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Flow-induced pulsations in Francis turbines during startup - A

consequence of an intermittent energy system

Saeed Salehi

*

, Håkan Nilsson

Division of Fluid Dynamics, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, SE, 412 96, Sweden

article info

Article history:

Received 3 November 2021

Received in revised form

10 January 2022

Accepted 26 January 2022

Available online 7 February 2022

Keywords:

High head Francis turbine

Startup sequence

Flow-induced pulsations

Plunging and rotating modes

Rotating vortex rope (RVR)

OpenFOAM

abstract

Hydraulic turbines are increasingly responsible for regulating the electric grid, due to the rapid growth of

the intermittent renewable energy resources. This involves a large increase in the number of starts and

stops, which cause severe ﬂow-induced pulsations and ﬂuctuating forces that deteriorate the machines.

Better knowledge of the evolution of the ﬂow in the machines during transients makes it possible to

avoid hazardous conditions, plan maintenance intervals, and estimate the costs of this new kind of

operation. The present work provides an in-depth and comprehensive numerical study on the ﬂow-

induced pulsations and evolution of the ﬂow ﬁeld in a high-head model Francis turbine during a

startup sequence. The ﬂow simulation is carried out using the OpenFOAM open-source CFD code. A

thorough frequency analysis is conducted on the ﬂuctuating part of different pressure probes and force

components, utilizing Short-Time Fourier Transform (STFT) to extract the evolution of the frequency and

amplitude of pulsations. Low-frequency oscillations are detected during the startup, which are induced

by the complex ﬂow structure in the draft tube. A decomposition is performed on the draft tube pressure

signals, and the variations of the synchronous (plunging) and asynchronous (rotating) modes are studied.

The plunging mode is stronger at minimum and deep part load conditions, whereas the rotating mode is

dominant during the presence of the Rotating Vortex Rope (RVR) at part load. The velocity ﬁeld in the

draft tube is validated against experimental data, and the complex ﬂow structures formed during the

startup procedure are explained using the

l

2

vortex identiﬁcation method.

©2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

The use of renewable electric energy resources has been

growing fast to respond to the increasing global electric energy

consumption. Nowadays, the inevitable intermittency of electrical

energy resources such as solar and wind power is compensated

through hydropower systems [1e3]. The hydraulic turbines are not

necessarily working at the steady Best Efﬁciency Point (BEP) con-

dition anymore. They are being used in different transient oper-

ating sequences to stabilize the electrical grid, leading to entirely

different engineering requirements for such machines.

Transient operations usually produce complex ﬂow structures,

such as ﬂow separation, vortices, destructive pressure pulsations,

cavitation, etc. Frequent occurrence of such undesirable ﬂow

structures could seriously deteriorate the turbine lifetime and

cause fatigue stresses, wear and tear on different components [4].

Currently, Francis turbines may experience over 500 start-stop

cycles per year [5], while they are usually designed to tolerate up

to 10 cycles [6,7]. Undoubtedly, the accumulated damages from

such abundant cycles degrade the machine's performance and may

lead to its failure. Hence, it is crucially important to study and

provide a profound understanding of the turbine ﬂow ﬁeld during

transient operations such as startup.

Gagnon et al. [8] examined the inﬂuence of startup schemes on

the fatigue-based life expectancy of a Francis turbine. It was

explained that an optimization of the scheme could improve the

turbine lifetime. Nicolle et al. [9] assessed the startup operations of

a low-head Francis turbine using a reduced CFD model. Two

different startup scenarios based on the guide vane opening

scheme were investigated. Comparisons were made with limited

experimental measurements and a general agreement was

achieved.

The impact of the guide vane opening scheme on the startup

procedure of a high-head Francis turbine has been experimentally

*Corresponding author.

E-mail addresses: saeed.salehi@chalmers.se (S. Salehi), hakan.nilsson@chalmers.

se (H. Nilsson).

Contents lists available at ScienceDirect

Renewable Energy

journal homepage: www.elsevier.com/locate/renene

https://doi.org/10.1016/j.renene.2022.01.111

0960-1481/©2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Renewable Energy 188 (2022) 1166e1183

assessed by Trivedi et al. [10]. The angular speed of the guide vanes

was for one scheme almost twice as for the other scheme. Inap-

propriate rapid rotation of the guide vanes ampliﬁed the unstead-

iness and developed undesirable pressure pulsations. Goyal et al.

[7] performed an experimental study on the same high-head

Francis turbine during startup. The startup sequence was split

into two phases, namely, phase I, to synchronize the turbine with

the generator, and phase II, to reach the steady-state condition. The

second phase was accomplished using three different guide vane

opening schemes which ended in Part Load (PL), BEP, and High Load

(HL) conditions, respectively. The Rotating Vortex Rope (RVR) fre-

quency was observed in both velocity and pressure data of the ﬁrst

scheme.

More recently, the startup of a prototype Francis turbine was

experimentally and numerically investigated [11]. Two guide vane

opening schemes, namely, conventional and reduced opening limit

schemes were studied and it was shown that the reduced scheme

decreased the fatigue damage. The draft tube vortices were shown

to have a signiﬁcantly higher impact on the dynamical stresses

compared to the interblade vortices. It was concluded that dis-

turbing the draft tube vortex could alleviate the damaging effects

on the runner during startup.

Although the experimental investigations are trustworthy re-

sources to assess the turbine ﬂow ﬁeld during startup, they are

expensive and there are many limitations on accessibility and

measured ﬂow details. Numerical studies provide a reliable addi-

tion to assess and understand the details of the ﬂow ﬁeld during

turbine startup. The startup is recognized as one of the most

harmful operating conditions of hydraulic turbines [8]. Therefore,

achieving a profound understanding of the complex ﬂow ﬁeld of a

hydraulic turbine during startup is essential to reduce the

damaging effects and improve the life expectancy of these

machines.

The present article provides a comprehensive and detailed

analysis of the transient ﬂow ﬁeld and its pulsations during a

startup sequence of a Francis turbine. Such in-depth analyses are

crucial for a better understanding of the hazardous pulsations to be

able to ultimately reduce and avoid them. The simulation is per-

formed utilizing the OpenFOAM open-source CFD code. The varia-

tion of the pressure ﬁeld, velocity ﬁeld, and forces are carefully

assessed. One of the main focuses of the present study is to extract

the ﬂow-induced pulsations. No investigations are found in the

literature on the draft tube pressure signal decomposition during a

startup sequence. In the current study, for the ﬁrst time, the vari-

ation of plunging and rotating modes of the ﬂuctuating pressure

during the startup operation is examined. An in-depth explanation

of the complex ﬂow structures downstream the runner, which play

a crucial role in the generation of the pulsations, is presented. The

paper is organized as follows. The investigated test case, including

the geometrical and operational details, is introduced in Section 2.

The mathematical formulations of the assessed problem are

described in Section 3.1, while the details of the numerical frame-

work are described in Section 3. Section 4provides the numerical

results and discussions, and ﬁnally, the concluding remarks of the

paper are provided in Section 5.

2. Investigated test case

A high-head Francis turbine model is used as the investigated

test case. The Francis-99 turbine model, provided by the Francis-99

workshop series [12], is a 1:5.1 scale model of a prototype Francis

turbine [13]. The runner consists of 15 full-length and 15 splitter

blades. The prototype and model net heads are about H

prototype

z

377 m and H

model

z12 m, respectively.

Fig. 1a and b show two cross-sections of the Francis-99 model.

The axial and horizontal in-plane velocity components have been

experimentally measured at a PIV plane. The PIV plane is shown as

a red line and a gray shaded area in the z-normal and y-normal

sections, respectively. The velocity measurements are reported on

three PIV lines, two horizontal lines (Lines 1 and 2), and one axial

line (Line 3). Moreover, the static pressure is reported for three

sensor locations, namely, VL2, DT5, and DT6. In the experiments,

the draft tube pressure sensors were piezoelectric, and only

instantaneous ﬂuctuation of pressure was measured [14]. Two

additional numerical probes (RP1 and RP2) are deﬁned in the

rotating zone (Runner) to sample the pressure ﬁeld throughout the

sequence. The numerical probes are placed in the middle of one

runner passage (in between two neighboring main and splitter

blades) at different axial positions.

The current work concerns a startup sequence that commences

from the minimum load operating condition. The guide vanes are

nearly closed with an opening angle of

a

¼0.8

and the ﬂow rate is

Q¼0.022 m

3

/s. The guide vanes open up, rotating around their

axes, and the ﬂow rate increases. The transient sequence ends at

the BEP condition in which

a

¼9.84

and Q¼0.199 59 m

3

/s. The

runner rotational speed remains constant at

u

¼333 rpm during

the entire transient sequence.

3. Computational framework and numerical aspects

The CFD simulation is carried out with OpenFOAM-v1912

[15,16]. The governing equations are discretized using the ﬁnite-

volume approach on a collocated mesh. The current section

brieﬂy describes the governing equations and the employed nu-

merical methods and schemes. More detailed information about

the numerical aspects of the performed CFD simulation is provided

by Salehi et al. [17], who used the same approach for a shutdown

sequence of the same case.

3.1. Mathematical formulation

A transient incompressible turbulent ﬂow can be modelled by

the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equa-

tions, given by

vU

j

vx

j

¼0;(1)

vU

i

vtþ

vðU

i

U

j

Þ

vx

j

¼1

r

vp

vx

i

þv

vx

j

n

vU

i

vx

j

u

i

u

j

!;(2)

where

r

u

i

u

j

represents the unknown Reynolds stress tensor. The

Shear Stress Transport (SST) based Scale-Adaptive Simulation

URANS model (i.e., SST-SAS) [18,19] is here employed for the

calculation of the Reynolds stress tensor. SST-SAS is a turbulence-

resolving URANS model, used for simulations of industrial tran-

sient ﬂows. Its formulation decreases the local eddy viscosity to

resolve the turbulent spectrum and break-up of large eddies,

providing LES-like solutions. Several research studies veriﬁed the

performance of the SST-SAS model in the simulation of hydraulic

machinery ﬂows [11,20e25].

3.2. Discretization schemes

The second-order backward implicit scheme is employed for the

discretization of the temporal derivative terms. The time step of the

simulation is chosen as

D

t¼1.25 10

4

s, corresponding to runner

and guide vane rotations of 0.25

and 1.625 10

4

in each time

step. The average and maximum CFL numbers at the highest ﬂow

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

116 7

rate (BEP) are 0.025 and 55. It should be noted that the CFL number

is less than 2 for 99.4% of the cells.

The convective terms in the momentum equation are dis-

cretized using the Linear-Upwind Stabilised Transport (LUST)

scheme [26], which blends the central and second-order upwind

schemes with a blending factor of 0.75. In other words, the face

values are calculated blending 75% second-order central and 25%

second-order upwind schemes, balancing accuracy and numerical

stability. The second-order upwind scheme approximates other

convective terms (i.e. in kand

u

equations).

The Laplacian terms in the transport equations are estimated

using the second-order central scheme. An explicit non-orthogonal

correction due to the high skewness of the cells at some locations is

inevitable because of the complex geometry.

3.3. Pressure-velocity coupling

The PIMPLE pressure correction algorithm is employed for the

pressure-velocity coupling. It combines two pressure correction

algorithms, namely, SIMPLE [27] and PISO [28] as outer and inner

correction loops, respectively. A maximum of 10 outer correction

loops is performed in each time step, controlled by a residual cri-

terion. At most time steps the ﬂow solution is converged after four

outer correction loops. Each outer loop conducts two inner

correction loops. After each inner loop, one additional non-

orthogonal correction loop is performed to assure convergence of

Fig. 1. Two sections of the Francis-99 model, showing PIV plane, velocity lines, pressure sensors.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

116 8

explicit terms. It has been shown that the OpenFOAM imple-

mentation of the pressure correction algorithm is in line with the

Rhie-Chow interpolation technique [29,30].

3.4. Boundary conditions

The guide vanes open up by rotating with a constant rotational

speed of 1.3

/s. The time-variation of the guide vane opening angle

is plotted in Fig. 2a. As seen in the ﬁgure, a smooth transition is

implemented at the start and stop of the rotation (t¼2 and t¼9s)

to minimize the numerical instability caused by the sudden

movement of the guide vanes. The total time of the sequence,

t¼12 s, corresponds to 66.52 runner revolutions.

The guide vane movement is imposed through an ad-hoc

developed boundary condition that requires the guide vane rota-

tional speed as input. Therefore, the rotational speed

u

of the guide

vanes is shown in Fig. 2b.

It is assumed that the inlet volume ﬂow rate of the turbine varies

linearly with respect to the guide vanes angle. This assumption is

according to the Francis-99 workshop series recommendation due

to inaccurate measurements of the ﬂow rate during transient

operation [12]. Hence, a time-varying spatially uniform velocity,

according to the ﬂow rate, is imposed at the inlet of the spiral

casing. A ﬁxed turbulence intensity (I¼7%) and viscosity ratio (

n

t

/

n

¼100) is considered for the inﬂow condition. The inlet pressure is

extrapolated from the inside domain using a zero-gradient

assumption. All quantities at the outlet boundary are computed

using the zero-gradient condition, except the pressure which is set

by a ﬁxed value.

As previously described, there are four different mesh regions in

the simulation (spiral casing, guide vanes, runner, and draft tube).

The Cyclic Arbitrary Mesh Interface (cyclicAMI)[31,32] was uti-

lized to transfer the information between the different domains.

In order to reach a statistically stationary state at minimum load

condition, the ﬂow is solved for 4 s ﬂow time corresponding to over

22 runner rotations, and then the startup sequence presented in

Fig. 2 is initiated.

3.5. Dynamic mesh framework

CFD analysis of the transient operation of Francis turbines in-

cludes two types of simultaneous mesh motion, i.e, mesh defor-

mation of the guide vane domain due to the rotation of each guide

vane and solid body rotation of the runner domain. Therefore, a

Laplacian displacement mesh morphing solver is employed to

deform the guide vane domain mesh while the solid-body rotation

function handled the runner rotations. In each time step, the mesh

is updated at the beginning of the ﬁrst PIMPLE outer correction

loop. Then, the face ﬂuxes are calculated based on the face swept

volumes and relative ﬂuid velocity [33,34].

The mesh morphing is governed by a Laplace equation, given by

V,ð

G

V

d

cell

Þ¼0;(3)

where

G

is the motion diffusivity and

d

cell

is the displacement

vector of the cell centers. The Laplace equation is solved for the cell-

centered displacement (

d

cell

) and then the solution is interpolated

to get the point displacements (

d

points

). Finally, the new point lo-

cations (at time tþ

D

t) are simply computed as

x

tþ

D

t

point

¼x

t

point

þ

d

t

point

:(4)

The motion diffusivity (

G

) is obtained using a quadratic inverse

distance scheme with respect to the guide vane surfaces.

Severe mesh deformation of the guide vane region due to the

large rotation of the guide vanes during the startup sequence could

potentially result in low-quality mesh cells and consequently

deterioration of convergence and accuracy of the numerical results.

Therefore, in this study, the mesh quality parameters were moni-

tored during the mesh deformation. The guide vane region was

remeshed two times at guide vane openings of

a

¼3.47

and

a

¼6.85

to maintain an acceptable mesh quality. More informa-

tion on the numerical aspects and mesh deformation, as well as the

open-source case and codes of the current study, is provided by

Salehi and Nilsson [35], as the same case and codes are employed in

the present work.

A block-structured mesh is created for the CFD simulation. The

mesh at BEP contains a total of 16 million cells (for more infor-

mation please see our previous studies [17,35]).

3.6. Parallel processing

The scotch [36] domain decomposition approach is used to split

the computation domain and distribute roughly equal loads to the

processors while minimizing their interconnections. The job is

submitted to a Linux cluster using 320 CPU cores. The full startup

sequence consumed a computational cost of 170,000 core hours.

4. Results and discussion

This section presents the results of the transient startup

sequence of the Francis-99 model turbine.

Fig. 2. Variation of (a) guide vane angle and (b) guide vane rotational speed during the startup sequence.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

116 9

4.1. Pressure ﬂuctuations

As previously described, a number of pressure probes, namely

VL2, DT5, DT6, RP1, and RP2, were deﬁned in the computational

domain (see Fig. 1), and the variation of the static pressure is

recorded throughout the entire startup sequence. The experimental

results of the static pressure are available for the VL2 probe, while

only the pressure ﬂuctuations were monitored at DT5 and DT6. In

transient (time-varying) turbulent ﬂows, as in the current case, the

obtained signals (for instance, pressure) consists of two different

parts, the mean and ﬂuctuating parts ðp

0

¼pp

̄

Þ. The mean signal

changes through time due to the variation of the operating condi-

tion. Therefore, in order to extract the ﬂuctuating pressure, the

instantaneous mean should be calculated. The present study em-

ploys the Savitzky-Golay ﬁnite impulse response ﬁlter [37] for

smoothing the obtained signals and calculating instantaneous

mean and ﬂuctuations. A variable window size is chosen to capture

the ﬂuctuations more accurately. The window is much smaller at

the start and end of the transient sequence, where the variation of

the pressure level due to the change in operating condition is

sharper.

Fig. 3 shows the time-variation of the static pressure, its

instantaneous mean, and the ﬂuctuations of the static pressure

from its instantaneous mean. In general, the numerical prediction

of the VL2 pressure (Fig. 3a) sufﬁciently matches the experimental

data, although with slightly lower values at the BEP condition at the

end of the sequence. The maximum relative error, calculated as |

p

num

p

exp

|/p

exp

100, is 4.25%. Each plot contains a zoomed view

that covers a 90

rotation of the runner in either the stationary

minimum load or BEP condition. The VL2 zoomed views show clear

smooth pressure pulsations due to the Rotor-Stator Interaction

(RSI) in the vaneless space (between the runner blades and the

guide vanes). Since the runner consists of 30 full and splitter blades,

7.5 pressure pulsations can be seen in these zoomed views. The

vaneless space static pressure ﬂuctuates around a nearly constant

mean pressure at the minimum load condition. Some low-

frequency oscillations are also visible at the minimum load condi-

tion in the VL2 pressure, which could be due to large unsteady ﬂow

structures in the massively separated ﬂow in the draft tube. When

the startup sequence commences at t¼2 s, the guide vanes start

opening up, and consequently, the pressure increases with the

turbine ﬂow rate growth. The rate of the pressure increment is

initially higher and then it reduces and reaches a constant level

until the end of the sequence. The numerical results suggest an

overall pressure rise from 160 kPa (at minimum load) to 174 kPa (at

BEP). The numerical results reach a stationary condition at t¼9s

when the sequence ﬁnishes. In contrast, the experimental pressure

results show that the ﬂow still needs some time to reach the steady

condition, due to dynamics in the experimental open-loop hy-

draulic system. Some low-frequency oscillations are also visible in

the numerical pressure results after the initiation of the sequence.

These oscillations are most likely produced by large ﬂow structures

formed in the draft tube in the low load conditions and will be

discussed in detail later. One can see such pulsations more appar-

ently in the ﬂuctuating pressure shown in Fig. 3b. Distinct periodic

oscillatory patterns are seen between t¼4.5 s and t¼6.5 s that are

probably caused by the formation and diminish of the RVR. The

static and ﬂuctuating pressure in one of the draft tube probes (DT6)

is also shown in Fig. 3c and d. There is not a clear sign of the RSI

ﬂuctuations in the presented zoomed views at BEP. Here again,

Fig. 3. Time-variation of static pressure (a and c) and its ﬂuctuations from the instantaneous mean (b and d) for two probe locations during startup.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1170

large oscillations are visible in the draft tube pressure at low load

conditions.

There are two statistically stationary phases in the whole

simulated sequence, namely, the initial minimum load and the ﬁnal

BEP conditions. The Fast Fourier Transform (FFT) analysis technique

enables us to identify the excited frequencies and their amplitude

of the obtained signals. Therefore, FFT was applied on the ﬂuctu-

ating part of the VL2 and DT6 pressures at both stationary condi-

tions, and the results are plotted in Fig. 4. It should be noted that in

the present study, all the frequencies are normalized by the runner

rotational frequency f

n

¼5.543 Hz. The runner blade passing fre-

quency f

b

¼30f

n

(15 full-length blades and 15 splitter blades) is the

dominant frequency in the VL2 probe. The amplitude of f

b

is much

larger at BEP compared to the minimum load condition. Peaks are

visible at the harmonics of the runner passing frequency (15f

n

and

60f

n

). A low frequency of approximately 0.3f

n

is also excited at the

minimum load condition of the VL2 pressure, which could be

explained by the large separated ﬂow region in the draft tube at

such conditions. The draft tube ﬂuctuating pressure (DT6) seems to

be most excited at the above-mentioned low frequency. A moderate

peak can also be seen at the frequency of 15f

n

, corresponding to the

full-length blade passing frequency, as only full-length blades are

elongated to the draft tube. In other words, the DT6 draft tube

probe can sense the rotation of the full-length blades much more

than the splitters.

Due to the time-varying nature of the obtained signals in tran-

sient sequences, such as turbine startup, both the excited fre-

quencies and their amplitudes change throughout the sequence.

Hence, a Short Time Fourier Transform (STFT) analysis is required

for time-frequency analysis. STFT divides the full-time domain into

small subdomains and performs the Fourier transform on each

subdomain. The time-variations of the amplitudes of different

frequencies of the VL2 and DT6 ﬂuctuating pressures are illustrated

as spectrograms in Fig. 5. The runner blade passing frequency

(f

b

¼30f

n

) is the dominant frequency of the vaneless space pressure

throughout the whole sequence (Fig. 5a). The harmonic frequencies

(i.e., 15f

n

,45f

n

,60f

n

,75f

n

, etc.) are also clearly excited. A wide range

of excited stochastic frequencies are visible in the minimum load

condition (t<2 s), indicating a complex ﬂow ﬁeld including large

separations and vortex breakup. When the guide vanes start to

open up and the ﬂow rate increases, such frequencies diminish

slightly after t¼2 s. The zoomed view of the VL2 spectrogram

suggests the existence of low-frequency high-amplitude oscilla-

tions during the transient sequence. The RVR phenomenon is most

likely responsible for such types of pulsations. The DT6 spectro-

gram denotes a deterministic frequency of 15f

n

, corresponding to

the passing of the full-length blades. The RVR low-frequency os-

cillations are also clearly visible here.

The time-variation of the amplitude of different excited fre-

quencies is extracted from the STFT calculations and presented in

Fig. 6. For the VL2 sensor, the runner blade passing frequency (30f

n

)

is dominant throughout the whole sequence. The amplitude is

nearly constant and slightly increases when the turbine reaches the

BEP condition. The amplitude of the RVR frequency (0.3f

n

)is

increased with the initiation of the transient sequence and then

decreases as the large RVR structures diminish when the turbine

approaches the BEP condition. On the other hand, for the DT6

probe, the amplitude of 0.3f

n

is dominant in the entire sequence,

except for the BEP condition where the large draft tube vortical

structures are washed away. A sudden rise and then decrease is

observed in the amplitude of 0.3f

n

in the middle of the sequence

due to the formation and collapse of the RVR.

Hydraulic turbine draft tube cones generally experience two

different types of pressure pulsations at low load conditions

[38,39]. The pressure signals can be decomposed into synchronous

and asynchronous modes. The synchronous mode (also known as

the plunging mode) is somehow similar to the water hammer

pressure waves which travel throughout the whole hydraulic sys-

tem. The asynchronous mode (rotating mode), produced by the

local instabilities such as the RVR, is only active in the cross-

sections. The pressure signal decomposition can be performed us-

ing the unsteady signals of two different pressure probes which are

positioned at the opposite sides of the draft tube cone with the

same height, through

p

sync

¼p

1

þp

2

2ðSynchronous component or plunging modeÞ;

p

async

¼p

1

p

2

2ðAsynchronous component or rotating modeÞ:

(5)

A few researchers have studied the draft tube pressure signal

decomposition to identify the appearance of plunging and rotating

modes at low load conditions of hydraulic turbines (e.g.,

Refs. [38e42]). However, no investigation can be found in the

literature on the decomposition of plunging and rotating modes of

a hydraulic draft tube during a startup sequence. Extracting such

modes from pressure signals can be particularly helpful for

explaining the appearance and collapse of the RVR in transient

sequences like shutdown and startup.

In the present test case, the DT5 and DT6 sensors are placed on

opposite sides (180

apart) of the conical part of the draft tube and

could be used for signal decomposition. First, the synchronous and

Fig. 4. Fast Fourier Transform of the ﬂuctuating pressure in the stationary conditions at the beginning and end of the sequence (minimum load and BEP).

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1171

asynchronous modes of the draft tube pressure are computed by

inserting DT5 and DT6 pressure signals into Eq. (5) and then the

ﬂuctuating parts of each mode are extracted. Fig. 7a presents the

time-variation of the ﬂuctuating part of both modes of the draft

tube pressure. The high-frequency pressure ﬂuctuations are mostly

captured by the synchronous mode. In other words, such ﬂuctua-

tions are in-phase for both probes and are sensed by DT5 and DT6

probes at the same time. Low-frequency oscillations are seen in

both synchronous and asynchronous modes at minimum load

conditions which decreases when the turbine approaches the BEP

condition, indicating that complex ﬂow structures formed at deep

part load conditions have strong plunging effects. On the other

hand, the asynchronous mode does not show any clear sign of high-

frequency ﬂuctuations, and only low-frequency pulsations are

observed. The sudden rise of rotating mode after t¼4 s could be a

sign of the formation of rotating vortical structures (i.e., RVR) which

decays with further increasing turbine load after t¼6 s. After t>7s

the turbine approaches the BEP condition and the large vortical

ﬂow structures inside the draft tube cone vanish, the pressure

ﬂuctuations predominantly contribute to the synchronous mode,

and the asynchronous mode is rather negligible at the design

condition.

In order to better understand the formation and collapse of the

RVR and its impact on the decomposed pressuremodes, a bandpass

ﬁlter with a narrow frequency range of 0.1f

n

, centered at the

fundamental frequency of RVR (0.3f

n

), was applied to the decom-

posed signals to isolate the RVR effects in the plunging and rotating

modes. As previously seen in Figs. 4 and 5, the frequency of 0.3f

n

is

Fig. 5. Spectrogram of ﬂuctuating pressure signal throughout startup sequence.

Fig. 6. Variation of ﬂuctuating pressure amplitude over time.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1172

the dominant frequency inside the draft in a wide range of low-load

conditions. The ﬁltered signals displayed in Fig. 7b reveal that the

plunging effect is mostly the dominant mode at minimum load and

deep part load conditions (before t¼4 s), suggesting that dis-

integrated stochastic ﬂow structures at such conditions primarily

cause axial pulsations that are sensed throughout the whole system

at the same time. Nonetheless, when the startup sequence of the

turbine initiates the rotating effects gradually increase in time

while the plunging mode weakens. The fact that the rotating mode

is dominant between t¼4.5 s and t¼6.5 s could be a clear sign of

the formation and collapse of the RVR. As expected, no large

vortical structures should exist at the BEP condition. Therefore,

both the plunging and rotating modes decay after t¼7s.

A time-dependent frequency analysis was performed on the

decomposed signals and the results are shown as spectrograms in

Fig. 8. Here again, synchronous ﬂuctuations are observed at mini-

mum load and deep part load conditions (t<4 s), while asyn-

chronous pressure pulsations can be detected between t¼4.5 s and

t¼6.5 s. More specially, the fundamental frequency of the RVR is

much more pronounced in the rotating mode than the plunging

mode during the presence of RVR (between t¼4.5 s and t¼6.5 s),

as also pointed out by Goyal et al. [42].

As explained in Section 2, two probes are deﬁned in the rotating

domain of the runner, namely, RP1 and RP2 (see Fig. 1b) and their

pressure variation throughout the startup sequence is demon-

strated in Fig. 9. Predictably, the RP1 pressure is generally higher

than that at RP2, as it is closer to the runner inlet. Both pressure

probes exhibit a gradual rise during the transient sequence. The

RP1 pressure increases by 13.3 kPa, whereas the RP2 pressure

grows by 7.2 kPa. High-frequency RSI ﬂuctuations are visible

through the provided zoomed views. Here the probes are rotating

with the runner and therefore the pressure is expected to show a

peak whenever the probe is passing a guide vane trailing edge. The

ﬂuctuating part of the pressure shows stronger high-frequency RSI

ﬂuctuations for RP1 as it is closer to the guide vanes. Both probes

contain low-frequency oscillations which are slightly ampliﬁed

between t¼4.5 s and t¼6.5 s.

Fig. 10 plots the FFT of the ﬂuctuating pressure of the rotating

probes at the stationary conditions (minimum load and BEP). As

expected, the ﬂuctuations have a dominant frequency at the guide

vane passing frequency (f

gv

¼28f

n

) which is stronger at BEP. The ﬁrst

harmonic of this frequency (f

gv

¼56f

n

) also shows a small peak.

Additionally, some low-frequency peaks, due to the formation and

breakup of vortical ﬂow structures are detected by the FFTanalysis at

minimum load conditions. Since the probes are rotating, the runner

rotation frequency (f

n

) and its ﬁrst few harmonics (2f

n

,3f

n

,4f

n

,etc.)

are also excited at both conditions. An STFT analysis can further

explain the variation of the amplitudes of the excited frequency

during the transient sequence. Fig. 11 presents rather similar trends

for the time-variation of the amplitudes for both rotating probes. The

guide vane passing frequency is a deterministic and dominant fre-

quency during the whole sequence. The zoomed views (Fig. 11band

d) denote that at minimum load condition, a vast range of stochastic

frequencies is excited which decay after a short while into the

Fig. 7. Time-variation of ﬂuctuating synchronous and asynchronous pressure modes. (a) Decomposed signal and (b) bandpass ﬁltered signals.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1173

transient sequence. Although an excited low frequency is observed

during the formation of the RVR (between t¼4.5 s and t¼6.5 s), the

value of that frequency is larger than the RVR fundamental fre-

quency. When the turbine reaches the design condition, the excita-

tion of the runner rotation frequency (f

n

) and its harmonics are

clearly visible in the zoomed view of both probes.

4.2. Force pulsations

Sharp variations and oscillations of forces and moments exerted

on different parts of hydraulic turbines during transient operations

could cause serious damages and negatively affect the lifetime of

the turbine. Therefore, performing force analysis during transient

sequences like the startup is essential for mitigating such damaging

effects. Forces and moments acting on the runner surfaces (i.e., hub,

shroud, main blades, and splitters) as well as a single guide vane are

monitored during the startup sequence and the results are pre-

sented in this section. Although the runner force analysis is per-

formed on the whole runner in the present work, investigating the

ﬂuctuating forces on one individual runner blade is suggested for

future studies as it could be beneﬁcial for assessing the fatigue ef-

fects and lifetime.

Fig. 12 shows the xand zcomponents of the force acting on the

runner, as well as the runner torque (zcomponent of moment

Fig. 8. Spectrogram of ﬂuctuating part of (a) plunging and (b) rotating modes.

Fig. 9. Time-variation of static pressure (a and c) and its ﬂuctuations from the instantaneous mean (b and d) for two rotating probes (RP1 and RP2) during startup.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1174

vector). F

x

shows strong low-frequency oscillations between

t¼4.5 s and t¼6.5 s, in which the vortex rope is formed and rotates

around the turbine axis (Fig. 12a). At the BEP condition, the x-force

is ﬂuctuating around a non-zero value, indicating that the ﬂow

distribution around the runner is not perfectly axisymmetric. The

zoomed view of the ﬂuctuating part of F

x

(Fig. 12d) denotes both

high and low-frequency oscillations at the BEP condition. The axial

force (z-force) is initially oscillating at negative (downward) values

at the minimum load condition and shortly after the commence-

ment of the transient sequence it increases and becomes positive

(upward) and continues its growth until the BEP condition

(Fig. 12b). Comparing the ﬂuctuating parts of F

z

and F

x

suggests that

the low-frequency oscillations during the formation and collapse of

the RVR are much weaker for F

z

(compared to their corresponding

instantaneous mean). In other words, the RVR mostly affects the

horizontal (radial) forces rather than the axial force. This is

compatible with the signal decomposition analysis presented in

Section 4.1. The axial forces are expected to oscillate with the

plunging mode of the RVR, while the radial forces vary with the

rotating mode. As elaborated in Fig. 7b, the rotating mode of the

RVR is the dominant mode during t¼4.5 s and t¼6.5 s, and thus

the radial force oscillations are greater. The variation of the runner

axial torque through time exhibits a smooth linear growth in ab-

solute value of the torque with turbine load increase, from 29.8 N m

at minimum load to 630.3 N m at BEP. It is also seen that the

ﬂuctuating part of the torque signal is negligible with respect to its

instantaneous mean. Fig. 12f reveals that the formation of the RVR

barely affects the ﬂuctuating torque and the maximum ﬂuctuating

Fig. 10. Fast Fourier Transform of the ﬂuctuating pressure of the rotating probes (RP1 and RP2) during the stationary conditions (minimum load and BEP).

Fig. 11. Spectrogram of ﬂuctuating pressure of rotating probes (RP1 and RP2) throughout startup sequence.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1175

torque that occurs at the minimum load condition is less than

1.5 N m .

The spectrograms in Fig. 13 exhibit STFT analysis of the runner

forces. The runner blade passing frequency is a deterministic

dominant frequency throughout the entire sequence for both the

horizontal and axial forces (Fig. 13a and c). The f

b

frequency is less

isolated in the f

z

force and it is more affected by the wide range of

stochastic frequencies. The zoomed view of the F

x

spectrogram

(Fig. 13b) shows mainly stochastic frequencies at minimum load

that vanish with the initiation of the sequence. Then the impacts of

the RVR on the horizontal forces are clearly seen as low-frequency

oscillations. However, the axial forces present a wide range of

excited low-frequencies that are not limited to the formation or the

collapse of the RVR (Fig. 13d). Here again, we can deduce that

complex ﬂow structures at deep part load have strong plunging

effects and result in ﬂuctuations of the axial force. The runner

rotation frequency (f

n

) has an important role in the variation of the

horizontal forces at the BEP condition.

To further assess the variation of forces in the Francis-99 startup

sequence, the forces and moments acting on a single guide vane are

studied. Fig. 14 depicts the time-variation of the radial force and

torque (axial moment around the guide vane rotational axis) of the

guide vane nearest to the volute tongue. The negative torque acts as

to open the guide vane and vice versa. Both plots display smooth

variations during the transient sequence with nearly constant

ranges of RSI ﬂuctuations, which are larger for the radial force. The

F

r

is maximum at minimum load and reduces with load increase.

More importantly, during the formation and collapse of the RVR

(between t¼4.5 s and t¼6.5 s), F

r

oscillates with some low-

frequency oscillation but M

z

does not show any impact from the

RVR. The spectrogram of F

0

r

, illustrated in Fig. 15, demonstrates a

broad span of stochastic frequencies at the minimum load condi-

tion. This could be the impact of complex separated ﬂow structures

formed behind the trailing edge of the guide vanes at minimum

load condition. Fig. 16 employs an iso-surface of

l

2

¼7500 s

2

to

reveal these structures. As expected, the 0.3f

n

frequency is

distinctly evident during the existence of the RVR in Fig. 15.

4.3. Velocity variation

The velocity ﬁeld is sampled through the entire startup

sequence along the three lines shown in Fig. 1 and the numerical

results are compared to the experimental data for validation. The

variation of the ﬂow ﬁeld is carefully examined to understand and

explain the draft tube ﬂow ﬁeld during the turbine startup. It

should be mentioned that in this work, the horizontal velocity (U)

represents the velocity component parallel to Line 1 and 2 (similar

but not identical to radial velocity), while the normal velocity (V)is

the velocity component normal to the PIV plane (similar but not

identical to tangential velocity).

Figs. 17e19 present the time-variation of the numerical velocity

components along the three PIV lines (previously shown in Fig. 1).

The axial and horizontal velocity components are compared to the

experimental measurements. The variable srepresents the curve

length of each line, which is normalized by its maximum in all

plots. The comparison reveals that the numerical axial velocity (W)

trend is quite similar to the experiment and thus is adequately well

predicted by the simulation. At minimum load condition, the axial

velocity direction is upward all over both Lines 1 and 2, varying

with low-frequency oscillations. This indicates a massive reversed

ﬂow region that covers the entire extent of both lines, while the

small mass ﬂow through the draft tube cone passes outside those

lines. Then, when the guide vanes start to open up at t¼2 s, the

reversed ﬂow region gradually gets smaller. The low-frequency

oscillations amplify with the establishment of the RVR. After

reaching the BEP condition, the reversed ﬂow region completely

vanishes and the ﬂow is entirely in the downward direction. At the

design condition, the magnitude of Wincreases with the distance

Fig. 12. Variation of components of forces acting on the runner during startup.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1176

Fig. 13. Spectrogram of ﬂuctuating forces.

Fig. 14. Variation of radial force and torque acting on one guide vane.

Fig. 15. Spectrogram of ﬂuctuating part of radial force acting on one guide vane.

Fig. 16. Complex vortical structures behind guide vane trailing edges at minimum load

condition. Iso-surface of

l

2

¼7500 s

2

.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1177

to the draft tube walls, whereas it is slightly decreased at the center

(s/s

max

¼0.5) due to the runner cone wake. The ﬂuctuations around

the center are induced by the vortex shedding created behind the

runner cone. The Wcontours on Line 3, which is located at the

center of the draft tube, denote the existence of the same reversed

ﬂow region which is diminished just before reaching the design

condition. Both the numerical and experimental data show a rather

sharp change in velocity direction around t¼8s.

Fig. 18 indicates that the horizontal velocity mainly ﬂuctuates

around zero in both the numerical and experimental data. The

ﬂuctuations are initially moderate at minimum load condition and

clearly magnify during the formation and collapse of the RVR (be-

tween t¼4.5 s and t¼6.5 s). Then, at the design conditions, both

the numerical and experimental results show near-zero Uvalues

with small ﬂuctuations.

The normal velocity component (V) was not measured in the

experimental study. Therefore, Fig. 19 displays only the numerical

results of the time-variation of the normal velocity. A strong

swirling ﬂow exists at minimum load condition. The commence-

ment of the startup sequence and load increase temporarily re-

duces the normal velocity. However, the Vcomponent remarkably

increases and oscillates with the creation of the RVR. After the

collapse of the RVR, the Vvelocity smoothly reduces. Suddenly

before the steady BEP condition, the direction of the Vvelocity and

consequently the swirl orientation changes and a weak counter-

rotating ﬂow exists at the design condition.

The time-variation of the velocity ﬁeld is further assessed using

two points, namely Point 1 and 2 (see Fig. 1), in Fig. 20. Both point

are placed on Line 1 at radial positions of R

Point1

¼46.5 mm and

R

Point2

¼125.80 mm, corresponding the normalized curve lengths

of s/s

max

¼0.367 and 0.038, respectively. Generally, the horizontal

velocity oscillates around a near-zero instantaneous mean value.

After t¼4 s, large oscillations are visible in the Uvelocity of Point 2,

which is closer to the draft tube wall, whereas Point 1 (close to the

center) mainly experience such large ﬂuctuation later (After t¼6 s).

This implies that the rotating vortical structures (i.e., RVR) form far

away from the draft tube center. With load increment, the vortical

structures integrate and form a more stable vortex around the

center, which results in remarkable ﬂuctuations of Uon Point 1

after t¼6 s. At the BEP condition, where normally a slender central

vortex is observed, Point 1 ﬂuctuates to some extent while Point 2 is

quite stable.

The axial velocity initially oscillates around a positive (upward)

instantaneous mean at both points in Fig. 20. The turbine load

increment gradually increases the magnitude of the axial velocity

to a stable point at BEP. The numerical and experimental data show

compatible trends. Similar to the Ucomponent, the Wcomponent

at Point 1 does not show large oscillations until t¼6 s, while at

Point 2 it exhibits extensive ﬂuctuations already after t¼4s.

To examine the swirling ﬂow in the draft tube, the normal ve-

locity (V) is presented in Fig. 20 as well, although no experimental

data is available. Positive values of Vat Points 1 and 2 indicate a

swirling ﬂow in the same direction as the runner rotation, and vice

versa.

Water turbines are designed such that a nearly non-swirling

ﬂow leaves the runner at BEP. The presence of a weak swirling

ﬂow at the design condition could help the ﬂow to stay attached to

the draft tube walls. A residual positive (in the same direction of the

runner) swirling ﬂow exists at partial load condition, while a higher

ﬂow rate than design condition (high load) forms a negative

(counter-rotating) residual swirl.

As expected, at minimum load condition a considerable positive

tangential component exists, especially on Point 2 which is further

from the draft tube center, indicating a large remaining positive

Fig. 17. Time-variation of axial velocity (W) along experimental PIV lines.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1178

swirl in the draft tube. Similar to Uand W, the Vvelocity at Point 2

experiences the large oscillations of the RVR sooner than at Point 1.

When the large rotational RVR structures in the draft tube are

diminished, the Vvelocity decreases as the load increases. It settles

at an insigniﬁcant negative value, indicating a weak counter-

rotating swirl at the design condition which could be intentional

to keep the ﬂow attached to the draft tube walls.

4.4. Flow structures in the draft tube

The formation and breakup of the vortical ﬂow structures inside

the draft tube during the startup sequence is analyzed in this sec-

tion. Based on a previous study [17], the

l

2

-criterion is employed to

identify and visualize the vortical ﬂow structures. It assumes a

vortex to be a region with two negative eigenvalues of the S

2

þ

U

2

tensor [43], where Sand

U

are the strain and rotation tensors, given

by

S¼1

2VUþVU

T

;

U

¼1

2VUVU

T

:(6)

Therefore, a vortex can be identiﬁed as a region with a negative

second largest eigenvalue,

l

2

. The OpenFOAM function object

Lambda2 changes the sign of the S

2

þ

U

2

tensor eigenvalues, and

thus a positive value should be used for the creation of the

l

2

iso-

surfaces.

Fig. 18. Time-variation of horizontal velocity (U) along experimental PIV lines.

Fig. 19. Time-variation of normal velocity (V) along experimental PIV lines.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1179

A video is supplied with the article for the readers to see the

time-evolution of the vortical structures during the startup oper-

ation. Fig. 21 utilizes an iso-surface of

l

2

¼750 s

2

to unveil the

evolution of the draft tube vortical structures by 12 snapshots

during the turbine startup sequence. The corresponding times (t),

guide vane opening angles (

a

), and the turbine load (normalized

ﬂow rate Q/Q

BEP

) are denoted below each ﬁgure. The transient

sequence starts from the minimum load condition. At this condi-

tion, a massively separated ﬂow ﬁeld with a signiﬁcant residual

positive swirl exists downstream of the runner (Fig. 21a). As a

result, large persistent vortical structures are visible upstream of

the draft tube elbow that produces low-frequency pulsations in the

ﬂow ﬁeld and turbine forces. When the transient sequence initiates

at t¼2 s, the guide vanes start to open up and the turbine load

increases. Consequently, the growing ﬂow rate washes down the

large vortical structures (Fig. 21b and c).

At t¼4.2 s (Fig. 21d) the aforementioned large vortices are

completely vanished and instead elongated vortical structures are

formed downstream the runner. These are formed due to the

instability of the shear layer between the swirling downward and

separated upward ﬂow regions. The separated region is still quite

large and thus the shear layer is close to the draft tube wall. Four

distinct draft tube vortices are formed in this region. Continuing the

startup sequence, the vortical ﬂow structures develop and expand

(Fig. 21e). Thereafter, further opening the guide vanes, the stagnant

(reversed ﬂow) region shrinks. Accordingly, the unstable vortical

structures gradually integrate and form a large unstable coherent

structure that is helically wrapped around the stagnant region

(Fig. 21f and g). An integrated rotating vortex rope is clearly

distinguishable at time t¼6.0 s (Fig. 21g) due to KelvineHelmholtz

instability of the sharp shear layer. This is in accordance with the

results presented in Sections 4.1e4.3, where distinct low-frequency

high-amplitude oscillations were observed between t¼4.5 s and

t¼6.5 s.

The additional augmentation of the ﬂow rate decreases the

runner residual swirl and squeezes the stagnant region. Inevitably,

the integrated central vortex becomes more stable and moves to-

ward the center of the draft tube (Fig. 21h and i). One can see small

vortices that rotate around the central axis and merge into a stable

slender vortex that is attached to the runner cone (Fig. 21j and k).

Finally, the turbine reaches the BEP condition where a small

negative (counter-rotating) swirl leaves the runner and forms a

stable and nearly stationary vortex at the center of the draft tube.

5. Conclusion

The present paper provides a detailed numerical study on the

pulsations originated by the transient ﬂow features during the

startup of a high-head model Francis turbine. Our results contribute

to a better knowledge of the evolution of the ﬂow in the hydraulic

turbines during startup operation that could provide the possibility

to avoid harmful conditions and have a better estimate of mainte-

nance intervals and costs.

The high-frequency pulsations generated by the blade passing

rotor-stator interaction (30f

n

) were the dominant excited frequency

in the vaneless space throughout the entire startup sequence, while

the guide vane passing frequency (28f

n

) was the dominant mode

for the pressure probe inside the runner rotating domain. Low-

frequency high-amplitude oscillations were observed in the mid-

dle of the sequence, suggesting the formation of the RVR. A signal

decomposition of the draft tube pressure indicated that the com-

plex ﬂow structures formed at minimum and deep part load con-

ditions have strong plunging (synchronous) effects. Increasing

turbine load gave a sudden rise in rotating (asynchronous) mode

during the formation of the RVR.

Low-frequency oscillations of the RVR affect the radial forces

Fig. 20. Time-variation of horizontal (U), axial (W), and normal (V) velocity components on Points 1 and 2 compared to the experimental PIV data.

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1180

acting on the runner more than the axial force. The blade passing

frequency is less isolated in the axial force compared to the radial

component. The axial force is greatly affected by the plunging ef-

fects at the minimum load condition and thereby its STFT shows

mainly stochastic frequencies. A frequency analysis of the

ﬂuctuating radial force exerted on the guide vanes revealed a broad

span of stochastic frequencies at the minimum load condition due

to the massively separated ﬂow ﬁeld behind the nearly closed guide

vanes.

The velocity ﬁeld in the draft tube revealed the presence of a

Fig. 21. Illustration of draft tube vortical structures using an iso-surface of

l

2

¼750 s

2

at different times corresponding to different guide vane openings (

a

).

S. Salehi and H. Nilsson Renewable Energy 188 (2022) 1166e1183

1181

large quasi-stagnant region with a large positive residual swirl that

reduces during the sequence. Large persistent vortical structures

were observed inside the draft tube at the minimum load condi-

tion. They are responsible for the low-frequency oscillations in such

conditions. Gradually increasing the turbine load results in an

integration of the unstable vortical structures and the formation of

the RVR. At BEP a slender stable vortical structure was observed

near the center of the draft tube.

CRediT authorship contribution statement

Saeed Salehi: Conceptualization, Methodology, Software,

Investigation, Writing ereview &editing. Håkan Nilsson:

Conceptualization, Supervision, Writing ereview &editing,

Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing

ﬁnancial interests or personal relationships that could have

appeared to inﬂuence the work reported in this paper.

Acknowledgements

The current research was carried out as a part of the “Swedish

Hydropower Centre - SVC”. SVC is established by the Swedish En-

ergy Agency, EnergiForsk and Svenska Kraftn€

at together with Luleå

University of Technology, The Royal Institute of Technology,

Chalmers University of Technology and Uppsala University, www.

svc.nu.

The computations were enabled by resources provided by the

Swedish National Infrastructure for Computing (SNIC) at NSC

partially funded by the Swedish Research Council through grant

agreement no. 2018e05 973.

The investigated test case is provided by NTNU eNorwegian

University of Science and Technology under the Francis-99 work-

shop series.

Appendix A. Supplementary data

Supplementary data to this article can be found online at

https://doi.org/10.1016/j.renene.2022.01.111.

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