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Title: A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces

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. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. 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. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. 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.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1133990
Report Number(s):
PNNL-SA-89043
NN2001000
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Communications in Computational Physics, 15(1):76-92
Country of Publication:
United States
Language:
English

Citation Formats

Lin, Guang, Bao, Jie, Xu, Zhijie, Tartakovsky, Alexandre M., and Henager, Charles H. A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces. United States: N. p., 2014. Web. doi:10.4208/cicp.300612.210313a.
Lin, Guang, Bao, Jie, Xu, Zhijie, Tartakovsky, Alexandre M., & Henager, Charles H. A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces. United States. doi:10.4208/cicp.300612.210313a.
Lin, Guang, Bao, Jie, Xu, Zhijie, Tartakovsky, Alexandre M., and Henager, Charles H. Sun . "A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces". United States. doi:10.4208/cicp.300612.210313a.
@article{osti_1133990,
title = {A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces},
author = {Lin, Guang and Bao, Jie and Xu, Zhijie and Tartakovsky, Alexandre M. and Henager, Charles H.},
abstractNote = {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. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. 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. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. 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.},
doi = {10.4208/cicp.300612.210313a},
journal = {Communications in Computational Physics, 15(1):76-92},
number = ,
volume = ,
place = {United States},
year = {Sun Feb 02 00:00:00 EST 2014},
month = {Sun Feb 02 00:00:00 EST 2014}
}
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