0
Review Article

Numerical Techniques Applied to Hydraulic Turbines: A Perspective Review

[+] Author and Article Information
Chirag Trivedi

Department of Energy and Process Engineering,
Norwegian University of
Science and Technology,
Trondheim NO-7491, Norway
e-mail: chirag.trivedi@ntnu.no

Michel J. Cervantes

Professor
Department of Engineering Sciences and Mathematics,
Luleå University of Technology,
Luleå SE-97187, Sweden;
Department of Energy and Process Engineering,
Norwegian University of
Science and Technology,
Trondheim NO-7491, Norway
e-mail: Michel.Cervantes@ltu.se

Ole Gunnar Dahlhaug

Professor
Department of Energy and Process Engineering,
Norwegian University of
Science and Technology,
Trondheim NO-7491, Norway
e-mail: ole.g.dahlhaug@ntnu.no

1Corresponding author.

Manuscript received April 30, 2015; final manuscript received January 22, 2016; published online February 23, 2016. Assoc. Editor: Gianluca Iaccarino.

Appl. Mech. Rev 68(1), 010802 (Feb 23, 2016) (18 pages) Paper No: AMR-15-1051; doi: 10.1115/1.4032681 History: Received April 30, 2015; Revised January 22, 2016

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Daugherty, R. L. , 1920, Hydraulic Turbines: With a Chapter on Centrifugal Pumps, McGraw-Hill Book Company, New York.
Round, G. F. , 2004, Incompressible Flow Turbomachines Design, Selection, Applications, and Theory, Elsevier-Gulf Professional Publishing, Burlington, MA.
Sawin, J. L. , and Martinot, E. , 2013, “ Renewables 2013 Global Status Report,” Renewable Energy Policy Network for 21st Century, REN21 Secretariat, Paris, France.
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.
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.
Raabe, J. , 1985, Hydro Power: The Design, Use, and Function of Hydromechanical, Hydraulic, and Electrical Equipment, VDI Verlag, Dusseldorf, Germany.
Keck, H. , and Sick, M. , 2008, “ Thirty Years of Numerical Flow Simulation in Hydraulic Turbomachines,” Acta Mech., 201(1–4), pp. 211–229. [CrossRef]
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. [CrossRef]
Dörfler, P. , Sick, M. , and Coutu, A. , 2013, Flow-Induced Pulsation and Vibration in Hydroelectric Machinery, Springer-Verlag, London.
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.
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.
Dean, R. C. , 1959, “ On the Necessity of Unsteady Flow in Fluid Machines,” Trans. ASME, 81(1), pp. 24–28.
Kumar, P. , and Saini, R. P. , 2010, “ Study of Cavitation in Hydro Turbines—A Review,” Renewable Sustainable Energy Rev., 14(1), pp. 374–383. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
IEC 60193, 1999, Hydraulic Turbines, Storage Pumps and Pump-Turbines: Model Acceptance Tests, International Standard, International Electrotechnical Commission, Geneva, Switzerland, p. 578.
Gordon, J. L. , 2001, “ Hydraulic Turbine Efficiency,” Can. J. Civ. Eng., 28(2), pp. 238–253. [CrossRef]
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. [CrossRef]
Yuanfang, H. , Guangning, L. , and Shiying, F. , 2012, Research on Prototype Hydro-Turbine Operation, Foreign Language Press, Beijing, China.
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.
Brekke, H. , 2001, “ State of the Art in Turbine Design,” Congress-International Association for Hydraulic Research, 29th IAHR World Congress, pp. 544–551.
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. [CrossRef]
Osterwalder, J. , 1978, “ Efficiency Scale-Up for Hydraulic Turbo-Machines With Due Consideration of Surface-Roughness,” J. Hydraul. Res., 16(1), pp. 55–76. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
Thum, S. , and Schilling, R. , 2005, “ Optimization of Hydraulic Machinery Bladings by Multilevel CFD Techniques,” Int. J. Rotating Mach., 2005(2), pp. 161–167. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
Kawajiri, H. , Enomoto, Y. , and Kurosawa, S. , 2014, “ Design Optimization Method for Francis Turbine,” 27th IAHR Symposium Hydraulic Machinery and Systems, p. 8.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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.
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.
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.
Mulu, B. , 2012, “ An Experimental and Numerical Investigation of a Kaplan Turbine Model,” Ph.D. thesis, Luleå University of Technology, Luleå, Sweden.
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.
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.
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.
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.
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. [CrossRef]
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.
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. [CrossRef]
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.
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. [CrossRef]
Amiri, K. , 2014, “ An Experimental Investigation of Flow in a Kaplan Runner: Steady-State and Transient,” Licentiate thesis, Luleå Tekniska Universitet, Luleå, Sweden.
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.
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.
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. [CrossRef]
Wu, Y. , Li, S. , Liu, S. , Dou, H.-S. , and Qian, Z. , 2013, Vibration of Hydraulic Machinery, Springer, The Netherlands.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Nicolle, J. , and Cupillard, S. , 2015, “ Prediction of Dynamic Blade Loading of the Francis-99 Turbine,” J. Phys.: Conf. Ser., 579(1), p. 012001. [CrossRef]
ANSYS, 2015, Ansys 16.0 Release Documentation, Theory and Modelling Guide, ANSYS, Inc., Canonsburg, PA.
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. [CrossRef]
Sagaut, P. , 2002, Large Eddy Simulation for Incompressible Flows: An Introduction, Springer-Verlag, Berlin, Germany.
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.
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.
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. [CrossRef]
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.
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.
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
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. [CrossRef]
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.
Huth, H.-J. , 2005, “ Fatigue Design of Hydraulic Turbine Runners,” Ph.D. thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.
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. [CrossRef]
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.
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. [CrossRef]
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.
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.
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.
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.
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.
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
Thapa, B. S. , Thapa, B. , and Dahlhaug, O. G. , 2012, “ Empirical Modelling of Sediment Erosion in Francis Turbines,” Energy, 41(1), pp. 386–391. [CrossRef]
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. [CrossRef]
Zhao, W. , 2012, “ Investigation of Seal Technology for Francis Turbines,” Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway.
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. [CrossRef]
He, L. , 1992, “ Method of Simulating Unsteady Turbomachinery Flows With Multiple Perturbations,” AIAA J., 30(11), pp. 2730–2735. [CrossRef]
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.
He, L. , 2010, “ Fourier Methods for Turbomachinery Applications,” Prog. Aerosp. Sci., 46(8), pp. 329–341. [CrossRef]
Blumenthal, R. , Hutchinson, B. , and Zori, L. , 2011, “ Investigation of Transient CFD Methods Applied to a Transonic Compressor Stage,” ASME Paper No. GT2011-46635.
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.
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.
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.
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.
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.
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.
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. [CrossRef]
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.
Pejovic, S. , and Karney, B. , 2014, “ Guidelines for Transients are in Need of Revision,” 27th IAHR Symposium Hydraulic Machinery and Systems, p. 11.
Trivedi, C. , 2014, “ Investigations of Transient Pressure Loading on a High Head Francis Turbine,” Ph.D. thesis, Luleå University of Technology, Luleå, Sweden.
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. [CrossRef]
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. [CrossRef]
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.
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.
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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.

Figures

Grahic Jump Location
Fig. 1

Modulation process between the runner blades and guide vanes of a hydraulic turbine. (Reproduced with permission from Zobeiri et al. [82]. Copyright 2006 by IAHR.)

Grahic Jump Location
Fig. 2

Constant efficiency hill diagram of a high head model Francis turbine [68]. α is the guide vane angular position in degree, nED is the speed factor, and QED is the discharge factor.

Grahic Jump Location
Fig. 3

Comparison of the experimental and numerical hydraulic efficiencies of a model Francis turbine [68]. ηh is the hydraulic efficiency and Q is the discharge in m3 s−1.

Grahic Jump Location
Fig. 4

Comparison of experimental and numerical amplitude of pressure pulsations developed by the RSIs [85]. VL01 corresponds to the location of pressure measurement in the vaneless space (see Ref. [111]); EXP—experimental, ZLES—zonal LES, BG—medium mesh of 12 × 106 nodes, and NG—fine mesh of 14 × 106 nodes. (Reproduced with permission from Jošt et al. [85]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 5

Pressure variation at the runner downstream of a Kaplan turbine; the oscillations correspond to blade passing frequency; point 29 corresponds to the measurement location below the runner hub [56]

Grahic Jump Location
Fig. 6

Three approaches of a turbine passage modeling. Left-hand side figure shows stay vane, guide vane, blade and splitter, and draft tube [43]. Middle figure shows a complete spiral casing, guide vanes, a blade passage with splitter, and a draft tube. Right-hand side figure shows a blade passage with split, extended runner outlet and a draft tube. (Reproduced with permission from Mössinger et al. [43]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 7

Axial (left) and radial (right) velocity distribution at the runner outlet during BEP operating condition of a model Francis turbine [43]. G1 corresponds to numerical simulation of a complete Francis turbine. G2 corresponds to numerical simulation with a guide vane passage and a blade passage. G3 correspond to numerical simulation with spiral casing, distributor, a blade passage, and a draft tube. G4 corresponds to numerical simulation with spiral casing, distributor, a blade passage with extended outlet, and a draft tube. c0, cax, and cu are the mean, axial, and tangential velocity, respectively. (Reproduced with permission from Mössinger et al. [43]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 8

Comparison of k–ω-based SST and SAS-SST turbulence models used to simulate the draft tube flow during PL operation [104]. Runner revolution from 0 to 60 corresponds to k–ω-based SST model and from 61 to 180 corresponds to SAS-SST model; DT11 and DT21 are the numerical monitoring points under PL operating conditions locations. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 9

Decomposition of the energy spectrum in the solution associated with RANS and LES. (Reproduced with permission from Buntic et al. [70]. Copyright 2005 by Politehnica University of Timisoara, Romania.)

Grahic Jump Location
Fig. 10

Comparison of hydraulic efficiency, head, and torque at the BEP, PL, and HL operating conditions; CC—commercial code, OF—open foam, Exp—experimental, and Exp. corr—experimental data with correction factor [102]. (Reproduced with permission from Amstutz et al. [102]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 11

Head oscillations over the operating range of a Francis turbine; Δγ corresponds to guide vane opening, H is the head. (Reproduced with permission from Magnoli [116]. Copyright 2014 by Marcelo Vinicius Magnoli.)

Grahic Jump Location
Fig. 12

Amplitude of pressure pulsations in a model Francis turbine [68]. Left-hand side figure indicates the amplitude observed at BEP. Right-hand side figure indicates the amplitude observed at HL (full-load instability region). VL01, P42, S51, and P71 are the locations of pressure sensors at vaneless space, blade pressure side, suction side, and trailing edge, respectively. DT11 and DT21 are the sensors located on the wall of the draft tube cone. The frequency is normalized by the runner angular speed.

Grahic Jump Location
Fig. 13

Comparisons of head, discharge, torque, and hydraulic efficiency of a model Francis turbine at PL operating condition [85]. Dark color bar indicates the difference with flow leakage losses based on labyrinth seal modeling. (Reproduced with permission from Jošt et al. [85]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 14

Unsteady pressure variation in the vaneless space (VL01) during PL conditions of a model Francis turbine [68]; t is the time in seconds, n is the runner angular speed in revolution per second, and p̃E is the ratio of absolute amplitude in kPa and density times specific hydraulic energy at the BEP

Grahic Jump Location
Fig. 15

Comparison of flow modeling approaches applied to a Francis turbine. Left-hand side configuration used for Fourier transform, middle configuration used for PT, and right side configuration shows complete turbine [104]. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 16

Variation of the blade and splitter torque in a model Francis turbine at BEP operating condition. PT—profile transform, FT—Fourier transform, and 360—complete turbine modeling [104]. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

Grahic Jump Location
Fig. 17

Closing of the radial flow turbine distributor vanes during load variation and the corresponding change of mesh. Mesh at 88%, 70%, and 30% opening represents the vane position at HL, BEP, and PL during turbine shutdown, respectively.

Grahic Jump Location
Fig. 18

Comparison of blade loading during Francis turbine startup [146]. (Reproduced with permission from Nicolle et al. [146]. Copyright 2014 by IOP Science.)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In