Page 236 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 217

Table 4.1 The threshold flow velocity for
flutter, ucf = (M/EI)’/’ U,jL, for various values
of and for zero dissipation (Pai‘doussis & Luu
1985).

(kg) Dissipation 4
182 x lo3 Taken into account 1.13
1820 Taken into account 0.935
0 Taken into account 0.895
Any value Neglected Of

the magnitude of E does not alter this value dramatically. If, however, the dissipative
forces are taken to be zero, the system loses stability at U = O+.
Therefore, it would appear from these results that ocean mining designers and operators
need to worry about flutter in their systems since, if a small safety factor were added,
U < 1 m/s would be too small to live with - especially since, for the more realistic
L = 5 km, one obtains U,f 5 0.2 m/s! Furthermore, the problem is of fundamental interest
and hence work on experimental validation started anew.
A new apparatus was built at McGill in 1986, shown in Figure 4.14(a). This time the
entire pipe, hung vertically, was immersed in water in a steel tank; water was supplied at
the top of the tank, and was forced up the hanging pipe and out of the vessel. Compressed
air was supplied at the top of the tank to achieve higher flows, but also to conduct exper-
iments entirely with air up-flow. Several experiments were conducted, with thicker pipes
to postpone the buckling collapse of Figure 4.1 l(a), and some with different-shaped inlet
forms added, but the system remained unnervingly stable. The experiment was discon-
tinued when, with ever-increasing air-pressure to force higher water flow up the pipe,
the rubber hose leading the water to the drain burst free of its clamp, spraying water
all over the laboratory and all over the instrumentation nearby, and giving the author
an unwelcome cold shower! At that point, the author was certain that something was
wrong with the theory; for one thing, the flow into the pipe is not exactly tangential, thus
not replicating in reverse the outpouring jet in the case of down-flow. However, these
negative results were not published,+ precisely because they were negative and not fully
understood - which is why the tale is worth telling.
Meanwhile, even without experimental verification, it was taken for granted that the
Pai‘doussis & Luu flutter at infinitesimally small aspirating flow really does exist, and several
more papers were published giving similar results [e.g. Sallstrom & Akesson (1 990)] and
methods for suppressing the unwanted flutter [e.g. Kangaspuoskari et al. (1993)l. The only
reference to absence ‘of any physical evidence of this phenomenon’ came out in the discus-
sion by Dupuis & Rousselet (1991a), to which this author also contributed.

4.3.3 Recent developments

It was in 1995, during a visit by the author to Cambridge and upon recounting this para-
doxial behaviour to Dr D.J. Maull, that the latter recalled reading ‘something similar’
in Richard Feynman’s biography (Gleick 1992). It turns out that in 1939 or 1940,

+At least not until much later (Pa;idoussis 1997). when the reason why was much better understood.