Nonspherical Vapor Bubble Collapse

Citation

Chapman, Richard Bruce (1970) Nonspherical Vapor Bubble Collapse. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TDCB-D645. https://resolver.caltech.edu/CaltechTHESIS:04142011-083038797

Abstract

Vapor bubble collapse problems lacking spherical symmetry are solved using a method of simulation designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method of simulation uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid a finite distance from the free surface. Two cases of initially spherical bubbles collapsing near a plane solid wall were simulated, a bubble initially in contact with the wall and a bubble initially half its radius from the wall. at the closest point. In both cases the bubble developed a jet directed towards the wall. Free surface shapes and velocities are presented at various stages in the collapses. Velocities are scaled like √^(∆p)/_ ρ where p is the density of the liquid and ∆p is the difference between the ambient liquid pressure and the vapor pressure. For ^(∆p)/_ ρ = 10^6 (^(cm)/_(sec))^2 ≈ ^(1 atm.)/_(density of water) the jet had a speed of about 130m/ sec in the first case and 170 m/ sec in the second when it struck the opposite side of the bubble. Collapse in a homogeneous liquid was simulated for bubbles with nonspherical initial shapes described by the radii r_s = R_o [1 + 1/10 P_2(cos θ)] and r_s = R_o [l – 1/10 P_2(cos θ)] where P_2 (cos θ) is the second degree Legendre polynomial. Bubble shapes in both cases were close to those predicted by linearized theory. A simple perturbation study of the effect of a small pressure gradient on a collapsing bubble shows that gravity is ordinarily negligible for bubbles initially one cm. in radius or less.

Thesis Files