Analytical and computational methods for solidification problems of liquid that expands during freezing

[+] Author and Article Information
Deqi Liu

20 Avenue Albert Einstein Villeurbanne, Rhone 69100 France deqi.liu@insa-lyon.fr

Hubert Maigre

20 Avenue Albert Einstein Villeurbanne, 69100 France hubert.maigre@insa-lyon.fr

Fabrice Morestin

20, Avenue Albert Einstein Laboratory of Contact and Structural Mechanics Villeurbanne, 69621 France fabrice.morestin@insa-lyon.fr

Philippe Géoris

214 avenue de la Mare Gessart Venette, 60280 France philippe.georis@plasticomnium.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received December 18, 2018; final manuscript received February 15, 2019; published online xx xx, xxxx. Assoc. Editor: Gerard F. Jones.

ASME doi:10.1115/1.4043261 History: Received December 18, 2018; Accepted February 16, 2019


Both analytical and computational methods for solidification problems are introduced. First, the inward solidification process in a spherical vessel is studied. Expressions of the stress, displacement in the solid phase and the liquid pressure are deduced based on the solidification interface position. A phase-change expansion orientation factor is introduced to characterize the non-isotropic expansion behavior at the freezing interface. Then an efficient coupled thermo-mechanical finite-element method is proposed to evaluate the thermal stress, strain, displacement and pressure in solidification problems with highly nonlinear constitutive relations. Two particular methods for treating the liquid phase with fixed-grid approaches are introduced. The thermal stress is computed at each integration point by integrating the elasto-viscoplastic constitutive equations. Then, the boundary value problem described by the global finite-element equations is solved using the full Newton-Raphson method. This procedure is implemented into the finite-element package Abaqus via a Fortran subroutine UMAT. Detailed implementation steps and the solution procedures are presented. The numerical model is validated first by the analytical solutions and then by a series of benchmark tests. Finally, an example of solidification in an open reservoir with a free liquid surface is introduced. Potential industrial applications of the numerical model are presented.

Copyright © 2019 by ASME
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