Flow Module

Fig. 1. Automatic 3D Grid Generation from the 2D Grid using octagonal blocks near the symmetry axis

Flow Module is designed for professional analysis of 3D or 2D turbulent and laminar convection in the crystallization zone including the melt, crystal, crucibles, and gas or encapsulant domains. A unique approach is used to couple this analysis with global heat transfer. The module allows the user to account for the following phenomena:

• conductive heat transport;
• radiative heat transfer in semitransparent domains;
• laminar flow;
• turbulent flow within the RANS, LES,or DNS approaches;
• prediction of crystallization front shape;
• magnetic field effect;
• impurity transport;
• stress computation;
• scalar transport.

Automatic Generation of a 3D Grid

To provide grids for 3D computations, the Flow Module has an automatic 3D grid generator that builds 3D grids on the basis of 2D grids. Not only does it rotate the 2D grid around the vertical axis, but also incorporates blocks with quadragonal horizontal cross section in the central domains of the geometry, providing the area around the rotation axis with high-quality grid, see Fig. 1.

Turbulence models

The user can choose the RANS, LES/URANS, DNS, or quasi DNS approaches and apply a model of turbulence specially adapted for the melt turbulent flow computations. Advanced approximations of convective and diffusive terms allow application of coarser computational grids and faster analysis. There are special tools for operative control of a computation.

Fig. 2. Flow pattern in the reactor and 1D temperature distribution along one of the boundaries

Crystallization front geometry

Flow Module accurately describes the geometry of the crystallization front, temperature gradients, distributions of velocity vectors and scalars, heat and mass fluxes along interfaces. There are options to analyze unsteady effects in several monitoring points and in cross sections of a 3D grid. Parallel version of the solver is also developed for using on Linux clusters or on several PCs in a Windows network.

Magnetic field effects

Flow Module was extended by options for calculating magnetic field effects (MFs) in the crystallization zone, including the conjugated electric current flow in the crystal and melt]. There are automatic options for direct current magnetic fields of uniform (vertical or horizontal) and cusp configurations. Alternative current MFs can be implemented in a customized software version. Melt flow and the crystallization front can be analyzed in both 3D unsteady and 2D steady approaches. The examples on this page are provided for 400 mm diameter Si Cz growth.

Fig. 3. Temperature distribution and velocity distribution in the melt for 400 mm diameter Si CZ growth with zero magnetic field (top) and with horizontal magnetic field of 30 mT (bottom)

Solution control and visualization

To control the computation execution, there is Computation Manager built-in into the program, which visualizes:

• the equation residuals;
• the averaged crystallization rate;
• the crystallization front shape and the crystallization rate distribution along the melt-crystal interface;
• distributions of the computed variables.

The computations are visualized with the CGSim Viewer program. Besides, it is possible to store a movie on a hard disk, showing the time behavior of the flow pattern.