Numerical modeling of solidification combustion synthesis
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INTRODUCTION
TIlE recent interest in the development of new materials through combustion synthesis has highlighted the importance of the phase change phenomena during combustion and the subsequent solidification process. Few articles have dealt with the complete numerical solution of the heat conduction process in materials prepared by combustion synthesis, tl-51 Several important problems have not yet been tackled or need further addressing. These relate to the physics of the combustion process and the macro-micro models of synthesis from condensed initial constituents. The aim of the macro-micro models should be to relate the final microstructure to the combustion process. This article is a first report in this direction. Anderson and Zienkiewicz I~] have solved for the steadystate and transient solutions for the spontaneous ignition problem with the Frank-Kamenetskii parameter as an incremental loading variable using the Galerkin finite element method. Numerical prediction of the modes o f flame-front propagation and stability phenomena in condensed single-phase systems (i.e., no melting) has been reported by Shkadinskii et al. tel The steady-state and oscillating regimes of combustion regimes have been obtained numerically by Holt and Munir, f4~ although M.G. LAKSHMIKANTHA, Graduate Research Assistant, Department of Aerospace Engineering and Department of Materials Science and Engineering, and J.A. SEKHAR, Associate Professor, Department of Materials Science and Engineering, and Director, Center for Micropyretics, are with the University of Cincinnati, Cincinnati, OH 45221-0012. A. BHAITACHARYA, formerly Fellow, Department of Materials Science and Engineering, University of Cincinnati, is Scientist, Los Alamos National Laboratory, Los Alamos, NM 87545. This paper is based on a presentation made in the symposium "Reaction Synthesis of Materials" presented during the TMS Annual Meeting, New Orleans, LA, February 17-2l, 1991, under the auspices of the TMS Powder Metallurgy Committee. METALLURGICAL TRANSACTIONS A
numerical solutions have not been discussed in detail. A detailed analysis and modeling of exothermic solid-solid noncatalytic reactions has been carried out by Puszynski et al.,15] who developed the criteria for stable, unstable, and degenerated combustion, as well as the approximate relations for the velocity of a steady-state profile as a function of the heat-transfer coefficient. The heat-transfer coefficient was applied arbitrarily to all nodes of their numerical scheme, tsj A recent review by Margolis t61 has shown that several oscillatory modes of combustion may manifest during the condensed phase combustion process. No detailed numerical investigation of the phase change heat conduction problems and subsequent solidification process has been reported for combustion synthesis. Margolis 17~has, however, considered the case of a phase change leading to a change in the combustion kinetics during the melting of a reactant phase. The aim of the present article is to deal with the numerical investigatio
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