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Numerical Simulation and Validation of a High Head Model Francis Turbine at Part Load Operating Condition

  • Rahul Goyal
  • Chirag Trivedi
  • Bhupendra Kumar Gandhi
  • Michel J. Cervantes
Original Contribution

Abstract

Hydraulic turbines are operated over an extended operating range to meet the real time electricity demand. Turbines operated at part load have flow parameters not matching the designed ones. This results in unstable flow conditions in the runner and draft tube developing low frequency and high amplitude pressure pulsations. The unsteady pressure pulsations affect the dynamic stability of the turbine and cause additional fatigue. The work presented in this paper discusses the flow field investigation of a high head model Francis turbine at part load: 50% of the rated load. Numerical simulation of the complete turbine has been performed. Unsteady pressure pulsations in the vaneless space, runner, and draft tube are investigated and validated with available experimental data. Detailed analysis of the rotor stator interaction and draft tube flow field are performed and discussed. The analysis shows the presence of a rotating vortex rope in the draft tube at the frequency of 0.3 times of the runner rotational frequency. The frequency of the vortex rope precession, which causes severe fluctuations and vibrations in the draft tube, is predicted within 3.9% of the experimental measured value. The vortex rope results pressure pulsations propagating in the system whose frequency is also perceive in the runner and upstream the runner.

Keywords

Numerical simulation Francis turbine Part load Pressure pulsation Rotor–stator interaction Vortex rope 

Notations

BEP

Best efficiency point

D

Diameter of runner, m

GVO

Guide vane’s opening, degree

FFT

Fast Fourier transform

f

Observed frequency, Hz

fn

Runner rotational frequency, Hz

f*

Normalised frequency, minus

frh

Rheingans (vortex rope) frequency, Hz ≡ f/3.6

g

9.821465 m/s2, as tested and measured at NTNU

H

Head, m

N

Sampling length

n

Runner speed, rev/s

nED

Speed factor [−], \({\text{n}}_{\text{ED}} { = }\frac{\text{nD}}{{\sqrt {{\text{gH}}_{\text{M}} } }}\)

ns

Specific speed [−], \({\text{n}}_{\text{s}} = \frac{{\left( {{\text{n}}_{\text{P}} \frac{\uppi }{180}} \right)\sqrt {{\text{Q}}_{\text{P}} } }}{{\left( {2{\text{gH}}_{\text{P}} } \right)^{{\frac{3}{4}}} }}\)

Δp

Pressure difference across the turbine, Pa

\({\tilde{\text{p}}}\)

Acquired pressure signal, kPa

\({\bar{\text{p}}}\)

Mean pressure, kPa

\({\text{p}}_{{}}^{ *}\)

Fluctuating pressure, kPa

p

Pressure, kPa, harmonic order (1, 2,…)

P

Power, MW

Q

Flow rate, m3/s−1

qED

Discharge factor [−], \({\text{q}}_{\text{ED}} { = }\frac{\text{Q}}{{{\text{D}}^{2} \sqrt {{\text{gH}}_{\text{M}} } }}\)

R

Runner inlet radius, m

GVO

Guide vane’s opening, degree

RSI

Rotor stator interactions

RVR

Rotating vortex rope

TS

Time step

TKE

Turbulence kinetic energy

t

Time, s

UPW

Upwind

X

Discrete quantity

\(\overline{\text{X}}\)

Average value

λ

Wavelength, m

α

Angular vane/blade position, degree

ω

Angular velocity, rad/s

ηh

Hydraulic efficiency, %

References

  1. 1.
    C. Trivedi, B. Gandhi, M.J. Cerventes, Effect of transients on Francis turbine runner life: a review. J. Hydraul. Res. (2013). doi: 10.1080/00221686.2012.732971 CrossRefGoogle Scholar
  2. 2.
    Y.Z. Liu, H.P. Chen, H.S. Koyama, Joint investigation of rotating flow with vortex breakdown using CFD, visualization and LDV. J. Hydrodyn. 17(4), 455–458 (2005)Google Scholar
  3. 3.
    C. Trivedi, M.J. Cerventes, B. Gandhi, O.G. Dahlhaug, Experimental and numerical studies for a high head francis turbine at several operating points. J. Fluids Eng. 135(11), 111102 (2013). doi: 10.1115/1.4024805 CrossRefGoogle Scholar
  4. 4.
    F-J. Wang, X-Q. Li, J-M. Ma, M. Yang, Experimental investigation of characteristic frequency in unsteady hydraulic behaviour of a large hydraulic turbine. J. Hydrodyn. 21(1), 12–19 (2009)CrossRefGoogle Scholar
  5. 5.
    H. Keck, M. Sick, Thirty years of numerical flow simulation in hydraulic turbomachines. Acta Mech. 201, 211–229 (2008). doi: 10.1007/s00707-008-0060-4 CrossRefzbMATHGoogle Scholar
  6. 6.
    X-B. Liu, Y-Z. Zeng, Numerical prediction of vortex flow in hydraulic turbine draft tube for LES. J. Hydrodyn. Ser. B 17(4), 448–454 (2005)zbMATHGoogle Scholar
  7. 7.
    H. Brekke, A Review on Oscillatory Problems in Francis Turbine. New Trends in Technologies: Devices, Computer, Communication and Industrial Systems. ed. by Meng Joo Er. A review on work on oscillatory problems in Francis turbines (2010) pp. 217–232Google Scholar
  8. 8.
    C. Nicolet, Hydroacoustic Modelling and Numerical Simulation of Unsteady Operation of Hydroelectric Systems, PhD thesis No 3751. ÉcolePolytechniqueFédérale de Lausanne (2007)Google Scholar
  9. 9.
    T. Staubli, F. Senn, M. Sallaberger, Instability of Pump-Turbines during Start-up in the Turbine Mode (Hydro, Ljubljana, 2008)Google Scholar
  10. 10.
    Y.X. Xiao, Z. Wang, Z. Yan, Experimental and numerical analysis of blade channel vortices in a francis turbine runner. Int. J. Comput. Aided Eng. Softw. 28(2), 154–171 (2011)CrossRefGoogle Scholar
  11. 11.
    V. Hasmatuchi, M. Farhat, S. Roth, F. Botero, F. Avellan, Experimental evidence of rotating stall in a pump-turbine at off-design conditions in generating mode. ASME J. Fluids Eng. 133(5), 051104, 1–8, doi: 10.1115/1.4004088 (2011)
  12. 12.
    A. Zobeiri, J-L. Kueny, M. Farhat, M. F. Avellan, Pump-turbine rotor-stator interactions in generating mode: pressure fluctuation in distributor channel. 23rd IAHR Symposium, October 2006, Yokohama, Japan,  1–10 (2006)Google Scholar
  13. 13.
    R-K. Zhang, et al., Characteristics and control of the draft-tube flow in part-load francis turbine. ASME J. Fluids Eng. 131(2), 021101, 1–9, doi: 10.1115/1.3002318 (2009)
  14. 14.
    A. Ruprecht, Simulation of vortex rope in turbine draft tube. Proceedings of Hydraulics Machinery Systems. 21st IAHR symposium, Lausanne (2002)Google Scholar
  15. 15.
    A.V. Minakov, D.V. Platonov, A.A. Dekterev, A.V. Sentyabov, A.V. Zakharov, The numerical simulation of low frequency pressure pulsations in the high-head Francis turbine. Comput. Fluids 111, 197–205 (2015), doi: 10.1016/j.compfluid.2015.01.007 CrossRefzbMATHGoogle Scholar
  16. 16.
    C. Nicolet, et al., Methodology for Risk Assessment of Part Load Resonance in Francis Turbine Power Plant. IAHR International Meeting of WG on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Barcelona, Spain, 1–16 (2006)Google Scholar
  17. 17.
    M. J. Cerventes, U. Andersson, H. M. Lövgren, Turbine-99 Unsteady Simulations—Validation. IOP Conference Series: Earth and Environmental Science, Vol. 12(1), 012014, 1–10, doi: 10.1088/1755-1315/12/1/012014 (2010)
  18. 18.
    R. Susan-Resiga, G.D. Ciocan, I. Anton, F. Avellan, Analysis of the swirling flow downstream a francis turbine runner. ASME J. Fluids Eng. 128(1), 177–189 (2005), doi: 10.1115/1.2137341 CrossRefGoogle Scholar
  19. 19.
    O. I. Buntic, S. Dietze, A. Ruprecht, Numerical Simulation of the Flow in Turbine-99 Draft Tube. Turbine-99 III, Proceedings of the Third IAHR/EROCOFTAC Workshop on Draft Turbine Flow, Porjus, Sweden (2005)Google Scholar
  20. 20.
    H. Wallimann, R. Neubauer, Numerical study of a high head Francis turbine with measurements from the Francis-99 project. J. Phys. Conf. Ser. 579(1), 012003 (2015), doi: 10.1088/1742-6596/579/1/012003 CrossRefGoogle Scholar
  21. 21.
    J. Wu, K. Shimmei, K. Tani, K. Niikura, J. Sato, CFD-based design optimization for hydro turbines. ASME J. Fluid Eng. 129(2), 159–168 (2007), doi: 10.1115/1.2409363 CrossRefGoogle Scholar
  22. 22.
    G.D. Ciocan, M.S. Iliescu, T.C. Vu, B. Nennemann, F. Avellan, Experimental study and numerical simulation of the FLINDT draft tube rotating vortex. ASME J. Fluids Eng. 129(2), 146–158 (2007). doi: 10.1115/1.2409332 CrossRefGoogle Scholar
  23. 23.
    T. Staubli, D. Meyer, Draft Tube Calculations. Turbine 99, EROCOFTAC/IAHR Workshop on Draft Tube Flow. Porjus, Sweden (1999)Google Scholar
  24. 24.
    C. Luis, O. D. S. Eduardo, D. D. M. Marcelo, C. P. B. J. Antonio, Assessment of Turbulence Modelling for CFD Simulations into Hydroturbines: Spiral Casing. 17th International Mechanicsl Engineering Congress (COBEM), Sao Paulo, Brazil (2003)Google Scholar
  25. 25.
    C. Widmer, T. Staubli, N. Ledergerber, Unstable characteristics and rotating stall in turbine brake operation of pump-turbines. ASME J. Fluids Eng. 133(4), 041101 (2011). doi: 10.1115/1.4003874 CrossRefGoogle Scholar
  26. 26.
    P. Mossinger, R. Jester-Zurker, A. Jung, 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), 012005 (2015). doi: 10.1088/1742-6596/579/1/012005 CrossRefGoogle Scholar
  27. 27.
    D. Jost, A. Skerlavaj, M. Morgut, P. Meznar, E. Nobile, 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), 012006 (2015). doi: 10.1088/1742-6596/579/1/012006 CrossRefGoogle Scholar
  28. 28.
    R. Goyal, C. Trivedi, B. Gandhi, M.J. Cerventes, O.G. Dahlhaug, Transient pressure measurements at part load operating condition of a high head model Francis turbine. Sadhana (Springer). 41 (11), 1311–1320 (2016). doi: 10.1007/s12046-016-0556-x CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  • Rahul Goyal
    • 1
  • Chirag Trivedi
    • 2
  • Bhupendra Kumar Gandhi
    • 1
  • Michel J. Cervantes
    • 3
  1. 1.Department of Mechanical and Industrial EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Norwegian University of Science and TechnologyTrondheimNorway
  3. 3.Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and MathematicsLuleå University of TechnologyLuleåSweden

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