This paper addresses the question of damping of multispan heat exchanger tubes with liquids (mostly water) on the shell side. The different energy dissipation mechanisms that contribute to damping are investigated. The available experimental data from the literature and from our own measurements are reviewed and analyzed. Three important energy dissipation mechanisms emerge. These are viscous damping between the tube and liquid, squeeze-film damping in the clearance between the tube, and support and friction damping at the support. Viscous damping only accounts for approximately 25% of the total damping of a typical tube. Thus, about 75% of the damping energy is dissipated at the support. Squeeze-film damping appears to be the most important energy dissipation mechanism. Squeeze-film damping is related to the support width and is inversely proportional to the tube frequency. Damping is formulated in terms of tube and tube-support parameters. Semi-empirical formulations for damping of heat exchanger tubes in liquids are recommended for design purposes.

1.
Goyder
,
H. G. D.
, 1982, “
Measurement of the Natural Frequencies and Damping of Loosely Supported Tubes in Heat Exchangers
,”
Proceedings of the Third International Conference on Vibration in Nuclear Plants
, Keswick, UK, Paper No. 2.7.
2.
Haslinger
,
K. H.
, and
Thompson
,
J. P.
, 1980, “
Determination of Damping Properties in Lightly Damped Systems
,”
Proceedings of the ASME-WAM HTD
, Chicago, IL, Vol.
9
, pp.
53
63
.
3.
Chen
,
S. S.
, and
Jendrzejczyk
,
J. A.
, 1980, “
Flow-Velocity-Dependence of Damping in Tube Arrays Subjected to Liquid Cross Flow
,” ASME Paper No. 80-C2/PVP-129.
4.
Scriven
,
A. H.
, and
Hopley
,
C. E.
, 1980, “
The Effect of an Internal Two-Phase Flow on the Damping Characteristics of a Vibrating Tube
,”
Proceedings of the European Two-Phase Flow Group Meeting
, Strathclyde University, Glasgow, UK, Paper No. F2.
5.
Gravelle
,
A.
,
Ross
,
A.
,
Pettigrew
,
M. J.
, and
Mureithi
,
N. W.
, 2007, “
Damping of Tubes Due to Internal Two-Phase Flow
,”
J. Fluids Struct.
0889-9746,
23
(
3
), pp.
447
462
.
6.
Carlucci
,
L. N.
, and
Brown
,
J. D.
, 1983, “
Experimental Studies of Damping and Hydrodynamic Mass of a Cylinder in Confined Two-Phase Flow
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
105
, pp.
83
89
.
7.
Pettigrew
,
M. J.
,
Tromp
,
J. H.
, and
Mastorakos
,
J.
, 1985, “
Vibration of Tube Bundles Subjected to Two-Phase Cross Flow
,”
ASME J. Pressure Vessel Technol.
0094-9930,
107
, pp.
335
343
.
8.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
, and
Kim
,
B. S.
, 1989, “
Vibration of Tube Bundles in Two-Phase Cross Flow—Part 1: Hydrodynamic Mass and Damping
,”
ASME J. Pressure Vessel Technol.
0094-9930,
111
, pp.
466
477
.
9.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
, 2004, “
Damping of Heat Exchanger Tubes in Two-Phase Flow: Review and Design Guidelines
,”
ASME J. Pressure Vessel Technol.
0094-9930,
126
(
4
), pp.
523
533
.
10.
Fisher
,
N. J.
,
Han
,
Y.
,
Guérout
,
F. M.
, and
Janzen
,
V. P.
, 2005, “
Comparison of Predicted and Observed Fretting-Wear Damage in Nuclear Steam Generators
,” ASME Paper No. PVP2005-71390.
11.
Morandin
,
G. D.
, and
Sauvé
,
R. G.
, 2003, “
Probabilistic Assessment of Fretting Wear in Steam Generator Tubes Under Flow-Induced Vibrations
,” ASME Paper No. PVP2003-2081.
12.
Rao
,
M. S. M.
,
Laskowski
,
L. J.
,
Srikantiah
,
G. S.
, and
Ahluwalia
,
K. S.
, 1997, “
Prediction of Tube Wear Due to Flow-Induced Vibration in PWR Steam Generators
,”
Proceedings of the Fourth International Symposium on Fluid-Structure Interaction, Aeroelasticity, Flow-Induced Vibration and Noise, ASME Congress and Exhibition
, Dallas, TX, Nov. 16–21, Vol.
53
, pp.
257
264
.
13.
Pettigrew
,
M. J.
,
Carlucci
,
L. N.
,
Ko
,
P. L.
,
Holloway
,
A. G. L.
, and
Campagna
,
A. O.
, 1985, “
Computer Techniques to Analyze Shell-and-Tube Heat Exchangers
,”
Heat Transfer Eng.
0145-7632,
6
(
3
), pp.
40
52
.
14.
Gorman
,
D. J.
, 1988, “
Exact Analytical Solutions for the Free Vibration of Steam Generator U-Tubes
,”
ASME J. Pressure Vessel Technol.
0094-9930,
110
, pp.
422
429
.
15.
Pettigrew
,
M. J.
,
Goyder
,
H. G. D.
,
Qiao
,
Z. L.
, and
Axisa
,
F.
, 1986, “
Damping of Multispan Heat Exchanger Tubes—Part 1: In Gases
,”
Proceedings of the Symposium on Special Topics of Structural Vibration, ASME Pressure Vessels and Piping Conference
, Chicago, IL.
16.
Pettigrew
,
M. J.
,
Rogers
,
R. J.
, and
Axisa
,
F.
, 1986, “
Damping of Multispan Heat Exchanger Tubes—Part 2: In Liquids
,”
Proceedings of the Symposium on Special Topics of Structural Vibration, ASME Pressure Vessels and Piping Conference
, Chicago, IL.
17.
Pettigrew
,
M. J.
,
Rogers
,
R. J.
, and
Taylor
,
C. E.
, 1985, “
Damping of Heat Exchanger Tubes
,” Atomic Energy of Canada Limited, Report No. AECL-8701.
18.
Pettigrew
,
M. J.
,
Axisa
,
F.
, and
Qiao
,
Z. L.
, 1985, “
Amortissement des Tubes d’Échangeur de Chaleur en Milieu Liquide
,” Commissariat à 1’Énergie Atomique, CEN Saclay, France, Report No. DEMT/85/462.
19.
Taylor
,
C. E.
,
Pettigrew
,
M. J.
,
Dickinson
,
T. J.
,
Currie
,
I. G.
, and
Vidalou
,
P.
, 1998, “
Vibration Damping in Multispan Heat Exchanger Tubes
,”
ASME J. Pressure Vessel Technol.
0094-9930,
120
(
3
), pp.
283
289
.
20.
Hartlen
,
R. T.
, 1974, “
Effect of Support-Point Details Upon Natural Frequency and Damping of Heat Exchanger Tubes: Preliminary Laboratory Investigation
,” Ontario Hydro Research, Report No. 74-440-K.
21.
Chen
,
S. S.
, 1983, “
Design Guide for Calculating Fluid Damping for Circular Cylindrical Structures
,” Argonne National Laboratory, Report No. ANL-83-54.
22.
Collinson
,
A. E.
, and
Warneford
,
I. P.
, 1978, “
Vibration Tests of Single Heat Exchanger Tubes in Air and Static Water
,”
Proceedings of the Second International Conference on Vibration in Nuclear Plant
, Keswick, UK, Paper No. 3.3.
23.
Mulcahy
,
T. M.
, 1980, “
Fluid Forces on Rods Vibrating in Finite Length Annular Regions
,”
ASME J. Appl. Mech.
0021-8936,
47
(
2
), pp.
234
240
.
24.
Jendrzejczyk
,
J. A.
, 1984, “
Dynamic Characteristics of Heat Exchanger Tubes Vibrating in a Tube Support Plate Inactive Mode
,” Argonne National Laboratory, Report No. ANL-84-39.
25.
Rogers
,
R. J.
,
Taylor
,
C.
, and
Pettigrew
,
M. J.
, 1984, “
Fluid Effects on Multispan Heat Exchanger Tube Vibration
,” ASME Paper No. H00316.
26.
Shin
,
Y. S.
,
Jendrzejczyk
,
J. A.
, and
Wambsganss
,
M. W.
, 1977, “
Vibration of a Heat Exchanger Tube With Tube/Support Impact
,” ASME Paper No. 77-JPGC-NE-5.
27.
Kim
,
B. S.
,
Pettigrew
,
M. J.
, and
Tromp
,
J. H.
, 1988, “
Vibration Damping of Heat Exchanger Tubes in Liquids: Effects of Support Parameters
,”
J. Fluids Struct.
0889-9746,
2
, pp.
593
614
.
28.
Chen
,
S. S.
,
Wambsganss
,
M. W.
, and
Jendrzejczyk
,
J. A.
, 1976, “
Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids
,”
ASME J. Appl. Mech.
0021-8936,
43
, pp.
325
329
.
29.
Rogers
,
R. J.
, and
Ahn
,
K. J.
, 1986, “
Fluid Damping and Hydrodynamic Mass in Finite Length Cylindrical Squeeze Films With Rectilinear Motion
,”
Flow-Induced Vibration
,”
ASME
,
New York
, Vol.
104
, pp.
99
105
.
30.
Aikin
,
J. A.
,1977, personal communication.
31.
Antunes
,
J.
,
Villard
,
B.
, and
Axisa
,
F.
, 1985, “
Cross-Flow Induced Vibration of U-Bend Tubes of Steam Generator
,”
Proceedings of the Eighth International Conference on Structural Mechanics in Reactor Technology
, Brussels, Belgium, Paper No. F16/9.
32.
Gorman
,
D. J.
, 1982, personal communication.
33.
Gorman
,
D. J.
, 1983, “
Experimental Studies of the Liquid Cross-Flow Induced Vibration of Multispan Heat Exchanger Tube Bundles in Triangular and Square Arrays
,”
Proceedings of the 20th Congress of the IAHR
, Moscow, Vol.
IV
, pp.
415
426
.
34.
Halle
,
H.
, and
Wambsganss
,
M. W.
, 1980, “
Tube Vibration in Industrial Size Heat Exchanger
,” Argonne National Laboratory, Report No. ANL-CT-80-18.
35.
Heilker
,
W. K.
, 1978, personal communication.
36.
Kobate
,
K.
,
Suzuki
,
M.
,
Koishikawa
,
A.
, and
Hashimoto
,
T.
, 1980, “
Vibration Testing of a Straight Tube Type Steam Generator for FBR
,”
ASME Publication
,
PVP-41
, pp.
19
31
.
37.
Nagpal
,
V.
,
Campagna
,
A. O.
, and
Pettigrew
,
M. J.
, 1981, “
Tube Vibration in the Entrance Region of a Steam Generator for a 600 MW Nuclear Power Station
,” Atomic Energy of Canada Limited, Report No. CRNL-2093.
38.
Pettigrew
,
M. J.
,
Platten
,
J. L.
, and
Sylvestre
,
Y.
, 1973, “
Experimental Studies on Flow Induced Vibration to Support Steam Generator Design, Part II: Tube Vibration Induced by Liquid Cross-Flow in the Entrance Region of a Steam Generator
,”
Proceedings of the International Symposium on Vibration Problems in Industry
, Keswick, UK, Paper No. 424. Also, Atomic Energy of Canada Limited Report No. AECL-4515.
39.
Wambsganss
,
M. W.
,
Halle
,
H.
, and
Lawrence
,
W. P.
, 1981, “
Tube Vibration in Industrial Size Test Heat Exchanger (30° Triangular Layout—Six Crosspass Configuration)
,” Argonne National Laboratory, Report No. ANL-CT-81-42.
40.
Skop
,
R. A.
,
Ramberg
,
S. E.
, and
Ferer
,
K. M.
, 1976, “
Added Mass and Damping Forces on Circular Cylinders
,” ASME Paper No. 76-Pet-3.
41.
Rogers
,
R. J.
, 1985, personal communication.
42.
Ouziaux
,
R.
, and
Perrier
,
J.
, 1966, “
Mécanique des Fluides Appliquée
,”
Fluides Incompressibles
, 2nd ed.,
Dunod
,
Paris
, Vol.
1
.
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