Abstract

The amplitudes induced by random excitation forces on the tubes bring continuous friction between the tube and supports, which results in gradual failure of the tubes due to fretting wear. Therefore, it is very important to determine the envelope lines of the random excitation force spectrum for the coil tube. To the authors' knowledge, there are no published studies on the normalized force spectrum of coil tubes. In this paper, a simplified three-layer experimental model was established. The robustness of the numerical method was demonstrated by comparing the experimental and simulated results, including the vibration response and the fluid excitation force spectrum. Then, a semi-empirical equation for predicting the dominant frequency of turbulent buffeting was constructed by employing the threshold envelope method. Through the observation of time-history and root-mean-square (RMS) data, it was found that the pitch diameter ratio between adjacent tube layers, a, had the greatest influence on the force coefficients. The smaller a is, the larger the force coefficients are. The pitch diameter ratio in the same layer, b, and helix angle, α, had little effect on the force coefficients. With the increase of α, the flow instability in the shell-side flow enhanced and the fluctuation of force coefficients became larger. Finally, the mechanisms of the tube position, Reynolds number (Re), and bundle structure on the normalized force spectrum were studied. The normalized envelope force spectrum for coil tubes was proposed as the guidelines to predict and evaluate the random excitation force acting on the tubes.

References

1.
Hu
,
H. T.
,
Ding
,
C.
,
Ding
,
G. L.
,
Chen
,
J.
,
Mi
,
X. G.
, and
Yu
,
S. C.
,
2019
, “
Heat Transfer Characteristics of Two-Phase Mixed Hydrocarbon Refrigerants Flow Boiling in Shell Side of LNG Spiral Wound Heat Exchanger
,”
Int. J. Heat Mass Transfer
,
131
, pp.
611
622
.10.1016/j.ijheatmasstransfer.2018.11.106
2.
Abolmaali
,
A. M.
, and
Afshin
,
H.
,
2020
, “
Numerical Study of Heat Transfer Between Shell-Side Fluid and Shell Wall in the Spiral-Wound Heat Exchangers
,”
Int. J. Refrig.
,
120
, pp.
285
295
.10.1016/j.ijrefrig.2020.08.010
3.
Sabir
,
A.
, and
Jiang
,
J.
,
2022
, “
Comparing the Dynamic Response of U-Tube and Helical Coil Steam Generators in Small Modular Reactor Flexible Operation
,”
Nucl. Eng. Des.
,
388
, p.
111610
.10.1016/j.nucengdes.2021.111610
4.
Han
,
Y.
,
Wang
,
X. S.
,
Zhang
,
H. N.
,
Chen
,
Q. Z.
, and
Zhang
,
Z.
,
2020
, “
Multi-Objective Optimization of Helically Coiled Tube Heat Exchanger Based on Entropy Generation Theory
,”
Int. J. Therm. Sci.
,
147
, p.
106150
.10.1016/j.ijthermalsci.2019.106150
5.
Wu
,
J. X.
,
Wang
,
L.
, and
Liu
,
Y. H.
,
2018
, “
Research on Film Condensation Heat Transfer of the Shell Side of the Spiral Coil Heat Exchanger
,”
Int. J. Heat Mass Transfer
,
125
, pp.
1349
1355
.10.1016/j.ijheatmasstransfer.2018.05.029
6.
Gao
,
W. K.
,
Li
,
X. W.
,
Wu
,
X. X.
,
Zhao
,
J. Q.
, and
Luo
,
X. W.
,
2020
, “
Influences of Fabrication Tolerance on Thermal Hydraulic Performance of HTGR Helical Tube Once Through Steam Generator
,”
Nucl. Eng. Des.
,
363
, p.
110665
.10.1016/j.nucengdes.2020.110665
7.
Yang
,
Y. P.
,
Wang
,
C. L.
,
Zhang
,
D. L.
,
Lan
,
Z. K.
,
Zhu
,
D. H.
,
Qiu
,
S. Z.
,
Su
,
G. H.
, and
Tian
,
W. X.
,
2022
, “
Numerical Analysis of Liquid Metal Helical Coil Once-Through Tube Steam Generator
,”
Ann. Nucl. Energy
,
167
, p.
108860
.10.1016/j.anucene.2021.108860
8.
Ingersoll
,
D. T.
,
Houghton
,
Z. J.
,
Bromm
,
R.
, and
Desportes
,
C.
,
2014
, “
NuScale Small Modular Reactor for Co-Generation of Electricity and Water
,”
Desalination
,
340
, pp.
84
93
.10.1016/j.desal.2014.02.023
9.
Guo
,
K.
,
Xu
,
W.
,
Jia
,
Z. B.
, and
Tan
,
W.
,
2020
, “
Investigation of Fluid-Elastic Instability in Tube Arrays at Low Mass Damping Parameters in Cross-Flow
,”
ASME J. Pressure Vessel Technol.
,
142
(
1
), p.
011401
.10.1115/1.4045022
10.
Kevlahan
,
N. K. R.
,
2011
, “
The Role of Vortex Wake Dynamics in the Flow-Induced Vibration of Tube Arrays
,”
J. Fluid Struct.
,
27
(
5–6
), pp.
829
837
.10.1016/j.jfluidstructs.2011.03.023
11.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
2003
, “
Vibration Analysis of Shell-and-Tube Heat Exchangers: An Overview—Part 1: Flow, Damping, Fluidelastic Instability
,”
J. Fluid Struct.
,
18
(
5
), pp.
469
483
.10.1016/j.jfluidstructs.2003.08.007
12.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
2003
, “
Vibration Analysis of Shell-and-Tube Heat Exchangers: An Overview—Part 2: Vibration Response, Fretting-Wear, Guidelines
,”
J. Fluid Struct.
,
18
(
5
), pp.
485
500
.10.1016/j.jfluidstructs.2003.08.008
13.
Owen
,
P. R.
,
1965
, “
Buffeting Excitation of Boiler Tube Vibration
,”
J. Mech. Eng. Sci.
,
7
(
4
), pp.
431
439
.10.1243/JMES_JOUR_1965_007_065_02
14.
Weaver
,
D. S.
, and
Frrzpatrick
,
J. A.
,
1988
, “
A Review of Cross-Flow Induced Vibrations in Heat Exchanger Tube Arrays
,”
J. Fluid Struct.
,
2
, pp.
73
93
.10.1016/S0889-9746(88)90137-5
15.
Blevins
,
R. D.
, and
Burton
,
T. E.
,
1976
, “
Fluid Forces Induced by Vortex Shedding
,”
ASME J. Fluids Eng.
,
98
(
1
), pp.
19
24
.10.1115/1.3448196
16.
Blevins
,
R. D.
,
Gibert
,
R. J.
, and
Villard
,
B.
,
1981
, “
Experiments on Vibration of Heat-Exchanger Tube Arrays in Cross Flow
,”
Transactions Sixth International Conference on Structural Mechanics in Reactor Technology
, Paris, France, Aug. 17, pp.
1
31
.https://inis.iaea.org/search/search.aspx?orig_q=RN:13675708
17.
Chen
,
S. S.
, and
Jendrzejczyk
,
J. A.
,
1987
, “
Fluid Excitation Forces Acting on a Square Tube Array
,”
ASME J. Fluids Eng.
,
109
(
4
), pp.
415
423
.10.1115/1.3242682
18.
Taniguchi
,
S.
, and
Miyakoshi
,
K.
,
1990
, “
Fluctuating Fluid Forces Acting on a Circular Cylinder and Interference With a Plane Wall
,”
Exp. Fluids
,
9
(
4
), pp.
197
204
.10.1007/BF00190418
19.
Taylor
,
C. E.
,
Pettigrew
,
M. J.
,
Axisa
,
F.
, and
Villard
,
B.
,
1988
, “
Experimental Determination of Single and Two-Phase Cross Flow-Induced Forces on Tube Rows
,”
ASME J. Pressure Vessel Technol.
,
110
(
1
), pp.
22
28
.10.1115/1.3265563
20.
Axisa
,
F.
,
Antunes
,
J.
, and
Vilard
,
B.
,
1990
, “
Random Excitation of Heat Exchanger Tubes by Cross-Flows
,”
J. Fluid Struct.
,
4
, pp.
321
341
.10.1016/S0889-9746(05)80018-0
21.
Paїdoussis
,
M. P.
, and
Price
,
S. J.
,
1988
, “
The Mechanisms Underlying Flow-Induced Instabilities of Cylinder Arrays in Crossflow
,”
J. Fluid Mech.
,
187
, pp.
45
59
.10.1017/S0022112088000333
22.
Norberg
,
C.
,
1993
, “
Pressure Forces on a Circular Cylinder in Cross Flow
,”
Bluff-Body Wakes, Dynamics and Instabilities
,
Gottingen, Germany
, pp.
275
278
.
23.
Norberg
,
C.
,
2001
, “
Flow Around a Circular Cylinder: Aspects of Fluctuating Lift
,”
J. Fluid Struct.
,
15
, pp.
459
469
.10.1006/jfls.2000.0367
24.
Perrot
,
E. S.
,
Mureithi
,
N. W.
,
Pettigrew
,
M. J.
, and
Ricciardi
,
G.
,
2011
, “
Vibration Excitation Forces in a Normal Triangular Tube Bundle Subjected to Two-Phase Cross Flow
,”
ASME
Paper No. PVP2011-57102.10.1115/PVP2011-57102
25.
Liu
,
L. Y.
,
Feng
,
J. X.
,
Wu
,
H.
,
Xu
,
W.
, and
Tan
,
W.
,
2017
, “
Fluid Excitation Forces on a Tightly Packed Tube Bundle Subjected in Cross-Flow
,”
ASME J. Pressure Vessel Technol.
,
139
(
3
), p.
031307
.10.1115/1.4035318
26.
Sun
,
K. J.
,
Nie
,
X. C.
,
Tan
,
T.
,
Yu
,
Z. Y.
, and
Yan
,
Z. M.
,
2022
, “
Coupled Vortex-Induced Modeling for Spatially Large-Curved Beam With Elastic Support
,”
Int. J. Mech. Sci.
,
214
, p.
106903
.10.1016/j.ijmecsci.2021.106903
27.
Blevins
,
R. D.
,
1994
, “
Turbulence-Induced Vibration of Heat Exchanger Tubes in Cross Flow
,” Paper No. 273, pp.
199
210
.
28.
Xu
,
X. Q.
,
Mallet
,
M.
, and
Liszkai
,
T.
,
2014
, “
Turbulent Buffeting of Helical Coil Steam Generator Tubes
,”
ASME
Paper No. PVP2014-28868.10.1115/PVP2014-28868
29.
Yuan
,
H. M.
,
Solberg
,
J.
,
Merzari
,
E.
,
Kraus
,
A.
, and
Grindeanu
,
I.
,
2017
, “
Flow-Induced Vibration Analysis of a Helical Coil Steam Generator Experiment Using Large Eddy Simulation
,”
Nucl. Eng. Des.
,
322
, pp.
547
562
.10.1016/j.nucengdes.2017.07.029
30.
Wang
,
Y.
,
Ren
,
P.
,
Zhu
,
G. R.
, and
Tan
,
W.
,
2021
, “
Numerical Studies on Modal Analysis of Curved Tube and Coil Tube in Coil-Wound Heat Exchanger
,”
ASME
Paper No. PVP2021-61657.10.1115/PVP2021-61657
31.
Wang
,
Y.
,
Ren
,
P.
,
Huang
,
G. F.
, and
Tan
,
W.
,
2022
, “
Investigation in the Natural Frequency of Wound Tube for Coil-Wound Heat Exchanger
,”
ASME J. Pressure Vessel Technol.
,
144
(
6
), p.
061402
.10.1115/1.4054621
32.
Wang
,
Y.
,
Guo
,
S.
, and
Tan
,
W.
,
2022
, “
Detached-Eddy Simulation of the Flow Behavior in the Shell-Side of the Coil Tube Bundle in Turbulent Flow
,”
Chem. Eng. Sci.
,
261
, p.
117940
.10.1016/j.ces.2022.117940
33.
Taylor
,
C. E.
, and
Pettigrew
,
M. J.
,
2000
, “
Random Excitation Forces in Heat Exchanger Tube Bundles
,”
ASME J. Pressure Vessel Technol.
,
122
(
4
), pp.
509
514
.10.1115/1.1286040
34.
Fan
,
X. T.
,
Wang
,
Z. C.
,
Wang
,
Y.
, and
Tan
,
W.
,
2021
, “
The Effect of Vortices Structures on the Flow-Induced Vibration of Three Flexible Tandem Cylinders
,”
Int. J. Mech. Sci.
,
192
, p.
106132
.10.1016/j.ijmecsci.2020.106132
35.
Chen
,
S. S.
,
Jendrzejczyk
,
J. A.
, and
Wambsganss
,
M. W.
,
1983
, “
Tube Vibration in a Half-Scale Sector Model of a Helical Tube Steam Generator
,”
J. Sound Vib.
,
91
(
4
), pp.
539
569
.10.1016/0022-460X(83)90832-5
36.
Fan
,
X. T.
,
Guo
,
K.
,
Jia
,
Z. B.
,
Wang
,
Y.
, and
Tan
,
W.
,
2020
, “
Vibration Mode and Velocity Interference Mechanism of Tandem Cylinders at Subcritical Reynolds Number
,”
J. Wind Eng. Ind. Aerodyn.
,
199
, p.
104136
.10.1016/j.jweia.2020.104136
37.
Fan
,
X. T.
,
Wang
,
Y.
, and
Tan
,
W.
,
2021
, “
Aerodynamic Wake Oscillator for Modeling Flow-Induced Vibration of Tandem Cylinders With Short Spans
,”
Int. J. Mech. Sci.
,
204
, p.
106548
.10.1016/j.ijmecsci.2021.106548
38.
Guo
,
X.
,
Cai
,
J.
, and
Wang
,
Y. D.
,
2018
, “
Modal Analysis of the Helical Tube in a Small Nuclear Reactor's Steam Generator Using a Finite Element Method
,”
Ann. Nucl. Energy
,
114
, pp.
354
358
.10.1016/j.anucene.2017.12.006
39.
Jo
,
J. C.
, and
Jhung
,
M. J.
,
2008
, “
Flow-Induced Vibration and Fretting-Wear Predictions of Steam Generator Helical Tubes
,”
Nucl. Eng. Des.
,
238
(
4
), pp.
890
903
.10.1016/j.nucengdes.2006.12.001
40.
Liu
,
Y.
,
Guan
,
X. R.
, and
Xu
,
C.
,
2017
, “
A Production Limiter Study of SST-SAS Turbulence Model for Bluff Body Flows
,”
J. Wind Eng. Ind. Aerodyn.
,
170
, pp.
162
178
.10.1016/j.jweia.2017.08.014
41.
Egorov
,
Y.
, and
Menter
,
F.
,
2008
, “
Development and Application of SST-SAS Turbulence Model in the DESIDER Project
,”
Advances in Hybrid RANS-LES Modelling
,
Springer
,
Berlin, Heidelberg
, pp.
261
270
.10.1007/978-3-540-77815-8_27
42.
Munoz-Paniagua
,
J.
,
García
,
J.
, and
Lehugeur
,
B.
,
2017
, “
Evaluation of RANS, SAS and IDDES Models for the Simulation of the Flow Around a High-Speed Train Subjected to Crosswind
,”
J. Wind Eng. Ind. Aerodyn.
,
171
, pp.
50
66
.10.1016/j.jweia.2017.09.006
43.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
44.
Zhang
,
P. F.
,
Wang
,
J. J.
, and
Huang
,
L. X.
,
2006
, “
Numerical Simulation of Flow Around Cylinder With an Upstream Rod in Tandem at Low Reynolds Numbers
,”
Appl. Ocean Res.
,
28
(
3
), pp.
183
192
.10.1016/j.apor.2006.08.003
45.
Zhang
,
M.
,
Hu
,
G. B.
, and
Wang
,
J. L.
,
2020
, “
Bluff Body With Built-In Piezoelectric Cantilever for Flow-Induced Energy Harvesting
,”
Int. J. Energy Res.
,
44
(
5
), pp.
3762
3777
.10.1002/er.5164
46.
Kaneko
,
S.
,
Nakamura
,
T.
,
Inada
,
F.
, and
Kato
,
M.
,
2008
,
Flow-Induced Vibrations: Classifications and Lessons From Practical Experiences
, 1st ed.,
Elsevier
,
Oxford, UK
.
47.
ASME,
2019
,
ASME Appendices-III-2019
,
ASME
,
New York
.
48.
Delgado
,
M.
,
Porter
,
G. A.
,
Hassan
,
Y. A.
, and
Anand
,
N. K.
,
2020
, “
Experimental Shell-Side Surface Pressure Measurements on Tubes Within a Model Helical Coil Heat Exchanger
,”
Nucl. Eng. Des.
,
370
, p.
110906
.10.1016/j.nucengdes.2020.110906
You do not currently have access to this content.