Condensing flow induced vibration (CFIV) of the rotor blade is a tough problem for designers of nuclear turbines because nonequilibrium condensing flow excitation (NECFE) is hard to be directly modeled. Generally, in design, NECFE is assumed as equilibrium condensing flow excitation (ECFE), of which the pressure fluctuations caused by phase temperature difference (PTD) between gaseous and liquid are ignored. In this paper, a novel method to calculate the equivalent load of NECFE based on the principle of virtual work was proposed. This method could consider the effects of PTD-induced pressure fluctuations by simulating nonequilibrium condensation with ANSYS cfx, and improve computational efficiency. Once the equivalent NECFE load is determined, CFIV of the rotor blade, which was modeled as a pretwisted asymmetric cantilever beam, can then be predicted by the finite element method (FEM). Additionally, to estimate the effects of PTD-induced pressure fluctuations, comparisons between NECFE and ECFE as well as their induced vibrations were presented. Results show that PTD in nucleation area could change the position and type of shock waves, restructure the pressure distribution, as well as enhance the pressure fluctuations. Compared with ECFE, the frequency ingredients and amplitude of the equivalent NECFE load and its induced vibrations are increased. Specifically, the amplitude of the equivalent NECFE load is increased by 9.38%, 15.34%, and 7.43% in the tangential component, axial component, and torsion moment. The blade vibration responses induced by NECFE are increased by 11.66% and 19.94% in tangential and axial.

References

1.
White
,
A. J.
, and
Walters
,
P. T.
,
1996
, “
Experimental Validation of Condensing Flow Theory for a Stationary Cascade of Steam Turbine Blades
,”
Philos. Trans. R. Soc., A
,
354
(
1704
), pp.
59
88
.
2.
Naudascher
,
E.
, and
Rockwell
,
D.
,
2012
,
Flow-Induced Vibrations: An Engineering Guide
,
Dover Publications
,
Mineola, NY
.
3.
Lau
,
Y. L.
,
Leung
,
R. C. K.
, and
So
,
R. M. C.
,
2007
, “
Vortex-Induced Vibration Effect on Fatigue Life Estimate of Turbine Blades
,”
J. Sound Vib.
,
307
(
3–5
), pp.
698
719
.
4.
Wang
,
D.
,
Chen
,
Y.
,
Wiercigroch
,
M.
, and
Cao
,
Q.
,
2016
, “
A Three-Degree-of-Freedom Model for Vortex-Induced Vibrations of Turbine Blades
,”
Meccanica
,
51
(11), pp. 2607–2628.
5.
Fuhrer
,
C.
,
Grübel
,
M.
,
Vogt
,
D. M.
, and
Petrie-Repar
,
P.
,
2016
, “
The Influence of Non-Equilibrium Wet Steam Effects on the Aeroelastic Properties of a Turbine Blade Row
,”
ASME
Paper No. GT2016-57899.
6.
Petrie-Repar
,
P.
,
Makhnov
,
V.
,
Shabrov
,
N.
,
Smirnov
,
E.
,
Galaev
,
S.
, and
Eliseev
,
K.
,
2014
, “
Advanced Flutter Analysis of a Long Shrouded Steam Turbine Blade
,”
ASME
Paper No. GT2014-26874.
7.
Gong
,
S.
,
Ren
,
L.
, and
Liu
,
H.
,
2007
, “
Fluid-Solid Interaction of Rotor Blade in Last Stage of Steam Turbine
,”
Therm. Turbine
,
36
(
3
), pp.
153
157
.
8.
García
,
J.
,
Kubiak
,
J.
,
Sierra
,
F.
,
Urquiza
,
G.
, and
Rodríguez
,
J.
,
2007
, “
Numerical Analysis of the Blade Forces Caused by Wake/Blade Interaction in the Last Stage of a Steam Turbine
,”
ASME
Paper No. POWER2007-22029.
9.
Baik
,
Y. S.
,
Bernal
,
L. P.
,
Granlund
,
K.
, and
Ol
,
M. V.
,
2012
, “
Unsteady Force Generation and Vortex Dynamics of Pitching and Plunging Aerofoils
,”
J. Fluid Mech.
,
709
, pp.
37
68
.
10.
Carnegie
,
W.
,
1959
, “
Vibrations of Pre-Twisted Cantilever Blading
,”
Proc. Inst. Mech. Eng.
,
173
(
1
), pp.
343
374
.
11.
Carnegie
,
W.
, and
Dawson
,
B.
,
1971
, “
Vibration Characteristics of Pre-Twisted Blades of Asymmetrical Aerofoil Cross-Section
,”
Aeronaut. Q.
,
22
(
3
), pp.
257
273
.
12.
Rao
,
J.
, and
Banerjee
,
S.
,
1977
, “
Coupled Bending-Torsional Vibrations of Rotating Cantilever Blades—Method of Polynomial Frequency Equation
,”
Mech. Mach. Theory
,
12
(
4
), pp.
271
280
.
13.
Subrahmanyam
,
K. B.
,
Kulkarni
,
S. V.
, and
Rao
,
J. S.
,
1981
, “
Coupled Bending-Torsion Vibrations of Rotating Blades of Asymmetric Aerofoil Cross Section With Allowance for Shear Deflection and Rotary Inertia by Use of the Reissner Method
,”
J. Sound Vib.
,
75
(
1
), pp.
17
36
.
14.
Zheng Runseng
,
W. H.
,
1991
, “
A Finite Element Method With Twisted Beam Elements for Analysing Vibration of Long Blades of Steam Turbine
,”
J. Xi'an Jiaotong Univ.
,
25
(
3
), pp.
99
110
.http://xueshu.baidu.com/s?wd=paperuri%3A%288cb1f578815afd5e92695a46b610be59%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fen.cnki.com.cn%2FArticle_en%2FCJFDTOTAL-XAJT199103014.htm&ie=utf-8&sc_us=1789015856372650716
15.
Thomas
,
J.
, and
Sabuncu
,
M.
, 1979, “
Finite Element Analysis of Rotating Pretwisted Asymmetric Cross-Section Blades
,”
ASME Paper No.
79-DET-95.
16.
Rao
,
S. S.
, and
Gupta
,
R. S.
,
2001
, “
Finite Element Vibration Analysis of Rotating Timoshenko Beams
,”
J. Sound Vib.
,
242
(
1
), pp.
103
124
.
17.
Sabuncu
,
M.
, and
Evran
,
K.
,
2006
, “
Dynamic Stability of a Rotating Pre-Twisted Asymmetric Cross-Section Timoshenko Beam Subjected to an Axial Periodic Force
,”
Int. J. Mech. Sci.
,
48
(
8
), pp.
579
590
.
18.
Chen
,
L. W.
, and
Peng
,
W. K.
,
1995
, “
Dynamic Stability of Rotating Blades With Geometric Non-Linearity
,”
J. Sound Vib.
,
187
(
3
), pp.
421
433
.
19.
Celep
,
Z.
,
1985
, “
Dynamic Stability of Pretwisted Columns Under Periodic Axial Loads
,”
J. Sound Vib.
,
103
(
1
), pp.
35
42
.
20.
Lee
,
H. P.
,
1994
, “
Buckling and Dynamic Stability of Spinning Pre-Twisted Beams Under Compressive Axial Loads
,”
Int. J. Mech. Sci.
,
36
(
11
), pp.
1011
1026
.
21.
Gürgöze
,
M.
,
1985
, “
On the Dynamic Stability of a Pre-Twisted Beam Subject to a Pulsating Axial Load
,”
J. Sound Vib.
,
102
(
3
), pp.
415
422
.
22.
Şakar
,
G.
, and
Sabuncu
,
M.
,
2003
, “
Dynamic Stability of a Rotating Asymmetric Cross-Section Blade Subjected to an Axial Periodic Force
,”
Int. J. Mech. Sci.
,
45
(
9
), pp.
1467
1482
.
23.
Şakar
,
G.
, and
Sabuncu
,
M.
,
2004
, “
Buckling and Dynamic Stability of a Rotating Pretwisted Asymmetric Cross-Section Blade Subjected to an Axial Periodic Force
,”
Finite Elem. Anal. Des.
,
40
(
11
), pp.
1399
1415
.
24.
Sabuncu
,
M.
, and
Evran
,
K.
,
2006
, “
The Dynamic Stability of a Rotating Pre-Twisted Asymmetric Cross-Section Timoshenko Beam Subjected to Lateral Parametric Excitation
,”
Int. J. Mech. Sci.
,
48
(
8
), pp.
878
888
.
25.
Ford
,
I.
,
2004
, “
Statistical Mechanics of Nucleation: A Review
,”
Proc. Inst. Mech. Eng., Part C
,
218
(
8
), pp.
883
899
.
26.
Young
,
J. B.
,
1992
, “
Two-Dimensional Nonequilibrium, Wet-Steam Calculations for Nozzles and Turbine Cascades
,”
ASME J. Turbomach.
,
114
(
3
), pp.
569
579
.
27.
Young
,
J. B.
,
1982
, “
The Spontaneous Condensation of Steam in Supersonic Nozzles
,”
Physico Chem. Hydrodyn.
,
3
(
1
), pp.
57
82
.
28.
Moses
,
C. A.
, and
Stein
,
G. D.
,
1978
, “
On the Growth of Steam Droplets Formed in a Laval Nozzle Using Both Static Pressure and Light Scattering Measurements
,”
ASME J. Fluids Eng.
,
100
(
3
), pp.
311
322
.
29.
Grübel
,
M.
,
Starzmann
,
J.
,
Schatz
,
M.
,
Eberle
,
T.
,
Vogt
,
D. M.
, and
Sieverding
,
F.
,
2014
, “
Two-Phase Flow Modeling and Measurements in Low-Pressure Turbines—Part I: Numerical Validation of Wet Steam Models and Turbine Modeling
,”
ASME
Paper No. GT2014-25244.
30.
Schatz
,
M.
,
Eberle
,
T.
,
Grübel
,
M.
,
Starzmann
,
J.
,
Vogt
,
D. M.
, and
Suerken
,
N.
,
2014
, “
Two-Phase Flow Modeling and Measurements in Low-Pressure Turbines—Part II: Turbine Wetness Measurement and Comparison to Computational Fluid Dynamics-Predictions
,”
ASME
Paper No. GT2014-25245.
31.
Wroblewski
,
W.
,
Dykas
,
S.
,
Gardzilewicz
,
A.
, and
Kolovratnik
,
M.
,
2009
, “
Numerical and Experimental Investigations of Steam Condensation in LP Part of a Large Power Turbine
,”
ASME J. Fluids Eng.
,
131
(
4
), p.
041301
.
32.
Dykas
,
S.
,
Majkut
,
M.
,
Strozik
,
M.
, and
Smołka
,
K.
,
2015
, “
Experimental Study of Condensing Steam Flow in Nozzles and Linear Blade Cascade
,”
Int. J. Heat Mass Transfer
,
80
, pp.
50
57
.
33.
K. Ishazaki, T. I., and
Daiguji
,
H.
,
1995
, “
A High-Resolution Numerical Method for Transonic Non-Equilibrium Condensation Flows Through a Steam Turbine Cascade
,” Sixth International Symposium on Computational Fluid Dynamics, Lake Tahoe, NV, Sept. 4–8, pp.
479
484
.
You do not currently have access to this content.