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Twenty-First Symposium on NAVAL HYDRODYNAMICS
almost simultaneously on all four transducers, are of higher amplitude, radiate substantial far field noise and are repeated at the same point of each oscillation cycle. Global pulses are caused by large scale cloud cavitation collapse and were not observed on the static foil.
By calculating the acoustic impulse, a quantitative measure of the effect of reduced frequency, k, cavitation number, σ, and tunnel velocity on the strength of the pressure pulses was obtained. The reduced frequency is an important parameter in the determination of the total impulse level and the local and global pulse distribution. The cavitation number has a significant effect on the global impulse strength, but large impulses are still present on the foil surface at values of σ where acoustic radiation is minimal and global pulses are rare or non-existent. The changes with tunnel velocity were significantly different for the stationary and oscillating foils. The local impulses on the stationary foil increased greatly with tunnel velocity and the global impulses on the oscillating foil did likewise. However, the local impulses on the oscillating foil did not change so dramatically with tunnel velocity. We also note that the spatial distribution of the impulse measurements, while highly influenced by the cavitation number, are virtually independent of the reduced frequency and tunnel velocity.
It seems clear that both the local and global surface pressure pulses could contribute to foil damage. Indeed, the very large magnitudes of these surface impacts could be responsible for the foil damage reported by Morgan (42), who observed trailing edges bent away from the suction surface and toward the pressure surface.
In order to shed some light on the experimental observations we have included results from calculations of the dynamics and acoustics of a spherical bubble cloud. These clearly confirm that shock wave formation is an integral part of the collapse of such a cloud provided the cloud interaction parameter, β, is of order one or greater. Fundamentally, this requires either the initial void fraction, α0, or the ratio of cloud size to bubble size, A0/R0, be sufficiently large and this, in turn, is qualitatively in accord with the observation that cavitation must be quite extensive for the cloud phenomenon to be manifest. There is also a cautionary lesson to be drawn from the theoretical analysis. This concerns the scaling of cloud cavitation phenomena. Even if the nuclei have the same size, population and void fraction in the model and prototype, the cloud cavitation effects could be much larger in the prototype due to the larger value of β.
Of course, most clouds are far from spherical. But, nevertheless the collapse of all or part of non-spherical clouds will produce points at which shock waves focus to produce large radiated pulses. However, it is not currently clear what three-dimensional forms the propagating shocks might take in the highly non-uniform bubbly environments which occur in real flows. The experimental observations do suggest that the bubbly region near the surface may act as a wave-guide for the propagation of the crescent-shaped shock structures associated with local impulses. But much clearly remains to be understood regarding these structures and their consequences.
We wish to thank John Van Deusen and Rodney Rojas for their help in fabricating the foil. The authors are also very grateful for the assistance provided by Amir Alagheband, Amy Herr, Don Kwak, Tricia Waniewski and Cecilia Lin. We are also deeply appreciative of the support of the Office of Naval Research who sponsored this research under grant number N00014–91-J-1295.
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