Page 288 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I1 269

research; alas, commercial confidentiality of products and methods precludes reporting
much on this.
The work, however, continues. For instance, Tsutsui & Tomikawa (1993) propose a new
straight-pipe mass-flow meter, on which is mounted an additional I-shaped oscillator. As
described in conjunction with Figure 3.25(b), there is a phase difference in the two halves
of the pipe when vibrating in its first mode; second-mode vibration actually produces a
moment, and the operation of the new design is related to this effect and to the associated
motion of the attached I-oscillator.

4.7.2 Hydroelastic ichthyoid propulsion

Noticing the similarity between the mode shapes of a fluttering cantilevered pipe
(Figures 3.45 and 3.48) and a swimming slender fish, e.g. an eel as shown in
Figure 4.38(a), a novel method of aquatic propulsion for watercraft was devised
(PaYdoussis 1976) and patented. It is recalled that for the cantilevered system, no classical
modes exist: the limit-cycle motion envelope comprises standing and travelling wave
components, the latter propagating from the clamped towards the free end, similarly to the
anguiliform swimming motions of slender fish (Lighthill 1969; Triantafyllou et al. 1993).
By mounting a pair of Tygon pipes on either side of a straight thin brass plate as
shown at the bottom of Figure 4.38(b), one can generate undulating motions of the plate
(perpendicular to the plane of the paper) at sufficiently high flow rates in the pipe, beyond
the flutter boundary. The system was tested by mounting this arrangement beneath a small
vessel. The flow was generated by a motor-pump unit on board, powered in tram- or
trolley-fashion by an overhead electrical conductor.
‘Sea trials’ were conducted in a long flume, approximately 0.9 m by 0.9 m in section
and 15 m long. Propulsion of course occurs even without undulation of the plate, simply
by the jet issuing from the twin pipes. Hence, two arrangements were tested: (i) one in
which the plate was allowed to undulate, and (ii) another in which it was immobilized
by attaching thin wooden stiffeners, shaped so as not to increase the drag. Typically, the
forward speed was V 2: 1 ds, the wavelength of the motion h 2: 0.6L and the frequency
o 2 15 rad/s, so that the reduced frequency oh/V 2 10. Allowing about 4 m for a constant
speed to be reached, the motion of the vessel was timed over the next 8.5 m, establishing
an average value of V.
It was found that 30% higher speeds, i.e. approximately 60% higher thrust, could be
achieved with undulation as compared to without, provided that the downstream propa-
gating wave velocity was faster than the forward speed of the vessel - alas, however, at
considerably inferior efficiency to a propeller. Because of its similarity to fish motions,
the name of ichthyoid propulsion was coined.
The experiments just described were, in effect, proving tests, with no attempt to optimize
the system: in an optimized design, both the momentum flux and mass would be axially
distributed in such a way as to give the most desirable wave-propagation characteristics,
and hence propulsion efficiency.+ This method of propulsion was put forward as a possible
propulsion scheme for special purposes, e.g. where propellers are undesirable because of
sealing (in great depths) or noise problems.

~
‘See also Sugiyama & PaYdoussis (1982).