Computational fluid dynamic (CFD) techniques have played a significant role in improving the efficiency of the hydraulic turbines. To achieve safe and reliable design, numerical results should be trustworthy and free from any suspicion. Proper verification and validation (V&V) are vital to obtain credible results. In this work, first we present verification of a numerical model, Francis turbine, using different approaches to ensure minimum discretization errors and proper convergence. Then, we present detailed validation of the numerical model. Two operating conditions, best efficiency point (BEP) (100% load) and part load (67.2% load), are selected for the study. Turbine head, power, efficiency, and local pressure are used for validation. The pressure data are validated in time- and frequency-domains at sensitive locations in the turbine. We also investigated the different boundary conditions, turbulence intensity, and time-steps. The results showed that, while assessing the convergence history, convergence of local pressure/velocity in the turbine is important in addition to the mass and momentum parameters. Furthermore, error in hydraulic efficiency can be misleading, and effort should make to determine the errors in torque, head, and flow rate separately. The total error is 9.82% at critical locations in the turbine. The paper describes a customized V&V approach for the turbines that will help users to determine total error and to establish credibility of numerical models within hydraulic turbines.

References

References
1.
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
.
2.
Dörfler
,
P.
,
Sick
,
M.
, and
Coutu
,
A.
,
2013
,
Flow-Induced Pulsation and Vibration in Hydroelectric Machinery
,
Springer-Verlag
,
London
.
3.
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
.
4.
Li
,
D.
,
Gong
,
R.
,
Wang
,
H.
,
Wei
,
X.
,
Liu
,
Z.
, and
Qin
,
D.
,
2015
, “
Numerical Investigation on Transient Flow of a High Head Low Specific Speed Pump-Turbine in Pump Mode
,”
J. Renewable Sustainable Energy
,
7
(
6
), p. 063111.
5.
Keck
,
H.
, and
Sick
,
M.
,
2008
, “
Thirty Years of Numerical Flow Simulation in Hydraulic Turbomachines
,”
Acta Mech.
,
201
(
1–4
), pp.
211
229
.
6.
Nennemann
,
B.
,
Vu
,
T. C.
, and
Farhat
,
M.
,
2005
, “
CFD Prediction of Unsteady Wicket Gate-Runner Interaction in Francis Turbines: A New Standard Hydraulic Design Procedure
,”
International Conference and Exhibition
(
HYDRO
), Villach, Austria, Oct. 17–20, p.
9
.https://www.researchgate.net/publication/37439188_CFD_prediction_of_unsteady_wicket_gate-runner_interaction_in_Francis_turbines_A_new_standard_hydraulic_design_procedure
7.
Thapa
,
B. S.
,
Trivedi
,
C.
, and
Dahlhaug
,
O. G.
,
2015
, “
Design and Development of Guide Vane Cascade for a High Head Francis Turbine
,”
J. Hydrodyn., Ser. B
,
28
(
4
), pp.
676
689
.
8.
Risberg
,
S.
,
Jonassen
,
M.
, and
Jonassen
,
R.
,
2008
, “
Design of Francis Turbine Runners Based on a Surrogate Model Approach
,”
Int. J. Hydropower Dams
,
15
(
5
), p.
11
.
9.
Kawajiri
,
H.
,
Enomoto
,
Y.
, and
Kurosawa
,
S.
,
2014
, “
Design Optimization Method for Francis Turbine
,”
27th IAHR Symposium Hydraulic Machinery and Systems
, Montreal, QC, Canada, Sept. 22–26, p.
8
.
10.
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
.
11.
Enomoto
,
Y.
,
Kurosawa
,
S.
, and
Kawajiri
,
H.
,
2012
, “
Design Optimization of a High Specific Speed Francis Turbine Runner
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
15
(
3
), p.
032010
.
12.
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
.
13.
Thum
,
S.
, and
Schilling
,
R.
,
2005
, “
Optimization of Hydraulic Machinery Bladings by Multilevel CFD Techniques
,”
Int. J. Rotating Mach.
,
2
, pp.
161
167
.
14.
Flores
,
E.
,
Bornard
,
L.
,
Tomas
,
L.
,
Liu
,
J.
, and
Couston
,
M.
,
2012
, “
Design of Large Francis Turbine Using Optimal Methods
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
15
(
2
), p.
022023
.
15.
Kurosawa
,
S.
,
Lim
,
S.
, and
Enomoto
,
Y.
,
2010
, “
Virtual Model Test for a Francis Turbine
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(
1
), p.
012063
.
16.
Oberkampf
,
W. L.
, and
Barone
,
M. F.
,
2006
, “
Measures of Agreement Between Computation and Experiment: Validation Metrics
,”
J. Comput. Phys.
,
217
(
1
), pp.
5
36
.
17.
Oberkampf
,
W.
,
2001
, “
What are Validation Experiments?
,”
Exp. Tech.
,
25
(
3
), pp.
35
40
.
18.
Trucano
,
T. G.
,
Swiler
,
L. P.
,
Igusa
,
T.
,
Oberkampf
,
W. L.
, and
Pilch
,
M.
,
2006
, “
Calibration, Validation, and Sensitivity Analysis: What's What
,”
Reliab. Eng. Syst. Saf.
,
91
(
10
), pp.
1331
1357
.
19.
Stern
,
F.
,
Wilson
,
R. V.
,
Coleman
,
H. W.
, and
Paterson
,
E. G.
,
2001
, “
Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures
,”
ASME J. Fluids Eng.
,
123
(
4
), pp.
793
802
.
20.
Wilson
,
R. V.
,
Stern
,
F.
,
Coleman
,
H. W.
, and
Paterson
,
E. G.
,
2001
, “
Comprehensive Approach to Verification and Validation of CFD Simulations—Part 2: Application for RANS Simulation of a Cargo/Container Ship
,”
ASME J. Fluids Eng.
,
123
(
4
), pp.
803
810
.
21.
Mehta
,
U. B.
,
1998
, “
Credible Computational Fluid Dynamics Simulations
,”
AIAA J.
,
36
(
5
), pp.
665
667
.
22.
Oberkampf
,
W. L.
,
DeLand
,
S. M.
,
Rutherford
,
B. M.
,
Diegert
,
K. V.
, and
Alvin
,
K. F.
,
2002
, “
Error and Uncertainty in Modeling and Simulation
,”
Reliab. Eng. Syst. Saf.
,
75
(
3
), pp.
333
357
.
23.
Trivedi
,
C.
,
Cervantes
,
M. J.
, and
Dahlhaug
,
O. G.
,
2016
, “
Numerical Techniques Applied to Hydraulic Turbines: A Perspective Review
,”
ASME Appl. Mech. Rev.
,
68
(
1
), p.
010802
.
24.
Aeschliman
,
D. P.
, and
Oberkampf
,
W. L.
,
1998
, “
Experimental Methodology for Computational Fluid Dynamics Code Validation
,”
AIAA J.
,
36
(
5
), pp.
733
741
.
25.
Roache
,
P. J.
,
1997
, “
Quantification of Uncertainty in Computational Fluid Dynamics
,”
Annu. Rev. Fluid Mech.
,
29
(
1
), pp.
123
160
.
26.
Stern
,
F.
,
Wilson
,
R.
, and
Shao
,
J.
,
2006
, “
Quantitative V&V of CFD Simulations and Certification of CFD Codes
,”
Int. J. Numer. Methods Fluids
,
50
(
11
), pp.
1335
1355
..
27.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
, and
Freitas
,
C. J.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.
28.
Roy
,
C. J.
, and
Oberkampf
,
W. L.
,
2011
, “
A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
25–28
), pp.
2131
2144
.
29.
Cervantes
,
M. J.
,
Trivedi
,
C.
,
Dahlhaug
,
O. G.
, and
Nielsen
,
T.
,
2015
, “
Francis-99 Workshop 1: Steady Operation of Francis Turbines
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
011001
.
30.
Cervantes
,
M. J.
,
Trivedi
,
C.
,
Dahlhaug
,
O. G.
, and
Nielsen
,
T.
,
2017
, “
Francis-99 Workshop 2: Transient Operation of Francis Turbines
,”
J. Phys.: Conf. Ser.
,
782
(
1
), p.
011001
.
31.
Cervantes
,
M. J.
,
Engström
,
T. F.
, and
Gustavsson
,
L. H.
,
2005
, “
Turbine-99 III
,”
Third IAHR/ERCOFTAC Workshop on Draft Tube Flows
, Porjus, Sweden, Dec. 7–9, p.
198
.
32.
Javadi
,
A.
, and
Nilsson
,
H.
,
2015
, “
Time-Accurate Numerical Simulations of Swirling Flow With Rotor-Stator Interaction
,”
Flow, Turbul. Combust.
,
95
(
4
), pp.
1
20
.
33.
Gerolymos
,
G. A.
,
Neubauer
,
J.
,
Sharma
,
V. C.
, and
Vallet
,
I.
,
2001
, “
Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model
,”
ASME J. Turbomach.
,
124
(
1
), pp.
86
99
.
34.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2015
, “
Unsteady Numerical Simulation of Flow in Draft Tube of a Hydroturbine Operating Under Various Conditions Using a Partially-Averaged Navier-Stokes Model
,”
ASME J. Fluids Eng.
,
137
(6), p.
061101
.
35.
Minakov
,
A. V.
,
Platonov
,
D. V.
,
Dekterev
,
A. A.
,
Sentyabov
,
A. V.
, and
Zakharov
,
A. V.
,
2015
, “
The Numerical Simulation of Low Frequency Pressure Pulsations in the High-Head Francis Turbine
,”
Comput. Fluids
,
111
, pp.
197
205
.
36.
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
.
37.
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
.
38.
Cervantes
,
M.
,
Andersson
,
U.
, and
Lövgren
,
H.
,
2010
, “
Turbine-99 Unsteady Simulations–Validation
,”
IOP Conf. Ser.: Earth and Environ. Sci.
,
12
, p.
012014
.
39.
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.https://www.researchgate.net/publication/283563238_Hydrodynamics_of_a_Pump-Turbine_Operating_at_Off-Design_Conditions_in_Generating_Mode
40.
Yan
,
J.
,
Koutnik
,
J.
,
Seidel
,
U.
, and
Huebner
,
B.
,
2010
, “
Compressible Simulation of Rotor-Stator Interaction in Pump-Turbines
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(
1
), p.
012008
.
41.
Trivedi
,
C.
,
Cervantes
,
M. J.
, and
Gandhi
,
B. K.
,
2016
, “
Numerical Investigation and Validation of a Francis Turbine at Runaway Operating Conditions
,”
Energies
,
9
(
3
), p.
22
.
42.
Trivedi
,
C.
,
Cervantes
,
M.
, and
Dahlhaug
,
O. G.
,
2016
, “
Experimental and Numerical Studies of a High-Head Francis Turbine: A Review of the Francis-99 Test Case
,”
Energies
,
9
(
2
), p.
24
.
43.
Li
,
Z.
,
Bi
,
H.
,
Wang
,
Z.
, and
Yao
,
Z.
,
2016
, “
Three-Dimensional Simulation of Unsteady Flows in a Pump-Turbine During Start-Up Transient Up to Speed No-Load Condition in Generating Mode
,”
Proc. Inst. Mech. Eng., Part A
,
230
(
6
), pp.
570
585
.
44.
IEC,
1999
, “
Hydraulic Turbines, Storage Pumps and Pump-Turbines: Model Acceptance Tests
,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 60193.
45.
IEC
,
1991
, “
Field Acceptance Tests to Determine the Hydraulic Performance of Hydraulic Turbines, Storage Pumps and Pump-Turbines
,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 41.
46.
IEC
,
1991
, “
Guide for Field Measurement of Vibrations and Pulsations in Hydraulic Machines (Turbines, Storage Pumps and Pump-Turbines)
,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 994.
47.
IEC
,
2010
, “
Hydraulic Machines—Acceptance Tests of Small Hydroelectric Installations
,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 62006.
48.
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
.
49.
Iliescu
,
M. S.
,
Ciocan
,
G. D.
, and
Avellan
,
F.
,
2008
, “
Analysis of the Cavitating Draft Tube Vortex in a Francis Turbine Using Particle Image Velocimetry Measurements in Two-Phase Flow
,”
ASME J. Fluids Eng.
,
130
(
2
), p.
021105
.
50.
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/Fluids
,
42
, pp.
121
128
.
51.
Duquesne
,
P.
,
Maciel
,
Y.
,
Ciocan
,
G. D.
, and
Deschênes
,
C.
,
2014
, “
Flow Separation in a Straight Draft Tube, Particle Image Velocimetry
,”
27th IAHR Symposium Hydraulic Machinery and Systems
, Montreal, QC, Canada, Sept. 22–26, p.
10
.
52.
ISA
,
2002
, “
A Guide for the Dynamic Calibration of Pressure Transducers
,” International Society of Automation, Durham, NC, Standard No. ISA-37.
53.
Yan
,
Z. G.
,
Zhou
,
L. J.
, and
Wang
,
Z. W.
,
2012
, “
Turbine Efficiency Test on a Large Hydraulic Turbine Unit
,”
Sci. China-Technol. Sci.
,
55
(
8
), pp.
2199
2205
.
54.
Gordon
,
J. L.
,
2001
, “
Hydraulic Turbine Efficiency
,”
Can. J. Civ. Eng.
,
28
(
2
), pp.
238
253
.
55.
ASME,
2009
, “
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
,” American Society of Mechanical Engineers, New York, Standard No. V V 20-2009.
56.
AIAA
,
1998
,
Guide for the Verification and Validation of Computational Fluid Dynamics Simulations
,
American Institute of Aeronautics and Astronautics
,
Reston, VA
, Standard No. AIAA G-077.
57.
Goyal
,
R.
,
Cervantes
,
M. J.
, and
Gandhi
,
B. K.
,
2017
, “
Vortex Rope Formation in a High Head Model Francis Turbine
,”
ASME J. Fluids Eng.
,
139
(
3
), p.
041102
.
58.
ANSYS
,
2016
, “
Ansys 17.0 Release Documentation, Theory and Modelling Guide
,” ANSYS, Canonsburg, PA.
59.
Kuntz
,
M.
, and
Menter
,
F. R.
,
2006
, “
Contribution of Ansys: Main Achievements in Flomania
,”
Flomania—A European Initiative on Flow Physics Modelling
,
W.
Haase
,
B.
Aupoix
,
U.
Bunge
, and
D.
Schwamborn
, eds.,
Springer
,
Berlin
, pp.
21
28
.
60.
Madenci
,
E.
, and
Guven
,
I.
,
2015
,
The Finite Element Method and Applications in Engineering Using Ansys
,
Springer
,
New York
.
61.
Egorov
,
Y.
, and
Menter
,
F.
,
2008
, “
Development and Application of SST-SAS Turbulence Model in the Desider Project
,”
Advances in Hybrid RANS-LES Modelling
,
S.-H.
Peng
, and
W.
Hasse
, eds.,
Springer
,
Berlin
pp.
261
270
.
62.
Menter
,
F. R.
, and
Egorov
,
Y.
,
2006
, “
SAS Turbulence Modelling of Technical Flows
,”
Direct and Large-Eddy Simulation VI
,
E.
Lamballais
,
R.
Friedrich
,
B.
Geurts
, and
O.
Métais
, eds.,
Springer
,
Dordrecht, The Netherlands
, pp.
687
694
.
63.
Langtry
,
R.
, and
Menter
,
F.
,
2005
, “
Transition Modeling for General CFD Applications in Aeronautics
,”
AIAA
Paper No. 2005-522.
64.
Younsi
,
M.
,
Djerrada
,
A.
,
Belamri
,
T.
, and
Menter
,
F.
,
2008
, “
Application of the SAS Turbulence Model to Predict the Unsteady Flow Field Behaviour in a Forward Centrifugal Fan
,”
Int. J. Comput. Fluid Dyn.
,
22
(
9
), pp.
639
648
.
65.
Nicolle
,
J.
, and
Cupillard
,
S.
,
2015
, “
Prediction of Dynamic Blade Loading of the Francis-99 Turbine
,”
J. Phys.: Conf. Ser.
,
579
(
1
), p.
012001
.
66.
Menter
,
F. R.
,
2009
, “
Review of the Shear-Stress Transport Turbulence Model Experience From an Industrial Perspective
,”
Int. J. Comput. Fluid Dyn.
,
23
(
4
), pp.
305
316
.
67.
Smirnov
,
P. E.
, and
Menter
,
F. R.
,
2009
, “
Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term
,”
ASME J. Turbomach.
,
131
(
4
), p.
041010
.
68.
Egorov
,
Y.
,
Menter
,
F. R.
,
Lechner
,
R.
, and
Cokljat
,
D.
,
2010
, “
The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions—Part 2: Application to Complex Flows
,”
Flow, Turbul. Combust.
,
85
(
1
), pp.
139
165
.
69.
Menter
,
F. R.
, and
Egorov
,
Y.
,
2010
, “
The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions—Part 1: Theory and Model Description
,”
Flow, Turbul. Combust.
,
85
(
1
), pp.
113
138
.
70.
Menter
,
F.
,
Schutze
,
J.
, and
Kurbatskii
,
A.
,
2011
, “
Scale-Resolving Simulation Techniques in Industrial CFD
,”
AIAA
Paper No. 2011-3474.
71.
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 Conf. Ser.: Mater. Sci. Eng.
,
52
(
2
), p.
022032
.
72.
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
.
73.
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
.
74.
Li
,
Z.-R.
,
Pourquie
,
M.
, and
van Terwisga
,
T.
,
2014
, “
Assessment of Cavitation Erosion With a URANS Method
,”
ASME J. Fluids Eng.
,
136
(
4
), p.
041101
.
75.
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
.
76.
Hosseinimanesh
,
H.
,
Devals
,
C.
,
Nennemann
,
B.
,
Reggio
,
M.
, and
Guibault
,
F.
,
2016
, “
A Numerical Study of Francis Turbine Operation at No-Load Condition
,”
ASME J. Fluids Eng.
,
139
(
1
), p.
011104
.
77.
Oberkampf
,
W. L.
, and
Roy
,
C. J.
,
2010
,
Verification and Validation in Scientific Computing
,
Cambridge University Press
,
Cambridge, UK
.
78.
Roache
,
P. J.
,
1998
,
Verification and Validation in Computational Science and Engineering
,
Hermosa Publishers
,
Socorro, NM
.
79.
Roache
,
P. J.
,
2009
, “
Perspective: Validation—What Does It Mean?
,”
ASME J. Fluids Eng.
,
131
(
3
), p.
034503
.
80.
Javadi
,
A.
,
Bosioc
,
A.
,
Nilsson
,
H.
,
Muntean
,
S.
, and
Susan-Resiga
,
R.
,
2016
, “
Experimental and Numerical Investigation of the Precessing Helical Vortex in a Conical Diffuser, With Rotor-Stator Interaction
,”
ASME J. Fluids Eng.
,
138
(
8
), p.
081106
.
81.
Qian
,
R.
,
2008
, “
Flow Field Measurements in a Stator of a Hydraulic Turbine
,” Ph.D. thesis, Laval University, Laval, Canada.
82.
Eça
,
L.
, and
Hoekstra
,
M.
,
2014
, “
A Procedure for the Estimation of the Numerical Uncertainty of CFD Calculations Based on Grid Refinement Studies
,”
J. Comput. Phys.
,
262
, pp.
104
130
.
83.
Krappel
,
T.
,
Riedelbauch
,
S.
,
Jester-Zuerker
,
R.
,
Jung
,
A.
,
Flurl
,
B.
,
Unger
,
F.
, and
Galpin
,
P.
,
2016
, “
Turbulence Resolving Flow Simulations of a Francis Turbine in Part Load Using Highly Parallel CFD Simulations
,”
28th IAHR Symposium on Hydraulic Machinery and Systems
, Grenoble, France, July 4–8, pp.
1
10
.
84.
Menter
,
F. R.
, and
Egorov
,
Y.
,
2006
, “
Revisiting the Turbulent Scale Equation
,”
IUTAM Symposium on One Hundred Years of Boundary Layer Research
,
G. E. A.
Meier
,
K. R.
Sreenivasan
, and
H. J.
Heinemann
, eds.,
Springer
,
Dordrecht, The Netherlands
, pp.
279
290
.
85.
Dolecek
,
G. J.
,
2013
,
Random Signals and Processes Primer With Matlab
,
Springer
,
New York
.
86.
Engelberg
,
S.
,
2008
,
Digital Signal Processing an Experimental Approach
,
Springer
,
London
.
87.
Trivedi
,
C.
, and
Cervantes
,
M.
,
2017
, “
Fluid Structure Interaction in Hydraulic Turbines: A Perspective Review
,”
Renewable Sustainable Energy Rev.
,
68
(
2
), pp.
87
101
.
88.
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 Conf. Ser.: Earth Environ. Sci.
,
15
(
6
), p.
051401
, p.
062030
.
89.
Zeng
,
W.
,
Yang
,
J.
, and
Guo
,
W.
,
2015
, “
Runaway Instability of Pump-Turbines in S-Shaped Regions Considering Water Compressibility
,”
ASME J. Fluids Eng.
,
137
(
5
), p.
051401
.
90.
Hanjalic
,
K.
,
2005
, “
Will RANS Survive LES? A View of Perspectives
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
831
839
.
91.
Trivedi
,
C.
,
2017
, “
Investigations of Compressible Turbulent Flow in a High Head Francis Turbine
,”
ASME J. Fluids Eng.
,
140
(
1
), p.
011101
.
92.
Trivedi
,
C.
, and
Dahlhaug
,
O. G.
,
2018
, “
Interaction Between Trailing Edge Wake and Vortex Rings in a Francis Turbine at Runaway Condition: Compressible Large Eddy Simulation
,”
Phys. Fluids
,
30
(
7
), p.
075101
.
93.
Trivedi
,
C.
,
2018
, “
Compressible Large Eddy Simulation of a Francis Turbine During Speed-No-Load: Rotor Stator Interaction and Inception of a Vortical Flow
,”
ASME J. Eng. Gas Turbines Power
,
140
(
11
), p.
112601
.
You do not currently have access to this content.