Application of the proper orthogonal decomposition to turbulent convective flows in a simulated Czochralski system

International Journal of Heat and Mass Transfer

Volumn 51, Issue 17-18, 2008, Pages 4216-4227

  Rahal, S ^a   Cerisier, P ^b   Azuma, H ^c  

^a UNIVERSITY OF BATNA   (Algeria)

^b AIX MARSEILLE UNIVERSITÉ   (France)

^c Osaka Prefecture University   (Japan)

Author keywords

Convection; Czochralski; Orthogonal decomposition; Turbulence; Ultrasound

Indexed keywords

CRYSTAL ORIENTATION; GARNETS; REYNOLDS NUMBER;

CONVECTIVE FLOWS; CRYSTAL ROTATIONS; CZOCHRALSKI (CZ); GENERAL ASPECTS; NEW METHODS; PROPER ORTHOGONAL DECOMPOSITION (POD); REYNOLDS (CO);

HEAT CONVECTION;

EID: 47349113913     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2008.01.021     Document Type: Article

References (38)

1. Prasad V., Zhang H., and Anselmo A.P. Transport phenomena in Czochralski growth process. In: Hartnett J.P., Irvine Jr. T.F., Cho Y.I., and Greene G.A. (Eds). Advances in Heat Transfer vol. 30 (1997), Academic Press 313-435
2. Miller W., Rehse U., and Bottcher K. Melt convection in a Czochralski crucible. Cryst. Res. Technol. 34 4 (1999) 481-489
3. Kalaev V.V., Zhmakin A.I., and Smirnov E.M. Modelling of turbulent melt convection during Czochralski bulk crystal growth. J. Turbulence 3 (2002) 13-24
4. Voigt A., Weichmann C., Nitschkowski J., Dormberger E., and Holz R. Transient and quasi-stationary simulation of heat and mass transfer in Czochralski silicon crystal growth. Cryst. Res. Technol. 38 6 (2003) 499-505
5. Li Y.R., Ruan D.F., Imaishi N., Wu S.Y., Peng L., and Zeng D.L. Global simulation of a silicon Czochralski furnace in an axial magnetic field. Int. J. Heat Mass Transfer 46 15 (2003) 2887-2898
6. Liu L., and Kakimoto K. Partly three-dimensional global modelling of a silicon Cz furnace. I. Principles, formulation and implementation of the model. Int. J. Heat Mass Transfer 48 22 (2005) 4481-4491
7. Hirata A., Okano Y., Yakushiji K., and Harrison B. Czochralski process. In: Mujumdar A.S., and Mashelkar R.A. (Eds). Advances in Transport Processes VIII (1992), Elsevier
8. Kanda T., Hourai M., Miki S., Shigematsu T., Tomokage H., Miyano T., Morita H., and Shintani A. Influence of melt-temperature fluctuations on striation formation in large-scale Czochralski Si growth systems. J. Cryst. Growth 166 (1996) 663-668
9. Eckmann J.P., Oliffson-Kamphorst S., Ruelle D., and Ciliberto S. Liapunov exponents from time series. Phys. Rev. A 34 (1986) 4971-4979
10. Caponeri M., and Ciliberto S. Thermodynamics aspects of the transition to spatiotemporal chaos. Physica D 58 (1992) 365-383
11. Lumley J.L. Coherent structures in turbulence. In: Meyer R.E. (Ed). Transition and Turbulence (1981), Academic Press, New York 215-242
12. Berkooz G., Holmes P., and Lumley J.L. The proper orthogonal decomposition in the analysis of turbulent flow. Ann. Rev. Fluid Mech. 25 (1993) 539-575
13. Broomhead D.S., and King G.P. Extracting qualitative dynamics from experimental data. Physica D 20 (1986) 217-236
14. Aubry N., Holmes P., Lumley J.L., and Stone E. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192 (1988) 115-173
15. Glezer A., Kadioglu Z., and Pearlstein A.J. Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layer. Phys. Fluids A 1 8 (1989) 1363-1373
16. Ciliberto S., and Nicolaenko B. Estimating the number of degrees of freedom in spatially extended systems. Europhys. Lett. 14 4 (1991) 303-308
17. Chauve M.P., and LeGal P. Complex bi-orthogonal decomposition of a chain of coupled wakes. Physica D 58 (1992) 407-413
18. Sirovich L. Empirical eigenfunctions and low dimensional systems. New Perspectives in Turbulence (1991), Springer-Verlag pp. 139-163
19. Sirovich L. Chaotic dynamics of coherent structures. Physica D 37 (1989) 126-145
20. Knight B., and Sirovich L. Kolmogorov inertial range for inhomogeneous turbulent flows. Phys. Rev. Lett. 65 (1990) 1356-1359
21. Moin P., and Moser R. Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200 (1989) 471-509
22. Sirovich L., Ball K.S., and Keefe L.R. Plane waves and structures in turbulent channel flow. Phys. Fluids A 2 12 (1990) 2217-2226
23. Webber G.A., Handler R.A., and Sirovich L. The Karhunen-Loeve decomposition of minimal channel flow. Phys. Fluids 9 4 (1997) 1054-1066
24. Pedersen J., and Meyer K. POD analysis of flow structures in a scale model of a ventilated room. Exp. Fluids 33 6 (2002) 940-949
25. Fogleman M., Lumley J., Rempfer D., and Haworth D. Application of the proper orthogonal decomposition to datasets of internal combustion engine flows. J. Turbulence 5 (2004) 1-18
26. Sirovich L., and Rodriguez J.D. Coherent structures and chaos: a model problem. Phys. Lett. A 120 (1987) 211-214
27. Takeda Y. Development of an ultrasound velocity profile monitor. Nucl. Eng. Des. 126 (1991) 277-284
28. Takeda Y. Velocity profile measurements by ultrasound Doppler shift method. Int. J. Heat Fluid flow 7 (1986) 313-318
29. Brito D., Nataf H.C., Cardin P., Aubert J., and Masson J.P. Ultrasonic Doppler velocimetry in liquid gallium. Exp. Fluids 31 (2001) 653-663
30. Choi J., and Sung H.J. Suppression of temperature oscillation in Czochralski convection by superimposing rotating flows. Int. J. Heat Mass Transfer 40 (1997) 1667-1675
31. Inoue Y., Yamashita S., and Kondo K. The ultrasonic velocity profile measurement of flow structure in the near field of a square free jet. Exp. Fluids 32 (2002) 170-178
32. Daviaud F., Bonetti M., and Dubois M. Transition to turbulence via spatiotemporal intermittency in one-dimensional Rayleigh-Bénard convection. Phys. Rev. A 42 (1990) 3388-3399
33. Yanagita T., and Kaneko K. Rayleigh-Bénard convection patterns, chaos, spatiotemporal chaos and turbulence. Physica D 82 (1995) 288-313
34. Lumley J.L. The structure of inhomogeneous turbulence. In: Yaglom A.M., and Tatarski V.I. (Eds). Atmospheric Turbulence and Wave Propagation (1967), Nauka, Moscow 166-178
35. Peshev P., Nikolov V., and Iliev K. Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth by the TSSG method. J. Cryst. Growth 65 (1983) 173-186
36. Kakimoto K., Eguchi M., Watanabe H., and Hibiya T. Flow instability of molten silicon in the Czochralski configuration. J. Cryst. Growth 102 (1990) 16-20
37. Fontaine J.P., Randriamampianina A., and Bontoux P. Numerical simulation of flow structures and instabilities occurring in a liquid-encapsulated Czochralski process. Phys. Fluids A 3 10 (1991) 2310-2331
38. Schwabe D., and Sumathi R.R. An intermittent transition to chaotic flow by crystal rotation during Czochralski growth. J. Cryst. Growth 275 (2005) 15-19