Large-eddy simulation of melt turbulence in a 300-mm Cz–Si crystal growth

We built a curvilinear dynamic Smagorinsky subgrid-scale (SGS) model based on filtering the covariant physical velocity components in the computational space. We implemented our proposed SGS model in large-eddy simulations (LES) of turbulent flows in complex configurations. Our model was validated when compared with direct numerical simulation (DNS) data of the melt turbulent flow in an idealized cylindrical crucible in a Cz–Si crystal growth. Then, we carried out LES computations for the melt turbulence in a real ellipsoidal crucible in a 300 mm Cz–Si crystal growth. We studied instantaneous behaviors and statistical features of the melt turbulence. Spectral analyses of the temperature fluctuations show that the melt flow is in a soft turbulence state of Rayleigh–Bénard convection under the rotating crystal. A cluster of big vortices is formed in the time-averaged bulk flow due to the complex interaction among the thermal buoyancy, surface tension and crucible/crystal rotations. Heat transport in the melt flow is turbulence-dominated with notable fluctuations. The maximal temperature fluctuation in the crystallization zone is close to the crystal edge with a value of 1.8 K. The flow instability mainly attributes to the thermal buoyancy in the melt.