33

ＯＴＥＣ
Vol. 25（2020），33 ～ 45

Numerical simulation of pressure pulsation in vane area of a
pump-turbine at pump mode
Yao GUO*1, Pengcheng GUO*1, Yoichi KINOUE*2, Longgang SUN*1*1 State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China,
Xi’an University of Technology, Xi'an 7, 10048, China*2 Institute of Ocean Energy, Saga University, 840-8502, Japan

Abstract
When a reversible pump-turbine is running under the low-flow conditions in pump mode, it is easy to produce
low-frequency and high-amplitude pressure pulsation, which affects the stability of the unit. In order to study thepressure pulsation characteristics of guide vane and stay vane passage during pump operation, this paper takes apower station pump-turbine model as research object, based on the SST k-ω turbulence model for its internaltransient flow, a three-dimensional unsteay simulation of the whole flow channel is carried out. The results showthat in hump zone, the first main frequency of the pressure pulsation in guide vane and bladeless zone is 0.2 times
the rotation frequency, and the second main frequency is the blade passing frequency and its multiple. When flowrate is increased to the best efficiency conditions, the 0.2 times rotation frequency pulsation amplitude isdisappeared. The main frequency of the pressure pulsation in vane channel and the vaneless zone is the blade
passing frequency and its multiples. In order to clarify the reason for the high-amplitude pressure pulsation at the
0.2 times rotation frequency, the internal flow field of the hump zone was further analyzed based on the velocity
coefficient. It was found that there are almost evenly distributed three stall groups in guide vane and stay vane.
The change rotates at a low speed in a counterclockwise circumferential direction. Finally, the Q criterion is used
to identify the vortex structure of the cascade channel. There are flow vortices and spanwise vortices of different
strengths in the cascade channels. These vortex structures continuously rotate counterclockwise at low speed overtime and block the flow channel. This leads to the appearance of low frequency and high amplitude pressure
pulsation of 0.2 times the rotation frequency.
Key words : pump – turbine, pump working condition, vane area, pressure pulsation, rotating stall

1. Introduction
In order to meet the needs of power system load regulation, pump-turbine often needs to change operating conditions
and deviate from the design operating conditions (Nan W., 2008). When the unit is operating under non-design conditions,pressure pulsation is likely to occur, which will cause unit vibration and even damage the its flow-through components,
which will seriously affect unit stability (Dongming G et al., 2018). When the unit is operating under turbine conditions,an "S" characteristic area appears on the characteristic curve (Zeng W et al., 2016). This area will make it difficult for theunit to connect to the power grid. Unlike operated under turbine conditions, when the unit is operated under pumpconditions, the hump phenomenon may occur on flow-head curve, which seriously affects its stability. In addition, there
are unstable flow phenomena such as rotating stall (Chunze Z., 2017) and flow separation (Li Z J., 2016) in pump mode.
In summary, the stability requirements of pump operating conditions are more stringent, and the pressure pulsation
problem needs to be analyzed in depth. Analyzing the pressure pulsation produced by the flow-through components of a
pump-turbine operated under non-design conditions, and exploring the causes and characteristics of the pressure pulsation
are of great significance to the stability of the unit.
In recent years, many experts and scholars have carried out relevant research work on the stability of a pump-turbine
Date of Manuscript Acceptance 2020.11.20
E-mail of corresponding author: guoyicheng@xaut.edu.cn

34

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUNin pump operation condition. Guo L (2014), Deyou L (2018), Qifei L (2018), etc. carried out numerical simulations on a
pump-turbine under non-design working conditions, and obtained the law of the propagation of pressure pulsation in thecircumferential and flow directions. When studying the pump conditions, it was found that the amplitude of the pressure
pulsation at guide vane, stay vane and the vaneless area is relatively high, which has a significant impact on the stabilityof the unit. When Yin J L et al. (2010) analyzed the velocity field of the cascade channel, they found that the hydraulicloss at guide vane and stay vane was relatively large, resulting in a positive slope area (ie, hump area) on the head-flow
curve. Sun Y (2014), Ziwu G (2017), etc. studied the pressure pulsation of a pump-turbine when the guide vane opening
is small and found that the pressure pulsation amplitude in the vaneless zone was much higher than that in other areas. R
Hongjuan R et al. (2012) analyzed the pressure pulsation of the first hump zone condition of the near design condition,
obtaining that the dominant frequency of the pressure pulsation in guide vane was 0.2 times rotation frequency of the unit,
and that the pressure pulsation was caused by the bad flow of slab in guide vane channel, which is consistent with theresults obtained by Giovanna Cavazzini (2018). YANG J et al. (2015) analyzed a pump-turbine under pump design
conditions and small flow conditions and showed that there is 0.6625 times passing frequency of guide vane under thesetwo conditions, and pointed out that the bad flow occurred in the U-shaped stay vane suction surface is the internal causeof the pressure pulsation. Under small flow conditions, there is a pressure pulsation of 0.335 times pass frequency ofguide vane. This pressure pulsation is caused by the unstable flow at guide vane, but it does not conduct a more in-depth
analysis of the bad flow under these two working conditions. In summary, the current research work on the pressure
pulsation in vane area of the unit under the non-design working conditions of a pump-turbine pump is not yet complete,
and the cause, characteristics and propagation law of pressure pulsation have not yet reached a unified understanding.
Based on the SST k-ω turbulence model, this paper firstly develops a full-flow three-dimensional unsteady simlutionof a pump-turbine with different flow under pump conditions to discuss the frequency components and the internal causesof the pressure pulsation in the vane area.

2. Calculation model and numerical method
2.1 Physical model
The calculation takes a model pump-turbine of a pumped storage power station as the object. The three-dimensional
full flow channel geometric model is shown in Figure 1. The model has five flow parts, the runner, draft tube, spiral case,guide vane and stay vanes. The solid model of the pump-turbine is established by the three-dimensional modeling software
UG. When it is operated under pump conditions, the fluid flows in through draft tube and flows out through spiral case.
The geometric parameters of the model are: runner inlet diameter D1=553mm, outlet diameter D2=251.98mm, runnerblade number Zb=9, guide vane height b0=37.76mm, stay vane number Zc=20, and the number of guide vane Z0=20. In
addition, the rated speed of the pump - turbine is 1150r/min, and guide vane opening used in the calculation is α=14°.

2.2 Computational domain meshing
The professional grid generation software ICEM is used to divide computational fluid domain grid of the model, andeach flow component uses a hexahedral structured grid, as shown in Figure 2. When dividing the grid, the boundary layer
grid near the wall of each flow component is locally encrypted, so that it can more effectively capture the flow state ofboundary layer near the wall. At the same time, the quality of the grid is controlled not less than 0.3 and its angle is notless than 18° to ensure a high grid quality standard.
When the opening of guide vane is 14°, select the highest efficiency operating point in pump mode to perform steadysimulation, gradually increase the number of grids, and select head and torque as the evaluation criteria, so as to verify
grid independence. The numerical calculation results are shown in Figure 3. It can be seen that when the number of grid
nodes is greater than 3.99 million, the change of calculated values of head and torque do not exceed 1% due to theincreasing grid nodes. A precision grid can simulate actual flow more effectively and accurately, but the more grid nodes,
the higher the computer resources and calculation cycle requirements for calculations. Therefore, 5.56 million grid nodes
is selected in this paper. Among them, the grid nodes number of draft tube, runner, guide vane, stay vane and spiral caseare 0.71 million, 2.07 million, 1 million, 1.06 million and 0.708 million respectively. The details of the grid quality are
shown in Table 1.

Numerical simulation of pressure pulsation in vane area of a pump-turbine at pump mode

35

The commercial software ANSYS CFX was used to perform a three-dimensional unsteady simulation of the full flow
channel of the model pump - turbine. The turbulence model adopts the SST k-ω model, and dynamic and static interfaceof the unsteady calculation is set to the Transient Rotor Stator type. Draft tube is used as inlet, and the boundary conditionis set as pressure; the spiral case is used as outlet, and the boundary condition is set as mass flow. The wall condition isset as no slip and no friction, and both the convection term and the turbulence term adopt the high-order solution format;
the transient term adopts the second-order backward Euler format. In unsteady calculations, the size of time step setting
is related to the convergence speed and the accuracy of the calculation results. In this paper, the impeller is set to rotate
1° at each time step, and corresponding time step is 4.4348×10-4 s. The maximum iteration of each time step is 10 steps,
and the maximum value of the convergence residual is not more than 1.0×10-3. It takes 360 steps for runner to rotate one
round, and the calculation processing should be no less than 20 rotation cycles, and take the results of the last 5 cycles foranalysis.

Fig.1 Geometrical model of a pump - turbine(a) Spiral case(b) Guide vane and stay vanes(c) Runner(d) Draft tube
Fig.2 The grids of each flow components

36

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUN

1140
Head
Torque

55.0

1135
1130

54.5

54.0

Torque (N•m)

Head(m)

55.5

1125

2

3

4

5

6

7

N (106)

8

9

10 11

1120

Fig.3 Grid independence analysis
Table 1 The number and quality of grid nodes of each flow component

Guide Vane

Stay Vane

RunnerDraft Tube

Spairl Case

Total

Node Number

1063920

100176520752887089207108275560720

Grid Quality

0.5

0.46

0.5

0.3

0.35

3. Analysis of calculation results
3.1 Experimental verification of numerical results
In order to verify the reliability of the numerical calculation, this paper carried out the model tests of the pump-turbine
flow-efficiency and flow-head. In the tests, an electromagnetic flowmeter is used to record the flow, and a differential
pressure sensor is used to measure the differential pressure between draft tube and spiral case and then to calculate thehead. According to the IECS60193 Standard, the flowmeter, head differential pressure, main torque, friction torque andother sensors are calibrated within the test range using standard measuring instruments or instruments (1999). The random
error and system error of the hydraulic efficiency of the model test bench are calculated according to Eq. (1) and Eq. (2),Eηr = ±

t0.95( N −1) ×∑ (η −η ) ×100%i

N ( N − 1) ×ηEηs =± EQ2 + EH2 + ET2 + En2

2

(1)

(2)

Where, N is the number of measurements, t0.95(N-1) is the t distribution value of (N-1) degrees of freedom

corresponding to the 0.95 confidence probability, and ηi is the measured efficiency value of the i th of the experiment,η is the average efficiency. EQ, EH, ET and En are the relative uncertainty of flow, head, torque and rotation speed,which are ±0.0853%, ±0.0759%, ±0.1416%, ±0.006% , respectively. After calculation, the random error and systemerror of hydraulic efficiency are ±0.0363% and ±0.182%, respectively, which meet the test requirements.
Figure 4 shows the comparison between the experimentally measured pressure coefficient as well as efficiency
value and the numerical simulation. In the figure, the discharge coefficient φ and the head coefficient ψ are definedby Eqs.(3) and (4).

ϕ=

π
4

Q
× D2 × u(3)

37

Numerical simulation of pressure pulsation in vane area of a pump-turbine at pump modeψ=

2× g × H
u2(4)

Where, D is the inlet diameter of a pump-turbine on pump mode whose unit is 'm'; n is the speed of a pump-turbine
whose value is 1150 r/min; Q is the flow rate of a pump–turbine whose unit is 'm3/s'; u is circumferential velocity at the
inlet of runner under pump conditions whose unit is 'm/s'; H is the head of a pump – turbine whose unit is 'm'.
Figure 4 shows that numerical calculation results are in good agreement with the experimental results. Moreover, as
the flow changes, numerical results of the pressure coefficient and efficiency are basically consistent with experimental
values. However, the head result obtained by numerical calculation is higher than the test result as a whole, and as theflow rate increases, the difference gradually increases. The numerical calculation result of efficiency is also higher than
the test result. The occurrence of these phenomena may due to factors such as mechanical loss caused by bearing friction
which is not considered in the simulation, improper sealing and volume loss caused by blade tip clearance.
Table 2 reflects the pressure coefficient error and efficiency error at each operation condition point when comparedwith experimental results. At 14° guide vane opening, the best efficiency point in the numerical simulation results isnamed the optimal working condition point written as Qb. It can be seen that the pressure coefficient error of numericalcalculation does not exceed 3.15%, and the efficiency error value does not exceed 3.70%. Therefore, the numerical
5.6

94

5.4

92

5.2

90

5.0

88

η [-]

ψ [-]

calculation method used in this paper has high reliability.

4.8

exp
sim

4.6
4.4

exp
sim

84
82
80

4.2
4.0

86

0.18

0.21

0.24

0.27

ϕ [-]

0.30

0.33

0.36

78

0.18

(a) Head-flow curve

0.21

0.24

0.27

0.30

ϕ [-]

0.33

0.36

(b) Efficiency-flow curve

Fig.4 External characteristic curve of water pump turbine

This paper analyzes the small flow conditions at 14° guide vane opening, that is 0.76Qb operating condition (Op1),
hump zone operating condition 0.78Qb (Op2) and the best efficiency point Qb (Op3), the details of operating point are
shown in Table 2.
Table 2 Parameters of operating condition point of at 14° guide vane opening

Conditions

Flow
Coefficient φ

Flowpressure coefficientefficiency

error (%)

error (%)

Op1

0.24147

0.76Qb

0.21

2.76

Op2

0.24763

0.78Qb

-1.40

0.78

Op3

0.31822

Qb

2.20

3.70

description
small flow operating condition
hump zone operating condition（CFD）
best efficiency point（CFD）

3.2 Settings of monitoring points
When a pump-turbine is operating under pump conditions, the hydraulic loss of vane channel and vaneless zone

38

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUN

accounts for a large proportion, and the pressure pulsation is more obvious (Leqin W et al., 2013, Chunze Z et al.,2017).
In order to analyze the pressure pulsation of guide vane, stay vane, and vaneless area between runner and guidevane, 27 pressure monitoring points are set along the flow direction. The monitoring points distributes in thevaneless area between runner and guide vane, guide vane and stay vane. The first number after the monitoring point
name represents the position on the spanwise surface. The surface close to Span 0.02 is 0, the surface Span0.5 is 1,
and the surface Span0.98 is 2. The second number represents the position of the monitoring point in the flow
direction, as shown in Figure 5.

Fig.5 The distribution of monitoring point

3.3 Distribution of average pressure and standard deviation of pressure in guide vane and stay vane
The average pressure and pressure standard deviation of each monitoring point are shown in Figure 6. The abscissaof Figure 6 represents the serial number of the monitoring points (i. e., GV01-GV25 in guide vane or SV01-SV25 in stayvane). The pressure standard deviation can reflect the magnitude of pressure pulsation at each monitoring point. In the
Op1 working condition, the average pressure and standard deviation of pressure at the monitoring points GV01-GV25
are shown in Figure 6(a). On the hub side, the middle spanwise surface and the shroud side, the average pressure of themonitoring points is almost equal. As the distance between the monitoring points and the runner increases, the averagepressure first increases and then decreases. The average values of pressure at the tail of guide vane (GV04, GV14, GV24)
are the largest. The value of pressure standard deviation is the largest in the middle spanwise surface, and the pressure
standard deviations at the hub side and the shroud side are almost the same. The value of the pressure standard deviation
decreases as the distance between the monitoring points and the runner increases.
The average pressure and pressure standard deviation of stay vane channel monitoring points SV01-SV24 are shownin Figure 6(b). Along the flow direction, the average value of pressure is proportional to the distance between themonitoring points and the guide vane, that is, the farther the monitoring points are from the guide vane, the greater the
average pressure value. However, the pressure standard deviation is the opposite. The closer to the vaneless area, thegreater the pressure standard deviation of the monitoring point, that is, the greater the pressure pulsation amplitude. In theaxial direction, the average pressure and standard deviation of the pressure at the monitoring points at the shroud side, themiddle spanwise surface and the hub side are almost equal.
The average pressure and standard deviation of pressure at the monitoring points of the guide vane under the Op2
condition are shown in Figure 6(c). Compared with the Op1 condition, the average value of pressure of the guide vane
monitoring points increases, while the pressure standard deviation amplitude increases sharply. Under this condition, thefarther the monitoring point is from the runner, the larger the average pressure value and the smaller the pressure standard
deviation. Among the three planes, the average pressure and the pressure standard of the middle spanwise surface are thelargest.
The average pressure and pressure standard deviation of the stay guide vane channel monitoring points SV01-SV24
are shown in Figure 6(d). Compared with Op1 condition, the pressure standard deviation of each monitoring point
increases significantly. Along the flow direction, as the distance between the monitoring point and the guide vane increases,
the average pressure gradually increases, while the pressure standard deviation gradually decreases. Along the axial
direction, except for the stay vane inlet monitoring point on the shroud side (GV21), the pressure standard deviation is
the largest. On the middle span, the pressure standard deviation of the other monitoring points is the largest.

39

Numerical simulation of pressure pulsation in vane area of a pump-turbine at pump modespan 0.98

6.6
6.4
6.2
6.0
5.8

0

5

10

15

20

Monitoring points [-]span 0.02

span 0.5

6.4
6.2
6.0
0

(c)

5

20

span 0.5

span 0.02

5.6
5.4
5

10

15

20

Monitoring points [-]

0

5

10

15

20

Monitoring points [-]span 0.02

25

25

Monitoring points in guide vane under Op3 condition

span 0.5

span 0.98

6.90
6.85
6.80
6.75
0

(d)

5

10

15

20

Monitoring points [-]25

Monitoring points in stay vane under Op2 condition

span 0.98

5.8

0

6.7

25

6.0

5.2

6.8

6.95

span 0.02

Average pressure [105 Pa]

Average pressure [105 Pa]

15

Monitoring points in guide vane under Op2 condition

6.2

(e)

10

Monitoring points [-]span 0.98

6.9

7.00

Average pressure [105 Pa]

6.6

span 0.5(b) Monitoring points in stay vane under Op1 condition

span 0.98

6.8

span 0.02

7.0

6.6

25

Monitoring points in guide vane under Op1 condition

Average pressure [105 Pa](a)span 0.5

span 0.02

Average pressure [105 Pa]

Average pressure [105 Pa]

6.8

span 0.5

span 0.98

6.6

6.5

6.4

6.3

0

5

10

15

20

Monitoring points [-]25(f) Monitoring points in stay vane under Op3 condition

Fig. 6 The average pressure and the pressure deviation of monitoring points

When the flow increases to Qb (i. e., under condition Op3), the average pressure and pressure standard deviation ofeach monitoring point of guide vane are shown in Figure 6(e). Compared with the previous operating condition, theaverage pressure and the pressure standard deviation of each monitoring point are further reduced. As the distance between
the monitoring point and runner increases, the average pressure value first increases and then decreases, however, thepressure standard deviation first decreases and then increases. In the axial direction, the average pressure of the monitoring
points on the three planes are nearly equal, but the difference in the pressure standard of the monitoring points in the
middle spanwise plane is slightly larger than that of the other two planes. The average pressure and pressure standard

40

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUN

deviation of the stay guide vane channel monitoring points are shown in Figure 6(f). As the flow increases, the averagepressure and the pressure standard deviation of the monitoring points decrease. Along the flow direction, as the distance
between the monitoring point and the guide vane increases, the average pressure increases, while the pressure standard
deviation gradually decreases. In the axial direction, the average pressures and standard deviations of the three planes are
not much different. The pressure standard deviations on the hub side are slightly larger than the other two planes.
To sum up, for the same operating point, the pressure pulsation amplitudes of the three plane monitoring points on
the hub side, the shroud side and the middle spanwise surface are not much different, but the pressure pulsation amplitude
on the middle spanwise surface is slightly larger than the pressure pulsation amplitude of the other two planes. For themonitoring points, the closer to the vaneless area between the runner and the guide vane, the smaller the average pressure,but the greater the pressure pulsation amplitude.

3.4 Analysis of pressure pulsation in guide vane and stay vane
Based on the analysis above, fast Fourier transform (FFT) is performed on the pressure data collected by themonitoring point on the middle spanwise surface to analyze its frequency domain characteristics. Figure 7 shows thefrequency spectrum of the pressure pulsation at the monitoring point on the middle spanwise surface under 4 working
conditions. In the Op1 condition, the pressure spectrogram of the guide vane monitoring points GV11-GV15 is shown in
Figure 7(a). The first main frequency of each monitoring point is 0.2fn (fn is the rotation frequency), followed by 9fn (theblade passing frequency). Among them, from the inlet to the outlet of guide vane, the amplitude of 0.2fn first increases
and then decreases, and the maximum value appears at GV13 (the middle of guide vane) while the minimum value appears
at the GV15 (between guide vane and stay vane). The second main frequency 9fn is caused by the rotor and stator
interference(RSI) between runner and guide vane. The farther the monitoring point is from runner, the less it is affectedby the RSI, and the smaller the pulsation amplitude. The pressure spectrogram of the stay vane channel monitoring points
SV11-SV14 is shown in Figure 7(b), the main frequency is also 0.2fn, and the second main frequency is 18fn (2 times ofthe blade passing frequency). The frequency 0.2fn has the largest amplitude at the monitoring point SV12 (the middle ofstay vane channel); from stay vane inlet to outlet, the amplitude of 18fn gradually decreases. Comparing Figure 7 (a) with
Figure 7 (b), the dominant frequency of this operating condition is 0.2fn, and the amplitude is the largest near the middleof guide vane.
When the flow increases to the Op2 working condition, the dominant frequency of each monitoring point is also 0.2fn.
Compared with the Op1 working condition, the amplitude of guide vane monitoring point 0.2fn increases significantly, as
shown in Figure 7(c). The first dominant frequency of guide vane channel is 0.2fn, and the trend of its amplitude isconsistent with that of the Op1 condition, and the amplitude at GV13 is the largest. The second main frequency is 9fn(blade passing frequency), and its amplitude gradually decreases from inlet to outlet of the guide vane, and the amplitudeis the largest at GV11. The pressure pulsation spectrum of stay vane monitoring point is shown in Figure 7(d). The first
dominant frequency is 0.2fn, and its amplitude is much smaller than that of guide vane monitoring point. The second mainfrequency is 18fn, and SV11 has the largest amplitude. Compared with Fig. 7(c) and (d), the main frequency of thiscondition is still 0.2fn, and the amplitude is the largest at guide vane monitoring point GV13. In the Op3 working condition,
the pressure pulsation amplitude of each monitoring point is significantly reduced. The first main frequency is changed
from 0.2fn to 18fn, which is caused by the rotor and stator interference of runner and guide vane. The second mainfrequency is 9fn, and the pulsation amplitude of the low-frequency component 0.2fn at the monitoring point of the vanechannel decreases sharply or even disappears.
To sum up, in Op3 (the highest efficiency condition), the dominant frequency at guide vane and stay vane is 18fn, whichis twice the blade passing frequency; in Op1 (small flow condition) and Op2 (hump zone operating condition), thedominant frequency of the pressure pulsation at guide vane and stay guide vane is 0.2fn, which is consistent with theexperimental results of Hongjuan R et al., (2012). In order to explore the reason for the 0.2fn low-frequency pressure
pulsation, the internal flow field at the Op2 (that is, 0.78Qb condition) is further analyzed.

Numerical simulation of pressure pulsation in vane area of a pump-turbine at pump mode(a)Monitoring points in guide vane under Op1 condition

(b)

(c)

Monitoring points in guide vane under Op2 condition(d) Monitoring points in stay vane under Op2 condition(e)Monitoring points in guide vane under Op3 condition (f) Monitoring points in stay vane under Op3 condition
Fig. 7 Pressure spectrogram of monitoring point

41

Monitoring points in stay vane under Op1 condition

3.5 Analysis of flow characteristics
Figure 8 shows the absolute velocity cloud diagrams of the runner and the guide vane channel and the evolution of thestall vortex at different times in the 0.78Qb operating condition. In this figure, Ust is the velocity coefficient (Chunze Z etal., 2017), which is defined by Eq. (5).

U st =

Vu(5)

Where, V is the instantaneous absolute velocity, and u is the circumferential velocity of runner outlet. It can be seenfrom the figure that three sets of stall clusters appeared in the circumferential direction of cascade channel composed ofstay vanes and guide vanes, and these three sets of stall clusters are almost evenly distributed in the guide vanes and thestay vane channels. As time changes, the stall cluters rotates at low speed in the circumferential direction in acounterclockwise direction. Comparing Figure 8(a) and Figure 8(e), it can be seen that when the impeller rotates for fivecycles (T0+5T), the three sets of stall cluters all rotate 120° in the series cascade channel. The distribution is similar to42

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUN

that at t=T0, so the low-speed rotating motion of these three set of rotating stall cluters is the internal cause of the 0.2fn
low-frequency and high-amplitude pressure pulsation in the series cascade channel.

(a) T0(b) T0+T(c) T0+2T(d) T0+3T(e) T0+4T(f) T0+5T

Fig. 8 Absolute velocity pressure cloud diagrams in 0.78Qb condition at different time

The vortex identification criterion can clearly and objectively reflect the vortex structure in complex flows (Yuning Z etal., 2018). In order to further clarify the characteristics of the internal rotating stall clusters of cascade channel, this paper
adopts the Q criterion (ZHANG Y N et al., 2018) to identify the vortex structure appearing in the series cascade channel
where the monitoring points are arranged. The Q criterion can simultaneously capture the strong and weak vortexes in
the flow channel. According to the definition of Q criterion by Hunt et al.(1988), it is based on the decomposition of thelocal velocity tensor Dij, which is defined by Eq. (6).
Dij=Sij+ωij(6)

Where, Sij is the symmetric tensor, which represents the deformation part of the fluid; ωij is the antisymmetric tensor
representing the rotating part of the fluid. The characteristic equation of Dij is defined by Eq. (7).

λ 3 + Pλ 2 + Qλ + R =0(7)

Where, P，Q，R are three invariants related to the velocity tensor gradient. Q is defined by Eq. (8).

Q=

( )

(

2
2
2
2
1
1
tr D - tr D  =ωij - Sij
 2
2 

( )

)

(8)

When Q>0, the rotation of flow state in the flow channel is greater than the deformation of the flow state, that is,there is vortex motion.
The vorticity distribution on the middle spanwise surface of stay vane and guide vane in the 0.78Qb condition isanalyzed. Based on experience and combined with the actual flow characteristics in the flow channel, the Q value isselected as 15000S-2 in this paper. Figure 9 shows the vortex structures of guide vane and stay vane channel at different
times. Among them, the circle in the figure is the channel where the monitoring points are arranged. At time T0, there are
streamwise vortex and spanwise vortices at guide vane of channel A, and these vortex structures block the channel.

Numerical simulation of pressure pulsation in vane area of a pump-turbine at pump mode

43

Streamwise vortex of different intensities appears in stay vane channel. At time T0+T, the vortex flows counterclockwise
to the next channel. There is still a vortex structure in channel A, but the streamlines at guide vane is smooth, and there is
only a shedding vortex at the outlet. After two cycles (that is, t=T0+2T), the streamlines at stay vanes and guide vanes ofchannel A are relatively smooth, and there is only a streamwise vortex at the inlet on suction surface of stay vane. At
t=T0+3T, the volume of the streamwise vortex at the inlet on suction surface of stay vane increases, and the spanwise
vortex appears again at the outlet of the suction surface of guide vane. After four cycles, the volume of the spanwise
vortex at guide vane of channel A increases, and the streamwise vortex also appears in the vaneless area between guidevane and stay vane. At T0+5T, the vortex intensity of channel A is weakened, and the vortex structure is broadcast to thenext channel. Comparing diagrams (a)-(f), it can be found that the vortex structures are circumferentially distributed in
guide vane channel, blocking the flow channel, and rotating counterclockwise at low speed over time, resulting in theappearance of the 0.2fn low frequency and high amplitude pressure pulsation.

(a) T0(b) T0+T(c) T0+2T(d) T0+3T(e) T0+4T(f) T0+5T

Fig. 9 Vortex structures in guide vane channel under 0.78Qb condition at different time

44

Yao GUO, Pengcheng GUO, Yoichi KINOUE, Longgang SUN

4. Conclusion
In this paper, a model pump turbine of a pumped-storage power station is developed with unsteady simulation in thewhole flow channel, and the guide vane channel is analyzed when the pump turbine is operated at the near hump area,
hump area and the highest efficiency point. And the pressure pulsation at the vaneless zone, the conclusions are as follows:(1) The pressure pulsation amplitudes at the corresponding monitoring points on the three planes close to the hub side,
the sproud side and the middle spanwise surface under the same working condition are nearly equal, and the pressure
pulsation amplitude of the spanwise surface in the middle is slightly larger than the pressure pulsation amplitude of othertwo planes. (2) When the unit is operated at the highest efficiency point, the main frequency of the pressure pulsation at
the monitoring point is 18fn, which is twice the blade passing frequency. The 18fn frequency is caused by the static anddynamic interference between the runner and the guide vane. The second main frequency is 9fn; when in the near humparea and the hump area, the main frequency of the pressure pulsation at the monitoring point is 0.2fn, and the second mainfrequency is 9fn; (3) Analyzing the absolute velocity cloud diagrams of the runner and the guide vane channel at different
times under 0.78Qb conditions shows that the series cascade channel is almost evenly distributed with three rotating stallclusters. After the impeller rotates five cycles, the three stall clusters are all counterclockwise for 120°, at this time theabsolute flow velocity cloud image is the same as when at the initial time. Finally, the Q criterion is used to identify thevortex structure of the rotating stall cluster in the series cascade channel, and it is found that there are vortexes of different
shapes and different intensities in the series cascade channel. These vortex structures block the flow channel and continue
to rotate counterclockwise at a low speed over time causeing the appearance of high amplitude and low frequency pressure
pulsation at a frequency of 0.2fn.

Acknowledgement
This work was supported by the National Natural Science Foundation of China(Grant No. (51839010), the Key
Research and Development Program of Shaanxi Province(Grant No. 2017ZDXM-GY-081) , The Youth Innovation Teamof Shaanxi Universities(Grant No. 2020-29) and the cooperative Research Program of IOES(No.18A07).

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