The swirling flow exiting the runner of a hydraulic turbine is further decelerated in the discharge cone of the draft tube to convert the excess of dynamic pressure into static pressure. When the turbine is operated far from the best efficiency regime, particularly at part load, the decelerated swirling flow develops a self-induced instability with a precessing helical vortex and the associated severe pressure fluctuations. This phenomenon is investigated numerically in this paper, for a swirl apparatus configuration. The unsteady three-dimensional (3D) flow field is analyzed using a proper orthogonal decomposition (POD), and within this framework we examine the effectiveness of an axial jet injection for mitigating the flow instability. It is shown that a limited number of modes can be used to reconstruct the flow field. Moreover, POD enables to reveal influence of the jet injection on the individual modes of the flow and illustrates continuous suppression of the modes from higher-order modes to lower-order modes as the jet discharge increases. Application of POD offers new view for the future control effort aimed on vortex rope mitigation because spatiotemporal description of the flow is provided. Thereby, POD enables better focus of the jets or other flow control devices.

References

References
1.
Dörfler
,
P.
,
Sick
,
M.
, and
Coutu
,
A.
,
2013
,
Flow-Induced Pulsations and Vibration in Hydraulic Machinery
,
Springer-Verlag
,
London
.
2.
Wu
,
Y. L.
,
Li
,
S. C.
,
Liu
,
S. H.
,
Dou
,
H.-S.
, and
Qian
,
Z. D.
,
2013
,
Vibration of Hydraulic Machinery
, Vol. 11,
Springer
,
Dordrecht, The Netherlands
.
3.
Frunzaverde
,
D.
,
Muntean
,
S.
,
Marginean
,
G.
,
Campian
,
V.
,
Marsavina
,
L.
,
Terzi
,
R.
, and
Serban
,
V.
,
2010
, “
Failure Analysis of a Francis Turbine Runner
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(1), p.
012115
.
4.
Thicke
,
R. H.
,
1981
, “
Practical Solutions for Draft Tube Instability
,”
Int. Water Power Dam Constr.
,
33
(
2
), pp.
31
37
.
5.
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
,”
18th IAHR Symposium on Hydraulic Machinery and Cavitation
(
IAHR
),
E.
Cabrera
,
V.
Espert
, and
F.
Martínex
, eds., Valencia, Spain, Sept. 16–19,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
, pp.
905
914
.
6.
Miyagawa
,
K.
,
Sano
,
T.
,
Kunimatsu
,
N.
,
Aki
,
T.
, and
Nishi
,
M.
,
2006
, “
Flow Instability With Auxiliary Parts in High Head Pump–Turbines
,”
23rd IAHR Symposium on Hydraulic Machinery and Systems
, Yokohama, Japan, Oct. 17–21, Paper No. F307.
7.
Vevke
,
T.
,
2004
, “
An Experimental Investigation of Draft Tube Flow
,”
Ph.D. thesis
, Norwegian University of Science and Technology, Trondheim, Norway.
8.
Qian
,
Z. D.
,
Li
,
W.
,
Huai
,
W. X.
, and
Wu
,
Y. L.
,
2012
, “
The Effect of the Runner Cone Design on Pressure Oscillation Characteristics in a Francis Hydraulic Turbine
,”
Proc. Inst. Mech. Eng., Part A
,
226
(
1
), pp.
137
150
.
9.
Kurokawa
,
J.
,
Kajigaya
,
A.
,
Matusi
,
J.
, and
Imamura
,
H.
,
2000
, “
Suppression of Swirl in a Conical Diffuser by Use of J-Groove
,”
20th IAHR Symposium on Hydraulic Machinery and Systems
(
IAHR
), Charlotte, NC, Aug. 6–9, Paper No. DY-01.
10.
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
.
11.
Pappilon
,
B.
,
Sabourin
,
M.
,
Couston
,
M.
, and
Deschenes
,
C.
,
2002
, “
Methods for Air Admission in Hydro Turbines
,” 21st IAHR Symposium on Hydraulic Machinery and Systems (
IAHR
), F. Avellan, G. D. Ciocan, and S. Kvicinsky, eds., Lausanne, Switzerland, Sept. 9–12, pp. 1–6.
12.
Kjeldsen
,
M.
,
Olsen
,
K.
,
Nielsen
,
T.
, and
Dahlhaug
,
O.
,
2006
, “
Water Injection for the Mitigation of Draft Tube Pressure Pulsations
,”
1st IAHR International Meeting of Working Group on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Barcelona, Spain, pp.
1
11
.
13.
Susan-Resiga
,
R.
,
Vu
,
T. C.
,
Muntean
,
S.
,
Ciocan
,
G. D.
, and
Nennemann
,
B.
,
2006
, “
Jet Control of the Draft Tube in Francis Turbines at Partial Discharge
,”
23rd IAHR Symposium on Hydraulic Machinery and Systems
(
IAHR
), Yokohama, Japan, Oct. 17–21, Paper No. F192.
14.
Kirschner
,
O.
,
Schmidt
,
H.
,
Ruprecht
,
A.
,
Mader
,
R.
, and
Meusburger
,
P.
,
2010
, “
Experimental Investigation of Vortex Control With an Axial Jet in the Draft Tube of a Model Pump-Turbine
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(1), p.
012092
.
15.
Oberleithner
,
K.
,
Terhaar
,
S.
,
Rukes
,
L.
, and
Paschereit
,
C. O.
,
2013
, “
Why Non-Uniformity Density Suppresses the Precessing Vortex Core
,”
ASME J. Eng. Gas Turbines Power
,
135
(
12
), p.
121506
.
16.
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
.
17.
Muntean
,
S.
,
Susan-Resiga
,
R. F.
, and
Bosioc
,
A. I.
,
2009
, “
Numerical Investigation of the Jet Control Method for Swirling Flow With Precessing Vortex Rope
,”
3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
(
IAHR
), Brno, Czech Republic, Oct. 14–16, Paper No. B2.
18.
Bosioc
,
A.
,
Tanasa
,
C.
,
Muntean
,
S.
, and
Susan-Resiga
,
R.
,
2009
, “
2D LDV Measurements and Comparison With Axisymmetric Flow Analysis of Swirling Flow in a Simplified Draft Tube
,”
3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Brno, Czech Republic, Paper No. P6.
19.
Nishi
,
M.
,
Kubota
,
T.
,
Matsunaga
,
S.
, and
Senoo
,
Y.
,
1980
, “
Study on Swirl Flow and Surge in an Elbow Type Draft Tube
,”
10th IAHR Symposium on Hydraulic Machinery, Equipment and Cavitation
(
IAHR
), Tokyo, Japan, Vol.
1
, pp.
557
568
.
20.
Nishi
,
M.
, and
Liu
,
S. H.
,
2013
, “
An Outlook on the Draft-Tube-Surge Study
,”
Int. J. Fluid Mach. Syst.
,
6
(
1
), pp.
33
48
.
21.
Bienkiewicz
,
B.
,
Ham
,
H. J.
,
Sun
,
Y.
,
1993
, “
Proper Orthogonal Decomposition of Roof Pressure
,”
J. Wind Eng. Ind. Aerodyn.
,
50
, pp.
193
202
.
22.
Lumley
,
J. L.
,
1967
, “
The Structure of Inhomogeneous Turbulence
,”
Atmospheric Turbulence and Wave Propagation
,
A. I.
Yaglom
and
I. V.
Tatarski
, eds.,
Nauka
,
Moscow, Russia
.
23.
Berkooz
,
G.
,
Holmes
,
P.
, and
Lumley
,
J. L.
,
1993
, “
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
25
(
1
), pp.
539
575
.
24.
Holmes
,
P.
,
Lumley
,
J. L.
,
Berkooz
,
G.
, and
Rowley
,
C. W.
,
2012
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
,
2nd ed.
,
Cambridge University Press
,
Cambridge, UK
.
25.
Grinberg
,
L.
,
Yakhot
,
A.
, and
Karniadakis
,
G. E.
,
2009
, “
Analyzing Transient Turbulence in a Stenosed Carotid Artery by Proper Orthogonal Decomposition
,”
Ann. Biomed. Eng.
,
37
(
11
), pp.
2200
2217
.
26.
Sirovich
,
L.
,
1987
, “
Turbulence and the Dynamics of Coherent Structures—Part I: Coherent Structures
,”
Q. Appl. Math.
,
45
(3), pp.
561
571
.
27.
Lumley
,
J. L.
,
1970
,
Stochastic Tools in Turbulence
,
Academic Press
,
New York
.
28.
Anton
,
A.
,
Creţu
,
V.
,
Ruprecht
,
A.
, and
Muntean
,
S.
,
2013
, “
Traffic Replay Compression (TRC): A Highly Efficient Method for Handling Parallel Numerical Simulation Data
,”
Proc. Rom. Acad., Ser. A
,
14
(
4
), pp.
385
392
.
29.
Jerri
,
A. J.
,
1977
, “
The Shannon Sampling Theorem—Its Various Extensions and Applications: A Tutorial Review
,”
Proc. IEEE
,
65
(
11
), pp.
1565
1596
.
30.
Susan-Resiga
,
R.
, and
Muntean
,
S.
,
2008
, “
Decelerated Swirling Flow Control in the Discharge Cone of Francis Turbines
,”
4th International Symposium on Fluid Machinery and Fluid Mechanics
(
ISFMFE
), Beijing, China, Nov. 24–27, Paper No. IL-18.
31.
Susan-Resiga
,
R.
,
Muntean
,
S.
,
Tanasa
,
C.
, and
Bosioc
,
A. I.
,
2008
, “
Hydrodynamic Design and Analysis of a Swirling Flow Generator
,”
4th German–Romanian Workshop on Turbomachinery Hydrodynamics
(
GRoWTH
), Stuttgart, Germany, June 12–15, pp.
1
16
.
32.
Bosioc
,
A.
,
Susan-Resiga
,
R. F.
, and
Muntean
,
S.
,
2008
, “
Design and Manufacturing of a Convergent-Divergent Test Section for Swirling Flow Apparatus
,”
4th German–Romanian Workshop on Turbomachinery Hydrodynamics
(
GRoWTH
), Stuttgart, Germany, June 12–15, pp. 1–15.
33.
Susan-Resiga
,
R.
,
Muntean
,
S.
,
Bosioc
,
A.
,
Stuparu
,
A.
,
Miloş
,
T.
,
Baya
,
A.
,
Bernad
,
S.
, and
Anton
,
L. E.
,
2007
, “
Swirling Flow Apparatus and Test Rig for Flow Control in Hydraulic Turbines Discharge Cone
,”
2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamics Problems in Hydraulic Machinery and Systems
(
IAHR
), Timisoara, Romania, Oct. 24–26, pp.
203
216
.
34.
Tanasa
,
C.
,
Susan-Resiga
,
R.
,
Bosioc
,
A.
, and
Muntean
,
S.
,
2010
, “
Mitigation of Pressure Fluctuations in the Discharge Cone of Hydraulic Turbines Using Flow-Feedback
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(1), p.
012067
.
35.
Tanasa
,
C.
,
Susan-Resiga
,
R.
,
Muntean
,
S.
, and
Bosioc
,
A. I.
,
2013
, “
Flow-Feedback Method for Mitigating the Vortex Rope in Decelerated Swirling Flows
,”
ASME J. Fluids Eng.
,
135
(
6
), p.
061304
.
36.
Muntean
,
S.
,
Nilsson
,
H.
, and
Susan-Resiga
,
R.
,
2009
, “
3D Numerical Analysis of the Unsteady Turbulent Swirling Flow in a Conical Diffuser Using FLUENT and OpenFOAM
,”
3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Brno, Czech Republic, Oct. 14–16, Paper No. C4.
37.
Petit
,
O.
,
Bosioc
,
A. I.
,
Nilsson
,
H.
,
Muntean
,
S.
, and
Susan-Resiga
,
R.
,
2011
, “
Unsteady Simulations of the Flow in a Swirl Generator Using OpenFOAM
,”
Int. J. Fluid Mach. Syst.
,
4
(
1
), pp.
199
208
.
38.
Bergman
,
O.
,
2010
, “
Numerical Investigation of the Flow in a Swirl Generator Using OpenFOAM
,”
M.S. thesis
, Chalmers University of Technology, Gothenburg, Sweden.
39.
Petit
,
O.
,
2012
, “
Towards Full Predictions of the Unsteady Incompressible Flow in Rotating Machines Using OpenFOAM
,”
Ph.D. thesis
, Chalmers University of Technology, Gothenburg, Sweden.
40.
Ojima
,
A.
, and
Kamemoto
,
K.
,
2010
, “
Vortex Method Simulation of Three-Dimensional and Unsteady Vortices in a Swirling Flow Apparatus Experimented in Politehnica University of Timisoara
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(1), p.
012065
.
41.
Stefan
,
D.
,
Rudolf
,
P.
,
Muntean
,
S.
, and
Susan-Resiga
,
R. F.
,
2012
, “
Structure of Flow Fields Downstream of Two Different Swirl Generators
,”
18th International Conference of Engineering Mechanics
(
ICEM
), Svratka, Czech Republic, May 14–17, pp.
1331
1342
.
42.
Fluent
,
2006
, “
Gambit 2.0 User's Guide
,” Fluent Inc., Lebanon, NH.
43.
Ansys
,
2011
, “
ANSYS FLUENT 14.0 User's Guide
,”
Ansys Inc.
, Canonsburg, PA.
44.
Jawarneh
,
A. M.
, and
Vatistas
,
G. H.
,
2006
, “
Reynolds Stress Model in the Prediction of Confined Turbulent Swirling Flows
,”
ASME J. Fluids Eng.
,
128
(
6
), pp.
1377
1382
.
45.
Rudolf
,
P.
, and
Skoták
,
A.
,
2001
, “
Unsteady Flow in the Draft Tube With Elbow—Part B: Numerical Investigation
,”
10th International Meeting of IAHR Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
, Trondheim, Norway, pp. 52–62.
46.
Gibson
,
M. M.
, and
Launder
,
B. E.
,
1978
, “
Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer
,”
J. Fluid Mech.
,
86
(
3
), pp.
491
511
.
47.
Fu
,
S.
,
Launder
,
B. E.
, and
Leschziner
,
M. A.
,
1987
, “
Modeling Strongly Swirling Recirculating Jet Flow With Reynolds-Stress Transport Closures
,”
Sixth Symposium on Turbulent Shear Flows
, Toulouse, France, Sept. 7–9, pp. 1–6.
48.
Launder
,
B. E.
,
1989
, “
Second-Moment Closure and Its Use in Modeling Turbulent Industrial Flows
,”
Int. J. Numer. Methods Fluids
,
9
(
8
), pp.
963
985
.
49.
Muntean
,
S.
,
Ruprecht
,
A.
, and
Susan-Resiga
,
R.
,
2005
, “
A Numerical Investigation of the 3D Swirling Flow in a Pipe With Constant Diameter—Part 1: Inviscid Computation
,”
Sci. Bull. Politeh. Univ. Timisoara, Trans. Mech.
,
50
(
64
), pp.
77
86
.
50.
Muntean
,
S.
,
Buntić
,
I.
,
Ruprecht
,
A.
, and
Susan-Resiga
,
R.
,
2005
, “
A Numerical Investigation of the 3D Swirling Flow in a Pipe With Constant Diameter—Part 2: Turbulent Computation
,”
Sci. Bull. Politeh. Univ. Timisoara, Trans. Mech.
,
50
(
64
), pp.
87
96
.
51.
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
.
52.
Roache
,
P. J.
,
2003
, “
Conservatism of the GCI in Finite Volume Computations on Steady State Fluid Flow and Heat Transfer
,”
ASME J. Fluids Eng.
,
125
(
4
), pp.
731
732
.
53.
Roache
,
P. J.
,
Ghia
,
K. N.
, and
White
,
F. M.
,
1986
, “
Editorial Policy Statement on the Control of Numerical Accuracy
,”
ASME J. Fluids Eng.
,
108
(
1
), p.
2
.
54.
MathWorks
,
2010
, “
MATLAB 7.10 User's Guide
,” MathWorks Inc., Natick, MA.
55.
Houde
,
S.
,
Iliescu
,
M. S.
,
Fraser
,
R.
,
Lemay
,
S.
,
Ciocan
,
G. D.
, and
Deschenes
,
C.
,
2011
, “
Experimental and Numerical Analysis of the Cavitating Part Load Vortex Dynamics of Low-Head Hydraulic Turbines
,”
ASME
Paper No. AJK2011-33006.
56.
Mayer
,
K. E.
,
Pedersen
,
J. M.
, and
Özcan
,
O.
,
2007
, “
A Turbulent Jet in Crossflow Analysed With Proper Orthogonal Decomposition
,”
J. Fluid Mech.
,
583
, pp.
199
227
.
57.
Andrianne
,
T.
,
Razak
,
N. A.
, and
Dimitriadis
,
G.
,
2011
, “
Flow Visualization and Proper Orthogonal Decomposition of Aeroelastic Phenomena
,”
Wind Tunnels
,
S.
Okamoto
, ed., InTech, Rijeka, Croatia.
58.
Kellnerová
,
R.
,
Kukačka
,
L.
,
Juračková
,
K.
,
Uruba
,
V.
, and
Jaňour
,
Z.
,
2012
, “
PIV Measurement of Turbulent Flow Within a Street Canyon: Detection of Coherent Motion
,”
J. Wind Eng. Ind. Aerodyn.
,
104–106
, pp.
302
313
.
59.
Oberleithner
,
K.
,
Sieber
,
M.
,
Nayeri
,
C. N.
,
Paschereit
,
C. O.
,
Petz
,
C.
,
Hege
,
H.-C.
,
Noack
,
B. R.
, and
Wygnanski
,
I.
,
2011
, “
Three-Dimensional Coherent Structures in a Swirling Jet Undergoing Vortex Breakdown: Stability Analysis and Empirical Mode Construction
,”
J. Fluid Mech.
,
679
, pp.
383
414
.
60.
Perrin
,
R.
,
Braza
,
M.
,
Cid
,
E.
,
Cazin
,
S.
,
Barthet
,
A.
,
Servain
,
A.
,
Mockett
,
C.
, and
Thiele
,
F.
,
2007
, “
Obtaining Phase Averaged Turbulence Properties in the Near Wake of Circular Cylinder at High Reynolds Number Using POD
,”
Exp. Fluids
,
43
(2), pp.
341
355
.
61.
Oberleithner
,
K.
,
Sieber
,
M.
,
Nayeri
,
C. N.
, and
Paschereit
,
C. O.
,
2011
, “
On the Control of Global Modes in Swirling Jet Experiments
,”
J. Phys.: Conf. Ser.
,
318
(
3
), p.
032050
.
62.
Tutkun
,
M.
,
Johansson
,
P. B. V.
, and
George
,
W. K.
,
2008
, “
Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disc
,”
AIAA J.
,
46
(
5
), pp.
1118
1134
.
63.
Citriniti
,
J. H.
, and
George
,
W. K.
,
2000
, “
Reconstruction of the Global Velocity Field in the Axisymmetric Mixing Layer Utilizing the Proper Orthogonal Decomposition
,”
J. Fluid Mech.
,
418
, pp.
137
166
.
64.
Rudolf
,
P.
, and
Štefan
,
D.
,
2012
, “
Decomposition of the Swirling Flow Field Downstream of Francis Turbine Runner
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
15
(
6
), p.
062008
.
65.
Ciocan
,
G. D.
,
Iliescu
,
S. M.
,
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
.
66.
Stefan
,
D.
, and
Rudolf
,
P.
,
2013
, “
Computational Fluid Dynamic Study of the Flow Downstream of the Swirl Generator Using Large Eddy Simulation
,” HPC-EUROPA 2, Stuttgart, Germany, pp.
1
2
.
You do not currently have access to this content.