A generalized formulation of latent heat functions in enthalpy-based mathematical models for multicomponent alloy solidi
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The authors thank Lang Shy, Geology Department, McGill University, for performing the microanalysis and A.K. Cafferata for reviewing this manuscript. REFERENCES 1. M. Marraha, J.-C. Heughebaert, and M. Heughebaert: J. Mater. Chem., 1992, vol. 2 (2), pp. 231-34. 2. P. Coursol, A.D. Pelton, P. Chartrand, and M. Zamalloa: Can. Met. Q., 2005, vol. 44, pp. 547-53. 3. R.G. Reddy and M.F. Jonkion: Metall. Mater. Trans. B, 2003, vol. 34B, pp. 565-71.
A Generalized Formulation of Latent Heat Functions in Enthalpy-Based Mathematical Models for Multicomponent Alloy Solidification Systems SUVANKAR GANGULY and SUMAN CHAKRABORTY A systematic and generalized procedure for mathematical formulation of latent heat functions, as applicable for enthalpy-based solidification modeling of multicomponent alloy systems, is developed. The method uses a metallurgically appropriate thermo-solutal coupling strategy, in conjunction with updating of respective phase fractions, in order to obtain solutions of field variables that are consistent with the pertinent phase-change morphology. The present approach can model the solidification of multicomponent alloys for a wide range of local scale diffusion behavior of the constituent species.
In recent years, considerable progress has been made in the development of fixed-grid enthalpy-based macroscopic models,[1] in order to simulate transport phenomena during alloy solidification processes. In such models, enthalpy is related to the liquid fraction of a control volume in the phase changing domain, in an implicit fashion, without the requirement of any explicit imposition of interfacial boundary conditions, which is in sharp contrast with the so-called moving grid front-tracking algorithms.[2] The fixed-grid approach simplifies the numerical modeling requirements of a phasechange process to a great extent, since explicit tracking of SUVANKAR GANGULY, Research Scholar, Department of Mechanical Engineering, Indian Institute of Technology, is Researcher, Research and Development Division, Tata Steel, Jamshedpur – 831001, India. SUMAN CHAKRABORTY, Assistant Professor, is with the Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur – 721302, India. Contact e-mail: [email protected] Manuscript submitted May 11, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS B
topologically-complicated interfaces can be avoided. Voller and Prakash[3] applied this formulation for modeling mushy zone phase-change problems, where a linear variation of temperature within the mushy zone was assumed. Subsequently, a number of advanced numerical models, following a fixed-grid enthalpy-based continuum formulation, have been established, and have been reported in detail in the literature.[4–6] An important aspect of the aforementioned fixed-grid enthalpy-based method is the prediction of liquid fraction in a control volume of the phase-changing domain. For accurate prediction of the same, the latent heat content of each computational cell needs to be updated according to the temperature or sp
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