A finite difference model for the combustion of zirconium in oxygen
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U. Anselmi-Tamburini Department of Physical Chemistry, University of Pavia, Pavia, Italy
Z.A. Munir a) Facility for Advanced Combustion Synthesis (FACS), Department of Chemical Engineering and Materials Science, University of California, Davis, California 95616 (Received 3 February 2000; accepted 16 June 2000)
The combustion of zirconium in oxygen was simulated using a two-dimensional finite difference model. The model accounts for heat generation by the oxidation reaction and heat loss due to convective and radiative processes. Using geometric considerations along with the heat transfer conditions, the model was utilized to determine the effect of dilution and particle size on the combustion process. Dilution was examined in regular and random geometries and the results showed a marked influence on the nonlinearity of the wave. The effect of particle size was also examined as a function of the geometry of diluent dispersion.
I. INTRODUCTION A. Background
It is generally recognized that gas–solid interactions in the self-propagating high-temperature synthesis (SHS) process are more complex than those of the solid–solid type. Gas–solid SHS reactions are influenced by the local availability of the gaseous molecules and hence are strongly dependent on the pressure of the gas and on the porosity of the solid. Many solid–gas reactions, particularly those between metals and oxygen or nitrogen, are very exothermic, reaching adiabatic temperatures well above the melting point of the metal, and in some cases, above the melting point of the oxide. The melting of the metal has a direct effect on the magnitude and nature of the porosity (i.e., continuous versus isolated) within the sample, and hence on the local availability of the gas.1 Because of these considerations, the observed self-sustaining wave of gas–solid interaction is typically a surface phenomenon with the interior lagging behind considerably and giving rise to the after-burn phenomenon.2 The porosity of the solid reactant plays a key role in the degree of conversion to the product. In the case of the combustion of titanium in nitrogen, it was observed that
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J. Mater. Res., Vol. 15, No. 9, Sep 2000 Downloaded: 30 Mar 2015
the maximum conversion corresponds to an intermediate porosity.1 With high porosity, the large internal surface area results in a high rate of heat generation, and consequently a more extensive melting of the titanium. The melting process causes a reduction in the open porosity and hence a reduction in the degree of conversion. The combustion of zirconium in oxygen is another example showing the complex nature of gas–solid SHS processes. The reaction between Zr and O2 is extremely exothermic with an enthalpy of formation at 298 K of −1100.8 kJ mol−1. The adiabatic combustion temperature, Tad, is difficult to calculate exactly because of the uncertainty in the high-temperature phase transformation and heat capacity data. But on the basis of reported data3,4
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