Partially-Averaged Navier-Stokes (PANS) approach for study of fluid flow and heat transfer characteristics in Czochralski melt

Abstract

The Partially-Averaged Navier-Stokes (PANS) approach has been applied for the first time to model turbulent flow and heat transfer in an ideal Czochralski set up with the realistic boundary conditions. This method provides variable level of resolution ranging from the Reynolds-Averaged Navier-Stokes (RANS) modelling to Direct Numerical Simulation (DNS) based on the filter control parameter. For the present case, a low-Re PANS model has been developed for Czochralski melt flow, which includes the effect of coriolis, centrifugal, buoyant and surface tension induced forces. The aim of the present study is to assess improvement in results on switching to PANS modelling from unsteady RANS (URANS) approach on the same computational mesh. The PANS computed results were found to be in good agreement with the reported experimental, DNS and Large Eddy Simulation (LES) data. A clear improvement in computational accuracy is observed in switching from the URANS approach to the PANS methodology. The computed results further improved with a reduction in the PANS filter width. Further the capability of the PANS model to capture key characteristics of the Czochralski crystal growth is also highlighted. It was observed that the PANS model was able to resolve the three-dimensional turbulent nature of the melt, characteristic flow structures arising due to flow instabilities and generation of thermal plumes and vortices in the Czochralski melt.