Jets and Shock Waves from Cavitation 



develop higher pressures. The trouble with this is that the assumption of 

 spherical collapse ceases to be valid due to proximity of the solid surface. 

 That this is true, at least for bubble collapse which is not flow generated, has 

 been demonstrated by Naude' and Ellis (12). Very little work has been done on 

 single bubble collapse in a flowing liquid with the notable exception of Maurice 

 Rattray (18). His perturbation analysis breaks down during the later stages of 

 collapse but does indicate that spherical symmetry is not maintained If the bubble 

 is closer than about one maximum diameter from a wall or if the bubble has a 

 relative velocity to the free stream such as one would expect in the presence of 

 pressure gradients, which usually exist in cases of practical interest. 



It appears, then, that the case of hemispherical collapse on a solid, which 

 for ideal fluids is theoretically equivalent to spherical collapse in an infinite 

 fluid, is the only case where spherical symmetry might be preserved and yet 

 keep the collapse point near or on the solid. Some experimental work has been 

 done by Jones and Ellis (19) using a quartz force gage and simultaneous high- 

 speed photography. The big objection to their work was that the bubbles were 

 spark generated and thus contained relatively large and unknown amounts of 

 permanent gas from electrolysis. Despite this, a lower bound of about 10,000 

 atmospheres pressure was obtained. This was in agreement with work done by 

 Jones and Edwards (20) without benefit of high-speed photography. 



Although the hemispherical mode of collapse is undoubtedly very damaging, 

 such experimental observations as are available indicate it is not a very likely 

 occurrence either in flow (21) or acoustically generated (22) cavitation. It ap- 

 pears much more common, at least for pressure distributions on ogival bodies 

 such as were used by Knapp and Hollander (23) and Plesset (24) and Ellis (21), 

 that when the cavity is in actual contact with the solid it may be of roughly 

 spherical shape but it is likely to be either less or more than a hemisphere (i.e., 

 the center of curvature is within or without the solid surface). Such examples 

 are shown in Fig. 1 from the work of Ellis (21). A theoretical and experimental 

 study of the latter type but in the absence of flow was made by Naude' and Ellis 

 (12). The method of bubble generation used was a spark, but as was indicated 

 theoretically, high-speed photography showed that a jet developed and struck the 

 solid before there was enough cavity volume reduction to increase the internal 

 pressure significantly. It was thus felt that spark generation with resultant per- 

 manent gas was not objectionable for this mode of collapse, whereas it would be 

 for the spherically symmetric mode. Figure 2 shows the collapsing jet. Al- 

 though the photographs in this figure had been taken at the time of the original 

 paper, they were not published until later (25). If one takes a conservative esti- 

 mate of the jet velocity by assuming that it has just reached the solid in the next 

 frame, a value of about 600 feet per second is obtained. The impact pressure 

 would then be about 3000 atmospheres. This is about a third of the experimental 

 estimate for the hemispherical bubble of Ref . 19, but it is quite adequate to pit 

 aluminum, and indeed this was done, as shown in Fig. 3. 



It should be mentioned that in similar subsequent work by others (26) no jet 

 damage was observed but instead cavitation damage due to vortex generated 

 cavitation was evident. In the author's opinion this did nothing to disprove the 

 jet mechanism because of a simple difference in the spark generator. The dis- 

 charge was from a 0.02 -microfarad capacitor in the case of Naude and Ellis and 



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