Page 334 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: NONLINEAR AND CHAOTIC DYNAMICS 3 15

state by integrating numerically the time-independent version of the full equations of
motion.
Experiments have also been conducted by Yoshizawa et al. (1985, 1986), utilizing
vertical silicone rubber pipes (Do = 5 mm, Di = 3 mm, L = 600mm) conveying water.
Two stainless steel wires were attached to the pipe in one plane, to ensure that motions
occur normal to that plane. The pinned, axially-sliding lower end was achieved by a short
bar perpendicular to the pipe axis, in contact with the pipe.
Typical results are shown in Figure 5.10(a) for the variation of the first-mode eigen-
frequency up to divergence, when theoretically w1 = 0. The experimental frequencies are
in excellent agreement with theory. Nevertheless, for obvious reasons, the experimental
frequencies could not be measured all the way to divergence, the precise onset of which
was difficult to pin-point.

Figure 5.10 (a) Variation of the first-mode eigenfrequency with u2 for a clamped-pinned pipe
with an axially sliding downstream end (B = 0.273, y = 34.4, a! = 4.68): -, theory; 0, exper-
iments. (b) The post-divergence maximum static pipe deflection, qmax versus u2 (a! = 5.56): - - -,
approximate analytical; -, numerical; 0, experimental (Yoshizawa et al. 1985, 1986).

The variation of the maximum, steady post-divergence amplitude with u2 is given in
Figure 5.10(b). It is seen that (i) the approximate analytical and the numerical solutions
agree for qmax i 0.1 approximately, and (ii) agreement with experimental values is very
good overall, particularly for the more accurate numerical results.

5.5.4 Impulsively excited 3-D motions

An interesting, application-related study, examines the dynamics of inhibited flow/porous
tubes (INPORTs) used to protect the inner wall of inertial confinement fusion (ICF)
reactors? from X-rays, neutron bombardment and dCbris (Engelstad & Love11 1985, 1995;
Engelstad 1988). The porous, braided silicon-carbide-fibre tubes convey Li-Pb (molten
lithium-lead), the fluid acting both as a coolant and a breeder; the tubes are porous, to
ooze out a liquid film for protection from the same hazards. These very slender tubes

+The ICF is a precursor concept to the LIBRA fusion reaction chamber.