15 



collapse were found, while for surface tension, some cases are worked out to illustrate the 

 effects in retarding growth and accelerating the collapse. 



MECHANISM OF STEADY- STATE CAVITIES AND 

 THEIR ANALYTICAL DESCRIPTION 



INTRODUCTORY REMARKS 



A complete review and analysis of the experimental and analytical work on steady- 

 state cavities would require a much more detailed and voluminous discussion than is intended 

 here. Some results of more immediate interest in technical applications were presented in 

 Reference 3. In this report, the discussion will again be confined to a few more-immediately 

 applicable results and only mention made of the direction of other researches. 



The recognition of the applicability of free streamline theory (classical wake theory) 

 to the steady-state cavity problem has greatly stimulated the mathematical work on such flows 

 -and has resulted in a rapidly growing literature in this field. The two-dimensional problem is 

 now well understood and the theory is available for the solution of flows about a large class 

 of solid boundaries. However, very few numerical results are, as yet, available and will be 

 required before application in engineering problems can be made. These results would be of 

 much interest in connection with so-called "supercavitatihg" propellers, for example, as well 

 as other problems requiring knowledge of the forces on fully cavitating hydrofoils. The suc- 

 cessful treatment of the two-dimensional cases has been possible through the very powerful 

 conformal mapping techniques. However, the extreme difficulty of the general problem (arising 

 from the nonlinearity of the boundary conditions) has precluded general treatments, and in the 

 three-dimensional case, progress has been made only in the treatment of flows with axial sym- 

 metry. 



In the following paragraphs, some additional thoughts on cavities in real liquids will be 

 outlined and some recent results on the analytical treatment will be presented. 



SOME REMARKS ON STEADY-STATE CAVITIES IN REAL LIQUIDS 



The degree to which the theoretical models of steady-state cavities represent such 

 flows in real liquids was discussed to some extent in Reference 3. The added complications 

 of the properties of the liquid and of the surface conditions of the solid boundaries require 

 further clarification and much work remains to be done in this direction. Furthermore, the 

 question of the maintenance of such cavities in real liquids requires further investigation— 

 for example, the vaporization process at the cavity wall, the processes in removal of all 

 liquid phase from cavities in which cavitation first occurs only in the small scale eddies on 

 the boundary of a viscous wake, and the processes of entrainment and condensation at the 

 tail of cavities which have been observed to oscillate rather violently. The latter questions 

 were also discussed to some extent in Reference 3 and, in this report, only a few additional 



