Types of boundaries for azimuthal velocity

Typically Dirichlet boundary condition is applied for the azimuthal velocity either at the interface melt-crystal or at the interface melt-crucible. The values are entered in Hz. By the calculation the frequency will be recalculated into the linear velocity in the azimuthal direction by multiplication of the frequency with the full circle length.

The Dirichlet values for the azimuthal velocity should be prescribed everywhere in case of the unstructured mesh if the rotation is accounted for. The default boundary condition for the unstructured mesh is no shear stress in azimuthal direction for the azimuthal momentum component.

For the structured mesh and the Czochralski configuration of crystal growth the manual setting of the boundary conditions for the azimuthal velocity can be avoided by the procedure of automatic boundary setup for structured mesh . The corresponding checkbox should be then checked in the Czochralski tab of the Process parameters dialog. Additionally the phase transition should be defined by the generation of the structured mesh. The Dirichlet values of the azimuthal velocity will be set properly everywhere according to the parameters Crystal rotation and Crucible rotation, see dialog fields in the same dialog.

Furthermore, for the shared interface between two fluids, both meshed with the structured mesh, no manual settings for azimuthal velocity are necessary. The total force balance in azimuthal direction is assembled automatically, provided convection is computed in both media. In this case the shear stress in both fluids is balanced. The balance boundary condition is applied for calculation of the boundary value of the azimuthal velocity. The Marangoni effect in the azimuthal direction is not accounted, because of the axial symmetry of the temperature distribution at the free fluid surface within the 2D approach.