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Eulerian equilibrium and non-equlibrium macroscopic modelling of binary system solidification

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Języki publikacji
EN
Abstrakty
EN
Two models of macroscopic computer simulation of binary system solidification on a fixed grid are discussed. First, it is shown that the single-domain enthalpy-porous medium model not only provides complete information on the evoluation of macroscopic entities, but also enables a detailed analysis of the role of the mushy zone properties in the progress of solidification. In this context, the results of FEM calculations for aqueous ammonium chloride solutions are presented showing the importance of anisotropy of permeability and thermal conductivityof the mushy zone. Next, to account for non-equilibrium phenomenon of the constitutional undercooling a new front tracking technique on a fixed grid, which is based on the kinetics of dendritic growth, (see a companion paper [13]), is used. The model is compared with the enthalpy approach showing its superiority in the detection of the undercooled zone in front of dendrite tips and, thus, in modelling of columnar /equiaxed grain structures. It is, then, further used to address the question of the influence of alloy composition on the size of the undercooled liquid zone in front of columnar dendrite tips during solidification of Al-Cu alloys driven by conduction in a square mould. Eventually, a possible scenario of the coupling of both models, in order to develop a comprehensive computer simulation of binary alloys solidification driven by both conduction and natural convection, is outlined.
Rocznik
Strony
37--57
Opis fizyczny
Bibliogr. 22 poz.,
Twórcy
autor
  • University College Dublin, Ireland
  • Warsaw University of Technology
  • University College Dublin, Ireland
autor
  • Warsaw University of Technology
Bibliografia
  • [1] TONHARDT R., AND AMBERG G.: Phase field simulation of dendritic growth in a shear flow, J. of Crystal Growth, 194(1998), 406-425.
  • [2] SHYY, W., UDAYKUMAR, H. S., RAO, M. .M., SMITH, R. W.: Computational fluid dynamics with moving boundaries, Taylor & Francis, Washington DC, 1996.
  • [3] JURIC, D. AND TRYGGVASON, G.: A front-tracking method for dendritic solidifica- tion, J. of Computational Physics, 123(1996), 127-148.
  • [4] BENNON W. D., INCROPERA F. P.: A continuum model for momentum, heat and solute transfer in binary solid-liquid phase change systems - I and II, Int. J. of Heat Mass Transfer, 30(1987), 2161-2187.
  • [5] BECKERMANN C., VISKANTA R.: Mathematical modelling of transport phenomena during alloy solidification, Appl. Mech. Review 46(1993), 1-27.
  • [6] PRAKASH C.: Two-phase model for binary solid-liquid phase change, Part I and Part II, Num. Heat Transfer, Part B, 18(1990), 131-169.
  • [7] BATCHELOR G. K.: Transport properties of two-phase materials with random struc- ture, Annual Rev. in Fluid Mechanics, 6(1974), 227-255.
  • [8] FURMANSKI P.: Microscopic-Macroscopic Modelling of Transport Phenomena Dur- ing Solidification in Heterogeneous Systems, Lecture Notes from CISM Course Phase Change with Convection: Modelling and Validation, coordinated by T. Kowalewski and D. Gobin, September 2-6, 2002, CISM, Udine, distr. by Springer Verlag (to be printed).
  • [9] VOLLER V. R., PRAKASH C.: A fixed grid numerical modeling methodology for convection-diffusion mushy region phase-change problems, Int. J. Heat and Mass Transfer, 30(1987), 1709-1719.
  • [10] PRAKASH C., VOLLER V. R.: On the numerical solution of continuum mixture model equations describing binary solid-liquid phase, Num. Heat Transfer, Part B, 15(1989), 171-189.
  • [11] RAPPAZ M.: Modelling of microstructure formation in solidification processes, Int. Materials Reviews, 34(1989), 93-123.
  • [12] BROWNE D. J, HUNT J. D.: A model of columnar growth using a front tracking technique, Modeling of Casting, Welding and Advanced Solidification Processes IX, Shaker Verlag, Aachen, Germany, 437-444, 2000.
  • [13] BROWNE D. J, HUNT J. D.: An interface-tracking model of moving boundaries in multi-phase systems: application to solidification, Arch. of Thermodynamics, 24(2003), No. 1, 25-36.
  • [14] BROWNE D. J.: Modelling columnar and equiaxed growth, DPhil Thesis, University of Oxford, UK, 2002.
  • [15] ZIENKIEWICZ O. C.AND TAYLOR R. L.: Finite element method, Fourth Edition, McGraw-Hill Company, London, 1989.
  • [16] GRESHO P. M.: On the theory of semi-implicit projection methods for viscous in- compressible flow and its implementation via a finite element method that also in- troduces a nearly consistent mass matrix. Part 1: Theory, Num. Heat Transfer, Part A, 29(1996), 49-63.
  • [17] BANASZEK J., JALURIA Y., KOWALEWSKI T. A., REBOW M.: Semi-implicit FEM analysis of natural convection in freezing water, Num. Heat Transfer, Part A 36(1999), 449-472.
  • [18] BANASZEK J., FURMANSKI P.: FEM analysis of binary dilute system solidification using the anisotropic porous medium model of a mushy zone, Computer Assisted Mech. and Eng. Sci., 7(2000), 343-362.
  • [19] POIRIER D. R.: Permeability for flow of interdendritic liquid in columnar-dendritic alloys, Metallurgical Transactions B, 18(1987), 245-255.
  • [20] KURZ, W., FISHER, D. J.: Fundamentals of Solidification, Third Edition, Trans Tech Publications, Aedermannsdorf, Switzerland, 1989
  • [21] BURDEN, M. H., HUNT, J. D.: Cellular and dendritic growth, J. of Crystal Growth, 22(1974), 99-116.
  • [22] BROWNE D. J, BANASZEK J., HUNT J. D.: Front tracking on a fixed grid versus enthalpy approach in modelling of binary alloy solidification, Proc. of the ASME Int. Mech. Eng. Congress and Exhibition, New Orleans, USA, Paper IMECE2002-32875, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BGPK-0638-2835
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