Numerical Calculation of Viscous Force Balance in Free Bubble Rising in Quiescent Water

This work tackles the problem of numerically resolving the viscous forces in a free air bubble rising in quiescent water. Previous simulations have been able to reproduce the wobbling motion observed in the experimental studies of Moreto et al. (2022). In those simulations, the viscous drag was not captured numerically, due to under-resolution in the boundary layer. A new numerical approach reported here rectifies this, by using three overset curvilinear deforming grids, called the x-, y- and z-grids. The numerical method uses level set phase boundaries, and the governing equations are discretized using a finite-difference approach. The velocity-pressure coupling is solved using the SIMPLE algorithm. Strong flow quantity variations are found near the bubble surface and across the vortex rings shed from the bubble in the wake. To handle the challenges posed by the highly unsteady and thin boundary layer formed on the bubble surface, the three overset grids each place a higher amount of grid cells near the bubble’s surface which is mostly normal to that grid’s direction. Interpolation is performed between the three grids in the regions where the largest component of the surface normal vector changes. Comparison of the experimental data with the numerical simulations is implemented, to offer a reliable way of verification and validation of both results. A resolved simulation of the bubble boundary layer allows us to understand the physics by which the viscous forces are automatically balanced by the pressure force.