A multiblock/multigrid computational method for materials processing

The multiple time and length scale phenomena emerged from materials processing impose serious challenges to successful manifestation of numerical simulation. The complexities generated by multiple physics interactions and irregular shapes further complicate the problem. Advancement in materials processing demands a general computational framework to resolve these complexities with low computational cost.; To resolve the geometric, dynamic and computational complexities, a generic program has been developed based on curvilinear finite volume method. The generic approach employs the multiblock method in conjunction with multizone adaptive grid generation (MAGG) technique to resolve the topological complexity and multiscale coupling. A conservative block interface treatment is developed and a geometric multigrid method is integrated into current multiblock approach to optimize the outer iteration of the nonlinear equations. This is the first multi-resolution model for materials processing which can resolve the geometric, dynamic and computational complexities. The numerical model has been extensively validated by solving a variety of problems ranging from a lid-driven cavity flow to the Bénard convection. Numerical experiments have also been performed to demonstrate the capability of multigrid acceleration on the current multiblock method. The capability of current numerical model might be limited for high Reynolds number flows and the acceleration of the multigrid solver is not significant for transient problems.; The multiblock/multigrid method has been employed to investigate the induction heating and heat/mass transfer phenomena in the edge-defined film-fed growth (EFG) of polycrystalline silicon tubes, an important technique in photovoltaic industry. An overset grid system is introduced to decouple the electromagnetic field and energy equation, and a multiblock method is used to resolve the length scale difference in the temperature field calculation. Excellent agreement has been obtained between the thermocouple measured temperature profiles and numerical predictions. A 10 cm tube system has been upscaled to 12.5cm system based on numerical simulations. It has been found that the EFG system has a very good upscale capability and temperature distribution is closely related to geometric configuration. It is a very important conclusion that can be a guideline for the future system design. Small scale transport phenomena in the growth system is also studied. By integrating with a local silicon tube model, heat transfer in the die tip region, stress distribution and buckling mechanism in the as-grown silicon tube have been studied. Theoretical analysis is used to explain the buckling behavior in the tube production. The information gained through this research will help in designing a better EFG system with optimum operating conditions.; The numerical methodology developed in this thesis can be applied to resolve the multiphysics and multi-time/length scales in a broad class of problems, including other materials processes such as Czochralski growth, Bridgeman growth and thermal spray process. Implementations of the current numerical model not only can cut the computational cost but also will yield high numerical accuracy and efficiency.