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Research Papers

A Systematic Validation of a Francis Turbine Under Design and Off-Design Loads

[+] Author and Article Information
Chirag Trivedi

Mem. ASME
Waterpower Laboratory,
NTNU—Norwegian University of
Science and Technology,
Trondheim 7491, Norway
e-mail: chirag.trivedi@ntnu.no

Manuscript received May 14, 2017; final manuscript received June 3, 2019; published online June 20, 2019. Assoc. Editor: David Moorcroft.

J. Verif. Valid. Uncert 4(1), 011003 (Jun 20, 2019) (16 pages) Paper No: VVUQ-17-1018; doi: 10.1115/1.4043965 History: Received May 14, 2017; Revised June 03, 2019

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.

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References

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]
Dörfler, P. , Sick, M. , and Coutu, A. , 2013, Flow-Induced Pulsation and Vibration in Hydroelectric Machinery, Springer-Verlag, London.
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]
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.
Keck, H. , and Sick, M. , 2008, “ Thirty Years of Numerical Flow Simulation in Hydraulic Turbomachines,” Acta Mech., 201(1–4), pp. 211–229. [CrossRef]
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
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. [CrossRef]
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.
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.
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]
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.
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]
Thum, S. , and Schilling, R. , 2005, “ Optimization of Hydraulic Machinery Bladings by Multilevel CFD Techniques,” Int. J. Rotating Mach., 2, pp. 161–167. [CrossRef]
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.
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.
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. [CrossRef]
Oberkampf, W. , 2001, “ What are Validation Experiments?,” Exp. Tech., 25(3), pp. 35–40. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Mehta, U. B. , 1998, “ Credible Computational Fluid Dynamics Simulations,” AIAA J., 36(5), pp. 665–667. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Aeschliman, D. P. , and Oberkampf, W. L. , 1998, “ Experimental Methodology for Computational Fluid Dynamics Code Validation,” AIAA J., 36(5), pp. 733–741. [CrossRef]
Roache, P. J. , 1997, “ Quantification of Uncertainty in Computational Fluid Dynamics,” Annu. Rev. Fluid Mech., 29(1), pp. 123–160. [CrossRef]
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.. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [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]
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]
Cervantes, M. , Andersson, U. , and Lövgren, H. , 2010, “ Turbine-99 Unsteady Simulations–Validation,” IOP Conf. Ser.: Earth and Environ. Sci., 12, p. 012014.
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
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
IEC, 1999, “ Hydraulic Turbines, Storage Pumps and Pump-Turbines: Model Acceptance Tests,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 60193.
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.
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.
IEC, 2010, “ Hydraulic Machines—Acceptance Tests of Small Hydroelectric Installations,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. 62006.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
ISA, 2002, “ A Guide for the Dynamic Calibration of Pressure Transducers,” International Society of Automation, Durham, NC, Standard No. ISA-37.
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. [CrossRef]
Gordon, J. L. , 2001, “ Hydraulic Turbine Efficiency,” Can. J. Civ. Eng., 28(2), pp. 238–253. [CrossRef]
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.
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.
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. [CrossRef]
ANSYS, 2016, “ Ansys 17.0 Release Documentation, Theory and Modelling Guide,” ANSYS, Canonsburg, PA.
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.
Madenci, E. , and Guven, I. , 2015, The Finite Element Method and Applications in Engineering Using Ansys, Springer, New York.
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.
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.
Langtry, R. , and Menter, F. , 2005, “ Transition Modeling for General CFD Applications in Aeronautics,” AIAA Paper No. 2005-522.
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. [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]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Menter, F. , Schutze, J. , and Kurbatskii, A. , 2011, “ Scale-Resolving Simulation Techniques in Industrial CFD,” AIAA Paper No. 2011-3474.
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.
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]
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]
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. [CrossRef]
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]
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. [CrossRef]
Oberkampf, W. L. , and Roy, C. J. , 2010, Verification and Validation in Scientific Computing, Cambridge University Press, Cambridge, UK.
Roache, P. J. , 1998, Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Socorro, NM.
Roache, P. J. , 2009, “ Perspective: Validation—What Does It Mean?,” ASME J. Fluids Eng., 131(3), p. 034503. [CrossRef]
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. [CrossRef]
Qian, R. , 2008, “ Flow Field Measurements in a Stator of a Hydraulic Turbine,” Ph.D. thesis, Laval University, Laval, Canada.
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. [CrossRef]
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.
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.
Dolecek, G. J. , 2013, Random Signals and Processes Primer With Matlab, Springer, New York.
Engelberg, S. , 2008, Digital Signal Processing an Experimental Approach, Springer, London.
Trivedi, C. , and Cervantes, M. , 2017, “ Fluid Structure Interaction in Hydraulic Turbines: A Perspective Review,” Renewable Sustainable Energy Rev., 68(2), pp. 87–101. [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 Conf. Ser.: Earth Environ. Sci., 15(6), p. 051401, p. 062030.
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. [CrossRef]
Hanjalic, K. , 2005, “ Will RANS Survive LES? A View of Perspectives,” ASME J. Fluids Eng., 127(5), pp. 831–839. [CrossRef]
Trivedi, C. , 2017, “ Investigations of Compressible Turbulent Flow in a High Head Francis Turbine,” ASME J. Fluids Eng., 140(1), p. 011101. [CrossRef]
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. [CrossRef]
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. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Experimental setup of a model Francis turbine. The circular ring manifold was used to acquire the inlet and outlet pressure of the turbine.

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Fig. 2

Locations of pressure sensors in the turbine. Sensors R1–R4 are in the runner; DT1–DT4 are in the draft tube cone; VL1 and VL2 are in the vaneless space.

Grahic Jump Location
Fig. 3

Hexahedral mesh of the model Francis turbine with labyrinth seals. The right-top, - right-middle, and right--bottom figures correspond to zoomed-in views of the blade leading edge, upper labyrinth and lower labyrinth, respectively.

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Fig. 4

Computational domain of a Francis turbine considered for the numerical simulations. Labyrinth seals are not shown.

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Fig. 5

Mesh convergence study of the efficiency, torque, head, and pressure in the turbine. The mesh densities m1 and m4correspond to 9 × 106 and 30 × 106 nodes, respectively. The pressure in the vaneless space, runner, and draft tube correspond to the point locations on the no-slip boundary.

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Fig. 6

Relative error in the power values computed using the whirl component at the runner inlet and outlet (see Eq. (15)). m1 is the coarse mesh, with 9 × 106 nodes, and m4 is the fine mesh, with 30 × 106 nodes.

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Fig. 7

The effect of the temporal discretization in the runner of a high-head Francis turbine at the BEP. The pressure variation corresponds to the guide vane passing frequency and the amplitudes at the blade leading edge.

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Fig. 8

Iterative convergence of pressure values at the casing inlet (SC), vaneless space (VL1), runner (R1), and draft tube (DT1) during BEP. Cp = (p − pref)/(0.5 ρu2).

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Fig. 9

Time-average validation of the pressure data at six locations inside the turbine. êitr=(pexp − pnum) × 100/pexp.

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Fig. 10

Unsteady pressure (head) fluctuations in the vaneless space (VL1), runner (R2) and draft tube (DT1) under the BEP (left) and PL (right) operating conditions. The x-axis scale for DT1 PL and the y-axis scale for all plots are different to ensure a clear visualization of the fluctuations.

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Fig. 11

Validation of numerical pressure data in the vaneless space (VL1), runner (R2) and draft tube (DT1) under the BEP (right) and PL (left) operating conditions

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Fig. 12

Validation of the pressure amplitudes in the vaneless space (VL1), runner (R2), and draft tube (DT1) using power spectral analysis under the BEP (right) and PL (left) operating conditions. fb, fgv, and frh are the blade passing, guide vane passing and vortex rope frequencies, respectively. On the x-axis, the frequencies are normalized by the runner rotational speed, i.e., 5.5 Hz.

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