Direct Navier-Stokes simulations of turbulent Czochralski flows

Direct numerical simulations of turbulent convection in an idealized Czochralski crystal growth configuration were performed with a three-dimensional, time-dependent Navier-Stokes solver. The analysis of the how data focusses on the influence of crystal and crucible rotation on the flow structures and the development of temperature fluctuations. Therefore, simulations were performed for different melt heights and various crystal and crucible rotation rates. It was found that the counter-rotation of the crystal and crucible leads to a complex how with three major recirculation zones, when crucible rotation dominates the flow. The dynamics of the flow are controlled by centrifugal forces counteracting buoyancy and surface tension effects. High temperature fluctuations are created within or close to the cristalization zone. Neither variation of the melt height nor reducing the crystal rotation rate has a major effect an the bulk flow structure and overall heat transfer, but temperature fluctuations are reduced due to the decreased rotation of the flow. Increasing rotation of the crystal changes the bulk flow structure tremendously. Additionally the value of maximum rms temperature fluctuations is increased and its position is shifted towards the crucible bottom.