Johnson and Hsieh 



-0.8 -0.6 -0.4 -I-, -0.2 



LONGITUDINAL POSITION 'HALF ULTIMATE BODY WIDTH 



Fig. 4 - Gas nuclei trajectories about a two-dimensional 

 half body (h = 0.6 inch; U = 50 fps) 



The results presented in Figs. 4 and 5 also show the influence of vapor 

 cavitation number on the stability and the trajectories of bubbles. For instance, 

 the bubble with initial radius of 0.02 remains stable throughout its entire path at 

 cf ^ = 0.58 and becomes unstable at ^^ = 0.4. The reason for this effect may be 

 seen in Eq. (4); that is, for the same initial bubble size, the smaller the vapor 

 cavitation number, the higher will be the critical pressure for bubble stability. 

 The influence of „ on the bubble path is expected, because at different vapor 

 cavitation numbers, the same initial bubble size will contain different numbers 

 of gas molecules; thus as the pressure surrounding the bubble varies, the bubble 

 size will change a different amount for different vapor cavitation numbers. 

 Since for the same initial bubble size, fewer gas molecules are contained in the 

 bubbles for a lower vapor cavitation number; the same size bubble which initi- 

 ally maintained equilibrium at a lower vapor cavitation number, will decrease 

 more in size as it approaches the stagnation region than it will at the higher 

 cavitation number. Because the smaller bubbles are associated with lower val- 

 ues of the Reynolds number and thus higher drag coefficients; the net effect of 

 lower vapor cavitation number is that the bubble remains closer to its initial 

 streamline. Figure 6 shows the variation of bubble radius along its trajectory 

 for an initial bubble nondimensional radius of R^ = 0.02 and for ^, = 0.2, 0.4, 

 and 0.58. It may be noted in Fig. 6 that at o ^ = 0.2 the bubble grows at a higher 



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