The variable energy demand requires a great flexibility in operating a hydroturbine, which forces the machine to be operated far from its design point. One of the main components of a hydroturbine where undesirable flow phenomena occur under off-design conditions is the draft tube. Using computational fluid dynamics (CFD), the present paper studies the flow in the draft tube of a Francis turbine operating under various conditions. Specifically, four operating points with the same head and different flow rates corresponding to 70%, 91%, 99%, and 110% of the flow rate at the best efficiency point (BEP) are considered. Unsteady numerical simulations are performed using a recently developed partially averaged Navier–Stokes (PANS) turbulence model, and the results are compared to the available experimental data, as well as the numerical results of the traditionally used Reynolds-Averaged Navier–Stokes (RANS) models. Several parameters including the pressure recovery coefficient, mean velocity, and time-averaged and fluctuating wall pressure are investigated. It is shown that RANS and PANS both can predict the flow behavior close to the BEP operating condition. However, RANS results deviate considerably from the experimental data as the operating condition moves away from the BEP. The pressure recovery factor predicted by the RANS model shows more than 13% and 58% overprediction when the flow rate decreases to 91% and 70% of the flow rate at BEP, respectively. Predictions can be improved significantly using the present unsteady PANS simulations. Specifically, the pressure recovery factor is predicted by less than 4% and 6% deviation for these two operating conditions. A similar conclusion is reached from the analysis of the mean velocity and wall pressure data. Using unsteady PANS simulations, several transient features of the draft tube flow including the vortex rope and associated pressure fluctuations are successfully modeled. The formation of the vortex rope in partial load conditions results in severe pressure fluctuations exerting oscillatory forces on the draft tube. These pressure fluctuations are studied for several locations in the draft tube and the critical region with highest fluctuation amplitude is found to be the inner side of the elbow.

References

References
1.
Martinot
,
E.
,
2013
, “
Renewables Global Futures Report 2013. REN21
,” http://www.ren21.net/gfr
2.
Dörfler
,
P.
,
Sick
,
M.
, and
Coutu
,
A.
,
2013
, “
Flow-Induced Pulsation and Vibration in Hydroelectric Machinery
,”
Springer
,
London
.
3.
Vu
,
T. C.
,
Koller
,
M.
,
Gauthier
,
M.
, and
Deschênes
,
C.
,
2010
, “
Flow Simulation and Efficiency Hill Chart Prediction for a Propeller Turbine
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
12
(1), p.
012040
.
4.
Susan-Resiga
,
R. F.
,
Muntean
,
S.
,
Avellan
,
F.
, and
Anton
,
I.
,
2011
, “
Mathematical Modeling of Swirling Flow in Hydraulic Turbines for the Full Operating Range
,”
Appl. Math. Modell.
,
35
(
10
), pp.
4759
4773
.
5.
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
.
6.
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. dissertation, Paper No. 4272, EPFL.
7.
Mauri
,
S.
,
2002
, “
Numerical Simulation and Flow Analysis of an Elbow Diffuser
,” Ph.D. dissertation, Paper No. 2527, EPFL.
8.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2012
, “
Simulation of Flow in a Simplified Draft Tube: Turbulence Closure Considerations
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
15
(1), p.
022020
.
9.
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
.
10.
Zhang
,
R. K.
,
Mao
,
F.
,
Wu
,
J. Z.
,
Chen
,
S. Y.
,
Wu
,
Y. L.
, and
Liu
,
S. H.
,
2009
, “
Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine
,”
ASME J. Fluids Eng.
,
131
(
2
), p.
021101
.
11.
Sick
,
M.
,
Michler
,
W.
,
Weiss
,
T.
, and
Keck
,
H.
,
2009
, “
Recent Developments in the Dynamic Analysis of Water Turbines
,”
Proc. Inst. Mech. Eng. Part A
,
223
(
4
), pp.
415
427
.
12.
Vu
,
T. C.
,
Devals
,
C.
,
Zhang
,
Y.
,
Nennemann
,
B.
, and
Guibault
,
F.
,
2011
, “
Steady and Unsteady Flow Computation in an Elbow Draft Tube With Experimental Validation
,”
Int. J. Fluid Mach. Syst.
,
4
(
1
), pp.
85
96
.
13.
Ruprecht
,
A.
,
Helmrich
,
T.
,
Aschenbrenner
,
T.
, and
Scherer
,
T.
,
2002
, “
Simulation of Vortex Rope in a Turbine Draft Tube
,”
Proceedings of 21st IAHR Symposium on Hydraulic Machinery and Systems
, Lausanne, Switzerland, pp. 1–8.
14.
Paik
,
J.
,
Sotiropoulos
,
F.
, and
Sale
,
M.
,
2005
, “
Numerical Simulation of Swirling Flow in Complex Hydroturbine Draft Tube Using Unsteady Statistical Turbulence Models
,”
J. Hydraul. Eng.
,
131
(
6
), pp.
441
456
.
15.
Jošt
,
D.
, and
Lipej
,
A.
,
2011
, “
Numerical Prediction of Non-Cavitating and Cavitating Vortex Rope in a Francis Turbine Draft Tube
,”
J. Mech. Eng.
,
57
, pp.
445
456
.
16.
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
.
17.
Girimaji
,
S. S.
,
2006
, “
Partially-Averaged Navier–Stokes Model for Turbulence: A Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation Bridging Method
,”
ASME J. Appl. Mech.
,
73
(
3
), pp.
413
421
.
18.
Chen
,
Y. S.
, and
Kim
,
S. W.
,
1987
, “
Computation of Turbulent Flows Using an Extended k-ε Turbulence Closure Model
,” Report No. NASA CR-179204.
19.
Han
,
X.
,
Krajnović
,
S.
, and
Basara
,
B.
,
2013
, “
Study of Active Flow Control for a Simplified Vehicle Model Using the PANS Method
,”
Int. J. Heat Fluid Flow
,
42
, pp.
139
150
.
20.
Avellan
,
F.
,
2000
, “
Flow Investigation in a Francis Draft Tube: The FLINDT Project
,”
Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems
, Charlotte, NC.
21.
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
.
22.
Susan-Resiga
,
R.
,
Muntean
,
S.
,
Hasmatsuchi
,
V.
,
Anton
,
I.
, and
Avellan
,
F.
,
2010
, “
Analysis and Prevention of Vortex Breakdown in the Simplified Discharge Cone of a Francis Turbine
,”
ASME J. Fluids Eng.
,
132
(
5
), p.
051102
.
23.
Arpe
,
J.
,
2003
, “
Analyse du Champ de Pression Pariétale d'un Diffuseur Coudé de Turbine Francis
,” Ph.D. dissertation, Paper No. 2779, EPFL.
24.
Stein
,
P.
,
Sick
,
M.
,
Dörfler
,
P.
,
White
,
P.
, and
Braune
,
A.
,
2006
, “
Numerical Simulation of the Cavitating Draft Tube Vortex in a Francis Turbine
,”
Proceedings of the 23rd IAHR Symposium on Hydraulic Machinery and Systems
, Yokohama, Japan.
25.
Wilcox
,
D. C.
,
2006
, “
Turbulence Modeling for CFD
,”
DCW Industries
,
La Canada, CA
.
26.
Alligné
,
S.
,
2011
, “
Forced and Self-Oscillations of Hydraulic Systems Induced by Cavitation Vortex Rope of Francis Turbines
,” Ph.D. dissertation, Paper No. 5117, EPFL.
27.
Avellan
,
F.
,
2004
, “
Introduction to Cavitation in Hydraulic Machinery
,”
Proceedings of the 6th International Conference on Hydraulic Machinery and Hydrodynamics
, Timisoara, Romania, pp. 11–22.
28.
Mauri
,
S.
,
Avellan
,
F.
, and
Kueny
,
J. L.
,
2000
, “
Numerical Prediction of the Flow in a Turbine Draft Tube: Influence of the Boundary Conditions
,”
Proceedings of the ASME Fluids Engineering Division Summer Meeting
, Boston, MA, Paper No. FEDSM2000-11056, pp. 1–7.
29.
ANSYS,
2011
, “
ansys fluent 14.0 User's Guide
,”
Ansys Inc.
,
Canonsburg, PA
.
30.
Dörfler
,
P. K.
,
1994
, “
Observation of the Pressure Pulsation on Francis Model Turbine With High Specific Speed
,”
Int. J. Hydropower Dams
, pp.
21
26
.
31.
American Society of Civil Engineers Hydropower Task Committee,
2007
, “
Civil Works for Hydroelectric Facilities: Guidelines for Life Extension and Upgrade
,”
ASCE Publications
,
Reston, VA
.
You do not currently have access to this content.