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Volume 15, Issue 1
A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces

Guang Lin, Jie Bao, Zhijie Xu, Alexandre M. Tartakovsky & Charles H. Henager Jr.

DOI: 10.4208/cicp.300612.210313a

Commun. Comput. Phys., 15 (2014), pp. 76-92.

Published online: 2014-01

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  • Abstract

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

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@Article{CiCP-15-76, author = {Guang Lin, Jie Bao, Zhijie Xu, Alexandre M. Tartakovsky and Charles H. Henager Jr.}, title = {A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {1}, pages = {76--92}, abstract = {

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300612.210313a}, url = {http://global-sci.org/intro/article_detail/cicp/7088.html} }
TY - JOUR T1 - A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces AU - Guang Lin, Jie Bao, Zhijie Xu, Alexandre M. Tartakovsky & Charles H. Henager Jr. JO - Communications in Computational Physics VL - 1 SP - 76 EP - 92 PY - 2014 DA - 2014/01 SN - 15 DO - http://doi.org/10.4208/cicp.300612.210313a UR - https://global-sci.org/intro/article_detail/cicp/7088.html KW - AB -

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

Guang Lin, Jie Bao, Zhijie Xu, Alexandre M. Tartakovsky and Charles H. Henager Jr.. (2014). A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces. Communications in Computational Physics. 15 (1). 76-92. doi:10.4208/cicp.300612.210313a
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