Modeling of the bubbling process in a planar co-flow configuration

Abstract

This work presents an analytical model developed to describe the bubbling regime resulting from the injection of an air sheet of thickness 2H(o) with a mean velocity u(a) between two water streams of thickness H-w - H-o, moving at a uniform velocity u(w). Based on previous experimental and numerical characterizations of this flow, the gas stream is modeled as a two-dimensional sheet divided into three different parts in the streamwise direction: a neck that moves downstream at the water velocity, a gas ligament attached to the injector upstream of the neck, and a forming bubble downstream of the neck, whose uniform dimensionless half-thicknesses are eta(n)(tau), eta(l)(tau), eta(b)(tau) respectively, and the corresponding pressures are given by Pi(n)(tau), Pi(l)(tau), and Pi(b)(tau) Pi(n)(tau). Lengths are made dimensionless with H-o, and pressures with rho(a)u(a)(2) where rho(a) is the air density.