Numerical Study of Melting of Large-Diameter Crystals Using an Orbital Solar Concentrator

Abstract

The melting of large-diameter crystals using an orbital solar concentrator is studied numerically. In the proposed configuration, a parabolic dish imaging concentrator is used to focus the sun’s radiation onto an ampoule which holds the solid charge material to be processed. The charge will start melting in the vicinity of the focal height, after which it is translated in order for the melt to resolidify as a single crystal. A ray-trace method has been developed to determine the incident concentrated solar heat flux on the ampoule’s surface for both perfectly aligned and misaligned configurations. For the perfectly aligned charge, a transient two-dimensional conduction problem with phase change is formulated, whereas once the perfect alignment of the charge’s symmetry axis with the sun’s incoming ray is perturbed, the problem becomes three-dimensional due to the complex surface heat flux boundary condition. The commercial code FIDAP is used to solve the governing transport equation. By ignoring the participation of the ampoule in the heat transfer process, preliminary results highlighting the feasibility of growing GaAs, Ge, and Si crystals with diameters of the order of 20 cm using the orbital solar concentrator concept are presented. The transient temperature fields within various charge materials during the heat-up process are quantified. The resulting melting pattern within the charge due to the uncolumnated beam is observed to be uniform along the charge when compared to the idealized limiting case of columnated beams. Finally, the effect of the misalignment angle on the melting process is quantified.