A modified hypothesis of Reynolds stress tensor modeling for mixed turbulent convection in crystal growth

Abstract

Within implicit large eddy simulation, we have provided unsteady 3D numerical study of turbulent melt convection during 100 mm diameter Si Cz growth, using refined time step and material properties. Comparison of calculated and measured time-averaged temperature profiles along the melt/crucible interface has demonstrated advantages of using updated material properties. Reference data on the spatial distributions of the turbulent stress tensor and heat fluxes in the melt have been obtained and used for validation of the conventional and modified hypothesis of Reynolds stress tensor modeling. Contrary to the conventional Boussinesq assumption of isotropic turbulent viscosity, our modified hypothesis has reproduced qualitative and quantitative details of reference Reynolds stress tensor distributions, including the boundary layer anisotropy due to the wall and free surface effects, mean velocity shear effect, and the buoyancy contribution to enhance vertical velocity fluctuations. Using our modified hypothesis and generalized Reynolds analogy for turbulent heat transport modeling, it become feasible to reproduce quantitatively the distributions of the turbulent heat flux, shear and buoyancy production terms of the kinetic energy transport equation, which is the necessary basis for further turbulence model development.