Cavitation (Influence of Free Gas Content) 
BUBBLE TRAJECTORY ANALYSIS 
Implicit in all discussions on the role of free stream gas bub- 
bles in the cavity nucleation process is that they will be transported 
into a sufficiently low pressure region to be available to nucleate the 
cavity. The mere existence of gas bubbles in water is not in itself 
sufficient to conclude a knowledge of their importance. For this 
reason the bubble trajectory and its radial dynamics must be evalua- 
ted. When this information is combined with the bubble size and 
population information, then a better understanding of the importance 
of these bubbles can be developed. 
The trajectory of a bubble in a flow field with large pressure 
gradients has been considered by Johnson and Hsieh [1 1] ,» Hsieh 
[12] , and Schrage and Perkins i 3] . The governing equations de- 
rived by these authors can be reduced to essentially the same form 
and contain the following assumptions: 
1. The flow field is axisymmetric. 
2. The bubble remains a sphere throughout its trajectory. 
3. The fluid is assumed to be inviscid for the purpose of the 
flow velocities and pressures. 
4. The bubble is assumed to be sufficiently small so that the 
flow field is not affected by the presence of the bubble. 
5. The fluid is not taken to be inviscid with respect to the 
bubble, i.e., the bubble experiences a drag dependent on 
the relative velocity between bubble and fluid (see ref. 14). 
6. Diffusion of gas and heat transfer through the bubble wall 
are negligible. 
The equation for the dynamics of bubble radius, r 
shown to be 
2 3 
2 
r 4 *b - ci a % 12. P_+(P -P po acne ns Bes - P(x,y)} (1) 
b V s TAY 3 : 
dt p Tho Th Th 
eit can be 
t is time, 
p is the fluid density, 
Py is the vapor pressure of the fluid, 
b135 
