Bridgman process is one of the commonly used methods for the manufacturing and growth of semiconductor crystals. In this process, thermal convection plays an important role by affecting heat and mass transfer. Asymmetric flow patterns can lead to an inhomogeneous structure of the growing crystal and also there exist special flow patterns in a fluid domain which determine the governing transport structure and mechanics of the flow.
In this work, we analyze the bulk mixing properties of the melt flow in vertical Bridgman process through the novel approach of Lagrangian coherent structures. A mixed formulation, based on the general form of the enthalpy, is employed for the governing equations coupling Navier-Stokes, continuity and energy equations. A fully implicit second order accurate temporal and spatial finite element discretizations is also used. The obtained velocity field is utilized to identify the transport barriers in terms of finite time Lyapunov exponent ridges whose movements govern the mixing in the melt flow and Lagrangian Coherent Structures are visually revealed to show the transport barriers and flow structure.