Abstract
A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ∼ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.
Highlights
Czochralski (Cz) technology has been widely applied to produce single-crystalline materials
This paper mainly studies the fluid-thermal coupling properties of crystal growth under the influence of strong natural convection and complex forced convection
A multiple-relaxation-time lattice Boltzmann method (MRT-LBM) combined with the finitedifference method (FDM) is proposed in this paper to study the principles of melt convection and heat transfer in Cz crystal growth
Summary
Czochralski (Cz) technology has been widely applied to produce single-crystalline materials. The melt flow in the Cz crystal growth contains the natural convection and the forced convection, which are generated by thermal gradients and rotation of crystal and crucible, respectively These two convections make the convection and heat transfer very complex in the field of thermodynamics and hydrodynamics. Peng et al first proposed the axisymmetricswirling D2Q9 model of Cz crystal growth, and derived the velocity source terms of the momentum equations, including thermal buoyancy and circumferential rotation inertial force.[21] Huang et al improved a precise two-dimensional axisymmetric-swirling LBM in Cz crystal growth and studied the melt flow and temperature distribution with a high Grashof number.[22] Most of the existing researches on the LBM based on the Bhatnagar-Gross-Krook (BGK) collision operator and single relaxation time (SRT) model have defects in the calculation precision and stability of low-viscosity fluid.[23]. Melt convection and temperature distribution with different Grashof (Gr) numbers and Reynolds (Re) numbers, respectively, are analyzed
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