Average momentum equation for interdendritic flow in a solidifying columnar mushy zone

International Journal of Heat and Mass Transfer - Tập 45 - Trang 3651-3665 - 2002
P. Bousquet-Melou1, B. Goyeau2, M. Quintard3, F. Fichot1, D. Gobin2
1Institut de Protection et de Sûreté Nucléaire, C.E.A Cadarache, Bât. 700, 13108 Saint Paul Lez Durance, France
2Laboratoire FAST, Universités Paris VI et Paris XI, UMR CNRS 7608, Bât. 502, Campus Universitaire, 91405 Orsay Cedex, France
3Institut de Mécanique des Fluides de Toulouse, Avenue du Professeur Camille Soula, 31400 Toulouse, France

Tài liệu tham khảo

Flemings, 1974 Rappaz, 1990, Modeling of micro-macrosegregation in solidification processes, Met. Trans. A, 21, 749, 10.1007/BF02671947 Prescott, 1996, Convection heat and mass transfer in alloy solidification, Adv. Heat Transfer, 28, 231, 10.1016/S0065-2717(08)70142-4 Szekely, 1978, An experimental and analytical study of the solidification of a binry dendritic system, Met. Trans. B, 9, 389, 10.1007/BF02654412 Ridder, 1981, Effect of fluid flow on macrosegregation in axi-symmetric ingots, Met. Trans. B, 12, 435, 10.1007/BF02654312 Worster, 1991, Natural convection in a mushy layer, J. Fluid Mech., 224, 335, 10.1017/S0022112091001787 Kaviany, 1995 Hills, 1983, A thermodynamically consistent model of a mushy zone, Quart. J. Mech. Appl. Math., 36, 505, 10.1093/qjmam/36.4.505 Bennon, 1987, A continuum model for momentum heat and species transport in binary solid–liquid phase change systems—I. Model formulation, Int. J. Heat Mass Transfer, 30, 2161, 10.1016/0017-9310(87)90094-9 Prescott, 1991, Modeling of dendritic solidification systems reassessment of the continuum momentum equation, Int. J. Heat Mass Transfer, 34, 2351, 10.1016/0017-9310(91)90060-R Ganesan, 1990, Conservation of mass and momentum for the flow of interdendritic liquid during solidification, Met. Trans. B, 21, 173, 10.1007/BF02658128 Ni, 1991, A volume-averaged two-phase model for transport phenomena during solidification, Met. Trans. B, 22, 349, 10.1007/BF02651234 T. Benihaddadene, Modélisation Macroscopique des écoulements et des Transferts dans un milieu poreux hétérogene: application à la solidification, Ph.D. Thesis, Université de Paris VI Mai, 1997 Voller, 1989, The modelling of heat mass and solute transport in solidification systems, Int. J. Heat Mass Transfer, 32, 1719, 10.1016/0017-9310(89)90054-9 Kececioglu, 1989, A continuum model for the propagation of discrete phase-change fronts in porous media in the presence of coupled heat flow fluid flow and species transport processes, Int. J. Heat Mass Transfer, 32, 1111, 10.1016/0017-9310(89)90011-2 Prescott, 1992, The effects of undercooling, recalescence and solid transport on the solidification of binary metal alloys, Transport Phenom. Mater. Process. Manufact., 196, 31 Bennon, 1987, A continuum model for momentum heat and species transport in binary solid–liquid phase change systems—II. Application to solidification in a rectangular cavity, Int. J. Heat Mass Transfer, 30, 2171, 10.1016/0017-9310(87)90095-0 Bennon, 1987, The evolution of macrosegregation in statically cast binary ingots, Met. Trans. B, 18, 611, 10.1007/BF02654275 Christenson, 1989, Solidification of an aqueous ammonium chloride solution in a rectangular cavity—II. Comparison of predicted and measured results, Int. J. Heat Mass Transfer, 32, 69, 10.1016/0017-9310(89)90091-4 Neilson, 1991, Unidirectional solidification of a binary alloy and the effects of induced fluid motion, Int. J. Heat Mass Transfer, 34, 1717, 10.1016/0017-9310(91)90148-8 Prescott, 1994, Convective transport phenomena and macrosegregation during solidification of a binary metal alloy: I–Numerical predictions, J. Heat Transfer, 116, 735, 10.1115/1.2910929 Whitaker, 1969, Advances in theory of fluid motion in porous media, Ind. Eng. Chem., 61, 14, 10.1021/ie50720a004 Bear, 1972 Beckermann, 1988, Double-diffusive convection during dendritic solidification of a binary mixture, Physicochem. Hydrodyn., 10, 195 Beckermann, 1993, Mathematical modeling of transport phenomena during alloy solidification, Appl. Mech. Rev., 46, 1, 10.1115/1.3120318 Schneider, 1995, 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, 38, 3455, 10.1016/0017-9310(95)00054-D Beckermann, 1995, Mutiphase/scale modeling of alloy solidification, Annu. Rev. Heat Transfer, 6, 115, 10.1615/AnnualRevHeatTransfer.v6.50 Bensoussan, 1978 Sanchez, 1980, vol. 127 Bennon, 1989, An experimental investigation of binary solidification in a vertical channel with thermal and solutal mixed convection, J. Heat Transfer, 111, 706, 10.1115/1.3250740 Prescott, 1994, Convective transport phenomena and macrosegregation of a binary metal alloy: II—Experiments and comparisons with numerical predictions, J. Heat Transfer, 116, 742, 10.1115/1.2910930 Goyeau, 1997, Averaged momentum equation for flow through a non-homogeneous porous structure, Transport Porous Media, 28, 19, 10.1023/A:1006578602112 Nandapurkar, 1991, Momentum equation for dendritic solidification, Numer. Heat Transfer, 19, 297, 10.1080/10407789108944851 Poirier, 1987, Permeability for flow of interdendritic liquid in columnar–dendritic alloys, Met. Trans. B, 18, 245, 10.1007/BF02658450 Ganesan, 1992, Permeability for flow parallel to primary dendrite arms, Mater. Sci. Eng. A, 151, 97, 10.1016/0921-5093(92)90186-5 Bhat, 1995, Permeability for cross flow through columnar–dendritic alloys, Met. Mater. Trans. B, 26, 1049, 10.1007/BF02654107 Goyeau, 1999, Numerical calculation of the permeability tensor in a dendritic mushy zone, Met. Mater. Trans. B, 30, 613, 10.1007/s11663-999-0022-9 Whitaker, 1986, Flow in porous media I: A theoretical derivation of Darcy's law, Transport Porous Media, 1, 3, 10.1007/BF01036523 Barrère, 1992, On the closure problem for Darcy's law, Transport Porous Media, 7, 209, 10.1007/BF01063960 Quintard, 1994, Transport in ordered and disordered porous media III: Closure and comparison between theory and experiment, Transport Porous Media, 15, 31, 10.1007/BF01046157 Cushman, 1984, On unifying the concept of scale, instrumentation, and stochastics in the development of multiphase transport theory, Water Resour. Res., 20, 1668, 10.1029/WR020i011p01668 Huppert, 1990, The fluid mechanics of solidification, J. Fluid Mech., 212, 209, 10.1017/S0022112090001938 Trivedi, 1984, Constrained dendritic growth and spacing, Mater. Sci. Eng., 65, 65, 10.1016/0025-5416(84)90200-3 Gray, 1975, A derivation of the equations for multi-phase transport, Chem. Eng. Sci., 30, 229, 10.1016/0009-2509(75)80010-8 Carbonell, 1984, 121 Quintard, 1994, Transport in ordered and disordered porous media II: Generalized volume averaging, Transport Porous Media, 14, 179, 10.1007/BF00615200 C. Misbah, Instabilité morphologique et convection solutale en solidification directionnelle des mélanges binaires dilués, Ph.D. Thesis, Université Paris VII mars, 1985 Krane, 1995, Analysis of the effect of shrinkage on macrosegregation in alloy solidification, Met. Mater. Trans. A, 26, 2329, 10.1007/BF02671247 Poirier, 1987, A thermodynamic prediction for microporosity formation in aluminium-rich Al–Cu alloys, Met. Trans. A, 18, 1979, 10.1007/BF02647028 Xu, 1991, Gravity- and solidification-shrinkage-induced liquid flow in a horizontally solidified alloy ingot, Numer. Heat Transfer A, 20, 203, 10.1080/10407789108944817 Chiareli, 1995, Flow focusing instability in a solidifying mushy layer, J. Fluid Mech., 297, 293, 10.1017/S0022112095003107 Quintard, 1994, Convection dispersion and interfacial transport of contaminants: homogeneous porous media, Adv. Water Resour., 17, 221, 10.1016/0309-1708(94)90002-7 Whitaker, 1996, The Forchheimer equation: a theoretical development, Transport Porous Media, 25, 27, 10.1007/BF00141261 Cvetković, 1986, A continuum approach to high velocity flow in a porous medium, Transport Porous Media, 1, 63, 10.1007/BF01036526 Nield, 1999 Forchheimer, 1901, Wasserbewegung durch boden, Z. Ver. Deutsch. Ing., 45, 1782 Mei, 1991, The effect of weak inertia on flow through a porous medium, J. Fluid Mech., 222, 647, 10.1017/S0022112091001258 Firdaouss, 1995, Sur l'homogénéisation des equations de Navier–Stokes à faible nombre de reynolds, Comptes Rendus de l'Académie des Sciences, 320, 245 Hassanizadeh, 1987, High velocity flow in porous media, Transport Porous Media, 2, 521, 10.1007/BF00192152 Ma, 1993, The microscopic analysis of high Forchheimer number flow in porous media, Transport Porous Media, 13, 139, 10.1007/BF00654407 Ochoa-Tapia, 1995, Momentum transfer at the boundary between a porous medium and a homogeneous fluid: I theoretical development, Int. J. Heat Mass Transfer, 38, 2635, 10.1016/0017-9310(94)00346-W J. Ni, Development of a two-phase model of transport phenomena during equiaxed solidification, Ph.D. Thesis, University of Iowa, 1991 Wright, 1996, Core melt progression status of current understanding and principal uncertainties Quintard, 1993, Transport in ordered and disordered porous media volume-averaged equations, closure problems and comparison with experiment, Chem. Eng. Sci., 48, 2537, 10.1016/0009-2509(93)80266-S Marle, 1967, Ecoulements monophasiques en milieu poreux, Revue de L'Institut Francais du Pétrole, XXII, 1471 Wodie, 1991, Correction non linéaire de la loi de Darcy, Comptes Rendus de l'Académie des Sciences, 312, 157