Derivation of closures for single air bubbles in water using an improved 3D front tracking model 2-phase flow

Using a 3D Front Tracking (FT) model, closures for the drag, lift and virtual mass forces have been derived for single freely deformable air bubbles rising in water. The combination of a large surface tension force, a high density ratio as well as a high Reynolds number poses a severe numerical challenge for Direct Numerical Simulations. Therefore, the numerical implementation of the FT model was improved to allow simulation of very small air bubbles (~1 mm) in water using realistic physical properties without numerical problems or unphysical volume changes. The computed drag force coefficients for air bubbles in the range of 1-5 mm compare reasonably well with experimental data from literature. The small discrepancies may be explained by the extremely high sensitivity of the air/water system for surface contaminants, as has been extensively reported in the literature. For an initially spherical air bubble in initially quiescent water a virtual mass coefficient of 0.53 was computed for all diameters air bubbles, which compares very well with the theoretical result of 0.50. The simulated coefficient converges to the theoretical value when the grid is further refined. Finally, a lift force coefficient of 0.5 was found for a 4 mm air bubble rising in a linear shear flow, which is somewhat higher than experimental data reported in the literature for lower Reynolds numbers