An anisotropic lattice Boltzmann – Phase field scheme for numerical simulations of dendritic growth with melt convection

•An anisotropic LB – PF scheme is proposed to study dendritic growth with melt flows.•Dendritic growth is numerically modeled by implementing the anisotropic LB framework.•The scheme offers a simple and effective solution to solve the phase field equation. An anisotropic lattice Boltzman – phase fie...

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Bibliographic Details
Published inInternational journal of heat and mass transfer Vol. 133; pp. 1240 - 1250
Main Authors Sun, Dongke, Xing, Hui, Dong, Xianglei, Han, Yongsheng
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.04.2019
Elsevier BV
Subjects
Anisotropy
Computer simulation
Crystals
Dendritic growth
Dendritic structure
Distribution functions
Evolution
Free convection
Heat transfer
Lattice Boltzmann
Mathematical models
Melt convection
Microstructure
Numerical simulation
Phase transitions
Solidification
Dendritic growth
Numerical simulation
Lattice Boltzmann
Microstructure
Melt convection
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Summary:•An anisotropic LB – PF scheme is proposed to study dendritic growth with melt flows.•Dendritic growth is numerically modeled by implementing the anisotropic LB framework.•The scheme offers a simple and effective solution to solve the phase field equation. An anisotropic lattice Boltzman – phase field scheme is proposed to study dendritic growth in the presence of melt convection. In this work, the lattice Boltzmann method is extended to model dendritic growth with heat transfer and melt convection. It implements an anisotropic streaming-relaxation step based on the lattice Bhatnagar-Gross-Krook scheme. Three sets of distribution function are defined to describe the evolution of melt convection, heat transfer and phase transition. The D2Q9 lattice vectors are utilized to describe the advancement of ordering parameter, and coupled with a convective-diffusion equation for heat transfer during phase transition. After model validation, dendritic growth with incoming flows and natural convection are numerically investigated, respectively. The results show that the present model is an alternative numerical approach to study convective dendritic growth with relatively high efficiency, and it would like to facilitate the understanding of microstructure evolution in solidification.
ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2018.12.095