Scaling Ideas 



With these results from bubble mechanics in hand the main features of 

 travelling-bubble- inception scaling scenarios become apparent: A micro- 

 bubble, or nucleus of some size, may be imagined to be swept through the low 

 pressure region of a flow. The small nuclei have a very high natural fre- 

 quency and so react quasi-statically to the imposed pressure change. It 

 may happen that the critical pressure difference is exceeded for a certain 

 freestream microbubble; then it follows that there will be a period of 

 exponential growth which, if of sufficient duration, will ensure a visible 

 macroscopic bubble. Indeed many workers (e.g., Johnson and Hsieh 1966, 

 Schiebe 1972, Silberman 1975) are concerned only with that portion of the 

 fluid flow at below the critical pressure, since the subsequent bubble 

 growth is so rapid,. There is an additional possibility that turbulent 

 pressure fluctuations in transition locations may actually excite nuclei 

 there to unstable growth by resonance. In any case, from such arguments it 

 is evident that the number of travelling-bubble cavitation "events" will be 

 proportional to the number of microbubbles that can grow exponentially or 

 explosively; this then, depends upon the nuclei density distribution, the 

 pressure difference (p -p ), and the particular body. 



Inception for travelling-bubble cavitation, then, is determined by 

 the rate of such events for a particular body. This concept of "event 

 counting" as previously mentioned has been followed vigorously by the St. 

 Anthony Falls Hydraulic Laboratory (e.g., Silberman 1975, Schiebe 1972). 

 In fact, these authors turn the process around to infer the number density 

 distribution, N(R), by the number of such events on "standard" bodies. 

 Apart from this, their measurements of events show impressive correlation 

 with their acoustically determined nuclei distributions. These facilities 

 contain many nuclei at the 100 micrometer level so that only a slight 

 pressure difference (p -p ) is needed to establish criticality (see, e.g., 

 Table 2). But travelling-bubble cavitation is rare in the Caltech HSWT, 

 and tensions of up to 1/2 atmosphere are readily sustained in flows past 

 bodies at minimum pressure points. From this we conclude that freestream 



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