Added mass and hydrodynamic damping play significant roles in fluid-structure interaction (FSI) in hydraulic turbines. Added mass can reduce natural frequencies, while hydrodynamic damping could result in a higher amplitude decay speed of the vibration. In order to quantify the added mass and hydrodynamic damping of a three-dimensional (3D) NACA 0009 hydrofoil with a blunt trailing edge, a two-way FSI simulation method was employed. The effects of grid scale, time-step, turbulence model, exciting force, and numerical damping on the calculation accuracy of the two-way FSI numerical simulation were analyzed in great detail through comparison with the previously published experimental data. Hydraulic force was obtained by using a transitional shear stress transport model at the flow region of the Reynolds number ReL = 0.2 × 106–2 × 106. The vortex shedding frequency, the natural frequency of the first-order bending mode in water, and the hydrodynamic damping ratio obtained from the numerical simulations agree well with the experimental data, with maximum deviations in 6.12%, 4.53%, and 8.82%, respectively. As the flow velocity increases, the natural frequency may not significantly change, while the added mass coefficient gradually increases, considering the effect of added stiffness. Above the first-order bending mode lock-in region, the results indicate that the first-order bending mode hydrodynamic damping ratio increases linearly with velocity. The present numerical achievements offer a higher level of accuracy for predicting the added mass and hydrodynamic damping characteristics of a hydrofoil.

References

1.
Trivedi
,
C.
, and
Cervantes
,
M. J.
,
2017
, “
Fluid-Structure Interactions in Francis Turbines: A Perspective Review
,”
Renewable Sustainable Energy Rev.
,
68
, pp.
87
101
.
2.
Liang
,
Q. W.
,
Rodríguez
,
C. G.
,
Egusquiza
,
E.
,
Escaler
,
X.
,
Farhat
,
M.
, and
Avellan
,
F.
,
2007
, “
Numerical Simulation of Fluid Added Mass Effect on a Francis Turbine Runner
,”
Comput. Fluids
,
36
(
6
), pp.
1106
1118
.
3.
Zhu
,
W. R.
,
Gao
,
Z. X.
,
Lu
,
L.
, and
Wang
,
F. J.
,
2013
, “
Analysis and Optimization on Natural Frequencies Depreciation Coefficient of Centrifugal Pump Impeller in Water
,”
J. Hydraulic Eng.
,
44
(
12
), pp.
1455
1461
.
4.
Liu
,
X.
,
Zhou
,
L. J.
,
Escaler
,
X.
, and
Wang
,
Z. W.
,
2017
, “
Numerical Simulation of Added Mass Effects on a Hydrofoil in Cavitating Flow Using Acoustic Fluid–Structure Interaction
,”
ASME J. Fluids Eng.
,
139
(
4
), p. 041301.
5.
Kramer
,
M. R.
,
Liu
,
Z. K.
, and
Young
,
Y. L.
,
2012
, “
Free Vibration of Cantilevered Composite Plates in Air and in Water
,”
Compos. Struct.
,
95
, pp.
254
263
.
6.
Torre
,
O. D. L.
,
Escaler
,
X.
,
Egusquiza
,
E.
, and
Farhat
,
M.
,
2014
, “
Numerical and Experimental Study of a Nearby Solid Boundary and Partial Submergence Effects on Hydrofoil Added Mass
,”
Comput. Fluids
,
91
(
7
), pp.
1
9
.
7.
Torre
,
O. D. L.
,
Escaler
,
X.
,
Egusquiza
,
E.
, and
Farhat
,
M.
,
2013
, “
Experimental Investigation of Added Mass Effects on a Hydrofoil Under Cavitation Conditions
,”
J. Fluids Struct.
,
39
(
5
), pp.
173
187
.
8.
Yao
,
Z. F.
,
Wang
,
F. J.
,
Dreyer
,
M.
, and
Farhat
,
M.
,
2014
, “
Effect of Trailing Edge Shape on Hydrodynamic Damping for a Hydrofoil
,”
J. Fluids Struct.
,
51
, pp.
189
198.
9.
Seeley
,
C.
,
Coutu
,
A.
,
Monette
,
C.
,
Nennemann
,
B.
, and
Marmont
,
H.
,
2012
, “
Characterization of Hydrofoil Damping Due to Fluid-Structure Interaction Using Piezocomposite Actuators
,”
Smart Mater. Struct.
,
21
(
3
), pp.
35027
35035
.
10.
Coutu
,
A.
,
Seeley
,
C.
,
Monette
,
C.
,
Nennemann
,
B.
, and
Marmont
,
H.
,
2012
, “
Damping Measurements in Flowing Water
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
15
(
6
), p.
062060
.
11.
Gauthier
,
J. P.
,
Giroux
,
A. M.
,
Etienne
,
S.
, and
Gosselin
,
F. P.
,
2017
, “
A Numerical Method for the Determination of Flow-Induced Damping in Hydroelectric Turbines
,”
J. Fluids Struct.
,
69
, pp.
341
354
.
12.
Chaplin
,
J. R.
, and
Subbiah
,
K.
,
1998
, “
Hydrodynamic Damping of a Cylinder in Still Water and in a Transverse Current
,”
Appl. Ocean Res.
,
20
(
4
), pp.
251
259
.
13.
Chaplin
,
J. R.
, and
Retzler
,
C. H.
,
2001
, “
Hydrodynamic Damping of the Vertical Motion of a Horizontal Cylinder Beneath Waves at Large Scale
,”
J. Fluids Struct.
,
15
(
7
), pp.
929
940
.
14.
Chaplin
,
J. R.
,
2000
, “
Hydrodynamic Damping of a Cylinder at β ≈ 106
,”
J. Fluids Struct.
,
14
(
8
), pp.
1101
1117
.
15.
Roth
,
S.
,
Calmon
,
M.
,
Farhat
,
M.
,
Muench
,
C.
,
Huebner
,
B.
, and
Avellan
,
F.
,
2009
, “
Hydrodynamic Damping Identification From an Impulse Response of a Vibration Blade
,”
Third IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems
,
Brno, Czech Republic
,
Oct. 14–16
, pp.
253
260
.
16.
Bergan
,
C. W.
,
Solemslie
,
B. S.
,
Østby
,
P.
, and
Dahlhaug
,
O. G.
,
2018
, “
Hydrodynamic Damping of a Fluttering Hydrofoil in High-Speed Flows
,”
Int. J. Fluid Mach. Syst.
,
11
(
2
), pp.
146
153
.
17.
Trivedi
,
C.
,
2017
, “
A Review on Fluid Structure Interaction in Hydraulic Turbines: A Focus on Hydrodynamic Damping
,”
Eng. Failure Anal.
,
77
, pp.
1
22
.
18.
Monette
,
C.
,
Nennemann
,
B.
,
Seeley
,
C.
, and
Coutu
,
A.
,
2014
, “
Hydro-Dynamic Damping Theory in Flowing Water
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
22
(
3
), p.
032044
.
19.
Nennemann
,
B.
,
Monette
,
C.
, and
Chamberland-Lauzon
,
J.
,
2016
, “
Hydrodynamic Damping and Stiffness Prediction in Francis Turbine Runners Using CFD
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
49
(
7
), p.
072006
.
20.
Tengs
,
E. O.
,
Bergan
,
C. W.
,
Jakobsen
,
K.-R.
, and
Storli
,
P. T.
,
2018
, “
Numerical Simulation of the Hydrodynamic Damping of a Vibrating Hydrofoil
,”
29th IAHR Symposium on Hydraulic Machinery and Systems
,
Kyoto, Japan
,
Sept. 16–21
, Paper No. 033.
21.
Bergan
,
C. W.
,
Tengs
,
E. O.
,
Solemslie
,
B. W.
, and
Dahlhaug
,
O. G.
,
2018
, “
An Experimental Investigation of the Hydrodynamic Damping of Vibrating Hydrofoils
,”
29th IAHR Symposium on Hydraulic Machinery and Systems,
Kyoto, Japan
,
Sept. 16–21
, Paper No. 211.
22.
Liaghat
,
T.
,
Guibault
,
F.
,
Allenbach
,
L.
, and
Nennemann
,
B.
,
2014
, “
Two-Way Fluid-Structure Coupling in Vibration and Damping Analysis of an Oscillating Hydrofoil
,”
ASME
Paper No. IMECE2014-38441.
23.
Zeng
,
Y. S.
,
Yao
,
Z. F.
,
Yang
,
Z. J.
,
Wang
,
F. J.
, and
Hong
,
Y. P.
,
2017
, “
The Prediction of Hydrodynamic Damping Characteristics of a Hydrofoil With Blunt Trailing Edge
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
163
(
1
), p.
012041
.
24.
Dörfler
,
P.
,
Sick
,
M.
, and
Coutu
,
A.
,
2013
,
Flow-Induced Pulsation and Vibration in Hydroelectric Machinery
,
Springer
,
London
.
25.
Ausoni
,
P.
,
2009
, “
Turbulent Vortex Shedding From a Blunt Trailing Edge Hydrofoil
,”
Ph.D. dissertation
, Swiss Federal Institute of Technology Lausanne, Lausanne.https://infoscience.epfl.ch/record/138935?ln=en
26.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
, and
Huang
,
P. G.
,
2004
, “
A Correlation-Based Transition Model Using Local Variables: Part I—Model Formulation
,”
ASME
Paper No. GT2004-53452.
27.
Li
,
Y. J.
,
Chen
,
J.
,
Yao
,
Z. F.
,
Liu
,
Z. Q.
, and
Yang
,
W.
,
2017
, “
Numerical Investigation of Flow Around Blunt Trailing Edge Hydrofoil Using Transition SST Model
,”
J. Hydraulic Eng.
,
48
(
8
), pp.
993
1001
.
28.
Zheng
,
Z. W.
, and
Lei
,
J. M.
,
2016
, “
Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder
,”
Flow Turbul. Combust.
,
97
(
2
), pp.
401
426
.
29.
Langtry
,
R. B.
,
Menter
,
F. R.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
,
2006
, “
A Correlation-Based Transition Model Using Local Variables—Part II: Test Cases and Industrial Applications
,”
ASME J. Turbomach.
,
128
(
3
), pp.
423
434
.
30.
Langtry
,
R. B.
, and
Menter
,
F. R.
,
2009
, “
Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes
,”
AIAA. J.
,
47
(
12
), pp.
2894
2906
.
31.
De Silva
,
C. W.
,
2000
,
Vibration: Fundamentals and Practice
,
CRC Press
, Boca Raton, FL.
32.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
,
Freitas
,
C. J.
,
Coleman
,
H.
, and
Raad
,
P. E.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.
33.
Abdi
,
D. S.
,
Giraldo
,
F. X.
,
Constantinescu
,
E. M.
,
Carr
,
L. E.
,
Wilcox
,
L. C.
, and
Warburton
,
T. C.
,
2019
, “
Acceleration of the Implicit-Explicit Non-Hydrostatic Unified Model of the Atmosphere on Manycore Processor
,”
Int. J. High Perform. Comput. Appl.
,
33
(2), pp.
242
267
.
34.
Vu
,
T. C.
,
Nennemann
,
B.
,
Ausoni
,
P.
,
Farhat
,
M.
, and
Avellan
,
F.
,
2007
, “
Unsteady CFD Prediction of Von Kármán Vortex Shedding in Hydraulic Turbine Stay Vanes
,”
Hydro
, Granada, Spain, Oct. 15–17.https://infoscience.epfl.ch/record/113757/files/Ausoni%20et%20al.pdf
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