Semi-implicit method for thermodynamically linked equations in phase change problems (SIMTLE) |
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Authors: | A Jafari SH Seyedein MR Aboutalebi |
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Institution: | Centre of Excellence for Advanced Materials and Processing (CEAMP), School of Metallurgy and Materials Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114 Tehran, Iran |
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Abstract: | Thermodynamic coupling of temperature and composition fields in phase-change problems has been a challenge for decades. A compromise has been always desired between numerical efficiency and detailed physical consideration, toward a general scheme. In the present work, a macro–micro numerical method is proposed to link the conservation equations of energy and species with the thermodynamics of the solidification problems. Firstly, the basic structure of the method, simplified with a local equilibrium assumption, is presented. The method is then extended to a multi-phase model, demonstrating a three-phase approach to the solidification of a eutectic binary alloy. Relaxing the limitations imposed by the equilibrium assumption, non-equilibrium and microscale considerations was also included subsequently by a suggested modification to the macroscopic mathematical model. Advantages gained through the general algorithm proposed are concerned with two features of the method; (a) consistency with the energy and species equations. (b) No need of a predefined solidification path; that allows for the usage of raw phase diagram curves and offers simplicity and generality for extension through complex problems (i.e. microscopic, multi-phase or non-equilibrium). A benchmark problem was employed to test the performance of the proposed method in two cases of local equilibrium and Scheil-like solidification. The obtained results were validated in comparison with available semi-analytical solution. |
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Keywords: | Numerical modeling Phase-change Solidification Macrosegregation Thermodynamics Phase diagram |
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