Abstract

Differential longitudinal thermal expansion between the shell and the tube bundle is a well-known problem in fixed tubesheet heat exchanger design. An expansion bellows provide flexibility for thermal expansion and also function as a pressure retaining part. In this paper, guidelines for design of flanged and flued type (thick wall) expansion bellows available in international codes and standards including ASME VIII-1 and 2, EN-13445, and TEMA and EJMA codes are presented. These codes and standards are compared in terms of information available for thick wall expansion bellows design with regard to condition of applicability of design formula, spring rate determination, parameter to define the initial geometry, stress determination, and fatigue evaluation. Inherent limitations of these codes with respect to expansion bellows design, research gape, and recommendations for effective design are also presented in this paper. Brief history and information provided in various codes and standards related to unreinforced thin wall expansion bellows (bellows expansion joints) are also presented to understand evaluation of expansion bellows design.

References

1.
EJMA,
2008
, “
Standards of the Expansion Joint Manufacturers Association
,” Expansion Joint Manufacturers Association, Tarrytown, NY, Chap. 4.
2.
ASME
,
2017
, “
ASME Boiler and Pressure Vessel Code, Section VIII, Division 1—Pressure Vessels
,” American Society of Mechanical Engineers, New York, Chap. UHX, Appendix 26, Appendix 5.
3.
ASME,
2017
, “
ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, Pressure Vessels Alternative Rules
,” American Society of Mechanical Engineers, New York, Chap. 4.19, 4.8.12, and 4.20.
4.
EN-13445-3
,
2013
, “
Unfired Pressure Vessels
,” Berlin, Chap. 14.
5.
TEMA,
2007
, “
Standards of the Tubular Exchanger Manufacturers Association
,” Tubular Exchanger Manufacturers Association, Tarrytown, NY, Chap. RCB-8.
6.
Kopp
,
S.
, and
Sayre
,
1952
, “
Expansion Joints for Heat Exchangers
,”
ASME Winter Annual Meeting, New York
.
7.
Thulukkanam
,
K.
,
2013
,
Heat Exchanger Design Handbook
, 2nd ed.,
CRC Press
,
Boca Raton, FL
, pp.
644
652
.
8.
AD 2000-Merkblatt
, “
Design of Pressure Vessels, Single-Ply Bellows Expansion Joints
,” Berlin.
9.
GOST,
2002
, “
Steel Vessels and Apparatus, Bellows-Type Expansion Joints, Strength Calculation Methods
,” Russian Federation, Russia, Standard No. 30780.
10.
Indian Standard
,
1993
, “
Specification for Shell and Tube Type Heat Exchangers
,” New Delhi, India, Standard No. IS:4503.
11.
GB16749,
1997
, “
National Standard for the People's Republic Of China, Bellows, Expansion Joint for Pressure Vessel
,” Russian Federation, Russia, Chap. 4.
12.
Anderson
,
W. F.
,
Analysis of Stresses in Bellows
,
Division of North American Aviation
,
Inglewood, CA
, Report No. NAA-SR-4527.
13.
Wolf
,
L. J.
, and
Mains
,
R. M.
,
1973
, “
The Stress Analysis of Heat Exchanger Expansion Joints in the Elastic Range
,”
ASME J. Eng. Ind.
,
95
(
1
), pp.
145
150
.10.1115/1.3438090
14.
Chand
,
S.
, and
Garg
,
S. B. L.
,
1981
, “
Design Formulas for Expansion Bellows
,”
J. Mech. Des.
,
103
, p.
881
.10.1115/1.3255001
15.
Singh
,
K. P.
, and
Soler
,
A. I.
,
1984
,
Mechanical Design of Heat Exchangers and Pressure Vessel Components
,
Arcturus
,
Cherry Hill, NJ
.
16.
Singh
,
K. P.
, and
Soler
,
A. I.
,
1991
, “
A Rational Procedure for Analyzing Flanged and Flued Expansion Joints
,”
ASME J. Pressure Vessel Technol.
,
113
(
1
), pp.
64
70
.10.1115/1.2928729
17.
Becht
,
C.
, IV
,
2002
, “
An Evaluation of EJMA Stress Calculation for Unreinforced Bellows
,”
ASME J. Pressure Vessel Technol.
,
124
(
1
), pp.
124
129
.10.1115/1.1426405
18.
Sheng
,
S.
, and
Li
,
Y.
,
2004
, “
Strength Analysis and Structural Optimization of U-Shaped Bellows
,”
Int. J. Pressure Vessels Piping
,
42
(
1
), pp.
33
46
.10.1016/0308-0161(90)90053-K
19.
Zhiming
,
L.
,
Jie
,
J.
,
Zengliang
,
G.
, and
Yi
,
Q.
,
2003
, “
Effects of Axial Deformation Load on in-Plane Instability of U-Shaped Bellows
,”
ASME J. Pressure Vessel Technol.
,
125
(
4
), p.
475
.10.1115/1.1613302
20.
Tsukimori
,
K.
,
2001
, “
Theoretical Modeling of Creep Behavior of Bellows and Some Applications
,”
ASME J. Pressure Vessel Technol.
,
123
(
2
), pp.
179
190
.10.1115/1.1320817
21.
Koh
,
B. K.
, and
Park
,
G. J.
,
1998
, “
Analysis and Optimization of Bellows With General Shape
,”
ASME J. Pressure Vessel Technol.
,
120
(
4
), pp.
325
333
.10.1115/1.2842339
22.
Morishita
,
M.
,
Ikahata
,
N.
, and
Kitamura
,
S.
,
1991
, “
Simplified Dynamic Analysis Methods for Metallic Bellows Expansion Joints
,”
ASME J. Pressure Vessels Technol.
,
113
(
4
), pp.
504
510
.10.1115/1.2928787
23.
Kim
,
J.-B.
,
2015
, “
The Effects of Convolution Geometry and Boundary Condition on the Failure of Bellows
,”
Indian J. Sci. Technol.
,
8
(
S1
), pp.
462
466
.http://www.indjst.org/index.php/indjst/article/view/59417/0
24.
Dahl
,
N. C.
,
1953
, “
Toroidal-Shell Expansion Joint
,”
ASME J. Appl. Mech.
,
20
, pp.
497
503
.
25.
Turner
,
C. E.
, and
Ford
,
H.
,
1957
, “
Stress and Deflection Studies of Pipeline Expansion Bellows
,”
Proc. Inst. Mech. Eng.
,
171
(
1
), pp.
526
552
.10.1243/PIME_PROC_1957_171_047_02
26.
Hamada
,
M.
, and
Takezono
,
S.
, “
Strength of U-Shaped Bellows: 3rd Report, Case of Loading of Internal Pressure
,”
Bull. Jpn. Soc. Mech. Eng.
,
9
(
35
), pp.
513
523
.10.1299/jsme1958.9.513
27.
Hamada
,
M.
,
Nakagawa
,
K.
,
Miyata
,
K.
, and
Nakade
,
K.
,
1971
, “
Bending Deformation of U-Shaped Bellows
,”
Bull. Jpn. Soc. Mech. Eng.
,
14
(
71
), pp.
401
409
.10.1299/jsme1958.14.401
28.
Hamada
,
M.
,
Inoue
,
Y.
,
Nakatani
,
T.
, and
Moriishi
,
M.
,
1976
, “
Design Diagrams and Formulae for U-Shaped Bellows
,”
Int. J. Pressure Vessels Piping
,
4
(
4
), pp.
315
328
.10.1016/0308-0161(76)90003-X
29.
Janzen
,
P.
,
1979
, “
Formulae and Graphs of Elastic Stresses for Design and Analysis of U-Shaped Bellows
,”
Int. J. Pressure Vessels Piping
,
7
(
6
), pp.
407
423
.10.1016/0308-0161(79)90006-1
30.
Becht
,
C.
, and
Skopp
,
G.
,
1981
, “
Stress Analysis of Bellows
,” ASME PVP-Vol. 51.
31.
Hamada
,
M.
, and
Tanaka
,
M.
,
1978
, “
Design of U-Shaped Bellows Considering Low-Cycle Fatigue
,”
ASME J. Pressure Vessel Technol.
,
100
(
4
), pp.
382
388
.10.1115/1.3454485
32.
Hamada
,
M.
, and
Tanaka
,
M.
,
1974
, “
A Consideration on the Low-Cycle Fatigue Life of Bellows: The Fatigue Life under Completely-Reversed-Deflection Cycles
,”
Bull. Jpn. Soc. Mech. Eng.
,
17
(
103
), pp.
41
49
.10.1299/jsme1958.17.41
33.
Campbell
,
R. D.
,
Cloud
,
R. L.
, and
Bushnell
,
D.
,
1981
, “
Creep Instability in Flexible Piping Joints
,” The Joint Conference of the Pressure Vessels and Piping, Materials, Nuclear Engineering, Solar Energy Divisions, Denver, CO, June 21–25.
34.
Kobatake
,
K.
,
Takahashi
,
S.
,
Osaki
,
T.
,
Shimakawa
,
T.
, and
Baba
,
O.
,
1981
, “
Fatigue Life Prediction of Bellows Joints at Elevated Temperature
,”
ASME
Paper No. 280.
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