A simple computational model for bubble plumes

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 col umn, which is directly proportional to the injected gas flow-rate and inver sely proportional to depth and velocity. This bubble-induced acceleration h as been implemented with a k-epsilon turbulence model in a three-dimensiona l, single-phase computational fluid dynamics (CFD) code, whose numerical pr edictions indicate that the velocity outside the plume is relatively insens itive to the column radius and the bubble slip velocity. Using a median obs erved value of 25 cm/s for the bubble slip velocity, and a column radius gi ven by an empirical formula based on the work of Cedarwall and Ditmars, the model renders predictions for velocity that compare favorably with experim ental data taken outside single and double plumes in water. Predicted veloc ity increases in less-than-linear fashion with the gas flow-rate, and the f low-rate exponent approaches 1/2 in the lower limit, and 1/3 in the upper l imit. In the range of how-rates (200-22,000 cm(3)/s) for which the model is validated herein, the exponent is roughly 2/5. (C) 2000 Elsevier Science I nc. All rights reserved.