Abstract
A Czochralski melt flow encounters the effects of anisotropic body forces owing to the system rotation as well as significant streamline curvature due to inherent vortical structures and flow past curved surfaces. Two-equation eddy-viscosity models lack the ability to capture the flow anisotropy and curvature effects. Here we present the first study on the thermo-fluid characteristics of Czochralski melt using rotation and streamline curvature corrected Partially-Averaged Navier-Stokes (PANS) adaptations of the low-Re k-ε and SST k-ω models. The paper presents physical insights to the new PANS turbulence modelling approach highlighting improvements in the predicting capability of PANS models with the incorporation of rotation and curvature corrections. The PANS models showed good agreement with the results available in the literature (both experimental and computational). In addition for the PANS low-Re k-ε model it was observed that the prediction of the typical Czochralski melt flow structure in terms of shape, relative size and orientation of the characteristic cells improved with rotation and curvature corrections. Further thermal fluctuations and vortex cores also reduced in the melt in the case of the PANS low-Re k-ε model showing stabilization of flow. The corresponding rotation and curvature modification to the PANS SST k-ω model corrected the flow dynamics from a buoyancy dominated to rotationally driven along with an increase in the thermal fluctuations and vortex cores in the Czochralski melt resulting in a destabilization of the melt flow.
Published Version
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