Renewable Energy 207 (2023) 40–46
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Renewable Energy
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Design and verification of Francis turbine working in sand laden
hydro-power plant☆
Jing Yang a, Chong Peng b, Changquan Li b, Xinjun Liu b, Jian Liu c, Zhengwei Wang c, *
a
Institute of Science and Technology, China Three Gorges Corporation, Beijing, 100038, China
Xinjiang Xinhua Muzhati Hydropower Company Ltd., Xinjiang, Akesu, 842399, China
c
Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China
b
A R T I C L E I N F O
A B S T R A C T
Keywords:
Rotational speed
Splitter runner
Sand erosion
Francis turbine
Sand erosion is usually severe for hydraulic turbine operated in sediment-laden river hydro-power plant.
Continuous erosion and abrasion in hydro-turbine components not only deteriorate the turbine performance but
also bring frequent maintenance work. Thus, special attentions should be paid to anti-erosion performance be­
sides the efficiency and stability during the hydraulic design stage. In this paper, the performances of a prototype
Francis turbine used for a high head heavy sediment power station were investigated by reducing the rotational
speed and using splitter runner. The hydraulic performance, anti-erosion characteristics and cavitation perfor­
mance were focused and analyzed. The results proved that the velocity in the runner can be effectively reduced
by lower the rotational speed, but the rotational speed reduction was also limited by the efficiency and velocity
near the guide vane. The splitter runner can significantly improve the disorder flow in runner by re-distributing
the velocity field. The erosion resistance of guide vane can be improved by increasing the pitch diameter of the
guide vane appropriately. 3100 h of operation after commissioning further confirmed the anti-erosion and sta­
bility performance of the designed Francis turbine. This research provide a good reference for the Francis turbine
design operated in heavy sediment hydro-power plant.
1. Introduction
For the hydro-power plant operating in sandy river, severe sediment
erosion always occurs on the surface of the turbine while water flowing
through it. Abrasion and erosion in turbine components will not only
shorten the unit maintenance period and operating life, but also cause
serious hydraulic turbine performance degradation [1].
There are many factors affecting the hydraulic turbine abrasion,
mainly including the relative velocity, sand content in river, the struc­
ture materials, the operating conditions of turbine and so on [2]. Many
researchers believed that it was a high order and nonlinear relationship
between the relative velocity and abrasion [3]. Therefore, the relative
velocity can be seen as an indication of erosion intensity in erosion
damage zone. Controlling the relative velocity through the turbine was
the primary measure that need to be taken in the design stage. Because
of the higher relative velocity in Francis turbine runner, China national
standard⟪Technique guide for dealing with sand abrasive erosion in
reaction hydraulic turbine⟫(GB/T 29403–2012) suggests the relative
velocity of blade trailing edge should less than 40 m/s. Acharya et al. [4]
tried to alleviate the erosion in runner by changing the blade angle,
Khanal et al. [5] proposed to change the blade profile curvature per­
centage and blade outlet angle to minimize the sediment erosion, both of
them obtained a satisfactory result.
For high head Francis turbine, the guide vane is another component
that more prone to wear [6] due to the leakage vortex flow from end
clearance gap and higher relative velocity flow [7]. Zhang et al. [8] put
forward to some suggestions to optimize the runner and guide vane by
their profiles and dimensions to improve sediment erosion. Chitrakar
et al. [9] studied on the flow through the clearance gap of the guide vane
by PIV measurements, the results showed the guide vane shape affects
the pressure and velocity field, the improper flow angle could have
disadvantage effects on the runner flow field. Brekke et al. [10] also
believed that the secondary flow and leakage flow from the guide vane
will eventually pass through the runner inlet causing damages. Thapa
et al. [11] and Koirala et al. [7,12] investigated the guide vane erosion in
a Francis turbine, they found that erosion were observed at the upper
Project supported by the National Natural Science Foundation of China (Grant No. 51876099).
* Corresponding author.
E-mail addresses: yangjingshirley@163.com (J. Yang), wzw@mail.tsinghua.edu.cn (Z. Wang).
☆
https://doi.org/10.1016/j.renene.2023.02.088
Received 15 August 2022; Received in revised form 30 January 2023; Accepted 17 February 2023
Available online 24 February 2023
0960-1481/© 2023 Elsevier Ltd. All rights reserved.
J. Yang et al.
Renewable Energy 207 (2023) 40–46
and lower ends, leading and trailing edge and surfaces of the guide vane,
the small clearance gap size had less effects on the leakage flow and
recommended to use non-symmetric guide vane, which can reduce the
erosion damage.
Neopane et al. [13] believed that re-distributing the velocity field by
changing the blade shape may bring efficiency drops. The trade-off be­
tween hydraulic performance and anti-erosion performance should be
focused for hydro-turbine operating on sediment-laden river. They tried
to use the variable speed turbines to improve anti-erosion performance,
the results proved the improvement for both of the efficiency and
sediment erosion. But the cost of variable speed unit will be greatly
increased [6]. Both Lama et al. [1] and Aponete et al. [14] proposed a
multi-objective optimization technique by utilizing CFD, which simul­
taneously considered the erosion, cavitation and efficiency of turbine as
the optimization parameters, the new turbine can largely reduce the
wear rate and keep higher efficiency.
Because of the unique parameters of each power station, the runner
and guide vane shape optimization of one power station is not neces­
sarily effective for other power stations. The anti-wear design methods
and more quantification studied to minimize erosion of Francis turbine
still needed. For hydraulic turbine operating in this scenario, conven­
tional hydraulic design method considered to reduce the unit rotational
speed by one or two stages to alleviate the runner abrasion [15]. Since
the complex flow under off-design conditions of Francis turbine may
obviously increase runner erosion, the splitter runner had been tried to
use in many low specific speed power station like Lubge power station in
China to achieve a smooth flow in the runner flow field. Splitter runner
was initially used to reduce blade channel vortexes [16] and improve
unit stability as the cavitation performance, pressure pulsation and
structure stress [17].
In this paper, a low specific speed Francis turbine operated in sandy
river power plant was studied by simulation. In order to simultaneously
meet the requirements of reducing the relative velocity in the easy wear
components and improving the operation stability of the unit, the
effectiveness of downshift rotational speed, splitter runner and guide
vane optimization were analyzed. The performance indicators erosion
resistance, efficiency, cavitation and stability were fully considered
during the hydraulic optimization design stage. After 3100 h of opera­
tion on site showed that the abrasion extent in runner and guide vane
were much better than the other power station in this district. This paper
can provide a valuable reference for improving the anti-erosion per­
formance and stability of turbine operating in sandy river.
Fig. 1. Power station upstream flow.
Table 1
Main design parameters of the study hydro-turbine.
Parameters
Value
Parameters
Value
Maximum head
Minimum head
Rated head
Weighted average head
308.1 m
278.35 m
279 m
286.86m
Output
Discharge
Suction head
Design output range
10.5 MW
4.2 m3/s
− 8.5 m
45％～100％
3. Numerical method
With the development of computational fluid dynamics, numerical
simulations have been widely used in hydraulic turbine design. This
paper also used ANSYS-CFX software for flow analysis in hydraulic
design. The flow governing equations are shown in equations (1) and (2)
as follows:
( )
∂ →
u i =0
(1)
∂xi
[
(
)
∂ui ∂ (
∂p
∂ (μ + μt ) ∂ui ∂uj
ui uj = −
+
+
+
∂t ∂xj
ρ∂xi ∂xj
ρ
∂xj ∂xi
)]
+ fi
(2)
Here, ρ is the water density, u is the velocity, p is the pressure, μ and μt
represent the laminar and turbulent viscosity. Subscript i and j represent
the coordinate directions.
The SST k − ω turbulence model was chosen for the simulations in
this paper. The SIMPLEC algorithm was used to discrete the timedependent equations. The second-order upwind scheme was used for
the convection terms and the central difference scheme for the diffusion
terms in the momentum and the transport equations. The total pressure
inlet boundary condition was set at the spiral casing inlet and the outlet
boundary condition was set to be static pressure. Single-phase calcula­
tions were used for energy and velocity field analysis in the early stage
and two phase flow were used for cavitation flow. The internal relative
velocity was chosen as erosion identification and the pressure pulsation
as the stability identification. A time step of Δt = 0.00028 s, which is the
1/360 of one runner rotation cycle, was found to give the most
reasonable results with relatively short calculation times in unsteady
analysis.
The calculated flow passage used in this paper was from spiral casing
inlet to draft tube outlet, as shown in Fig. 2. Unstructured tetrahedral
2. Power station parameters and design requirement
The analyzed hydro-power station Muzhati is located in Aksu City,
Xinjiang Uygur Autonomous Region. Most of the hydro-power plants
operating in this river were affected by severe sediment erosion [8]. In
order to adapt to the great changes of river incoming flow in different
seasons, two large hydraulic turbines with the capacity of 70,000 kW
and two small hydro-turbines with the capacity of 10,000 kW were
installed in this power plant. In general, the influence of sediment wear
on turbine should be considered when the average particle size of
sediment is over 0.050 mm and the average sediment content passing
through the turbine is over 0.200–0.400 kg/m3 [6]. However, in this
river, 3.45 kg/m3 annual average sediment concentration was reported,
and the maximum sediment concentration in actual operation is even
more than 28 kg/m3 during the flood season [18]. Besides, a high pro­
portions of quartz sand and feldspar were reported.
Fig. 1 shows the upstream flow in this power station. It is obviously
that the turbines operated in this river will undergo severe components
abrasion due to excessive and hard sediment particles. Thus, investiga­
tion was carried on the small hydro-turbine to improve the anti-erosion
performance. The main specifications of the studied hydro-turbine are
presented in Table 1.
Fig. 2. Calculation flow passage domain and mesh.
41
J. Yang et al.
Renewable Energy 207 (2023) 40–46
grid was used for spiral casing, runner and draft tube, and structured
hexahedron grid for stay vane and guide vane. Besides, the runner and
guide vane were partially encrypted. After grid independence verifica­
tion shown, a total number of 3.439 million grid cells were finally
adopted.
Table 2
Hydraulic performance parameters of turbine using different rated speed.
4. Calculated results and discussion
In order to reasonably determine the unit rotational speed, the rated
speed of similar head Francis turbine operating in sandy river power
stations of China were investigated, including Yuzixi power station
(rated head 270m), Yaoheba power station (rated head 280m) and
Nanyahe III power station (rated head 265m), the results were shown in
√̅̅̅̅̅̅̅̅̅ 5
Fig. 3 (left) below. Here, specific speed ns = n P/H 4 , n is the rota­
tional speed, P is the output, H is the rated head. According to the
traditional design method, the recommended unit rotational speed
should be 1000r/min, see Muzhati-1000. However, it had been found in
the Yuzixi power stations that the unit wear was very serious (see Fig. 3
right). Besides, the average sediment content in Yuzixi was less than the
Muzhati power station studied in this paper. Obviously, it was unrea­
sonable to adopt the 1000r/min for Muzhati river power station. In
order to improve the anti-wear characteristics of the hydro-turbine,
reducing the rotational speed was necessary.
As stated in previously studies, erosion was mainly observed near the
outlet of runner and guide vane for all cases, where the relative velocity
is higher [14]. To speed up the analysis time, the relative velocity was
chosen as the discriminant factor of sediment wear extent for the next
analysis. To study the effects of different rotational speeds, the efficiency
and maximum velocity in the runner and guide vane were analyzed
using an initial hydro-turbine flow passage, the results were shown in
Table 2. As can be seen from it, the lower rotational speed can directly
reduce the relative velocity in the runner, which can effectively improve
the wear extent of the runner. However, the velocity near the tailing
edge of the guide vane increased with the decrease of the speed, see
Fig. 4. Besides, the hydraulic efficiency decreased obviously with the
decrease of speed. That is to say, the speed downshift was limited by the
energy performance of the unit on the one hand and the anti-erosion
performance of the guide vanes on the other hand. Thus, 600r/min
was chosen as the unit rated speed to ensure the comprehensive
anti-wear performance and energy performance.
The reference runner (Fig. 5 left) was a traditional Francis turbine
used in 300m head. In order to reduce the flow separation and avoid the
unstable flow phenomena near the leading edge of runner, the splitter
runner was used in this Francis turbine runner design. The geometric
parameters and blade profiles of long and short blades were also
modified. The short blades were placed in the middle of two adjacent
long blades to improve the flow stability. After several rounds of opti­
mization, the final runner with 15 long blades and 15 short blades was
determined, and the length of short blades was about 0.6 times
compared with that of long blades. The final blade profile were shown in
Rated
speed (r/
min）
Specific
speed
velocity near the
guide vane trailing
edge（m/s）
velocity near the
runner crown
（m/s）
efficiency
（%）
1000
750
600
94.1
71.9
51.2
54
55
57
44
39
28
94
87
82
Fig. 5 right.
The hydraulic performances of the final Francis turbine were shown
in Fig. 6. Because the difference between the minimum head and rated
head is only 0.65m, only the results of efficiency and output under rated
head and maximum head were presented. It can be seen the overall ef­
ficiency of the splitter runner was largely improved and the maximum
efficiency reached to 92.4% with output 9.1 MW under the rated head.
To guarantee the stability of the designed Francis turbine, the flow
and pressure pulsations were analyzed. The streamlines in runner under
four typical conditions were given in Fig. 7. It can be seen the flow in the
designed operating range were smooth without obvious vortex and
separation, especially for the high load region where the unit runs more.
That means the erosion intensity may be largely reduced due to the
improvement of the complex flow with the load increasing.
Fig. 8 shows the velocity comparisons between the original and final
Francis turbine runner and wicket gate under rated condition. The green
zone represents the velocity lower than the set value and the red zone
represents the velocity higher than the set value. The comparative of the
relative velocity at 90% span-wise section between splitter runner and
convention runner showed that the highest relative velocity concen­
trated at the blade trailing edge. The relative velocity zone higher than
34 m/s near the runner trailing edge with splitter runner was much
smaller than that of the conventional runner, which means the erosion
intensity will decrease with the splitter runner due to improved flow
condition in the blade channel. To reduce the relative velocity near the
wicket gate trailing edge, the vane profile was redesigned. The thickness
and the overlap degree of wicket gate were reduced and the pitch
diameter was increased. The results were satisfying because the relative
velocity zone higher than 42 m/s far from the trailing edge of the wicket
gate, which means the improvement of the wicket gate anti-erosion
performance.
For hydraulic machinery working in sand laden water, the erosion
rate of the Francis turbine may be accelerated under the dual affections
of cavitation and sediment [19]. Therefore, the cavitation performance
of the hydraulic turbine must be predicted accurately in the design stage
to avoid the abrasion damage to the unit. Here, the
Zwart-Gerber-Belamri (ZGB) [20] cavitation model was used to simulate
the two-phase cavitation flow in this paper. Fig. 8 shows the curve of the
Thoma number with the efficiency under rated condition and maximum
head. The suction head in this power station is − 8.5m, and the Thoma
number can be calculated according to equation (3).
/
Fig. 3. The unit specific speed of similar head power station in China (left) and the guide vane erosion in Yuzixi power station (right).
42
J. Yang et al.
Renewable Energy 207 (2023) 40–46
Fig. 4. Velocity distribution in the middle section. (left:750 r/min; right: 600r/min).
Fig. 5. Reference runner (left) and the final splitter runner (right).
To ensure the operation of the unit without cavitation, a certain
margin of the suction head is required. Generally, the margin of the noncavitation safety factor is about 1.8 times compared to that of the critical
cavitation. The critical cavitation condition is always defined as the
efficiency drop by 1%. For this studied Francis turbine, the plant cavi­
tation number σ = 0.066 as Hs = − 8.5m under rated condition. It can be
seen from Fig. 9 the efficiency drop by 0.8% as the Thoma number
decreased to σ = 0.035, which has not reach to critical cavitation con­
dition. The cavitation margin had reached 1.89 times compared with the
plant cavitation number. Besides, the efficiency drop by 0.3% corre­
sponding to Thoma number 0.03 under maximum head full load con­
dition. The cavitation margin had reached to 2 times compared with the
plant cavitation number, in which condition the σ = 0.06. These results
proved the reliable cavitation performance of the hydro-turbine.
For a low specific speed hydro-turbine operated at 300m head, the
pressure pulsations in vane-less area (between the guide vane and run­
ner) and draft tube were the mainly concerned stability indicators. Thus,
the unsteady calculations were carried out using the new designed tur­
bine. The pressure pulsations at four points of the middle section of the
vane-less area (agvrv1, agvrv2, agvrv3, agvrv4) and four points in the
middle of the draft tube cone (bdt1,bdt2, bdt3, bdt4) were recorded. The
Fig. 6. Hydraulic performances of the splitter runner by numerical simulation.
(
σ=
)/
pa
pv
− Hs −
H
ρg
ρg
(3)
Here, σ is the Thoma number, Pa is the atmosphere, Pv is the saturated
pressure and Pv = 3540Pa, Hs is the suction head, H is the head, ρ is the
water density and g is the gravity.
Fig. 7. Streamlines in runner at different loads under rated head.
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J. Yang et al.
Renewable Energy 207 (2023) 40–46
Fig. 8. Relative velocity zone near the 90% span-wise section and wicket gate.
Fig. 9. Efficiency drop curve and cavitation evolution with the Thoma number under rated head (left) and maximum head (right).
simulation results of peak-to-peak (ptp) value of the pressure pulsations
were shown in Fig. 10. Six typical conditions were taken into consid­
eration for ptp values analysis. The overall pressure pulsations were
lower compared with the conventional runner. The maximum ptp value
of the pressure pulsations in vane-less region is 2.2% under 100% load at
maximum head. In addition, all of the ptp values of pressure pulsation in
draft tube were lower than 0.5%, which indicates the good operation
stability of the new turbine.
whole operation zone. The unit noise was low and the flow out of the
draft tube was calm. Which means the output and the stability perfor­
mances successfully reached the design requirements. The measured
vibration data near the upper brackets, lower brackets and head cover in
the field under the operation loads from 15% to 100% were presented in
Fig. 11. The unit vibration double amplitude values were lower than 30
μm. According to the national standard demands in China, the hori­
zontal and vertical vibration amplitudes at brackets vibration should
less than 40 μm and 50 μm (GB/T7894-2009) and the vibration near the
head cover should not exceed 30 μm (GB/T15468-2006). All of the vi­
bration data were much lower than the standard requirements.
To check the anti-erosion characteristics, the runner and guide vane
were hoisted out of the pit for inspection after 3102.57 h operation in
the field. Fig. 12 shows the actual erosion situation in runner and guide
vane. Despite of the high sediment content in this power station, there
5. Operation after commissioning
To validate the erosion resistance and stability performances of the
new hydraulic turbine, the operation situation of this unit was tracked
after commissioning. The new turbine received great feedback from the
field operators of the power plant. The unit stability was very well in the
Fig. 10. Peak to peak values of pressure pulsation in vane-less area and draft tube cone by simulation.
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Renewable Energy 207 (2023) 40–46
Fig. 11. Vibration double amplitude values in three typical positions on site.
was only slightly sediment wear on the surface of the guide vane and
runner. Erosion in the upper and lower end faces of guide vane may due
to the leakage flow. Compared to the serious surfaces abrasive of runner
and guide vanes in the other hydro-power stations in this district, the
hydraulic design in Muzhati hydro-power station was very successful.
erosion in the runner and guide vane of prototype Francis turbine,
proved the good performance of the new designed hydraulic turbine.
The anti-wear design methods used in this paper were the universally
applicable methods, which can be used to most of the hydraulic turbines
operating in sediment laden river to prolong the overhaul cycle of the
turbine and reduce the maintenance cost of the unit. To further improve
the comprehensive performance of the Francis turbine, it is necessary to
precise predict the sediment erosion of the turbine and establish the
relationship between velocity and erosion extent in the future.
6. Conclusion
Hydraulic machinery working in sand laden river always subjected
to abrasive erosion problems. In order to effectively reduce the sediment
erosion and improve the Francis turbine’s performances in a high head
hydro-power station, this paper analyzed the effects of different antierosion optimization design schemes of the turbine.
The results showed that the downshift of rated speed was effective
for reducing the relative velocity and then improve the anti-erosion
performance of runner. Nevertheless, it was limited by hydraulic per­
formance and velocity near the guide vane. Thus, the final rotational
speed was lower from 1000r/min to 600r/min, rather than a lower
value. The relative velocity in splitter runner was much lower and can
therefore mitigated the blade wear extent compared with the conven­
tional runner. To improve the guide vane anti-erosion characteristics,
the relative velocity near the guide vane was lower by increasing the
pitch diameter of the guide vane and decreasing the overlap degree
between them. Besides, it is necessary to optimize the profile of runner
and guide vane to further improve the flow and erosion resistance
characteristics. The relative velocity near the runner and guide vane
flow filed were controlled about 34 m/s and 42 m/s, respectively. The
performance analysis results of the new designed turbine showed the
pressure pulsations and the cavitation performance of the hydro-turbine
can meet the requirements very well. Which indicates the great antiwear performance and operation stability of the unit. The results from
on-site 3102 h operation after commissioning showed that only slightly
Funding
The authors gratefully acknowledge the supports from National
Natural Science Fund of China (No.51876099).
Ethical approval
This article does not contain any studies with human participants or
animals performed by any of the authors.
Informed consent
Informed consent was obtained from all individual participants
included in the study.
CRediT authorship contribution statement
Jing Yang: Conceptualization, Methodology, Investigation, Writing
– review & editing. Chong Peng: Project administration, Validation.
Changquan Li: Data curation. Xinjun Liu: Validation. Jian Liu:
Investigation, Writing – review & editing. Zhengwei Wang: Supervi­
sion, Funding acquisition.
Fig. 12. Runner and guide vane wear extent after 3100 h operation.
45
J. Yang et al.
Renewable Energy 207 (2023) 40–46
Declaration of competing interest
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lationships which may be considered as potential competing interests:
Zhengwei Wang reports financial support was provided by National
Natural Science Foundation of China.
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