Johnson and Hsieh 



-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 



LONGITUDINAL POSITION/VlALF ULTIMATE BODY WIDTH - x 



Fig. 6 - Variation of the size of a gas nucleus along its trajectory 



Upper Critical Bubble Radii 



As described previously, a bubble coming from upstream is pushed away 

 when it approaches the body. The larger the bubble is, the greater the distance 

 it is pushed out by the pressure gradient. Thus, although the large bubbles have 

 a less critical pressure, they may still not encounter this critical pressure 

 throughout their entire path. Consequently, it is possible to find for a given 

 vapor cavitation number and body size a corresponding value of bubble radius 

 Rq^ such that all bubbles with radius greater than R*^ will remain stable in the 

 flow field. R*^j is defined as the upper critical bubble radius. That is, for a 

 given value of <y^, bubbles with radius less than R*^ cannot possibly become 

 unstable regardless of their trajectory; for this same value of \^, bubbles with 

 radius greater than R*^j cannot become unstable because their trajectory re- 

 moves them from the low-pressure zones required for instability. 



The determination of this upper critical bubble size, R*^, for various body 

 sizes and vapor cavitation numbers is tedious work. It was accomplished by the 

 trial and error method, using different sizes of bubbles in the trajectory equa- 

 tions until the critical radius was obtained. The Runge-Kutta method and an 

 IBM 1130 digital computer were used. Results for the two-dimensional half body 

 with h = 3, 1.8, 1.2, 0.6, 0.4, 0.2, 0.1, and 0.05 inch are shown by the dashed 

 lines in Fig. 7. 



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