Three-dimensional simulation of flow and thermal field in a Czochralski melt using a block-structured finite-volume method

Abstract

The three-dimensional and time-dependent turbulent flow field and heat transfer of the melt in a Czochralski crystal growth process were predicted using an efficient block-structured finite-volume Navier–Stokes solver. The present paper is a first step towards adopting a block-structured finite-volume method for simulating turbulent flow in a Czochralski melt. Different ways of creating high-quality block-structured grids for the crucible are described along with their advantages over structured grids. In order to study the cellular convection pattern in an industrial Czochralski melt, three-dimensional simulations of turbulent flow and thermal field were carried out on two grid levels in five blocks. Using a special form of discretization of the convective fluxes, the flow field was predicted without applying any turbulence model. The accuracy of the discretization of the convective terms and size of control volumes were shown to affect greatly the characteristics of the flow field. With fine grids, the predicted thermal field was seen to be in close agreement with the reported experimental observation and numerical prediction of melt surface thermal field as well as temperature fluctuations. The flow field was shown to transform through a number of intermediate stages such as spoke pattern, n-folded pattern with island, etc., until a stable cellular flow field is established with weak co-rotating waves at the surface. The mechanism of these waves is baroclinic instability.