The development of a novel electricity system integrating hydropower, wind, solar, and energy storage requires enhanced rapid-response capabilities from hydropower units, which are expected to undergo prolonged transitional processes. Pelton turbines, equipped with a dual regulation system comprising needles and deflectors, offer significant advantages in maintaining stability during transitional processes. However, the transient flow and hydrodynamic characteristics of Pelton turbine during load rejection remain inadequately understood. This study employs a one-dimensional method of characteristics coupled with three-dimensional computational fluid dynamics to numerically investigate the load rejection process of a Pelton turbine. The results reveal that deflector-jet interference causes pressure fluctuations in the water supply system, with a maximum amplitude reaching 5% of the gross head. The deflector alters the jet flow direction, which simultaneously exerts a braking effect on the runner's rotation and causes a significant increase in the radial force on the runner, by an order of magnitude. Moreover, the peak rotational speed and maximum radial force on the runner are observed at a similar deflector opening, independent of the initial load and deflector closure scheme.

1.
X. L.
Fu
,
D. Y.
Li
,
J. W.
Lv
,
B.
Yang
,
H. J.
Wang
, and
X. Z.
Wei
, “
High-amplitude pressure pulsations induced by complex inter-blade flow during load rejection of ultrahigh-head prototype pump turbines
,”
Phys. Fluids
36
,
034115
(
2024
).
2.
Y. M.
Su
,
J. F.
Lin
,
G.
Zhao
,
C. Y.
Guo
, and
H.
Guo
, “
Influence of a pre-swirl stator and rudder bulb system on the propulsion performance of a large-scale ship model
,”
Ocean Eng.
218
,
108189
(
2020
).
3.
J.
Lin
,
H.-D.
Yao
,
C.
Wang
,
Y.
Su
, and
C.
Yang
, “
Hydrodynamic performance of a rim-driven thruster improved with gap geometry adjustment
,”
Eng. Appl. Comput. Fluid
Mech.
17
,
2183902
(
2023
).
4.
B.
Yao
,
Y.
Zhou
,
B.
Wu
,
J.
Pang
,
D.
Jiang
,
H.
Zhang
,
J.
Liu
,
B.
Qin
, and
X.
Liu
, “
Effect of sediment erosion on pressure pulsations in a large Pelton turbine
,”
Energy Sci. Eng.
12
,
4040
(
2024
).
5.
N.
Shrivastava
and
A. K.
Rai
, “
Parametric investigation of Pelton turbine injector under hydro-abrasive erosion conditions
,”
J. Appl. Fluid Mech.
17
,
89
(
2024
).
6.
G. A.
Ibarra
,
J. A.
Ladino
,
F. J.
Larrahondo
, and
S. A.
Rodriguez
, “
Optimization and reconstruction of Pelton buckets based on statistical techniques, artificial neural networks, and CFD modelling
,”
Renewable Energy
231
,
120933
(
2024
).
7.
B.
Semlitsch
, “
Effect of inflow disturbances in Pelton turbine distributor lines on the water jet quality
,”
Int. J. Multiphase Flow
174
,
104786
(
2024
).
8.
H.
Meng
,
J.
Zhang
,
X.
Ge
, and
J.
Huang
, “
Research on the influence of needle roughness of Pelton turbine on flow characteristics
,”
J. Phys.: Conf. Ser.
2707
,
012072
(
2024
).
9.
S.
Geeri
,
A.
Kolakoti
,
O. D.
Samuel
,
M.
Abbas
,
P. A.
Aigba
,
H. A.
Ajimotokan
,
C. C.
Enweremadu
,
N.
Elboughdiri
, and
M. A.
Mujtaba
, “
Investigation of flow behaviour in the nozzle of a Pelton wheel: Effects and analysis of influencing parameters
,”
Heliyon
10
,
e28986
(
2024
).
10.
L.
Sandmaier
,
P.
Meusburger
, and
H.
Benigni
, “
Transient 3D CFD simulation of a Pelton turbine—A state-of-the-art approach for Pelton development and optimization
,”
Int. J. Turbomach. Propuls. Power
8
,
10
(
2023
).
11.
W.
Fan
,
L.
Sun
, and
P.
Guo
, “
Investigation on unstable flow characteristics and energy dissipation in Pelton turbine
,”
Eng. Appl. Comput. Fluid Mech.
18
,
2304643
(
2024
).
12.
F.
Khan
and
A.
Kumar
, “
Pelton turbine jet flow investigations using laser Doppler velocimetry
,”
Phys. Fluids
35
,
125138
(
2023
).
13.
H.
Deng
,
K.
Song
,
F.
Deng
,
Y.
Huang
,
T.
Luo
,
Y.
Zhou
,
B.
Qin
,
Y.
Zeng
,
Z.
Yu
,
J.
Pang
, and
X.
Liu
, “
Nozzle jet deviation from bucket pitch circle's effect on the stability and efficiency of Pelton turbine
,”
Processes
11
,
1342
(
2023
).
14.
G. R.
Pisaturo
,
F. F.
Nicolosi
,
D.
Gusmerotti
,
M.
Righetti
, and
M.
Renzi
, “
Laser Doppler anemometry technique to study the flow field in the nozzle and in the water jet of a Pelton turbine
,”
J. Phys.: Conf. Ser.
2511
,
012008
(
2023
).
15.
J.
Huang
,
X.
Ge
,
D.
Chu
,
J.
Zhang
,
B.
Xu
,
F.
Gao
, and
Y.
Zheng
, “
Research on the effect of needle eccentricity on the jet flow characteristics
,”
Front. Energy Res.
10
,
882747
(
2022
).
16.
D.
Nedelcu
,
V.
Cojocaru
, and
R. C.
Avasiloaie
, “
Numerical investigation of nozzle jet flow in a Pelton microturbine
,”
Machines
9
,
158
(
2021
).
17.
L.
Sun
,
W.
Fan
,
H.
Zhou
,
Z.
Wang
, and
P.
Guo
, “
Numerical assessment of the hydrodynamic excitation characteristics of a Pelton turbine
,”
Sustainability
16
,
10667
(
2024
).
18.
X. D.
Wang
,
W. Q.
Wang
,
J. F.
Yang
,
C. B.
Zhang
, and
W. Z.
Cao
, “
Numerical study on the influence of the bucket offset angle on the flow field of Pelton turbines with six-nozzles
,”
J. Phys.: Conf. Ser.
2752
,
012038
(
2024
).
19.
X. D.
Wang
,
W. Q.
Wang
,
C. B.
Zhang
, and
Y.
Xu
, “
Old wine in a new bottle: Energy loss evaluation in a six-nozzle Pelton turbine with entropy production theory
,”
Energy
319
,
135132
(
2025
).
20.
Y.
Xiao
,
Z.
Liu
,
Q.
Liang
,
J.
Liu
,
J.
Zhang
,
Y.
Zhu
,
X.
Li
, and
C.
Gu
, “
The interaction between bucket number and performance of a Pelton turbine
,”
Energy
287
,
129646
(
2024
).
21.
H.
Zhao
,
B.
Zhu
,
B.
Xu
,
P.
Tang
,
N.
Guo
, and
W.
Zhang
, “
Investigation on the influence of bucket's flow patterns on energy conversion characteristics of Pelton turbine
,”
Eng. Appl. Comput. Fluid
Mech.
17
,
2234435
(
2023
).
22.
J.
Sun
,
X. F.
Ge
, and
Y.
Zheng
, “
SPH method used for characteristic predictions at Pelton turbine buckets: Comparing with the mesh-based method
,”
Eng. Comput.
40
,
1245
(
2023
).
23.
X.
Chen
,
Y.
Guo
, and
G.
Zhu
, “
The influence of different runner widths on the performance of micro Pelton turbine
,”
J. Phys.: Conf. Ser.
2528
,
012004
(
2023
).
24.
L.
Sun
,
Z.
Wang
,
H.
Zhou
,
Z.
Wang
, and
P.
Guo
, “
Numerical assessment of transient flow and energy dissipation in a Pelton turbine during startup
,”
Phys. Fluids
36
,
094119
(
2024
).
25.
A. L.
Alerci
,
E.
Vagnoni
, and
M.
Paolone
, “
Structural impact of the start-up sequence on Pelton turbines lifetime: Analytical prediction and polynomial optimization
,”
Renewable Energy
218
,
119341
(
2023
).
26.
M.
Egusquiza
,
D.
Valentin
,
C.
Valero
,
A.
Presas
, and
E.
,
Egusquiza
,
Transient Analysis of Pelton Turbine Prototypes
(
IOP Publishing Ltd.
,
2021
).
27.
J. F.
You
,
X.
Lai
,
W.
Zhou
, and
Y. G.
Cheng
, “
3D CFD simulation of the runaway process of a Pelton turbine
,”
Proc. Inst. Mech. Eng., Part A
230
,
234
(
2016
).
28.
X. F.
Ge
,
H.
Meng
,
Z. C.
Deng
, and
L. N.
Cao
, “
Transient flow characteristics of water distribution ring during load rejection of impact water turbines
,”
J. Huazhong Univ. Sci. Technol. (Nat. Sci.)
52
,
20
(
2024
).
29.
F.
Khan
,
A.
Kumar
, and
T.
Staubli
, “
Measurement of the jet deflector torque for model Pelton turbine and associated uncertainties in test rig development
,”
Meas. Sci. Technol.
34
,
125302
(
2023
).
30.
F.
Khan
,
A.
Kumar
,
T.
Staubli
,
A.
Abbas
, and
L.
Devinar
, “
Control of a Pelton turbine with partial jet cutting driven by a cut-in jet deflector
,”
Renewable Energy
239
,
122063
(
2025
).
31.
P.
Zhang
,
Y.
Cheng
,
S.
Xue
,
Z.
Hu
,
M.
Tang
, and
X.
Chen
, “
1D-3D coupled simulation method of hydraulic transients in ultra-long hydraulic systems based on OpenFOAM
,”
Eng. Appl. Comput. Fluid
Mech.
17
,
2229889
(
2023
).
32.
F. Y.
Jin
,
H. M.
Wang
,
Y. Y.
Luo
,
A.
Presas
,
H. L.
Bi
,
Z. W.
Wang
,
K.
Lin
,
X. C.
Lei
, and
X. L.
Yang
, “
Visualization research of energy dissipation in a pump turbine unit during turbine mode's starting up
,”
Renewable Energy
217
,
119172
(
2023
).
33.
X. L.
Fu
,
D. Y.
Li
,
H. J.
Wang
,
J. L.
Yang
, and
X. Z.
Wei
, “
Influence and multi-objective optimization on three-stage guide vane closure scheme of a pumped storage power plant
,”
J. Energy Storage
72
,
108545
(
2023
).
34.
X. X.
Zhang
,
Y. G.
Cheng
,
Z. Y.
Yang
,
Q. H.
Chen
, and
D. M.
Liu
, “
Water column separation in pump-turbine after load rejection: 1D-3D coupled simulation of a model pumped-storage system
,”
Renewable Energy
163
,
685
(
2021
).
35.
D. M.
Liu
,
X. X.
Zhang
,
Z. Y.
Yang
,
K.
Liu
, and
Y. G.
Cheng
, “
Evaluating the pressure fluctuations during load rejection of two pump-turbines in a prototype pumped-storage system by using 1D-3D coupled simulation
,”
Renewable Energy
171
,
1276
(
2021
).
36.
X. X.
Zhang
,
Y. G.
Cheng
,
J. D.
Yang
,
L. S.
Xia
, and
X.
Lai
, “
Simulation of the load rejection transient process of a Francis turbine by using a 1-D-3-D coupling approach
,”
J. Hydrodyn.
26
,
715
(
2014
).
37.
X. X.
Zhang
and
Y. G.
Cheng
, “
Simulation of hydraulic transients in hydropower systems using the 1-D-3-D coupling approach
,”
J. Hydrodyn.
24
,
595
(
2012
).
38.
F. J. J.
Hahn
,
B.
Semlitsch
, and
C.
Bauer
, “
On the numerical assessment of flow losses and secondary flows in Pelton turbine manifolds
,”
IOP Conf. Ser.: Earth Environ. Sci.
1079
,
012082
(
2022
).
39.
M.
Qin
,
Z.
Yu
,
B.
Wu
,
J.
Pang
,
D.
Jiang
,
H.
Zhang
,
J.
Liu
,
H.
Hua
, and
X.
Liu
, “
Numerical simulation of multiphase flow and prediction of sediment wear in a large Pelton turbine
,”
Energy Sci. Eng.
12
,
5031
(
2024
).
40.
X. F.
Ge
,
J.
Sun
,
Y.
Zhou
,
J. G.
Cai
,
H.
Zhang
,
L.
Zhang
,
M. Q.
Ding
,
C. Z.
Deng
,
M.
Binama
, and
Y.
Zheng
, “
Experimental and numerical studies on opening and velocity influence on sediment erosion of Pelton turbine buckets
,”
Renewable Energy
173
,
1040
(
2021
).
41.
X.
Wang
,
J.-F.
Yang
,
X.-W.
Huang
, and
W.-Q.
Wang
, “
Using bionic tubercles to control swirling flow instabilities of a hydraulic turbine during the load rejection process
,”
Energy
311
,
133354
(
2024
).
42.
X.
Wang
,
Y.
Yan
,
W. Q.
Wang
, and
Z. P.
Hu
, “
Evaluating energy loss with the entropy production theory: A case study of a micro horizontal axis river ducted turbine
,”
Energy Convers. Manage.
276
,
116553
(
2023
).
43.
P. J.
Roache
, “
Quantification of uncertainty in computational fluid dynamics
,”
Annu. Rev. Fluid Mech.
29
,
123
(
1997
).
44.
I. B.
Celik
,
U.
Ghia
,
P. J.
Roache
,
C. J.
Freitas
,
H.
Coleman
, and
P. E.
Raad
, “
Procedure for estimation and reporting of uncertainty due to discretization in CFD applications
,”
J. Fluid Eng. Trans. ASME
130
,
078001
(
2008
).
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