The flow in the off-design operation of a Francis turbine may lead to the formation of spiral vortex breakdowns in the draft tube, a diffuser installed after the runner. The spiral vortex breakdown, also named a vortex rope, may induce several low-frequency fluctuations leading to structural vibrations and a reduction in the overall efficiency of the turbine. In the present study, synchronized particle image velocimetry, pressure, and turbine flow parameter (Q, H, α, and T) measurements have been carried out in the draft tube cone of a high head model Francis turbine. The transient operating condition from the part load to the best efficiency point was selected to investigate the mitigation of the vortex rope in the draft tube cone. The experiments were performed 20 times to assess the significance of the results. A precession frequency of 1.61 Hz [i.e., 0.29 times the runner rotational frequency (Rheingans frequency)] is observed in the draft tube cone. The frequency is captured in both pressure and velocity data with its harmonics. The accelerating flow condition at the center of the cone with a guide vane opening is observed to diminish the spiral form of the vortex breakdown in the quasi-stagnant region. This further mitigates the stagnant part of the cone with a highly dominated axial flow condition of the turbine at the best efficiency point. The disappearance of the stagnant region is the most important state in the present case, which mitigates the spiral vortex breakdown of the cone at high Reynolds numbers. In contrast to a typical transition, a new type of transition from wake to jet is observed during the mitigation of the breakdown. The obtained 2D instantaneous velocity fields demonstrate the disappearance region of shear layers and stagnation in the cone. The results also demonstrate the existence of high axial velocity gradients in an elbow draft tube cone.
REFERENCES
1.
C.
Trivedi
, B. K.
Gandhi
, and M.
Cervantes
, “Effect of transients on Francis turbine runner life: A review
,” J. Hydraul. Res.
51
(2
), 121
–132
(2013
).2.
N.
Kroner
and R.
Bérubé
, “Maintaining power grid reliability through individual unit stability
,” in Hydro Vision
(HCI Publications
, California
, 2008
), pp. 1
–10
, paper-128.3.
C.
Trivedi
, “Investigation of transient pressure loading on a high head Francis turbine
,” Ph.D. thesis, Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Lulea University of Technology
, Lulea, Sweden
, 2014
.4.
K.
Amiri
, B.
Mulu
, M.
Raisee
, and M.
Cervantes
, “Unsteady pressure measurements on the runner of a Kaplan turbine during load acceptance and load rejection
,” J. Hydraul. Res.
54
(1
), 56
–73
(2015
).5.
H.
Foroutan
, “Simulation, analysis, and mitigation of the vortex rope formation in the draft tube of hydraulic turbines
,” Ph.D. thesis, The Graduate School College of Engineering, The Pennsylvania State University
, Pennsylvania, USA
, 2014
.6.
D.
Stefan
, P.
Rudolf
, A.
Skotak
, and L.
Motcak
, “Energy transformation and flow topology in an elbow draft tube
,” Appl. Comput. Mech.
6
, 93
–106
(2012
).7.
M.
Nishi
, S.
Matsunaga
, T.
Kubota
, and Y.
Senoo
, “Flow regimes in an elbow-type draft tube
,” in Proceedings of the 11th IAHR Symposium: Operating Problems of Pump Stations and Power Plant
(IAHR
, Amsterdam, Netherlands
, 1982
), Vol. 2, pp. 1
–13
.8.
A.
Müller
, A.
Bullani
, M.
Dreyer
, S.
Roth
, A.
Favrel
, C.
Landry
, and F.
Avellan
, “Interaction of a pulsating vortex rope with the local velocity field in a Francis turbine draft tube
,” in 26th IAHR Symposium on Hydraulic Machinery and Systems
, Beijing, China
, 2012
.9.
A.
Favrel
, A.
Muller
, C.
Landry
, K.
Yamamoto
, and F.
Avellan
, “Study of the vortex-induced pressure excitation source in a Francis turbine draft tube by particle image velocimetry
,” Exp. Fluids
56
, 215-1
–215-15
(2015
).10.
P.
Dorfler
, M.
Sick
, and A.
Coutu
, Flow-Induced Pulsation and Vibration in Hydroelectric Machinery
(Springer-Verlag
, London
, 2013
).11.
Y.
Wu
, S.
Li
, S.
Liu
, H.-S.
Dou
, and Z.
Qian
, Vibration of Hydraulic Machinery
(Springer Dordrecht Heidelberg
, New York, London
, 2013
).12.
R.
Goyal
, M. J.
Cervantes
, and B. K.
Gandhi
, “Vortex rope formation in a high head model Francis turbine
,” J. Fluids Eng.
139
, 041102-1
–041102-14
(2017
).13.
M.
Hall
, “Vortex breakdown
,” Annu. Rev. Fluid Mech.
4
(1
), 195
–218
(1972
).14.
O.
Lucca-Negro
and T.
O’doherty
, “Vortex breakdown: A review
,” Prog. Energy Combust. Sci.
27
, 431
–481
(2001
).15.
H.
Ludwieg
, “Stabilität der stromung in einem zylindrischen ringraum
,” Z. Flugwiss.
8
(5
), 135
–140
(1960
).16.
T. B.
Benjamin
, “Theory of the vortex breakdown phenomenon
,” J. Fluid Mech.
14
(04
), 593
–629
(1962
).17.
P.
Billant
, J.-M.
Chomaz
, and P.
Huerre
, “Experimental study of vortex breakdown in swirling jets
,” J. Fluid Mech.
376
, 183
–219
(1998
).18.
P.
Meliga
, F.
Gallaire
, and J.-M.
Chomaz
, “A weakly nonlinear mechanism for mode selection in swirling jets
,” J. Fluid Mech.
699
, 216
–262
(2012
).19.
T.
Sarpkaya
, “On stationary and travelling vortex breakdowns
,” J. Fluid Mech.
45
(3
), 545
–559
(1971
).20.
F.
Novak
and T.
Sarpkaya
, “Turbulent vortex breakdown at high Reynolds numbers
,” AIAA J.
38
(5
), 825
–834
(2000
).21.
F.
Gallaire
, S.
Rott
, and J.-M.
Chomaz
, “Experimental study of free and forced swirling jet
,” Phys. Fluids
16
(8
), 2907
–2917
(2004
).22.
F.
Gallaire
, M.
Ruith
, E.
Meiburg
, and J.-M.
Chomaz
, “Spiral vortex breakdown as a global mode
,” J. Fluid Mech.
549
, 71
–80
(2006
).23.
J.
Harvey
, “Some observations of the vortex breakdown phenomenon
,” J. Fluid Mech.
14
(4
), 585
–592
(1962
).24.
J. J.
Cassidy
and H. T.
Falvey
, “Observations of unsteady flow arising after vortex breakdown
,” J. Fluid Mech.
41
(4
), 727
–736
(1970
).25.
J. H.
Faler
and S.
Leibovich
, “Disrupted states of vortex flow and vortex breakdown
,” Phys. Fluids
20
, 1385
–1400
(1977
).26.
C.
Brucker
and W.
Althaus
, “Study of vortex breakdown by particle tracking velocimetry (PTV)
,” Exp. Fluids
13
(5
), 339
–349
(1992
).27.
M.
Hall
, “A new approach to vortex breakdown
,” in Proceedings of the Heat Transfer and Fluid Mechanics Institute
(Stanford University Press
, 1967
), pp. 319
–340
.28.
V. L.
Okulov
, “The transition from right to left helical symmetry during vortex breakdown
,” Tech. Phys. Lett.
22
(10
), 798
–800
(1996
).29.
X.
Shi
and X.
Shan
, “Relation between the quasi-cylindrical approximation and the critical theory for swirling flow
,” in Vortex Control and Breakdown Behaviour. Second International Colloquium on Vortical Flows
(BBC
, 1987
), pp. 72
–82
.30.
M.
Escudier
, “Vortex breakdown: Observations and explanations
,” Prog. Aeronaut. Sci.
25
(2
), 189
–229
(1988
).31.
T.
Jacob
, J. E.
Prenat
, and G.
Angelico
, “Unstable part-load operation of a model Francis turbine: Evaluation of disturbance magnitude
,” in Proceedings of the 17th IAHR Symposium on Hydraulic Machinery and System
(IAHR
, Beijing, China
, 1994
), pp. 933
–942
.32.
R.
Susan-Resiga
, T. C.
Vu
, S.
Muntean
, G. D.
Ciocan
, and B.
Nennemann
, “Jet control of the draft tube vortex rope in Francis turbines at partial discharge
,” in Proceedings of the 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan
(IAHR
, 2006
), pp. 17
–21
.33.
P. A.
Kuibin
, V. L.
Okulov
, R.
Susan-Resiga
, and S.
Muntean
, “Validation of mathematical models for predicting the swirling flow and the vortex rope in a Francis turbine operated at partial discharge
,” in IOP Conference Series: Earth and Environmental Science
(IOPScience
, 2010
), Vol. 12, pp. 012051-1–012051-11
.34.
R.
Susan-Resiga
, S.
Muntean
, F.
Avellan
, and I.
Anton
, “Mathematical modelling of swirling flow in hydraulic turbines for the full operating range
,” Appl. Math. Modell.
35
(10
), 4759
–4773
(2011
).35.
M. S.
Iliescu
, G. D.
Ciocan
, and F.
Avellan
, “3D PIV and LDV measurements at the outlet of a Francis turbine draft tube
,” in Proceedings of FEDSM’02: The 2002 Joint US ASME-European Fluids Engineering Summer Conference
, Montreal, Quebec, Canada
, 2002
.36.
J.
Arpe
, C.
Nicolet
, and F.
Avellan
, “Experimental evidence of hydroacoustic pressure waves in a Francis turbine elbow draft tube for low discharge conditions
,” J. Fluids Eng.
131
(8
), 081102-1
–081102-9
(2009
).37.
G. D.
Ciocan
, F.
Avellan
, and J.-L.
Kueny
, “Optical measurement techniques for experimental analysis of hydraulic turbines rotor-stator interaction
,” in Proceedings of the ASME Fluids Engineering Division Summer 2000 Meeting
, Boston, MA, USA
, 2000
.38.
M. S.
Iliescu
, G. D.
Ciocan
, and F.
Avellan
, “Analysis of the cavitating draft tube vortex in a Francis turbine using particle image velocimetry measurements in two-phase flow
,” J. Fluids Eng.
130
(2
), 021105-1–021105-
10
(2008
).39.
M.
Nishi
and S.
Liu
, “An outlook on the draft-tube-surge study
,” Int. J. Fluid Mach. Syst.
6
(1
), 33
–48
(2013
).40.
Field Acceptance Tests to Determine the Hydraulic Performance of Hydraulic Turbines, Storage Pumps and Pump-Turbines
, 3rd ed. (International Electrotechnical Commission
, Geneva, Switzerland
, 1991
).41.
Hydraulic Turbines, Storage Pumps and Pump-Turbines—Model Acceptance Tests
(International Electrotechnical Commission
, Geneva 20, Switzerland
, 1999-11
).42.
Hydraulic Turbines and Pump-Turbines, Performance Test Codes
(ASME
, New York, NY
, 2011
).43.
D.
Garcia
, “Robust smoothing of gridded data in one and higher dimensions with missing values
,” Comput. Stat. Data Anal.
54
, 1167
–1178
(2010
).44.
D.
Garcia
, “A fast all in one method for automated post-processing of PIV data
,” Exp. Fluids
50
, 1247
–1259
(2011
).45.
K.
Amiri
, B.
Mulu
, M.
Raisee
, and M.
Cervantes
, “Experimental study on flow asymmetry after the draft tube bend of a Kaplan turbine
,” Adv. Appl. Fluid Mech.
19
(2
), 441
–472
(2016
).46.
F.
DIAS
, “Ship waves and Kelvin
,” J. Fluid Mech.
746
, 1
–4
(2014
).47.
A. L.
Bosioc
, R.
Susan-Resiga
, S.
Muntean
, and C.
Tanasa
, “Unsteady pressure analysis of a swirling flow with vortex rope and axial water injection in a discharge cone
,” J. Fluids Eng.
134
, 081104-1–081104-
11
(2012
).48.
B.
Mulu
, “An experimental and numerical investigation of a Kaplan turbine model
,” Ph.D. thesis, Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Lulea University of Technology
, Lulea, Sweden
, 2012
.49.
A. W.
Cary
, D. L.
Darmofal
, and K. G.
Powell
, “Onset of the spiral mode of vortex breakdown
,” AIAA Paper No. 97-0439, 1997
.50.
C. M.
Velte
, V. L.
Okulov
, and M. O. L.
Hansen
, “Alteration of helical vortex core without change in flow topology
,” Phys. Fluids
23
, 051707
(2011
).51.
J. N.
Sorensen
and V. L.
Okulov
, “Analysis of different vortex breakdown states
,” in XXIII ICTAM
, Beijing China
, 19–24 August 2012
.52.
V. L.
Okulov
, J. N.
Sørensen
, and L. K.
Voigt
, “Vortex scenario and bubble generation in a cylindrical cavity with rotating top and bottom
,” Eur. J. Mech. B/Fluids
24
, 137
(2005
).© 2017 Author(s).
2017
Author(s)
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