2. Numerical Model
2.1. Governing Equations
2.2. Rotating Magnetic Field
3. Results and Discussion
3.1. Effect of Input Parameters on the Melt Flow
3.2. Effect of External RMF on the Melt Flow
3.3. Combined Effect of Seed Rotation and RMF
- Fluid flow in the melt of the TSSG system is mainly the combination of an electromagnetic flow induced by the Lorentz force in the melt body, and Marangoni convection along the melt free surface driven by surface tension gradient.
- Higher coil frequency can reduce the Lorentz force density and enhance the heating temperature.
- Electromagnetic flow can suppress Marangoni convection near the seed. At the higher coil frequency, the downward flow below the seed due to Marangoni convection becomes more pronounced.
- Marangoni convection leads to a non-uniform supersaturation distribution in the melt along the seed surface. The supersaturation profile exhibits a high-low-high pattern from the seed center to its edge.
- An applied RMF can reduce supersaturation below the seed center, and the effect of RMF becomes more significant as the electromagnetic field weakens. When 3400, / is 3.6 or slightly smaller than 3.6 a uniform supersaturation distribution can be achieved; however, when 3400, / should be reduced significantly in order to obtain the desired uniformity.
- When RMF and the seed rotate in the same direction, supersaturation below the seed increases.
Conflicts of Interest
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|Si melt||Density ()||2550||kg m|
|Viscosity ()||8.0||Pa s|
|Electrical conductivity ()||1.2||S m|
|Thermal conductivity (k)||65||W m K|
|Specific heat ()||1.0||J kg K|
|Surface tension coefficient of temperature ()||−2.5||N m K|
|Thermal expansion coefficient ()||1.4||K|
|Graphite||Electrical conductivity ()||7.54||S m|
|Thermal conductivity (k)||108 − 0.0864T + 2.304||W m K|
|Insulator||Electrical conductivity ()||0||S m|
|Thermal conductivity (k)||0.3||W m K|
|Helium||Electrical conductivity ()||0||S m|
|Thermal conductivity (k)||6.35 + 3.1|
|W m K|
|Quartz||Thermal conductivity (k)||1 + 1.25||W m K|
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