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Research Papers

Thermofluid Characteristics of Czochralski Melt Convection Using 3D URANS Computations

[+] Author and Article Information
Sudeep Verma

Solid State Physics Laboratory, DRDO,
Timarpur, Delhi 110054, India;
Department of Applied Mechanics,
Indian Institute of Technology Delhi,
Hauz Khas, New Delhi 110016, India
e-mail: sudeep.verma@sspl.drdo.in

Anupam Dewan

Department of Applied Mechanics,
Indian Institute of Technology Delhi,
Hauz Khas, New Delhi 110016, India
e-mail: adewan@am.iitd.ac.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received February 1, 2019; final manuscript received April 8, 2019; published online May 22, 2019. Assoc. Editor: Sandip Mazumder.

J. Thermal Sci. Eng. Appl 11(6), 061017 (May 22, 2019) (8 pages) Paper No: TSEA-19-1047; doi: 10.1115/1.4043513 History: Received February 01, 2019; Accepted April 10, 2019

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

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References

Ristorcelli, J. R., and Lumley, J. L., 1992, “Instabilities, Transition and Turbulence in the Czochralski Crystal Melt,” J. Cryst. Growth, 116(3–4), pp. 447–460. [CrossRef]
Müller, G., 1993, “Convective Instabilities in Melt Growth Configurations,” J. Cryst. Growth, 128(1–4), pp. 26–36. [CrossRef]
Kobayashi, S., Miyahara, S., Fujiwara, T., Kubo, T., and Fujiwara, H., 1991, “Turbulent Heat Transfer Through the Melt in Silicon Czochralski Growth,” J. Cryst. Growth, 109(1–4), pp. 149–154. [CrossRef]
Lipchin, A., and Brown, R. A., 1999, “Comparison of Three Turbulence Models for Simulation of Melt Convection in Czochralski Crystal Growth of Silicon,” J. Cryst. Growth, 205(1–2), pp. 71–91. [CrossRef]
Jones, W. P., and Launder, B. E., 1972, “The Prediction of Laminarization With a Two-Equation Model of Turbulence,” Int. J. Heat. Mass Transfer, 15(2), pp. 301–314. [CrossRef]
Kalaev, V. V., Evstratov, I. Y., and Makarov, Y. N., 2003, “Gas Flow Effect on Global Heat Transport and Melt Convection in Czochralski Silicon Growth,” J. Cryst. Growth, 249(1–2), pp. 87–99. [CrossRef]
Chien, K., 1982, “Predictions of Channel and Boundary-Layer Flows With a Low-Reynolds-Number Turbulence Model,” AIAA J., 20(1), pp. 33–38. [CrossRef]
Krauze, A., Muižnieks, A., Mühlbauer, A., Wetzel, T., and Ammon, W. V., 2004, “Numerical 3D Modelling of Turbulent Melt Flow in Large CZ System With Horizontal DC Magnetic Field—I: Flow Structure Analysis,” J. Cryst. Growth, 262(1–4), pp. 157–167. [CrossRef]
Son, S., Nam, P., and Yi, K., 2006, “The Effect of Crystal Rotation Direction on the Thermal and Velocity Fields of a Czochralski System With a Low Prandtl Number Melt,” J. Cryst. Growth, 292(2), pp. 272–281. [CrossRef]
Nam, P., Sang-Kun, O., and Yi, K., 2008, “3-D Time-Dependent Numerical Model of Flow Patterns Within a Large-Scale Czochralski System,” J. Cryst. Growth, 310(7), pp. 2126–2133. [CrossRef]
Nam, P., and Yi, K., 2010, “Simulation of the Thermal Fluctuation According to the Melt Height in a CZ Growth System,” J. Cryst. Growth, 312(8), pp. 1453–1457. [CrossRef]
Zhou, X., and Huang, H., 2012, “Numerical Simulation of Cz Crystal Growth in Rotating Magnetic Field With Crystal and Crucible Rotations,” J. Cryst. Growth, 340(1), pp. 166–170. [CrossRef]
Liu, X., Liu, L., Li, Z., and Wang, Y., 2012, “Effects of Cusp-Shaped Magnetic Field on Melt Convection and Oxygen Transport in an Industrial CZ-Si Crystal Growth,” J. Cryst. Growth, 354(1), pp. 101–108. [CrossRef]
Fang, H. S., Jin, Z. L., and Huang, X. M., 2012, “Study and Optimization of Gas Flow and Temperature Distribution in a Czochralski Configuration,” J. Cryst. Growth, 361, pp. 114–120. [CrossRef]
Verma, S., and Dewan, A., 2014, “Solidification Modeling: Evolution, Benchmarks, Trends in Handling Turbulence and Future Directions,” Metall. Mater. Trans. B, 45(4), pp. 1456–1471. [CrossRef]
Menter, F. R., 1994, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Menter, F. R., Kuntz, M., and Langtry, R., 2003, “Ten Years of Industrial Experience With the SST Turbulence Model,” Turbulence, Heat and Mas Transfer 4, K. Hanjalic, Y. Nagano and M. Tummers, eds., Begell House, Inc., pp. 625–632.
Launder, B. E., and Sharma, B. I., 1974, “Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc,” Lett. Heat Mass Transfer, 1(2), pp. 131–138. [CrossRef]
Raufeisen, A., Breuer, M., Botsch, T., and Delgado, A., 2008, “DNS of Rotating Buoyancy- and Surface Tension-Driven Flow,” Int. J. Heat Mass Transfer, 51(25–26), pp. 6219–6234. [CrossRef]
Raufeisen, A., Breuer, M., Botsch, T., and Delgado, A., 2009, “LES Validation of Turbulent Rotating Buoyancy- and Surface Tension-Driven Flow Against DNS,” Comput. Fluids, 38(8), pp. 1549–1565. [CrossRef]
Spalart, P. R., and Shur, M., 1997, “On the Sensitization of Turbulence Models to Rotation and Curvature,” Aerosp. Sci. Technol., 5(5), pp. 297–302. [CrossRef]
Gräbner, O., Müller, G., Virbulis, J., Tomzig, E., and Ammon, W. V., 2001, “Effects of Various Magnetic Field Configurations on Temperature Distributions in Czochralski Silicon Melts,” Microelectron. Eng., 56(1–2), pp. 83–88. [CrossRef]
Basu, B., Enger, S., Breuer, M., and Durst, F., 2000, “Three-Dimensional Simulation of Flow and Thermal Field in a Czochralski Melt Using a Block-Structured Finite-Volume Method”, J. Cryst. Growth, 219(1–2), 123–143. [CrossRef]
Wagner, C., and Friedrich, R., 2004, “Direct Numerical Simulation of Momentum and Heat Transport in Idealized Czochralski Crystal Growth Configurations,” Int. J. Heat Fluid Flow, 25(3), pp. 431–443. [CrossRef]
Atia, A., Ghernaout, B., Bouabdallah, S., and Bessaa, R., 2016, “Three-Dimensional Oscillatory Mixed Convection in a Czochralski Silicon Melt Under the Axial Magnetic Field,” Appl. Therm. Eng., 105, pp. 704–715. [CrossRef]
Geers, L. F. G., Tummers, M. J., and Hanjali, K., 2005, “Particle Imaging Velocimetry-Based Identification of Coherent Structures in Normally Impinging Multiple Jets,” Phys. Fluids, 17(5), pp. 1–13. [CrossRef]

Figures

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Fig. 1

A schematic of computational setup (all dimensions are in millimeters)

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Fig. 2

(a) Blocks used in the computational domain and (b) grid topology

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Fig. 3

Results of grid sensitivity study: comparison of mean temperature (K) at r = 0.024 m

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Fig. 4

Distribution of mean temperature (K) along a vertical cross section of the computational domain computed using (a) low-Re k-ε model and (b) SST k-ω model (left side represents crucible axis and right side represents crucible wall)

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Fig. 5

Variation of mean temperature along the melt free surface computed using (a) low-Re k-ε model and (b) SST k-ω model

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Fig. 6

Instantaneous velocity distribution along a vertical cross-sectional plane of the computational domain computed using (a) low-Re k-ε model and (b) SST k-ω model (arrows depict characteristics flow cells in Czochralski melt flow with left and right sides representing the crucible axis and crucible wall, respectively)

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Fig. 7

Isosurface of Q-criterion (value = 0.2) of the computational domain computed using (a) low-Re k-ε model and (b) SST k-ω model (legend represents the distance along vertical (z) direction in meters)

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Fig. 8

Turbulent eddy viscosity (kg/m s) distribution in the melt of the computational domain computed using (a) low-Re k-ε model and (b) SST k-ω model (left side represents crucible axis and right side represents crucible wall)

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Fig. 9

Vortex cores distribution in the melt of the computational domain computed using (a) low-Re k-ε model and (b) SST k-ω model

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