Ahlmct-A
model has been developed to destibe the formation of single bubbles at a submerged orifice. The model is based on a q odiied Rayleigh equation for bubble growth and describes the effect of gas momentum by assuming that the flow field inside the growing bubble is in the form of a circulating toroidal vortex. The equations descriiing the bubbling system are solved numerically using an explicit finite-difference technique. The model shows that bubble growth is character&d by an initial outward movement of the base of the bubble along the plate Boor followed by an inward movement back towards the orike which leads to a severing of the bubble from the orifice and termination of tbc growth cycle.
Computed bubble growth rates, formation times and chamber pressure fluctuations are shown to be in good agreement with available experimental data for a wide range of system pressure (O-l.37 MN/m2) and computed bubble shapes are simiiar to those observed experimentally.
UWltODUCTION
The formation of bubbles at a submerged or&e has been the subject of numerous theoretical and experimental studies (Kumar and Kuloor [ 11) and a number of models have been developed to describe the complex interaction of liquid and gas which occurs during the bubbling process. Typical of the more comprehensive models which include the effect of the chamber volume below the orifice are those of McCann and Prince[Z], Kupferberg and Jameson [3], LaNauze and Harris [4] and Marmur and Rubin [5]. The models all follow the earlier approach of Davidson and Schuler[6] which requites a simultaneous solution of the equations of motion for the growing bubble and gas flow through the orifice. Although reasonable agreement between prediction and experimental observation has been demonstrated over a limited range of conditions for the various bubbling models no one model is capable of providing an adequate description of the bubbling process over a wide range of gas flow rates and system pressures.
The models of McCann and Prince[2] and Kupferberg and Jameson[f] assume spherical growth and neglect the momentum of the gas phase (i.e. neglect gas density). At high gas rates or high system pressures (or both) gas momentum is observed to have a considerable influence on bubble growth (Wraith[71, LaNauze and Harris[4]) which limits the applicability of the above models to low system pressures and moderate gas rates.
LaNauze and Harris[4] extended the above models to higher system pressures by the inclusion of a term for gas momentum in the equation of motion for the growing bubble. Although their model correctly predicts the trend of the experimental data there remains a considerable discrepancy between the computed bubble growth rate curves and those measured experimentally. Moreover, in common with the previous models their model cannot predict bubble detachment. This necessitates the inclusion of an arbitrary detachment criteria to terminate the growth cycle.