Johnson and Hsieh 



To achieve at least an approximate quantitative understanding of the screen- 

 ing process in which the body and its pressure gradients influence the nuclei 

 distribution in the flow field, we have set up and solved the following problem. 

 We assume a size distribution of spherical gas bubbles in the oncoming free 

 stream. It is assumed that the bubbles remain spherical throughout their tra- 

 jectory. It is assumed that the flow field is potential; that is, no boundary layer 

 exists on the body, and the velocities and pressures surrounding the body are 

 given by potential theory and are not influenced by the presence of the entrained, 

 small gas bubbles. It is not, however, assumed that the liquid is inviscid insofar 

 as the bubbles are concerned; that is, it is assumed that one of the forces acting 

 on the bubble is the drag created by the relative velocity between the bubble and 

 the liquid and the drag coefficient which determines this force is assumed to be 

 that which would exist for a solid sphere at the Reynolds number based on the 

 bubble diameter, the relative speed, and the viscosity of the liquid. The other 

 forces which act on the spherical bubble are, of course, the pressure forces 

 established by the potential field of the body and the inertial forces associated 

 with the acceleration and virtual mass of the spherical bubble. Using this 

 model, trajectories of various bubble sizes are determined and the stability of 

 each bubble is examined during its passage, for various body sizes and flow 

 conditions. Computations have been made only for a two-dimensional half body; 

 but the results reveal important scale effects on the inception of cavitation 

 which are caused by the screening process that the pressure gradient field im- 

 poses on the oncoming entrained gas nuclei. 



STATIC STABILITY OF SPHERICAL GAS BUBBLES 



The conditions for the static stability of a spherical gas volume surrounded 

 by a liquid has been analyzed in Ref. 1. The equation relating the bubble size 

 and the surrounding pressure is given by 



(1) 



where 



p = surrounding pressure of the bubble 



p^ = vapor pressure of the liquid 



Po = initial equilibrium pressure for Rq 



Rg = initial bubble size 



R' = bubble size at pressure p 



jg/y = Weber number 



U = free stream velocity 



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