A combined Lagrangian and Eulerian method for simulating the melting process of quartz glass

Quartz glass with excellently optical and thermal properties is characterized by an ultra-low defect concentration. Remelting the raw glass in a vacuumed electric-heating furnace is an instrumental technique for removal of gas impurities. During the glass melting, heat transfer, phase change and very large surface deformation occur simultaneously. Numerical methods based on the grids encounter difficulties in tracking the highly distorted free surface, while smoothed particle hydrodynamics (SPH), a meshless Lagrangian algorithm, can track it conveniently. However, complex heat transfer cannot be treated in the current SPH method sophisticatedly. In this study, advantages of SPH and FEM are considered into a combined scheme specifically for study of the quartz glass melting. In the proposed scheme, FEM is employed to get the temperature distribution by calculating the dominant heat transfer, and SPH is adopted to model the melt flow and free surface deformation. The ingot is divided into three phases of liquid, mush and solid. A correction factor is employed to the acceleration term in the momentum equation, similar to the volume force in the mesh method, for adjusting the mush and solid velocities. Based on the combined scheme, influences of heating conditions on the melting process are carefully studied. Furnace design with a bottom heater, as well as an optimized heating strategy, is proposed to improve the melting process by suppressing the incomplete melting phenomenon.