Comparison and application of several turbulence models in simulation of crystal growth

A typical industry-scale CZ furnace for growing single crystal of silicon was numerically discretized with multi-block structured grids. All heat transfer modes in the furnace, including the melt convection, solid conduction and surface radiation, are solved together in a conjugated way. To model the melt turbulence of Si in the crucible, a few turbulence models were deliberately selected and applied. These turbulence models include the low Reynolds number k-ε model, the standard k-ε model and a modified two-layer turbulence model. The simulation results obtained with these turbulence models were compared. The comparison shows that the melt flow structures predicted with these turbulence models are quite similar, while the difference in the predicted crystal-melt interface shape is obvious due to different treatment of the near wall turbulence in each model.