Dissertation report

M.Tech. dissertation –Vibration Analysis Of Heat Exchanger Using CFD 1
CHAPTER .1
INTRODUCTION
Flow-induced vibration in heat exchangers has been a major cause of concern in
the nuclear industry for several decades. Some examples of tube failures in
commercial steam generators are reported in the review by Pettigrew and Taylor
(1991). Almost all heat exchangers have to deal with this problem during their
operation. The phenomenon has been studied since the 1970s. The database of
experimental studies on flow-induced vibration is constantly updated with new
findings and improved design criteria for heat exchangers. In the nuclear industry,
steam generators are often affected by this problem. However, flow induced
vibration is not limited to nuclear power plants, but to shell & tube type of heat
exchanger used in many industrial applications such as chemical processing,
refrigeration and air conditioning. Shell and tube type heat exchangers experience
flow induced vibration due to high velocity flow across the tube banks. Flow-
induced vibration in these heat exchangers leads to equipment breakdown and
hence expensive repair and process shutdown.
Flow-induced vibration, as the name suggests, is the vibration of a structure
(in this case, heat exchanger tubes) due to the flow of a fluid across it. It is a fluid
and tube bundle interaction problem. When certain critical conditions are
exceeded, instability is induced in the system causing the tubes to vibrate with
large amplitudes. The consequence of this is the damage of tubes in any of the
three following ways:
(1) For tubes rigidly attached to a supporting plate such as at the base, vibrations
induce stress at the tube root causing a circumferential crack and hence snapping
of the tube.
(2) For tubes located near the mid span where the holes in the supporting plate are
larger the tube to allow the flow of fluid through it, large amplitude vibrations
cause the tubes to hit against the holes causing a groove to be formed at the
support.
(3) Finally in the absence of supporting plates, the tubes might hit each other
when the amplitude of vibrations is large. In all the three cases, fretting wear of
the tubes and hence damage will result in the long run.
Flow-induced vibration in structures is caused by three mechanisms. When a
fluid flows over a bluff structure, vortices are shed behind it that cause an
alteration of the flow field. This change in the flow field causes vibrations. This is
known as vortex shedding instability. Another mechanism is galloping or flutter
that induces vibrations in a noncircular or asymmetric body. Galloping in ice
coated transmission wires is a common example. In aerodynamics, this
mechanism is known as flutter as applied to airfoils. For flow over a tube bank or
array, a third type of instability mechanism known as fluidelastic instability is the
major cause of flow-induced vibration. Since fluid-elastic instability is the most
important mechanism for heat exchangers and forms the basis of this research
work, a description of this instability mechanism is provided in the next chapter
no 2.

CHAPTER. 2
LITERATURE REVIEW
The relevant literature for the flow induced vibration in shell and tube heat
exchanger is present in this chapter.
S.S.Chen [1] presents a mathematical model for cross flow induced vibration of
tube banks. Motion dependent fluid forces and various types of flow noises are
incorporated in a model. An analytical solution for the fluid inertia force,
hydrodynamic damping force, and fluid elastic forces is given for tube banks
arranged in a arbitrary pattern. Based on the model, a better understanding of the
vibration of heat exchanger tube banks subjected to various flow excitations can
be developed.
Fluid flowing across a heat exchanger tube banks can cause various types of
tube vibration and instability. These problems have become more important with
the demand for larger and more efficient heat exchangers. From a practical point
of view, heat exchanger designers needed to know when and why detrimental
flow induced vibration occur and how to suppress them. To be able to answer this
question one must understand the mechanism involved. In what follows several
excitation mechanisms are briefly reviewed.
M.J.Pettigrew, C.E.Taylor [2] presented design guidelines to prevent tube
failures due to excessive flow induced vibration in shell and tube heat exchangers.
An overview of vibration analysis procedures and recommended design
guidelines is presented in this paper. This paper gives insight in to liquid, gas, and
two phase flow. The paper reveals about flow, damping parameters, fluid elastic
instability. The paper summarizes design guidelines for flow induced vibration of
heat exchangers. The overview can be used by designer as a guideline for
vibration analysis, by the project engineer to get an overall appreciation of flow
induced vibration concerns. The damping ratios are derived. These are for heat
exchanger tube in gases, heat exchanger tubes in liquids, and damping in 2 phase
flow. There are friction damping, viscous damping, squeeze film damping, two
phase damping, support damping. The dynamic stiffness and support
effectiveness is derived. The other important parameter in vibration in heat
exchanger is fluid elastic instability which is derived for single phase flow and
two phase flow.
M.J.Pettigrew, C.E.Taylor[3] gave brief guideline to analyze heat exchanger
vibration. The heat exchange vibration analysis consists of the following steps:
flow distribution calculation, dynamic parameter evaluation i.e. damping,
effective tube mass and dynamic stiffness, formulation of vibration excitation
mechanism, vibration response prediction and resulting damage assessment.
Forced vibration excitation mechanisms are analyzed. The important term in flow
induced vibration analysis is periodic wake shedding is derived. It is also known
as vortex shedding. It may be of concern in liquid cross flow where the flow is
relatively uniform. It is not normally a problem at entrance region of steam

generator because the flow is very no uniform and quite turbulent. Turbulence
inhibits periodic wake shedding. Vortex shedding resonance is usually not a
problem in gas heat exchangers. The density is usually too low to cause
significant periodic forces at flow velocities close to resonance.
M.J.Pettigrew, G.D. Knowles[4] described a simple experiment to study
damping of heat exchanger tubes in 2 phase mixtures. A single cantilever tube
was subjected to various air water mixtures up to 30% void fraction. The effects
of void fraction, surface tension, tube frequency and degree of confinement were
investigated. The results are presented and discussed in this paper. It is hoped that
this information will lead to a better understanding of the energy dissipation
mechanism that covers damping in 2 phase flow. A experimental rig constructed.
It consisted of a vertical cantilevered tube immersed in a 2 phase mixture, as
shown in figure:
Figure 1. Experimental Apparatus for Vibration Measurement
Both the logarithmic decrement technique and the random vibration response
technique were used to measure damping. The transverse vibration was measured
with 2 pairs of strain gauges mounted at 900
from each other, inside the tube, near
the tube sheet. Damping decreases as void fraction increases.

Figure 2. Effect Of Surface Tension On Vibration Response To Mixture
Turbulence.
The conclusions were: 2 phase damping increases with surface tension.
Dependence of 2 phase damping on tube frequency is weak.
M.J.Pettigrew et al.[5] explained the effect of support and tube damping
parameter. The damping forces were also calculated.
Figure 3. Type Of Dynamic Interaction Between Tube And Tube Support.
Figure.4 Eccentric Lateral Motion (A) Squeeze Film Force Due To Radial
Motion: (B) Viscous Shear Force Due To Tangential Motion.

Damping was measured using the logarithmic decrement technique. Time traces
of the tube vibration were recorded with an ultra-violet recorder. Also, a
frequency spectrum was obtained with a real-time spectrum analyzer for every
test, to make sure no higher modes were excited. The damping ratio of the tube
was calculated from
01
ln
2 n
Y
n Y


 
  
 
2.1
where n is the number of cycles and Y is the peak vibration amplitude. The tests
were usually repeated three times to assure repeatability. A large number of
cycles, typically 150 cycles in air and 40 cycles in water, were considered for
accuracy and to investigate linearity.
The various damping coefficient are derived for squeeze film. The conclusions
were:
1. Squeeze film damping is proportional to dimensionless support thickness L/l.
2. Squeeze film damping dependent on eccentricity being proportional to the
proximity of the tube to the tube support.
3. It is inversely related to the diametral clearance.
4 Dependent on the inverse of the tube frequency.
5 Independent of amplitude.
Kenan Yakut, Bayram Sahin [6] conducted. an experiment. to determine heat
transfer and friction loss characteristics. Air enters the experimental set up by air
compressor. Then air goes to pressure tank where it stored. The flow of air was
measured by anemometer. The pressure amplitude of the vortex wave was
measured using a calibrated condenser microphone with a 13 mm diameter, low
pass filter, ADA converter card.
Figure 5 Setup For Flow Induced Vibration Calculation
In this paper an experimental study has been carried out to investigate flow
induced vibration and heat transfer characteristics for conical ring turbulators.

Nusselt number increased significantly for all conical ring arrangements because
the contact of fluid with tube wall is better than for smooth tube. The heat transfer
results indicate that Nusselt number is a function of Reynolds number Prandtl
number and pitches. The correlation is
( 0.0716)
0.367 0.4
4.497Re Pr
t
Nu
D

 
  
 
2.2
The conical ring turbulator also cause an important increase in friction factor. The
turbulator with 10mm pitch was fond to improve rate of heat transfer by
250%under the condition of constant pumping power. The vortices having
maximum amplitude values were produced by turbulator with 10mm pitch. The
maximum amplitude values were increased by almost 4.5 fold compared with
those for an empty smooth tube. On the other hand, the vortices with maximum
shedding frequencies were generated by turbulators having 30mm pitch. In the
case of flow acoustic coupling condition, vortex shedding frequencies are in a
frequency band of 200-220 Hz for all arrangements. The vortices with maximum
amplitudes were produced by 10 mm pitches between Reynolds number of 8000
and 18 000.
Ulrich Mohr, Horst Gelbe [7] presented method to produce equivalent velocity
distribution and corresponding cross sectional areas in real heat exchanger
bundles and enables the designer to predict the vibration excitation by fluid elastic
instability more accurate than before. The various equations are derived for fluid
elastic instability.
E.Longatte, Z.Bendjeddou, M.Souli [8] derived governing vibration differential
equation. In order to reduce experiments and to be able to study many
configurations involving complex flow induced vibration problems, numerical
methods are also considered. Owing to recent developments incorporated in to
computational fluid dynamic codes, numerical simulation of flow structure
coupling is investigated. The paper uses new CFD code names ALE (Arbitrary
Langrage Euler). This method is better to model 2 phase flows for explosion
modeling for instance.
S.Pasto [9] derived experimental results on the behavior of a freely vibrating
circular cylinder in laminar and turbulent flows are presented. Wind tunnel tests
have been performed by varying the cylinder roughness and the mass-damping
parameter, mζ. An experiment was done on VIV(Vortex Induced Vibration) setup.
VIV tests on a circular cylinder have been performed in the laboratory. The wind
tunnel has a cross-section 2.2m wide and 1.6m high, slightly divergent from the
inlet to the test-section whose dimensions are 2.4m X 1.6m. The global length of
the wind tunnel, from the inlet to the end of the diffusers, is about 24 m. The value
of the velocities is obtained by means of both the regulation of the pitch of the ten
blades constituting the fan, and the rotating speed. The maximum velocity
attainable is 35 m/s. The setup is drawn schematically as below.

Figure 6 Flow induced vibration experimental setup.
The setup is given in photographically as below.
Figure 7 Front view photograph of experimental setup.
The side view is given below.
Figure 8 side view photograph of experimental setup.

The sample tested in the wind tunnel is a circular hollow cylinder 2.3m long and
with a diameter of about 0.155 m.
C. Liang, G. Papadakis [10] modeled the single cylinder and row of cylinders in
2-D computer model. They used the Large Eddy Simulation (LES) to solve the
property. They also developed the 3-D model and modeled it in FLUENT with
LES. The experiments, against which the simulations are compared, were carried
out in a stainless steel water tunnel with cross-section 72mm X 72 mm. The
computational domain is described in a fixed Cartesian coordinate system x; y; z.
The x-axis is along the streamwise (longitudinal) flow direction, the z-axis is
parallel to the cylinder axis (spanwise direction), while the y-axis is perpendicular
to both the x- and z-axis (transverse or cross-stream direction). The diameter of
each cylinder is 10 mm. The bulk approaching velocity is 0.62 m/s and the gap
velocity 0.86 m/s and the corresponding Reynolds numbers are equal to 6200 and
8600, respectively. For the examined arrangement the measured r.m.s. values
normalized by the gap velocity at x =0 are 6.25% and 4.29% for the streamwise
and cross-stream velocities, respectively. As will be shown in the results section,
the levels of r.m.s. velocities after the second row are significantly higher
compared to these values which suggests that turbulence is generated mainly due
to the presence of the cylinder walls and the vortex shedding processes behind the
tubes. Therefore, inlet conditions are quickly overshadowed by turbulence
generated downstream.
Figure 9. Configuration of the six-row staggered tube array and tube (row)
numbering.
H.G.D.Goyder [11] gave the various mechanisms acting in heat exchanger
vibration. The main were fuidelastic instability, vortex shedding, multi-phase
buffeting acoustic resonance, turbulence buffeting, hydraulic transients,
environmental excitation, and transmitted mechanical vibration. Figure shows an
example of three mechanisms (buffeting, vortex shedding and fluidelastic
instability) which induce vibration on a laboratory tube bundle. The large
amplitudes of vibration due to vortex shedding and fluidelastic instability should
be noted. In this study, the fluid was water and the tubes were simple cantilevers.
The behavior shown in this figure will be discussed subsequently.

Figure 10 Tube vibration response to increasing flow velocity.
Referring to Figure 15 it may be seen that for small flow velocities there is
relatively little vibration compared to the significant vibration that starts at a flow
velocity of about 0.21m/s. The flow rate of 0.21m/s marks a definite threshold and
beyond this threshold the fluidelastic mechanism is acting. This threshold is often
called the critical flow velocity, and the relationship between this critical flow
velocity and the fluid and tube properties is of key importance in predicting the
onset of instability in tube bundles.
Figure 11 a heat exchanger tube bundle showing some window and tubes.
Figure 17 shows a typical plot that gives the threshold velocity for the onset of
fluidelastic instability in single span tube bundles. The two axes are
nondimensional properties of the fluid and the tubes. The vertical axis is a non
dimensional flow velocity U/f D. The property plotted on the horizontal axis,
2πζm/ρD2
, is a mixture of damping and mass ratios. Here m is the tube mass per
unit length; ζ is the mechanical damping ratio (see below) and the ρ fluid density.
This plot is for a rotated triangular tube layout. Similar plots for other tube layouts

may be found in Weaver and Fitzpatrick [21]. These plots are based on
compilations of experimental data, such as that shown in figure 15, from which
critical flow velocities have been extracted and nondimensionalized.
Figure 12 Fluid elastic instability chart for rotated triangular tubes.
H.G.D.Goyder [12] gave the assessment method for unstable vibration in
multipass tube heat exchanger. Figure 18 shows a typical heat exchanger
configuration. The tubes are supported by single segmental baffles which also
have the purpose of directing the flow.
Figure 13 Typical heat exchanger with U tubes.
It is the flow outside and between the tubes which causes the fluidelastic
instability. Figure 19 shows the results of a laboratory experiment in which a
single span tube bundle was exposed to an increasing air-flow. As may be seen,
the tube vibration amplitude suddenly increases when a certain flow velocity is
exceeded. This flow velocity is known as the critical flow velocity for the onset of
fluidelastic vibration. The damping of the tube has a significant effect, and
increasing the damping increases the critical flow velocity. It can also be seen that
the vibration amplitude reaches a plateau value at about 16 m/s2
and then does not
increase much beyond this value. This is because the instrumented tube impacted
against neighboring tubes and was unable to vibrate with a larger amplitude. The
parameter on the horizontal axis is known as the mass-damping parameter, while
that on the vertical axis is known as the reduced velocity. The correlations link
these parameters in the form.
2
2
n
U m
K
fD D


 
  
 
2.3
Here the reduced velocity, on the left-hand side is given by the gap flow velocity,
U; divided by the tube natural frequency, f (Hz), and the tube diameter, D: The

reduced velocity is the nondimensional critical flow velocity on the threshold of
instability. The mass-damping parameter is given by the tube mass per unit length,
m; the damping ratio, ζ; and the fluid density, ρ: The mass-damping parameter is
raised to an exponent n. The initial value of this is taken as 0.5.
.
Figure 14 Experimental data and correlations describing fluidelastic
instability in a rotated triangular laboratory tube bundle.
P.A. Feenstra, D.S. Weaver, F.L. Eisinger [13] conducted an experiment on
vibration in tube bundle. An experimental laboratory study was performed to
measure the effect of acoustic noise on the magnitude of tube vibrations in a
staggered tube array and to measure the effectiveness of baffles on suppressing
transverse duct modes. Experiments were also performed to determine the effect
of baffles for reducing the noise of acoustic resonance. The layout of 473 tubes is
shown in figure.
Figure 15 Plan view of the tube bank superimposed with the fundamental
transverse acoustic standing wave.
The parameters of the bundle are, D=19.1 mm, T=30 mm, L=20.6mm with side
spacing ratio of T/D=1.57 and longitudinal spacing ratio of L/D=1.083. Acoustic
noise measurements for the datum case of no baffles is presented in figure below

where the dominant frequencies of the acoustic modes and the sound pressure
level amplitudes in decibels (dB) are plotted as a function of upstream flow
velocity, Vu. The solid straight line which connects many of the frequency data
points corresponds to a Strouhal number based upon average gap velocity of,
St=0.41 (or, based on upstream velocity, St=1.13).
Figure 16 Acoustic noise level and frequency measurements for the datum case of
no baffles.
By this experiment he derived the following conclusion:
1. Tubes in an array can be excited to vibrate when subjected to an acoustic
standing wave within the duct. The source of the excitation is apparently
the pressure gradient across the tube due to the acoustic standing wave.
The highest tube loading occurred when the tube was located at an
acoustic pressure node (i.e., pressure was lowest) but this is also where the
pressure gradient across the tube is highest. For a fundamental transverse
duct mode, the maximum tube vibration occurred when the tube was
located in the center of the duct. The simple theory presented in this paper
under-predicted the magnitude of the acoustic tube loading, but the trend
with peak noise level was correctly predicted.
2. The insertion of a single baffle plate in the test-section effectively
eliminated the 1st mode resonance as long as the baffle was located near
the center of the duct. For the 2nd and higher acoustic modes, some noise
reduction was achieved. However, from a design standpoint, these
experiments showed that a single baffle cannot be relied upon to suppress
any but the 1st mode.
3. The insertion of double baffles effectively eliminated the 1st and 2nd
mode resonances for all three cases tested. Precise spacing of the baffles in
the duct width was not necessary to achieve this effect. Two baffles had
some effect on the 3rd mode resonance but, in general, were not effective
in eliminating the 3rd and higher mode resonances.
WANG Yi-wei [14] presented the paper on combination of CFD and CSD
package for fluid structure interaction. In this article the UDF script file in the
Fluent software was rewritten as the ―connecting file‖ for the Fluent and the
ANSYS/ABAQUS in order that the joined file can be used to do aero-elastic
computations. In this way the fluid field is computed by solving the Navier-Stokes
equations and the structure movement is integrated by the dynamics directly. An
analysis of the computed results shows that this coupled method designed for

simulating aero-elastic systems is workable and can be used for the other fluid-
structure interaction problems. The two problems of FSI are considered. They are
as below.
3-D elastic flag swings in the wind
This example presents a coupling simulation between ABAQUS and Fluent. The
elastic flag hangs on the top part of the channels. The angle between the normal of
the flag and the normal of inlet is 20o
. The velocity of the wind is 6 m/s. The scale
of elastic flag is specified in Fig.26.
Figure 17 Flag geometry.
The mesh of Fluent is generated by ICEM and it is unstructured, which are
illustrated in Figs 27 and 28.
Figure 18 Flag meshing by Fluent. Figure 19 Boundary of fluid zone.
In the Fluent portion the flag surface is specified as an adiabatic, moving, no-slip
wall and the location of the nodes of flag surface is calculated by ABAQUS, and
then updated by the fluent dynamic mesh UDF. The situation is unsteady, and a
segregated-implicit solver is used, with the 0.001s per time step. In the ABAQUS
portion, all degrees of the upside of elastic flag are constrained. As shown in Fig
29, meshing and the element types are C3D8R of the flag. The material property is
constant, isotropic, and linear, Young’s modulus is 2 X 106
N/m2, Poisson's ratio
is 0.45, and the density is 3000 kg/m3. The time step size is set as 0.001s.

Figure 20 Flag mesh of ABAQUS.
The whole simulation process uses 0.38 s. The largest flag deformation is shown
in Fig.30.
Figure 21 Largest flag deformation.
Chin-Cheng Huang, Jen-Sheng Hsieh, Pay-Chung Chen, Chin-Ho Lee [15]
presented the paper flow analysis and flow induced vibration analysis of nuclear
generator using CFD software CFX-4. This paper performs a three-dimensional
flow analysis and flow-induced vibration evaluation of a tube bundle for the low-
pressure feedwater heater of a nuclear power plant. Using a commercial
computational fluid dynamics software, CFX-4. Based on the design, 1,725,278
kg/h boiler feedwater is heated from 126.3 to 147.31C0
using extraction steam at
476.6 kPa, which, together with cascading drains from the upstream heaters, is
subcooled to 131.9 1C. The steam flow rate of 46,992 kg/h is used as the steam
inlet boundary condition in the analysis model associated with the inlet area. The
drain flow rate of 581,363 kg/h.

Figure 23 Computational domain and mesh generation.
The results of tube natural frequency, Strouhal number and vibration amplitude
are shown in Table 1. These results are shown for different areas with relative
large tube spans and local high velocity conservatively. As shown in Table 1, S,
Fn,V and Amp denote the tube span, tube natural frequency, cross-flow velocity
and vibration amplitude at the area in consideration, respectively. St denotes the
Strouhal number, Vcr is the critical flow velocity and SF is the safety factor for
fluid-elastic instability; SF equals Vcr divided by V. Area A is the area near the
cascading drain inlet, B is the area with short tube support plate above the drain
cooler, C is the area with long tube support plate near the extraction steam inlet
and D is the area near the tubesheets. As for the vortex shedding, larger velocity
with a smaller value of St is observed at area C. The maximum vibration
amplitude is about 7.9 x 10-5
m.
Table 1. Evaluation result of flow induced vibration in condensing zone.
Area S(m) Fn(Hz) V(m/s) St Amp(m) Vcr(m/s) SF
A 0.629 155.17 0.09 31.3 3.60E-05 46.46 491.68
B 0.629 99.62 1.83 1.04 7.90E-05 29.83 16.28
C 0.61 105.95 6.51 0.31 7.90E-05 30.71 4.72
D 0.61 165.02 4.45 0.71 3.30E-05 47.84 10.76
Results of the flow-induced vibration for tubes in the drain cooling zone are
shown in Table 2. Areas E and F are at the windows of condensate inlets for the
areas with short and long spans, respectively. G is the area at the middle of the
drain cooler and H is the area near the drain outlet and tubesheets. Basically,
vortex shedding is not a concern for the tubes in the drain cooling zone. The safety
factor for fluid-elastic instability SF is 2.87, which is the largest value in the drain
cooling zone. The smallest value of SF is found at area G. It means that the tubes
at the middle of the drain cooler are found to be with relatively smaller safety
factors against fluid-elastic instability.

Table 2 Evaluation result of flow induced vibration in drain cooling zone.
Area S(m) Fn(Hz) V(m/s) St Amp(m) Vcr(m/s) SF
E 0.743 54.85 0.9 1.16 4.80E-07 2.21 2.45
F 1.099 25.09 0.4 1.19 1.05E-06 1.16 2.87
G 0.718 58.8 1.11 1.01 4.50E-07 2.34 2.12
H 0.718 91.58 1.29 1.36 2.87E-07 3.38 2.63
V. Prakash, M. Thirumalai, R. Prabhakar, G. Vaidyanathan [16] presented
paper on flow induced vibration assessment in Na-Na heat exchanger. The
500MWe Prototype Fast Breeder Reactor (PFBR) is under construction at
Kalpakkam. It is a liquid metal sodium cooled pool type fast reactor with all
primary components located inside a sodium pool. The heat produced due to
fission in the core is transported by primary sodium to the secondary sodium in a
sodium to sodium Intermediate Heat Exchanger (IHX), which in turn is
transferred to water in the steam generator. PFBR IHX is a shell and tube type
heat exchanger with primary sodium on shell side and secondary sodium in the
tube side. To validate the design and the adequacy of the support system provided
for the IHX, flow induced vibration (FIV) experiments were carried out in a water
test loop on a 60◦ sector model. The IHX of PFBR consists of tube bundle having
1782 straight tubes of 24mmOD×1mm wall thick rolled and welded to tube sheets
at both ends. The tubes are arranged in circular pitch in 18 concentric rows around
central down comer (radial/circumferential pitch being 30/31.4 mm). The primary
sodium enters at 817K radially at top, flows vertically down and finally leaves at
667K to the cold pool. The secondary sodium enters through a central down
comer pipe takes 180◦ turn at bottom end then enters the tube at 628K and leaves
at 798K.
Figure 24 Prototype intermediate heat exchanger (PIHE)
Using finite element techniques, the IHX tube support system is designed to
provide adequate margin against flow induced vibrations. Fortunately the sodium
properties such as density and viscosity are comparable with water, the model was
tested in water. When water is used as the test fluid,
Re for 60◦ sector model (water at 333 K) = 6.2×10E + 04 (at 583m3
/h).

Re for Prototype IHX at 673K=12.7×10E + 04 (at 3500m3
/h)
For this range of fully turbulent regime of Reynolds number, Strouhal number is
independent of Re and is essentially a function of tube layout, is maintained same
in the model and the prototype. With Strouhal similitude between model and
prototype, the vortex shedding frequency calculated at the nominal flow of
3500m3
/h in Prototype IHX is the same as the corresponding 1/6th flow (the
nominal flow of 583m3
/h) in the model. However the natural frequency for the
tubes in the model (first mode as well as isolated first span frequency) is slightly
higher for the tube-empty condition and hence it is necessary to test the model at a
higher flow to maintain fn/fvortex constant, where fn is the natural frequency of the
tube. For this condition the required test flow rate is calculated as 690m3
/h. The
tube natural frequency is given by:
2
0
n
K EI
f
L M
 2.8
where fn – natural frequency of the tube,
K – constant whose value depends on end. Support condition:
L – length of tube between supports,
E – modulus of elasticity,
I – moment of inertia of the tube,
M0 – virtual mass of the tube/unit length, where M0 is given by
M0=mass of tube+ mass of fluid inside the tube + C×mass of fluid outside the tube
where C is the added mass coefficient for the given tube layout.
In prototype, sodium is flowing around the tubes at a temperature range of 667–
817K, whereas in the model the tubes are surrounded by water at 303–323 K. The
fluid inside the tube is sodium in case of PFBR, whereas in the model the tubes
are empty (air). It is preferable to have the ratio of modulus of elasticity to mass
per unit length (E/m) as close as possible in the model and the prototype so that
the natural frequency could be simulated in the model without much variation in
the span length.
Table 3 Comparison of √ E/m value for model and prototype.
Location E(Pa)xE11 M(kg/m)
(E/M)^0.5 x
E05
Ratio with
model
Model 2 1.56 3.58 1
IHX Inlet(prototype) 1.64 1.4 3.42 0.96
Ihx outlet(Prototype) 1.82 1.45 3.54 0.98
Table 5 Natural frequency estimation for PFBR-IHX and sector model.
Model Sector model PFBR IHX (Hz)
Shell side water filled and
tube side empty (Hz)
Shell and tube side
water filled (Hz)
First 21.5 21.2 21.2
Second 55.9 46.5 30.4
Third 79.9 66.6 47.8

Table 4 Comparison of model and prototype heat exchanger.
Description Prototype IHX Model
Cross section of tube bundle Circular 60 degree
Number of tubes 1782 315
Number of tube rows 18 18
Tube o.d./i.d.(mm) 24/22 24/22
Circumferential pitch 31.4 31.4
Radial pitch (mm) 30 30
Tube length (mm) 6980 4600
Tube material. SS316IN Carbon steel
Number of antifriction belts 5 3
Experimental facility and measurements
Sector model was installed in 300mmdiameter size pipe water loop (Fig.37)
having a circulating pump rated for a flow of 1000m3
/h and a pressure of 1.5
kg/cm2. Flow through the model was controlled by adjusting the pump bypass
valve and the butterfly valve in the discharge pipeline. Flow was measured using
an annular type flow meter which averages the velocity across the pipe cross
section. The range of the flow meter is 250–1500m3
/h, and the overall accuracy of
flow measurement was ±1%. The important specifications of strain gages used
are given below:
Type: Micro measurement foil strain gage
Gage factor: 1.8
Gage resistance: 120 Ω
Size: 6mm×3mm grid size
Strain gages were bonded to the outer surface of the tubes using cyanoacrylate
compound and water protected with silicon rubber and araldite. Salient
specifications of the accelerometers are given below:
Model: B&K 4393 Piezoelectric Accelerometer
Sensitivity: 3.1 pC/g
Frequency range: 0.2 to 12,000 Hz.
Instruments were calibrated before and after the FIV measurement using
programmable oscillator and FFT analyzer. Accelerometer sensitivity was
obtained from the calibration certificates provided by the manufacturer.
Accelerometers are calibrated in comparison with a reference accelerometer by
back to back method. The overall accuracy for the sensitivity value is ±2%.
Measurements with analyzer were generally carried out with following settings:
Window: Hanning
Frequency: 400 Hz
Number of data points: 1024
Resolution: 1Hz
Number of averages: 50 (0% overlap)

Power spectral density plots obtained from accelerometer is in acceleration units
(Y-axis in PSD plots). For obtaining the displacement levels at any frequency (f),
area under Power spectral density (PSD) curve around a particular frequency was
found and the resulting acceleration levels were converted to displacement level
using following relationship. Displacement = acceleration/4π2
f2
, where f is the
frequency of excitation.
Figure 25 IHX sector model test loop.
The transducers are mounted on some of tubes which are as shown in figure 38
below. Vibration measurements were carried out for flows ranging from 30% to
125% of nominal flow.
Figure 26 Instrumented tube in sector model.

The overall vibration (acceleration) is plotted with flow for tube no. 305 at its first
span in fig. 45. Fig. 46 shows the probability density function plots of the tube
vibration signal. This PDF plot indicates that the excitation is random in nature
caused by turbulence. Periodic excitation due to vortex shedding or fluid elastic
instability was not indicated in any of the PDF plots recorded in the experiment.
Figure 27 Flow Vs acceleration.
Figure 28 PSD plot of vibrational signals.
Conclusion.
The following are conclusions made by this experiment.
1. The modal frequencies excited were in good agreement with the analytically
predicted values.
2. From the PSD, PDF and flow sweep test, it is inferred that the excitation is
random in nature caused by turbulence and no instability phenomenon is
observed.
3. The maximum vibration values of different rows are comparable (Table 6)
almost with little variation and vibration levels are lower in the tubes of inner
rows.
4. The maximum vibration value is recorded in tube no. 281 in the first span
(72μm RMS at 125% of nominal flow). The resulting bending stress (4MPa)
is much less than the endurance limit for the tube material.
5. As expected, the magnitude of vibration in the outlet regions is less compared
to the inlet region.

6. Though the vibration levels are low, these types of experiments are necessary
to validate the design and also to demonstrate that fabrication and
manufacturing methodology and inspection followed is in the right direction
and also to qualify the nuclear components against flow induced vibration.
M. Hassan, M. Hayder [17] presented paper on modeling of fluid elastic
vibration of heat exchange tube loose support. A cantilever tube of 1000-mm
length, 12.6-mm outer diameter, and 0.25-mm wall thickness was utilized in this
study. The equivalent mass per unit length and elasticity modulus is 0.085 kg/m
and 108 GPa, respectively. Fig 47 shows the finite element model of the tube in
which 40 beam elements, i.e. 41 nodes. The predicted fundamental frequency is
found to be f = 8.6 Hz. The model shown in Fig 47a is used for the linear
computations (no loose support at the free end) and model validation. Nonlinear
simulations (tube with loose support) will utilize the tube model shown in Fig 47
b. In Fig 47 b, the tube end consists of a clamped-free beam with a loose support
at the free. Radial clearance cases of 0.1, 0.2, 0.4, 0.6, 0.8 and 1.0mm were
studied. A single coefficient of friction value of 0.4 was utilized, which is a
reasonable value (the coefficient of friction in heat exchangers can be as high as
0.6). The mass-damping parameter (MDP) is 60 which is defined as
2
m
MDP
d


 
  
 
2.9
Figure 29 Finite element model of cantilever beam (a) linear model (b) non linear
model.
Fig. 48 shows the fluidelastic response curve simulated for a mass damping
parameter of 60. For this type of array, the steady state channel width (Ao) and the
channel length (so) are P − D and P respectively. The attachment and separation
angles are set to 10◦. The relevant fluid length parameter ε was set to 2.

Figure 30 Tube response at mass damping parameter 60.
The inlet flow velocity Uo is varied in the range of 1–12 m/s and the rms lift
displacement is calculated for each of these velocities. The dimensionless rms lift
response wL is expressed as a percentage of the tube diameter and is plotted
versus the dimensionless flow velocity (Ur = U/fd). The graph is shown below.
Figure 31 Stability plot comparing published experimental data and present
simulation for an inline square array with pitch-to-diameter ratio of 1.5.
R. L Judd, R. Dam, D. S. Weaver [18] A photo-optical technique has been
developed for monitoring the dynamic displacement of cantilevered tubes in fluid
flow. The technique employs an optical fiber to transmit light through the tube and
a phototransistor array to measure the motion of the light beam that is projected
from the end of the tube. The device is simple, inexpensive, and very sensitive to
small displacements. Details are given for the development of the technique,
analysis of performance, and static calibration. The device was tested by
monitoring the dynamic response of a bundle of cantilevered tubes in both single-
phase and two-phase Freon 11 flows. The results are compared with those of a

standard strain gauge bridge. The purpose of this paper is to describe a novel
vibration- monitoring device for determining the response of closely spaced tubes
in two-phase flow using a beam of light transmitted through any one of the tubes
in the array by means of fiber optics.
M. K. AU-YANG [19] conducted the numerical experiment to measure the
crossing frequency of heat exchanger support plate. The crossing frequency is the
number of times per second the vibration amplitude crosses the zero displacement
line from negative displacement to positive displacement. In flow-induced
vibration in which the motions are often random and/or a number of modes
contribute to the vibration amplitudes, the crossing frequencies are modal-
weighted average frequencies of the vibration. A tube in a large commercial
nuclear steam generator (Figure 55) was used to study the effect of tube-to-
support-plate clearance on the crossing frequency, and hence on fluidelastic
loading, during normal operations (below the critical velocity) and as the velocity
increased beyond the critical velocity. A frequency-domain linear analysis (that is,
without tube support-plate clearances) was carried out first. As shown in Figure
56 are the initial crossing frequencies when the vibration amplitudes were small,
and the crossing frequencies as the vibration amplitudes started to grow and the
system approached instability. In each case, 4 s of record is shown. Figure 56
shows that during the initial 5 s when the amplitudes were small, the crossing
frequencies depended on the tube-to-support-plate clearances. As the vibration
amplitudes grew and the tube
Figure 37 Finite element model of tube under study.

Figure 38 Initial crossing frequency versus crossing frequency as the tube
approaches the instability threshold.
Wang Guoxing, Wang Shaqing, L.I.Huajun[20] presented paper on numerical
simulation of flow past a circular cylinder. He used a standard k-ε model [9].
Geometry is as shown below in figure 57.
Figure 39 Schematic diagram of 2-DOF circular cylinder.
The finite volume approach and semi implicit method for pressure linked
equations(SIMPLE) algorithm are utilized to discretized and solve the partial
differential equation in the standard k- ε model on non orthogonal boundary fitted
O type grids. A moderate Reynolds number 16250 was chosen to animate the
turbulent wake patterns. A typical vortex shedding is depicted in figure 60 below.

Figure 40 Streamlines and turbulent kinetic energy contours for flow past the
circular cylinder at Re=16250.
The contour plots at Re=16250 shown in fig 60 are in good agreement with
Blevins [2]. An important parameter, the Strouhal number, was defined to depict
this relationship as S=fd/U. For single cylinder the Strouhal number is 0.2[2, 4]
approximately in this range of Reynolds numbers.
Figure 41 Variation of Strouhal number with Reynolds number.

CHAPTER 3.
THEORY OF FLOW INDUCED VIBRATION.
Fluid flowing across a heat exchanger tube bank can cause various types of tube
vibration and instability. These problems have become more important with the
demand for larger and more efficient heat exchangers. From a practical point of
view, heat exchanger designers need to know when and why detrimental flow-
induced vibrations occur and how to suppress them. To be able to answer these
questions one must understand the mechanisms involved. In what follows several
excitation mechanisms are briefly reviewed. The various literatures are available
for heat exchanger in nuclear power plant. The few of them are discussed in
literature survey. We will discuss the above mentioned parameter in detail.
The flow induced vibration analysis consists of following steps:
(i) Flow distribution calculation.
(ii) Dynamic parameter evaluation like damping, effective tube mass and
dynamic stiffness.
(iii) Formulation of vibration excitation mechanisms
(iv) Vibration response prediction.
(v) Resulting damage assessment.
3.1 Flow distribution calculation.
The end results of the flow analysis should be the shell-side cross flow velocity,
Up, and fluid density, ρ distributions along the critical tubes. For flow-induced
vibration analyses, the flow velocity is defined in terms of the pitch velocity:
( )
p
U P
U
P D



3.1.1
Where U is the free stream velocity (i.e., the velocity that would prevail if the
tubes were removed). P is the pitch between the tubes and D is the tube diameter.
For finned tubes, the equivalent hydraulic diameter, Dh; is used. The pitch velocity
is sometimes called the reference gap velocity. The pitch velocity is a convenient
definition since it applies to all bundle configurations. The situation is somewhat
more complex in two-phase flow. Another parameter, steam quality or void
fraction, is required to define the flow conditions. Two-phase mixtures are rarely
homogeneous or uniform across a flow path. However, it is convenient and simple
to use homogeneous two-phase mixture properties as they are well defined. This is
done consistently here for both specifying vibration guidelines and formulating
vibration mechanisms. The homogeneous two-phase flow model assumes that
both liquid and gas phases flow with equal velocity. The homogeneous void
fraction, εg; is defined in terms of the volume flow rates of gas, Vg; and liquid, Vl:
g
g
g l
V
V V
 

3.1.2
For complex components such as nuclear steam generators and power condensers,
a comprehensive three dimensional thermo-hydraulic analysis is required. In such
analyses, the component is divided into a large number of control volumes. The
equations of energy, momentum and continuity are solved for each control
volume. This is done with numerical methods using a computer code such as the
THIRST code for steam generators. The grid must be sufficiently fine to

accurately predict the flow distribution along the tube. For flow-induced vibration
analyses, the results must be in the form of pitch flow velocity and fluid density
distributions along a given tube. These distributions constitute the input to the
flow-induced vibration analysis of this particular tube. Some knowledge of flow
regime is necessary to assess flow-induced vibration in two-phase flow. Flow
regimes are governed by a number of parameters such as surface tension, density
of each phase, viscosity of each phase, geometry of flow path, mass flux, void
fraction and gravity forces. Flow regime conditions are usually presented in terms
of dimensionless parameters in the form of a flow regime map. As yet, very little
information is available on flow regimes in tube bundles subjected to two-phase
cross flow. The axes on the Grant flow regime map are defined in terms of a
Martinelli[3] parameter, X; and a dimensionless gas velocity, Ug: The Martinelli
parameter is formulated as follows:
0.9 0.4 0.1
1 g l l
g g g
X
  
  
     
           
     
3.1.3
3.2 Dynamic parameter evaluation.
Generally, in heat exchangers there are several significant damping mechanisms:
(i) friction damping between tube and tube-support, (ii) squeeze-film damping at
the support, and (iii) viscous damping between tube and shell-side fluid. In
nuclear steam generators, damping due to two-phase flow is also important. The
other parameters are hydraulic diameter and hydrodynamic mass. We see these in
detail.
3.2.1 Hydraulic diameter.
For unfinned tubes the hydraulic diameter is simply the tube outside diameter, D:
From a hydraulic viewpoint, the fins may be approximated by an unfinned tube of
equivalent diameter, Dh. The hydraulic diameter is based on the ratio, RF ; of the
area occupied by the fins over the available area between the root diameter, Dr;
and the outer diameter of the fins, Do:
( )h r o rD D D D   3.2.1.1
3.2.2 Hydrodynamic mass.
The hydrodynamic mass is the equivalent dynamic mass of external fluid
vibrating with a tube. In liquid flow, the hydrodynamic mass per unit length of a
tube confined within a tube bundle may be expressed by:
2
2
2
( / ) 1
4 ( / ) 1
e
h
e
D d
m D
D d


  
   
  
3.2.2.1
Where De is the equivalent diameter of the surrounding tubes and the ratio De/D
is a measure of confinement. The effect of confinement is formulated by
0.96 0.5eD P P
D D D
 
  
 
3.2.2.2

The total dynamic mass of the tube per unit length, mS; comprises the
hydrodynamic mass per unit length, mh; the tube mass per unit length, mt; and the
mass per unit length of the fluid inside the tube, mi
S h t im m m m   3.2.2.3
3.2.3 Damping
As said earlier, the damping is of 3 main type. The various correlations are
available for it The heat exchanger may be of gas to gas, liquid to liquid, liquid to
gas. It is also acting upon two phase flow. The correlations are derived below.
3.2.3.1. Heat exchanger tube in gases.
As discussed in Pettigrew et al.[5] the dominant damping mechanism in heat
exchangers with gas on the shell side is friction between tubes and tube-supports.
All the available information on damping of heat exchanger tubes in gases has
recently been reviewed. Most of these data pertain to unfinned tubes. This work
yielded the following design recommendation for estimating the friction damping
ratio, ζF ; in percent
1/2
1
5F
m
N L
N l

  
   
  
. 2.3.1.1
which takes into account the effect of support thickness, L; span length lm; and
number of spans, N. When their minimum damping values are generalized
following the formulation of 2.3.1.1 we obtain the following
1/2
1
4F
m
N L
N l

  
   
  
3.2.3.1.2
In this case when tubes are in gases ζF = ζT
3.2.3.2 Heat exchanger tubes in liquid.
When heat exchanger tubes are in liquid then it undergoes below viscous damping
of flowing fluid, squeeze film friction damping, and friction damping. The viscous
damping is given by
32
2 2 2
1 ( / )100 2
(1 ( / ) )8
e
v
e
D DD
m fD D D
  


    
    
    
3.2.3.2.1.
Where ν is the kinematic viscosity of the fluid and f is the tube natural
frequency. Clearly, viscous damping is frequency dependent. Calculated values of
damping 3.2.3.2.1 are compared against experimental data in figure below.

Figure 42. Viscous Damping for A Cylinder in Unconfined and Confined
Liquids.
The squeeze film damping ζSF and friction damping ζF take place at support. Based
on experimental data for total tube damping shown in figure below semi empirical
expressions were developed, to formulate friction and squeeze film damping as
discussed by Pettigrew et al.
Figure.43 Damping Data For Multispan Heat Exchanger Tubes In Water.
It is formulated by.
1/2
2
1 1460
SF
m
N D L
N f m l


                 
3.2.3.2.2.
And friction damping is given by:

1/2
1
0.5F
m
N L
N l

   
    
    
3.2.3.2.3
The total friction is given by
T v SF F      3.2.3.2.4
3.2.3.3. Damping in two phase flow.
The total damping ratio, ζT of a multispan heat exchanger tube in two-phase flow
comprises support damping, ζS viscous damping, ζV and two-phase damping, ζTP
T S V TP      3.2.3.3.1.
Depending on the thermal hydraulic conditions the supports may be dry or wet. If
the supports are dry, which is more likely for high heat flux and very high void
fraction, only friction damping takes place. Support damping in this case is
analogous to damping of heat exchanger tubes in gases. Damping due to friction
in dry support may be expressed as eq 2.3.1.1. The above situation is similar to
heat exchanger tube in gas.
When there is liquid between the tube and support, support damping includes both
squeeze film damping, friction damping. The correlation is given by
2
1 1460
0.5l
S SF F
DN
N f m

  
   
      
    
3.2.3.3.2
32
2 2 2
1 ( / )2100
(1 ( / ) )8
eTP TP
V
e
D DD
m fD D D
 


    
     
    
3.2.3.3.3
Where νTP is the equivalent two phase kinematic viscosity. There is a two-phase
component of damping in addition to viscous damping. Two-phase damping is
strongly dependent on void fraction, fluid properties and flow regimes, directly
related to confinement and to the ratio of hydrodynamic mass over tube mass, and
weakly related to frequency, mass flux or flow velocity, and tube bundle
configuration. A semi-empirical expression was developed from the available
experimental data to formulate the two-phase component of damping, ζTP in
percent:
2 3
2 2
1 ( / )
4 ( )
[1 ( / ) ]
l e
TP g
e
D D D
f
m D D

 
   
    
   
3.2.3.3.4
3.2.4. Dynamic stiffness and support effectiveness
For unfinned tubes, the dynamic stiffness of multispan heat exchanger tubes is
simply the flexural rigidity, EI. For finned tubes, the increase in flexural rigidity
due to the fins is equivalent to an increase in wall thickness equal to 1/4 of the fin
width, a at the root of the fin over the length of the fin. Thus the equivalent
stiffness, EIes is found using the following equation:

1 1 1
es a b
a b
EI a b EI a b EI
   
    
    
3.2.4.1.
3.3. Vibration excitation mechanisms.
It means that by which mechanism vibration is being generated. Several vibration
excitation mechanisms are normally considered in heat exchanger tube bundles in
cross flow namely (i) fluid elastic instability (ii) Periodic wake shedding (iii)
Acoustic resonance (iv) Turbulent buffeting.
3.3.1 Fluid elastic instability.
When a cylinder in an array of cylinders is displaced, the flow field shifts,
changing the fluid forces on the cylinders. These fluid forces can induce
instability if the energy input by the fluid force exceeds the energy expended in
damping. The cylinders, or tubes, generally vibrate in oval orbits. In tube and shell
heat exchangers, these vibrations are called fluid elastic instability. In arrays of
power transmission lines, the vibrations are called wake galloping. Fluid elastic
instability is a dominant cause of tube failure in heat exchangers. Similarly wake
galloping instability of power lines is a major concern in transmission line design.
Analysis of fluid elastic instability requires an accurate theoretical description of
the unsteady fluid forces imposed on a tube in an array of vibration tubes. This
very difficult problem has not yet been fully resolved. In fact, none of the current
models are capable of prediction the instability of an untested heat exchange tube
array with better accuracy than the band of data. However theory does provide
insight into the nature of the instability and estimates for instability when data are
not available. Fluidelastic instability is formulated in terms of a dimensionless
flow velocity, Up=fD; and a dimensionless mass-damping parameter, 2πζm/ρD2
1/2
2
2pU m
K
fD D


 
  
 
3.3.1.1
Where f is the tube natural frequency, ρ is the fluid density, m is the tube mass per
unit length and Up is the threshold, or critical, flow velocity for fluid elastic
instability. A fluid elastic instability constant K = 3:0 is recommended for all tube
bundle configurations, the damping ratio ζ is the total damping ratio as defined in
the previous topics as total damping ratios.
Fluid elastic excitation is most commonly associated with aircraft wing flutter and
with galloping of ice laden transmission lines. It is readily explained bhy
considering the flow of fluid past a vibration bluff body whose cross section is not
symmetrical with respect to the direction of fluid flow. A group of circular
cylinders submerged in crossflow can be subjected to dynamic instability,
typically referred to as fluid elastic instability. Fluid elastic vibration sets in at a
critical flow velocity and can become of large amplitude if the flow is increased
further. The familiar examples of FEI vibration are aircraft wing flutter,
transmission line galloping, and vibration of tube arrays in heat exchangers. A
sudden change in vibration pattern within the tube array indicates instability and is
attained when the energy input to the tube mass-damping system exceeds the
energy dissipated by the system. Fluid elastic instability has been recognized as a

mechanism that will almost lead to tube failure in a relatively short period of time,
and this is to be avoided at any cost by limiting the crossflow velocity. However,
some tube response due to turbulent buffeting or vortex shedding cannot be
avoided, and this may lead to long-term fretting failure. If vortex shedding
resonances are predicted at velocities above the fluid elastic critical velocity, then
vortex shedding is not a concern and it is not necessary to predict the associated
amplitudes of vibration.
CONNORS’ FLUID ELASTIC STABILITY ANALYSIS
The pioneering work on FE1 was initiated by Connors. In 1970, Connors studied a
tube row in a wind tunnel using a quasi-static model. The Connors single-row tube
model is shown schematically in Fig. 59. The model, using fluid dynamic
coefficients obtained from tests on a stationary body to determine the fluid
dynamic forces acting on a vibrating body, is generally called a quasi-static
model. According to Connors, the FE1 results when the amount of energy input to
tubes in crossflow exceeds the amount of energy that can be dissipated by the
system damping. As a result of energy imbalance, the tube vibration will intensify
to the point that clashing with adjacent tubes takes place. From his model, he
measured quasi-steady force coefficients and developed a semi-empirical stability
criterion for predicting the onset of fluid elastic instability of tube arrays. The
stability criterion relates the critical flow velocity Ucr, to the properties of the fluid
and structures of the form
2
n
cr
n
U m
K
f D D


 
  
 
3.3.1.2
Where Ucr is the critical velocity and δ is equal to 2πζ. For his single-row
experimental model with p/D= 1.41, the value of K is 9.9 and a = 0.5.
Accordingly, the expression for instability is given by
2
9.9cr
n
U m
f D D


 
  
 
3.3.1.3
In this expression, the two main parameters are Ucr/fnD ,the reduced velocity, and
mδ/ρD2
, the mass damping parameter. The Connors vibration mechanism was
later referred to as a displacement mechanism and the model is known as a quasi-
static model. For tube bundles, the parameter K = 9.9 does not hold good, and
hence numerous investigators conducted extensive experiments to form a more
appropriate instability parameter K. Several new models-the analytical model and
the unsteady model have been proposed. A few researchers refined the quasi-static
model. A mechanism called the velocity mechanism was suggested by Blevins.
Many reviews and the state of the art have been presented. However, most of the
researchers proposed a stability criterion similar to the Connors stability equation
form. In the following sections, various instability models are discussed briefly.
Subsequently the design guidelines and acceptance criteria are presented.
Wherever these criteria are common with TEMA and ASME Code, this is
specified.

Figure 44 Connors’ single row FEI model.
EXAMPLE: TUBEINSTABILITYIN A HEAT EXCHANGER
Consider the single shell pass and single tube pass heat exchanger as shown in
figure 45 below. Water enters the shell side through a nozzle, then flows in a
serpentine pattern over eight baffle and exits on the opposite side. Some of
dimensions of heat exchanger are given below.
Figure 45 Single shell pass and single tube pass heat exchanger.
Tube length=3580 mm
Shell inside diameter=591 mm
Baffle thickness=9.5 mm
Baffle cut=134 mm
Baffle hole diameter=19.5 mm
Baffle spacing = 256 mm
Nozzle baffle spacing=895 mm

Tube outside diameter=19.1 mm
Tube material density = 8500 kg/m3
Tube material modulus of elasticity=110 GPa
Tube pattern= 30 degree layout
Pitch to diameter ratio=1.33
Shell side fluid= water
Fluid density=1000 kg/m3
Kinematic viscosity of fluid=0.00001 m
2
/s
There are 449 brass tubes in this heat exchanger. The potential for flow induced
instability is found by utilizing figure 47 below.
Figure 46 Dimensionless presentation of fluidelastic instability results in two
phase cross flow.
The correlation presented in this figure is utilized in the following steps
1. Calculate mass damping parameter m(2πζ)/ρD2
2. From the figure determine value of reduced velocity U/fD for onset of
instability.
3. Calculate tube natural frequency f.
4. Relate the critical unstable velocity Ucr to the shell side flow through the
heat exchanger.
These steps will be followed in order.
The mass per unit length of tubes m includes both mass of internal fluid and added
mass due to external fluid. Consider the tubes to b empty. The mass per unit
length of bare tubing is easily calculated to be 0.6 kg/m. The added mass of water
is equal to the mass of water displaced by the tube times an added mass
coefficient. For pitch to diameter ratio of 1.33 an added mass coefficient of 1.6 is
suggested by R.D.Blewins[2]. This gives average value of 0.456 kg/m. Thus the
total mass per unit length is 1.08 kg/m. The damping measurement of these tubes
showed a range of damping from 1% to 5% of critical with damping decreasing
with increasing frequency. A typical value of damping ζ=0.02 will be used in this
example. With this information the mass damping parameter is

2
(2 )
0.374
m
D



From figure 61 the critical reduced velocity is Ucr/fD=2.
The natural frequency of tubes bending between baffles is given by
2
2
2
EI
f
L m



L is distance between the tube supports, E is the tube modulus of elasticity, I is the
tube moment of inertia for bending, 0.277 10E-8 m4
and λ is dimensionless
parameter that is function of vibration mode and baffle spacing. The tubes tend to
pivot freely at oversized holes in baffle, but their extremities are clamped at tube
sheets. Taking into account the clamping of extreme ends gives λ=3.393 for. The
cross flow velocity for instability must be related to overall shell side flow
through the heat exchanger. This would require a detailed evaluation of flow field
and tube mode shape to evaluate the integral equation. A simple estimate can be
obtained using conservation of mass
Q=UA
An estimate of average cross flow area is the distance between baffle less the
baffle thickness, times the length of straight edge of baffle times the fraction of
free flow area between tubes to total area. In unit of millimeter square it gives
A=(256-9.5)*484*0.33/1.33=29602.24mm2
= 0.0296 m2
.
Thus the flow rate of 1cusec through heat exchanger would yield an effective
velocity of 33.78 m/s. There is some additional area associated with leakage. This
increase area by 30%, which gives 0.0385 square meter.
3.3.2 Periodic wake shedding
Periodic wake shedding, or vortex shedding, may be a problem when the shedding
frequency coincides with a tube natural frequency. This may lead to resonance
and large vibration amplitudes. Periodic wake shedding resonance may be of
concern in liquid cross flow where the flow is relatively uniform. It is not
normally a problem at the entrance region of steam generators because the flow is
very non-uniform and quite turbulent Turbulence inhibits periodic wake shedding
Periodic wake shedding is generally not a problem in two-phase flow except at
very low void fractions Periodic wake shedding resonance is usually not a
problem in gas heat exchangers. The gas density is usually too low to cause
significant periodic forces at flow velocities close to resonance. Normal flow
velocities in gas heat exchangers are usually much higher than those required for
resonance. However, it may be possible in high-pressure components with higher
density gas on the shell side. It could also happen for higher modes of vibration
with higher frequencies corresponding to higher flow velocities. Thus, periodic
wake shedding resonance cannot always be ignored in gas heat exchangers.
Generally, there is little information on the magnitude of periodic wake shedding
forces in tube bundles. There is more information on periodic wake shedding
frequencies. However, this information is often contradictory. Periodic wake
shedding is described in terms of a Strouhal number S = fsD/Up; which formulates

the wake shedding frequency, fs; and a fluctuating lift or drag coefficient, CL;
which is used to estimate the periodic forces, Fs; due to wake shedding. Thus,
21
2
s L pF C D U 3.3.2.1
As a fluid particle flows toward the leading edge of cylinder, the pressure in the
fluid particle rises from the free stream pressure to stagnation pressure. The high
fluid pressure near the leading edge impels flow about the cylinder as boundary
layers develop about both sides. However, the high pressure is not sufficient to
force the flow about the back of the cylinder at high Reynolds numbers. Near and
widest section of cylinder the boundary layers separate from each side of cylinder
surface and form two shear layers that trail aft in the flow around the wake. Since
the innermost portion of the shear layers, which is contact with the cylinder,
moves much more slowly than the outermost portion of the shear layers, which is
in contact with the free flow, the shear layers toll into the near wake, where they
fold on each other and coalesce into discrete swirling vortices. A regular pattern of
vortices called vortex street trails aft in wake. The vortices interact with the
cylinder and they are the source of the effect called vortex induced vibration.
Figure 47 Vortex street.

Figure 48 Vortexes at various Reynold number.
It is shown diagrammatically in the figure 59 above. Von Karman (1912) found
that these vortexes are shed behind the body. These vortexes follow a regular
frequency pattern. The area in which these vortexes pass is known as Vortex
Street. The vortex frequency can be found by Strouhal number. It is dimensionless
proportionality constant between the predominant frequency of vortex shedding
and free stream velocity divided by the cylinder width,

s
SU
f
D
 3.3.2.2
The frequency of vortex shedding can also be given by empirical formula
19.7
0.198 1
Re
sf D
U
 
  
 
3.3.2.3
Where fs is vortex shedding frequency in Hertz, U is free stream flow velocity and
D is diameter of the cylinder.
EFFECT OF CYLINDER MOTION ON WAKE.
Transverse cylinder vibration with frequency at or near the vortex shedding
frequency has large effect on vortex shedding. The cylinder vibration can:
1. Increase the strength of vortices.
2. Increase the span wise correlation of the wake.
3. Cause the vortex shedding frequency to shift to the frequency of cylinder
vibration. This effect is called lock-in or synchronization, and it can also
be produced to lesser extent if the vibration frequency equals a multiple of
submultiples of shedding frequency.
4. Increase the mean drag on the cylinder.
5. Alter the phase, sequence, and pattern of vortices in wake.
As the flow velocity is increases or decreased so that the vortex shedding
frequency approach the natural frequency of structure, so that
n s
SU
f f
D
  or
1
5
n s
U U
f D f D S
   3.3.2.4
For single cylinder the value of Strouhal number is 0.2. The various models for
vortex induced vibration analysis are available. These are simple linear harmonic
model that does not incorporate feedback effects, but it does serve to develop the
appropriate nondimensional parameters and provide forum for experimental data.
The second models vortex shedding as nonlinear oscillator. Its nonlinear solutions
are correspondingly more difficult, but they have the potential for describing a
much larger range of phenomena. These models will be compared with
experimental data. These data, suitably nondimensionalized are cast as the final
model.
MODEL 1: HARMONIC MODEL (LINEAR MODEL)
Because vortex shedding is a more or less sinusoidal process, it is reasonable to
model the vortex shedding transverse force imposed on a circular cylinder as
harmonic in time at the shedding frequency:
21
sin( )
2
L L sF U DC t  3.3.2.5
The alphabet has usual notation. This force is applied to a spring mounted damped
rigid cylinder shown in figure 60 below. The cylinder is restrained to move
perpendicular to the flow.

Figure 49 Cylinder and coordinate system.
The equation of motion of the cylinder is
21
2 sin( )
2
y L L smy m y ky F U DC t       3.3.2.6
Where y = displacement of cylinder in vertical plane.
m = mass per unit length of cylinder.
ζ = structure damping factor.
ωy =(k/m)1/2
=2πfy , circular natural frequency of cylinder.
Solution of this linear equation are found by postulation a sinusoidal steady state
response with amplitude Ay, frequency and phase φ,
sin( )y sy A t   3.3.2.7
And substituting this in to equation 3.3.2.6 we get
2
2
2 2
1
sin( )
2
1 ( ) (2 )
L L s
s s
y y
F U DC t
y
D
k
  
 

 
 

 
  
  
3.3.2.8
Where phase angle is defined as
2 2
2
tan
( )
s y
s y
 

 


3.3.2.9
The phase angle shifts by 180 degree as cylinder passes through fs=fy. The
response is largest when the shedding frequency approximately equals the
cylinder natural frequency, fs=fy, a condition called resonance. Using equation of
y and y/D the resonant vibration amplitude is
2
2
4 4y s
y L L
f f r
A U C C
D k S

  
  3.3.2.10

The resonant amplitude decreases with increasing reduced damping δr, which
defined as the mass ration times the structural damping factor,
2
2 (2 )
r
m
D



 3.3.2.11
The equation 3.3.2.10 implies that amplitude at resonance is independent of flow
velocity. So that we can write as below
*yA D G or 1.5yA D in most of cases 3.3.2.12
Where G is constant.
MODEL 2: WAKE OSCILATOR MODEL( NON LINEAR MODEL)
The nature of self excited vortex shedding suggests that the fluid behavior might
be modeled by a simple, nonlinear, self excited oscillator. The Blewins-Iwan[2]
model described in the following section utilizes a Van der Pol type equation with
flow variable to describe the effects of vortex shedding. Model parameters e
determined by curve fitting experimental results for stationary and forced
cylinders in the Reynolds number range between 1000 to 100000. The basic
assumptions of model are given below:
1. Inviscid flow provides a good approximation for the flow field outside the
near wake.
2. There exist a well formed two dimensional vortex street with a well
defined shedding frequency.
3. The force exerted on the cylinder by the flow depends on the velocity and
acceleration of the flow relative to the cylinder.
REDUCTION OF VORTEX INDUCED VIBRATION.
The amplitude of resonant vortex induced vibration and the associated
magnification of steady drag can be substantially reduced by modifying either the
structure of the flow as follow:
1. Increase reduced damping. If the reduced damping (eq 3.3.2.11) can be
increased, then the amplitude of vibration will be reduced as predicted by
the formulas of Table 3.2 (Flow induced vibration by R. D. Blevins). In
particular if the reduced damping exceeds about 64,
2
2 (2 )
64r
m
D



  3.3.2.13
then peak amplitude s at resonance are ordinarily less than 1% of diameter
and are ordinarily negligible in comparison with the deflection induced by
drag. Reduced damping can be increased by either increasing structural
damping of increasing structural mass. Increased damping can be achieved
by permitting scraping or banging between structural elements, by using
materials with high internal damping such as viscoelastic materials,
rubber, wood or by using external dampers. The stockbridge damper has
been used to reduce vortex induced vibration of power lines.
2. Avoid resonance. If the reduced velocity is kept below U/fD <1 where f is
the natural frequency of structure in the mode of interest, the inline and

transverse resonances are avoided. This is ordinarily achieved by stiffening
the structure. Stiffening is often most practical for smaller structures.
3. Streamlined cross section. If separation from the structure can be
minimized, then vortex shedding will be minimized and drag will be
reduced. Streamlining the downstream side of structure ordinarily requires
a taper of 6 longitudinal for each unit lateral, or an included angle of taper
no bigger than 8 to 10 degrees, to be effective. The NACA 0018 airfoil has
been used for streamline fairing.
3.3.3. Acoustic resonance.
Acoustic resonance may take place in heat exchanger tube bundles when vortex or
periodic wake shedding frequencies coincide with a natural frequency for acoustic
standing waves within a heat exchanger. Such resonance normally causes intense
acoustic noise and often serious tube and baffle damage. Acoustic resonance is
possible in gas heat exchangers with both finned and unfinned tubes. Acoustic
resonance requires two conditions: (i) coincidence of shedding and acoustic
frequency, and (ii) sufficient acoustic energy or sufficiently low acoustic damping
to allow sustained acoustic standing wave resonance. In heat exchanger tube
bundles, acoustic standing waves are generally normal to both the tube axes and
the flow direction. The acoustic standing wave frequencies, fan are defined by
2
an
nC
f
W
 3.3.3.1
where W is the dimension of the heat exchanger tube bundle cavity in the
direction normal to the flow and the tube axes, n is the mode order and C is the
effective speed of sound which is given by
0
1
C
C



3.3.3.2
Where C0 is speed of sound in the working medium. And ζ is the solidity ratio.
This is the ration of the volume occupied by the tubes over the volume of the tube
bundle. For triangular tube bundle,
2
2
2 3
D
P

  3.3.3.3
And for square tube bundle
2
2
D
P

  3.3.3.4
Where P is pitch of tubes.
3.3.4. Turbulence induced excitation mechanism.
Turbulent buffeting in a tube bank, sometimes called subcritical vibration, refers
to the low amplitude response before the critical velocity is reached and away
from the vortex lock-in velocity region due to unsteady forces developed on a
body exposed to a high turbulence in the flow field. The turbulent flow has been
characterized by random velocity perturbations associated with turbulent eddies
spread over a wide range of frequencies distributed around a central dominant
frequency. When the dominant central frequency in the flow field coincides with

the lowest natural frequency of the tube, a considerable amount of energy transfer
takes place, leading to resonance and high-amplitude tube vibration. Even in the
absence of resonance, turbulent buffeting can cause fretting wear and fatigue
failure. With a design objective of 40 years codal life for nuclear power plant
steam generators and heat exchangers, even relatively small tube wear rates
cannot be acceptable. Hence, turbulence excitation becomes an important design
consideration in the design of reliable heat exchangers.
OWEN’S EXPRESSION FOR TURBULENT BUFFETING FREQUENCY
Based on experimental study of gas flow normal to a tube bank, Owen [5]
correlated an expression for the central dominant frequency of the turbulent
buffeting, fcr as
2
1
3.05 1 0.28tb
l t t
U
f
DX X X
  
    
   
3.3.4.1
Where Xl=longitudinal pitch ratio=Lp/D
Xt=transverse pitch ratio=Tp/D.
The approach is most reliable for predicting the peak frequency in turbulence,
provided the minimum gap velocity is used in expression. The preceding
correlation ins applicable for tube bank with transverse pitch ratio more than 1.25.
Since this correlation has not been tested for liquids, it should be restricted to
gases only.
3.4. Vibration response prediction.
Due to the complexity of a multispan heat exchanger tube, a computer code must
be used to predict vibration response accurately and to determine the susceptibility
of a tube to periodic wake shedding resonance and fluidelastic instability. This
computer code must be capable of calculating the mode shapes and natural
frequencies for a number of modes at least equal to the number of tube spans.
Generally the code will be in two parts:
(1) The first part will calculate the free vibration tube characteristics such as mode
shapes and natural frequencies, while (2) The second part is a forced vibration
analysis that calculates the tube response to turbulence-induced excitation and
periodic wake shedding, and the fluidelastic instability ratios. A forced vibration
analysis involves the application of the distributed flow velocities and densities.
From a mechanics point-of-view, the tubes are simply multispan beams clamped
at the tube sheet and held at the supports with varying degrees of constraint. To
predict tube response, it is convenient and appropriate to assume that the
intermediate supports are hinged. With this assumption, the analysis is linear and
either a finite-element code or an analytical code can be used. If the tube-to-
support clearances are too large, the tube supports will not be effective and the
assumption of hinged supports will not be valid. Tube-to-support diametral
clearances of 0.38mm (0.015 in) or less are typically used in nuclear heat
exchanger design. Effective supports can become ineffective if a heat exchanger is
subjected to significant corrosion or a chemical cleaning technique is used to clean
a fouled unit. The effects of future chemical cleaning and corrosion should be
considered in the vibration response analysis.
3.5. Fretting wear and damage assessment.

The ultimate goal of vibration analyses is to ensure that fretting-wear or fatigue
damage does not occur in heat exchangers. Although a linear analysis does not
predict fretting-wear, significant fretting-wear can be avoided by keeping the
predicted vibration amplitudes below the allowable provided later in this paper. In
addition, fretting-wear damage can be estimated Fretting-wear damage may be
assessed using the following methodology. The total fretting-wear damage over
the life of the heat exchanger must not exceed the allowable tube wall reduction or
wear depth, dw. Fretting-wear damage may be estimated using the following
modified Archard equation.
FW NV K W  3.5.1
Where V is the volume fretting-wear rate, KFW is the fretting-wear coefficient,
and NW is the normal work-rate. The work-rate is the available mechanical energy
in the dynamic interaction between tube and support and is an appropriate
parameter to predict fretting-wear damage. The work-rate may be calculated by
performing a nonlinear time domain simulation of a multispan heat exchanger
tube vibrating within its supports. Alternately, the work-rate may be estimated
with the following simplified expression
3 3 2
max16N sW f ml y  3.5.2
Where m is the total mass of tube per unit length, and 2
maxy and f are, respectively,
the maximum mean-square vibration amplitude and the natural frequency of the
tube for the worst mode. The worst mode of a given region is defined as the mode
of vibration that has the highest value for the normal work-rate term WN; in Eq.
5.2 The length l is that of the span where the vibration amplitude is maximum and
ζs is the damping ratio attributed to the supports.
WEAR DEPTH CALCULATION
It may be assumed to be conservative that fretting-wear is taking place
continuously for a total time, Ts corresponding to the life of the component. The
total fretting-wear volume, V is calculated from Eq. 3.5.1
S S FW NV T V T K W   3.5.3
The resulting tube wall wears depth, dw; can be calculated from the wear volume.
This requires the relationship between dw and V. For example, for a tube within a
circular hole or a scalloped bar, it may be assumed that the wear is taking place
uniformly over the thickness L and half the circumference πD of the support.
Thus:
2
w
V
d
DL
 3.5.4
Fretting wear coefficient depends on choice of material and systems corrosion,
heat transfer consideration. Tube and tube-support materials should be chosen to
minimize fretting-wear damage. Similar materials such as Inconel-600 (I600)
tubes and I600 supports must be avoided. Incoloy-800 (I800), Inconel-690 (I690)
and I600 tubes with 410S, 304L, 316L, 321SS or carbon steel supports are
considered acceptable material combinations from a fretting-wear point of view.

The value of fretting wear coefficient KFW of 20X10-15
m2
/N may be used as first
approximation for tube and support of above material.
3.6. Mathematical modeling
In many industrial configurations, mechanical structures such as PWR
components are subjected to complex flows causing possible vibrations and
damage and as far as nuclear security is concerned, it is necessary to prevent wear
problems generated by vibration fatigue. The forces acting on tubes are turbulent
forces and fluid elastic forces. These forces can sometimes be directly measured
by transducers but with direct approaches it is often difficult to stand between the
different physical mechanisms involved when a distributed external loading is
considered. On the contrary, indirect experimental prediction methods have shown
their ability to provide fluid force estimates. Most of them rely on force density
analytical models depending themselves on unknown spectral scaled parameters
In order to reduce experiments and to be able to study many configurations
involving complex flow-induced vibration problems, numerical methods are also
considered. Owing to recent developments incorporated into Computational Fluid
Dynamic (CFD) codes, numerical simulation of flow structure coupling is
investigated. In nuclear power plants heat exchanger tube bundles carrying
primary fluid are subjected to cross flows of secondary fluid. External fluid forces
may generate high magnitude vibrations of tubular structures causing possible
dramatic damages in terms of nuclear safety. Vibrations result from four kinds of
fluctuations (i) random fluctuations generated by turbulence in fluid at large
Reynolds numbers; (ii) fluctuations induced by structure flow motion coupling
due to fluid-elastic effects; (iii) resonance with flow periodicity due to vortex
shedding; and (iv) possible acoustic excitation.
Figure 50 Lift And Drag Force Effect On A Flexible Tube Belonging To A Fixed
Tube Bundle In Cross Flow

Figure 51 Tube ,damper, spring system for model.
Geometric parameters characterizing a regular tube bundle are the following: tube
external and internal diameters D = De and Di, tube gap or pitch P; tube row angle
θ and tube bundle length L: From a mechanical point of view, the flexible tube
motion is characterized by tube mass mS; tube stiffness Ks; tube damping Cs. The
equation of motion without fluid in tube is given by:
0t tm x Cx K x    3.6.1
Where mt is tube mass, C is external damping if provided, Kt is tube material
stiffness. Or equivalent we can write
2
2 0t tx x x     3.6.2
Where ωt is tube natural frequency without fluid, ζ is tube damping ratio without
fluid. We can also write that
Kt=mt ωt
2
3.6.3
And C=2mtωtζ 3.6.4
Concerning the hydraulics parameters, the flow is supposed to cross-
perpendicularly the tube bundle and the axial component is zero. The flow is
totally defined by its Reynolds number,
Re
UD

 3.6.5
where U = Ugap=[P/(P-D)]UN designates the gap velocity, UN the inlet flow
velocity before crossing the tube bundle and μ the fluid dynamic viscosity.
Concerning the structural motion in the fluid at rest, the apparent mode mass and
damping are affected by added mass effects (represented by mh), by internal fluid
mass effects (represented by mi) and by fluid viscosity (represented by Cv) . The
equation of motion becomes
( ) ( ) 0t h i v sm m m x C C x K x       3.6.6
Where Ks is stiffness of tube and fluid inside tube or system stiffness. Or we can
write
2
2 0T s sx x x      3.6.7

This is governing free damped vibration. The value of ζT can be obtained from
equation number 3.2.3.2.4 or 3.2.3.3.1 what ever may be the case.

CHAPTER4.
GEOMETRY AND GRID MODELING.
The present chapter deals with geometrical modeling of U-type STHE
using GAMBIT (Geometry and Mesh Building Intelligent Tool) as preprocessor.
It has a hybrid mesh capabilities. It is user friendly and capability of modeling
complicated geometry
4.1. Modeling of Shell Side Fluid Domain
The STHE consists of many parts. For simplicity the minute details of geometry is
eliminated. For present case, Shell, nozzle, and baffle are considering for
modeling. The shell is cylindrical domain with nozzle merged in it. During the
modeling of shell, geometry of Baffle is subtracted from the shell portion. First
edge meshing has carried out for shell. Triangular mesh elements were used in
face meshing. For volume meshing, hybrid mesh was used. The Shell of STHE is
meshed by the element type Tet / hybrid with type T Grid.
For Shell side , geometrical parametric analysis, five baffle with six different
baffle cut and one is without baffle have been modeled for each three tube layout.
Baffle has been cut by following equation:
100c
s
H
B
D
 
Figure 52 Heat exchanger dimensions.

Figure 53 Geometry model of Baffle.
Figure 54 Isometric view of shell fluid domain
4.2 Tube Side Fluid Domain
In this present work, in the tube side, three different tube layouts (300
, 600
and
900
) have been modeled. In the case 450
layout tubes with same number of tubes it
is not possible to place in diameter of shell. This case is not considere in present
study. In tube side fluid domain consist of head, nozzle and U type tubes. Nozzle
of tube side domain is also merged with head. A tube inside the shell is split from
the Shell domain. In tube side First edge meshing is carried out. The complex
geometry of tube for face meshing, triangular elements were used for all faces.
For volume meshing, hybrid mesh was selected. The Tube of STHE is also
meshed by the element type tet / hybrid with type T Grid.

Figure 55 Isometric view of tube fluid domain
4.3 The complete geometry of Shell and Tube Heat Exchanger.
Figure 56 Isometric view of complete geometry of Shell and tube heat exchanger.
4.3 Boundary Conditions
The boundary conditions are described as follows:
(1) The shell inlet:
u = w = 0, v = 0.5 m/s (uniform inlet velocity),
Ti = 363 K (90 C) (uniform inlet temperature),
(2) The tube inlet:
u = 1m/s, w =v = 0(uniform inlet velocity),
Ti = 303K (30 C) (uniform inlet temperature),

(3) The shell outlet:
po = 0 Pas (gauge pressure)
(4) The Tube outlet:
po= 0 Pas (gauge pressure)
(5) The outer shell walls:
u = v = w = 0 (Thermal insulation walls)
(6) The heat exchange tube wall surfaces:
u = v = w = 0
(7) The baffle walls:
u = v = w = 0
During this analysis, all inlet boundary condition are Velocity inlet and out let
boundary condition are Pressure outlets. They are as presented below.
Inlet / outlet Boundary condition type
Shell inlet Velocity inlet
Tube inlet Velocity inlet
Shell outlet Pressure outlet
Tube outlet Pressure outlet
Tube wall Wall

CHAPTER 5
RESULT AND DISCUSSION.
RESULTS
The CFD analysis using FLUENT is interesting. We can do vibration analysis in
two parts. First part is does the fluid flow analysis while second part does the
vibration analysis.
5.1 FLUID FLOW ANALYSIS
The fluid flow analysis gives interesting results. In this analysis fluent gives
velocity, pressure, temperature, mass imbalance, shear stress, viscosity plots.
These plots are given in detail as below.
5.1.1. Velocity contours.
Figure 57 Velocity magnitude.

Figure 58 velocity vector colored by velocity magnitude.
Figure 59 Velocity vector colored by static temperature.
Discussion.
As shown in figure 57 the velocity magnitude at tube inlet is approximately 1.01
m/s and at tube outlet is 0.953 m/s. The shell inlet velocity is 0.536 m/s and at
shell outlet is 0.477 m/s. The velocity is decreases as we go from inlet to outlet
because of velocity losses.

5.1.2. Pressure contour.
Figure 60 Total pressure contour.
Discussion.
The pressure at tube inlet is 7440 Pa on gage scale while at outlet of tube is 252
Pa. The pressure drop is presented here. The baffle near to tube inlet has pressure
of 4630 Pa while baffle near U-bend is 3060 Pa. At some region near tube outlet
negative pressure is also happening.
5.1.3. Shear stress contours.
Figure 61 Wall shear stress.

Figure 62 Mean wall shear stress.
Discussion.
Wall shear stress and mean wall shear stress are nearly same as seen from figure
61 and 62. The maximum wall shear stress is at tube inlet nozzle wall with
magnitude 1.21 Pa. While the wall shear stress is uniform at tube inside surface of
1.07 Pa. This is due to fact that fluid velocity is maximum at inlet section so
obviously wall shear stress will be maximum at inlet.
5.1.4. Skin friction coefficient contour.
Figure 63 Skin friction coefficient.

Figure 64 Mean skin friction coefficient.
Discussion.
There is no much difference in skin friction and mean skin friction. The maximum
skin friction coefficient is at tube inlet nozzle wall and tube inside wall of the
magnitude 0.000538. This shows there is low friction between tube surface and
fluid.
5.1.5. Temperature contours.
Figure 65 Static temperature contour.

Discussion.
The Shell side temperature is decreasing from shell inlet to shell outlet from 363
K to 353 K. While tube side temperature is increases with magnitude of 302 K at
tube inlet nozzle to 333 K at near to the U bend region of the tube. This shows
there is very drastic change in tube side temperatur than shell side temperature.
We took both the fluid as water so there is no change in specific value. But this
difference is due to different mass flow rate.
5.1.6. Mass imbalance contour.
Figure 66 Mass imbalance contour.
Discussion.
There is not noticeable change in mass flow rate across both shell side and tube
side fluid.
5.1.7. Fluid property contours.

Figure 67 Mean surface heat transfer coefficient contour.
Figure 68 Subgrid turbulent viscosity contour.
Discussion.
The mean surface heat transfer (h.t.c.) coefficient is approximately uniform at tube
inlet to outlet of the magnitude -6.16 W/m2
K. While there is different h.t.c. at tube
outside surface near the shell inlet nozzle of the magnitude 5.85 W/m2
K. On the
other hand if we check the turbulent viscosity then it is uniform at tube inside with
the magnitude 0.00543 Pa.s and inside shell side fluid is approximately uniform of
the magnitude 0.0011 Pa.s. The viscosity is maximum at tube inlet of the

magnitude 0.0249 Pa.s. This is due to fact that at tube inlet section the turbulence
is maximum so that viscosity is also high.
5.1.8. Other contours.
Figure 69 Strain Rate Contour.
Figure 70 Cell Volume Change Contour.

Figure 71 Cell Warpage Contour.
Discussion.
As shown in figure 69, strain rate is maximum near tube wall surface of the
magnitude 203 per second. While it is minimum at tube inlet nozzle center line of
the magnitude 0.165 per second. This is due to fact that at near wall surface the
fluid has surface tension due to adhesion between fluid and tube wall so strain is
maximum at that location.
5.2. VIBRATION ANALYSIS.
In vibration analysis we are able to measure only acoustic frequency as explained
in the topic 3.3.3. In that analysis we are measuring acoustic noise generated due
to tube vibration inside the heat exchanger. A designer can judge what wrong is
happening inside the heat exchanger with the help of noise coming out of it. Some
time this acoustic noise is becoming too high so that it can be heard in the 10 m of
area around heat exchanger. To catch this acoustic noises we have placed 4
acoustic receiver across the heat exchanger. These receivers are shown in figure
below.
Figure 72 Receiver Location.
The receivers are coinciding with the heat exchanger shell axis. The receiver
exactly below shell inlet nozzle and coinciding with shell inlet nozzle is receiver
1. The subsequent receivers are at equal distance from receiver 1 at spacing of 0.1
m. Total 4 receivers were placed.

SIGNALS ANALYSIS AT RECEIVER 1
The sound pressure level (SPL) at receiver 1 reaches maximum at 120 db and
maximum frequency is achieved as 2500 Hz. The SPL is 100 db at maximum
frequency of 2500 Hz. The power spectral density (PSD) is approximately
uniform at this location and attains value of 10 at 2500 Hz. The PSD plot is
uniform, which indicate that sound is generated at uniform rate at this location.
The PSD attains peak value of 225 at this location which indicate signal is strong
at this location.

Figure 73 Plot at receiver 1.
SIGNAL ANALYSIS AT RECEIVER 2.
The SPL reaches maximum of 115 db at this location while frequency attains
maximum value of 2500 Hz. The SPL is 105 at maximum frequency of 2500 Hz.
The PSD plot is not uniform at this location which indicate that noise is generated
at that location is not uniform. This is due to reduce in span length at the location.
The PSD is approximately 10 at this location at maximum frequency of 2500 Hz
and attains peak value of 70 at this location. This is lesser than receiver 1(225)
which indicate that signal is weaker than receiver 1.

The SPL reaches maximum value of 104 db at this location while frequency
attains maximum value of 2500 Hz. The SPL is 100 at maximum frequency of
2500 Hz. The PSD plot is highly irregular that previous receivers which indicate
noise is not generated uniformly compared to previous receivers. This is due to
increased support strength at this location. The PSD is approximately 3 at this
location at maximum frequency of 2500 Hz and attains peak value of 11. The
peak PSD is lesser than all 2 previous receivers. Which indicate that signals are
weaker than previous receivers.

The SPL reaches maximum of 114 db at this location while frequency attains
maximum value of 2500 Hz. The SPL is 105 at maximum frequency of 2500 Hz.
The PSD plot is not uniform at this location which indicate that noise is in not
generated uniformly at this location. The PSD is approximately 5 at maximum
frequency of 2500 Hz and attains peak value of 60. This is lesser than receiver 1
and 2.

RESULT.
From above graphs we can prepare following table.
Table 6 Result table.
Property. Receiver-1 Receiver-2 Receiver-3 Receiver-4
Maximum SPL (in db) 120 115 105 114
Maximum frequency (in Hz) 2500 2500 2500 2500
SPL at maximum frequency (in db) 100 105 100 105
PSD at maximum frequency 10 10 3 5
Peak PSD value 225 70 11 60
CONCLUSION
From above graphs and table 8 we can conclude that as we go from receiver 1 to
receiver 4 the maximum sound pressure level goes on decreasing from 120db,
110db, 105db and 110db respectively. So we note that vibration is maximum at
receiver 1 which is below the inlet nozzle of shell side fluid and coinciding with
shell axis and shell inlet nozzle axis. If we look at the geometry of heat exchanger
then we notice that tubes in that region is fixed at one end and simply supported at
other end. So this will acting like beam. And the uniformly distributed load is
acted upon in the form of fluid elastic instability which result in flow induced
vibration. If we not provide sufficient end condition then tube in that region may
wear out at baffle interface and can cause serious damage. We also conclude that
in the receiver 2,3,4 region the tube is acting as simply supported beam. Also
there is decreasing in pressure from inlet to outlet so also decreases pressure force.
Due to this less vibration in tube because lesser fluid elastic instability. To avoid
flow induced vibration following few methods can be adopted by practicener.
1. If damage is predicted at shell side inlet nozzle then we can place
impingement plate.
2. Additional safety may be provided by reducing baffle tube clearance.
3. By increasing baffle thickness the tube support converts from simply
supported to fixed beam. Since this is case of uniformly distributed beam, the
maximum amplitude of deflection is lesser in fixed beam than simply
supported beam.
4. We can use the baffle material softer than tube material so that due to abrasion
tube will wear baffle and tube will not damaged.
5. When the vortex frequency coincides with tube natural frequency then
resulting in vibration. Not to happen this we can change tube natural
frequency. Natural frequency is proportional to young’s modulus E and
second moment of area I. We can vary both these parameter. Since decreasing
the natural frequency causes problem when flow reduces so practically we
should increase tube natural frequency.
6. To increase the tube natural frequency we can either increase E or I. Most of
tube material used in heat exchanger is steel due to its high temperature
sustainability and red hardness. But it has disadvantage that it has less thermal
conductivity than copper so it is transferring less heat than copper. Steel has E
value more than copper. Also it harder than copper so it is preferable over
copper if one compromises little with heat transfer rate.
7. To increase tube natural frequency we can increase I.

SCOPE OF DISSERTATION.
We can descretize the governing vibration differential equation by finite
difference method and from that we can develop the computer program which
calculates the amplitude of vibration. Further we can prepare experimental setup
and can compare this amplitude value and experimental value. We can also do
same for other type of heat exchanger like single shell pass and single tube pass.

CHAPTER 6
ANALYTICAL PROCEDURE FOR HEAT EXCHANGER DESIGN
FOR FLOW INDUCED VIBRATION.
Draw the 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 in meter.
a. calculate hydrodynamnic mass coefficient, Cm by TEMA method from the
figure V-7.11. or you can also do by Blewins method:
1 0.5eD p p
D D D
 
  
 
2
2
( / ) 1
( / ) 1
e
m
e
D D
C
D D



b. Calculate the tube mass per unit length ,
2 2 2 2
( )
4 4 4
m s i i iD C p D p D D
m
   
  
Step 2. calculate tube natural frequency, fn
For straight tube
a. calculate the area moment of inertia of tube cross section, I:
4 4
( )
64
iI D D

 
b. calculate cross section of the tube At
2 2
( )
4
i
t
D D
A


c. Calculate tube axial longitudinal load, Fa
Fa=ζt At (positive for tensile and negative for compressive)
d. Identify the span with pinned-pinned condition between two baffles in window
zone. Find out the tube span length L to calculate natural frequency and other
parameters. L is given by
L=LBC +LBC
e. calculate the buckling load for tube span:
2
2cr
EI
F
L

 for pinne-pinned condition
f. Calculate natural frequency multiplier:
B a crFl F 

g. From table below choose value of frequency constant λn
Table 7 Numerical values of frequency constant up to fifth mode
End Condition
First
Mode
Second
mode
Third
mode
Fourth
mode
Fifth
mode
Pinned-Pinned 3.1416 6.2832 9.4248 12.5664 15.708
Fixed-Pinned 3.9269 7.0686 10.2102 13.3518 16.4934
Fixed-Fixed 4.7124 7.854 10.9956 14.1372 17.2788
h. Calculate natural frequency fn
2
2
1
2
B n
n
i
EI
f
L m
 

 for Li=LBC + LBC
For U-Tube:
a. Draw a sketch of u-bend section and identify the configuration with TEMA
figure V-5.3 to V-5.3.3
b. Determine Cu from TEMA chart V-5.3 to V-5.3.3
c. calculate the natural freque3ncy for the first mode.
, 2
68.06 u
n u
C EI
f
R m
 
  
 
Step 3. Calculate damping parameter δ
TEMA method suggest that
δ1=3.41D/mfn and δ2= 0.012D/m*(ρsμ/fn)0.5
δ=max{ δ1, δ2}
Step 4. Calculate the cross flow velocity, U
Calculate U for the shell under consideration by TEMA/Bell/other methods.
Otherwise, take the value from the TEMA thermal specification sheet.
Step 5 Check for vortex shedding.
a. Calculate Strouhal number S
S=1/1.73Xt for 30 degree or triangular layout
S=1/1.16Xt for 60 degree of rotated triangular layout.
S=1/2Xt for 90 and 45 degree layout.
b. Calculate vortex shedding frequency, fs
fs=SU/D
c. Check

0.8fs<fn<1.2fs Resonance
fnD/U>2S Acceptable
fnD/U<2.2S Acceptable
Step 6. Turbulent induced excitation.
a. Determine CR from figure 74 below.
Figure 79 Random excitation force coefficient CR.
b. Mean square response for a pinned-pinned span is given by
2 2
2
max 3 3 2
( )
128
R
n n
C f U D
y
f m

 

2
maxrmsy y
c. Check if yrms <0.254 mm.
Step 7 Fluid elastic instability.
According to TEMA
a. Calculate reduced velocity parameter
2
m
D




b. Calculae critical velocity by referring to table 9 given below.

Table 8 Flow induced vibration specification sheet for liquid.
c. Check if U<Ucr or U/Ucr<0.5
Step 8Result.
Fill the preceding parameters in to the flow induced vibratiohn specification sheet
liquids shown in table 9.

REFERANCES:
1. Cross flow induced vibration of heat exchanger tube banks. By S.S. Chen. p.p.
Nuclear Engineering and Design 47 (1978) 67-86.
2. Vibration analysis of shell-and-tube heat exchangers an overview—Part 1:
Flow, damping, fluidelastic instability. By M.J. Pettigrew, C.E. Taylor. p.p.
Journal of Fluids and Structures 18 (2003) 469–483.
3. Vibration analysis of shell-and-tube heat exchangers: an overview—Part 2:
vibration response, fretting-wear, guidelines. By M.J. Pettigrew, C.E. Taylor.
p.p. Journal of Fluids and Structures 18 (2003) 485–500.
4. Some aspects of heat exchanger tube damping in two phase mixtures. By M. J.
Pettigrew and G. D. Knowles. p.p. Journal of Fluids and Structures (1997) 11,
929–945.
5. Vibration damping of heat exchanger tubes in liquids: Effect of support
parameters. By M.J. Pettigrew, B.S. Kim, J.H. Tromp. p.p. Journal of fluids
and structures (1988)2, 593-614.
6. Flow induced vibration analysis of conical rings used for heat transfer
enhancement in heat exchanger. By Kenan Yakut, Bayram Sahin. p.p. Applied
energy 78 (2004) 273-288.
7. Velocity distribution and vibration excitation in tube bundle heat exchangers.
By Ulrich Mohr, Horst Gelbe. Int. p.p. Journal of thermal science 39(200),
414-421.
8. Methods of numerical study of tube bundle vibration in cross flows. By
E.Longatte, Z. Bendjeddou, M. Souli. p.p. Journal of fluids and structures
18(2003) 513-528.
9. Vortex induced vibration of circular cylinder in laminar and turbulent flow. By
S. Pasto Journal of Fluids and Structures 24 (2008) 977–993.
10. Large Eddy simulation of cross flow through staggered tube bundle at
subcritical Reynolds number. By C.Liang, G.Papadakis. Journal of Fluids and
Structures 23 (2007) 1215–1230.
11. Flow induced vibration in heat exchangers. By H.G.D.Goyder. Institute of
chemical engineers. 80(2002).
12. An assessment method for unstable vibratin in multispan tube bundle. By
H.G.D.Goyder. Journal of Fluids and Structures 18 (2003) 555–572.
13. Acoustic resonance in staggered tube array: Tubve response and effect of
baffle. By P.A.Feenstra, D.S. Weaver, F.I.Eisinger. Journal of Fluids and
Structures 21 (2005) 89–101.
14. Combination of CFD and CSD packages for fluid structure interaction. By
WANG-Yi-wei. Journal of hydrodynamic 2008,20(6):756-761.
15. Flow analysis and flow induced vibration evaluation for low pressure feed
water heater of nuclear power plant. By Chin-Cheng Huang, Jen-Sheng Hsieh,
Pay-Chung Chen, Chin-Ho Lee. International Journal of Pressure Vessels and
Piping 85 (2008) 616– 619.
16. Assessment of flow induced vibration in sodium-sodium heat exchanger. By
V. Prakash, M. Thirumalai, R. Prabhakar, G. Vaidyanathan. Journal of
Nuclear Engineering and Design 239 (2009) 169–179.
17. Modeling of fluid elastic vibration of heat exchanger tubes with loose support.
By M. Hassana, M. Hayderb. Journal of Nuclear Engineering and Design 238
(2008) 2507–2520.

18. Photo optical technique for measuring flow induced vibration in cantilevered
tube bundle. By R.I.Judd, R.Dam, D.S.Weaver. Journal of experimental
thermal and fluid science. 5(1992)747-754.
19. Crossing frequency as measure of heat exchanger support plate effectiveness.
By M.K. Au-Yang. Journal of Fluids and Structures (2002) 16(1), 83-92.
20. Numerical investigation of vortex induced vibrations for flow past a circular
cylinder. By Wang Guoxing, Wang Shaqing, L.I.Huajun. Journal of odean
university of china 5(2006) 174-180.
21. Review of cross flow induced vibrations in heat exchanger tube arrays. By
D.S. Weaver, T.A.Fitzpatrick. Journal of fluid and structure 2(1988),73-93.
Reference Readings:
1. ―Flow induced vibration of circular cylindrical structures‖ (1986) By
S.S.Chen, Hemispherical Publication Company. Washington.
2. ―Flow induced vibration‖ (1994). By Robert D. Blevins. Krieger
publication company. Florida.
3. ―Flow induced vibration: an engineering guide.‖(1994) Naudascher and
Donald Rockwell. A.A.Balkema publishing company. Netherlands.
4. ―Design of heat exchangers‖ E. A. D. Saunders. Scientific Longman
publication.
5. ―Heat exchanger design handbook‖(2000) T.Kuppan. Marcel Dekker, Inc.
New york.
6. ―Mechanical design of heat exchanger and pressure vessel component‖
(1984) By K.P.Singh, A.I.Soler. Arcturus publishers, New Jercy.
7. ―Fundamental of heat exchanger design‖(2003) By R.K.Shah, D.P.Sekulic.
John wiley and sons inc.
8. ―Standard of tubular Exchanger Manufacturer Association‖ 8th
edition.
9. M.Tech. Seminar report on ―Turbulence flow and turbulence modeling‖ by
D.M.Patadiya. MED,SVNIT.

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