A FIXED GRID FRONT-TRACKING MODEL OF THE GROWTH OF A COLUMNAR FRONT AND AN EQUIAXED GRAIN DURING SOLIDIFICATION OF AN ALLOY

REFERENCES

• Mampaey , F. and Stable , A . 1990 . Alternating Direction Method for Simulating Multi-dimensional Solidification Problems . Int. J. Numer. Meth. Eng. , 30 : 711 – 728 .
   Web of Science ®Google Scholar
• Voller , V. R. 1997 . “ An Overview of Numerical Methods for Solving Phase Change Problems ” . In Advances in Numerical Heat Transfer , Edited by: Minkowycz , W. J. and Sparrow , E. M. Washington, DC : Taylor & Francis . chap. 9
   Google Scholar
• Flemings , M. C. 1974 . Solidification Processing , McGraw-Hill : McGraw-Hill .
   Google Scholar
• Turnbull , D. and Fisher , J. C. 1949 . Rate of Nucleation in Condensed Systems . J. Chem. Phys. , 17 ( 1 ) : 71 – 73 .
   Web of Science ®Google Scholar
• Browne , D. J. 2002 . Modelling Columnar and Equiaxed Growth , Oxford, , UK : University of Oxford . D.Phil. thesis
   Google Scholar
• Hunt , J. D. 1984 . Steady State Columnar and Equiaxed Growth of Dendrites and Eutectic . Mater. Sci. Eng. , 65 : 75 – 83 .
   Google Scholar
• Thevoz , P. h. , Desbiolles , J. L. and Rappaz , M. 1989 . Modeling of Equiaxed Microstructure Formation in Casting . Metall. Trans. , 20A : 311 – 322 .
   Web of Science ®Google Scholar
• Grong , O. , Dahle , A. K. , Ons⊘ien , M. I. and Arnberg , L. 1998 . Analytical Modelling of Equiaxed Solidification . Acta Mater. , 46 ( 14 ) : 5045 – 5052 .
   Web of Science ®Google Scholar
• Gandin , C. h. A. and Rappaz , M. 1994 . A Coupled Finite Element-Cellular Automaton Model for the Prediction of Dendritic Grain Structures in Solidification Processes . Acta Metall. Mater. , 42 ( 7 ) : 2233 – 2246 .
   Google Scholar
• Vandyoussefi , M. and Greer , A. L. 2002 . Application of Cellular Automata-Finite Element Model to the Grain Refinement of Directionally Solidified Al-4.15 wt.%Mg alloys . Acta Mater. , 50 : 1693 – 1705 .
   Web of Science ®Google Scholar
• Rappaz , M. and Gandin , C. h. A. 1993 . Probabilistic Modelling of Microstructure Formation in Solidification Processes . Acta Metall. Mater. , 41 ( 2 ) : 345 – 360 .
   Google Scholar
• Warnken , N. , Rezende , J. , Schadt , R. , Wagner , I. and Sahm , P. R. 2000 . “ Simulating Grain Structure Formation with a Rotated-Grid Cellular Automaton Model ” . In Modeling of Casting, Welding and Advanced Solidification Processes IX , Edited by: Sahm , P. R. , Hansen , P. N. and Conley , J. G. 566 – 573 . Aachen, , Germany : Shaker-Verlag .
   Google Scholar
• Provatas , N. , Goldenfeld , N. and Dantzig , J. 1998 . Efficient Computation of Dendritic Microstructures Using Adaptive Mesh Refinement . Phys. Rev. Lett. , 80 ( 15 ) : 3308 – 3311 .
   Web of Science ®Google Scholar
• Boettinger , W. J. and Warren , J. A. 1999 . Simulation of the Cell to Plane Front Transition during Directional Solidification at High Velocity . J. Cryst. Growth , 200 ( 3–4 ) : 583 – 591 .
   Web of Science ®Google Scholar
• Lobkovsky , A. E. and Warren , J. A. 2001 . Phase-Field Model of Crystal Grains . J. Cryst. Growth , 225 ( 2–4 ) : 282 – 288 .
   Web of Science ®Google Scholar
• Nestler , B. , Wheeler , A. A. and Multi-Phase-Field , A . 2000 . Model of Eutectic and Peritectic Alloys: Numerical Simulation of Growth Structures . Physica D , 138 ( 1–2 ) : 114 – 133 .
   Google Scholar
• Shyy , W. 1994 . Computational Modelling for Fluid Flow and Interfacial Transport , 396 – 424 . Amsterdam : Elsevier .
   Google Scholar
• Shyy , W. , Udaykumar , H. S. , Rao , M. M. and Smith , R. W. 1996 . Computational Fluid Dynamics with Moving Boundaries , 195 – 248 . Washington, DC : Taylor & Francis .
   Google Scholar
• Juric , D. , Tryggvason , G. and Front-Tracking , A . 1996 . Method for Dendritic Solidification . J. Comput. Phys. , 123 : 127 – 148 .
   Web of Science ®Google Scholar
• Zhao , P. and Heinrich , J. C. 2001 . Front-Tracking Finite Element Method for Dendritic Solidification . J. Comput. Phys. , 173 : 765 – 796 .
   Web of Science ®Google Scholar
• Zhao , P. H. and Heinrich , J. C. 2003 . Approximation to the Interface Velocity in Phase Change Front Tracking . Commun. Numer. Meth. Eng. , 18 ( 2 ) : 77 – 88 .
   Web of Science ®Google Scholar
• Zhao , P. , Vénere , M. , Heinrich , J. C. and Poirier , D. R. 2003 . Modeling Dendritic Growth of a Binary Alloy . J. Comput. Phys. , 188 : 434 – 461 .
   Web of Science ®Google Scholar
• Lakehal , D. , Meier , M. and Fulgosi , M. 2002 . Interface Tracking towards the Direct Simulation of Heat and Mass Transfer in Multiphase Flows . Int. J. Heat Fluid Flow , 23 : 242 – 257 .
   Web of Science ®Google Scholar
• Yadigaroglu , G. 2002 . “ Application of Cascades of CFD Methods to Two-Phase Flow Problems ” . In Proc. 3rd Int. Conf. Transport Phenomena in Multiphase Systems , 179 – 186 . Poland : Baranów Sandomierski .
   Google Scholar
• Burden , M. H. and Hunt , J. D. 1974 . Cellular and Dendritic Growth. II . J. Cryst. Growth , 22 : 109 – 116 .
   Web of Science ®Google Scholar
• Hunt , J. D. 1984 . Steady State Columnar and Equiaxed Growth of Dendrites and Eutectic . Mater. Sci. Eng. , 65 : 75 – 83 .
   Google Scholar
• Burden , M. H. 1973 . Factors Affecting Grain Size in Castings , Oxford, , UK : University of Oxford . D.Phil. thesis
   Google Scholar
• Hunt , J. D. and Lu , S. Z. 1996 . Numerical Modelling of Cellular/Dendritic Array Growth: Spacing and Structure Predictions . Metall. Mater. Trans. , 27A : 611 – 623 .
   Web of Science ®Google Scholar
• Browne , D. J. and Hunt , J. D. 2000 . “ A Model of Columnar Growth Using a Front-Tracking Technique ” . In Modelling of Casting, Welding and Advanced Solidification Processes , Edited by: Sahm , P. R. , Hansen , P. N. and Conley , J. G. 437 – 444 . Aachen, , Germany : Shaker-Verlag .
   Google Scholar
• Borisov , A. G. , Federov , O. P. and Maslov , V. V. 1991 . Growth of Succinonitrile Dendrites in Different Crystallographic Directions . J. Cryst. Growth , 112 : 463 – 466 .
   Web of Science ®Google Scholar
• 1992 . ASM Handbook, Volume 3, Alloy Phase Diagrams , Materials Park, OH : ASM International .
   Google Scholar
• O'Mahoney , D. and Browne , D. J. 2000 . Use of Experiment and an Inverse Method to Study Interface Heat Transfer during Solidification in the Investment Casting Process . Exp. Thermal Fluid Sci. , 22 : 111 – 222 .
   Web of Science ®Google Scholar
• Browne , D. J. and O'Mahoney , D. 2001 . Interface Heat Transfer in Investment Casting of Aluminum Alloys . Metall. Mater. Trans. , 32A : 3055 – 3063 .
   Google Scholar
• Coone , N. 2003 . Investigation of Thermal Boundary Conditions in Sand and Permanent Mould Casting , Dublin, , Ireland : University College Dublin . M.Eng.Sc. thesis
   Google Scholar
• Jaluria , Y. and Torrance , K. E. 1986 . Computational Heat Transfer , 49 – 55 . Washington, DC : Hemisphere .
   Google Scholar
• Banaszek , J. , Browne , D. J. and Furmanski , P. 2003 . Eulerian Equilibrium and Non-equilibrium Macroscopic Modelling of Binary System Solidification . Arch. Thermodynam. , 24 ( 1 ) : 37 – 57 .
   Google Scholar