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Sediment Erosion on Pelton Turbines: A Review


The Pelton turbine has been widely used to develop high-head water resources with sediments because of its advantages in life cycle costs. When a flood or monsoon season occurs, the sediment concentration in the river increases suddenly, causing severe erosion to the nozzle, needle, and runner of Pelton turbines. After decades of development, researchers have developed practical engineering experience to reduce the sediment concentration of the flow through the turbine and ensure the safety and efficiency of power generation. Research on the mechanism of sediment erosion, development of anti-erosion materials, and establishment of erosion prediction models have attracted scholarly interest in recent years. Extensive research has been conducted to determine a complete and valuable syndication erosion model. However, owing to the complexity of the flow and wear mechanisms, the influence of specific parameters of erosion and the syndication effect is still difficult to determine. Computational fluid dynamics and erosion monitoring technology have also been evaluated and applied. This paper presents a comprehensive review of the erosion of Pelton turbines, some of the latest technical methods, and possible future development directions.

1 Introduction

Hydropower plays a key role in today’s world as a vital renewable energy source. Hydropower accounts for the largest proportion of renewable energy. By 2018, the global installed capacity of hydropower had reached 1292 GW [1]. As the world’s largest hydropower producer, China has an installed capacity of 352.3 GW [2]. However, several rivers worldwide have high sediment concentrations. For example, in 2019, the Yellow River, which has the largest sediment load, had an annual sediment discharge of 168 million tons [3]. The river sediment concentrations in the Himalayas, Andes, Alps, Pacific coastal mountains, and Nepal are among the world’s largest. With global warming, melting glaciers, and frequent rainstorms, turbines installed in these river areas suffer from severe sediment abrasion [4,5,6,7,8,9,10]. Power interruption and maintenance caused by sediment problems disrupt the economic benefits of power stations. Sediment abrasion, cavitation, and corrosion combine to cause more damage to metallic materials. In addition, silt erosion aggravates vibration and fatigue damage, shortens a unit's life, increases maintenance costs, and threatens the safety and stable operation of the unit. All these factors adversely affect national electricity consumption [11,12,13,14,15].

For all hydropower stations installed on a high silt river, the eroded parts and erosion rates differ according to the various heads. Generally, power plants with medium and high heads are eroded more severely [16, 17]. The installed head of Francis turbines is often 30–700 m, and the runner, guide vanes, bottom ring, and labyrinth ring are easily eroded [18, 19]. The installed head of Pelton turbines is often 30–3000 m, and nozzles, needles, and buckets are easily eroded [20]. A large part of the head sections of the Pelton and Francis turbines coincide, as shown in Figure 1. However, the Pelton turbine has more advantages in terms of life cycle cost, has a head of 300–2000 m, and eroded parts are easier to replace [21, 22]. Therefore, Pelton turbines are widely used in high-head and sediment basins.

Figure 1
figure 1

Turbine application chart [23]

Impulse turbines include Pelton, Turgo, and cross-flow turbines. Among these, the Pelton turbine is the most efficient and widely used [24]. The Pelton turbine was invented in 1880 [25], and its performance was significantly improved [26] after experimental tests [27] and optimizations [28,29,30,31,32,33,34,35,36,37]. The characteristic of the Pelton turbine is that the centerline of the working jet is tangent to the runner’s pitch circle. The main components are an inlet pipe, injector, runner, regulating mechanism, and casing. The inlet pipe distributes the water evenly to the injector, which converts the pressure energy into kinetic energy. The high-speed jet periodically impacts each bucket of the runner to complete the conversion of kinetic energy into mechanical energy, and the flow rate and output torque can be adjusted through the movement of the needle. The most common arrangement of a Pelton turbine is shown in Figure 2. The Turgo turbine was invented in 1920 [38], and its applied head is 15–300 m. Because of the lower application of Turgo and cross-flow turbines, this paper focuses on introducing the Pelton turbine.

Figure 2
figure 2

Typical layouts of the Pelton turbine [39, 40]

Pelton turbines are susceptible to erosion by sediment-laden flows, and the basic mechanisms of sediment erosion are cutting, fatigue, and brittle failure of materials [20]. The efficiency of the turbine is affected by erosion, as shown in Figure 3. This is the curve between the width of the splitter and the decrease in efficiency [41]. Three main factors affect the sediment erosion:

  1. a.

    Factors related to the operating conditions, such as flow rate, velocity, impact angle, temperature, and fluid medium.

  2. b.

    Factors related to the physical parameters of sediment, such as particle size, concentration, shape, and density.

  3. c.

    Properties of flow-passage components, such as chemical properties, materials, and coatings.

Figure 3
figure 3

Calculated efficiency drops caused by eroding main splitters of Pelton buckets [41]

The surface of the damaged metal is characterized by fish-scale pits, ripples, and grooves. Sediment erosion is often combined with cavitation and chemical corrosion, resulting in the large-area spalling of the material [42].

The methods generally used to study Pelton turbines are field cases, experiments, and computational fluid dynamics (CFD). From the initial stage of operation of the Pelton power station, it has encountered a severe problem of sediment erosion. To solve practical problems, engineers have proposed many methods, such as building sand traps, replacing runner materials, and stopping operations during high sediment periods [11, 17, 43]. Researchers have systematically studied sediment erosion from both experimental and theoretical perspectives [5, 6, 44,45,46]. In the 20th century, CFD was significantly developed, and the first numerical simulation study on the Pelton turbine appeared in 1998 [47]. Currently, researchers can use CFD to study the unsteady complex flow phenomenon more deeply, promoting the sediment erosion problem and dramatically improving runner performance [16].

In addition to the methods mentioned above, theoretical research, erosion monitoring technology, and standard protective measures have been developed. The aim of this paper is to provide a comprehensive overview of the erosion of Pelton turbines, some of the latest technical methods, and possible future development directions.

2 Field Case Investigation

Many Pelton turbines installed in areas with high sediment-laden flow have suffered from severe erosion. An investigation of power stations indicated the following.

After an operation of 600 h with a net head of 920 m, the needle was severely eroded at a hydropower station in the Himalayas [15]. The injector of the Chennai power station was also severely eroded after 2712 h of operation [49]. The Khimki power station had been operating for only a year, and the splitter was eroded and serrated [7, 20]. For the Chilime power station with a capacity of 22 MW, the unit efficiency was reduced by 1.2% owing to sediment abrasion. The erosion rate of the bucket and needle was estimated to be 3.4 mm/year [50]. Technical experts suggested increasing the water level to solve sediment abrasion in the Kulekhani-I hydropower station with a 550 m head. Although the high sediment concentration was solved, the water storage and power generation capacity decreased [51]. The Zhala hydropower station in Tibet, with a total installed capacity of 1000 MW, has a head of 690.55 m and an average annual sediment concentration of 0.259 kg/m3. The annual erosion depth of the bucket was estimated to reach 0.1 mm [52]. Two Pelton turbines installed in a power station in China were severely damaged after 1020 h of operation [53]. After the sediment period, the unit efficiency loss of the Fieschertal Power Station reached 1%. The depth of the cutout increased by 9 mm and the height of the splitter decreased by 6 mm [54]. The Alfalfal Hydropower Station, with a head of 690 m, suffered severe erosion during its operation because of an uncoated runner. After technical improvements, two coatings were successively used: sxhtm70 and sxhtm8x. Even if the runner is coated, it is difficult to operate in a high-flood season without severe erosion [10].

Based on the above investigation, the conclusions are presented in Table 1. Figures 4 and 5 show examples of the eroded needle and runners in hydropower plants (HPPs). We can observe that the needle, splitter, and cutout are the most vulnerable parts of Pelton turbines.

Table 1 Field case investigation
Figure 4
figure 4

Field erosion of a needle [15, 49, 50]

Figure 5
figure 5

Field erosion of runners in different power stations: (a) Toss HPP, India [8]; (b) Alfalfal HPP, Chile [10]

The sediment particle size has different erosion tendencies for the needle and runner. Thapa and Brekke [57] observed that fine particles cause more severe erosion on the needle, coarse particles cause more severe erosion on the bucket, and medium-sized particles cause significant abrasion on the needle and bucket.

The erosion of the injector affects the quality of the jet and the energy transfer between the jet and runner. In particular, the eccentric jet may be caused by erosion, which causes the efficiency of the unit to decrease rapidly [58,59,60,61].

As an energy-conversion component, runner wear affects the output characteristics of the unit, resulting in a decrease in the torque. Therefore, the pattern and division of the runner erosion zone have also been the focus of research. Refs. [17, 41, 62,63,64] observed runner erosion at different power stations and divided the erosion zone of buckets into five parts (Figure 6). Although the erosion zone division of buckets is based on many cases, erosion position standards have not been widely promoted. However, this has not been applied in actual field evaluations.

Figure 6
figure 6

Classifications of the erosion position of buckets [62]

Although the position of erosion and estimated erosion rate for maintenance can be measured by a case investigation, different HPPs have different conditions, and generalizing the empirical erosion formula is difficult. Erosion assessment requires a large workforce and financial resources, but the results are not universal, which is very uneconomical for HPPs.

Researchers have used experimental methods to study Pelton turbines to determine erosion factors and an erosion model (Section 3).

3 Experimental Studies

Many sediment erosion test rigs exist, such as jet test benches, rotating discs, slurry pot testers, model units, and single bucket fixed experimental devices [65,66,67]. The experimental systems described below have been commonly used to study silt erosion in recent years.

3.1 Rotating Disk Test System

The rotating disk test system is a common experimental device used to study the multiphase-flow impact damage of hydraulic turbines. It was initially used to study sediment erosion of low-head turbines [68]. As shown in Figure 7, the high-head hydraulic mechanical erosion test system (ETS-HM) was developed by the China Institute of Water Resources and Hydropower (IWHR). The experimental device comprises a rotating disc, nozzle, and erosion chamber. During an experiment, a trapezoidal specimen is fixed to a support plate. The motor controls the disc speed, and the high-speed jet is ejected from the nozzle. Liu et al. [44, 69, 70] used this device to test the anti-erosion properties of different materials with different sediment characteristics (concentration, hardness, and mineral content). Erosion prediction models for different materials were established based on experimental data and multiple linear regression analyses. Subsequently, the erosion rates of the Pelton turbine flow passage components in the Tibet and Pakistan Allai Khwar power stations were evaluated.

Figure 7
figure 7

Rotating disc test system [44]

3.2 Pelton Turbine Test Rig

Because the actual flow process is complex, it is impossible to consider the changes in the bucket surface curve and jet angle on the rotating disc. Therefore, more scholars have used the Pelton turbine model unit to conduct experiments.

Padhy et al. [5] collected sediment from the Bhagirathi River. After screening and drying, it was added to a water tank and stirred evenly to simulate sediment-laden flow under natural conditions. Subsequently, an experiment was conducted on a small Pelton turbine. The runner fabricated from brass is shown in Figure 8. By weighing the runner after the test, the related data of sediment parameters and runner mass loss under different velocities, particle sizes, and concentrations were collected, and the first-order regression expression of the erosion rate was established. Later, based on this test, these scholars further studied the relationship between efficiency loss and erosion parameters and obtained a correlation expression and error range of ±10% [6]. Thakur et al. [71] also studied the factors influencing bucket erosion using similar devices and research methods. The device is shown in Figure 9, and the error between the erosion model and experimental data was within ± 12.8%.

Figure 8
figure 8

Runner fabricated from brass [6]

Figure 9
figure 9

Experimental devices of a small Pelton turbine [71]

3.3 Pelton Turbine Rig for Hydro-Abrasive Erosion Testing

Although the Pelton turbine model unit in Section 3.2 is closer to the actual operating conditions than the rotating disc, because experimental results should be obtained quickly, the materials used are metals with low hardness, such as brass. The difference in materials results in different wear results for an actual turbine. Rai et al. [48] summarized and analyzed the advantages and disadvantages of previous experimental devices and proposed a new device, as shown in Figure 10. Rai et al. [72] not only verified the accuracy of the test rig but also proposed using an optical scanner and weighing method to simultaneously measure the bucket erosion and mass loss to ensure the accuracy of the measurement [48]. Rai et al. [45] conducted erosion experiments on runners of different materials to compensate for defects in which the runner material is brass. They summarized the exponential constant values of the velocity, concentration, size, and time.

Figure 10
figure 10

Diagram of Pelton turbine rig for hydro-abrasive erosion testing [72]

3.4 Summary

According to references, in the experimental process, the more consistent the test conditions with the field test conditions, the more accurate the results [73]. Jet test rigs focus on the abrasion resistance of materials [20, 74]. Simulating the actual erosion conditions of Pelton turbines using a slurry pot tester is challenging [48]. The limitations of a single bucket fixed experimental device are the lack of the Coriolis force, the Coanda effect, and secondary erosion [48]. For a rotating disk, the bucket shape and jet angle change cannot be considered. Although the Pelton turbine model unit is closer to field operating conditions, the material used differs significantly from the actual material. The Pelton turbine rig for hydro-abrasive erosion testing is closest to the field unit in terms of material and operating conditions. However, it has some limitations:

  1. a.

    Observing sediment erosion, such as that during the monsoon season, often requires a long time. The experiment frequently requires several weeks; therefore, quantitatively observing the specific effect of certain sediment parameters is difficult.

  2. b.

    Ensuring that the operating conditions of the prototype unit and experiment are entirely consistent is challenging.

Table 2 shows the erosion models developed by scholars according to experimental data. We can observe that under different experimental conditions, the test results differ significantly, and the influence of different parameters on the erosion results is not fully understood [48].

Table 2 Summary of erosion models based on experiments

4 Theoretical Studies on Wear Mechanism

4.1 Research and Development of the Wear Mechanism of Sediment Particles

Scholars have discussed and analyzed the surface erosion patterns of hydraulic machinery [75]. The wear of hydraulic machinery is an action process involving a compound mechanism. The main reason for hydraulic machinery wear is sediment particle erosion. The wear mechanism is generally divided into impact and sliding wear [15], with impact wear playing a significant role in the wear mechanism. These two mechanisms are primarily caused by shear and deformation, as shown in Figure 11.

Figure 11
figure 11

Two wear mechanisms [15]

(a) Impact wear: A single particle impacts the solid surface at a certain speed and angle. After a long development period, the surface material undergoes microscale deformation, cutting, and fatigue cracks.

(b) Sliding wear: A large number of particles move along a solid surface at a tangential speed. After a long period of development, the scratching on the solid surface removes the material.

Sand erosion in hydraulic machinery can be divided into three types [15]:

  1. a.

    Abrasive surface erosion caused by small particles with strong fluidity (S ≤ 60 μm) at a high flow rate.

  2. b.

    Vortex erosion of secondary flow at the bend of the channel.

  3. c.

    The wear on the wall is caused by large particles (S ≥ 0.5 mm) separated from the streamline.

After sand abrasion, according to the surface wear state of the metal materials, the wear can be classified as follows [15]: (a) metallic luster, (b) fine-scale erosion, (c) scaly erosion, (d) large-scale scaly erosion, (e) in-depth erosion, and (f) through holes or entire erosion out of the metal.

However, no quantitative model exists that describes the specific wear degree of a Pelton turbine. The expression of wear commonly used in the early days was as follows [76]:

$$\, Wear \, \propto \, (velocity) \, ^{n}$$

where \(n\) is velocity index. Subsequently, many other wear models were developed [46, 50, 77,78,79,80]. In some authoritative studies and reference manuals, the wear models of the Pelton turbine are described as follows.

In the book “Abrasive erosion and erosion of hydraulic machinery”, the following wear reference model is provided [15]:

$$J = \frac{{A \cdot p \cdot t \cdot W^{3} }}{\varepsilon },$$

where \(J\) is the extent of the erosion (mm); \(p\) is the average annual concentration of abrasive particles (kg/m3); t is the time interval comprising the period within a year when abrasive particles attack the surface; \(W\) is the flow velocity (m/s); \(\varepsilon\) is the erosion resistance of the material used (equal to unity for carbon steel); \(A\) is the index of the slurry abrasively depending on the shapes of the particles and is to be determined experimentally (mm \(\cdot\) s3/year).

The theoretical wear model proposed by the International Electrotechnical Commission (IEC) 62364 is as expressed follows [73]:

$$\begin{gathered} \hfill \frac{{{\text{d}}S}}{{{\text{d}}t}} = f({\text{particle velocity,}}\;{\text{concentration,}}\;{\text{physical properties}}, \\ \hfill {\text{flow pattern,}}\;{\text{turbine material properties, and other factors}}), \\ \end{gathered}$$

where dS/dt is the hydroabrasive erosion rate (mm/year).

Although the IEC provides an empirical erosion model of hydraulic turbines, the model coefficient of the Pelton turbine is not provided because of the lack of field test data [62]. Based on the measured data of a power station, Rai et al. [8] supplemented and explained some parameters of the Pelton turbine in the IEC model, such as the flow coefficient (\({K}_{f}\)), material factor (\({K}_{m}\)), exponent (\(p\)), erosion depth (\(S\)), and shape factor (\({K}_{shape}\)).

The erosion model has been developed for many years, but the current theoretical research lacks quantification of the erosion rate of each part of the Pelton turbine. Duan et al. [15] proposed that the erosion depth of a splitter can determine the erosion rate. Felix [81] proposed quantifying erosion by measuring the splitter’s height change, cutout depth increase, and decrease in coating thickness. Rai et al. [8] also proposed a definition of the erosion depth for different parts to quantify erosion.

To study the mechanism of sediment erosion, in addition to analyzing the wear mechanism and establishing the corresponding wear formula, researchers use instruments such as stroboscopic photos and the scanning electron microscope (SEM) to verify these theories [82, 83]. Padhy et al. [83] verified the wear mechanism of particles using electron microscopy and studied the mechanism of the particle angle on bucket surface erosion. Using SEM, Rai et al. [46] observed that the erosion mechanisms of different bucket parts depended on the flow pattern.

In addition to the angle of particles, particle size significantly influences the erosion position and rate, as shown in Figure 12 [83, 84]. A high acceleration causes the particles to separate from the streamline, causing erosion of the material surface. Small particles are more likely to cause erosion at the outlet edge of the bucket, whereas large particles are more likely to cause erosion at the bucket inlet edge [83]. In addition, when the particles are separated from the streamline, the local flow of the wake became turbulent. This turbulence produces unsteady loads and oscillations on particles, and may increase erosion [84].

Figure 12
figure 12

Effect of particle size on erosion position [20, 84]

Based on data collected from 250 power stations worldwide, Rai [84] analyzed the mechanism of sediment erosion of Pelton turbines from the perspective of mechanics. The forces acting on the runner during operation were divided into four types: (a) centrifugal force with constant magnitude and outward direction, (b) Coriolis force changing along the streamline, (c) constant force due to path curvature, and (d) drag. The forces in the bucket are shown in Figure 13.

Figure 13
figure 13

Simplified flow in the bucket and force direction [84]

Parray et al. [49] studied the erosion mechanism of an injector (Figure 14). In Zones I and II, the impact angle is relatively small, and the erosion pattern of the surface is primarily ripples caused by scratching. The impact of a large angle and high velocity in Zone III results in fatigue damage and fracturing of the needle tip.

Figure 14
figure 14

Erosion zone of the nozzle and needle [49]

4.2 Combined Effects of Sediment Erosion and Cavitation

Sand abrasive erosion, cavitation, corrosion, and casting defects of materials form a combined effect that aggravates erosion. However, the most important factor is the cavitation–abrasive erosion caused by the combined hydrodynamic force of cavitation and sediment particles. Cavitation erosion and sediment abrasion interact and influence each other [15]. The silt particles increase the concentration of the gas nucleus in the water, and the surface becomes rough after silt erosion, which enhances the vortex and turbulence. All these factors strengthen the cavitation occurrence conditions. The "micro-jet" produced by bubble collapse accelerates the impact speed and cutting force of sand particles. The rough concave–convex surface caused by cavitation may increase the erosion angle of sand particles and intensify the cutting and damage of particles [85, 86]. The code GB/T 19184-2003 [87] provides the position accessible to the cavitation of the bucket.

Some scholars have studied cavitation in Pelton turbines [88,89,90,91,92]. They believe that most of the cavitation phenomenon can be avoided by good design, casting technology, and materials, such as cavitation-free geometry of buckets and integral casting runners [53, 93]. However, cutout region cavitation caused by high-speed jets is unavoidable. When the shape of the bucket surface changes owing to sediment abrasion, cavitation occurs on the inner surface, back surface, and outlet side of the buckets [94, 95]. To date, only a few studies have been conducted on the combined action of sediment abrasion and cavitation on Pelton turbines [86, 94]. Therefore, further studies should be conducted on the combined effect of Pelton turbines.

4.3 Summary

The erosion of Pelton turbines is primarily caused by shear and deformation caused by impact and sliding wear. After years of development and research on wear mechanisms, erosion models have improved, but quantifying the erosion of specific parts is still challenging. The combined action of sediment and cavitation is the primary factor that causes abrasion and fatigue failure in Pelton turbines. However, research on the combined effect remains insufficient, and further studies should be conducted.

5 State-of-Art Technology of Numerical Simulation

The CFD method can be divided into Eulerian and Lagrangian methods [24, 96,97,98,99]. The Eulerian method is mature, and commercial software codes include Fluent, CFX, and OpenFOAM. However, the Lagrangian method has not been widely used because of its low accuracy. Currently, smoothed particle hydrodynamics (SPH), moving particle semi-implicit (MPS) method, and fast Lagrangian solver (FLS) are the most popular Lagrangian methods. However, the Lagrangian method has more advantages in capturing the free surface, calculating costs, and addressing complicated geometric boundary problems [24, 96]. Figure 15 compares the two methods and the experiments used to capture the free surface. The advantage of the Lagrangian method in capturing a free surface can be observed [100, 101]. Currently, CFX is the most accurate tool in torque prediction [24] and is the most widely used, followed by Fluent. OpenFOAM requires further development because its computational cost is much higher than that of CFX and the torque is over-predicted [98]. For SPH, the Coanda effect on the back of the bucket is ignored, and the interference of the torque curve is severe, which requires further development [102, 103]. The solution speed of the FLS is the highest among all CFD methods, but the accuracy is significantly low [38]. Therefore, the FLS is only suitable for performance testing at the initial stage of runner modeling and not for optimization in the final stage [104]. The arbitrary Lagrangian–Eulerian (ALE) combines the advantages of Eulerian and Lagrangian methods and has been widely studied, but it is not yet very mature in technology [36, 96]. The MPS method [105], SPH–ALE [39, 102], and the finite volume particle method (FVPM) [106] are all new methods proposed in recent ten years, and their accuracy and applicability require improvement.

Figure 15
figure 15

Comparison of the relative flow pattern inside the buckets between FVPM (left), VOF (middle), and experimental (right) for the impinging angles of 62°, 72°, 87°, and 104° (top-down) [100]

The Eulerian–Lagrangian method is the most common method for solving the Pelton turbine sediment erosion problem using CFD. The fluid is calculated using the Eulerian method, and the Lagrangian method describes the motion of solid particles. According to the different methods of interaction between the solid and fluid, it can be divided into one-way and two-way coupling. In two-way coupling, the momentum exchange term is introduced into the equation to increase the influence of particles on the flow [107]. According to Newton’s second law, the empirical formula of hydrodynamic force determines the motion of particles, and particle–particle and particle–boundary interactions are not considered [16].

5.1 Numerical Simulations of Sediment Erosion

Cao et al. [108,109,110] studied the sediment erosion effect on a single fixed bucket (Figure 16), which differs from the actual high-speed rotating runner [111].

Figure 16
figure 16

Erosion rate of fixed bucket [110]

At least three buckets are required to study a high-speed rotating runner [112]. Kumar et al. [113] studied the influence of the sediment properties on runner erosion. Dynamic mesh technology was used in the simulation process, making the numerical simulation closer to engineering practice. Thakur et al. [71] analyzed the deformation of a runner using the finite element method. They observed that the deformation of the splitter and cutout was the largest, which was consistent with the field experiment (Figure 17).

Figure 17
figure 17

a Equivalent elastic strain on the Pelton bucket; b equivalent stress on the Pelton bucket; c total deformation in Pelton bucket

Nath and Kumar [114] conducted a numerical simulation of five buckets and observed that the splitter and innermost zone of the buckets were the most vulnerable positions to erosion. Recently, Leguizamón [112, 115,116,117,118] proposed a multi-scale model to estimate the erosion rate of buckets, avoiding the limitations of commercial software relying excessively on empirical formulas. The model consisted of two sub-models: a micro-scale model and a macro model. The two sub-models were connected through sequential multi-scale coupling. The contours of the jet-bucket interaction and eroded mass are depicted in Figure 18. However, the calculation cost of this method is extremely high for it to be popularized.

Figure 18
figure 18

Contours of the jet-bucket interaction and eroded mass [112]

Zeng et al. [119, 120] conducted a numerical simulation of the silt erosion of the injector, explored the relationship between the particle size and erosion position, and predicted the erosion characteristics of the needle. The erosion positions, particle tracks, and streamlines for different particle sizes are shown in Figure 19.

Figure 19
figure 19

Erosion position of the needle under different particle sizes: a D=1 mm [119]; b particle tracks and streamline [120]

Messa et al. [121] conducted a numerical simulation study on the relationship between nozzle opening, needle tip angle, and sediment erosion. They observed that the nozzle seat and needle were the parts most easily eroded. The opening significantly impacts needle erosion, but has a slight effect on the nozzle seat. The erosion contours are shown in Figure 20. Figure 20a displays the contours of the nozzle seat following sediment erosion, while Figure 20b illustrates the contours of the needle after erosion. It is noteworthy that the nozzle seat exhibits a larger wear area and wear amount compared to the needle.

Figure 20
figure 20

Erosion contours of nozzle seat and needle when \({\gamma }_{n}\)=27.5, s/\({D}_{0}\)=0.459 [121]

Guo et al. [122] used numerical simulations to study the erosion mechanism of the injector in depth. They considered that the secondary flow induced by the shedding of the Carmen vortex enhanced the impact velocity and impact times of the particles and strengthened the separation trend of particles, which was the main reason for the surface erosion asymmetry. The attached and extended vortex structures are shown in Figure 21.

Figure 21
figure 21

Vortex structure: a SR= 0.4; b SR=0.46; c SR= 0.54 [122]

Ge et al. [123] used the Eulerian–Lagrangian method to calculate the gas–liquid–solid three-phase unstable flow and studied the influence of the velocity and nozzle opening on the torque and erosion rate. In addition, they compared the erosion patterns and external characteristics between numerical simulations and experiments to ensure reliability. Figure 22 shows the erosion pattern of the bucket at different times under certain working conditions.

Figure 22
figure 22

Erosion pattern of a bucket at different times

Guo et al. [124] proposed a new Eulerian–Lagrangian method and applied it for the first time to simulate the transient air–water–sediment flow in a Pelton bucket. They observed that the speed of particle separation depends largely on the curvature of the bucket, position of the particles, and speed of the water sheet. Figure 23 shows the particle flow patterns and water sheets at these instants.

Figure 23
figure 23

Particle flow patterns and water sheet colored by their absolute velocities respectively at instants: a 1.0 T, b 1.25 T

5.2 Geometric Model, Boundary Conditions, and Computing Method

The injector and runner are frequently calculated separately to reduce interference factors. The computational geometry model of the injector frequently has a cylindrical jet domain such that the jet can be better and fully developed [119,120,121,122,123,124,125]. The calculation model and boundary conditions are shown in Figure 24. A structural grid or a mixed grid is often used for mesh division.

Figure 24
figure 24

Calculation model and boundary conditions of the nozzle [122]

The impact of sediment particles on a runner was initially studied using a fixed bucket [108,109,110]. Subsequently, the calculation domain is the entire runner that is closer to the actual flow scenario. However, owing to the large number of cells, only three to five buckets are selected for numerical simulations. Some scholars use symmetric boundaries to model only half of the runner, which is not only closer to the actual scenario but also reduces the number of total cells [29, 126]. This type of symmetric modeling is more commonly used, and its calculation domain and boundary conditions are shown in Figure 25. Because of the complexity of the geometric boundary, an unstructured mesh is used. The number of cells ranges from hundreds of thousands to tens of millions according to the differences in geometric size and calculation conditions.

Figure 25
figure 25

Computational domain and boundary conditions: a Rotating part (red) and stationary part with six inlet regions (blue); b boundary conditions: walls—red, opening—yellow, symmetry—magenta, outlet—transparent blue, inlets are colored with the water volume fraction [126]

Table 3 summarizes the numerical simulation method for silt erosion of Pelton turbines. The Eulerian–Lagrangian method is commonly used to simulate the silt erosion of the Pelton turbine. Other methods, such as the FVPM, have also been used to calculate sediment erosion.

Table 3 Numerical simulation method on the silt erosion of Pelton turbines

5.3 Numerical Simulation Verification and Calculation Model

The verification of numerical simulation results is conducted generally through the following methods: comparison of simulation and experimental results (torque, output power, efficiency, erosion pattern), consistency analysis of the grid [130], verification of the calculation model, and comparison and analysis with reference data [113, 131, 132]. For example, Xiao [133] compared the efficiencies of experiments and numerical simulations, as shown in Figure 26. Sebastián [112] compared the prediction results with experimental values and analyzed the relative errors. Messa et al. [121] performed grid consistency analysis and two-step validation (results of reference and experimental data). To verify the accuracy and reliability of a numerical simulation, Guo et al. [122] performed the following: Based on the IEC 60193 standard, the flow rate was verified under different openings; the efficiencies of the numerical simulation and experiment were compared; the erosion patterns were compared. Figure 27 depicts the experimental validation of the erosion model. The erosion model that was compared with the numerical simulation was the Mansouri model. In an experiment, Vieira et al. [134] observed that the Mansouri model is better than the Oka, Zhang, Det Norske Veritas (DNV), and Neilson–Gilchrist models in predicting sediment erosion of bends, and it is more suitable for predicting Pelton turbine injectors.

Figure 26
figure 26

Verification of numerical simulations and experimental results verification [133]

Figure 27
figure 27

Erosion rates comparisons along the axial direction of a pipe wall [122]

In the numerical simulation of sediment abrasion, the main calculation models used are the multiphase flow, turbulence, particle tracking, and erosion models. The latest applications of several models are discussed below.

5.3.1 Multiphase Model

A multiphase flow model is required when the Eulerian method is used for the calculation. In ANSYS Fluent, ANSYS CFX, STAR CCM+, and OpenFOAM, based on the Eulerian method, the VOF and homogeneous multiphase models are commonly used to study Pelton turbines. The model agrees well with experimental results [135]. When the Lagrangian method is used for calculation, the multiphase flow model is not required because it simulates the flow by tracking the trajectories of particles and flow [136,137,138].

5.3.2 Turbulence Model

Three-dimensional turbulence calculations can accurately predict the actual flow of fluids [139,140,141,142]. In earlier research, the standard kω turbulence model was the most widely used for the Pelton turbine, and the RNG kω model was also used [143,144,145,146,147,148]. In recent years, scholars have recognized the SST kω turbulence model and widely use it to calculate high-speed turbulence for a rotating bucket. The SST kω turbulence model increases the influence of turbulent shear stress and has higher accuracy and credibility in the simulation of rotational shear flow at high Reynolds numbers [29, 133, 149]. Sammartano et al. [96, 150] compared the accuracy of different turbulence models in a numerical simulation of the Pelton turbine. They observed that the calculation results of the SST model were closest to the experimental values. Currently, the SST kω turbulence model is the most widely recognized in the Pelton turbine [151].

5.3.3 Particle Tracking Model

Owing to the sparsity of particles in sediment-laden flow, the volume fraction does not exceed 10%. The collisions between the particles are not violent and can be ignored. Therefore, the Lagrangian particle tracking model or discrete particle model (DPM) is typically used to calculate sediment particles in the flow. In the particle tracking model, inertia, drag, and gravity are the main factors considered [121, 152].

5.3.4 Erosion Model

Erosion models are often used to calculate the erosion of solid walls by particles. Different CFD codes include different erosion models. For example, the erosion models in STAR CCM+ include the Ahlert, DNV, Neilson–Gilchrist, and Oka models. The erosion models in the Fluent code are the Finnie, McLaury, Oka, and generic models. The Finnie, Tabakoff, and Grant models are included in the CFX code. Other scholars have continually optimized the original model and developed new ones [153,154,155,156]. The equations for the erosion models are described as follows.

Mansouri model [134]:

$$ER = KF_{S} V_{P}^{2.41} F(\theta ),$$
$$F(\theta ) = \frac{1}{f}(\sin \theta )^{{n_{1} }} \left( {1 + HV^{{n_{3} }} (1 - \sin \theta )} \right)^{{n_{2} }} ,$$
$$K = C(BH)^{ - 0.59} ,$$
$$BH = \frac{HV + 0.1023}{{0.0108}},$$

where \(ER\) is the erosion equation;\(F_{S}\) is the sharpness factor; \(F(\theta )\) is the angle function. For SS316 (HV=1.83 GPa, BH=178.9) and 300 μm sand, the values of \(C\) and \(K\) are 4.62×10–7 and 2.16×10–8, respectively.

Oka model [153]:

$$ER = ER_{90} g(\theta ),$$
$$ER_{90} = K_{P} \left( {H_{V} } \right)^{{k_{1} }} \left( {V_{P} } \right)^{{k_{2} }} \left( {d_{P} } \right)^{{k_{3} }} ,$$
$$g(\theta ) = (\sin \theta )^{{n_{1} }} \left( {1 + H_{V} (1 - \sin \theta )} \right)^{{n_{2} }} ,$$

where \(k_{1}\) and \(k_{3}\) are empirical exponent factors; \(k_{2}\) is a function of the material hardness and particle properties; \(K_{P}\) is an independent factor that denotes particle properties, such as shape and hardness; \(H_{V}\) is the Vickers hardness.

Zhang model:

$$ER = 2.17 \times 10^{ - 7} (BH)^{ - 0.59} F_{S} V_{P}^{2.41} F(\theta ),$$
$$F(\theta ) = 5.4\theta - 10.11\theta^{2} + 10.93\theta^{3} - 6.33\theta^{4} + 1.42\theta^{5} ,$$

where θ is the particle incidence angle; \(BH\) is the Brinell hardness of the eroded material; \(F_{S}\) is the sharpness factor.

DNV model [80]:

$$\left\{ {\begin{array}{*{20}l} {ER = \dot{m}_{P} K_{N} V_{P}^{{n_{N} }} F(\theta ),} \hfill \\ {f(\theta ) = \sum\limits_{i - 1}^{8} {( - 1)^{i + 1} } A_{i} \left( {\frac{{\theta\uppi }}{180}} \right)^{i} ,} \hfill \\ \end{array} } \right.$$

where \(\dot{m}_{P}\) is the mass rate of solid particles; \(K_{N}\) and \(n_{N}\) are the material constants (\(K_{N}\) = 2.0 × 10–9, \(n_{N}\) = 2.6 for steels); \(A_{i}\) is a model constant.

Neilson–Gilchrist model [157]:

$$ER = ER_{{\text{C}}} + ER_{{\text{D}}} ,$$
$$ER_{{\text{C}}} = \left\{ {\begin{array}{*{20}l} {\frac{{V_{{\text{P}}}^{2} \cos^{2} \theta \sin \frac{n\theta }{{2\theta_{0} }}}}{{2e_{{\text{C}}} }},} \hfill & {\theta < \theta_{0} ,} \hfill \\ {\frac{{V_{{\text{P}}}^{2} \cos^{2} \theta }}{{2\varepsilon_{{\text{C}}} }},} \hfill & {\theta < \theta_{0} ,} \hfill \\ \end{array} } \right.$$
$$ER_{{\text{D}}} = \frac{{\max \left( {V_{{\text{P}}} \sin \theta - K_{D} ,0} \right)^{2} }}{{2\varepsilon_{{\text{D}}} }},$$

where \(ER_{{\text{C}}}\) and \(ER_{{\text{D}}}\) are the contributions of cutting and deformation, respectively; \(\theta_{0}\) is the transition angle, normally set as 45°; \(\varepsilon_{{\text{C}}}\) is the cutting coefficient, 3.332 × 107\(\varepsilon_{{\text{D}}}\) is the deformation coefficient, 7.742 × 107\(K_{D}\) is the cutoff velocity.

All models consider the particle’s reflection on the geometric walls, which depends on the properties of the particles and the surface of the solid. Therefore, erosion models are empirical or semi-empirical formulas based on numerous experiments [153, 154, 158]. The Finnie model is the most widely used model, but it often results in the over-prediction of erosion [128, 159]. Messa et al. [160, 161] studied the influence of different erosion models and parameters on the erosion rate. They observed that erosion results were highly dependent on these empirical or semi-empirical erosion models.

5.4 Summary

From a development perspective, this section comprehensively introduces numerical simulation methods, geometric model structures, boundary conditions, and calculation methods.

In the numerical simulation of the sediment erosion of the Pelton turbine, many simplifications are required; therefore, some uncertainties exist [8]. The accuracy of erosion prediction is based on the following two points: the erosion position, which can be obtained by comparing it with the eroded parts. The other is the erosion rate, which challenges the existing technology [112].

The accuracy of numerical simulations encounters significant challenges because many values are assumed under ideal conditions. Not all processes of sediment erosion can be realized using CFD, such as coating erosion, shear deformation of the substrate material after coating removal, and secondary cavitation caused by erosion [17]. In addition, secondary flow is difficult to simulate, and the problems of turbulence and inaccurate boundary conditions are difficult to avoid [38]. Accurate modeling of centrifugal and Coriolis forces is also a problem in CFD [162]. Finally, owing to the unsteady characteristics of the calculation, the calculation ability requirement is higher. All these factors result in inaccuracies in the simulation results. The cavitation phenomenon of Pelton turbines using CFD has been studied, but only a few studies have been conducted on the combined erosion of cavitation and sediment [90, 126, 163].

In addition to those mentioned above, the numerical simulation results depend on the erosion model used. Currently, no complete or standard erosion model is available [128].

Therefore, studying a general and valuable erosion model will be crucial and challenging in the future. In addition, obtaining a similarity between a model and an actual unit with respect to sediment erosion conditions is difficult. Therefore, dynamic similarity criteria and formulas should be established in the future [112].

6 Protection Measures for Sediment Erosion

6.1 Anti-Erosion Design

Anti-erosion design primarily includes the design of hydraulic structures and hydraulic turbines. The main direction of the optimization design of hydraulic structures is to reduce the sediment concentration of the flow through the turbine [164]. Several designs of hydraulic structures are introduced as follows.

  1. a.

    Sediment trapping systems

    As early as 1911, Dufour applied a sediment trapping system to a reaction turbine power station [17]. In 1919, sand traps were used at an impact turbine power station, and the effect proved useful [17]. For example, after applying the desilting basin in a CCS power station, the actual effect was satisfactory [165]. Sand trapping was also built to solve the problem of excessive sediment at the Chilime Power Station. However, during flooding, its role is minimal [50], and its control effect on fine silt is poor [166].

  2. b.

    Installation can include additional low-head weirs in the entire tributary upstream of power stations [49].

  3. c.

    The layout of the hydro project should be planned reasonably, and the unit should be arranged at a position conducive to reducing sediment passing through the turbine [22].

  4. d.

    Increase the sediment settling effect of the reservoir and design a multi-stage sediment reduction and desilting design system [165, 167].

    The structural design of Pelton turbines is the most important because the most easily eroded parts determine the maintenance period [10]. The primary method to optimize the structural design is to reduce the velocity and optimize the impact angle [10]. The ultimate goal of the design optimization is to achieve minimum erosion and maximum efficiency [168]. The selection of the design parameters of Pelton turbines in a high-sediment-laden river can be based on the following standards:

  5. e.

    Low-velocity inlet design [15]. \(S_{W}\)(silt concentration)<5 kg/m3\(U_{2}\) or \(W_{2}\)<38‒40 m/s; \(S_{W}\)(silt concentration)<12 kg/m3, \(U_{2}\) or \(W_{2}\)<34 m/s [169] (The velocity is related to the material of the flow passage parts).

  6. f.

    When the nozzle outlet velocity is large (≥ 150 m/s), the contact surface between the nozzle and needle in the closed position should be as small as possible (≤ 1 mm) [15]. The nozzle tip should be as sharp as possible [49].

  7. g.

    In the design, the separation angle between the particles and the streamline should be reduced [84].

  8. h.

    The bucket curvature, hydraulic radius, and nozzle hydraulic radius should be increased [170].

6.2 Wear-Resistant Materials, Manufacturing Technology, and Other Protection Measures

Fatigue failure and fracture of the Pelton turbine runner caused by wear severely affects the safe operation of the power station. The anti-abrasion design can effectively reduce the sediment concentration of the flow through the turbine; however, its effect is limited. Here, the reasonable selection of anti-resistant materials and manufacturing technology will significantly affect the protection.

6.2.1 Runner Materials

The early runner material was generally cast iron [17]. In 1934, the advantages of stainless steel were demonstrated [171]. After continuous exploration and development, 13Cr4Ni has become a standard material for turbine parts [73]. Hardness, toughness, and elasticity are essential indices for evaluating the wear resistance of materials [172]. Traditional cast stainless steel (SCSI, SCS5, and SCSI3), high-nickel, high-manganese chromium stainless steel (NMC and NMW), and high-carbon steel (DFME) exhibit good wear resistance [15]. In recent years, forged stainless steel has been proven to have excellent properties, particularly integrally forged stainless steel, which has almost no casting defects and strong fatigue resistance [173, 174]. Increasing surface hardening is also a more effective method of addressing wear [88]. However, the specific material selection should comprehensively consider the wear strength, environmental temperature, corrosion, impact load, static load, total cost, service life, functional requirements, available manufacturing equipment, and other factors [175,176,177,178].

6.2.2 Hard Coating

After 1980, researchers began to realize the role of coatings in resisting substrate erosion. The actual operation of a power plant has shown that the coating can effectively reduce the erosion rate [10, 54, 179]. Coatings are generally divided into three types: hard, elastomer, and composite [180]. Common coating and process methods include WC series cermet coating and high-velocity oxyfuel spraying (HVOF) [10, 17, 181, 182]. In addition, nano-coating [183], plasma spraying, rubber coating [15], boronizing coating [128], tungsten carbide coating [174], stainless steel coating [184] and non-metallic coating [185, 186] have strong wear resistance. In the selection of the coating type, the combination of coating and surface material, the performance of the coating, and the coating method should be considered comprehensively because they jointly determine the corrosion resistance of the coating [187].

6.2.3 Manufacturing Technology

Good manufacturing technology can avoid damage to runners to the greatest extent. The leading manufacturing technologies of hydraulic turbines include investment casting, sand casting, numerical control (NC) machining, and forging. Currently, most hydraulic turbine manufacturers worldwide use NC machining technology to manufacture hydraulic turbines [188, 189]. The companies Voith (Germany), ABB (Switzerland), VA (Austria), and ALSTOM (France) have mastered the advanced manufacturing technology of Pelton turbines [190]. The typical manufacturing technologies for Pelton turbines are integral casting [191, 192], MicroGussTM, and complete forging [193]. The structural optimization design of the Pelton turbine high-stress zone, casting process simulation, and deep cooperation between the manufacturing industry and academia will contribute to further improvements in manufacturing technology [188, 194].

6.2.4 Control of Operation Process and Maintenance

Based on anti-erosion design and wear-resistant material selection, regular maintenance and repair are necessary. Such a non-destructive test (DNT), which includes the dye penetration test (DPT) and magnetic particle test (MPT), has been used to detect the flow channel [195, 196]. Some operation control measures are frequently implemented to protect unit safety during a high sediment period, for example, an outage in the high sediment period [197]; in the monsoon season, the flow is reduced by diversion [49].

The methods mentioned above require the installation of real-time monitoring devices in a power station. The monitoring system evaluates the sediment condition, and then determines the operating strategy of the power station.

6.3 Summary

This section introduces the general protection measures for sediment erosion in detail, including the power station layout, hydraulic structure design, manufacturing technology, anti-wear materials, and maintenance. The structural optimization of the flow passage components and an in-depth study of anti-wear materials are still critical challenges for the future. Cooperation between the manufacturing industry and academic community can also further improve anti-wear technology.

Erosion prediction and fault diagnosis technologies are useful for structural optimization design, material selection, operation range selection, and repair work (see Section 7).

7 Monitoring and Prediction Technology of Sediment Erosion

The water conditions of the river can be obtained from hydrological observation data collected over many years. Before installing the unit, the erosion of the buckets can be estimated, and the positions accessible to erosion should be protected in the material selection and design stage. In addition, reliable and systematic monitoring of turbine erosion and efficiency, and a complete record of maintenance and associated costs can optimize the operation of hydropower stations in terms of profitability and generation capacity [197]. Therefore, a sediment monitoring system, erosion measurement, and prediction technology are essential.

Figure 28 shows a typical structural diagram of a power station monitoring system [198], which primarily includes monitoring of suspended sediment, inspection of bucket erosion, and monitoring of external characteristics of hydraulic turbines.

Figure 28
figure 28

Schematic of a hydropower station research project [194]

This section introduces the erosion detection technology for Pelton turbines, sediment characteristic measurement technology, and fault diagnosis technology. Advanced monitoring technology can ensure the benefits of hydropower stations, extend the service life of flow passage components, and provide better maintenance and scheduling [199].

7.1 Erosion Detection Technology of Buckets

In the laboratory, erosion loss is primarily expressed by mass loss, thickness changes, and surface roughness changes [166]. Generally, the size of the tested part is small; therefore, it is easy to measure [62]. Probes, thickness gauges, and mechanical calipers are commonly used as the traditional measuring instruments. However, traditional measuring instruments have difficulties measuring small erosion thickness changes. Recently, new measurement methods have been proposed. The following are several methods for measuring erosion.

7.1.1 3D-scanner

A three-dimensional (3D) scanner is often used to quantify the erosion of the bucket surface, which is primarily composed of an LED and cameras [62]. A 3D scanner is the most advantageous of all surface detection technologies because it can measure the erosion depth, blade profile, and material loss [62]. During the monitoring, some reference points will be made on the surface to better observe the change in the blade surface after erosion. The advantage of this method is that it can accurately monitor surface erosion; however, the scanning time is excessively long [8].

Parray [49] used 3D scanning technology to evaluate the erosion of the needle (Figure 29a) and nozzle seat (Figure 29b) of a power station operating for 2712 h. The accuracy of the 3D scanner was 10 μm and the scanning range was 500 mm. According to this assessment, the nozzle and needle erosion rates were 3.71% and 5%, respectively. The surface of the needle and nozzle seat after sediment erosion can be clearly observed in Figure 29a and b, respectively, using 3D scanning. The results show the presence of scratches and pits on the surface of both components. Morales [200] conducted a 3D scanning of the bucket surface, the results of which are shown in Figure 30.

Figure 29
figure 29

Nozzle seat and needle after erosion [49]

Figure 30
figure 30

Surfaces of the bucket: a Before erosion; b after erosion [200]

7.1.2 Imaging and Video Techniques

The advantages of imaging and video techniques are that large-scale disassembly is not required, the detection time is short, and the images can be compared offline [54, 62], such as through visualization technology and digital image processing. Visualization technology is a simple and effective tool for testing models. It can be used to analyze the interaction between the water flow and runner [201, 202], and it can also be used to diagnose the noise of prototype units [203]. It has been applied at Moccasin and other power plants [204]. Digital image processing technology is often combined with MATLAB to measure the final erosion profile of the buckets. Shrestha [166] used this technology to study Pelton turbines. The runner was operated continuously for 72 h in a sediment-laden flow, and the bucket profile was repeatedly measured ten times. The results showed that this method can accurately and quantitatively detect the erosion of sharp edges.

7.1.3 Template Inspection

The IEC recommends using a template to measure the erosion thickness of uncoated buckets [73]. This method can effectively detect changes in the shape of the bucket, as shown in Figure 31. However, quantifying the erosion of each part of the bucket is impossible, particularly the cutout position [62].

Figure 31
figure 31

Check the shape of the bucket after maintenance using a template [191]

7.1.4 Thickness Gauge Based on Magnetic Induction

Thickness gauges are often used in conjunction with 3D scanning to quantify the erosion. The variation in the erosion depth of the bucket after 3180 h of operation of a 10 MW hydropower station in India is shown in Figure 32 [205]. Three years of measurement at the Fieschertal power station was used to analyze the erosion of buckets with a hard coating. The profile changes at the splitter and cutout and thickness changes in the bucket coating are shown in Figure 33 [54, 197, 198].

Figure 32
figure 32

Variation in sediment erosion depth on the front and back of the bucket [205]

Figure 33
figure 33

Profile change and coating thickness change of buckets [54, 197, 198]

7.2 Measurement Technology of Sediment Characteristic Parameters and Fault Diagnosis Technology

Erosion results are affected by the concentration, size, shape, and mineral composition of the sediment. In the monsoon season, the sediment concentration and particle size distribution in the river frequently vary significantly. Hence, the power station must track the changes in suspended sediment concentration (SSC) and particle size distribution (PSD) over time. However, the particle shape and mineral composition of the sediment do not change in a short period, which does not require real-time monitoring. Gravity analysis, vibrating tube density, turbidity, acoustic attenuation, laser diffraction, and acoustic backscatter are commonly used to measure the SSC and PSD [62, 206,207,208,209]. SSC and PSD measurements are introduced below.

7.2.1 SSC Measurement

The traditional measurement method for SSC is to collect samples and conduct laboratory analyses [210]. However, when extreme weather, such as a rainstorm, occurs, many samples are often required, and the cost is very high [211,212,213]. In recent years, continuous measurement technology (CMT) based on turbidity, acoustics, lasers, and pressure differences has attracted increasing interest [208]. The combined application of measurement and CMT technology based on spectral reflection and image capture is a future development trend [208, 214, 215]. Although CMT has many apparent advantages over traditional measurement methods, it is affected by calibration, reliability standards, and microbial fouling. In future development, more research should be conducted to improve measurement accuracy, scope, and applicability. Further analysis of the relationship between sediment concentration and turbidity can be used to effectively detect water quality at the inlet [216, 217].

7.2.2 Measurement of PSD

The commonly used measurement methods for PSD are dynamic imaging (Camsizer) and laser diffraction (LISST) [49]. Some technical equipment, such as a multi-frequency acoustic instrument for monitoring, has been applied at the Toss power station, which can continuously monitor the SSC and PSD [114, 205]. Figure 34 compares the SSC and PSD measurement results of different methods [218].

Figure 34
figure 34

Comparison of the SSC and PSD measurement results of different methods: a Particle sizes obtained from LISST; b SSCs from six techniques, measured in the valve chamber of Fieschertal HPP [218]

7.2.3 Fault Diagnosis Technology of Condition Monitoring

There are three main types of damage: fatigue, sediment erosion, and cavitation [219]. Through monitoring and diagnosis, symptoms can be observed in the early stages of damage to reasonably plan the maintenance cycle or estimate unit life. Some scholars have studied this problem in recent years, but only a few references are available [220, 221]. The general monitoring and diagnosis technology method monitors the vibration, analyzes the vibration spectrum, and then determines the damage type and position by comparing it with the database. However, the Pelton turbine lacks historical cases and databases, and its applications are limited. Egusquiza et al. [173] collected the operation data of 28 Pelton turbines over 25 years, analyzed the database, and extracted different damage types. Åsnes [222] collected data from 27 power stations and used three methods to diagnose the Pelton turbines.

8 Conclusion and Prospects

The sediment carried by a high-head flow has high kinetic energy, severely damaging the flow passage parts of Pelton turbines. As plant manufacturers and scholars gain more interest the benefits, safety, and stability of hydropower station operations, many countries spend significantly to solve the problem of hydro-abrasive sediment erosion. With the development in recent years, engineering design and sediment reduction measures have become increasingly mature, and sediment concentration has been dramatically reduced. Experiments and case analyses have revealed the relationship between silt and unit erosion and external characteristics, and many erosion models have been established. However, owing to the complexity of flow, the influence of specific erosion parameters remains difficult to distinguish. Experimental research also has some limitations in solving this problem, such as excessively long erosion observation periods and limited experimental conditions.

With improvements in computing power and technology development, CFD has received increasing interest as a research method. CFD can model the Pelton turbine successfully, simulate the flow pattern of sediment-laden flow in the operation process, and be used to study a three-dimensional unsteady erosion on nozzles, needles, and runners. However, CFD has limitation, such as erosion prediction, over-reliance on empirical or semi-empirical formulas, and a lack of calculation of secondary flow and secondary cavitation. The development of a complete and valuable syndication erosion model, establishment of dynamic similarity criteria and similarity formulas, improvement of computational capability, and optimization of the calculation method are the development directions of CFD in the future.

The casting process and material selection are the key factors that determine the performance of a runner. In recent years, rapid progress has been achieved in technology that has significantly improved the erosion resistance of runners. In the future, an in-depth study of anti-erosion materials will be essential for technological development. Therefore, a better combination of science and engineering is required for the research and development, optimization, design, and manufacturing of hydraulic machinery. In addition, advanced monitoring technology can ensure the benefits of the power station, extend the service life of the flow passage components, and provide better maintenance scheduling. This paper discusses the development and latest progress in research on sediment erosion, which provides some references for technical researchers in related fields.

Data availability

The data used to support the findings of this study are included within the article.



Computational fluid dynamics


Smoothed particle hydrodynamics


Moving particle semi-implicit


Fast Lagrangian solver


Finite volume particle method


Hydro Power Plant


Suspended sediment concentration


Non-destructive test


Magnetic particle test


Arbitrary Lagrangian–Eulerian


High-velocity oxyfuel spraying


Suspended sediment concentration


Particle size distribution


Continuous measurement technologies

NC machining:

Numerical Control Machining


Particle size distribution


Dye penetration test


Volume of fluid


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We would like to thank those who have supported us along the way. Our team has set up a small Pelton turbine laboratory, in the process of the laboratory construction, we especially thank professor Li Zhihua, lab technician Liu Changhui, minister Qian Chaoyang and professor Wang Bing of Hohai University for their supports, which had solved the problem of project establishment and location of the laboratory.


Supported by National Natural Science Foundation of China (Grant No. 52279083).

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Authors and Affiliations



JS wrote the original draft; XG and JL assisted with manuscript review and editing; HC, KK, HZ, YZ, LZ, and DC conducted data collection; YZ and MB is responsible for supervision. All authors read and approved the final manuscript.

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Xinfeng Ge, born in 1981, is currently a lecturer at College of Energy and Electrical Engineering, Hohai University, China. He received his PhD degree from China Institute of Water Resources and Hydropower Research, China, in 2011. His research interests include fluid machinery multiphase flow and large equipment fault diagnosis. E-mail:

Jie Sun, born in 1995, is currently a PhD candidate at College of Water Conservancy and Hydropower Engineering, Hohai University, China. E-mail:

Dongdong Chu, is currently a research fellow at Jiangsu Water Conservancy Research Institute, China. E-mail:

Juan Liu, is currently a research fellow at China Institute of Water Resources and Hydropower Research, China. E-mail:

Ye Zhou, is currently a research fellow at China Institute of Water Resources and Hydropower Research, China. E-mail:

Hui Zhang, is currently an engineer at Chongqing Shipping Construction Development Co., Ltd., China.

Lei Zhang, is currently an engineer at Yellow River Institute of Hydraulic Research, China.

Huixiang Chen, born in 1989, is currently an associate professor at College of Agricultural Science and Engineering, Hohai University, China. E-mail:

Kan Kan, born in 1990, is currently an associate professor at College of Energy and Electrical Engineering, Hohai University, China. E-mail:

Maxime Binama, is currently a post-doctoral at College of Water Conservancy and Hydropower Engineering, Hohai University, China. E-mail:

Yuan Zheng, born in 1964, is currently a professor at College of Energy and Electrical Engineering, Hohai University, China. E-mail:

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Correspondence to Xinfeng Ge.

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Ge, X., Sun, J., Chu, D. et al. Sediment Erosion on Pelton Turbines: A Review. Chin. J. Mech. Eng. 36, 64 (2023).

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  • Pelton turbine
  • Sediment erosion
  • Sediment erosion mechanism
  • CFD
  • The experimental method