Two-Phase Outflows: Boundary Conditions and Algorithm

Steven Dong
Purdue University
Website of Steven Dong

Location: Purdue University

Apr 26, 2014 4:45 PM

Two-phase outflows, where the interface between two immiscible incompressible fluids passes through open portions of the domain boundary, are widely encountered in two-phase applications involving unbounded physical domains. To numerically simulate such problems, it is necessary to artificially truncate the domain to a finite size. Therefore, an open boundary condition will be required at the two-phase artificial boundary. The design of effective techniques for treating two-phase outflows presents new challenges beyond those encountered for single-phase outflows. In particular, two-phase outflows involve density contrast, viscosity contrast, fluid interface, and surface tension on the open boundaries, and the density ratio and viscosity ratio of the two fluids may be large.

In this talk, we present an effective outflow boundary condition, and an associated numerical algorithm, within the phase field framework for dealing with two-phase outflows and open boundaries. The set of two-phase outflow conditions for the phase-field and flow variables are designed to prevent the un-controlled growth in the total energy of the two-phase system, even in situations where strong backflows or vortices may be present at the outflow boundaries. The numerical challenges involved in the algorithmic treatment of these boundary conditions, especially that associated with the variable viscosity on the open boundary, will be discussed. Several numerical examples involving two-phase inflows/outflows with large density contrasts and viscosity contrasts will be presented to demonstrate the capabilities enabled by the method.