Abstract
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries.
Highlights
The current work focuses on the motion of a mixture of two immiscible incompressible fluids in a domain that is open on part of its boundary
In a recent work [6] we have proposed a set of effective two-phase outflow boundary conditions within the phase field framework
We have presented several new open boundary conditions for two-phase outflows, and a rotational pressure-correction based algorithm for solving the two-phase momentum equations together with these boundary conditions
Summary
The current work focuses on the motion of a mixture of two immiscible incompressible fluids in a domain that is open on part of its boundary. The problem will involve truly two-phase outflow/open boundaries. The slug/ churn/bubbly flows crucial in many industrial processes (see e.g. the experiments of [1,2,3] for their dynamical characterizations) provide other examples of two-phase flow situations of this type. These problems usually involve physically unbounded flow domains. Numerical simulation of such problems will need to truncate the domain to a finite size, and some open/outflow boundary condition (OBC) will be required on the artificial boundary.
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