High-order surface tension VOF-model for 3D bubble flows with high density ratio

An improved Volume of Fluid (VOF) method is presented which is applicable to high density ratio 3D flows for a large range of bubble Reynolds number (Re). The method is based on the Navier–Stokes equations for incompressible multi-phase flows which are discretized on a Cartesian staggered grid. The multi-grid technique together with the pressure–velocity coupling scheme for multi-phase flows have resulted in an efficient solver which nearly exponentially converge with the number of iterations. The convergence speed also shows negligible dependence on density ratio, viscosity ratio and Re. A second-order accurate, non-diffusive, mass conservative phase transport model is presented which does not suffer from unphysical over- or under-shoots of the phase variable. The high accurate normal, curvature and surface tension force model in combination with the high-order defect-correction scheme for multi-phase flows shows second-order global accuracy when applied to the transient bubble rise where the viscosity ratio is equal to one. In contrast, the commonly used viscosity model for VOF introduces a first order error for the same problem. The VOF method has been tested for different types of bubble flows at low Re and for path-oscillating and wobbling air bubbles (in water) with a diameter range of 1.82<D<6 mm. The numerical results agree quantitatively with the available experimental data. The investigations show that the proposed high accurate surface tension model can be used successfully for wobbling flows with bubble deformation while maintaining the mass of the phases. The error in mass conservation is directly proportional to the residual in solving the discrete problem.