LES validation of turbulent rotating buoyancy- and surface tension-driven flow against DNS

Computers and Fluids

Volumn 38, Issue 8, 2009, Pages 1549-1565

  Raufeisen, A ^a,b   Breuer, M ^c   Botsch, T ^a   Delgado, A ^b  

^a NUREMBERG INSTITUTE OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^c HELMUT SCHMIDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; HEAT TRANSFER; LARGE EDDY SIMULATION; MASS TRANSFER; NUMERICAL METHODS;

DISCRETIZATION SCHEME; FILTERED NAVIER-STOKES EQUATIONS; FINITE VOLUME SCHEMES; FLOW AND HEAT TRANSFER; QUALITATIVE DIFFERENCES; SECOND-ORDER ACCURACY; SUB-GRID SCALE MODELS; SURFACE-TENSION-DRIVEN FLOW;

NAVIER STOKES EQUATIONS;

EID: 67349120244     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2009.01.002     Document Type: Article

References (90)

1. Basu B., Enger S., Breuer M., and Durst F. Three-dimensional simulation of flow and thermal field in a Czochralski melt using a block-structured finite-volume method. J Cryst Growth 219 (2000) 123-143
2. Beaudan P, Moin P. Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number. Technical Report TF-62, Stanford University, 1994.
3. Ben Hadid H., and Roux B. Buoyancy- and thermocapillary-driven flows in differentially heated cavities for low-Prandtl-number fluids. J Fluid Mech 235 (1992) 1-36
4. Binninger B. Untersuchungen von Modellströmungen in Zylindern von Kolbenmotoren. PhD thesis, Aerodynamisches Institut, RWTH Aachen, 1989.
5. Bénard H. Les tourbillons cellulaires dans une nappe liquide. Deuxiéme partie: procédé mécaniques et optiques d'examen Lois numériques des phénoménes. Rev Gén Sci Pure Appl 12 (1900) 1309-1328
6. Bénard H. Les tourbillons cellulaires dans une nappe liquide. Premiére partie: description générale des phénoménes. Rev Gén Sci Pure Appl 12 (1900) 1261-1271
7. Boeck T, Bénard-Marangoni convection at low Prandtl numbers. PhD thesis, Technical University Ilmenau, Shaker Verlag, Aachen, 2000.
8. Bottaro A., and Zebib A. Three-dimensional thermal convection in Czochralski melt. J Cryst Growth 97 (1989) 50-58
9. Breuer M. Large-eddy simulation of the sub-critical flow past a circular cylinder: numerical and modeling aspects. Int J Numer Meth Fluids 28 (1998) 1281-1302
10. Breuer M. A challenging test case for large-eddy simulation: high Reynolds number circular cylinder flow. Int J Heat Fluid Flow 21 5 (2000) 648-654
11. Breuer M. Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Strömungen auf Hochleistungsrechnern. Habilitationsschrift, Universität Erlangen-Nürnberg, Berichte aus der Strömungstechnik, ISBN 3-8265-9958-6. Shaker Verlag, Aachen, 2002.
12. Breuer M., and Rodi W. Large-eddy simulation of complex turbulent flows of practical interest. In: Hirschel E.H. (Ed). Flow simulation with high-performance computers II. Notes on Numer Fluid Mech vol. 52 (1996), Vieweg, Braunchweig 258-274
13. Brown R.A. Theory of transport processes in single crystal growth from the melt. AIChE J 34 (1988) 881-910
14. Butcher J.C. On the attainable order of Runge-Kutta methods. Math Comp 19 (1965) 408-417
15. Chandrasekhar S. Hydrodynamic and hydromagnetic stability (1961), Oxford University Press, Oxford
16. Cioni S., Ciliberto S., and Sommeria J. Strongly turbulent Rayleigh-Bénard convection in mercury: comparison with results at moderate Prandtl number. J Fluid Mech 335 (1997) 111-140
17. Clever R.M., and Busse F.H. Transition to time-dependent convection. J Fluid Mech 65 (1974) 625-645
18. Clever R.M., and Busse F.H. Convection at very low Prandtl numbers. Phys Fluids A 2 (1990) 334-339
19. Cross M.C., and Hohenberg P.C. Pattern formation outside of equilibrium. Rev Mod Phys 65 3 (1993) 851-1112
20. Davis S.H. Thermocapillary instabilities. Ann Rev Fluid Mech 19 (1987) 403-435
21. Deardorff J.W. On the magnitude of the subgrid scale eddy coefficient. J Comput Phys 7 (1971) 120-133
22. Drazin P.G., and Reid W.H. Hydrodynamic stability (1981), Cambridge University Press
23. Eckert K., Bestehorn M., and Thess A. Square cells in surface-tension-driven Bénard convection: experiment and theory. J Fluid Mech 358 (1998) 149-197
24. Enger S. Numerical simulation of flow and heat transfer in Czochralski crucibles. PhD thesis, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, 2001.
25. Enger S., Gräbner O., Müller G., Breuer M., and Durst F. Comparison of measurements and numerical simulations of melt convection in Czochralski crystal growth of silicon. J Cryst Growth 230 (2001) 135-142
26. Evstratov I.Yu., Kalaev V.V., Zhmakin A.I., Makarov Yu.N., Abramov A.G., Ivanov N.G., et al. Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of Si crystals. J Cryst Growth 230 (2001) 22-29
27. Ferziger J.H., and Perić M. Computational methods for fluid dynamics. 3rd ed. (2002), Springer, Berlin
28. 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 (1991) 2310-2331
29. Germano M. Turbulence: the filtering approach. J Fluid Mech 238 (1992) 325-336
30. Germano M., Piomelli U., Moin P., and Cabot W.H. A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3 (1991) 1760-1765
31. Getling A.V. Rayleigh-Bénard convection (1998), World Scientific, Singapore
32. Glazier J.A., Segawa T., Naert A., and Sano M. Evidence against 'ultrahard' thermal turbulence at very high Rayleigh numbers. Nature 398 (1999) 307-310
33. Gräbner O., Müller G., Virbulis J., and Tomzig E. Effects of various magnetic field configurations on temperature distributions in Czochralski silicon melts. Micro Eng 56 (2001) 83-88
34. Grossmann S., and Lohse D. Scaling in thermal convection: a unifying theory. J Fluid Mech 407 (2000) 27-56
35. Hashim I., and Wilson S.K. The onset of Bénard-Marangoni convection in a horizontal layer of fluid. Int J Eng Sci 37 (1999) 643-662
36. Ivanov N.G., Korsakov A.B., Smirnov E.M., Khodosevitch K.V., Kalaev V.V., Makarov Y.N., et al. Analysis of magnetic field effect on 3D melt flow in CZ Si growth. J Cryst Growth 250 (2003) 183-188
37. Jou J.J., Kung K.Y., and Hsu C.H. Effects of Coriolis force and surface tension on Bénard-Marangoni convective instability. Int J Heat Mass Transfer 40 (1997) 1447-1458
38. Julien K., Legg S., McWilliams J., and Werne J. Hard turbulence in rotating Rayleigh-Bénard convection. Phys Rev E 53 (1996) R5557-R5560
39. Julien K., Legg S., McWilliams J., and Werne J. Rapidly rotating turbulent Rayleigh-Bénard convection. J Fluid Mech 322 (1996) 243-273
40. Kakimoto K. Flow instability during crystal growth from the melt. Prog Cryst Growth Ch 30 (1995) 191-215
41. Kalaev V.V., Evstratov I.Y., and Makarov Y.N. Gas flow effect on global heat transport and melt convection in Czochralski silicon growth. J Cryst Growth 249 (2003) 87-99
42. Kalaev V.V., Lukanin D.P., Zabelin V.A., Makarov Y.N., Virbulis J., Dornberger E., et al. Calculation of bulk defects in CZ Si growth: impact of melt turbulent fluctuations. J Cryst Growth 250 (2003) 203-208
43. Kays W.M. Turbulent Prandtl number - where are we?. J Heat Transfer 116 (1994) 284-295
44. Kek V., and Müller U. Low Prandtl number convection in layers heated from below. Int J Heat Mass Transfer 36 (1993) 2795-2804
45. Kerr R.M., and Herring J.R. Prandtl number dependence of Nusselt number in direct numerical simulations. J Fluid Mech 419 (2000) 325-344
46. Kishida Y., and Okazawa K. Geostrophic turbulence in CZ silicon crucible. J Cryst Growth 198/199 (1999) 135-140
47. Kishida Y., Tamaki T., Okazawa K., and Ohashi W. Geostrophic turbulence in CZ silicon melt under CUSP magnetic field. J Cryst Growth 273 (2005) 329-339
48. Koschmieder E.L. Bénard cells and Taylor vortices. 1st ed. Cambridge monographs on mechanics and applied mathematics (1993), Cambridge University Press
49. Krauze A., Muižnieks A., Mühlbauer A., Wetzel Th., and von Ammon W. Numerical 3D modelling of turbulent melt flow in large CZ system with horizontal DC magnetic field I: flow structure analysis. J Cryst Growth 262 (2004) 57-167
50. Kravchenko A.G., and Moin P. On the effect of numerical errors in large-eddy simulations of turbulent flows. J Comput Phys 131 (1997) 310-322
51. Krishnamurthi R. Some further studies on the transition to turbulent convection. J Fluid Mech 60 (1973) 285-303
52. Kumar V., Basu B., Enger S., Brenner G., and Durst F. Role of Marangoni convection in Si-Czochralski melts-part I: 3D predictions without crystal. J Cryst Growth 253 (2003) 142-154
53. Kumar V., Basu B., Enger S., Brenner G., and Durst F. Role of Marangoni convection in Si-Czochralski melts-part II: 3D predictions with crystal rotation. J Cryst Growth 255 (2003) 27-39
54. Lamprecht R., Schwabe D., Scharmann A., and Schutheiss E. Experiments on buoyant thermocapillary and forced convection in Czochralski configuration. J Cryst Growth 65 (1983) 143-152
55. Lilly D.K. A proposed modification of the Germano subgrid-scale closure method. Phys Fluids A 4 (1992) 633-635
56. Lipchin A., and Brown R.A. Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon. J Cryst Growth 205 (1999) 71-91
57. Lukanin D.P., Kalaev V.V., Makarov Yu.N., Wetzel T., Virbulis J., and von Ammon W. Advances in the simulation of heat transfer and prediction of the melt-crystal interface shape in silicon CZ growth. J Cryst Growth 266 (2004) 20-27
58. Müller G. Convective instabilities in melt growth configurations. J Cryst Growth 128 (1993) 26-36
59. Paul M.R., Chiam K.H., Cross M.C., Fischer P.F., and Greenside H.S. Pattern formation and dynamics in Rayleigh-Bénard convection: numerical simulations of experimentally realistic geometries. Physica D 184 (2003) 114-126
60. Piomelli U, Ferziger JH, Moin P. Models for large-eddy simulations of turbulent channel flows including transpiration. Technical Report TF-32, Dept. of Mech. Eng., Stanford University, 1987.
61. Poncet S., and Schiestel R. Numerical modeling of heat transfer and fluid flow in rotor-stator cavities with throughflow. Int J Heat Mass Transfer 50 (2007) 1528-1544
62. Pulicani J.P., Crespo del Arco E., Randriamampianina A., Bontoux P., and Peyret R. Spectral simulations of oscillatory convection at low Prandtl number. Int J Numer Meth Fluids 10 (1990) 481-517
63. Rahal S., Cerisier P., and Azuma H. Application of the proper orthogonal decomposition to turbulent convective flows in a simulated Czochralski system. Int J Heat Mass Transfer 51 (2008) 4216-4227
64. Raufeisen A., Breuer M., Botsch T., and Delgado A. DNS of rotating buoyancy- and surface tension-driven flow. Int J Heat Mass Transfer 51 (2008) 6219-6234
65. Rayleigh L. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Philos Mag (1916) 519-546
66. Rhie C.M., and Chow W.L. A numerical study of the turbulent flow past an isolated airfoil with trailing-edge separation. AIAA J 21 (1983) 1525-1532
67. Ristorcelli J.R., and Lumley J.L. Instabilities transition and turbulence in the Czochralski crystal melt. J Cryst Growth 116 (1992) 447-460
68. Ristorcelli J.R., and Lumley J.L. A second-order turbulence simulation of the Czochralski crystal growth melt: the buoyantly driven flow. J Cryst Growth 129 (1993) 249-265
69. Rossby H.T. A study of Bénard convection with and without rotation. J Fluid Mech 36 (1969) 309-335
70. Schäfer F., Kumar V., Breuer M., and Durst F. Visualization and computational steering of fluid motion in Czochralski crucibles during silicon crystal growth. Int J Comput Fluid Dyn 19 7 (2005) 501-515
71. Scheel J.D., and Cross M.C. Scaling laws for rotating Rayleigh-Bénard convection. Phys Rev E 72 5 (2005) 1-10
72. Siggia E.D. High Rayleigh number convection. Ann Rev Fluid Mech 26 (1994) 137-168
73. Smagorinsky J. General circulation experiments with the primitive equations, I: the basic experiment. Mon Weather Rev 91 (1963) 99-165
74. Smirnova O.V., and Kalaev V.V. 3D unsteady numerical analysis of conjugate heat transport and turbulent/laminar flows in LEC growth of GaAs crystals. Int J Heat Mass Transfer 47 (2004) 363-371
75. Stone H.L. Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J Numer Anal 5 530-558 (1968) 530-558
76. Takeshita T., Segawa T., Glazier J.A., and Sano M. Thermal turbulence in mercury. Phys Rev Lett 76 (1996) 1465-1468
77. Tanaka M., Hasebe M., and Saito N. Pattern transition of temperature distribution at Czochralski silicon melt surface. J Cryst Growth 180 (1997) 487-496
78. Thual O. Zero-Prandtl-number convection. J Fluid Mech 240 (1992) 229-258
79. Tucker P.G., Rumsey C.L., Spalart P.R., Bartels R.E., and Biedron R.T. Computations of wall distances based on differential equations. AIAA J 43 (2005) 539-549
80. van Driest E.R. On turbulent flow near a wall. J Aeronaut Sci 23 (1956) 1007-1011
81. Verzicco R., and Camussi R. Transitional regimes of low-Prandtl thermal convection in a cylindrical cell. Phys Fluids 9 (1997) 1287-1295
82. Verzicco R., and Camussi R. Prandtl number effects in convective turbulence. J Fluid Mech 383 (1999) 55-73
83. Vizman D., Gräbner O., and Müller G. Three-dimensional numerical simulation of thermal convection in an industrial Czochralski melt: comparison to experimental results. J Cryst Growth 233 (2001) 687-698
84. Wagner C. Turbulente Transportvorgänge in idealisierten Czochralski-Kristallzüchtungsanordnungen. Habilitationsschrift. Lehrstuhl für Fluidmechanik, Technische Universität München, 2003.
85. Wagner C., and Friedrich R. Direct numerical simulation of momentum and heat transport in idealized Czochralski crystal growth configurations. Int J Heat Fluid Flow 25 (2004) 431-443
86. Watanabe M., Vizman D., Friedrich J., and Müller G. Large modification of crystal-melt interface shape during Si crystal growth by using electromagnetic Czochralski method (EMCZ). J Cryst Growth 292 (2006) 252-256
87. Wetzel Th., Muižnieks A., Mühlbauer A., Gelfgat Y., Gorbunov L., Virbulis J., et al. Numerical model of turbulent CZ melt flow in the presence of AC and CUSP magnetic fields and its verification in a laboratory facility. J Cryst Growth 230 (2001) 81-89
88. Wu X., Kakimoto K., Ozoe H., and Guo Z. Numerical study of natural convection in Czochralski crystallization. Chem Eng J 71 (1998) 183-189
89. Yi K.W., Kakimoto K., Eguchi M., Watanabe M., Shyo T., and Hibiya T. Spoke patterns on molten silicon in Czochralski system. J Cryst Growth 144 (1994) 20-28
90. Zhu J. A low-diffusive and oscillation-free convection scheme. Commun Appl Numer Meth 7 (1991) 225-232