Direct numerical simulation of momentum and heat transport in idealized Czochralski crystal growth configurations

Turbulent momentum and heat transport in idealized Czochralski crystal growth configurations is investigated by means of direct numerical simulation. The analysis of the flow data focuses on the influence of crystal and crucible rotation on the flow structures and the development of temperature fluctuations. A numerical parameter study is performed to investigate how the variation of the numerous flow parameters affects the turbulent transport processes. Finally, a direct numerical simulation is conducted with parameters taken from experiment in order to allow a direct comparison between numerical and experimental results. It is found that counter-rotation of the crystal and crucible leads to a complex flow, which is characterized by three major recirculation zones, if 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 crystallization zone. Neither a variation of the melt height, nor a reduction of the crystal rotation rate or a change of the Grashof and Marangoni numbers has a major effect on the bulk flow structure and overall heat transfer. Increasing rotation of the crystal changes the bulk flow structure strongly and leads to an increased value of maximum rms temperature fluctuations, the position of which is shifted towards the crucible bottom. A shifted position of maximum rms temperature fluctuations is also observed if heat radiation across the free surface is taken into account.