Numerical simulation of MHD oscillatory mixed convection in CZ crystal growth by Lattice Boltzmann method

Abstract

A two-dimensional axisymmetric swirling thermal lattice Boltzmann model is presented to study the magnetohydrodynamics (MHD) oscillatory mixed convection in the melt of Czochralski silicon crystal growth in this paper. The governing equations are all solved by lattice Boltzmann method. The D2Q9 model is applied to solve the radial and axial velocities of the melt. Two D2Q5 models are adopted to solve the azimuthal (swirling) velocity and the temperature. The comparison with experiment and finite volume method proves that the presented model can be used as an alternative for simulating the axisymmetric crystal growth. Furthermore, simulations of the melt flow structure and heat transfer under a vertical magnetic field are conducted. And the critical Reynolds numbers Recr, which lead to the onset of the oscillatory melt convection, are calculated in different Richardson numbers (Ri), Ri=0.1,0.5,1.0,1.5,2.0,3.0, and different Hartmann numbers (Ha), Ha=0,10,20,30,40,50. In addition, the magnetic stability diagram is established according to a series of computations and the relationship between crystal rotation parameter and the state of the melt convection are analyzed. Compared with the traditional three-dimensional computational model, the proposed model in this paper has less computation time in simulating the axisymmetric swirling flow without affecting the accuracy of the results. The obtained critical Reynolds number has certain reference for improving the crystal growth parameter in practice. Keywords: A1. Computer simulation, A1. Oscillatory mixed convection, A1. Lattice Boltzmann method, A1. Heat transfer, A2. Magnetic field assisted Czochralski method