Prediction of bubble diameter at detachment from a wall orifice in liquid cross-flow under reduced and normal gravity conditions

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Bubble formation and detachment is an integral part of the two-phase flow science. The objective of the present work is to theoretically investigate the effects of liquid cross-flow velocity, gas flow rate embodied in the momentum flux force, and orifice diameter on bubble formation and detachment in a wall-bubble injection configuration. A two-dimensional one-stage theoretical model based on a global force balance on the bubble evolving from a wall orifice in a cross liquid flow is presented in this work. In this model, relevant forces acting on the evolving bubble are expressed in terms of the bubble center of mass coordinates and solved simultaneously. Relevant forces in low gravity included the momentum flux, shear-lift, surface tension, drag and inertia forces. Under normal gravity conditions, the buoyancy force, which is dominant under such conditions, can be added to the force balance. Two detachment criteria were applicable depending on the gas to liquid momentum force ratio. For low ratios, the time when the bubble acceleration in the direction of the detachment angle is greater or equal to zero is calculated from the bubble x and y coordinates. This time is taken as the time at which all the detaching forces that are acting on the bubble are greater or equal to the attaching forces. For high gas to liquid momentum force ratios, the time at which the y coordinate less the bubble radius equals zero is calculated. The bubble diameter is evaluated at this time as the diameter at detachment from the fact that the bubble volume is simply given by the product of the gas flow rate and time elapsed. Comparison of the model's predictions was also made with predictions from a two-dimensional normal gravity model based on Kumar–Kuloor formulation and such a comparison is presented in this work.