re) 
6 
Peterson 
a subscript denoting a value at the initial bubble position, 
is the surface tension of the fluid, 
P(x, y) is the external pressure of the fluid at (x, y), 
(x,y) refers to the location of the bubble in Cartesian coordi- 
nates. 
The vector equation of motion for the bubble moving in an axisymme- 
tric flow field, can be written as 
where 
—)> 
u 
2 3 du_ il a eee 
Be bei Sage = Bids Ch wr (v-u) | v-u | (2) 
4 dr cle 
B. 3 py lege LE Sie 2 he 
2nrr3 VP, = mV + 21p rr (v-u) 
are unit vectors in the x, y directions, respectively, 
is the fluid velocity vector = vi + =a 5 
is the drag coefficient, (see reference [1 4] im 
is the pressure due to flow, and 
is the pressure due to gravity. 
Using these equations, Schrage and Perkins 13] compared their 
analytical prediction of the bubble path with experiments in both 
rotating water and glycerin and obtained excellent agreement. 
A numerical study was carried out at NSRDC where the potential 
flow field around the headform was combined with equations I and 2 
to determine the trajectory and radial dynamics of a free stream gas 
bubble. The description of the pressure and velocity field around the 
body was determined through the use of a computer program for po- 
tential flow around an axisymmetric body {1 5] : 
The most important aspect of these calculations was the deter- 
1136 
