Johnson and Hsieh 



direction. To determine a starting point for the calculation of the bubble trajec- 

 tories, an initial bubble size of R = 0.02 in a flow field with u = 50 fps, cr^ =0.4, 

 h = 0.6 in., A = 1.94 slug/ft^, v = 1.05 x 10" ^ ftVsec, and / = 0.00497 lb/ft was 

 examined. Figure 2 shows the bubble trajectories when x^ = -20, -10, and -6 at 

 a fixed Yq = 0.01. It is seen that the difference in trajectories is negligibly 

 small. Thus, x^ = -10 is considered to be far enough upstream to avoid any 

 significant error and is thus used in later calculations. The star in Fig. 2 indi- 

 cates the location at which a given bubble becomes statically unstable. 



The trajectories of the same bubble size were also calculated for different 

 Yo values, while the remaining parameters were unchanged. The results are 

 shown in Fig. 3 for yg = 0.01, 0.02, 0.05, 0.10, and 0.20. As expected, the 

 trajectories are quite different for different values of y^. 



In a practical situation, various bubble sizes can be located in any position 

 in the free stream. However, in the problem of determining the conditions for 

 incipient cavitation, we are interested only in the initial bubble position which 

 will lead the bubble in its trajectory, to a pressure point lower than any other 

 point which the bubble could reach from another initial position. From the ex- 

 amples of bubble trajectories given in Fig. 3, it is noted that the closer the ini- 

 tial position of the bubble to the dividing streamline, the sooner the bubble will 



-1.2 -1.0 -0.8 -0.6 -0.4 - 1/n -0,2 0.2 



LONGITUDINAL POSITION/HALF ULTIMATE BODY WIDTH - x 



Fig. 2 - The influence of the starting point in the x direction 

 on the gas nuclei trajectories (h = 0.6 inch; U = 50 fps) 



170 



