Kuppan T. Heat Exchanger Design Handbook
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474
Chapter
10
11.
Singh, K. P., and Soler,
S.
I.,
Mechanical Design
of
Heat Exchangers and Pressure and Pressure
Vessel Components,
Arcturus, Cherry Hill, NJ,
1984.
12.
Gupta, J. P.,
Fundamentals
of
Heat Exchanger and Pressure Vessel Technology,
Hemisphere,
Washington, DC,
1984.
13.
Zukauskas, A. A., Vibration of tubes in heat exchangers, in
High Pe~ormance Single Phase Heat
Exchangers,
Hemisphere, Washington, DC,
1989,
pp.
3
16-348.
14.
Pettigrew, M. J., and Taylor, C.
E.,
Fluidelastic instability of heat exchanger tube bundles: Review
and design recommendations,
Trans. ASME,
J.
Pressure Vessel Technol.,
113,
242-255 (1991
).
15.
Chen,
S.
S.,
and Jendrzejczyk,
J.
A., Stability of tube arrays in crossflow,
Nuclear
Eng.
Design,
75(3), 35 1-374
(
1983).
16.
Chen,
S.
S.,
Some issues concerning fluid elastic instability of a group
of
circular cylinders
in
crossflow,
Trans. ASME,
J.
Pressure Vessel Technol., 111,
507-5 18 (1989).
17.
Shah, R. K., Flow induced vibration and noise in heat exchangers,
Proc. Seventh National Heat
and Mass Conf.,
India,
1981,
pp.
89-108.
18.
Chenoweth, J.
M.,
and Kistler,
R.
S.,
Tube vibration in shell and tube heat exchangers,
AIChE
Symp. Ser., Heat Transfer: Research and Application
(1978),
pp.
6-14.
19.
Standards of the Tubular Exchanger Manufacturers Association, 7th ed., Tubular Exchanger Manu-
facturers Association, Inc., Tarrytown, New York,
1989.
20.
American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section
111,
Appendix
N, Nonmandatory Code, New York,
1989.
21.
Paidoussis,
M.
P., and Besancon, P., Dynamics of arrays of cylinders with internal and external
axial flow,
J.
Sound Vibration,
76(3), 361-379 (1981).
22.
Goyder, H. G.
D.,
The structural dynamics of tube bundle vibration problem,
In?.
Conf.
Flair*
In-
duced Vibrations,
Bowness on Windermere, England,
12-14
May
1987.
23.
Gorman,
D.
J., Experimental study of peripheral problems in heat exchangers and steam generator,
Paper V.F4/g.,
Proc. Fourth Int. ConJ Structural Mechanics
in
Reactor Technology,
San Francisco,
1977.
24.
Chen, Y. N., and Weber,
M.,
Flow induced vibrations in tube bundle heat exchangers with crossflow
and parallel flow, in
Flow Induced Vibrations
in
Heat Exchangers, Proceedings
of
U
Symposium
Sponsored by the ASME,
New York,
1970,
pp.
57-77.
25.
Chen, Y. N., Flow induced vibration and noise in tube bank heat exchangers due
to
Von
Karmon
streets,
Trans. ASME,
J.
Eng.
Ind.,
February,
134-146 (1968).
26.
Owen, P. R., Buffeting excitation of boiler tube vibration,
J.
Mechanical
Eng.
Sci.,
(4), 431-439
(1965).
27.
Tinker, T., Shellside characteristics of shell and tube heat exchangers-A simplified rating system
for commercial heat exchangers,
Trans. ASME,
pp.
36-52 (1958).
28.
Bell, K. J.,
Delaware Method
for
Shellside Design in Heat Transfer Equipment Design
(R.
K.
Shah,
E.
C.
Subbarao, and R. A. Mashelkar, eds.), Hemisphere, Washington, DC,
1988,
pp.
145-166.
29.
Palen, J. W., and Taborek, J., Solution of shellside flow pressure drop and heat transfer by stream
analysis method,
CEP Symposium Ser. Heat Transfer,
92,
65,
Philadelphia,
1969,
pp.
53-63.
30.
Heat Transfer Research, Inc., Alambhara, CA.
31.
Heat Transfer and Fluid Flow Services, Oxon, UK.
32.
B-Jac International, Inc., Modlothian, VA.
33.
Fitz-Hugh, J.
S.,
Flow induced vibration in heat exchangers,
Int. Svmp. Vibration Problems in
Industry,
Keswick, UK,
10-12
April
1973.
34.
Zukauskas, A., and Katinas, V., Flow induced vibration in heat exchanger tube banks,
Proc. Symp.
Practical Experiences with Flow Induced Vibration,
1980,
pp.
188-196.
35.
Weaver, D.
S.,
Fitzpatrick,
J.
A., and El Kashlan,
M.
L.,
Strouhal numbers of heat exchanger tube
arrays in crossflow,
ASME Svmp.
Flow
Induced Vibration,
Chicago,
1986
(S. S.
Chen, J. C. Si-
monis, and Y.
S.
Shin, eds.), PVP vol.
104,
pp.
36.
Pettigrew, M. J., and Gorman, D. J., Vibration
of
tube bundles in liquid, and two phase crossflow,
in
Flow Induced Vibration Guidelines
(P.
Y.
Chen, ed.), PVP vol.
52
(ASME), New York,
1981.
37.
Pettigrew, M. J., and Gorman, D. J., Vibration of heat exchanger components in liquid and two
475
Flow-Induced
Vibration
phase crossflow, presented at
British Nuclear Society International Conference on Vibration
in
Nuclear Plant,
Keswick, UK, 9-12 May 1978.
38.
Rao,
M.
S.
M.,
Gupta,
G.
D.,
Eisinger,
F.
L.,
Hibbitt,
H.
D.,
and Steininger,
D.
A., Computer
modelling of vibration and wear of multispan tubes with clearances at the supports, presented at
Flow Induced Vibration Conference,
sponsored by BHRA, Bowness-Windermere, England, 12- 14
May 1987, pp. 437-448.
39.
Weaver,
D.
S.,
and Grover,
L.
K.,
Crossflow induced vibration in a tube bank-Turbulent buffeting
and fluid elastic instability,
J.
Sound Vibration,
59(2), 277-294
(
1978).
40.
Soper,
B.
M.
H.,
The effect of tube layout on the fluid elastic instability of tubes bundle in cross-
flow,
Trans.
ASME,
J.
Heat Transfer,
105,
744-750 (1983).
41.
Weaver, D.
S.,
and Schneider W., The effect of flat bar supports on the crossflow induced response
of heat exchanger U-tubes,
Trans. ASME,
J.
Eng. Power,
105,
775-78
1
(1983).
42.
Connors,
H.
J.,
Jr., Fluid elastic vibration
of
tube mays excitation by crossflow, in
Flow
Induced
Vibration in Heat Exchangers,
(D. D.
Reill, ed.), ASME, New York, 1970, pp. 42-56.
43.
Lever, J.
H.,
and Weaver,
D.
S.,
A theoretical model for fluid elastic instability in heat exchangers
tube bundles,
Trans. ASME,
J.
Pressure Vessel Technol.,
104,
147-158 (1982).
44.
Lever, J.
H.,
and Weaver,
D.
S.,
On the stability of heat exchanger tube bundles: Part 1-Modified
theoretical model,
J.
Sound Vibration,
107(3), 375-392 (1986).
45.
Lever,
J.
H.,
and Weaver,
D.
S.,
On the stability of heat exchanger tube bundles: Part 2-Numerical
results and comparison with experiments,
J.
Sound Vibration,
107(3), 393-41
1
(1986).
46.
Tanaka,
H.,
and Takahara,
S.,
Fluid elastic vibration of a tube array in crossflow,
J.
Sound Vibra-
tion,
77(1), 19-37 (1981).
47.
Tanaka,
H.,
and Takahara,
S.,
Unsteady fluid dynamic force
on
tube bundle and its dynamic effects
on vibration, in
Flow
Induced Vibration
of
Power Plant Components
(M.
K.
Au-Yang, ed.), ASME,
New York, 1980, Special Publication
No.
PVP 141, pp. 77-92.
48.
Price,
S.
J.,
and Paidoussis, M.
P.,
Fluid elastic instability of
a
double row of circular cylinders
subject to a crossflow,
Trans.
ASME,
J.
Vibration, Acoustics, Stress Reliahilih Design,
105,
59-66
(1983).
49.
Price,
S.
J., and Paidoussis,
M.
P., An improved mathematical model for the stability of cylinder
rows subjected to crossflow,
J.
Sound Vibration,
97(4), 615-640 (1984).
50.
Whiston,
G.
S.,
and Thomas,
G.
D.,
Whirling instabilities in heat exchanger tube arrays,
J.
Sound
Vibration,
81(1), 1-31 (1982).
51.
Chen,
S.
S.,
Instability mechanisms and stability criteria of a group of circular cylinders subjected
to
crossflow, Part
I,
ASME Paper No. 81-Det
21,
ASME, New York.
52.
Chen,
S.
S.,
Instability mechanisms and stability criteria-
of
a group of circular cylinders subjected
to
crossflow, Part 11: Numerical results and discussions, ASME Paper No. 81-Det 22, ASME, New
York.
53.
Chen,
S. S.,
Instability mechanism and stability criteria
of
a group of cylinders subjected
to
cross-
flow, Part I: Theory; Part 11: Numerical results and discussions,
J.
Vibration, Acoustics, Stress
Reliability Designs,
253-260 (1983).
54.
Chen,
S. S.,
and Jendrzejczyk,
J.
A., Experiments and analysis of instability of tube rows subjected
to liquid crossflow,
Trans.
ASME,
J.
Appl.
Mech.,
49, 704-709 (1982).
55.
Chen,
S.
S.,
and Jendrzejczyk,
J.
A., Experiments on fluid elastic instability in tube banks subjected
to liquid crossflow,
J.
Sound Vibration,
78,
355-381 (19
).
56.
Chen,
S. S.,
Flow induced vibration of circular cylindrical structures, Argonne National Laboratory
Rep. No. ANL-CT-85-5 1.
57.
Eisinger,
F.
L.,
Prevention and cure of flow induced vibration problems in tubular heat exchangers,
Trans. ASME,
J.
Pressure Vessel Technol.,
102, 138-145 (1980).
58.
Blevins,
R.
D.,
Review of sound induced by vortex shedding from cylinders,
J.
Sound Vibration,
92(4), 455-470 (1984).
59.
Blevins, R.
D.,
Acoustic modes of heat exchanger tube bundles,
J.
Sound Vibration,
109(
l),
19-30
(
1986).
60.
Blevins,
R.
D., and Bressler,
M.
M.,
Acoustic resonance in heat exchanger tube bundles, Part
476
Chapter
I0
I: Physical nature of the phenomenon,
Trans. ASME,
J.
Pressure Vessel Technol.,
109,
275-28 1
(
1987).
61,
Blevins, R. D., and Bressler, M. M., Acoustic resonance in heat exchanger tube bundles-Part
11:
Prediction and suppression of resonance,
Trans. ASME,
J.
Pressure Vessel Technol.,
109,
282-288
(1987).
62.
Pettigrew, M.
J.,
Taylor, C. E., and Yasuo, A., Vibration damping
of
heat exchanger tube bundles
in two phase cross flow,” and Blevins, R. D., Acoustic resonance in heat exchanger tube bundles,
Welding Research Bulletin No. 389, Welding Research Council, New York.
63.
Barrington, E. A., Experience with acoustic vibration in tubular heat exchangers,
Chern. Eng. Prog.,
69(7), 62-68 (1973).
64.
Parker, R., Acoustic resonance in passages containing bank
of
heat exchanger tubes,
J.
Sound Vibru-
tion,
57,
245-260 (1978).
65.
Burton,
T.
E.,
Sound speed in a heat exchanger tube bank,
J.
Sound Vibration,
71,
157-160 (1980).
66.
Grotz, B.
J.
and Arnold, F.
R.,
Flow induced vibration in heat exchangers, Department of Mechani-
cal Engineering Tech. Rep. No. 31, 1956, DTIC No. 104568, Stanford University, Stanford, CA.
67.
Barrington, E. A., Cure exchanger acoustic vibration,
Hydrocarbon Processing,
193-198
(
1978).
68.
Fitzpatrick,
J.
A., The prediction
of
flow induced noise in heat exchanger tube arrays,
J.
Sound
Vibration,
425-435 (1985).
69.
Ziada,
S.,
and Oengoren, A., Flow induced acoustical resonances
of
in-line tube bundles,
Sulzer
Tech. Rev.,
45-47 (1990).
70.
Rae, G.
J.,
and Murray, B. G., Flow induced acoustic resonances in heat exchangers,
lnt.
Cnnf.
Flow Induced Vibrations,
Bowness-on-Windermere, England, May 1987, pp. 221-23 1.
71.
Fitzpatrick,
J.
A., and Donaldson,
J.
A.,
Symposium on Flow Induced Vibrations,
(M.
P. Paidoussis,
ed.), vol. 2,
Eflects
of
Scale on Parameters Associated with Flow Induced Noise
in
Tube Arrays,
American Society of Mechanical Engineers, New York, 1984, pp. 243-250.
72.
Ziada,
S.,
Oengoren, A., and Buhlmann,
E.
T.
International Symposium on Flow Induced Vibration
and Noise
(M.
P. Paidoussis et al., eds.), vol. 3,
On Acoustical Resonance in Tube Arruys,
American
Society
of
Mechanical Engineers, New York, 1988, pp. 219-254.
73.
Reill, D.
D.,
Flow Induced Vibration in Heat Exchangers,
ASME, New York, 1970, pp. 2-7.
74.
Halle,
H.,
Chenoweth,
J.
M., and Wambsganss, M. W., Shellside water flow induced tube vibration
in heat exchanger configurations with tube pitch to diameter ratio of 1.42,
Trans. ASME,
J.
Pressure
Vessel Technol.,
Ill,
441-449 (1989).
75.
Saunders,
E.
A. D., Shellside flow induced tube vibration, in
Heat Exchanger: Design, Selection
and Construction,
John Wiley and Sons, New York, 19
,
Chapter 11, pp. 245-273.
76.
Halle, H., Chenoweth,
J.
M., and Wambsganss, M. W., Flow induced vibration in shell and tube
heat exchanger with double segmental baffles, pp. 2763-2768.
77.
Gentry, C. C., Young, R.
K.,
and Small, M. W., RODbaffle heat exchanger thermal-hydraulic
predictive methods, in
Heat Transfer
1982,
Hemisphere, Washington,
DC,
1982, vol.
6,
pp. 197-
202.
78.
Boyer, R. C., and Pase, G.
K.,
The energy saving NESTS concept,
Heat Transfer Eng.,
2(
l), 19-27
(1980).
79.
Byrne,
K.
P., The use
of
porous baffles to control acoustic vibration in cross flow acoustic vibrations
in crossflow tubular heat exchangers,
Trans. ASME,
J.
Heat Transfer,
105,
751-757 (1983).
80.
Walker, E.
M.,
and Reising, G.
F.
S.,
Flow induced vibrations in crossflow heat exchangers,
Chem.
Process Eng.,
49,
95-103 (1968).
81.
Rogers,
J.
D., and Penterson, C. A., Predicting sonic vibration in crossflow heat exchangers-Expe-
rience and model testing, American Society
of
Mechanical Engineers, New York, paper 77-FE-7,
1977.
82.
Zdravkovich, M., and Nuttal,
J.
A., On elimination
of
aerodynamic noise in staggered tube bank,
J.
Sound Vibration,
34,
173-177 (1974).
83.
Thorngren,
J.
T., Predict exchanger tube damage,
Hydrocarbon Processing,
April, 129- 13 1
(
1970).
84.
Blevins, R. D., Fretting wear of heat exchanger tubes, Part
1:
Experiments,
Trans.
ASME,
J.
Eng.
Power,
101,
625-629 (1979).
Flow-
Induced
Vibration
4
77
85.
Blevins, R. D., Fretting wear of heat exchanger tubes, Part 11: Models,
Trans. ASME,
J.
Eng. Pott*er,
101,
630-633 (1979).
86.
Haslinger, K. H., Martin, M. L., and Steininger, D. A., Pressurized water react or steam generator
tube wear prediction utilizing experimental techniques,
Proc. Int.
Conf.
Flow! Iitduced Vibration,
Bowness-on-Winderemere, England, May 1987, pp. 437-448.
87.
KO, P. L., and Basista, H., Correlation of support impact force and fretting wear for heat exchanger
tube,
Trans. ASME,
J.
Pressure Vessel Technol.,
Z06(
l), 69-77 (1984).
88.
Cha, J. H., Wambsganss, M. W., and Jendrzejcyk, J. A., Experimental study of impact/fretting wear
in heat exchanger tubes, Argonne National Laboratory publication
ANL-85-38,
1985.
89.
Hofmann, P. J., Schettler, T., and Steininger, D. A., Pressurized water reactor steam generator tube
fretting and fatigue wear characteristics,
Proc. ASME Pressure Vessel and Piping
CO?$
(ASME
86PVP-2), Chicago, July 1986.
90.
Fisher, N. J., Olsen, M., Rogers, R. J., and
KO,
P. L., Simulation of tube-to-support dynamic interac-
tion of heat exchange equipment,
Trans. ASME,
J.
Pressure Vessel Technol.,
111,
378-384 (1989).
91.
Eisinger,
F.
L., Rao, M.
S.
M., Steininger, D. A., and Haslinger,
K.
H., Numerical simulation of
fluid elastic vibration and comparison with experimental results, reprinted from PVP-Vol. 206,
Flo~,
Induced Vibration and Wear
Book,
No. H00632, ASME, New York, 1991, pp. 101-1
11.
92.
Rao, M.
S.
M., Steininger,
D.
A., and Eisinger, F. L., Computer simulation of vibration and wear
of steam generator and tubular heat exchanger tubes,
Int. Symp. Advanced Computers
for
Dynantics
and Design
'89,
Tsuchiura, Japan Mechanical Division, JSME, 6-8 September 1989.
93.
Rao, M.
S.
M., Steininger, D. A., and Eisinger,
F.
L., Numerical simulation of fluid elastic vibration
and wear of multispan tubes with clearances at supports, reprinted from
Flont
Induced Vibration
in
Heat Transfer Equipment,
Vol.
5,
book no. GO0445 (J.
M.
Paidoussis,
S.
S.
Chenoweth,
J.
R. Chen,
Stenner, and W. J. Bryan, eds.).
94.
Blevins, R. D., Vibration induced wear of heat exchanger tubes,
Trans. ASME,
J.
Eng. Materials
Technol.,
107,
61-67 (1985).
95.
Moretti, P. M., and Lowery, R. L., Hydrodynamic inertia coefficients for a tube surrounded by rigid
tube,
Trans. ASME, Pressure Vessel Technol.,
97
(1976).
96.
Timoshenko,
S.
P., and Young, D. H.,
Vibration Problems
in
Engineering,
Van Nostrand Reinhold
Co., Toronto, 1965, Chapter
5.
97.
ABAQUS, Version 4-7, Hibbits, Karlsson and Sorensen, Inc.
98.
Pettigrew, M. J., Goyder, H. G. D., Qiao,
Z.
L., and Axisa, F., Damping of multispan heat exchanger
tubes, Part 1: In gases, in
Flow
Induced Vibration
(S. S.
Chen,
J.
C. Simon, and Y.
S.
Shin, eds.),
PVP vol. 104, ASME, New York, 1986,
pp.
81-87.
99.
Pettigrew, M. J., Rogers,
R.
J., and Axisa,
F.,
Damping of multisoan heat exchanger tubes, Part
2:
In liquids, in
Flow Induced Vibration,
(1986), PVP vol. 104, ASME, New York, 1986, pp. 89-98.
SUGGESTED
READINGS
1.
Nguyen,
D.
C., Lester, T., Good, J.
K.,
Lowery, R. L., and Moretti,
P.
M., Lowest natural frequencies
of multiply supported U-tubes,
106,
p. 414 (1984).
2.
Moretti, P. M., Fundamental frequencies of U-tubes in tube bundles,
Vibration
in
Power Plant Piping
and Equipment,
ASME Symposium Volume, Denver, 21-25 June 1981.
3. Moretti, P. M., Fundamental frequencies of U-tubes in tube bundles,
J.
Pressure Vessel Techrtol.,
107/207 (1985).
4.
Gorman,
D.
J.,
Free Vibration Analysis
of
Beam and Shafis,
John Wiley and
Sons,
New York, 1975.
5.
MacDuff, J. N., and Felgar, R.
P.,
Vibration design charts,
Trans. ASME,
1459-1474 (1957).
6.
Bolleter, U., and Blevins, R. D., Natural frequences of finned heat exchanger tubes,
J.
Sound Vibra-
tion,
80,
367-37 1 (1982).
7.
Moretti, P. M., Fundamental frequencies of U-tubes in tube bundles,
Trans. ASME,
J.
Pressure
Vessel Technol,
107,
207-209 (1985).
8.
Naguyen,
D.
C., Lester, T., Good, J.
K.,
Lowery, R. L., and Moretti, P. M., Lowest natural frequen-
478
Chapter
10
cies
of
multiply supported U-tubes,
Truns.
ASME,
J.
Pressure Vessel Technol.,
106,
414-416 (1984).
9.
Sing,
K.
P.,
and Soler, A.
I.,
HEXDES
User Manual,
Arcturus,
Cherry
Hill,
NJ,
1984.
APPENDIX
Calculation Procedure for Shell-Side Liquids
Draw a sketch of the exchanger and identify the most probable zone susceptible for
FIV.
Then
follow these steps.
Step
1.
Calculate Tube Mass per Unit Length, m
a. Calculate hydrodynamic mass coefficient,
C,,
by
TEMA
method (read
C,,,
from Fig.
35):
c'll,
=
or by Blevins method:
D
IJD'Cinp,
+
___
+
n(D'
-
DZ)p
b. Calculate the tube mass per unit length,
m
=
______
IID:p,
4 4 4
Step
2:
Calculate Tube Natural Frequency,
f,
For Straight
Tube:
a.
Calculate the area moment of inertia of the tube cross section,
I:
71
I
=
-
(0'
-
0;')
64
b.
Calculate cross section of the tube,
A,:
A,
=
n(D'
-
D2)/4
C.
Calculate tube axial longitudinal load,
Fl,:
F,
=
o,A,
(positive for tensile load and negative for compressive,
oT
tube
longitudinal stress calculated as per TEMA
RCB-7.23
or
by any
other method)
d.
Identify the span with pinned-pinned condition between two baffles in window zone. Find
out the tube span length,
L,
to
calculatej, and other parameters.
L
is given by:
L
=
LBc
+
LB(.
(for central window zone)
e.
Calculate the buckling load for the tube span:
x'EZ
F,,
=
__
for pinned-pinned condition
L2
f.
Calculate natural frequency multiplier:
g.
From Table 10.4 choose the value of frequency constant
h,,
for central window span:
All
=
h.
Calculate natural frequency,
A,:
479
Flow-Induced Vibration
Note:J;, is calculated for the central baffle window region. If it is suspected that the tube span
between the tube sheet and the first baffle in the window zone will be controlling, then calcu-
late
fn
with
L
=
LBI
+
LBC
(inlet window zone).
For
U-
Tube:
a. Draw a sketch of the U-bend section and identify the configuration with
TEMA
Fig.
V-
5.3-v-5.3.3.
Calculate lh/r
=
s/r
=
b.
Determine
C,
from
TEMA
charts.
c. Calculate the natural frequency for the first mode.
c,,
EI
05
J!,,,
=
68.06
--
(use
TEMA
dimensional units)
R'im
-
1
Note:
TEMA
dimensional units are
E
=
psi,
I
=
in.',
m
=
lbm/ft,
R
=
in.
Step 3. Calculate damping parameter
6
TEMA Method.
3.41
D
6,
=-
m
fn
6
=
max{61,62}
Correlations
of
Pettigrew, Rogers, and Axisa.
D
-
=
(1,7p/D)-'
for triangular array
D*
=
(1.9p/D)-' for square array
6
=
2n5,,
Note: If
6
is less than 0.0377, then assume
6
=
0.0377.
Step 4. Calculate the crossflow velocity,
U
Calculate
U
for the shell under consideration by TEMA/Bell/other methods. Otherwise, take
the value from the
TEMA
thermal specification sheet.
1
480
Chapter
10
Step
5.
Check for Vortex Shedding
TEMA
Criterion.
Not available for liquids; only available for gas flow.
Correlations
of
Weaver and Fitzpatrick.
a. Calculate Strouhal number,
S,:
S"
=
____
for 30" layout
1.73x,
---
for
60"
layout
l.16X1
---
I
90"
and
45"
layout
2x1
b.
Calculate vortex shedding frequency,
fb:
c. Check
0.8
f,
c
AI
<
1.2f,
Resonance
filD/U
>
2Su Acceptable
f,,D/U
<
0.2s"
Acceptable
Au-Yang
et
al.
Criteria.
Calculate the reduced damping
C,,:
a. Both lift and drag direction lock-in are avoided if
U
-
<
1
Check:
OK
or not
OK
f"D
b. For a given vibration mode, if the reduced damping satisfies the following condition, then
lock-in will be suppressed in that vibration mode.
C,,
>
64
Check:
OK
or not
OK
c. For a given vibration mode, if
C,,
>
1.2 and the following condition is satisfied, then lift
direction lock-in
is
avoided and drag direction lock-in is suppressed:
U
-
<
3.3 Check:
OK
or
not
OK
fnD
Maximum Deflection Due
to
Vortex Shedding at Resonance.
a. Determine lift coefficient
CL
from Table
2.
Interpolation is not recommended. If
CL
for
the
pitch ratio under consideration is not available, assume the conservative value
of
0.091.
b.
Calculate the maximum response,
y,,,,
of the tube span between two baffles.
481
Flow-Induced Vibration
c. Check: If
ymax
<
0.020,
OK.
Step
6.
Turbulence-Induced Excitation
a. Determine
CR(J)
from Fig.
7.
b.
The mean square response for a pinned-pinned span is given by
c.
Check: If
ym\
<
0.01
in (0.254
mm),
OK.
Step
7:
Fluid Elastic Instability
TEMA
Criterion.
a. Calculate reduced velocity parameter,
x:
b.
Calculate critical velocity by referring to Table
5.
C.
Check: If
U
<
Ucr
or
UlUCr
<
0.5,
OK.
Au-Yang et
al.
Criteria.
Choose
K,,
from Table
4,
(a)
for the particular tube layout pattern
and (b) for all arrays.
a.
For the particular tube layout pattern:
Check: If
U
<
Ucr
or
UlUcr
<
0.5,
OK.
b.
K,,,,,,
=
4.0 for all arrays:
Check: if
U
<
Ucr
or
U/Ucr
<
0.5,
OK.
482
Chapter
10
c. Check as per conservative criteria. Assume
6
=
0.09425
and
K
=
2.1
Check: If
U
<
U,,,
certainly
FIV
will not be
a
problem.
Pettigrew and Taylor Criterion.
Check: If
U
<
Ucr
or
UlU,,
<
0.5,
OK.
Step
8
Fill the preceding parameters into the flow-induced vibration specification sheet-liquids shown
in Table
5.
Calculation Procedure for Shell-Side
Vapors
Repeat steps
1
to
7
as already described.
For
gases, the damping parameter is calculated by
this correlation:
N-
1
6
=
3.463
x
10-3
____
fh
for
th
c
12.7
N
for
t,,
2
12.7
and the criterion for amplitude
at peak resonance due
to
turbulent buffeting may be neglected.
Step
9.
Check for Acoustic Resonance
Calculate the acoustic vibration frequency,
h:
TEMA Method
(for
Cylindrical
Volume
Only).
(use TEMA dimensional units)
Blevins Method.
a. Calculate velocity of sound
C
through the tube bank.
b.
Calculate tube layout solidity factor,
0:
D:
0
=
0.9069
(
p
)
for
6
=
30"
or
6
=
60"
D-!
=
0.7853
(
p
1
for
6
=
90"
483
Flow-Induced Vibration
Dz
=
1.5707
[
p
1
for
8
=
45"
c. Calculate effective velocity of sound through the tube bank:
c
CelT
=
.I<
Parker
1
+
0)
C
Ctff
Burton
=
7-
1
+
C,0)
Note: Choose
Cell
by Burton method for conservative values.
d.
Calculate the acoustic resonance frequency,
h:
For a cylindrical volume,
CdTk
fa
=
-
27c
R
where
h,
=
1.84 and
=
3.054.
For a rectangular volume
L,
=
,L,
=
,
and
L,
=
where
i
=
0,
j
=
1,
and
k
=
0.
Note: In heat exchangers of normal size the fundamental or
the second mode is the most likely to occur. For large exchangers with shell diameter
of
the order of 20-30 m the acoustic vibration can be excited up to fifth
or
sixth mode.
Step
10.
Criteria for Occurrence of Acoustic Resonance
Criteria
for
Vortex Shedding Mechanism.
Calculate Strouhal number due to vortex shedding:
a.
Chen number and Eisinger criteria: Calculate Reynolds number, Re:
UD
Re=-
\.'
Calculate Chen number,
\v:
Re (2X,
-
1)2
w=
S"(4X
f
x,>
Check:
yl<2000 No vibration
yl
=
2000-4000
Low likelihood of vibration
w
>
4000
High likelihood of vibration
TEMA condition: Acoustic resonance is possible if
=
2000.