We describe a computational model based on Large Eddy Simulation to calculate 3D unsteady turbulent melt convection in Czochralski systems for Si-crystal growth. The model has been verified using temperature measurements inside the melt and along the melt-crucible surface. The effect of the crucible rotation rate on 3D turbulent structures developed in the melt is analyzed. Transformation of the melt flow with increasing argon flow rate is predicted, and the controlling effect of the argon flow on the oxygen content in the crystal is evaluated.