1. Towards wall functions for the prediction of solute segregation in plane front directional solidification
- Author
-
Valéry Botton, Soufyen Rhouzlane, Marc Chatelain, J.-P. Garandet, Mickael Albaric, Séverine Millet, Daniel Henry, David Pelletier, Institut National de L'Energie Solaire (INES), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), INSA Euro-Méditerranée, Institut National des Sciences Appliquées (INSA), The authors are indebted to the institute Carnot Ingnierie@Lyon for its support and funding., Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Département des Technologies Solaires (DTS), Laboratoire d'Innovation pour les Technologies des Energies Nouvelles et les nanomatériaux (LITEN), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Institut National de L'Energie Solaire (INES), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Materials science ,directional solidification ,Context (language use) ,02 engineering and technology ,boundary layer ,Thermal diffusivity ,01 natural sciences ,[SPI.MAT]Engineering Sciences [physics]/Materials ,[SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] ,Inorganic Chemistry ,Physics::Fluid Dynamics ,0103 physical sciences ,Materials Chemistry ,Conservation of mass ,Scaling ,ComputingMilieux_MISCELLANEOUS ,Directional solidification ,010302 applied physics ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph] ,Turbulence ,Laminar flow ,Mechanics ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,segregation ,scaling analysis ,turbulent transport ,Boundary layer ,Crystallography ,[SPI.MECA.THER]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Thermics [physics.class-ph] ,0210 nano-technology - Abstract
International audience; The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations , which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.
- Published
- 2017