Convective Effects in Simulated Czochralski Crystal Growth (Numerical, Bi-Harmonic, Interferometry, Compact, Instability).

A numerical parametric study of the convective effects in the Czochralski method of crystal growth was made. The study focuses primarily on the transition from a buoyancy dominated flow to one dominated by centrifugal force, and on the appearance of a stagnant layer caused by the cooling of the crucible bottom. The governing equations were solved by extended versions of the compact method originally suggested by Kreiss. Solutions were obtained for Rayleigh numbers up to 10('5), crucible aspect ratio ranging from 0.75 to 2.0, dimensionless crystal sizes from 0.1 to 0.7, and Pr and tl numbers ranging from 10 to 100. These solutions indicate that the transition mechanism depends on a relation between the Grashof number based on the crucible radius, and the Reynolds number. Furthermore, the equations and their solutions indicate that the results from experiments with different Pr and tl number fluids may be correlated by normalizing the data using the Reynolds number at which transition occurs, Re*. The effects of the crystal, with and without rotation, on the development of a stagnant layer was also investigated. The results indicate that this layer's thickness is controlled by the crystal size and the bottom temperature; rotation only affects the layer at small aspect ratios. For tall cavities and very large Reynolds numbers, Re >> Re*, the flow in the cavity is divided in two parts, the forced convection dominated region and the stagnant layer. Buoyancy effects are important only near the cavity walls. During the iterative numerical process, oscillations of the fluid variables, such as the stream function, were observed for some ranges of parameters. In these cases, convergent solutions are difficult to obtain. The situation has several similarites to the physical instabilities observed in the flow between rotating, concentric cylinders with an imposed horizontal temperature gradient. However, the mechanism that leads to these oscillations appears to be associated to the development of a reverse flow. Physical experiments that were performed are also discussed. In these experiments, measurements of the temperature profiles in a higher range of Rayleigh numbers were attempted using holographic interferometry. Several experimental difficulties severely limited the parameter range in which these experiments could be conducted.Ph.D.Mechanical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/160642/1/8520875.pd