Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010


extremely rapidly in a coherent manner, when intense impulsive pressures are created at the collapse site. For example, in the water tunnel facility at CalTech it was found that positive pressure pulses on the upper low pressure surfaces of the


cavitating hydrofoil had


amplitudes of the order of tens of atmospheres and durations of the order of tenths of milliseconds [2]. An observation concerning the pause in the cavitation of the hydrofoil tip vortex as it passed the trailing edge of the foil was also observed linking it with propeller observation described above.


5.2 CAVITATING VORTEX GENERATOR


Other tests in a Cavitating Vortex Generator (CVG), an experiment rig designed especially for determining the collapse pressures and durations of cavitating vortex breakdowns, has estimated a sample mean pressure of 900MPa (9kbar) and an extreme pressure of 2,200MPa (22kbar), the latter occurring in a time interval of tens of microseconds [3]. These pressures and timed events were determined with novel and elaborate techniques unlike using conventional strain gauges, for example. Repeated impulsive pressures of these magnitudes in the close vicinity of hard metals are known to cause erosion and metal fatigue. The vast difference in the collapse pressures obtained in the CVG and the Caltech water tunnel on hydrofoils is noteworthy and perhaps can be explained by the higher velocities in the CVG and the greater tensile strength of the water there, as well as the mechanism


used for initiating the solitary vortex


breakdowns and ensuing bubble clouds. 6.


FURTHER CONSIDERATIONS


The two-dimensional shape of the whitish-grey region seen in the aperture upstream of the port rudder in Fig. 1 does not give its athwartships position in relation to the entrance to the passageway formed by the closure of the ship’s centre-line skeg, the hull above and the inboard side of the port


rudder. The flow approaching this


passageway is highly irregular and it is conceivable that the static pressure in the vicinity of the rudder’s leading- edge had increased locally above that present in a uniform stream causing the cavitating vortex to collapse. This is a conjecture that could not be explored, but it was found that moving the rudders outwards by a small distance made little difference to the results. Also, it was noticed that when comparing the propulsive coefficients for this ship design with those of two similar type twin- screw ships all tested in the same towing tank using an identical thrust


identity testing method, the relative


rotative efficiency was lower for this vessel compared with the other two. However, the overall propulsive efficiencies, QPC’s, of all the vessels were acceptably close taking account of the uncertainties present in ship model


propulsion testing, Reference scepticism held in some quarters


[4], and the regarding the


breakdown of Propulsive Efficiency into its component parts.


The deductions drawn from the model experiments, including the image of the large model cavity and the hull surface harmonic


pressures, together with the


vibration measurements on the ship suggest that transient high impulsive pressures were created in the water from each propeller at random, relatively infrequent time intervals compared with blade passage times. Each shock pressure pulse can then be approximated by a solitary


The size of the breakdown cloud in the current propeller example appears be of the order of 0.1R across in the image plane, R being the propeller radius, which would categorise it as being large, if not very large, and a non- linear event in mathematical terms. However, it will be appreciated that at the instant of recording the image the breakdown cloud could be growing or collapsing and therefore its maximum size was likely to be greater.


Interestingly R E Apfel [5], using simple physical reasoning, described how the pressure intensity of a cavitating bubble at collapse depends on the sudden release of the potential energy stored in the liquid during the growth stage, being relatively larger for big bubbles than small ones.


Due to a delay in receiving the image in Fig. 1 and because the experimental programme had progressed the opportunity to investigate it in more detail did not arise.


Reference [6] cavitating ships’


contains some propellers


interesting pictures of in different modes of


operation, including one showing a cavitating propeller tip vortex breakdown emanating from a sheet or clump of cloud cavitation on the back of a blade near the tip. A common feature in these pictures and others of full scale merchant ship propellers is that invariably the cavitating tip vortices in the propeller slipstream have a cloudy whitish appearance, in common with the full scale pictures in [7] and those at model scale in [8] and Fig 1 of this


paper. From a modelling viewpoint cloud


cavitation should be present in the trailing tip vortices, as distinct from cavitation with a translucent appearance, because collapsing cloud cavitation produces strong impulsive pressures and noise [1].


7. PROBABLE CAUSE OF THE SHIP VIBRATION


It can be deduced, albeit subjectively, from the levels of the blade rate pressures recorded in these experiments, that the pressures associated with the collapse of large cavitation clouds like that shown in Fig 1 did not occur at successive blade passages, since if they had the blade rate pressures would have been exceptionally high. This points to the likelihood that


the broadband vibration


experienced by the ship was caused by shock pressures at random time intervals. This may have been confirmed if instrumentation for observing the real-time pressure transducer signals in the model experiments had also been installed which unfortunately it was not.


©2010: The Royal Institution of Naval Architects


A-177


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