Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010
• Part of the visual evidence took the form of sightings by eye, under stroboscopic lighting, of the cavitation on and near the propellers and far downstream in their slipstreams. The propeller blade cavitation was extensive but not unusual whilst the cavitation in the slipstreams, both near and far downstream, was quite unusual. This was because cavitating tip vortices were present in the helical arcs on the outboard sides of imaginary vertical planes passing close to the centre-lines of the propeller shafts, whilst it was absent in the arcs on the inboard side of these planes.
• It seems that the circulation of the helical tip vortices suffered discontinuities in strength occurring at the top and bottom of the imaginary vertical planes near the shaft axes.
• A single frame from a video recording showed an instant in the life of a large cavitation disturbance near a rudder’s leading edge. The cavitation emanated from a cavitating propeller tip vortex and probably marked the commencement of the curious vortex behaviour observed in the slipstreams, referred to above. The term ‘cavitating vortex collapse’ seems more appropriate for this behaviour than ‘cavitating vortex breakdown’, where the cavitating tip vortex is present after the singularity.
• The absence of exceptionally high rms pressure levels at bpf implies that similar large cavitation disturbances did not occur regularly at each blade passage. An inspection of
covering many model propeller revolutions supports this view. Indeed, the capture of this image was fortuitous and lent weight
to the belief that this
phenomenon occurred relatively infrequently and randomly on the ship and model. This suggested that the large transient impulsive pressures caused by the formation and collapse of cavitation disturbances, similar to that captured in the video recording, could be approximated by solitary pressure pulses of very short duration in time frames of infinite extent. It is this understanding that points to the source of the broadband vibration experienced by the ship.
• It is known that when propeller cavitating tip vortex breakdown or collapse occurs, the pressure levels at higher harmonic frequencies of blade rate can exceed the bpf pressures. These experiments also showed that rms pressure levels at three times bpf can exceed the pressures at twice bpf and bpf.
• The model experiments showed that the quadrature sums of the
rms higher harmonic pressures,
normalised by their bpf pressures, were about twice as high when cavitating vortex collapse was present compared with when it was not.
• The instrumentation commonly used for recording and analysing the pressure signals in model propeller/hull cavitation tests is suitable when the signals are of the continuously varying periodic type. However, when shock occurrences take place these are unrecognised. In order to detect the presence of transient impulsive pressures real-time signal recorders and analysers should also be installed.
the video recording, 10. ACKNOWLEDGEMENT
The author is grateful and indebted to Christopher E Brennen, recently retired as The Hayman Professor of Mechanical Engineering at Caltech, for supplying several cavitation references, amongst them [1], [2] and [3]. I suggest anyone with an interest in bubbles, cavitating or otherwise, would enjoy
reading his
available on the Internet. 11.
Article, “The
Amazing World of Bubbles”, Engineering and Science, California Institute of
Technology, LXX1, 30-41, REFERENCES
1. Reisman, G., McKenny, E., Brennen, C., “Cloud Cavitation on an Oscillating Hydrofoil”, Twentieth ONR Symp. on Naval Hydrodynamics, USCB, Aug. 1994, pp78-89.
2. Reisman G. E., Brennen C. E., “Pressure Pulses Generated by Cloud Cavitation”, Proc. ASME, Fluids Engineering Division-Vol. 236, 1996, pp 319- 328.
3. Avellen F., Farhat M., “Shock Pressure Generated by Cavitation Vortex Collapse”, Intl. Symposium on Cavitation, Noise and Erosion in Fluid Systems, Proc. ASME, Fluids Engineering Division-Vol. 88, pp 119-125.
4. English J. W., “Ship Model Propulsion Experiments Analysis and Random Uncertainty”, Preprint Trans. Institute Marine Engineers, London, 1995.
5. Apfel R. E., “Some New Results on Cavitation Threshold Prediction and Bubble Dynamics”, Cavitation and
Acoustics, Springer-Verlag, 1980, pp 79-89.
Inhomogeneities in Underwater Ed. W. Lauterborn,
6. Carlton J., “Marine Propellers and Propulsion”, 2nd Ed., Butterworth-Heinemann,
7. Willshare G. T., Bond J. H., “Propeller Excited Vibration: A Summary of Vibration Investigations Carried Out on Ships at Sea”, B.S.R.A Report NS 468, 1978.
8. English J. W., “Cavitation Induced Hull Surface Pressures - Measurements in a Water Tunnel”, Symposium on Propeller Induced Ship Vibration, RINA, 1979.
9. Broch J. T., “Mechanical Vibration and Shock Measurements”, Bruel & Kjaar, April 1984, pp 20-39.
10. Breslin J. P., Andersen P., “Hydrodynamics of Ship Propellers”, CUP, 1994, pp 393-401.
APPENDIX: Defining RMS
The root mean square, rms, of a continuous pressure versus time waveform having a period T is the square root of the integrated sum of the squares of the ordinates defining the waveform divided by the period T. It is an effective mean value as opposed to a simple mean in which negative contributions to the integral diminish the positive ones, leading to the misleading result of zero for a sinusoidal waveform over a single period T.
©2010: The Royal Institution of Naval Architects
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