Phase-bounded finite element method for two-fluid incompressible flow systems

TL;DR

This paper introduces a novel finite element method for two-fluid incompressible flow systems that ensures phase fraction constraints are maintained, improving the physical accuracy of multiphase CFD simulations.

Contribution

It develops a phase-bounded finite element approach using a nonlinear variational inequality solver for the two-fluid model, ensuring bounded phase fractions.

Findings

Method preserves phase fraction bounds accurately.

Compared to explicit methods, it offers improved stability.

Verification confirms the method's effectiveness.

Abstract

An understanding of the hydrodynamics of multiphase processes is essential for their design and operation. Multiphase computational fluid dynamics (CFD) simulations enable researchers to gain insight which is inaccessible experimentally. The model frequently used to simulate these processes is the two-fluid (Euler-Euler) model where fluids are treated as inter-penetrating continua. It is formulated for the multiphase flow regime where one phase is dispersed within another and enables simulation on experimentally relevant scales. Phase fractions are used to describe the composition of the mixture and are bounded quantities. Consequently, numerical solution methods used in simulations must preserve boundedness for accuracy and physical fidelity. In this work, a numerical method for the two-fluid model is developed in which phase fraction constraints are imposed through the use of an nonlinear variational inequality solver which implicitly imposes inequality constraints. The numerical method is verified and compared to an established explicit numerical method.