Page 290 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 27 I

structure, the vibrations of the structure-cum-pipe system would be damped. An
experiment with the set-up shown in Figure 4.39(a) demonstrates how the system can
work when the ‘structure’ is the pipe itself. When the pipe is disturbed, it vibrates,
and this is detected by a displacement sensor. If the vibration is above a predetermined
threshold, the valve opens, admitting a fluid flow such as to give optimum damping.
When the vibration level is reduced to below a given threshold, the valve closes, the pipe
having accomplished its task. The vibration of the pipe without flow (the controller totally
inoperative) and with control flow is shown in Figure 4.39(b,c).
The idea of such a vibration damper was also proposed by Lu et al. (1993).+
Of course, if the pipe is attached to a massive structure, the effective damping ratio
will then be = kcp/[(ms + rn,)(k, + kp)]’’*, where m, and mp are the modal masses
of the structure and the pipe, respectively, in the mode concerned, k, and k, are the
corresponding modal stiffnesses, while c, is the modal damping of the pipe - neglecting
c, since presumably c, << cp. Hence, will generally be considerably smaller than (
for the pipe alone. This renders the application useful only for special cases, but no less
interesting.

4.7.4 Stability of deep-water risers

Offshore risers are long pipes used in the exploration and production of oil and gas,
connecting the sea-floor to an offshore floating or fixed platform or to a ship. With
these activities moving to ever deeper waters, rigid-pipe risers have given way to flexible
ones, such as shown in Figure 4.40. Sessions on riser dynamics are regular features
of the annual Offshore Technology Conference (OTC), the ASME Ofshore Mechanics
and Arctic Engineering Conference (OMAE), ISOPE Offshore and Polar Engineering
Conference, and other specialist conferences in the field, to the proceedings of which
the interested reader is referred. All kinds of fluid-structure interactions are of concern,
involving currents, waves and internal flow. Sample papers of interest here are by Sparks
(1983). Vogel & Natvig (1987), Moe & Chucheepsakul (1988) and Moe et al. (1994).
Because of their great length, measured in kilometres, flexible risers may generally be
considered to be hoses or pipe-strings, thus neglecting flexural restoring forces. As such,
they are like any other string: effectively a limp strand of spaghetti, the configuration of
which is solely determined by the imposed tension (applied by special tensioning devices
and buoys), internal and external pressure, gravity and internal flow effects. The concept of
an ‘effective tension’, incorporating tension and pressure effects, T,ff = T + peA, - p,A,
as in equation (4.13) is widely used; cf. the ‘combined force’ I7 in Chapter 6, defined in
equations (6.46), and also refer to Section 3.4.2.
Elaborate computer codes exist for the calculation of the shape of, and stresses in,
risers subject to given Teff and to internal and external flow loading. Changes in pres-
sure and flow, operational or accidental, give rise to transient motions andor changes
in configuration. Also, if the tensioning devices fail, loss of tension may give rise to
‘instabilities’ in the sense of large and sudden changes in configuration. The effects of

‘In the oral presentation, when questioned as to possible applications, one of the authors proposed the
‘damping of space structures’. An interesting idea, but the cost of transporting fluid into space and then
sprinkling it all over the universe must be astronomical! The idea of damping wind-induced bridge vibrations
is also a bit far-fetched. Nevertheless. the usefulness of the concept for special applications still stands.