Numerical simulation of merging of two rising bubbles with different densities and diameters using an enhanced Volume-Of-Fluid (VOF) model

In this study, the transient evolution of two rising bubbles with different densities is investigated numerically using an enhanced version of the VOF model, aiming to establish an state-of-the-art benchmark solutions and upto-date data set for CFD validations. The simulations are performed on the staggered grid system where a novel third-order accurate monotone convection scheme is applied for the discretization of the convection terms in Navier-Stokes and volume fraction equations while the semi-iterative PISOC algorithm (a combined version of the classical PISO and Chorin's model) are used to solve the pressure-velocity coupling. To reduce the false diffusion errors and mitigate smearing of interface thickness in the regions of physical discontinuities, the interface compression technique is also incorporated into the transport equation. To further enhance the accuracy of the numerical solutions, the idea of Piecewise Linear Interface Calculation (PLIC) based on the ELVIRA technique (Efficient Least-square Volume-of-fluid Interface Reconstruction Algorithm) is also utilized for the interface reconstruction and accurate implementation of surface tension force. The validity and accuracy of the enhanced VOF model is further demonstrated against a series of challenging benchmark cases including draining of liquids from the storage tank (tank draining), single rising bubble, three-phase Rayleigh-Taylor Instability and dam-break flows over dry and wet beds. The comparison of the obtained results with previously published data vividly demonstrates the superiority of the proposed method over the standard VOF/Level-Set models in handling multiphase/multi-fluid flow problems with large topological changes. In the last stage, the morphology and hydrodynamic characteristics of merging of two rising bubbles with different densities and diameters are examined and analyzed in details. The results show that, the initial/final deformations and the subsequent steady-state rise of two bubbles are remarkably influenced by the diameters of leading (upper) and trailing (lower) bubbles.