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


A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces

Guang Lin 1*, Jie Bao 2, Zhijie Xu 1, Alexandre M. Tartakovsky 1, Charles H. Henager Jr. 3

1 Computational Mathematics Group, Pacific Northwest National Laboratory, Richland, WA 99352 USA.
2 Fluid and Computational Engineering Group, Northwest National Laboratory, Richland, WA 99352 USA.
3 Engineering Mechanics and Structure Materials Group, Northwest National Laboratory, Richland, WA 99352 USA.

Received 30 June 2012; Accepted (in revised version) 21 March 2013
Available online 26 July 2013
doi:10.4208/cicp.300612.210313a

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.

AMS subject classifications: 35Q20, 74N20, 74N05, 65Y05
Key words: Phase-field, crystal growth, diffusion, convection, lattice kinetics, modeling.

*Corresponding author.
Email: guang.lin@pnnl.gov (G. Lin), jie.bao@pnnl.gov (J. Bao), zhijie.xu@pnnl.gov (Z. Xu), alexandre.tartakovsky@pnnl.gov (A. M. Tartakovsky), chuck.henager@pnnl.gov (C. H. Henager Jr.)
 

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