Page 163 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 145

A successful experiment with a metal pipe was also conducted by Liu & Mote (1974)
with their apparatus, described in Section 3.4.4. They used an end-nozzle, so as to
reduce the effective B and achieve flutter with the available maximum flow rate (see
Section 3.3.5); ai = A/Aj, the ratio of pipe flow area to terminal flow area, was 2.42.
They obtained good agreement between the theoretical and experimental values of ucf :
2.89 and 3.27, respectively, as well as between the theoretical and experimental frequency
versus flow curves, as shown in Figure 3.52. In the absence of the nozzle, the agreement
in frequency was less good, because the pipe was less straight. However, this is the
second instance where the pressure drop in the pipe was very large, - 3 - 10 MPa, yet the
dynamics was essentially unaffected by it.

Figure 3.52 Variation of the second- and third-mode eigenfrequencies with increasing u for a
metal cantilevered pipe conveying fluid. Experimentalltheoretical reference frequencies (at u = 0):
%e(Q), = 8.0/8.0Hz for the second mode and 25321.7Hz for the third (Liu & Mote 1974).

An important theoretical and experimental study, mainly on forced vibrations of vertical
cantilevered pipes conveying fluid (see Section 4.6), was conducted by Bishop & Fawzy
(1976). They also examined the free vibration characteristics, and a few words about
that will be said here. The experiments were with surgical quality silicone rubber pipes
conveying water. The authors studied extensively the static distortion from the stretched-
straight state that they observed in their experiments and its evolution with flow. They
concluded that it was due to lack of perfect straightness and residual internal stresses
related to the manufacturing process, and not an instability (divergence) - in agreement
with previous studies - even though some other researchers later misinterpreted this
finding. Their experimental data and degree of agreement with theory were similar to
those reported already. A typical set is shown in Figure 3.53 for experiments without
(aj = A/Aj = 1) and with end-nozzles (a, = 1.5 and 2.49).
A simple but ingenious experiment was conducted by Becker et al. (1978) using
drinking straws (of unspecified material) as pipes and air flow. The supported end
was attached onto weighing scales and the flow-rate was determined from the reaction