The effects of several growth parameters in cylindrical and spherical Czochralski crystal process are studied numerically and particularly, we focus on the influence of the pressure field. We present a set of threedimensional computational simulations using the finite volume package Fluent in two different geometries, a new geometry as cylindro-spherical and the traditional configuration as cylindro-cylindrical. We found that the evolution of pressure which is has not been studied before; this important function is strongly related to the vorticity in the bulk flow, the free surface and the growth interface. It seems that the pressure is more sensitive to the breaking of symmetry than the other properties that characterize the crystal growth as temperature or velocity fields.

By using 3D finite element calculations, numerical simulations are performed to predict the thermal field as well as the thermal stress in a c-axis sapphire single crystal grown by Kyropoulos technique. The effects of additional resistive heating (placed under the crucible bottom) and crystal rotation are investigated and a comparison is made between the isotropic and anisotropic analysis. The anisotropy of the elastic constants and thermal expansion coefficients as well as their temperature dependence are considered in the anisotropy calculations while Young's modulus and the Poisson ratio are used in the isotropic analysis. Thermal stress is found to be smaller in the anisotropy analysis than that in the isotropic analysis and significant differences are found in their respective distribution patterns. Additional resistive heating acts to decrease both of the crystal-melt interface convexity and the von Mises stress. In addition, crystal rotation combined with additional resistive heating decreases significantly the thermal stress inside the sapphire crystal and along the melt-crystal interface. Therefore, optimizing the heating conditions and using a suitable crystal rotation rate seem to be favorable to control the growth interface shape and to reduce thermal-stress-related defects during the growth process.

In this paper, the effect of transverse magnetic field on a laminar liquid lead lithium flow in an insulating rectangular duct is numerically solved with three-dimensional (3D) simulations. Cases with and without buoyancy force are examined. The stability of the buoyant flow is studied for different values of the Hartmann number from 0 to 120. We focus on the combined influence of the Hartmann number and buoyancy on flow field, flow structure in the vicinity of walls and its stability. Velocity and temperature distributions are presented for different magnetic field strengths. It is shown that the magnetic field damps the velocity and leads to flow stabilization in the core fluid and generates magnetohydrodynamic (MHD) boundary layers at the walls, which become the main source of instabilities. The buoyant force is responsible of the generation of vortices and enhances the velocities in the core region. It can act together with the MHD forces to intensify the flow near the Hartmann layers. Two critical Hartmann numbers (Hac1 = 63, Hac2 = 120) are found. Hac1 is corresponding to the separation of two MHD regimes: the first one is characterized by a core flow maximum velocity, whereas the second regime is featured by a maximum layer velocity and a pronounced buoyancy effect. Hac2 is a threshold value of electromagnetic force indicating the onset of MHD instability through the generation of small vortices close to the side layers.

The effect of axial magnetic field of different intensities on pressure in silicon Czochralski crystal growth is investigated in cylindrical and hemispherical geometries with rotating crystal and crucible and thermocapillary convection. As one important thermodynamic variable, the pressure is found to be more sensitive than temperature to magnetic field with strong dependence upon the vorticity field. The pressure at the triple point is proposed as a convenient parameter to control the homogeneity of the grown crystal. With a gradual increase of the magnetic field intensity the convection effect can be reduced without thermal fluctuations in the silicon melt. An evaluation of the magnetic interaction parameter critical value corresponding to flow, pressure and temperature homogenization leads to the important result that a relatively low axial magnetic field is required for the spherical system comparatively to the cylindrical one.

The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.