ON JETS AND SHOCK WAVES 

 FROM CAVITATION 



A. T. Ellis 



California Institute of Technology 



Division of Engineering and Applied Science 



Pasadena, California 



Historically, the type of cavitation which consists of relatively small, tran- 

 sient cavities in a liquid first received attention by Euler (1) in the eighteenth 

 century. Very likely he and others had it forcefully called to their attention be- 

 cause of its well demonstrated capability of causing extreme damage to solid 

 surfaces such as turbine blades. This brief review will also concern itself pri- 

 marily with those hydrodynamic aspects of cavitation which are believed to be of 

 importance in the theory of cavitation damage. 



The early theoretical treatments by Besant in 1859 (2) and Rayleigh in 

 1917 (3) quite naturally adopted the simplest possible model, namely that of a 

 spherically symmetric cavity collapsing to very small or zero radius. It was 

 easily found theoretically that the bubble wall velocity approached infinity as the 

 radius approached zero. This result was readily seized upon as a firm explana- 

 tion of the amazingly high pressures which would be required to account for the 

 observed damage to solids. The pressure was, of course, expected to reach 

 enormous values as the inward motion was arrested either by gas in the cavity 

 or by wall to wall impact. The case of isothermal gas compression was in- 

 cluded in Rayleigh's work as well as the empty cavity. 



Some investigators at first refused to believe that the damage was not of an 

 exclusively chemical nature, but their number has been steadily declining since 

 the early part of this century. However, quantitative estimates of the pressure 

 involved covered an extremely wide range varying from thousands (4) to mil- 

 lions (5) of pounds per square inch. For a while there was also a strong reti- 

 cence to admit that both corrosion and erosion might play prominent roles de- 

 pending upon cavitation intensity and length of exposure. This feeling has lately 

 been largely dispelled due to good experimental work which is aimed at sepa- 

 rating these effects (6). Of course no one ever really believed that pressures 

 actually became infinite, but the problem was neatly bypassed by the convenient 

 fact that something involving real fluid effects or thermodynamic behavior was 

 always neglected. 



An undoubtedly better approximation for spherical collapse than the Rayleigh 

 theory was made by Gilmore (7) who included compressibility in his equations 

 and put in surface tension and viscosity through boundary conditions. The main 



137 



