Numerical Simulation of Fluid Flow and Heat Transfer in an Industrial Czochralski Melt Using a Parallel-Vector Supercomputer

Abstract

In this paper, the fluid flow and heat transfer in an industrial Czochralski melt was analyzed by solving the time-dependent three-dimensional Navier-Stokes equations on curvilinear boundary-fitted grids in a rotating frame of reference. In order to represent the ellipsoidal crucible, a grid with 720,896 control volumes was generated in six blocks. Using the natural advantage of block-structuring, computations were carried out on a parallel-vector machine (NEC SX-4) with an optimal load-balancing efficiency of 100{\%} using four processors. Simulations of the flow field were performed with and without the k --- $\epsilon$ turbulence model. It was seen that the turbulence model suppresses the fluid mechanical instabilities leading to an axisymmetric flow and thermal field, while the simulations without the turbulence model were found to predict the three-dimensional time-dependent features of the melt flow well. A total performance of 2.95 and 2.81 GFlops on four processors was reached for the simulation with and without turbulence model, respectively.