conditions to adjust the flow rate and pressure can effectively reduce the noise level [89,90].

3.2. Cavitation and Sediment Abrasion

The development of the cavitation mechanism is explored from a vacuolar microscopic perspective, and the cavitation influence is analyzed from a macroscopic perspective on flow fields and structural materials based on the theories of pressure waves from vacuole collapse shock and micro-jets [91,92]. Cavitation models (Singhal, Zwart-Gerber-Belamri, Schnerr and Sauer etc.) are widely used to simulate the cavitation process in hydraulic machinery. Techniques such as pulsating laser, high-speed photography, the use of ultrasonic cavitation instruments, etc., are used to observe vacuolar collapse in experiments, aiming to study material damage caused by incipient and developed cavitation and exfoliation [93,94]. The abrasion damage of sediment on metal materials is explored from the perspective of sand characteristics (composition, size, shape, concentration, etc.) and the interaction between sand swarms and the main stream is analyzed from the point of view of force (viscous resistance, additional mass force, acceleration force, pressure gradient force, etc.) based on multiphase flow dynamics [95,96]. Abrasion models (Finnie, Oka, McLaury, etc.) are applied in the simulation of fluid–solid erosion, with techniques like PIV, loss-in-weight, and micro-morphological analysis methods commonly employed in abrasion tests [97,98]. In addition to two-phase flow (air–fluid and solid–fluid flow) studies, several representative research directions are highlighted below. (1) Multiphase flow models, such as fluid volume, mixture, Eulerian, discrete-phase, population balance, and Lagrangian dispersed-phase models, are common multiphase models used in the flow field of hydraulic machinery, each with its own characteristics and applications [99,100]. The integrated application of artificial intelligence, big data, and other advanced technologies in the data processing and analysis of multiphase flow models can improve their accuracy and reliability, further expanding the scope of their utility [101,102]. (2) Interactions between different media, including typical non-linear features, such as convective migration, structural plastic damage, and destruction, are inevitable in the multiphase flow field of hydraulic machinery. These non-linear characteristics make it difficult to predict the behaviors of bubble and sand groups. Sand particle clusters affect the generation, development, and shedding process of cavitation and even the location, shape, and depth of cavitation. Meanwhile, effects such as air cushioning and wrapping of the bubble cluster can affect the trajectory and traveling speed of the sand particles [103,104]. This combined effect of abrasion and cavitation promotes mutual wear, significantly reducing the hydraulic performance of PTs and further threatening system safety and stability. (3) Space-time evolution, including material damage from bubble collapse, impacts, and sediment abrasion, increases with time. Currently, there is no systematic theory to explain the change rule of the material caused by cavitation and abrasion of hydraulic machinery over time. Exciting frequencies of cavitation and abrasion vary with spatial location. As different flow domains are manufactured with different materials (concrete and various metals), seeking wear-resistant coatings or materials is necessary in engineering. Consequently, it is necessary to reveal local and multi-scale properties, as well as transient and cyclic characteristics, in future cavitation and erosion research on space-time evolution. (4) Predictive models of cavitation and sediment erosion, including the discrete bubble method, the intensity function method, the erosion aggressiveness index, etc., are used to predict cavitation intensity, etc. [105,106]. The abrasion prediction model proposed by Durinev and Pelaev aims to predict the erosive wear of materials by solid particles under specific conditions; this method is widely used in the relative studies [95,97]. Recently, Yogesh proposed a novel mechanistic mathematical model for the prediction of solid-particle erosive wear, assuming angular particles of square pyramidal shapes [107]. The development of accurate predictive models for material damage due to cavitation and sediment erosion is crucial for the prevention of field failures and accidents. For example, Figure 5 shows abrasion damage of runner blades, which was discussed by the authors in the previous stage [108].

3.3. Operational Stability

Condition monitoring and fault diagnosis are key parts of ensuring safe and efficient operation of hydraulic machinery. In particular, big data analysis and cloud computing technology support the development of intelligent diagnosis systems. The monitoring information contains hydraulic and electrical parameters, wherein fluctuations of pressure, flow rate, temperature, vibration, noise, etc., are caused by flux oscillation. Consequently, the hydraulic design, manufacturing quality, and working conditions are the main factors influencing the operational stability of PTs. In addition to improvements in structural design, manufacturing, installation precision, etc., there are some effective ways to improve operational stability for PTs in field. (1) A misaligned guide vane (MGV) adjusts the openings of specific guide vanes to change the distribution of flow in front of the runner, particularly to mitigate the start-up instability in the “S” characteristic of PTs. This significantly reduces pressure fluctuations in the vaneless space close to synchronously opening guide vanes, with pressure fluctuations increasing near the misaligned opening guide vanes [109,110]. (2) Flow adjustment methods can also be adopted, such as guide vane closure laws with multi-segment and higher-order functions based on the development of governor technology [51,111]. Another such method is co-adjustment between different flow domains, for example, using both valve and guide-vane control flow under load rejection conditions in a PT [112,113]. (3) Air replenishment device can also be used. Air admission plays an important role in destroying cavity cavitation and reducing cavitation-induced vibration, especially when PTs operate under off-design conditions, in which case, the runner and the draft tube are the main domains that need air [16,114,115]. Moreover, although some research shows that air admission is hard to change, the frequency of pressure fluctuations, water supply, and deflector sets can effectively change the fluid frequency and avoid resonance [116]. (4) Variable-speed operation is another option, as lower speed allows for operation of the PT in the optimal zone, which also narrows the pressure fluctuation range in vaneless space [57,117]. Furthermore, variable-speed adjustment is beneficial to the stability of electrical operation, in combination with hydraulic stability to construct a stable system [58,61]. (5) High-performance materials such as composite materials reduce equipment weight, while their higher strength and better corrosion resistance can extend the life of hydraulic machinery [118,119]. It is worth noting that some high-performance materials have better dynamic response characteristics, quickly adapting to switching conditions during the operation of PTs, further reducing vibration and noise and, thus, improving operational stability [120,121].

4. Advanced Research Methods for Flow Domains

4.1. Dynamic Mesh Technology (DMT)

Dynamic mesh technology is mainly used to implement component motion in simulation calculations, and improved DMT can deal with boundary motion or deformation problems in fluid simulation; for example, the mesh sliding technique can be applied as mentioned in ref. [81]. Addressing the mesh dynamics of complex structures is a difficult problem, the process of which involves automatic mesh reconstruction, adaptive adjustment, real-time updating, etc. [122,123]. For example, smoothing, layering, and remeshing are three main methods used in Fluent 2023 R1 to predictively update the kinematic mesh. Additionally, these methods automatically check the quality of the updated mesh to avoid negative mesh volume. User-defined functions (UDFs) in Fluent, commands in CFX, and OpenFoam enable secondary development through code procedures to control mesh node movement. Programmatic customization of structural motion is a prevalent approach to ensure mesh quality [124,125,126]. The orthogonality, aspect ratio, skewness, Jacobi ratio, warping factor, minimum face angle, etc., are measures of mesh quality, among which orthogonality and the minimum face angle are more commonly used parameters in hydromachinery research. Figure 6 is a PT case with dynamic mesh during the load rejection period.

4.2. Improved Turbulence Models (ITMs)

The development of improved turbulence models is a significantly important research direction in the field of fluid mechanics, with the following objectives: (1) describing and predicting turbulence phenomena more accurately, (2) enhancing computational efficiency and providing reliable results in a shorter period of time, (3) adapting to different mobility conditions, and (4) promoting the development of technologies and fostering interdisciplinary research. With the development of high-performance computers, improved turbulence models are increasingly used to solve complex engineering problems [127,128]. Refs. [129,130] review various methods for treating and simulating turbulence and its effects on hydraulic flows from a historical perspective, as well as the main hybrid RANS-LES methods that are applicable to hydraulic machinery. In addition to hybrid methods, current research focuses on compressible effects, rotation and curvature effects, excitation instability effect, Reynolds stress anisotropy, the transition between laminar and turbulent flow, stress and strain deviations, data-driven techniques, adaptive modeling, and multi-scale modeling. Models for calculating cavitation and sediment abrasion phenomena of hydraulic machinery have been enhanced in recent years [103,131], especially to solve transient fluid dynamicsin PSPs with frequently and rapidly switching conditions (pumping of water back and forth in opposite directions results in the inability to sink sand as in conventional power or pump stations, so cavitation is more likely to occur due to long periods of off-design operation). Last but not least, advanced techniques from different disciplines have been utilized to develop turbulence models to improve modeling accuracy and speed, such as machine learning, secondary development of UDF, parallel computing, etc. [132,133,134]. The authors previously described turbulence models commonly used in pump turbines [135]. Modified partial averaged Navier–Stokes (MPANS) (Figure 7) Zwart–Gerber–Belamri (MZGB) models have now been proposed based on dynamic considerations of grid size, turbulence scale, and bubble fraction with the aim of enhancing the numerical accuracy of multiphase flow at transitions.

4.3. Liutex Vortex Identification Method (LVIM)

Vortex definition and identification methods have gone through several stages. The first generation of the vortex identification method is mainly based on the concept of vortex volume, but it suffers from the inability to distinguish between real vortices and shear flow. The second generation introduces thresholds to better describe vortex structure, but these thresholds are often arbitrary and subject to shear contamination. Liu’s team from the University of Texas at Arlington proposed Liutex vortex as the third generation, which provides a new perspective on the mathematical definition of vortices [136]. A Liutex vector is defined in the same direction as the rotational axis, the value of which is two times that of the rigid rotational angular velocity. It can more accurately identify and analyze vortex structures in complex flow fields, further providing a powerful tool for the study of fluid dynamics. LVIM can help to analyze and identify unstable flow structures, providing insights into reducing hydraulic instability and optimizing energy conversion efficiency [137,138]. Xiao et al. analyzed the flow and vortex distribution of each flow domain in the “S” region by using LVIM [139], and Qin et al. investigated the relationship between hydraulic loss and vortex evolution in pump mode of one PT (Figure 8, the black boxes show the distribution region and distribution intensity have medium similarity) [140].

4.4. Advanced Experimental Techniques

The construction of high-precision test benches is instrumental in accurately evaluating the performance of hydraulic machinery. The use of an intelligent electrical control system significantly contributes to ensuring the reliability, stability, and flexibility of the model test stand [141,142], especially for the application of intelligent monitoring systems, which facilitate real-time monitoring of pump turbine status, capturing key parameters such as temperature, pressure and flow rate. This capability allows for the early detection of potential issues and timely preventive maintenance. Moreover, high-resolution imaging systems for flow observation have enabled the development of test studies of hydraulic machinery from the perspective of external and internal characteristics. The detection of test errors is critical for verifying the reliability of test data, which is an important index for judging the advantages of the test bench, with both systematic and random errors as main factors [141,142].
Tests of energy efficiency, cavitation, pressure fluctuation, flyaway characteristics, four-quadrant full characteristics, pump–hump margin, zero flow of the pumping mode, abnormally low heads of pumping and generating modes, the hydraulic moment of the guide vane, water thrust, etc., are commonly conducted in pump turbine research or in the acceptance phase [143]. During the acceptance phase of pump turbine design, it is necessary to check the pressure measurement section dimensions, the main dimensions of the volute, stay/guide vane, runner, and draft tube, as well as the blade profiles, with all dimensional discrepancies between the design and test required to be within the deviation ranges stipulated in IEC60193 [144]. It is worth mentioning that the stability test for PTvs is a variable-power test, with the curve of operating points showing a stepwise increase in active power to the highest load. Dual optimization with variable speed and variable guide-vane opening can make full use of the advantages of frequency conversion across the full power range, avoiding areas of high-pressure pulsation [145,146]. Advanced test methods can yield twice the result with half the effort in research. The following aspects have been widely used in tests of PTs: Thermodynamic methods of measuring energy conversion have bee applied to achieve efficiency, including proportional-integral-derivative (PID) closed-loop control techniques for flow control and ultrasonic flow measurements using the propagation characteristics of ultrasonic waves in fluid to measure flow [147]. Sensor integration technology has been adopted to monitor and collect performance parameters automatically in real time (temperature, pressure, vibration, noise, etc.), setting different accelerated stress levels in the life test (voltage, frequency, stress, etc.) [148]. The mechanical systems of test stands have been optimized to reduce installation and adjustment time, further improving test efficiency. Remote monitoring technology has also been implemented to facilitate the adjustment of test parameters and evaluate the operational performance of hydraulic machinery. Furthermore, test processes have been standardized to ensure data comparability and consistency among different laboratories [149,150]. Advanced equipment is also used to accurately obtain experimental information, such as laser Doppler velocimeters (LDAs), adaptive speed control systems, dynamic pressure sensors, and particle image velocimetry (PIV) [151,152].

5. Conclusions

Research on reversible Francis pump turbines has made significant progress in recent years, but numerous avenues remain for further exploration to optimize their performance and address contemporary challenges. (1) It is necessary to enhance the understanding of transient behavior, the influence and mechanisms of multiphase flow, etc., of PSPs under frequently changing conditions, particularly the correlation mechanism between internal and external characteristics of units. (2) Methods like machine learning combined with CFD should also be explored, as advanced technology could make a great contribution to the development of hydraulic machinery. Further maturation and the application of an interdisciplinary approach to the study of PTs is an inevitable trend in the future. (3) Innovations in the structure and operational strategies of reversible PTs continue to be the focus of PT promotion, with the aim of addressing practical engineering needs. Moreover, research should seek out approaches like the use of variable speed to widen the operating region with high hydraulic efficiency, structural function, and operational stability. This brief review throws a brick to attract jade, and the authors look forward to exchanging and collaborating with scholars on PTs.

Funding

This work was supported by the National Natural Science Foundation of China (51909222), the China Postdoctoral Science Foundation (2024M752625), a postdoctoral special funding project of Shannxi province (2023BSHTBZZ22), the second “Young Talent Promotion” held by China society for hydropower engineering (CSHE-YESS-2024006), open research subject of key laboratory of fluid and power machinery (Xihua University), ministry of education (szjj2023-8). Xiuli Mao gratefully acknowledge the financial support provided by the China Scholarship Council (No. 202206305003).

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

v u Velocity (m/s)
rRadius (m)
a 0 Guide-vane opening (°)
α Inlet angle (°)
α d ′ , α d ″ , α d ‴ Outlet angles (°)
QMass flow rate ( m 3 /s)
HWater head (m)
δ Angle between incoming flow velocity and circumferential direction (°)
kSlope (-)
θ Angle of inclination (°)
PSPPumped storage plant
PTPump turbine
BEPBest efficient point
PATPump as turbine
IDMInverse problem design method
CFDComputational fluid dynamics
MOMMulti-objective optimization method
OTMOrthogonal test method
LELoad on leading edge of blade
NCStart point of streamline
NDEnd point of streamline
DMTDynamic mesh technology
UDFUser-defined function
MPANSModified partial averaged Navier–Stokes
RANSReynolds-Averaged Navier–Stokes
LESLarge Eddy Simulation
ITMImprovedturbulence model
MZGBModified Zwart–Gerber–Belamri
LVIMLiutex vortex identification method
PIDProportional-integral derivative
LDALaser Doppler velocimeter
PIVParticle image velocimetry
MGVMisaligned guide vane

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Figure 1. Flow field in the volute of one PT in generating mode.
Figure 1. Flow field in the volute of one PT in generating mode.
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Figure 2. Vanes with different blade profiles [16].
Figure 2. Vanes with different blade profiles [16].
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Figure 3. Efficiencies and load distribution on the blades of a PT designed by IDM [48].
Figure 3. Efficiencies and load distribution on the blades of a PT designed by IDM [48].
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Figure 4. Optimization process of one pump turbine by the authors in the previous stage [48].
Figure 4. Optimization process of one pump turbine by the authors in the previous stage [48].
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Figure 5. Abrasion damage of runner blades [108].
Figure 5. Abrasion damage of runner blades [108].
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Figure 6. Minimum face angle of guide-vane mesh at selected moments in the load rejection process [81].
Figure 6. Minimum face angle of guide-vane mesh at selected moments in the load rejection process [81].
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Figure 7. Recent study of MPANS used to solve for the flow field of one Francis turbine.
Figure 7. Recent study of MPANS used to solve for the flow field of one Francis turbine.
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Figure 8. Comparison of distributions between transportation effect and Liutex transport intensity ( T R ) in the draft tube [140].
Figure 8. Comparison of distributions between transportation effect and Liutex transport intensity ( T R ) in the draft tube [140].
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Table 1. PSPs under construction and proposed for construction in Shaanxi province.
Table 1. PSPs under construction and proposed for construction in Shaanxi province.
No.NameCapacityProject Progress
1Zhenan1200 MWFully operation at the end of 2024
2Shanyang1200 MWApproved in 2023
3Foping1400 MWFull-scale construction begins in 2024
4Caoping1400 MWApproved in 2022
5Mianxian1400 MWFull-scale construction beganin 2024
6Dazhuangli2100 MWApproval expected in 2024
7Danfeng1400 MWConfirmed qualifications of the investment subject
8Ningshanbei1800 MWConfirmed qualifications of the investment subject
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Mao, X.; Hu, J.; Pan, Z.; Zhong, P.; Zhang, N. A Brief Review of Recent Research on Reversible Francis Pump Turbines in Pumped Storage Plants. Energies 2025, 18, 394. https://doi.org/10.3390/en18020394

AMA Style

Mao X, Hu J, Pan Z, Zhong P, Zhang N. A Brief Review of Recent Research on Reversible Francis Pump Turbines in Pumped Storage Plants. Energies. 2025; 18(2):394. https://doi.org/10.3390/en18020394

Chicago/Turabian Style

Mao, Xiuli, Jiaren Hu, Zhongyong Pan, Pengju Zhong, and Ning Zhang. 2025. "A Brief Review of Recent Research on Reversible Francis Pump Turbines in Pumped Storage Plants" Energies 18, no. 2: 394. https://doi.org/10.3390/en18020394

APA Style

Mao, X., Hu, J., Pan, Z., Zhong, P., & Zhang, N. (2025). A Brief Review of Recent Research on Reversible Francis Pump Turbines in Pumped Storage Plants. Energies, 18(2), 394. https://doi.org/10.3390/en18020394

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