Three-dimensional phase-field simulations of water freezing and thawing at pore scale

This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition modeling is approached at both macroscale and microscale, combining heat transfer in a heterogeneous medium and a phase-field approximation of the Gibbs-Thomson relation by means of the Allen-Cahn equation. The formulation of the model contains novel components tailored for the given purpose. In addition to this general model, two limit scenarios are considered: At the macroscale, surface tension effects are negligible and phase transition focusing based on temperature can replace the Allen-Cahn equation. In contrast to that, simulations of equilibrium states at the microscale allow us to eliminate the heat equation by assuming constant supercooling. For numerical solution, an efficient hybrid parallel algorithm based on the finite volume method and the Runge-Kutta-Merson solver with adaptive time stepping are employed. The results of different model variants at different scales are discussed. In a parametric study, the full phase-field model is demonstrated to deliver consistent results across a wide range of surface tension values, exhibiting curvature-induced premelting if surface tension is artificially exaggerated. As surface tension tends to the realistic values, the results of the phase-field approach those of the simplified temperature-driven phase transition model. In addition, microscale simulations of water freezing at different supercooling values aim to predict the unfrozen water content and compare the results with data from literature. Numerical stability, accuracy, and computational costs are also discussed.