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quency approaches the tube natural frequency, although
the heat exchanger shell and the attached piping may
vibrate, accompanied with loud noise. Then the acoustic
resonant frequency approaches the tube natural fre-
quency, any tendency toward tube vibration will be ac-
centuated with possible tube failure.
There are several means available to correct a resonant
condition, but most could have some effect on exchanger
performance. The simplest method is to install dereso-
nating baffle(s) in the exchanger bundle to break the
wave(s) at or near the antinode (This can be done with-
out significantly affecting the shell side flow pattern. In
shell and tube exchangers, the standing wave forms are
limited to the first or the second mode. Failure to check
both modes can result in acoustic resonance, even with
deresonating baffles.
From Figure 3, it is observed that the tube natural fre-
quency almost remains constant from inlet to center and
then drastically decreases as it approaches to exit. From
analysis it is observed that the inpidual unsupported
span natural frequency is affected by tube elastic and
inertial properties, tube geometry, span shape, the type of
support at each end of the unsupported span and axial
loading on the tube unsupported span. Most heat ex-
changers have multiple baffle supports and varied indi-
vidual unsupported spans. Calculation of the natural fre-
quency of the heat exchanger tube is an essential step in
estimating its potential for flow induced vibration failure.
The current state-of-the-art flow induced vibration cor-
relations are not sophisticated enough to warrant treating
the multi-span tube vibration problem (or mode shapes
other than the fundamental) in one comprehensive analy-
sis. Therefore, the potential for vibration is evaluated for
each inpidual unsupported span, with the velocity and
natural frequency considered being that of the unsup-
ported span under examination.
One of the most important and least predictable pa-
rameters of flow induced vibration is fluid velocity. To
calculate the local fluid velocity at a particular point in
the heat exchanger is a difficult task. Various amounts of
fluid bypass the clearances between baffles and shell, or
tube and baffle tube holes. Until methods are developed
to accurately calculate local fluid velocities, the designer
may use average cross flow velocities based on available
empirical methods.
Figure 4 shows that the bundle cross flow velocity in-
creases from inlet to center and then drastically decreases
as it approaches to exit. It is seen that the cross flow ve-
locity in the bundle varies from span to span, from row
to row within a span, and from tube to tube within a row.
The reference cross flow velocity is calculated for each
region of interest and is based on the average velocity
across a representative tube row in that region. The
presence of pass partition lanes aligned in the cross flow
direction, clearance between the bundle and the shell,
tube-to-baffle hole annular clearances, etc. reduce the net
flow rate of the shell side fluid in cross flow. This should
be considered in computing the reference cross flow ve-
locity.
From Figure 5 it is seen that the cross flow velocity
constantly increases from inlet to center and then con-
stantly decreases as it approaches to exit.
From Figure 6 it is seen the log decrement constantly
increases from inlet to centre and then constantly de-
creases as it approaches to exit.
Figure 7 indicate that the vortex shedding ratio con-
stantly increases from inlet to center and then gradually
decreases as it approaches to exit. 7. Conclusions