Simulations of viscoelastic two-phase flows in complex geometries

A front-tracking/immersed-boundary (FT/IB) method is developed for direct numerical simulations of viscoelastic two-phase flow systems in complex geometries. One set of governing equations is written for the whole computational domain and different phases are treated as a single fluid with variable material and rheological properties. The interface is tracked explicitly using a Lagrangian grid while the flow equations are solved on a fixed Eulerian grid. An immersed boundary method is used to impose the boundary conditions on arbitrarily-shaped solid walls. The surface tension is computed at the interface using the Lagrangian grid and included into the momentum equations as a body force. The viscoelasticity is accounted for using the FENE-CR model. The viscoelastic model equations are solved fully coupled with the flow equations within the front-tracking framework. The FT/IB method is first validated for a single-phase and a two-phase Newtonian flow problems. Then it is applied to study motion and deformation of a viscoelastic drop in a pressure-driven flow through a capillary tube with a smooth and a sharp-edged constrictions. It is shown that the FT/IB method is robust, second order accurate in space and suitable to simulate viscoelastic two-phase flows interacting with a complex geometry.