Two-dimensional and axisymmetric bubble rise uisng the level set method

Gas bubbles in liquids are important in many industries, including power generation, steel making, as well as chemical and waste water treatment. A fundamental understanding of the bubble rising physics is helpful in many practical applications. A new level set code for incompressible, multiphase flows using the vorticity-streamfunction formulation in both two-dimensional and axisymmetric cases has been developed. The level set method is well suited to treating multiphase flows having complex interface shapes that may undergo topological changes such as merging and splitting of bubbles. Previous numerical and experimental results for single and multiple bubbles are used to determine the numerical parameters that should be used for the new code and to demonstrate the accuracy of the model. The shape and terminal velocities of air bubbles in mineral oil and water are found to duplicate other experimental and calculated results very closely. Results have been compared from two-dimensional and axisymmetric versions of the code for bubbles merging with various surface tension. It is found that prior to merging of the bubbles, the results for velocities and bubble shapes are very similar. However, surface tension is found to have a greater influence on the axisymmetric results. Once the bubbles merge, the combined bubble evolves toward the same shape and terminal velocity of a single bubble having the same volume. The initial acceleration of a single air bubble in water is analyzed and found to be approximately 3:3g, not 2g, which is the predicted value from added mass analysis based on potential flow theory. When the liquid density is increased, the acceleration is also found to increase.