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Numerical analysis of thermohydraulic behavior in a directional solidification furnace

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In this study, the crystallization process in a directional solidification furnace is studied by using the transient numerical simulation. The flow field in melt silicon in conjunction with different solidification stages is investigated. A separated side-heater design is proposed, showing a pronounced improvement on temperature gradient in axial direction normal to the solidification interface at late period. Result shows that the Voronkov ratio which can reflect the crystal quality is reduced by 16.5–24.8% and the energy consumption can be saved by 6% simultaneously. On the other hand, the airflow management for argon gas in the crucible chamber, which contains advantage to reduce chemical impurity in crystal during solidification process, is also numerically studied. By installing a guiding plate beneath the graphite cover can appreciably lower the oxygen mass fraction in contact with the cover plate and reduce the potential chemical reaction accordingly. The plate diameter and the spacing between the plate and graphite cover are optimized. Compared to the original design, the oxygen mass fraction at the graphite cover can be pronouncedly reduced by 10.6–33.3%, which can be further improved by combining a corner outlet configuration. Meanwhile, under the same volumetric flow rate of argon gas, yet the argon gas could be saved by almost half (e.g., from 40 SLM to 20 SLM) for the same chemical concentration with the optimized configuration.

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C :

Oxygen concentration, m3 m−3

c p :

Specific heat capacity, J kg−1 K−1

D b :

Diameter of guiding plate, mm

D L :

Concentration diffusivity, dimensionless

G cr :

Crystal thermal gradient, K mm−1

g :

Gravity, m s−2

H b :

Spacing between guiding plate and graphite cover, mm

K :

Isothermal crystallization rate

k :

Conductivity, W m−1 K−1

p :

Pressure, Pa

T :

Temperature, K

t :

Time, s

\(\vec{V}\) :

Velocity vector, m s−1

V cr :

Crystallization rate, mm min−1

α cv :

Oxygen mass fraction in crucible volume

α gc :

Oxygen mass fraction at graphite cover

μ :

Viscosity, Pa s

ρ :

Density, kg m−3

σ :



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The author would like to thank for the support from the Ministry of Science and Technology of Taiwan, under contract under Contract Number 108-2221-E-009-058-MY3.

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Correspondence to Chi-Chuan Wang.

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Chu, W., Yang, C. & Wang, C. Numerical analysis of thermohydraulic behavior in a directional solidification furnace. J Therm Anal Calorim (2020). https://doi.org/10.1007/s10973-020-09417-0

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  • Directional solidification
  • Numerical simulation
  • Separated heater
  • Airflow management