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A consistent and conservative Phase-Field model for thermo-gas-liquid-solid flows including liquid-solid phase change

Published: 15 January 2022 Publication History

Abstract

In the present study, a consistent and conservative Phase-Field model is developed to study thermo-gas-liquid-solid flows with liquid-solid phase change. The proposed model is derived with the help of the consistency conditions and exactly reduces to the consistent and conservative Phase-Field method for incompressible two-phase flows, the fictitious domain Brinkman penalization (FD/BP) method for fluid-structure interactions, and the Phase-Field model of solidification of pure material. It honors the mass conservation, defines the volume fractions of individual phases unambiguously, and therefore captures the volume change due to phase change. The momentum is conserved when the solid phase is absent, but it changes when the solid phase appears due to the no-slip condition at the solid boundary. The proposed model also conserves the energy, preserves the temperature equilibrium, and is Galilean invariant. A novel continuous surface tension force to confine its contribution at the gas-liquid interface and a drag force modified from the Carman-Kozeny equation to reduce solid velocity to zero are proposed. The issue of initiating phase change in the original Phase-Field model of solidification is addressed by physically modifying the interpolation function. The corresponding consistent scheme is developed to solve the model, and the numerical results agree well with the analytical solutions and the existing experimental and numerical data. Two challenging problems having a wide range of material properties and complex dynamics are conducted to demonstrate the capability of the proposed model.

Highlights

A Phase-Field model for multiphase flows with solidification/melting is developed.
Different parts of the model are physically coupled with the consistency conditions.
The model satisfies the mass, momentum, and energy conservation, and Galilean invariance.
Novel surface tension and drag forces are proposed.
A consistent and mass conserving scheme for the model is developed.

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            cover image Journal of Computational Physics
            Journal of Computational Physics  Volume 449, Issue C
            Jan 2022
            1103 pages

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            Academic Press Professional, Inc.

            United States

            Publication History

            Published: 15 January 2022

            Author Tags

            1. Consistent model
            2. Phase change
            3. Solidification/melting
            4. Multiphase flow
            5. Fluid-structure interaction
            6. Phase-Field

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