Applications of computational fluid dynamic (CFD) techniques to hydropower have increased rapidly in the last three decades. The majority of the experimental investigations of hydraulic turbines were supported by numerical studies and this has become a standard practice. In the paper, applied numerical techniques and flow modeling approaches to simulate the hydraulic turbines are discussed. Both steady-state and transient operating conditions of the turbines are considered for the review. The steady-state conditions include the best efficiency point (BEP), high load (HL), and part load (PL). The transient conditions include load variation, startup, shutdown, and total load rejection. The performance of the applied numerical models and turbulence modeling with respect to the operating conditions are discussed. The recently developed numerical technique (transient blade row modeling) using the Fourier transformation (FT) method is discussed. This technique allows guide vane and blade passages to be modeled with the pitch ratio other than unity. Numerical modeling and simulation of hydraulic turbines during the transient operating conditions is one of the most challenging tasks because guide vanes' angular movement is time-dependent and mesh should be dynamic/moving. Different approaches applied to simulate the transient conditions and their limitations are discussed. Overall, this review summarizes the role of numerical techniques, advantages, limitations, and upcoming challenges within hydropower.

References

1.
Daugherty
,
R. L.
,
1920
,
Hydraulic Turbines: With a Chapter on Centrifugal Pumps
,
McGraw-Hill Book Company
,
New York
.
2.
Round
,
G. F.
,
2004
,
Incompressible Flow Turbomachines Design, Selection, Applications, and Theory
,
Elsevier-Gulf Professional Publishing
,
Burlington, MA
.
3.
Sawin
,
J. L.
, and
Martinot
,
E.
,
2013
, “
Renewables 2013 Global Status Report
,” Renewable Energy Policy Network for 21st Century, REN21 Secretariat, Paris, France.
4.
Sawin
,
J. L.
,
Sverrisson
,
F.
, and
Martinot
,
E.
,
2014
, “
Renewables 2014 Global Status Report
,” Renewable Energy Policy Network for 21st Century, REN21 Secretariat, Paris, France,
Report No. 978-3-9815934-2-6
.
5.
Sawin
,
J. L.
,
Sverrisson
,
F.
, and
Rickerson
,
W.
,
2015
, “
Renewables 2015 Global Status Report
,” Renewable Energy Policy Network for 21st Century, REN21 Secretariat, Paris, France,
Report No. 978-3-9815934-6-4.
6.
Raabe
,
J.
,
1985
,
Hydro Power: The Design, Use, and Function of Hydromechanical, Hydraulic, and Electrical Equipment
,
VDI Verlag
,
Dusseldorf, Germany
.
7.
Keck
,
H.
, and
Sick
,
M.
,
2008
, “
Thirty Years of Numerical Flow Simulation in Hydraulic Turbomachines
,”
Acta Mech.
,
201
(
1–4
), pp.
211
229
.
8.
Keck
,
H.
,
Weiss
,
T.
,
Michler
,
W.
, and
Sick
,
M.
,
2009
, “
Recent Developments in the Dynamic Analysis of Water Turbines
,”
Proc. Inst. Mech. Eng., Part A
,
223
(
4
), pp.
415
427
.
9.
Dörfler
,
P.
,
Sick
,
M.
, and
Coutu
,
A.
,
2013
,
Flow-Induced Pulsation and Vibration in Hydroelectric Machinery
,
Springer-Verlag
,
London
.
10.
Meyers
,
J.
,
Geurts
,
B. J.
, and
Sagaut
,
P.
,
2008
,
Quality and Reliability of Large-Eddy Simulations
,
Springer Science and Business Media B.V.
,
The Netherlands
.
11.
Mill
,
O.
,
Dahlbäck
,
N.
,
Worman
,
A.
,
Knutsson
,
S.
,
Johansson
,
F.
,
Andreasson
,
P.
,
Yang
,
J.
,
Lundin
,
U.
,
Aidanpää
,
J.-O.
,
Nilsson
,
H.
,
Cervantes
,
M.
, and
Glavatskih
,
S.
,
2010
, “
Analysis and Development of Hydro Power Research: Synthesis Within Swedish Hydro Power Centre
,” Sweden, Europe,
Report No. 10:66
.
12.
Dean
,
R. C.
,
1959
, “
On the Necessity of Unsteady Flow in Fluid Machines
,”
Trans. ASME
,
81
(
1
), pp.
24
28
.
13.
Kumar
,
P.
, and
Saini
,
R. P.
,
2010
, “
Study of Cavitation in Hydro Turbines—A Review
,”
Renewable Sustainable Energy Rev.
,
14
(
1
), pp.
374
383
.
14.
Trivedi
,
C.
,
Gandhi
,
B.
, and
Cervantes
,
M.
,
2013
, “
Effect of Transients on Francis Turbine Runner Life: A Review
,”
J. Hydraul. Res.
,
51
(
2
), pp.
121
132
.
15.
Zuo
,
Z.
,
Liu
,
S.
,
Sun
,
Y.
, and
Wu
,
Y.
,
2015
, “
Pressure Fluctuations in the Vaneless Space of High-Head Pump-Turbines—A Review
,”
Renewable Sustainable Energy Rev.
,
41
, pp.
965
974
.
16.
Chen
,
C.
,
Nicolet
,
C.
,
Yonezawa
,
K.
,
Farhat
,
M.
,
Avellan
,
F.
, and
Tsujimoto
,
Y.
,
2008
, “
One-Dimensional Analysis of Full Load Draft Tube Surge
,”
ASME J. Fluids Eng.
,
130
(
4
), p.
041106
.
17.
Arpe
,
J.
,
Nicolet
,
C.
, and
Avellan
,
F.
,
2009
, “
Experimental Evidence of Hydroacoustic Pressure Waves in a Francis Turbine Elbow Draft Tube for Low Discharge Conditions
,”
ASME J. Fluids Eng.
,
131
(
8
), p.
081102
.
18.
Zobeiri
,
A.
,
2009
, “
Investigations of Time Dependent Flow Phenomena in a Turbine and a Pump-Turbine of Francis Type: Rotor-Stator Interactions and Precessing Vortex Rope
,”
Ph.D. thesis
, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
19.
Yang
,
S. S.
,
Kong
,
F. Y.
,
Chen
,
H.
, and
Su
,
X. H.
,
2012
, “
Effects of Blade Wrap Angle Influencing a Pump as Turbine
,”
ASME J. Fluids Eng.
,
134
(
6
), p.
061102
.
20.
Yin
,
J.
,
Wang
,
D.
,
Wang
,
L.
,
Wu
,
Y.
, and
Wei
,
X.
,
2012
, “
Effects of Water Compressibility on the Pressure Fluctuation Prediction in Pump Turbine
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
062030
.
21.
Hasmatuchi
,
V.
,
Farhat
,
M.
,
Roth
,
S.
,
Botero
,
F.
, and
Avellan
,
F.
,
2011
, “
Experimental Evidence of Rotating Stall in a Pump-Turbine at Off-Design Conditions in Generating Mode
,”
ASME J. Fluids Eng.
,
133
(
5
), p.
051104
.
22.
Hasmatuchi
,
V.
,
Roth
,
S.
,
Botero
,
F.
,
Avellan
,
F.
, and
Farhat
,
M.
,
2010
, “
High-Speed Flow Visualization in a Pump-Turbine Under Off-Design Operating Conditions
,”
IOP Conference Series: Earth and Environmental Science
, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
,
IOP Publishing, UK
, p.
012059
.
23.
Hasmatuchi
,
V.
,
2012
, “
Hydrodynamics of a Pump-Turbine Operating at Off-Design Conditions in Generating Mode
,”
Ph.D. thesis
, École polytechnique fédérale de Lausanne, Lausanne, Switzerland.
24.
IEC 60193
,
1999
,
Hydraulic Turbines, Storage Pumps and Pump-Turbines: Model Acceptance Tests
,
International Standard, International Electrotechnical Commission
,
Geneva, Switzerland
, p.
578
.
25.
Gordon
,
J. L.
,
2001
, “
Hydraulic Turbine Efficiency
,”
Can. J. Civ. Eng.
,
28
(
2
), pp.
238
253
.
26.
Maruzewski
,
P.
,
Hasmatuchi
,
V.
,
Mombelli
,
H.-P.
,
Burggraeve
,
D.
,
Iosfin
,
J.
,
Finnegan
,
P.
, and
Avellan
,
F.
,
2009
, “
Surface Roughness Impact on Francis Turbine Performances and Prediction of Efficiency Step Up
,”
Int. J. Fluid Mach. Syst.
,
2
(
4
), pp.
353
362
.
27.
Yuanfang
,
H.
,
Guangning
,
L.
, and
Shiying
,
F.
,
2012
,
Research on Prototype Hydro-Turbine Operation
,
Foreign Language Press
,
Beijing, China
.
28.
Brekke
,
H.
,
2010
, “
Performance and Safety of Hydraulic Turbines
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012061
.
29.
Brekke
,
H.
,
2001
, “
State of the Art in Turbine Design
,” Congress-International Association for Hydraulic Research, 29th IAHR World Congress, pp.
544
551
.
30.
Manness
,
J.
, and
Doering
,
J.
,
2005
, “
An Improved Model for Predicting the Efficiency of Hydraulic Propeller Turbines
,”
Can. J. Civ. Eng.
,
32
(
5
), pp.
789
795
.
31.
Osterwalder
,
J.
,
1978
, “
Efficiency Scale-Up for Hydraulic Turbo-Machines With Due Consideration of Surface-Roughness
,”
J. Hydraul. Res.
,
16
(
1
), pp.
55
76
.
32.
Ausoni
,
P.
,
Farhat
,
M.
,
Escaler
,
X.
,
Egusquiza
,
E.
, and
Avellan
,
F.
,
2007
, “
Cavitation Influence on von Kármán Vortex Shedding and Induced Hydrofoil Vibrations
,”
ASME J. Fluids Eng.
,
129
(
8
), pp.
966
973
.
33.
Lee
,
T. S.
, and
Pejovic
,
S.
,
1996
, “
Air Influence on Similarity of Hydraulic Transients and Vibrations
,”
ASME J. Fluids Eng.
,
118
(
4
), pp.
706
709
.
34.
Jacob
,
T.
,
1993
, “
Evaluation sur modele reduit et prediction de la stabilite de fonctionnement des turbines Francis
,” Ph.D. thesis, Ecode Polytechnique Federale de Lausanne, Lausanne, Switzerland.
35.
Wu
,
J.
,
Shimmei
,
K.
,
Tani
,
K.
,
Niikura
,
K.
, and
Sato
,
J.
,
2007
, “
CFD-Based Design Optimization for Hydro Turbines
,”
ASME J. Fluids Eng.
,
129
(
2
), pp.
159
168
.
36.
Enomoto
,
Y.
,
Kurosawa
,
S.
, and
Kawajiri
,
H.
,
2012
, “
Design Optimization of a High Specific Speed Francis Turbine Runner
,”
IOP
Conference Series: Earth and Environmental Science
, IOP Publishing, UK, p.
032010
.
37.
Necker
,
J.
, and
Aschenbrenner
,
T.
,
2010
, “
Model Test and CFD Calculation of a Cavitating Bulb Turbine
,”
IOP Conference Series: Earth and Environmental Science
, 25th
IAHR
Symposium on Hydraulic Machinery and Systems, IOP Publishing, UK, p.
012064
.
38.
Bucur
,
D.
,
Dunca
,
G.
, and
Cǎlinoiu
,
C.
,
2012
, “
Experimental Vibration Level Analysis of a Francis Turbine
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
062056
.
39.
Sun-Sheng
,
Y.
,
Fan-Yu
,
K.
,
Jian-Hui
,
F.
, and
Ling
,
X.
,
2012
, “
Numerical Research on Effects of Splitter Blades to the Influence of Pump as Turbine
,”
Int. J. Rotating Mach.
,
2012
, pp.
1
9
.
40.
Wang
,
W. Q.
,
Zhang
,
L. X.
,
Yan
,
Y.
, and
Guo
,
Y. K.
,
2007
, “
Large-Eddy Simulation of Turbulent Flow Considering Inflow Wakes in a Francis Turbine Blade Passage
,”
J. Hydrodyn.
,
19
(
2
), pp.
201
209
.
41.
Jester-Zuerker
,
R.
,
Jung
,
A.
, and
Maiwald
,
M.
,
2012
, “
Evaluation of a Francis Turbine Draft Tube Flow at Part Load Using Hybrid RANS-LES Turbulence Modelling
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
062010
.
42.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2014
, “
Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part II: Control of the Vortex Rope
,”
ASME J. Appl. Mech.
,
81
(
6
), p.
061011
.
43.
Mössinger
,
P.
,
Jester-Zürker
,
R.
, and
Jung
,
A.
,
2015
, “
Investigation of Different Simulation Approaches on a High-Head Francis Turbine and Comparison With Model Test Data: Francis-99
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012005
.
44.
Thum
,
S.
, and
Schilling
,
R.
,
2005
, “
Optimization of Hydraulic Machinery Bladings by Multilevel CFD Techniques
,”
Int. J. Rotating Mach.
,
2005
(
2
), pp.
161
167
.
45.
Yexiang
,
X.
,
Zhengwei
,
W.
,
Zongguo
,
Y.
, and
Jin
,
Z.
,
2010
, “
Experimental and Numerical Analysis of Pressure Pulses Characteristics in a Francis Turbine With Partial Load
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012023
.
46.
Yexiang
,
X.
,
Zhengwei
,
W.
, and
Zongguo
,
Y.
,
2011
, “
Experimental and Numerical Analysis of Blade Channel Vortices in a Francis Turbine Runner
,”
Eng. Comput.
,
28
(
2
), pp.
154
171
.
47.
Wu
,
Y.
,
Liu
,
S.
,
Dou
,
H.-S.
,
Wu
,
S.
, and
Chen
,
T.
,
2012
, “
Numerical Prediction and Similarity Study of Pressure Fluctuation in a Prototype Kaplan Turbine and the Model Turbine
,”
Comput. Fluids
,
56
, pp.
128
142
.
48.
Flores
,
E.
,
Bornard
,
L.
,
Tomas
,
L.
,
Liu
,
J.
, and
Couston
,
M.
,
2012
, “
Design of Large Francis Turbine Using Optimal Methods
,”
IOP
Conference Series: Earth and Environmental Science
, IOP Publishing, UK, p.
022023
.
49.
Choi
,
H.-J.
,
Zullah
,
M. A.
,
Roh
,
H.-W.
,
Ha
,
P.-S.
,
Oh
,
S.-Y.
, and
Lee
,
Y.-H.
,
2013
, “
CFD Validation of Performance Improvement of a 500 kW Francis Turbine
,”
Renewable Energy
,
54
, pp.
111
123
.
50.
Bahrami
,
S.
,
Tribes
,
C.
,
Fellenberg
,
S. V.
,
Vu
,
T. C.
, and
Guibault
,
F.
,
2014
, “
Multi-Fidelity Design Optimization of Francis Turbine Runner Blades
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
10
.
51.
Kawajiri
,
H.
,
Enomoto
,
Y.
, and
Kurosawa
,
S.
,
2014
, “
Design Optimization Method for Francis Turbine
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
8
.
52.
Minakov
,
A. V.
,
Sentyabov
,
A. V.
,
Platonov
,
D. V.
,
Dekterev
,
A. A.
, and
Gavrilov
,
A. A.
,
2015
, “
Numerical Modeling of Flow in the Francis-99 Turbine With Reynolds Stress Model and Detached Eddy Simulation Method
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012004
.
53.
Meng
,
L.
,
Zhang
,
S. P.
,
Zhou
,
L. J.
, and
Wang
,
Z. W.
,
2014
, “
Study on the Pressure Pulsation Inside Runner With Splitter Blades in Ultra-High Head Turbine
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
7
.
54.
Ciocan
,
G. D.
,
Iliescu
,
M. S.
,
Vu
,
T. C.
,
Nennemann
,
B.
, and
Avellan
,
F.
,
2007
, “
Experimental Study and Numerical Simulation of the Flindt Draft Tube Rotating Vortex
,”
ASME J. Fluids Eng.
,
129
(
2
), pp.
146
158
.
55.
Hellström
,
J. G. I.
,
Marjavaara
,
B. D.
, and
Lundström
,
T. S.
,
2007
, “
Parallel CFD Simulations of an Original and Redesigned Hydraulic Turbine Draft Tube
,”
Adv. Eng. Software
,
38
(
5
), pp.
338
344
.
56.
Cervantes
,
M.
,
Andersson
,
U.
, and
Lövgren
,
H.
,
2010
, “
Turbine-99 Unsteady Simulations—Validation
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems, Extensive Analysis of the Mesh Scaling Tests Specifically in the Draft Tube
, IOP Publishing, UK, p.
012014
.
57.
Qian
,
Z.-d.
,
Yang
,
J.-d.
, and
Huai
,
W.-x.
,
2007
, “
Numerical Simulation and Analysis of Pressure Pulsation in Francis Hydraulic Turbine With Air Admission
,”
J. Hydrodyn.
,
19
(
4
), pp.
467
472
.
58.
Liu
,
S.
,
Li
,
S.
, and
Wu
,
Y.
,
2009
, “
Pressure Fluctuation Prediction of a Model Kaplan Turbine by Unsteady Turbulent Flow Simulation
,”
ASME J. Fluids Eng.
,
131
(
10
), p.
101102
.
59.
Liu
,
S.
,
Zhang
,
L.
,
Nishi
,
M.
, and
Wu
,
Y.
,
2009
, “
Cavitating Turbulent Flow Simulation in a Francis Turbine Based on Mixture Model
,”
ASME J. Fluids Eng.
,
131
(
5
), p.
051302
.
60.
Lain
,
S.
,
Garcia
,
M.
,
Quintero
,
B.
, and
Orreg
,
S.
,
2010
, “
CFD Numerical Simulations of Francis Turbines
,”
Rev. Fac. Ing., Univ. Antioquia
,
51
, pp.
24
33
.
61.
Maruzewski
,
P.
,
Hayashi
,
H.
,
Munch
,
C.
,
Yamaishi
,
K.
,
Hashii
,
T.
,
Mombelli
,
H.
,
Sugow
,
Y.
, and
Avellan
,
F.
,
2010
, “
Turbulence Modeling for Francis Turbine Water Passages Simulation
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012070
.
62.
Seidel
,
U.
,
Hübner
,
B.
,
Löfflad
,
J.
, and
Faigle
,
P.
,
2012
, “
Evaluation of RSI-Induced Stresses in Francis Runners
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
052010
.
63.
Gong
,
R.
,
Wang
,
H.
,
Yao
,
Y.
,
Shu
,
L.
, and
Huang
,
Y.
,
2012
, “
Numerical Simulation of Pressure Fluctuation in 1000 MW Francis Turbine Under Small Opening Condition
,”
IOP
Conference Series: Earth and Environmental Science
, IOP Publishing, UK, p.
062038
.
64.
Luo
,
Y.
,
Wang
,
Z.
,
Zhang
,
J.
,
Zeng
,
J.
,
Lin
,
J.
, and
Wang
,
G.
,
2013
, “
Vibration and Fatigue Caused by Pressure Pulsations Originating in the Vaneless Space for a Kaplan Turbine With High Head
,”
Eng. Comput.
,
30
(
3
), pp.
448
463
.
65.
Shingai
,
K.
,
Okamoto
,
N.
,
Tamura
,
Y.
, and
Tani
,
K.
,
2014
, “
Long-Period Pressure Pulsation Estimated in Numerical Simulations for Excessive Flow Rate Condition of Francis Turbine
,”
ASME J. Fluids Eng.
,
136
(
7
), p.
071105
.
66.
Feng
,
J. J.
,
Li
,
W. F.
,
Wu
,
H.
,
Lu
,
J. L.
,
Liao
,
W. L.
, and
Luo
,
X. Q.
,
2014
, “
Investigation on Pressure Fluctuation in a Francis Turbine With Improvement Measures
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
9
.
67.
Aeschlimann
,
V.
,
Beaulieu
,
S.
,
Houde
,
S.
,
Ciocan
,
G. D.
, and
Deschênes
,
C.
,
2013
, “
Inter-Blade Flow Analysis of a Propeller Turbine Runner Using Stereoscopic PIV
,”
Eur. J. Mech., B: Fluid
,
42
, pp.
121
128
.
68.
Trivedi
,
C.
,
2014
, “
Experimental and Numerical Investigations on Steady State and Transient Characteristics of a High Head Model Francis Turbine
,” Ph.D. thesis, Indian Institute of Technology, Roorkee, India.
69.
Ruprecht
,
A.
,
Maihöfer
,
M.
,
Heitele
,
M.
, and
Helmrich
,
T.
,
2002
, “
Massively Parallel Computation of the Flow in Hydro Turbines
,” 21st
IAHR
Symposium on Hydraulic Machinery and Systems
, Lausanne, Switzerland, Sept. 9–12, p.
8
.
70.
Buntic
,
I.
,
Helmrich
,
T.
, and
Ruprecht
,
A.
,
2005
, “
Very Large Eddy Simulation for Swirling Flows With Application in Hydraulic Machinery
,”
Workshop on Vortex Dominated Flows–Achievements and Open Problems
, Timisoara, Romania, June 10–11, p.
8
.
71.
Duprat
,
C.
,
Balarac
,
G.
,
Métais
,
O.
,
Tridon
,
S.
,
Barre
,
S.
,
Ciocan
,
G. D.
, and
Tomas
,
L.
,
2009
, “
Large-Eddy Simulation of Draft Tube Flow and Validation From Experimental Measurements
,” 3rd
IAHR
International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Brno, Czech Republic, pp.
14
16
.
72.
Paik
,
J.
,
Sotiropoulos
,
F.
, and
Sale
,
M. J.
,
2005
, “
Numerical Simulation of Swirling Flow in Complex Hydroturbine Draft Tube Using Unsteady Statistical Turbulence Models
,”
J. Hydraul. Eng.
,
131
(
6
), pp.
441
456
.
73.
Hamba
,
F.
,
2006
, “
A Hybrid RANS/LES Simulation of High-Reynolds-Number Channel Flow Using Additional Filtering at the Interface
,”
Theor. Comput. Fluid Dyn.
,
20
(
2
), pp.
89
101
.
74.
Risberg
,
S.
,
Jonassen
,
M.
, and
Jonassen
,
R.
,
2008
, “
Design of Francis Turbine Runners Based on a Surrogate Model Approach
,”
The Int. J. Hydropower Dams
,
15
(
5
), p.
11
.
75.
Kerschberger
,
P.
, and
Gehrer
,
A.
,
2010
, “
Hydraulic Development of High Specific-Speed Pump-Turbines by Means of an Inverse Design Method, Numerical Flow-Simulation (CFD) and Model Testing
,”
IOP
Conference Series: Earth and Environmental Science
, IOP Publishing, UK, p.
012039
.
76.
Bergström
,
J.
, and
Gebart
,
R.
,
1999
, “
Estimation of Numerical Accuracy for the Flow Field in a Draft Tube
,”
Int. J. Numer. Methods Heat Fluid Flow
,
9
(
4
), pp.
472
486
.
77.
Martin
,
K.
,
Nilsson
,
H.
, and
Jan-Olov
,
A.
,
2008
, “
Influence of Inlet Boundary Conditions in the Prediction of Rotor Dynamic Forces and Moments for a Hydraulic Turbine Using CFD
,”
12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
(
ISROMAC
), Honolulu, Hawaii, Feb. 17–22, pp.
1
9
.
78.
Cervantes
,
M. J.
,
Engström
,
T. F.
, and
Gustavsson
,
L. H.
,
2005
, “
Turbine-99 III
,”
3rd IAHR/ERCOFTAC Workshop on Draft Tube Flows
, Luleå University of Technology, Luleå, Sweden, p.
198
.
79.
Gagnon
,
J.
,
Iliescu
,
M.
,
Ciocan
,
G.
, and
Deschênes
,
C.
,
2008
, “
Experimental Investigation of Runner Outlet Flow in Axial Turbine With LDV and Stereoscopic PIV
,” 24th
IAHR
Symposium on Hydraulic Machinery and Systems
, Oct. 27–31.
80.
Mulu
,
B.
,
2012
, “
An Experimental and Numerical Investigation of a Kaplan Turbine Model
,”
Ph.D. thesis
, Luleå University of Technology, Luleå, Sweden.
81.
Petit
,
O.
,
Mulu
,
B.
,
Nilsson
,
H.
, and
Cervantes
,
M.
,
2010
, “
Comparison of Numerical and Experimental Results of the Flow in the u9 Kaplan Turbine Model
,”
IOP
Conference Series: Earth and Environmental Science
, IOP Publishing, UK, p.
012024
.
82.
Zobeiri
,
A.
,
Kueny
,
J.-L.
,
Farhat
,
M.
, and
Avellan
,
F.
,
2006
, “
Pump-Turbine Rotor-Stator Interactions in Generating Mode: Pressure Fluctuation in Distributor Channel
,” 23rd
IAHR
Symposium
, Yokohama, Japan, Oct. 17–21, p.
10
.
83.
He
,
L. Y.
,
He
,
Y.
,
Luo
,
Y. Y.
, and
Wang
,
Z. W.
,
2013
, “
Investigation on Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Runner
,”
IOP Conf. Ser. Mater. Sci.
,
52
, p.
022038
.
84.
Buntic-Ogor
,
I.
,
Gyllenram
,
W.
,
Ohlberg
,
E.
,
Nilsson
,
H.
, and
Ruprecht
,
A.
,
2006
, “
An Adaptive Turbulence Model for Swirling Flow
,”
Conference on Turbulence and Interactions
,
TI2006
, Porquerolles, France, May 29–June 2, p.
5
.
85.
Jošt
,
D.
,
Škerlavaj
,
A.
,
Morgut
,
M.
,
Mežnar
,
P.
, and
Nobile
,
E.
,
2015
, “
Numerical Simulation of Flow in a High Head Francis Turbine With Prediction of Efficiency, Rotor Stator Interaction and Vortex Structures in the Draft Tube
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012006
.
86.
Liaghat
,
T.
,
2014
, “
Two-Way Fluid-Structure Coupling in Vibration and Damping Analysis of an Oscillating Hydrofoil
,” Master thesis, École Polytechnique de Montréal, QC, Canada.
87.
Kurokawa
,
J.
,
Imamura
,
H.
, and
Choi
,
Y.-D.
,
2010
, “
Effect of J-Groove on the Suppression of Swirl Flow in a Conical Diffuser
,”
ASME J. Fluids Eng.
,
132
(
7
), p.
071101
.
88.
Doerfler
,
P.
, and
Ruchonnet
,
N.
,
2012
, “
A Statistical Method for Draft Tube Pressure Pulsation Analysis
,”
IOP Conference Series: Earth and Environmental Science
, 26th
IAHR
Symposium on Hydraulic Machinery and Systems, IOP Publishing, UK, p.
062002
.
89.
Bosioc
,
A. I.
,
Susan-Resiga
,
R.
,
Muntean
,
S.
, and
Tanasa
,
C.
,
2012
, “
Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone
,”
ASME J. Fluids Eng.
,
134
(
8
), p.
081104
.
90.
Amiri
,
K.
,
2014
, “
An Experimental Investigation of Flow in a Kaplan Runner: Steady-State and Transient
,”
Licentiate thesis
, Luleå Tekniska Universitet, Luleå, Sweden.
91.
Sundstrom
,
L. R. J.
,
Amiri
,
K.
,
Bergant
,
C.
,
Cervantes
,
M. J.
, and
Dahlhaug
,
O. G.
,
2014
, “
LDA Measurements in the Francis-99 Draft Tube Cone
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
10
.
92.
Fay
,
A. A.
,
2010
, “
Analysis of Low-Frequency Pulsations in Francis Turbines
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012015
.
93.
Tridon
,
S.
,
Barre
,
S.
,
Ciocan
,
G. D.
, and
Tomas
,
L.
,
2010
, “
Experimental Analysis of the Swirling Flow in a Francis Turbine Draft Tube: Focus on Radial Velocity Component Determination
,”
Eur. J. Mech., B: Fluid
,
29
(
4
), pp.
321
335
.
94.
Wu
,
Y.
,
Li
,
S.
,
Liu
,
S.
,
Dou
,
H.-S.
, and
Qian
,
Z.
,
2013
,
Vibration of Hydraulic Machinery
,
Springer
,
The Netherlands
.
95.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2014
, “
Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load-Part I: Simulation of the Vortex Rope
,”
ASME J. Appl. Mech.
,
81
(
6
), p.
061010
.
96.
Cervantes
,
M. J.
,
2009
, “
Counter Rotating Runner Cone in a Kaplan Elbow Draft Tube for Increased Efficiency
,”
3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic in Hydraulic Machinery and Systems Proceeding
, p.
10
.
97.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2014
, “
A Partially-Averaged Navier-Stokes Model for the Simulation of Turbulent Swirling Flow With Vortex Breakdown
,”
Int. J. Heat Fluid Flow
,
50
, pp.
402
416
.
98.
Stoessel
,
L.
, and
Nilsson
,
H.
,
2015
, “
Steady and Unsteady Numerical Simulations of the Flow in the Tokke Francis Turbine Model, at Three Operating Conditions
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012011
.
99.
Wallimann
,
H.
, and
Neubauer
,
R.
,
2015
, “
Numerical Study of a High Head Francis Turbine With Measurements From the Francis-99 Project
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012003
.
100.
Côté
,
P.
,
Dumas
,
G.
,
Moisan
,
E.
, and
Boutet-Blais
,
G.
,
2014
, “
Numerical Investigation of the Flow Behavior Into a Francis Runner During Load Rejection
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
11
.
101.
Hosseinimanesh
,
H.
,
Vu
,
T. C.
,
Devals
,
C.
,
Nennemann
,
B.
, and
Guibault
,
F.
,
2014
, “
A Steady-State Simulation Methodology for Predicting Runaway Speed in Francis Turbines
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
22
(
3
), p.
032027
.
102.
Amstutz
,
O.
,
Aakti
,
B.
,
Casartelli
,
E.
,
Mangani
,
L.
, and
Hanimann
,
L.
,
2015
, “
Predicting the Performance of a High Head Francis Turbine Using a Fully Implicit Mixing Plane
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012009
.
103.
Buron
,
J. D.
,
Houde
,
S.
,
Lestriez
,
R.
, and
Deschênes
,
C.
,
2015
, “
Application of the Non-Linear Harmonic Method to Study the Rotor-Stator Interaction in Francis-99 Test Case
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012013
.
104.
Nicolle
,
J.
, and
Cupillard
,
S.
,
2015
, “
Prediction of Dynamic Blade Loading of the Francis-99 Turbine
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012001
.
105.
ANSYS
,
2015
,
Ansys 16.0 Release Documentation, Theory and Modelling Guide
,
ANSYS, Inc.
,
Canonsburg, PA
.
106.
Shur
,
M. L.
,
Spalart
,
P. R.
,
Strelets
,
M. K.
, and
Travin
,
A. K.
,
2008
, “
A Hybrid RANS-LES Approach With Delayed-DES and Wall-Modelled LES Capabilities
,”
Int. J. Heat Fluid Flow
,
29
(
6
), pp.
1638
1649
.
107.
Sagaut
,
P.
,
2002
,
Large Eddy Simulation for Incompressible Flows: An Introduction
,
Springer-Verlag
,
Berlin, Germany
.
108.
Su
,
W.
,
Li
,
X.
,
Li
,
F.
,
Han
,
W.
,
Wei
,
X.
, and
Guo
,
J.
,
2013
, “
Large Eddy Simulation of Pressure Fluctuations at Off-Design Condition in a Francis Turbine Based on Cavitation Model
,”
IOP Conference Series: Materials Science and Engineering, 6th International Conference on Pumps and Fans With Compressors and Wind Turbines
,
IOP
Publishing, UK, p.
022032
.
109.
Spalart
,
P. R.
,
2001
, “
Young-Person's Guide to Detached-Eddy Simulation Grids
,” Langley Research Center, Hampton, VA,
Report No. NASA/CR-2001-21 1032
.
110.
Čelič
,
D.
, and
Ondráčka
,
H.
,
2015
, “
The Influence of Disc Friction Losses and Labyrinth Losses on Efficiency of High Head Francis Turbine
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012007
.
111.
Trivedi
,
C.
,
Cervantes
,
M.
,
Gandhi
,
B.
, and
Dahlhaug
,
O. G.
,
2013
, “
Experimental and Numerical Studies for a High Head Francis Turbine at Several Operating Points
,”
ASME J. Fluids Eng.
,
135
(
11
), p. 111102.
112.
Li
,
Z. J.
,
Wang
,
Z. W.
, and
Bi
,
H. L.
,
2014
, “
Numerical Study of Similarity in Prototype and Model Pumped Turbines
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
10
.
113.
Lenarcic
,
M.
,
Eichhorn
,
M.
,
Schoder
,
S. J.
, and
Bauer
,
C.
,
2015
, “
Numerical Investigation of a High Head Francis Turbine Under Steady Operating Conditions Using Foam-Extend
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012008
.
114.
Wu
,
Y.
,
Liu
,
S.
,
Wu
,
X.
,
Dou
,
H.
,
Zhang
,
L.
, and
Tao
,
X.
,
2010
, “
Turbulent Flow Computation Through a Model Francis Turbine and Its Performance Prediction
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012004
.
115.
Wang
,
Z. W.
, and
Zhou
,
L. J.
,
2006
, “
Simulations and Measurements of Pressure Oscillations Caused by Vortex Ropes
,”
ASME J. Fluids Eng.
,
128
(
4
), pp.
649
655
.
116.
Magnoli
,
M. V.
,
2014
, “
Numerical Simulation of Pressure Oscillations in Large Francis Turbines at Partial and Full Load Operating Conditions and Their Effects on the Runner Structural Behaviour and Fatigue Life
,” Ph.D. thesis, Technische Universitat Munchen, Munchen, Germany.
117.
Magnoli
,
M. V.
, and
Maiwald
,
M.
,
2014
, “
Influence of Hydraulic Design on Stability and on Pressure Pulsations in Francis Turbines at Overload, Part Load and Deep Part Load Based on Numerical Simulations and Experimental Model Test Results
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, pp.
1
8
.
118.
Yexiang
,
X.
,
Zhengwei
,
W.
,
Zongguo
,
Y.
,
Mingan
,
L.
,
Ming
,
X.
, and
Dingyou
,
L.
,
2010
, “
Numerical Analysis of Unsteady Flow Under High-Head Operating Conditions in Francis Turbine
,”
Eng. Comput.
,
27
(
3
), pp.
365
386
.
119.
Vu
,
T.
,
Devals
,
C.
,
Disciullo
,
J.
,
Iepan
,
H.
,
Zhang
,
Y.
, and
Guibault
,
F.
,
2012
, “
CFD Methodology for Desynchronized Guide Vane Torque Prediction and Validation With Experimental Data
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
062004
.
120.
Huth
,
H.-J.
,
2005
, “
Fatigue Design of Hydraulic Turbine Runners
,”
Ph.D. thesis
, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.
121.
Lais
,
S.
,
Liang
,
Q.
,
Henggeler
,
U.
,
Weiss
,
T.
,
Escaler
,
X.
, and
Egusquiza
,
E.
,
2009
, “
Dynamic Analysis of Francis Runners-Experiment and Numerical Simulation
,”
Int. J. Fluid Mach. Syst.
,
2
(
4
), pp.
303
314
.
122.
Seidel
,
U.
,
Mende
,
C.
,
Hübner
,
B.
,
Weber
,
W.
, and
Otto
,
A.
,
2014
, “
Dynamic Loads in Francis Runners and Their Impact on Fatigue Life
,”
IOP Conf. Ser. Earth Env. Sci.
,
22
, p.
032054
.
123.
Mauri
,
S.
,
Kueny
,
J. L.
, and
Avellan
,
F.
,
2004
, “
Werlé–Legendre Separation in a Hydraulic Machine Draft Tube
,”
ASME J. Fluids Eng.
,
126
(
6
), pp.
976
980
.
124.
Dörfler
,
P.
,
Keller
,
M.
, and
Braun
,
O.
,
2010
, “
Francis Full-Load Surge Mechanism Identified by Unsteady 2-Phase CFD
,” IOP Conference Series: Earth and Environmental Science, 25th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
012026
.
125.
Antonsen
,
Ø.
,
2007
, “
Unsteady Flow in Wicket Gate and Runner With Focus on Static and Dynamic Load on Runner
,”
Ph.D. thesis
, Norwegian University of Science and Technology, Trondheim, Norway.
126.
Lewis
,
B.
,
Cimbala
,
J.
, and
Wouden
,
A.
,
2012
, “
Investigation of Distributor Vane Jets to Decrease the Unsteady Load on Hydro Turbine Runner Blades
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machineryand Systems
, IOP Publishing, UK, p.
022006
.
127.
Nishi
,
M.
,
Wang
,
X. M.
,
Yoshida
,
K.
,
Takahashi
,
T.
, and
Tsukamoto
,
T.
,
1996
, “
An Experimental Study on Fins, Their Role in Control of the Draft Tube Surging
,”
Hydraulic Machinery and Cavitation
,
Springer
,
Dordrecht
,
The Netherlands
, pp.
905
914
.
128.
Francke
,
H. H.
,
2010
, “
Increasing Hydro Turbine Operation Range and Efficiencies Using Water Injection in Draft Tubes
,”
Ph.D. thesis
, Norwegian University of Science and Technology, Trondheim, Norway.
129.
Melot
,
M.
,
Nennemann
,
B.
, and
Désy
,
N.
,
2014
, “
Draft Tube Pressure Pulsation Predictions in Francis Turbines With Transient Computational Fluid Dynamics Methodology
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
9
.
130.
Nicolet
,
C.
,
Arpe
,
J.
, and
Avellan
,
F.
,
2004
, “
Identification and Modeling of Pressure Fluctuations of a Francis Turbine Scale Model at Part Load Operation
,” 22nd
IAHR
Symposium on Hydraulic Machinery and Systems
, Stockholm, Sweden, June 29–July2, p.
14
.
131.
Brekke
,
H.
,
1996
, “
Analysis of Losses in Hydraulic Turbines
,”
Hydraulic Machinery and Cavitation
,
E.
Cabrera
,
V.
Espert
, and
F.
Martínez
, eds.,
Springer
,
Dordrecht
,
The Netherlands
, pp.
294
303
.
132.
Padhy
,
M. K.
, and
Saini
,
R. P.
,
2008
, “
A Review on Silt Erosion in Hydro Turbines
,”
Renewable Sustainable Energy Rev.
,
12
(
7
), pp.
1974
1987
.
133.
Liu
,
X.
,
Luo
,
Y.
,
Karney
,
B. W.
, and
Wang
,
W.
,
2015
, “
A Selected Literature Review of Efficiency Improvements in Hydraulic Turbines
,”
Renewable Sustainable Energy Rev.
,
51
, pp.
18
28
.
134.
Thapa
,
B. S.
,
Thapa
,
B.
, and
Dahlhaug
,
O. G.
,
2012
, “
Empirical Modelling of Sediment Erosion in Francis Turbines
,”
Energy
,
41
(
1
), pp.
386
391
.
135.
Mössinger
,
P.
,
Jester-Zürker
,
R.
, and
Jung
,
A.
,
2015
, “
Investigation of Different Simulation Approaches on a High-Head Francis Turbine and Comparison With Model Test Data: Francis-99
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012005
.
136.
Zhao
,
W.
,
2012
, “
Investigation of Seal Technology for Francis Turbines
,”
Ph.D. thesis
, Norwegian University of Science and Technology, Trondheim, Norway.
137.
Erdos
,
J. I.
,
Alzner
,
E.
, and
Mcnally
,
W.
,
1977
, “
Numerical-Solution of Periodic Transonic Flow Through a Fan Stage
,”
AIAA J.
,
15
(
11
), pp.
1559
1568
.
138.
He
,
L.
,
1992
, “
Method of Simulating Unsteady Turbomachinery Flows With Multiple Perturbations
,”
AIAA J.
,
30
(
11
), pp.
2730
2735
.
139.
Biesinger
,
T.
,
Cornelius
,
C.
,
Rube
,
C.
,
Braune
,
A.
,
Campregher
,
R.
,
Godin
,
P. G.
,
Schmid
,
G.
, and
Zori
,
L.
,
2010
, “
Unsteady CFD Methods in a Commercial Solver for Turbomachinery Applications
,”
ASME
Paper No. GT2010-22762.
140.
He
,
L.
,
2010
, “
Fourier Methods for Turbomachinery Applications
,”
Prog. Aerosp. Sci.
,
46
(
8
), pp.
329
341
.
141.
Blumenthal
,
R.
,
Hutchinson
,
B.
, and
Zori
,
L.
,
2011
, “
Investigation of Transient CFD Methods Applied to a Transonic Compressor Stage
,”
ASME
Paper No. GT2011-46635.
142.
Connell
,
S.
,
Braaten
,
M.
,
Zori
,
L.
,
Steed
,
R.
,
Hutchinson
,
B.
, and
Cox
,
G.
,
2011
, “
A Comparison of Advanced Numerical Techniques to Model Transient Flow in Turbomachinery Blade Rows
,”
ASME
Paper No. GT2011-45820.
143.
Connel
,
S.
,
Hutchinson
,
B.
,
Galpin
,
P.
,
Campregher
,
R.
, and
Godin
,
P.
,
2012
, “
The Efficient Computation of Transient Flow in Turbine Blade Rows Using Transformation Methods
,”
ASME
Paper No. GT2012-69019.
144.
Qizar
,
M. A.
,
Mansour
,
M. L.
, and
Goswami
,
S.
,
2013
, “
Study of Steady State and Transient Blade Row CFD Methods in a Moderately Loaded Nasa Transonic High-Speed Axial Compressor Stage
,”
ASME
Paper No. GT2013-94739.
145.
Vilmin
,
S.
,
Lorrain
,
E.
,
Hirsch
,
C.
, and
Swoboda
,
M.
,
2006
, “
Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Nonlinear Harmonic Method
,”
ASME
Paper No. GT2006-90210.
146.
Nicolle
,
J.
,
Giroux
,
A. M.
, and
Morissette
,
J. F.
,
2014
, “
CFD Configurations for Hydraulic Turbine Startup
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
10
.
147.
Deschênes
,
C.
,
Fraser
,
R.
, and
Fau
,
J.-P.
,
2002
, “
New Trends in Turbine Modelling and New Ways of Partnership
,”
IGHEM
, Toronto, ON, Canada, pp.
1
12
.
148.
Nilsson
,
O.
, and
Sjelvgren
,
D.
,
1997
, “
Hydro Unit Start-Up Costs and Their Impact on the Short Term Scheduling Strategies of Swedish Power Producers
,”
IEEE Trans. Power Syst.
,
12
(
1
), pp.
38
44
.
149.
Bjorkvoll
,
T.
, and
Bakken
,
B. H.
,
2002
, “
Calculating the Start-Up Costs of Hydropower Generators
,”
14th Power Systems Computation Conference
(
PSCC
), Seville, Spain, June 24–28, p.
7
.
150.
Pejovic
,
S.
, and
Karney
,
B.
,
2014
, “
Guidelines for Transients are in Need of Revision
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
11
.
151.
Trivedi
,
C.
,
2014
, “
Investigations of Transient Pressure Loading on a High Head Francis Turbine
,”
Ph.D. thesis
, Luleå University of Technology, Luleå, Sweden.
152.
Trivedi
,
C.
,
Cervantes
,
M.
,
Gandhi
,
B.
, and
Dahlhaug
,
O.
,
2014
, “
Experimental Investigations of Transient Pressure Variations in a High Head Model Francis Turbine During Start-Up and Shutdown
,”
J. Hydrodyn.
,
26
(
2
), pp.
277
290
.
153.
Trivedi
,
C.
,
Cervantes
,
M.
,
Gandhi
,
B.
, and
Dahlhaug
,
O.
,
2014
, “
Transient Pressure Measurements on a High Head Model Francis Turbine During Emergency Shutdown, Total Load Rejection, and Runaway
,”
ASME J. Fluids Eng.
,
136
(
12
), p.
121107
.
154.
Gagnon
,
M.
,
Jobidon
,
N.
,
Lawrence
,
M.
, and
Larouche
,
D.
,
2014
, “
Optimization of Turbine Startup: Some Experimental Results From a Propeller Runner
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
7
.
155.
Bucur
,
D. M.
,
Dunca
,
G.
,
Cervantes
,
M. J.
,
Călinoiu
,
C.
, and
Isbăşoiu
,
E. C.
,
2014
, “
Simultaneous Transient Operation of a High Head Hydro Power Plant and a Storage Pumping Station in the Same Hydraulic Scheme
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems
, p.
8
.
156.
Coutu
,
A.
,
Lauzon
,
J.
,
Monette
,
C.
,
Nennemann
,
B.
, and
Huang
,
X.
,
2013
, “
Francis Runner: Cost of Operation, Presentation
,”
5th IAHR International Workshop on Cavitation and Dynamic Problems in Hydraulic Machinery
, p.
12
.
157.
Melot
,
M.
,
Monette
,
C.
,
Coutu
,
A.
, and
Nenneman
,
B.
,
2013
, “
Speed-No-Load Operating Condition: A New Standard Francis Runner Design Procedure to Predict Static Stresses
,”
Hydro 2013
, p.
8
.
158.
Nennemann
,
B.
,
Morissette
,
J. F.
,
Chamberland-Lauzon
,
J.
,
Monette
,
C.
,
Braun
,
O.
,
Melot
,
M.
,
Coutu
,
A.
,
Nicolle
,
J.
, and
Giroux
,
A. M.
,
2014
, “
Challenges in Dynamic Pressure and Stress Predictions at No-Load Operation in Hydraulic Turbines
,” 27th
IAHR
Symposium Hydraulic Machinery and Systems,
p.
10
.
159.
Trivedi
,
C.
,
Gandhi
,
B.
,
Cervantes
,
M.
, and
Dahlhaug
,
O.
,
2015
, “
Experimental Investigations of a Model Francis Turbine During Shutdown at Synchronous Speed
,”
Renewable Energy
,
83
(0), pp.
828
836
.
160.
Kolšek
,
T.
,
Duhovnik
,
J.
, and
Bergant
,
A.
,
2006
, “
Simulation of Unsteady Flow and Runner Rotation During Shut-Down of an Axial Water Turbine
,”
J. Hydraul. Res.
,
44
(
1
), pp.
129
137
.
161.
Nicolle
,
J.
,
Morissette
,
J.
, and
Giroux
,
A.
,
2012
, “
Transient CFD Simulation of a Francis Turbine Startup
,” IOP Conference Series: Earth and Environmental Science, 26th
IAHR
Symposium on Hydraulic Machinery and Systems
, IOP Publishing, UK, p.
062014
.
You do not currently have access to this content.