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PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 21 1

- Cylindrical-conical. undamped
----- Cylindrical-conical. damped
0 I I

V Cylindricakonical (exp’t)
Cylindrical (exp’t)

Figure 4.8 Theoretical and experimental values of uiC and mc for the same system as in Figure
4.7, but immersed in stagnant water; all parameters are the same except ye = 1.9 (Hannoyer &
Pdidoussis 1979b).

It may be concluded, therefore, that these experiments validate the theoretical model.
Both theory and experiments for nonuniform pipes subjected concurrently to internal and
external axial flow are presented in Chapter 8 (Volume 2).

4.2.4 Other work on submerged pipes

Further work on the dynamics of uniform pipes immersed in fluid has been conducted,
partly motivated by vibration of the inverted U-shaped pipe connecting the reactor vessel
to the intermediate heat exchanger in a liquid-metal fast breeder reactor (LMFBR) [e.g.
Inagaki et al. (1987), Sugiyama et al. (1996a)], and by more general applications in the
marine and power-generating area [e.g. Shilling & Lou (1980), Langthjem (19931.
The model utilized by Sugiyama et al. (1996a) is a variant of that in the foregoing,
but modified to take into account immersion of only the lower part of the pipe. Similar
results are obtained, but the effects of added mass, buoyancy and damping are studied
more thoroughly through parametric calculations. The effect of partial immersion on
stability is shown in Figure 4.10. The effect of immersion is generally destabilizing, for
the reasons given following equation (4.25). However, partial immersion, as pointed out
by Sugiyama et al. has a selective effect on mode shapes as well, mainly because of the
discontinuous added-mass effect; see theoretical results for small I, in Figure 4.10(c).