A simple computational model for bubble plumes

Abstract

A simple approximation is proposed for the buoyant force in a bubble plume. Assuming a uniform radius and slip velocity for the entire bubble column, an expression is derived for the vertical acceleration of liquid in the column, which is directly proportional to the injected gas flow-rate and inversely proportional to depth and velocity. This bubble-induced acceleration has been implemented with a k– ϵ turbulence model in a three-dimensional, single-phase computational fluid dynamics (CFD) code, whose numerical predictions indicate that the velocity outside the plume is relatively insensitive to the column radius and the bubble slip velocity. Using a median observed value of 25 cm/s for the bubble slip velocity, and a column radius given by an empirical formula based on the work of Cedarwall and Ditmars, the model renders predictions for velocity that compare favorably with experimental data taken outside single and double plumes in water. Predicted velocity increases in less-than-linear fashion with the gas flow-rate, and the flow-rate exponent approaches 1/2 in the lower limit, and 1/3 in the upper limit. In the range of flow-rates (200–22,000 cm 3/s) for which the model is validated herein, the exponent is roughly 2/5.