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Volumn 154, Issue 2, 1999, Pages 468-496

Modeling Melt Convection in Phase-Field Simulations of Solidification

Author keywords

Coarsening; Convection; Dendritic growth; Phase field method

Indexed keywords

BINARY ALLOYS; PHASE INTERFACES; SOLIDIFICATION;

EID: 0002500769     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6323     Document Type: Article
Times cited : (638)

References (46)
  • 1
    • 36849120852 scopus 로고
    • Stability of a planar interface during solidification of a dilute binary alloy
    • W. W. Mullins and R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35, 444 (1964).
    • (1964) J. Appl. Phys. , vol.35 , pp. 444
    • Mullins, W.W.1    Sekerka, R.F.2
  • 2
    • 0002988332 scopus 로고    scopus 로고
    • Effects of buoyancy on the growth of dendritic crystals
    • edited by C. L. Tien Begell House, New York
    • Y.-W. Lee, R. N. Smith, M. E. Glicksman, and M. B. Koss, Effects of buoyancy on the growth of dendritic crystals, in Annual Review of Heat Transfer, edited by C. L. Tien (Begell House, New York, 1996), Vol. 7, p. 59.
    • (1996) Annual Review of Heat Transfer , vol.7 , pp. 59
    • Lee, Y.-W.1    Smith, R.N.2    Glicksman, M.E.3    Koss, M.B.4
  • 3
    • 33646109512 scopus 로고
    • The kinetics of precipitation from supersaturated solid solutions
    • M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19, 35 (1961).
    • (1961) J. Phys. Chem. Solids , vol.19 , pp. 35
    • Lifshitz, M.1    Slyozov, V.V.2
  • 4
    • 0001333772 scopus 로고
    • Theorie der Aeterung von Niederschlägen durch Umlösen (Ostwald-Reifung)
    • C. Wagner, Theorie der Aeterung von Niederschlägen durch Umlösen (Ostwald-Reifung), Z. Elektrochem. 65, 581 (1961).
    • (1961) Z. Elektrochem. , vol.65 , pp. 581
    • Wagner, C.1
  • 6
    • 49149147520 scopus 로고
    • Effect of gravity on coupled convective and interfacial instabilities during directional solidification
    • S. R. Coriell, M. R. Cordes, W. J. Boettinger, and R. F. Sekerka, Effect of gravity on coupled convective and interfacial instabilities during directional solidification, J. Cryst. Growth 49, 13 (1980).
    • (1980) J. Cryst. Growth , vol.49 , pp. 13
    • Coriell, S.R.1    Cordes, M.R.2    Boettinger, W.J.3    Sekerka, R.F.4
  • 7
    • 0025403598 scopus 로고
    • Hydrodynamic interactions in directional solidification
    • S. H. Davis, Hydrodynamic interactions in directional solidification, J. Fluid Mech. 212, 241 (1990).
    • (1990) J. Fluid Mech. , vol.212 , pp. 241
    • Davis, S.H.1
  • 8
    • 0024766059 scopus 로고
    • Dendritic growth of an elliptical paraboloid with forced convection in the melt
    • R. Ananth and W. W. Gill, Dendritic growth of an elliptical paraboloid with forced convection in the melt, J. Fluid Mech. 208, 575 (1989).
    • (1989) J. Fluid Mech. , vol.208 , pp. 575
    • Ananth, R.1    Gill, W.W.2
  • 9
    • 0028384851 scopus 로고
    • Dendritic growth from a melt in an external flow: Uniformly valid asymptotic solution for the steady state
    • J. J. Xu, Dendritic growth from a melt in an external flow: Uniformly valid asymptotic solution for the steady state, J. Fluid Mech. 263, 227 (1994).
    • (1994) J. Fluid Mech. , vol.263 , pp. 227
    • Xu, J.J.1
  • 10
    • 0006237048 scopus 로고    scopus 로고
    • A phase-field method for alloy solidification with convection
    • edited by J. Beech and H. Jones University of Sheffield, UK
    • H.-J. Diepers, C. Beckermann, and I. Steinbach, A phase-field method for alloy solidification with convection, in Solidification Processing 1997, edited by J. Beech and H. Jones (University of Sheffield, UK, 1997), p. 426.
    • (1997) Solidification Processing 1997 , pp. 426
    • Diepers, H.-J.1    Beckermann, C.2    Steinbach, I.3
  • 11
    • 0002071520 scopus 로고
    • Surface tension and supercooling in solidification theory
    • edited by L. Garrido Springer-Verlag, Berlin
    • G. Caginalp, Surface tension and supercooling in solidification theory, in Applications of Field Theory to Statistical Mechanics, edited by L. Garrido (Springer-Verlag, Berlin, 1985), p. 216.
    • (1985) Applications of Field Theory to Statistical Mechanics , pp. 216
    • Caginalp, G.1
  • 12
    • 35949007087 scopus 로고
    • Phase-field model for isothermal phase transitions in binary alloys
    • A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phase-field model for isothermal phase transitions in binary alloys, Phys. Rev. A 45, 7424 (1992).
    • (1992) Phys. Rev. A , vol.45 , pp. 7424
    • Wheeler, A.A.1    Boettinger, W.J.2    McFadden, G.B.3
  • 13
    • 34249817369 scopus 로고
    • Modeling and numerical simulations of dendritic crystal growth
    • R. Kobayashi, Modeling and numerical simulations of dendritic crystal growth, Phys. D 63, 410 (1993).
    • (1993) Phys. D , vol.63 , pp. 410
    • Kobayashi, R.1
  • 14
    • 4243643071 scopus 로고    scopus 로고
    • Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics
    • A. Karma and W.-J. Rappel, Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics, Phys. Rev. E 53, 3017 (1996).
    • (1996) Phys. Rev. E , vol.53 , pp. 3017
    • Karma, A.1    Rappel, W.-J.2
  • 15
    • 84998655143 scopus 로고
    • Development of a grid-supported marked particle scheme for interface tracking
    • Orlando, FL, AIAA-93-3384
    • H. S. Udaykumar and W. Shyy, Development of a grid-supported marked particle scheme for interface tracking, in 11th AIAA Comp. Fluid. Dyn. Conf. (Orlando, FL, 1993), AIAA-93-3384.
    • (1993) 11th AIAA Comp. Fluid. Dyn. Conf.
    • Udaykumar, H.S.1    Shyy, W.2
  • 16
    • 0029684784 scopus 로고    scopus 로고
    • A front-tracking method for dendritic solidification
    • D. Juric and G. Tryggvason, A front-tracking method for dendritic solidification, J. Comput. Phys. 123, 127 (1996).
    • (1996) J. Comput. Phys. , vol.123 , pp. 127
    • Juric, D.1    Tryggvason, G.2
  • 17
    • 0000655661 scopus 로고
    • Crystal growth and dendritic solidification
    • J. A. Sethian and J. Strain, Crystal growth and dendritic solidification, J. Comput. Phys. 98, 231 (1992).
    • (1992) J. Comput. Phys. , vol.98 , pp. 231
    • Sethian, J.A.1    Strain, J.2
  • 18
    • 4243428358 scopus 로고
    • Thermodynamically-consistent phase-field models for solidification
    • S. L. Wang et al., Thermodynamically-consistent phase-field models for solidification, Phys. D 69, 189 (1993).
    • (1993) Phys. D , vol.69 , pp. 189
    • Wang, S.L.1
  • 19
    • 85088356757 scopus 로고    scopus 로고
    • An energy approach to the continuum surface tension method
    • Reno, NV, AIAA-96-0858
    • D. Jacqmin, An energy approach to the continuum surface tension method, in 34th AIAA Aerospace Sciences Meeting & Exhibit (Reno, NV, 1996), AIAA-96-0858.
    • (1996) 34th AIAA Aerospace Sciences Meeting & Exhibit
    • Jacqmin, D.1
  • 20
    • 4243457001 scopus 로고    scopus 로고
    • Quantitative phase-field modeling of dendritic growth in two and three dimensions
    • A. Karma and W.-J. Rappel, Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys. Rev. E 57, 4323 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 4323
    • Karma, A.1    Rappel, W.-J.2
  • 21
    • 28144462923 scopus 로고
    • A continuum method for modeling surface tension
    • J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
    • (1992) J. Comput. Phys. , vol.100 , pp. 335
    • Brackbill, J.U.1    Kothe, D.B.2    Zemach, C.3
  • 22
    • 37249006592 scopus 로고
    • General conservation equations for multi-phase systems. I. Averaging procedure
    • M. Hassanizadeh and W. G. Gray, General conservation equations for multi-phase systems. I. Averaging procedure, Adv. Water Resources 2, 131 (1979).
    • (1979) Adv. Water Resources , vol.2 , pp. 131
    • Hassanizadeh, M.1    Gray, W.G.2
  • 23
    • 0020547432 scopus 로고
    • Mathematical modeling of two-phase flow
    • D. A. Drew, Mathematical modeling of two-phase flow, Ann. Rev. Fluid Mech. 15, 261 (1983).
    • (1983) Ann. Rev. Fluid Mech. , vol.15 , pp. 261
    • Drew, D.A.1
  • 24
    • 51249172169 scopus 로고
    • A volume-averaged two-phase model for transport phenomena during solidification
    • J. Ni and C. B eckermann, A volume-averaged two-phase model for transport phenomena during solidification, Metall. Trans. B 22, 349 (1991).
    • (1991) Metall. Trans. B , vol.22 , pp. 349
    • Ni, J.1    Eckermann, C.B.2
  • 25
    • 3042989856 scopus 로고
    • A molecular theory for the solid-liquid interface
    • D. J. Haymet and D. W. Octoby, A molecular theory for the solid-liquid interface, J. Chem. Phys. 74, 2559 (1981).
    • (1981) J. Chem. Phys. , vol.74 , pp. 2559
    • Haymet, D.J.1    Octoby, D.W.2
  • 26
    • 0001832671 scopus 로고    scopus 로고
    • The multiphase-field model with an integrated concept for modelling solute diffusion
    • J. Tiaden, B. Nestler, H. J. Diepers, and I. Steinbach, The multiphase-field model with an integrated concept for modelling solute diffusion, Phys. D 115, 73 (1998).
    • (1998) Phys. D , vol.115 , pp. 73
    • Tiaden, J.1    Nestler, B.2    Diepers, H.J.3    Steinbach, I.4
  • 27
    • 33645061081 scopus 로고
    • Phase-field model of solute trapping during solidification
    • A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phase-field model of solute trapping during solidification, Phys. Rev. E 47, 1893 (1993).
    • (1993) Phys. Rev. E , vol.47 , pp. 1893
    • Wheeler, A.1    Boettinger, W.J.2    McFadden, G.B.3
  • 28
    • 0001299959 scopus 로고
    • Phase-field and sharp-interface alloy models
    • G. Caginalp and W. Xie, Phase-field and sharp-interface alloy models, Phys. Rev. E 48, 1897 (1993).
    • (1993) Phys. Rev. E , vol.48 , pp. 1897
    • Caginalp, G.1    Xie, W.2
  • 29
    • 33746012315 scopus 로고
    • Free energy of nonuniform systems. I. Interface free energy
    • J. W. Cahn and J. E. Hilliard, Free energy of nonuniform systems. I. Interface free energy, J. Chem. Phys. 28, 258 (1958).
    • (1958) J. Chem. Phys. , vol.28 , pp. 258
    • Cahn, J.W.1    Hilliard, J.E.2
  • 31
    • 85190302351 scopus 로고    scopus 로고
    • unpublished notes
    • A. Karma, unpublished notes.
    • Karma, A.1
  • 32
    • 0012335753 scopus 로고
    • Velocity selection and instability spectrum in 3D dendritic growth
    • E. Brener and V. I. Melnikov, Velocity selection and instability spectrum in 3D dendritic growth, J. Exp. Theoret. Phys. 80, 341 (1995).
    • (1995) J. Exp. Theoret. Phys. , vol.80 , pp. 341
    • Brener, E.1    Melnikov, V.I.2
  • 33
    • 0020169176 scopus 로고
    • Slow flow through a periodic array of spheres
    • A. S. Sangani and A. Acrivos, Slow flow through a periodic array of spheres, Int. J. Multiphase Flow 8, 343 (1982).
    • (1982) Int. J. Multiphase Flow , vol.8 , pp. 343
    • Sangani, A.S.1    Acrivos, A.2
  • 34
    • 0021219457 scopus 로고
    • Laminar viscous flow through regular arrays of parallel solid cylinders
    • J. E. Drummond and M. I. Tahir, Laminar viscous flow through regular arrays of parallel solid cylinders, Int. J. Multiphase Flow 10, 515 (1984).
    • (1984) Int. J. Multiphase Flow , vol.10 , pp. 515
    • Drummond, J.E.1    Tahir, M.I.2
  • 36
    • 0001074012 scopus 로고
    • Dynamics of late stage phase separations in two dimensions
    • J. A. Marqusee, Dynamics of late stage phase separations in two dimensions, J. Chem. Phys. 81, 976 (1984).
    • (1984) J. Chem. Phys. , vol.81 , pp. 976
    • Marqusee, J.A.1
  • 37
    • 0022145870 scopus 로고
    • The influence of particle motion on ostwald ripening in liquids
    • L. Ratke and W. K. Thieringer, The influence of particle motion on ostwald ripening in liquids, Acta Metall. 33, 1793 (1985).
    • (1985) Acta Metall. , vol.33 , pp. 1793
    • Ratke, L.1    Thieringer, W.K.2
  • 38
    • 85190307527 scopus 로고    scopus 로고
    • Phase-field modeling of crystal growth: New asymptotics and computational limits
    • edited by L.-Q. Chen et al. TMS and SIAM, Warrendale, PA
    • A. Karma and W.-J. Rappel, Phase-field modeling of crystal growth: New asymptotics and computational limits, in Mathematics of Microstructural Evolution, edited by L.-Q. Chen et al. (TMS and SIAM, Warrendale, PA, 1996), p. 204.
    • (1996) Mathematics of Microstructural Evolution , pp. 204
    • Karma, A.1    Rappel, W.-J.2
  • 39
    • 25744454700 scopus 로고
    • Computation of dendrites using a phase field model
    • A. A. Wheeler, B. T. Murray, and R. J. Schaefer, Computation of dendrites using a phase field model, Phys. D 66, 243 (1993).
    • (1993) Phys. D , vol.66 , pp. 243
    • Wheeler, A.A.1    Murray, B.T.2    Schaefer, R.J.3
  • 40
    • 7444246069 scopus 로고
    • Fractal and compact growth morphologies in phase transitions with diffusive transport
    • T. Ihle and H. Muller-Krumbhaar, Fractal and compact growth morphologies in phase transitions with diffusive transport, Phys. Rev. E 49, 2972 (1994).
    • (1994) Phys. Rev. E , vol.49 , pp. 2972
    • Ihle, T.1    Muller-Krumbhaar, H.2
  • 41
    • 0003819961 scopus 로고
    • Convective heat transfer during dendritic growth
    • edited by J. Zierip and H. Oertel, Jr. G. Braun, Karlsruhe, West Germany
    • M. E. Glicksman and S. C. Huang, Convective heat transfer during dendritic growth, in Convective Transport and Instability Phenomena, edited by J. Zierip and H. Oertel, Jr. (G. Braun, Karlsruhe, West Germany, 1982), p. 557.
    • (1982) Convective Transport and Instability Phenomena , pp. 557
    • Glicksman, M.E.1    Huang, S.C.2
  • 42
    • 4243093192 scopus 로고    scopus 로고
    • Numerical simulation of three-dimensional dendritic growth
    • A. Karma and W.-J. Rappel, Numerical simulation of three-dimensional dendritic growth, Phys. Rev. Lett. 77, 4050 (1996).
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 4050
    • Karma, A.1    Rappel, W.-J.2
  • 43
    • 0001767939 scopus 로고
    • Existence of needle crystals in local models of solidification
    • J. S. Langer, Existence of needle crystals in local models of solidification, Phys. Rev. A 33, 435 (1986).
    • (1986) Phys. Rev. A , vol.33 , pp. 435
    • Langer, J.S.1
  • 45
    • 33846174389 scopus 로고
    • Effect of forced flow on dendritic growth
    • P. Bouissou and P. Pelcé, Effect of forced flow on dendritic growth, Phys. Rev. A 40, 6673 (1989).
    • (1989) Phys. Rev. A , vol.40 , pp. 6673
    • Bouissou, P.1    Pelcé, P.2
  • 46
    • 33846174389 scopus 로고
    • Influence of an external flow on dendritic crystal growth
    • P. Bouissou, B. Perrin, and P. Tabeling, Influence of an external flow on dendritic crystal growth, Phys. Rev. A 40, 509 (1989).
    • (1989) Phys. Rev. A , vol.40 , pp. 509
    • Bouissou, P.1    Perrin, B.2    Tabeling, P.3


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