A volume-averaged two-phase model for transport phenomena during solidification
Tóm tắt
A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.
Tài liệu tham khảo
R.N. Hills, D.E. Loper, and P.H. Roberts:Q. J. Mech. Appl. Mathematics, 1983, vol. 36, pp. 505–36.
V.C. Prantil and P.R. Dawson:Transport Phenomena in Materials Processing, ASME, New York, NY, 1983, pp. 469–84.
W.D. Bennon and F.P. Incropera:Int. J. Heat Mass Transfer, 1987, vol. 30, pp. 2161–2170.
D.A. Drew:Ann. Rev. Fluid Mech., 1983, vol. 15, pp. 261–91.
C. Beckermann and R. Viskanta:PhysicoChem. Hydrodyn., 1988, vol. 10, pp. 195–213.
M. Ishii:Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, 1975.
W.G. Gray:Adv. Water Resour., 1983, vol. 6, pp. 130–40.
S. Ganesan and D.R. Poirier:Metall. Trans. B, 1990, vol. 21B, pp. 173–181.
W.G. Gray and K. O'Neill:Water Resour. Res., 1976, vol. 12, pp. 148–154.
M. Hassanizadeh and W.G. Gray:Adv. Water Resour., 1979, vol. 2, pp. 131-41.
R. Viskanta and C. Beckermann:Interdisciplinary Issues in Materials Processing and Manufacturing, ASME, New York, NY, 1987, vol. 2, pp. 501–526.
M. Rappaz:Int. Mater. Rev., 1989, vol. 34, pp. 93–123.
W. Kurz and D.J. Fisher:Fundamentals of Solidification, Trans Tech Publications, Ltd., Aedermannsdorf, Switzerland, 1989.
M.S. Christenson, W.D. Bennon, and F.P. Incropera:Int. J. Heat Mass Transfer, 1989, vol. 32, pp. 69–79.
W.D. Bennon and F.P. Incropera:ASMEJ. Heat Transfer, 1989, vol. Ill, pp. 706–12.
V.R. Voller, A.D. Brent, and C. Prakash:Int. J. Heat Mass Transfer, 1989, vol. 32, pp. 1719–31.
M. Hassanizadeh and W.G. Gray:Adv. Water Resour., 1979, vol. 2, pp. 191–203.
S. Whitaker:AIChE J., 1967, vol. 13, pp. 420–27.
J.C. Slattery:AIChE J., 1967, vol. 13, pp. 1066–71.
W.T. Sha, B.T. Chao, and S.L. Soo:Nucl. Eng. Des., 1984, vol. 82, pp. 93–106.
M. Hassanizadeh and W.G. Gray:Adv. Water Resour., 1980, vol. 3, pp. 25–40.
M. Ishii and N. Zuber:AIChE J., 1979, vol. 25, pp. 843–55.
D.R. Poirier:Metall. Trans. B, 1987, vol. 18B, pp. 245–56.
P. Agarwal and B. O'Neill:Chem. Eng. Sci., 1988, vol. 43, pp. 2487–99.
I. Ohnaka:Trans. Iron Steel Inst. Jpn., 1986, vol. 26, p. 1051.
T. Hayakawa and M. Matsuoka:Heat Transfer—Jpn. Res., 1973, vol. 2, pp. 104–15.
P. Agarwal:Chem. Eng. Sci., 1988, vol. 43, pp. 2501–10.
J.A. Boure:Multiphase Science and Technology, Hemisphere Publishing Corp., 1987, vol. 3, pp. 3–30.
R.T. DeHoff and F.N. Rhines:Quantitative Microscopy, McGraw- Hill Book Co., New York, NY, 1968.
G.R. Speich and R.M. Fisher:Recrystallization, Grain Growth and Textures, ASM, Metals Park, OH, 1966, pp. 563–98.
S.P. Marsh, M.E. Glicksman, L. Meloro, and K. Tsutsumi:Modeling and Control of Casting and Welding Processes IV, TMS, Warrendale, PA, 1988, pp. 15–23.
J.W. Nunziato:Theory of Dispersed Multiphase Flow, Academic Press, New York, NY, 1983, pp. 191–226.
V. Laxmanan and M.C. Flemings:Metall. Trans. A, vol. 11 A, 1980, pp. 1927–37.
S. Whitaker:Chem. Eng. Sci., 1973, vol. 28, pp. 139–47.
W.G. Gray:Chem. Eng. Sci., 1975, vol. 30, pp. 229–33.
S.L. Soo:Particulates and Continuum, Hemisphere Publishing Corp., New York, NY, 1989.
M.C. Flemings:Solidification Processing, McGraw-Hill Book Co., New York, NY, 1974.
D.B. Spalding:Numerical Properties and Methodologies in Heat Transfer, Hemisphere Publishing Corp., Washington, DC, 1983.
P. Nandapurkar, D.R. Poirier, J.C. Heinrich, and S. Felicelli:Metall. Trans. B, 1989, vol. 20B, pp. 711–21.
S.C.Flood,L. Katgerman, A.H. Langille, S. Rogers, and C.M. Read:Light Metal 1989, AIME, Warrendale, PA, 1988, pp. 943–47.
M. Rappaz and V. Voller:Metall. Trans. B, 1990, vol. 21B, pp. 749–53.
J.L. Desbiolles, Ph. Thevoz, and M. Rappaz:Modeling and Con- trol of Casting and Welding Processes IV, TMS, Warrendale, PA, 1988, pp. 625–34.
C.S. Kanetkar and D.M. Stefanescu:Modeling and Control of Casting and Welding Processes IV, TMS, Warrendale, PA, 1988, pp. 697–708.