Page 231 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 213
The same problem is studied by means of potential- rather than plug-flow theory and
Timoshenko beam theory by Langthjem (1995) - see Section 4.4.10.

4.3 ASPIRATING PIPES AND OCEAN MINING

4.3.1 Background
In the discussion of energy transfer mechanisms for cantilevered pipes conveying fluid
(Section 3.2.2) in conjunction with equation (3.1 l), it has generally been presumed that
the flow velocity is ‘positive’, i.e. directed from the clamped towards the free end.
However, it is obvious that if U is replaced by -U, all the arguments on stability and
the predicted behaviour are reversed: for infinitesimally small U, and up to lUcrl, the
system would be unstable by flutter; then, for IUI > IUcrl, it would regain stability! If
dissipative forces were added, then perhaps ‘infinitesimally small’ would merely change
to ‘small’.
This intriguing possibility was explored experimentally by the author at the Chalk River
Nuclear Laboratories in the mid- 1960s, by immersing the lower end of an elastomer pipe
in a barrel and connecting the upper end to a pump, as shown in Figure 4.1 l(a). The
expected behaviour did not occur. However, a sort of amplified oscillation did occur, if the
immersion was shallow; but the mechanism was soon discovered to be one of parametric
resonance, involving the slurping of air-slugs into the pipe, sucked in at the extremes
of the cycle of oscillation when the pipe end is closest to the free surface, as shown in
F, TO pump
Figure 4.1 1 (b). Thus, the flow in the pipe has periodic density variations, with the optimum
2: 1 parametrichatural frequency ratio (Section 4.5). Deeper immersion eliminated this
mechanism of self-excitation. Attributing the non-occurrence of the expected ‘regular’
flutter at infinitesimal flow velocities to increased damping due to the water immersion,
the flow rate was increased further, until a sufficiently large transmural pressure (external
/z+
a+
pump
TO
,, :a
.:I
.....
..
..
..
...
Collapse E’
..
..
.. location
_.
..
..
..
..
:.:/ 1
..
f
/
Collapse
mode
..............
...............
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(a)
Figure 4.11 (a) Apparatus for experiments with water-aspirating pipes. (b) Diagram for under-
standing the mechanism of parametric resonance due to density pulsations occurring when the
immersion is shallow.