Page 294 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 275

4.7.7 Miscellaneous applications

(a) Educational rn odels

Some very interesting models for demonstrating the dynamics of nonconservative mechan-
ical systems have been proposed by Herrmann et al. (1966), the central item in which
is a cantilevered pipe conveying fluid. Every educator in the mechanics area should be
awarc of this publication.

(b) Buckling flow, turbulence and solar wind

In this case fluid-conveying pipes are used simply as conceptual devices in developing
models for much more complex phenomena.
In a paper entitled ‘Buckling flows: a new frontier in fluid mechanics’, Bejan (1987)
has assembled evidence to support the thesis that the buckling of flows is a generic
phenomenon which may explain, among other things, the origins and structure of turbu-
lence (Bejan 1989).
Bejan developed and systematized Taylor’s (1969) and others’ ideas and observations
(e.g. Cruickshank & Munson 1981; Suleiman & Munson 1981), suggesting that there
exists a characteristic wavelengthhtream-thickness ratio to the undulations that may be
seen in such diverse phenomena as the coiling of a honey (or maple syrup!) filament
or the folding of a sheet of batter under gravity upon a solid surface, the sinuous shape
taken by a jet of glycerine in quiescent water, the buckling of a falling sheet of toilet
paper, a water jet hitting a free water surface, hot-air plumes, meandering rivers, etc. The
interesting thing is that these phenomena are not confined to low-Reynolds-number flows.
Although this wavelength-to-thickness ratio is different for each case, it remains in the
range 1 - 10. The contention is that the large-scale structures in turbulent streams can be
regarded as the ‘fingerprint’ of buckling.
Of interest here is that one of the examples cited by Bejan to support this thesis is the
‘static buckling of a latex rubber hose’ hanging vertically and conveying water - from
his own experiments and those of Bishop & Fawzy (1976) and Lundgrcn et al. (1979).
Of course, as discussed in Section 3.5.6, this is due to residual internal stresses; hence,
in this context, the word ‘imperfect’ is required. However, this in itself is not dele-
terious to the thesis put forth by Bejan. Hence, this represents an unexpected use of
the simple garden-hose problem towards modelling such a complex subject as turbu-
lence!
Even more unexpected is the ‘application’ to an even more rarefied subject: solar wind
modelling. Solar wind refers to the fast movements of plasma from the surface of the sun
into space (all the way to earth), which, were it atmospheric air, would resemble wind. One
of the early theories of the origin of solar wind (Axisa 1988) was that electromagnetically
constricted ‘tubes’ of plasma develop, which are governed by fluid-dynamic equations
(Dessler 1967; Parker 1963; Montgomery & Tidman 1964), and which move spirally into
space. Bundles of such tubes of plasma could become unstable, similarly to fluttering
cantilevered pipes, and then become intertwined, something like the snakes on Medusa’s
head, thus giving rise to turbulent mixing of the plasma. Alas, the real phenomenon is
much more complex and such theories, though useful at the time, have long since been
abandoned.