Convection modeling in directional solidification

Juan C. Heinrich; David R. Poirier

doi:10.1016/j.crme.2004.02.001

Microgravity and Transfer/Solidification, crystal growth from the melt

Convection modeling in directional solidification
[Modélisation de la convection au cours de la solidification directionnelle]

Juan C. Heinrich ¹ ; David R. Poirier ²

¹ Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
² Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721, USA

Comptes Rendus. Mécanique, Microgravity / La micropesanteur, Volume 332 (2004) no. 5-6, pp. 429-445.

Résumé
Abstract

Nous exposons des modèles mathématiques et numériques de la solidification d'alliages dendritiques, binaires et multiconstituants, qui peuvent décrire la dynamique de la zone pâteuse ainsi que la région liquide. La discussion est centrée sur des modèles développés par les auteurs du présent article et basés sur la discrétisation en éléments finis des équations qui régissent les phénomènes. Nous discutons la capacité des programmes de simulation existants à modéliser les effets de la convection et de la macroségrégation qui en résulte dans les pièces coulées, et plus particulièrement la formation de « freckles » dans les monocristaux dendritiques solidifiés verticalement. Nous faisons ressortir les limites actuelles des modèles ainsi que les domaines dans lesquels des améliorations sont nécessaires. Des exemples numériques illustrent les différent aspects des simulations.

Mathematical and numerical models of solidification of binary and multicomponent dendritic alloys that can model the dynamics of the mushy zone as well as the all liquid region are examined. The discussion is centered around models based on finite element discretization of the governing equations that have been developed by the authors during the last fifteen years. The capabilities of existing simulation codes to model the effects of convection and the resulting macrosegregation in castings, and in particular, the development of ‘freckles’ in vertically solidified dendritic monocrystals are discussed. The current capabilities of the models as well as the areas in which more improvement is needed are noted. Numerical examples are presented to illustrate the different aspects of the simulations.

Publié le : 2004-04-12

DOI : 10.1016/j.crme.2004.02.001

Keywords: Dendritic solidification, Multicomponent alloys, Binary alloys, Directional solidification, Macrosegregation
Mots-clés : Solidification dendritiques, Alliages multiconstituants, Alliages binaires, Solidification directionnelle, Macroségrégation

Affiliations des auteurs :

Juan C. Heinrich ¹ ; David R. Poirier ²

¹ Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
² Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721, USA

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Juan C. Heinrich; David R. Poirier. Convection modeling in directional solidification. Comptes Rendus. Mécanique, Microgravity / La micropesanteur, Volume 332 (2004) no. 5-6, pp. 429-445. doi : 10.1016/j.crme.2004.02.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.02.001/

Bibliographie
Cité par

[1] G.J.S. Higginbotham From research to cost-effective directional solidification and single-crystal production – an integrated approach, Mater. Sci. Tech., Volume 2 (1986), pp. 442-460

[2] C. Frueh; D.R. Poirier; S.D. Felicelli Predicting freckle-defects in directionally solidified Pb–Sn alloys, Mat. Sci. Engrg. A, Volume 328 (2002), pp. 245-255

[3] M. McLean Directionally Solidified Materials for High Temperature Service, The Metals Society, London, 1983

[4] T.C. Midea; D. Schmidt Casting simulation software survey, Modern Casting, Volume 89 (1999), pp. 47-51

[5] M. Cruchaga; D. Celentano Numerical analysis of thermally coupled flow problems with interfaces and phase-change effects, Int. J. Comp. Fluid Dyn., Volume 16 (2002), pp. 247-262

[6] D. Juric; G. Tryggvason A front-tracking method for dendritic solidification, J. Comput. Phys., Volume 123 (1996), pp. 127-148

[7] H.S. Udaykumar; R. Mittal; W. Shyy Computation of solid–liquid phase fronts in the sharp interface limit on fixed grids, J. Comput. Phys., Volume 153 (1999), pp. 535-574

[8] P. Zhao; J.C. Heinrich Front – tracking finite element method for dendritic solidification, J. Comput. Phys., Volume 173 (2001), pp. 765-796

[9] A. Karma; W.J. Rappel Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys. Rev. E, Volume 57 (1998), pp. 4323-4349

[10] L.H. Ungar; R.A. Brown Cellular interface morphologies in directional solidification IV. The formation of deep cells, Phys. Rev. B, Volume 31 (1985), pp. 5931-5940

[11] J.A. Warren; W.J. Boettinger Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method, Acta Metall. Mater., Volume 43 (1995), pp. 689-703

[12] P. Zhao; M. Vénere; J.C. Heinrich; D.R. Poirier Modeling dendritic growth of a binary alloy, J. Comput. Phys., Volume 188 (2003), pp. 434-461

[13] J.S. Kirkaldy; W.V. Youdelis Contribution to the theory of inverse segregation, Trans. TMS-AIME, Volume 212 (1958), pp. 833-840

[14] M.C. Flemings; G.E. Nereo Macrosegregation: Part I, Trans. Metall Soc. AIME, Volume 239 (1967), pp. 1449-1461

[15] M.C. Flemings; G.E. Nereo Macrosegregation: Part II, Trans. Metall Soc. AIME, Volume 242 (1968), pp. 41-49

[16] M.C. Flemings; G.E. Nereo Macrosegregation: Part III, Trans. Metall Soc. AIME, Volume 242 (1968), pp. 50-55

[17] R. Mehrabian; M. Keane; M.C. Flemings Interdendritic fluid flow and macrosegregation: Influence of gravity, Metall Trans., Volume 1 (1970), pp. 1209-1220

[18] R. Mehrabian; M. Keane; M.C. Flemings Experiments on macrosegregation and freckle formation, Metall. Trans., Volume 1 (1970), pp. 3238-3241

[19] S. Kou; D.R. Poirier; M.C. Flemings Macrosegregation in ESR ingots, Electric Furnace Proc. ISS-IAME, Volume 35 (1977), pp. 221-228

[20] S. Kou; D.R. Poirier; M.C. Flemings Macrosegregation in rotated remelted ingots, Metall. Trans. B, Volume 9 (1978), pp. 711-719

[21] S.D. Ridder; F.C. Reyes; S. Chakravorty; R. Mehrabian; J.D. Nauman; J.H. Chen; H.J. Klein Steady-state segregation and heat flow in ESR, Metall. Trans. B, Volume 9 (1978), pp. 415-425

[22] T. Fujii; D.R. Poirier; M.C. Flemings Macrosegregation in a multicomponent low alloy steel, Metall. Trans. B, Volume 10 (1979), pp. 331-339

[23] D. Petrakis; M.C. Flemings; D.R. Poirier Some effects of forced convection on macrosegregation (H.D. Brody; D. Apelian, eds.), Modeling of Castings and Welding Processes, TMS-AIME, Warrendale, PA, 1981

[24] C.D.R. Poirier Convection of interdendritic liquid in unidirectionally solidified alloys, Proceedings of the U.S.–Japan Cooperative Science Program Seminar on Solidification Processing, Dedham, MA, 1983

[25] S.D. Ridder; S. Kou; R. Mehrabian Effect of fluid flow on macrosegregation in axi-symmetric ingots, Metall. Trans. B, Volume 12 (1981), pp. 435-447

[26] A.L. Maples; D.R. Poirier Convection in the two-phase zone of solidifying alloys, Metall. Trans. B, Volume 15 (1984), pp. 163-172

[27] D.R. Poirier; M.C. Flemings; R. Mehrabian; V. Weiss Modeling macrosegregation in electroslag remelted ingots (J.J. Burke; R. Mehrabian; V. Weiss, eds.), Advances in Metal Processing, Plenum, New York, 1981

[28] W.D. Bennon; F.P. Incropera A continuum model for momentum, heat and species transport in binary solid–liquid phase change systems-I. Model formulation, Int. J. Heat Mass Transfer, Volume 30 (1987), pp. 2161-2170

[29] S. Ganesan; D.R. Poirier Conservation of mass and momentum for the flow of interdendritic liquid during solidification, Metall. Trans. B, Volume 21 (1990), pp. 173-181

[30] D.R. Poirier; P.J. Nandapurkar; S. Ganesan The energy and solute conservation equations for dendritic solidification, Metall. Trans. B, Volume 22 (1991), pp. 889-900

[31] C. Beckermann; R. Viskanta Mathematical modeling of transport phenomena during solidification, Appl. Mech. Rev., Volume 46 (1993), pp. 1-27

[32] W.D. Bennon; F.P. Incropera A continuum model for momentum, heat and species transport in binary solid–liquid phase change systems-II; applications to solidification in a rectangular cavity, Int. J. Heat Mass Transfer, Volume 30 (1987), pp. 2171-2187

[33] S.D. Felicelli; J.C. Heinrich; D.R. Poirier Simulation of freckles during vertical solidification of a binary alloy, Metall. Trans. B, Volume 22 (1991), pp. 847-859

[34] G. Amberg Computation of macrosegregation in an iron-carbon cast, Int. J. Heat Mass Transfer, Volume 34 (1991), pp. 217-227

[35] D. Xu; Q. Li Numerical method for solution of strongly coupled binary alloy solidification problems, Numer. Heat Transfer A, Volume 20 (1991), pp. 181-201

[36] K.C. Chiang; H.L. Tsai Shrinkage induced fluid flow and domain change in two-dimensional alloy solidification, Int. J. Heat Mass Transfer, Volume 35 (1992), pp. 1763-1770

[37] M.C. Schneider; C. Beckermann A numerical study of the combined effects of microsegregation, mushy zone permeability and flow, caused by volume contraction and thermosolutal convection, on macrosegregation and eutectic formation in binary alloy solidification, Int. J. Heat Mass Transfer, Volume 38 (1995), pp. 3455-3473

[38] C.R. Swaminathan; V.R. Voller Towards a general numerical scheme for solidification systems, Int. J. Heat Mass Transfer, Volume 40 (1997), pp. 2859-2868

[39] G.F. Naterer Simultaneous pressure-velocity coupling in the two-phase zone for solidification shrinkage in an open casting, Model. Simul. Mater. Sci. Engrg., Volume 5 (1997), pp. 595-613

[40] N. Ahmad; H. Combeau; J.-L. Desbiolles; T. Jalanti; G. Lesoult; J. Rappaz; M. Rappaz; C. Stomp Numerical simulation of macrosegregation: a comparison between finite volume method and finite element method predictions and a confrontation with experiments, Metall. Mater. Trans. A, Volume 29 (1998), pp. 617-630

[41] V. Voller; C.M. Swaminathan; B.G. Thomas Fixed grid techniques for phase change problems: a review, Int. J. Numer. Methods Engrg., Volume 30 (1990), pp. 875-898

[42] C. Beckermann Modeling of macrosegregation: applications and future needs, Int. Mater. Rev., Volume 47 (2002), pp. 243-261

[43] J.C. Heinrich, D.R. Poirier, Effect of volume change during directional solidification of binary alloys, Model. Simul. Mater. Sci. Engrg. (2004), in press

[44] D.A. Nield The boundary correction for the Rayleigh–Darcy problem: limitations of the Brinkman equation, J. Fluid Mech., Volume 128 (1983), pp. 37-46

[45] D.A. Nield; D.D. Joseph Effect of quadratic drag on convection in a saturated porous medium, Phys. Fluids, Volume 28 (1985), pp. 995-997

[46] C. Beckerman; R. Viskanta Double-diffusive convection during dendritic solidification of a binary mixture, Phys.-Chem. Hydrodyn., Volume 10 (1988), pp. 195-213

[47] S.D. Felicelli; J.C. Heinrich; D.R. Poirier Finite element analysis of directional solidification of multicomponent alloys, Int. J. Numer. Methods Fluids, Volume 27 (1998), pp. 207-227

[48] J.C. Heinrich; E. McBride Calculation of pressure in a mushy zone, Int. J. Numer. Methods Engrg., Volume 47 (2000), pp. 735-747

[49] G. Amberg Parameter ranges in binary solidification from vertical boundaries, Int. J. Heat Mass Transfer, Volume 40 (1997), pp. 2565-2578

[50] J.C. Heinrich; D.W. Pepper Intermediate Finite Element Method; Fluid Flow and Heat Transfer Applications, Taylor & Francis, Philadelphia, 1999

[51] S.D. Felicelli; J.C. Heinrich; D.R. Poirier Numerical model for dendritic solidification of binary alloys, Numer. Heat Transfer B, Volume 23 (1993), pp. 461-481

[52] S.D. Felicelli; J.C. Heinrich; D.R. Poirier Finite element analysis of directional solidification of multicomponent alloys, Int. J. Numer. Methods Fluids, Volume 27 (1998), pp. 207-227

[53] E. McBride; J.C. Heinrich; D.R. Poirier Numerical simulation of incompressible flow driven by density variations during phase change, Int. J. Numer. Methods Fluids, Volume 31 (1999), pp. 787-800

[54] D.G. Nielson; F.P. Incropera Three-dimensional considerations of unidirectional solidification in a binary liquid, Numer. Heat Transfer, Volume 23 (1993), pp. 1-20

[55] S.D. Felicelli; J.C. Heinrich; D.R. Poirier Three-dimensional simulations of freckles in binary alloys, J. Crystal Growth, Volume 191 (1997), pp. 879-888

[56] S.D. Felicelli; D.R. Poirier; J.C. Heinrich Modeling freckle formation in three dimensions during solidification of multicomponent alloys, Metall. Mater. Trans. B, Volume 29 (1998), pp. 847-855

[57] D. Xu; Q. Li Gravity- and solidification-shrinkage-induced liquid flow in a horizontally solidified alloy ingot, Numer. Heat Transfer A, Volume 20 (1991), pp. 203-221

[58] H. Shahani; G. Amberg; H. Fredriksson On the formation of macrosegregations in unidirectionally solidified Sn–Pb and Pb–Sn alloys, Metall. Trans. A, Volume 23 (1992), pp. 2301-2311

[59] D.G. Westra, Simulation of directional solidification in a binary alloy using the fractional step method, Ph.D. Dissertation, The University of Arizona, Tucson, 2003

[60] A. Bejan Convective heat transfer in porous media (S. Kakacs; R.K. Shah; W. Aung, eds.), Handbook of Single Phase Convective Heat Transfer, Wiley, New York, 1987

[61] D.R. Poirier Permeability for flow of interdendritic liquid in columnar-dendritic alloys, Metall. Trans. B, Volume 18 (1987), pp. 245-255

[62] S. Ganesan; C.L. Chan; D.R. Poirier Permeability of flow parallel to dendrite arms, Mater. Sci. Engrg. A, Volume 151 (1992), pp. 97-105

[63] M.S. Bhat; D.R. Poirier; J.C. Heinrich Permeability for cross flow through columnar-dendritic alloys, Metall. Mater. Trans. B, Volume 26 (1995), pp. 1049-1056

[64] J.C. Heinrich; D.R. Poirier; D.F. Nagelhout Mesh generation and flow calculations in highly contorted geometries, Comp. Methods Appl. Mech. Engrg., Volume 133 (1996), pp. 79-92

[65] D.R. Poirier; J.C. Heinrich Continuum model for predicting macrosegregation in dendritic alloys, Mater. Character., Volume 32 (1994), pp. 287-298

[66] S.K. Sinha; T. Sundararajan; V.K. Garg A variable property analysis of alloy solidification using the anisotropic porous medium approach, Int. J. Heat Mass Transfer, Volume 35 (1992), pp. 2865-2877

[67] B. Goyeau; T. Bennihaddadene; D. Gobin; M. Quintard Averaged momentum equation for flow through a nonhomogeneous porous structure, Transp. Porous Media, Volume 28 (1997), pp. 19-50

[68] T. Motegi; A. Ohno Inverse segregation in unidirectionally solidified Al–Cu alloy ingots, Trans. Japan Inst. Metals, Volume 25 (1984), pp. 122-132

[69] M.G. Worster Instabilities of the liquid and mushy regions during solidification of alloys, J. Fluid Mech., Volume 237 (1992), pp. 649-669

[70] C.F. Chen; F. Chen Experimental study of directional solidification of aqueous ammonium chloride solutions, J. Fluid Mech., Volume 227 (1991), pp. 567-586

[71] T.P. Schulze; M.G. Worster A numerical investigation of steady convection in mushy layers during the directional solidification of binary alloys, J. Fluid Mech., Volume 356 (1998), pp. 199-220

[72] H.W. Huang; J.C. Heinrich; D.R. Poirier Simulation of directional solidification with steep thermal gradients, Model. Simul. Mater. Sci. Engrg., Volume 4 (1996), pp. 245-259

[73] S.N. Tewari; R. Shah Macrosegregation during steady-state arrayed growth of dendrites in directionally solidified Pb–Sn alloys, Metall. Trans., Volume 23A (1992), pp. 3383-3392

[74] S.D. Felicelli; D.R. Poirier; J.C. Heinrich Macrosegregation patterns in multicomponent Ni-base superalloys, J. Crystal Growth, Volume 177 (1996), pp. 145-161

[75] S.D. Felicelli; D.R. Poirier; A.F. Giamei; J.C. Heinrich Simulation of the solidification of DS and SC superalloys, JOM, Volume 49 (1997), pp. 21-25

[76] M.C. Schneider; C. Beckermann Formation of macrosegregation by multicomponent thermosolutal convection during solidification of steel, Metall. Mater. Trans. A, Volume 26 (1995), pp. 2373-2388

[77] S.D. Felicelli; P.K. Sung; D.R. Poirier; J.C. Heinrich Transport properties and transport phenomena in casting nickel superalloys, Int. J. Thermophys., Volume 19 (1998), pp. 1657-1669

B. Domeij; A. Diószegi A Review of Dendritic Austenite in Cast Irons, International Journal of Metalcasting, Volume 18 (2024) no. 3, p. 1968 | DOI:10.1007/s40962-023-01239-8
F. Bodaghi; M. Movahedi; A.H. Kokabi Estimation of solidification cracking susceptibility in Al–Si–Cu alloy weld: effects of anisotropic permeability and deformation orientation, Journal of Materials Research and Technology, Volume 23 (2023), p. 2351 | DOI:10.1016/j.jmrt.2023.01.138
Changjun Wang; Zhongqiu Liu; Baokuan Li; Jianxiang Xu An Improved Columnar Solidification Model Coupled With Anisotropic Mush Permeability, Metallurgical and Materials Transactions B, Volume 54 (2023) no. 3, p. 1275 | DOI:10.1007/s11663-023-02761-0
Björn Domeij; Jessica Elfsberg; Attila Diószegi Evolution of Dendritic Austenite in Parallel With Eutectic in Compacted Graphite Iron Under Three Cooling Conditions, Metallurgical and Materials Transactions B, Volume 54 (2023) no. 5, p. 2395 | DOI:10.1007/s11663-023-02842-0
Nicholas Cusato; Seyed Amin Nabavizadeh; Mohsen Eshraghi A Review of Large-Scale Simulations of Microstructural Evolution during Alloy Solidification, Metals, Volume 13 (2023) no. 7, p. 1169 | DOI:10.3390/met13071169
Yigong Qin; Yuanxun Bao; Stephen DeWitt; Balasubramanian Radhakrishnan; George Biros Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model, Computational Materials Science, Volume 207 (2022), p. 111262 | DOI:10.1016/j.commatsci.2022.111262
Chuanzhen Ma; Ruijie Zhang; Zixin Li; Xue Jiang; Yongwei Wang; Cong Zhang; Haiqing Yin; Xuanhui Qu Solidification shrinkage and shrinkage-induced melt convection and their relation with solute segregation in binary alloys, Computational Materials Science, Volume 215 (2022), p. 111815 | DOI:10.1016/j.commatsci.2022.111815
M. Vynnycky On the local solute redistribution equation of macrosegregation, remelting and the formation of channel segregates, International Journal of Heat and Mass Transfer, Volume 190 (2022), p. 122737 | DOI:10.1016/j.ijheatmasstransfer.2022.122737
Mirosław Seredyński; Jerzy Banaszek Coupled enthalpy-porosity and front tracking approach to modeling chemical inhomogeneity in solidifying metal alloys, International Journal of Heat and Mass Transfer, Volume 173 (2021), p. 121221 | DOI:10.1016/j.ijheatmasstransfer.2021.121221
Daniel M. Anderson; Peter Guba Convective Phenomena in Mushy Layers, Annual Review of Fluid Mechanics, Volume 52 (2020) no. 1, p. 93 | DOI:10.1146/annurev-fluid-010719-060332
Y Mitsuyama; T Takaki; S Sakane; Y Shibuta; M Ohno Permeability tensor for various columnar dendrite structures, IOP Conference Series: Materials Science and Engineering, Volume 861 (2020) no. 1, p. 012029 | DOI:10.1088/1757-899x/861/1/012029
Michael Vynnycky On the formation of centreline shrinkage porosity in the continuous casting of steel, Journal of Mathematics in Industry, Volume 10 (2020) no. 1 | DOI:10.1186/s13362-020-00084-2
Tomohiro Takaki; Shinji Sakane; Munekazu Ohno; Yasushi Shibuta; Takayuki Aoki Permeability prediction for flow normal to columnar solidification structures by large–scale simulations of phase–field and lattice Boltzmann methods, Acta Materialia, Volume 164 (2019), p. 237 | DOI:10.1016/j.actamat.2018.10.039
D. Tourret; M.M. Francois; A.J. Clarke Multiscale dendritic needle network model of alloy solidification with fluid flow, Computational Materials Science, Volume 162 (2019), p. 206 | DOI:10.1016/j.commatsci.2019.02.031
X. Zhang; J. Kang; Z. Guo; Q. Han Effect of the forced flow on the permeability of dendritic networks: A study using phase-field-lattice Boltzmann method, International Journal of Heat and Mass Transfer, Volume 131 (2019), p. 196 | DOI:10.1016/j.ijheatmasstransfer.2018.11.036
Murat Tiryakioğlu On the permeability of columnar dendritic networks in solidifying metals, Materials Science and Technology, Volume 35 (2019) no. 5, p. 632 | DOI:10.1080/02670836.2019.1577523
Menghuai Wu; Andreas Ludwig; Abdellah Kharicha Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification, Metals, Volume 9 (2019) no. 2, p. 229 | DOI:10.3390/met9020229
Andrew J. Wells; Joseph R. Hitchen; James R. G. Parkinson Mushy-layer growth and convection, with application to sea ice, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 377 (2019) no. 2146, p. 20180165 | DOI:10.1098/rsta.2018.0165
J. Draxler; J. Edberg; J. Andersson; L.-E. Lindgren Modeling and simulation of weld solidification cracking part II, Welding in the World, Volume 63 (2019) no. 5, p. 1503 | DOI:10.1007/s40194-019-00761-w
E. Karimi-Sibaki; A. Kharicha; M. Wu; A. Ludwig; J. Bohacek; H. Holzgruber; B. Ofner; A. Scheriau; M. Kubin A multiphysics model of the electroslag rapid remelting (ESRR) process, Applied Thermal Engineering, Volume 130 (2018), p. 1062 | DOI:10.1016/j.applthermaleng.2017.11.100
Tomohiro Takaki; Roberto Rojas; Shinji Sakane; Munekazu Ohno; Yasushi Shibuta; Takashi Shimokawabe; Takayuki Aoki Phase-field-lattice Boltzmann studies for dendritic growth with natural convection, Journal of Crystal Growth, Volume 474 (2017), p. 146 | DOI:10.1016/j.jcrysgro.2016.11.099
Yukinobu Natsume Numerical Simulation of Macrosegregation Formed Due to Solidification Shrinkage and Bridging of Solidification Structures, Tetsu-to-Hagane, Volume 103 (2017) no. 12, p. 738 | DOI:10.2355/tetsutohagane.tetsu-2017-062
Ebrahim Karimi‐Sibaki; Abdellah Kharicha; Jan Bohacek; Menghuai Wu; Andreas Ludwig On Validity of Axisymmetric Assumption for Modeling an Industrial Scale Electroslag Remelting Process, Advanced Engineering Materials, Volume 18 (2016) no. 2, p. 224 | DOI:10.1002/adem.201500391
Qiang Wang; Zhu He; Guangqiang Li; Baokuan Li Numerical investigation on species transport in electroslag remelting dual alloy ingot, Applied Thermal Engineering, Volume 103 (2016), p. 419 | DOI:10.1016/j.applthermaleng.2016.04.089
Mirosław Seredyński; Piotr Łapka; Jerzy Banaszek; Piotr Furmański Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media, International Journal of Heat and Mass Transfer, Volume 90 (2015), p. 790 | DOI:10.1016/j.ijheatmasstransfer.2015.07.016
C. Puncreobutr; A.B. Phillion; J.L. Fife; P.D. Lee Coupling in situ synchrotron X-ray tomographic microscopy and numerical simulation to quantify the influence of intermetallic formation on permeability in aluminium–silicon–copper alloys, Acta Materialia, Volume 64 (2014), p. 316 | DOI:10.1016/j.actamat.2013.10.044
A. Ludwig; A. Kharicha; C. Hölzl; J. Domitner; M. Wu; T. Pusztai 3D Lattice Boltzmann flow simulations through dendritic mushy zones, Engineering Analysis with Boundary Elements, Volume 45 (2014), p. 29 | DOI:10.1016/j.enganabound.2014.01.015
Yukinobu Natsume; Daiki Takahashi; Kasumi Kawashima; Eiji Tanigawa; Kenichi Ohsasa Evaluation of Permeability for Columnar Dendritic Structures by Three-dimensional Numerical Flow Analysis, ISIJ International, Volume 54 (2014) no. 2, p. 366 | DOI:10.2355/isijinternational.54.366
Ebrahim Karimi-Sibaki; Abdellah Kharicha; J. Korp; Meng Huai Wu; Andreas Ludwig Influence of Crystal Morphological Parameters on the Solidification of ESR Ingot, Materials Science Forum, Volume 790-791 (2014), p. 396 | DOI:10.4028/www.scientific.net/msf.790-791.396
Xi Li; Dafan Du; Annie Gagnoud; Zhongming Ren; Yves Fautrelle; Rene Moreau Effect of Multi-Scale Thermoelectric Magnetic Convection on Solidification Microstructure in Directionally Solidified Al-Si Alloys Under a Transverse Magnetic Field, Metallurgical and Materials Transactions A, Volume 45 (2014) no. 12, p. 5584 | DOI:10.1007/s11661-014-2496-6
Yukinobu Natsume; Daiki Takahashi; Kasumi Kawashima; Eiji Tanigawa; Kenichi Ohsasa Quantitative Model to Determine Permeability for Columnar Dendritic Structures, ISIJ International, Volume 53 (2013) no. 5, p. 838 | DOI:10.2355/isijinternational.53.838
Yukinobu Natsume; Daiki Takahashi; Kasumi Kawashima; Eiji Tanigawa; Kenichi Ohsasa Evaluation of Permeability for Columnar Dendritic Structures by Three Dimensional Numerical Flow Analysis, Tetsu-to-Hagane, Volume 99 (2013) no. 2, p. 117 | DOI:10.2355/tetsutohagane.99.117
Lang Yuan; Peter D. Lee A new mechanism for freckle initiation based on microstructural level simulation, Acta Materialia, Volume 60 (2012) no. 12, p. 4917 | DOI:10.1016/j.actamat.2012.04.043
J Domitner; C Hölzl; A Kharicha; M Wu; A Ludwig; M Köhler; L Ratke 3D simulation of interdendritic flow through a Al-18wt. | DOI:10.1088/1757-899x/27/1/012016
Arvind Kumar; Miha Založnik; Hervé Combeau Study of the influence of mushy zone permeability laws on macro- and meso-segregations predictions, International Journal of Thermal Sciences, Volume 54 (2012), p. 33 | DOI:10.1016/j.ijthermalsci.2011.11.014
J.-Q. Zhong; A. T. Fragoso; A. J. Wells; J. S. Wettlaufer Finite-sample-size effects on convection in mushy layers, Journal of Fluid Mechanics, Volume 704 (2012), p. 89 | DOI:10.1017/jfm.2012.219
J. Madison; J. E. Spowart; D. J. Rowenhorst; L. K. Aagesen; K. Thornton; T. M. Pollock Fluid Flow and Defect Formation in the Three-Dimensional Dendritic Structure of Nickel-Based Single Crystals, Metallurgical and Materials Transactions A, Volume 43 (2012) no. 1, p. 369 | DOI:10.1007/s11661-011-0823-8
C. L. Brundidge; D. van Drasek; B. Wang; T. M. Pollock Structure Refinement by a Liquid Metal Cooling Solidification Process for Single-Crystal Nickel-Base Superalloys, Metallurgical and Materials Transactions A, Volume 43 (2012) no. 3, p. 965 | DOI:10.1007/s11661-011-0920-8
Ehsan Khajeh; Daan M Maijer Permeability evolution during equiaxed dendritic solidification of Al–4.5 wt | DOI:10.1088/0965-0393/20/3/035004
Udaya K. Sajja; Sergio D. Felicelli; Juan C. Heinrich Numerical methods for improved efficiency in macrosegregation modeling, International Journal for Numerical Methods in Engineering, Volume 87 (2011) no. 1-5, p. 196 | DOI:10.1002/nme.3027
ABDEL ILLAH NABIL KORTI A NUMERICAL SIMULATION OF CONVECTIVE FLOW IN THE SOLIDIFICATION PROCESS, International Journal of Computational Methods, Volume 08 (2011) no. 01, p. 1 | DOI:10.1142/s0219876211002368
Ehsan Khajeh; Daan M. Maijer Physical and numerical characterization of the near-eutectic permeability of aluminum–copper alloys, Acta Materialia, Volume 58 (2010) no. 19, p. 6334 | DOI:10.1016/j.actamat.2010.07.055
Lang Yuan; Peter D. Lee Microstructural Simulations of the Influence of Solidification Velocity on Freckle Initiation during Directional Solidification, ISIJ International, Volume 50 (2010) no. 12, p. 1814 | DOI:10.2355/isijinternational.50.1814
J.W. Peterson; B.T. Murray; G.F. Carey Multi‐resolution simulation of double‐diffusive convection in porous media, International Journal of Numerical Methods for Heat Fluid Flow, Volume 20 (2010) no. 1, p. 37 | DOI:10.1108/09615531011008118
E. Khajeh; D. M. Maijer Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography, Materials Science and Technology, Volume 26 (2010) no. 12, p. 1469 | DOI:10.1179/174328409x411718
Arvind Kumar; Bernard Dussoubs; Miha Založnik; Hervé Combeau Effect of discretization of permeability term and mesh size on macro- and meso-segregation predictions, Journal of Physics D: Applied Physics, Volume 42 (2009) no. 10, p. 105503 | DOI:10.1088/0022-3727/42/10/105503
Lorenz Ratke; Amber Genau; Sonja Steinbach Flow effects on the dendritic microstructure of AlSi-base alloys, Transactions of the Indian Institute of Metals, Volume 62 (2009) no. 4-5, p. 337 | DOI:10.1007/s12666-009-0050-9
D.R. Poirier; J.C. Heinrich Modeling of Microsegregation and Macrosegregation, Casting (2008), p. 445 | DOI:10.31399/asm.hb.v15.a0005237
J. C. Heinrich; U. K. Sajja; S. D. Felicelli; D. G. Westra Projection method for flows with large local density gradients: Application to dendritic solidification, International Journal for Numerical Methods in Fluids, Volume 57 (2008) no. 9, p. 1211 | DOI:10.1002/fld.1812
Arvind Kumar; Pradip Dutta A Rayleigh number based dendrite fragmentation criterion for detachment of solid crystals during solidification, Journal of Physics D: Applied Physics, Volume 41 (2008) no. 15, p. 155501 | DOI:10.1088/0022-3727/41/15/155501
Devashish Fuloria; Peter D. Lee; D. Bernard Microtomographic characterization of columnar Al–Cu dendrites for fluid flow and flow stress determination, Materials Science and Engineering: A, Volume 494 (2008) no. 1-2, p. 3 | DOI:10.1016/j.msea.2007.10.093
Jacek Narski; Marco Picasso Adaptive finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage, Computer Methods in Applied Mechanics and Engineering, Volume 196 (2007) no. 37-40, p. 3562 | DOI:10.1016/j.cma.2006.10.033
Jayesh Jain; Arvind Kumar; Pradip Dutta Numerical Studies on Channel Formation and Growth During Solidification: Effect of Process Parameters, Journal of Heat Transfer, Volume 129 (2007) no. 4, p. 548 | DOI:10.1115/1.2709660
Jayesh Jain; Arvind Kumar; Pradip Dutta Role of plume convection and remelting on the mushy layer structure during directional solidification, Journal of Physics D: Applied Physics, Volume 40 (2007) no. 4, p. 1150 | DOI:10.1088/0022-3727/40/4/037
Marcelo J. Colaço; George S. Dulikravich Solidification of Double-Diffusive Flows Using Thermo-Magneto-Hydrodynamics and Optimization, Materials and Manufacturing Processes, Volume 22 (2007) no. 5, p. 594 | DOI:10.1080/10426910701322583
Arvind Kumar; Pradip Dutta; Suresh Sundarraj; Mike J. Walker Remelting of Solid and its Effect on Macrosegregation During Solidification, Numerical Heat Transfer, Part A: Applications, Volume 51 (2007) no. 1, p. 59 | DOI:10.1080/10407780600710391
Jacek Narski; Marco Picasso Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage, Free Boundary Problems, Volume 154 (2006), p. 327 | DOI:10.1007/978-3-7643-7719-9_32
R.G. Santos; M.L.N.M. Melo Permeability of interdendritic channels, Materials Science and Engineering: A, Volume 391 (2005) no. 1-2, p. 151 | DOI:10.1016/j.msea.2004.08.048

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