Numerical Simulation of Two-phase Flows Using a Hybrid Volume of Fluid and Immersed Boundary Method

In this paper a simulation model is presented for the Direct Numerical simulation (DNS) of multiphase flow. This method combines the Volume of fluid model and Immersed Boundary method in order to investigate water-oil flow-pattern. The simulations were carried out on structured cartesian adaptive mesh refinement (SAMR), where the the Immersed Boundary represents the circular tube via Direct Forcing Method (DFM). The Volume of Fluid based on piecewise linear reconstruction interface, allow to define the fluid-fluid interface using a three dimensional version of the continuum surface force (CSF) model of Brackbill et al. (1992). The Navier-Stokes equations are discretized in the entire domain using a finite difference scheme, where a temporal discretization is based on SBDF scheme, with adaptive time stepping. The capabilities of the hybrid VOF-IB model are demonstrated with examples in wich complex topological changes in the interface are encountered. The overall methodology has been through a careful, series of verification tests whose results are reported. An oil-water flow-pattern application is presented.